From a5de1e998975e48e2fa476e62508e86c54ff6c95 Mon Sep 17 00:00:00 2001 From: fp64 <106717720+fp64@users.noreply.github.com> Date: Fri, 17 Feb 2023 22:52:01 -0500 Subject: [PATCH 01/14] Implement sin/cos as per #16946 --- Core/MIPS/MIPSVFPUUtils.cpp | 297 +- Core/MIPS/MIPSVFPUUtils.h | 18 +- Core/MIPS/vfpu_sin_lut.h | 46687 ++++++++++++++++++++++++++++++++++ 3 files changed, 46829 insertions(+), 173 deletions(-) create mode 100644 Core/MIPS/vfpu_sin_lut.h diff --git a/Core/MIPS/MIPSVFPUUtils.cpp b/Core/MIPS/MIPSVFPUUtils.cpp index b60cd7c97c..e03badb91b 100644 --- a/Core/MIPS/MIPSVFPUUtils.cpp +++ b/Core/MIPS/MIPSVFPUUtils.cpp @@ -29,13 +29,6 @@ #define V(i) (currentMIPS->v[voffset[i]]) #define VI(i) (currentMIPS->vi[voffset[i]]) -// Flushes the angle to 0 if exponent smaller than this in vfpu_sin/vfpu_cos/vfpu_sincos. -// Was measured to be around 0x68, but GTA on Mac is somehow super sensitive -// to the shape of the sine curve which seem to be very slightly different. -// -// So setting a lower value. -#define PRECISION_EXP_THRESHOLD 0x65 - union float2int { uint32_t i; float f; @@ -896,176 +889,156 @@ float vfpu_rsqrt(float a) { return val.f; } -float vfpu_sin(float a) { - float2int val; - val.f = a; +//============================================================================== +// The code below attempts to exactly match the output of +// PSP's sin and cos instructions. For the sake of +// making lookup tables smaller (473KB) the code is +// somewhat gnarly. +// The key observation is that (ignoring range +// reduction) PSP effectively converts input to 9.23 +// fixed-point, and that output is always representable +// as 4.28 fixed-point (though that is probably not +// what is going on internally). +// The rest is mostly trying to obtain the same result +// with smaller tables (pretty ad-hoc, and almost certainly +// does not match what PSP does internally). +// Lookup tables store deltas from (explicitly computable) +// estimations, to allow to store them in smaller types: +// int8 and int16. +// See https://github.com/hrydgard/ppsspp/issues/16946 for details. - int32_t k = get_uexp(val.i); - if (k == 255) { - val.i = (val.i & 0xFF800001) | 1; - return val.f; - } +#include "Core/MIPS/vfpu_sin_lut.h" - if (k < PRECISION_EXP_THRESHOLD) { - val.i &= 0x80000000; - return val.f; - } - - // Okay, now modulus by 4 to begin with (identical wave every 4.) - int32_t mantissa = get_mant(val.i); - if (k > 0x80) { - const uint8_t over = k & 0x1F; - mantissa = (mantissa << over) & 0x00FFFFFF; - k = 0x80; - } - // This subtracts off the 2. If we do, flip sign to inverse the wave. - if (k == 0x80 && mantissa >= (1 << 23)) { - val.i ^= 0x80000000; - mantissa -= 1 << 23; - } - - int8_t norm_shift = mantissa == 0 ? 32 : (int8_t)clz32_nonzero(mantissa) - 8; - mantissa <<= norm_shift; - k -= norm_shift; - - if (k <= 0 || mantissa == 0) { - val.i &= 0x80000000; - return val.f; - } - - // This is the value with modulus applied. - val.i = (val.i & 0x80000000) | (k << 23) | (mantissa & ~(1 << 23)); - val.f = (float)sin((double)val.f * M_PI_2); - val.i &= 0xFFFFFFFC; - return val.f; +// Note: PSP sin/cos output only has 22 significant +// binary digits. +static inline uint32_t quantum(uint32_t x) { + return x < 1u << 22? + 1u: + 1u << (32 - 22 - clz32_nonzero(x)); } -float vfpu_cos(float a) { - float2int val; - val.f = a; - bool negate = false; +static inline uint32_t truncate_bits(u32 x) { + return x & -quantum(x); +} - int32_t k = get_uexp(val.i); - if (k == 255) { - // Note: unlike sin, cos always returns +NAN. - val.i = (val.i & 0x7F800001) | 1; - return val.f; +static inline uint32_t vfpu_sin_fixed(uint32_t arg) { + // Handle endpoints. + if(arg == 0u) return 0u; + if(arg == 0x00800000) return 0x10000000; + // Get endpoints for 8192-wide interval. + uint32_t L = vfpu_sin_lut8192[(arg >> 13) + 0]; + uint32_t H = vfpu_sin_lut8192[(arg >> 13) + 1]; + // Approximate endpoints for 64-wide interval via lerp. + uint32_t A = L+(((H - L)*(((arg >> 6) & 127) + 0)) >> 7); + uint32_t B = L+(((H - L)*(((arg >> 6) & 127) + 1)) >> 7); + // Adjust endpoints from deltas, and increase working precision. + uint64_t a = (uint64_t(A) << 5) + uint64_t(vfpu_sin_lut_delta[arg >> 6][0]) * quantum(A); + uint64_t b = (uint64_t(B) << 5) + uint64_t(vfpu_sin_lut_delta[arg >> 6][1]) * quantum(B); + // Compute approximation via lerp. Is off by at most 1 quantum. + uint32_t v = uint32_t(((a * (64 - (arg & 63)) + b * (arg & 63)) >> 6) >> 5); + v=truncate_bits(v); + // Look up exceptions via binary search. + // Note: vfpu_sin_lut_interval_delta stores + // deltas from interval estimation. + uint32_t lo = ((169u * ((arg >> 7) + 0)) >> 7)+uint32_t(vfpu_sin_lut_interval_delta[(arg >> 7) + 0]) + 16384u; + uint32_t hi = ((169u * ((arg >> 7) + 1)) >> 7)+uint32_t(vfpu_sin_lut_interval_delta[(arg >> 7) + 1]) + 16384u; + while(lo < hi) { + uint32_t m = (lo + hi) / 2; + // Note: vfpu_sin_lut_exceptions stores + // index&127 (for each initial interval the + // upper bits of index are the same, namely + // arg&-128), plus direction (0 for +1, and + // 128 for -1). + uint32_t b = vfpu_sin_lut_exceptions[m]; + uint32_t e = (arg & -128u)+(b & 127u); + if(e == arg) { + v += quantum(v) * (b >> 7 ? -1u : +1u); + break; + } + else if(e < arg) lo = m + 1; + else hi = m; } + return v; +} - if (k < PRECISION_EXP_THRESHOLD) - return 1.0f; - - // Okay, now modulus by 4 to begin with (identical wave every 4.) - int32_t mantissa = get_mant(val.i); - if (k > 0x80) { - const uint8_t over = k & 0x1F; - mantissa = (mantissa << over) & 0x00FFFFFF; - k = 0x80; +float vfpu_sin(float x) { + uint32_t bits; + memcpy(&bits, &x, sizeof(x)); + uint32_t sign = bits & 0x80000000u; + uint32_t exponent = (bits >> 23) & 0xFFu; + uint32_t significand = (bits & 0x007FFFFFu) | 0x00800000u; + if(exponent == 0xFFu) { + // NOTE: this bitpattern is a signaling + // NaN on x86, so maybe just return + // a normal qNaN? + float y; + bits=sign ^ 0x7F800001u; + memcpy(&y, &bits, sizeof(y)); + return y; } - // This subtracts off the 2. If we do, negate the result value. - if (k == 0x80 && mantissa >= (1 << 23)) { - mantissa -= 1 << 23; - negate = true; + if(exponent < 0x7Fu) { + if(exponent < 0x7Fu-23u) significand = 0u; + else significand >>= (0x7F - exponent); } - - int8_t norm_shift = mantissa == 0 ? 32 : (int8_t)clz32_nonzero(mantissa) - 8; - mantissa <<= norm_shift; - k -= norm_shift; - - if (k <= 0 || mantissa == 0) - return negate ? -1.0f : 1.0f; - - // This is the value with modulus applied. - val.i = (val.i & 0x80000000) | (k << 23) | (mantissa & ~(1 << 23)); - if (val.f == 1.0f || val.f == -1.0f) { - return negate ? 0.0f : -0.0f; + else if(exponent > 0x7Fu) { + // There is weirdness for large exponents. + if(exponent - 0x7Fu >= 25u && exponent - 0x7Fu < 32u) significand = 0u; + else if((exponent & 0x9Fu) == 0x9Fu) significand = 0u; + else significand <<= (exponent - 0x7Fu); } - val.f = (float)cos((double)val.f * M_PI_2); - val.i &= 0xFFFFFFFC; - return negate ? -val.f : val.f; + sign ^= ((significand << 7) & 0x80000000u); + significand &= 0x00FFFFFFu; + if(significand > 0x00800000u) significand = 0x01000000u - significand; + uint32_t ret = vfpu_sin_fixed(significand); + return (sign ? -1.0f : +1.0f) * float(int32_t(ret)) * 3.7252903e-09f; // 0x1p-28f +} + +// WARNING: not tested. +float vfpu_cos(float x) { + uint32_t bits; + memcpy(&bits, &x, sizeof(x)); + bits &= 0x7FFFFFFFu; + uint32_t sign = 0u; + uint32_t exponent = (bits >> 23) & 0xFFu; + uint32_t significand = (bits & 0x007FFFFFu) | 0x00800000u; + if(exponent == 0xFFu) { + // NOTE: this bitpattern is a signaling + // NaN on x86, so maybe just return + // a normal qNaN? + float y; + bits = sign ^ 0x7F800001u; + memcpy(&y, &bits, sizeof(y)); + return y; + } + if(exponent < 0x7Fu) { + if(exponent < 0x7Fu - 23u) significand = 0u; + else significand >>= (0x7F - exponent); + } + else if(exponent > 0x7Fu) { + // There is weirdness for large exponents. + if(exponent - 0x7Fu >= 25u && exponent - 0x7Fu < 32u) significand = 0u; + else if((exponent & 0x9Fu) == 0x9Fu) significand = 0u; + else significand <<= (exponent - 0x7Fu); + } + sign ^= ((significand << 7) & 0x80000000u); + significand &= 0x00FFFFFFu; + if(significand > 0x00800000u) { + significand = 0x01000000u - significand; + sign ^= 0x80000000u; + } + uint32_t ret = vfpu_sin_fixed(0x00800000u - significand); + return (sign ? -1.0f : +1.0f) * float(int32_t(ret)) * 3.7252903e-09f; // 0x1p-28f } void vfpu_sincos(float a, float &s, float &c) { - float2int val; - val.f = a; - // For sin, negate the input, for cos negate the output. - bool negate = false; - - int32_t k = get_uexp(val.i); - if (k == 255) { - val.i = (val.i & 0xFF800001) | 1; - s = val.f; - val.i &= 0x7F800001; - c = val.f; - return; - } - - if (k < PRECISION_EXP_THRESHOLD) { - val.i &= 0x80000000; - s = val.f; - c = 1.0f; - return; - } - - // Okay, now modulus by 4 to begin with (identical wave every 4.) - int32_t mantissa = get_mant(val.i); - if (k > 0x80) { - const uint8_t over = k & 0x1F; - mantissa = (mantissa << over) & 0x00FFFFFF; - k = 0x80; - } - // This subtracts off the 2. If we do, flip signs. - if (k == 0x80 && mantissa >= (1 << 23)) { - mantissa -= 1 << 23; - negate = true; - } - - int8_t norm_shift = mantissa == 0 ? 32 : (int8_t)clz32_nonzero(mantissa) - 8; - mantissa <<= norm_shift; - k -= norm_shift; - - if (k <= 0 || mantissa == 0) { - val.i &= 0x80000000; - if (negate) - val.i ^= 0x80000000; - s = val.f; - c = negate ? -1.0f : 1.0f; - return; - } - - // This is the value with modulus applied. - val.i = (val.i & 0x80000000) | (k << 23) | (mantissa & ~(1 << 23)); - float2int i_sine, i_cosine; - if (val.f == 1.0f) { - i_sine.f = negate ? -1.0f : 1.0f; - i_cosine.f = negate ? 0.0f : -0.0f; - } else if (val.f == -1.0f) { - i_sine.f = negate ? 1.0f : -1.0f; - i_cosine.f = negate ? 0.0f : -0.0f; - } else if (negate) { - i_sine.f = (float)sin((double)-val.f * M_PI_2); - i_cosine.f = -(float)cos((double)val.f * M_PI_2); - } else { - double angle = (double)val.f * M_PI_2; -#if defined(__linux__) - double d_sine; - double d_cosine; - sincos(angle, &d_sine, &d_cosine); - i_sine.f = (float)d_sine; - i_cosine.f = (float)d_cosine; -#else - i_sine.f = (float)sin(angle); - i_cosine.f = (float)cos(angle); -#endif - } - - i_sine.i &= 0xFFFFFFFC; - i_cosine.i &= 0xFFFFFFFC; - s = i_sine.f; - c = i_cosine.f; - return ; + // Just invoke both sin and cos. + // Suboptimal but whatever. + s = vfpu_sin(a); + c = vfpu_cos(a); } +//============================================================================== + void InitVFPUSinCos() { // TODO: Could prepare a CORDIC table here. } diff --git a/Core/MIPS/MIPSVFPUUtils.h b/Core/MIPS/MIPSVFPUUtils.h index 6506a0664d..a137245e8a 100644 --- a/Core/MIPS/MIPSVFPUUtils.h +++ b/Core/MIPS/MIPSVFPUUtils.h @@ -35,18 +35,14 @@ inline int Xpose(int v) { #endif // The VFPU uses weird angles where 4.0 represents a full circle. This makes it possible to return -// exact 1.0/-1.0 values at certain angles. We currently just scale, and special case the cardinal directions. +// exact 1.0/-1.0 values at certain angles. // -// Stepping down to [0, 2pi) helps, but we also check common exact-result values. -// TODO: cos(1) and sin(2) should be -0.0, but doing that gives wrong results (possibly from floorf.) -// -// We also try an alternative solution, computing things in double precision, multiplying the input by pi/2. -// This fixes #12900 (Hitman Reborn 2) but breaks #13705 (Cho Aniki Zero) and #13671 (Hajime no Ippo). -// #2921 is still fine. So the alt solution (vfpu_sin_double etc) are behind a compat flag. -// -// A better solution would be to tailor some sine approximation for the 0..90 degrees range, compute -// modulo manually and mirror that around the circle. Also correctly special casing for inf/nan inputs -// and just trying to match it as closely as possible to the real PSP. +// The current code attempts to match VFPU sin/cos exactly. +// Possibly affected games: +// Final Fantasy III (#2921 ) +// Hitman Reborn 2 (#12900) +// Cho Aniki Zero (#13705) +// Dissidia Duodecim Final Fantasy (#6710 ) // // Messing around with the modulo functions? try https://www.desmos.com/calculator. diff --git a/Core/MIPS/vfpu_sin_lut.h b/Core/MIPS/vfpu_sin_lut.h new file mode 100644 index 0000000000..d2bec30211 --- /dev/null +++ b/Core/MIPS/vfpu_sin_lut.h @@ -0,0 +1,46687 @@ +// Copyright (c) 2012- PPSSPP Project. + +// This program is free software: you can redistribute it and/or modify +// it under the terms of the GNU General Public License as published by +// the Free Software Foundation, version 2.0 or later versions. + +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License 2.0 for more details. + +// A copy of the GPL 2.0 should have been included with the program. +// If not, see http://www.gnu.org/licenses/ + +// Official git repository and contact information can be found at +// https://github.com/hrydgard/ppsspp and http://www.ppsspp.org/. + +//============================================================================== +// WARNING: this is partially automatically generated, +// and only meant to be included inside Core/MIPS/MIPSVFPUUtils.cpp, +// so no header guards. + +static uint32_t vfpu_sin_lut8192[1025]={ + 0, 411778, 823552, 1235322, + 1647089, 2058851, 2470610, 2882365, + 3294116, 3705858, 4117590, 4529310, + 4941018, 5352714, 5764400, 6176074, + 6587736, 6999380, 7411008, 7822616, + 8234204, 8645772, 9057324, 9468852, + 9880364, 10291848, 10703312, 11114744, + 11526152, 11937528, 12348880, 12760204, + 13171504, 13582768, 13994000, 14405196, + 14816360, 15227488, 15638580, 16049636, + 16460660, 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+267445632,267480640,267515008,267548736, +267581888,267614336,267646208,267677440, +267708096,267738048,267767424,267796160, +267824256,267851648,267878528,267904704, +267930240,267955200,267979520,268003200, +268026240,268048640,268070400,268091584, +268112064,268131968,268151232,268169856, +268187840,268205248,268221952,268238080, +268253504,268268352,268282560,268296128, +268309120,268321408,268333120,268344128, +268354560,268364352,268373504,268382080, +268389952,268397184,268403840,268409856, +268415232,268419968,268424064,268427520, +268430400,268432576,268434176,268435136, +268435456}; + +static int8_t vfpu_sin_lut_delta[131072][2]= +{ +{ 0, -3}, { -3, -6}, { -2, 0}, { -1, -4}, +{ 3, 1}, { 1, -1}, { 7, 4}, { 3, 1}, +{ 7, 8}, { 5, 3}, { 11, 8}, { 7, 7}, +{ 12, 11}, { 10, 8}, { 16, 13}, { 13, 10}, +{ 10, 6}, { 16, 12}, { 12, 10}, { 16, 15}, +{ 15, 11}, { 20, 16}, { 17, 12}, { 22, 19}, +{ 18, 16}, { 24, 22}, { 20, 18}, { 25, 24}, +{ 22, 22}, { 27, 26}, { 24, 24}, { 31, 28}, +{ 28, 25}, { 25, 21}, { 29, 28}, { 27, 25}, +{ 31, 30}, { 30, 26}, { 33, 33}, { 31, 28}, +{ 37, 34}, { 33, 32}, { 31, 28}, { 35, 33}, +{ 33, 31}, { 37, 37}, { 35, 33}, { 39, 39}, +{ 37, 35}, { 43, 40}, { 40, 37}, { 37, 35}, +{ 42, 40}, { 39, 37}, { 45, 42}, { 42, 38}, +{ 46, 45}, { 44, 42}, { 39, 40}, { 46, 43}, +{ 44, 41}, { 49, 44}, { 44, 43}, { 50, 16}, +{ 16, 13}, { 13, 10}, { 19, 14}, { 16, 12}, +{ 20, 18}, { 15, 17}, { 15, 11}, { 18, 18}, +{ 16, 15}, { 22, 19}, { 18, 16}, { 24, 22}, +{ 20, 18}, { 18, 16}, { 24, 21}, { 20, 18}, +{ 25, 24}, { 23, 20}, { 20, 17}, { 24, 24}, +{ 22, 20}, { 27, 25}, { 25, 21}, { 22, 19}, +{ 27, 22}, { 24, 22}, { 29, 26}, { 25, 24}, +{ 22, 22}, { 27, 26}, { 24, 24}, { 31, 28}, +{ 28, 25}, { 25, 21}, { 29, 28}, { 27, 25}, +{ 31, 30}, { 30, 26}, { 27, 22}, { 31, 28}, +{ 29, 26}, { 30, 32}, { 31, 28}, { 27, 26}, +{ 31, 31}, { 29, 28}, { 28, 25}, { 31, 31}, +{ 30, 26}, { 36, 31}, { 32, 29}, { 29, 26}, +{ 33, 33}, { 31, 28}, { 27, 26}, { 30, 32}, +{ 31, 28}, { 28, 25}, { 31, 31}, { 29, 28}, +{ 36, 31}, { 32, 31}, { 30, 26}, { 33, 1}, +{ 0, 29}, { 29, 26}, { 30, 32}, { 31, 28}, +{ 27, 26}, { 31, 31}, { 31, 28}, { 35, 33}, +{ 32, 31}, { 29, 28}, { 36, 31}, { 32, 29}, +{ 29, 26}, { 33, 33}, { 31, 28}, { 27, 26}, +{ 30, 32}, { 31, 28}, { 27, 26}, { 31, 31}, +{ 29, 28}, { 35, 33}, { 32, 31}, { 30, 26}, +{ 27, 22}, { 31, 30}, { 29, 26}, { 25, 24}, +{ 31, 28}, { 27, 26}, { 30, 32}, { 31, 28}, +{ 28, 25}, { 25, 21}, { 29, 28}, { 27, 25}, +{ 24, 22}, { 30, 26}, { 27, 22}, { 24, 21}, +{ 29, 26}, { 25, 24}, { 23, 20}, { 27, 26}, +{ 24, 24}, { 22, 20}, { 28, 25}, { 25, 21}, +{ 22, 19}, { 27, 25}, { 24, 22}, { 20, 18}, +{ 25, 24}, { 24, 21}, { 20, 18}, { 24, 24}, +{ 23, 20}, { 20, 17}, { 16, 15}, { 22, 20}, +{ 20, 16}, { 17, 12}, { 22, 19}, { 18, 16}, +{ 16, 45}, { 52, 50}, { 51, 46}, { 48, 44}, +{ 52, 50}, { 47, 49}, { 47, 43}, { 44, 41}, +{ 48, 47}, { 46, 43}, { 43, 40}, { 49, 44}, +{ 44, 43}, { 42, 40}, { 39, 37}, { 45, 42}, +{ 42, 38}, { 39, 36}, { 44, 42}, { 39, 40}, +{ 37, 35}, { 35, 33}, { 39, 39}, { 37, 35}, +{ 36, 31}, { 40, 37}, { 37, 34}, { 33, 33}, +{ 31, 28}, { 35, 33}, { 33, 32}, { 31, 28}, +{ 35, 33}, { 32, 31}, { 29, 28}, { 27, 25}, +{ 31, 30}, { 30, 26}, { 27, 22}, { 24, 21}, +{ 29, 26}, { 25, 24}, { 23, 20}, { 20, 17}, +{ 24, 24}, { 22, 20}, { 20, 16}, { 25, 21}, +{ 22, 19}, { 18, 16}, { 16, 13}, { 12, 11}, +{ 19, 14}, { 16, 13}, { 13, 10}, { 10, 6}, +{ 14, 13}, { 12, 10}, { 7, 8}, { 5, 3}, +{ 12, 9}, { 7, 7}, { 5, 3}, { 11, 8}, +{ 8, 37}, { 37, 34}, { 33, 32}, { 31, 28}, +{ 35, 33}, { 33, 31}, { 31, 28}, { 28, 25}, +{ 31, 31}, { 29, 28}, { 27, 25}, { 24, 22}, +{ 29, 26}, { 27, 22}, { 24, 21}, { 20, 18}, +{ 15, 17}, { 23, 20}, { 20, 17}, { 16, 15}, +{ 15, 11}, { 20, 48}, { 49, 44}, { 46, 43}, +{ 43, 40}, { 40, 37}, { 44, 43}, { 42, 40}, +{ 39, 37}, { 35, 33}, { 42, 38}, { 39, 36}, +{ 35, 33}, { 32, 31}, { 29, 28}, { 27, 25}, +{ 31, 30}, { 30, 26}, { 27, 22}, { 24, 21}, +{ 29, 26}, { 25, 24}, { 23, 52}, { 52, 49}, +{ 47, 49}, { 54, 52}, { 52, 48}, { 48, 47}, +{ 46, 43}, { 43, 40}, { 48, 45}, { 44, 43}, +{ 42, 40}, { 39, 37}, { 35, 35}, { 33, 32}, +{ 39, 36}, { 35, 33}, { 33, 31}, { 29, 28}, +{ 27, 25}, { 31, 31}, { 30, 26}, { 27, 22}, +{ 24, 53}, { 52, 50}, { 57, 56}, { 55, 52}, +{ 52, 50}, { 47, 49}, { 47, 43}, { 44, 41}, +{ 48, 47}, { 46, 43}, { 43, 40}, { 39, 39}, +{ 37, 35}, { 33, 33}, { 39, 37}, { 37, 34}, +{ 33, 32}, { 31, 28}, { 27, 26}, { 24, 24}, +{ 29, 28}, { 27, 57}, { 57, 53}, { 54, 51}, +{ 50, 48}, { 48, 45}, { 52, 50}, { 51, 46}, +{ 48, 44}, { 45, 42}, { 42, 38}, { 39, 36}, +{ 44, 42}, { 39, 40}, { 37, 35}, { 36, 31}, +{ 32, 29}, { 30, 26}, { 27, 22}, { 24, 21}, +{ 29, 26}, { 25, 24}, { 23, 52}, { 52, 49}, +{ 47, 49}, { 47, 43}, { 44, 41}, { 48, 47}, +{ 46, 43}, { 43, 40}, { 40, 37}, { 37, 35}, +{ 33, 33}, { 31, 28}, { 35, 35}, { 33, 32}, +{ 31, 28}, { 28, 25}, { 24, 24}, { 22, 20}, +{ 20, 16}, { 17, 12}, { 22, 19}, { 18, 16}, +{ 16, 45}, { 45, 42}, { 42, 40}, { 39, 37}, +{ 35, 33}, { 33, 31}, { 31, 28}, { 35, 33}, +{ 32, 31}, { 29, 28}, { 27, 25}, { 24, 22}, +{ 20, 18}, { 18, 16}, { 16, 45}, { 52, 50}, +{ 47, 49}, { 48, 44}, { 44, 42}, { 39, 40}, +{ 37, 35}, { 35, 33}, { 32, 31}, { 30, 26}, +{ 27, 22}, { 31, 30}, { 29, 26}, { 25, 24}, +{ 22, 54}, { 52, 50}, { 47, 49}, { 47, 43}, +{ 44, 42}, { 39, 40}, { 37, 35}, { 36, 31}, +{ 39, 39}, { 37, 35}, { 33, 33}, { 31, 28}, +{ 29, 26}, { 25, 24}, { 23, 52}, { 52, 49}, +{ 47, 49}, { 47, 43}, { 44, 41}, { 39, 39}, +{ 37, 35}, { 43, 40}, { 40, 37}, { 37, 35}, +{ 33, 33}, { 31, 28}, { 27, 26}, { 24, 24}, +{ 23, 52}, { 52, 49}, { 48, 47}, { 46, 43}, +{ 44, 41}, { 39, 39}, { 37, 35}, { 43, 40}, +{ 40, 37}, { 37, 34}, { 33, 32}, { 31, 28}, +{ 27, 26}, { 24, 24}, { 22, 20}, { 18, 50}, +{ 48, 47}, { 46, 43}, { 43, 40}, { 39, 39}, +{ 37, 35}, { 33, 33}, { 31, 28}, { 27, 26}, +{ 25, 24}, { 23, 20}, { 27, 26}, { 24, 24}, +{ 22, 20}, { 20, 48}, { 49, 44}, { 46, 43}, +{ 43, 40}, { 40, 37}, { 37, 34}, { 33, 33}, +{ 31, 28}, { 27, 26}, { 24, 24}, { 22, 20}, +{ 20, 17}, { 16, 15}, { 14, 11}, { 10, 41}, +{ 39, 39}, { 37, 35}, { 33, 33}, { 31, 28}, +{ 29, 26}, { 25, 24}, { 23, 20}, { 20, 17}, +{ 15, 17}, { 15, 11}, { 12, 9}, { 7, 7}, +{ 5, 3}, { 4, 31}, { 32, 29}, { 29, 26}, +{ 25, 24}, { 24, 21}, { 20, 18}, { 15, 17}, +{ 14, 13}, { 12, 10}, { 7, 8}, { 5, 3}, +{ 4, -1}, { 0, -1}, { -2, -6}, { 1, 1}, +{ -8, 21}, { 20, 18}, { 19, 14}, { 16, 12}, +{ 12, 10}, { 7, 8}, { 7, 4}, { 3, 1}, +{ 0, -1}, { -3, 28}, { 27, 25}, { 24, 22}, +{ 20, 18}, { 18, 16}, { 16, 13}, { 13, 10}, +{ 10, 6}, { 7, 4}, { 3, 33}, { 33, 31}, +{ 29, 28}, { 27, 25}, { 25, 21}, { 22, 19}, +{ 18, 16}, { 16, 13}, { 12, 11}, { 10, 40}, +{ 39, 37}, { 35, 33}, { 33, 32}, { 31, 28}, +{ 28, 25}, { 25, 21}, { 22, 19}, { 20, 16}, +{ 17, 44}, { 44, 43}, { 42, 40}, { 40, 37}, +{ 37, 34}, { 33, 32}, { 31, 28}, { 27, 26}, +{ 24, 24}, { 15, 43}, { 44, 41}, { 39, 39}, +{ 37, 35}, { 36, 31}, { 32, 29}, { 29, 26}, +{ 25, 24}, { 24, 21}, { 20, 50}, { 47, 49}, +{ 46, 45}, { 44, 42}, { 39, 40}, { 37, 35}, +{ 36, 31}, { 32, 31}, { 30, 26}, { 27, 22}, +{ 16, 45}, { 45, 42}, { 42, 40}, { 39, 37}, +{ 35, 33}, { 33, 31}, { 31, 28}, { 28, 25}, +{ 25, 21}, { 22, 51}, { 50, 48}, { 49, 44}, +{ 44, 43}, { 42, 40}, { 32, 27}, { 27, 26}, +{ 25, 24}, { 23, 20}, { 20, 49}, { 48, 47}, +{ 47, 43}, { 44, 41}, { 39, 39}, { 37, 35}, +{ 36, 31}, { 32, 29}, { 29, 26}, { 19, 46}, +{ 48, 44}, { 45, 42}, { 42, 38}, { 39, 36}, +{ 35, 33}, { 32, 31}, { 29, 28}, { 27, 25}, +{ 24, 54}, { 52, 52}, { 42, 40}, { 40, 37}, +{ 37, 34}, { 33, 32}, { 31, 28}, { 27, 26}, +{ 24, 24}, { 22, 52}, { 52, 48}, { 48, 47}, +{ 37, 35}, { 36, 31}, { 32, 29}, { 29, 26}, +{ 25, 24}, { 24, 21}, { 20, 50}, { 47, 49}, +{ 39, 36}, { 35, 33}, { 33, 31}, { 29, 28}, +{ 27, 25}, { 24, 22}, { 22, 19}, { 18, 16}, +{ 16, 45}, { 37, 34}, { 33, 32}, { 31, 28}, +{ 27, 26}, { 24, 24}, { 22, 20}, { 18, 50}, +{ 48, 47}, { 37, 35}, { 36, 31}, { 32, 29}, +{ 29, 26}, { 27, 22}, { 24, 21}, { 20, 50}, +{ 42, 38}, { 39, 36}, { 35, 33}, { 33, 31}, +{ 29, 28}, { 27, 25}, { 25, 53}, { 46, 43}, +{ 43, 40}, { 40, 37}, { 37, 34}, { 33, 33}, +{ 31, 28}, { 27, 26}, { 24, 56}, { 47, 43}, +{ 44, 42}, { 39, 40}, { 37, 35}, { 36, 31}, +{ 32, 29}, { 20, 52}, { 50, 48}, { 48, 45}, +{ 45, 42}, { 42, 38}, { 39, 37}, { 27, 26}, +{ 24, 24}, { 22, 52}, { 52, 48}, { 48, 47}, +{ 46, 43}, { 36, 31}, { 32, 29}, { 29, 26}, +{ 25, 56}, { 56, 53}, { 52, 50}, { 42, 38}, +{ 39, 36}, { 35, 33}, { 33, 31}, { 29, 28}, +{ 27, 57}, { 49, 44}, { 44, 43}, { 43, 40}, +{ 40, 37}, { 37, 34}, { 25, 24}, { 23, 52}, +{ 52, 50}, { 47, 49}, { 47, 43}, { 35, 33}, +{ 32, 31}, { 29, 28}, { 27, 25}, { 24, 54}, +{ 52, 50}, { 42, 40}, { 39, 37}, { 37, 34}, +{ 33, 32}, { 31, 28}, { 20, 49}, { 48, 47}, +{ 47, 43}, { 44, 41}, { 39, 39}, { 30, 26}, +{ 27, 22}, { 24, 22}, { 20, 50}, { 42, 40}, +{ 39, 37}, { 35, 33}, { 33, 32}, { 31, 28}, +{ 28, 25}, { 16, 47}, { 46, 43}, { 42, 41}, +{ 39, 39}, { 30, 26}, { 27, 22}, { 24, 21}, +{ 20, 18}, { 19, 46}, { 39, 37}, { 35, 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51}, { 35, 31}, +{ 31, 28}, { 28, 24}, { 24, 20}, { 20, 16}, +{ 16, 13}, { 13, 9}, { 36, 65}, { 37, 33}, +{ 33, 30}, { 30, 26}, { 26, 22}, { 22, 18}, +{ 18, 15}, { 15, 11}, { 11, 7}, { 7, 40}, +{ 35, 32}, { 32, 28}, { 28, 24}, { 24, 20}, +{ 20, 17}, { 17, 13}, { 13, 9}, { 9, 38}, +{ 5, 42}, { 2, 50}, { 30, 26}, { 26, 22}, +{ 22, 19}, { 19, 15}, { 15, 11}, { 11, 7}, +{ 10, 38}, { 4, 44}, { 0, 56}, { 12, 55}, +{ 18, 53}, { 21, 17}, { 17, 13}, { 13, 9}, +{ 9, 6}, { 6, 2}, { 2, -2}, { -2, -6}, +{ -6, -9}, { 20, 48}, { 19, 15}, { 15, 11}, +{ 11, 8}, { 8, 4}, { 4, 0}, { 0, -4}, +{ -4, -7}, { -7, -11}, { -11, -15}, { -15, 31}, +{ -12, 42}, { -1, 37}, { 4, 25}, { 2, -2}, +{ -2, -5}, { -5, -9}, { -9, -13}, { -13, -17}, +{ -17, -20}, { -20, -24}, { -24, -28}, { -28, 8}, +{ -32, 20}, { -24, 30}, { -12, 28}, { -5, 26}, +{ -5, -6}, { -6, -7}, { -7, -8}, { -8, -10}, +{ -10, -11}, { -11, -12}, { -12, -13}, { -13, -15}, +{ -15, -16}, { -16, -17}, { -7, 45}, { 5, 43}, +{ -20, 17}, { -21, 27}, { 10, 9}, { 9, 7}, +{ 7, 6}, { 6, 5}, { 5, 4}, { 4, 2}, +{ 2, 1}, { 1, 0}, { 0, -1}, { -1, -3}, +{ -3, -4}, { -3, 33}, { -5, 44}, { -1, 56}, +{ 13, 54}, { 21, 46}, { 22, 21}, { 21, 19}, +{ 19, 18}, { 18, 17}, { 17, 16}, { 16, 14}, +{ 14, 13}, { 13, 12}, { 12, 11}, { 11, 9}, +{ 9, 8}, { 8, 7}, { 7, 6}, { 6, 52}, +{ 36, 3}, { 3, 2}, { 4, 35}, { 1, 43}, +{ -1, 57}, { 12, 61}, { 22, 59}, { 28, 26}, +{ 26, 25}, { 25, 24}, { 24, 23}, { 23, 21}, +{ 21, 20}, { 20, 19}, { 19, 18}, { 18, 16}, +{ 16, 15}, { 15, 14}, { 14, 13}, { 13, 11}, +{ 11, 10}, { 10, 9}, { 9, 8}, { 8, 6}, +{ 6, 44}, { 37, 3}, { 9, 67}, { 35, 1}, +{ 1, 36}, { 0, 45}, { -1, 60}, { 14, 60}, +{ 23, 58}, { 27, 26}, { 26, 25}, { 6, 54}, +{ 16, 53}, { 22, 21}, { 21, 20}, { 20, 18}, +{ 18, 17}, { 17, 16}, { 16, 15}, { 15, 13}, +{ 13, 12}, { 12, 11}, { 11, 10}, { 10, 8}, +{ 8, 7}, { 7, 6}, { 6, 5}, { 5, 3}, +{ 3, 2}, { 2, 1}, { 1, 0}, { 0, -2}, +{ -2, -3}, { -3, -4}, { -4, -5}, { -5, -7}, +{ -7, -8}, { -8, -9}, { -9, -10}, { -10, -12}, +{ -12, -13}, { -13, -14}, { -14, -15}, { -15, -17}, +{ -17, -18}, { -18, -19}, { -19, -20}, { -20, -22}, +{ -22, -23}, { -23, -24}, { -24, -25}, { -25, -27}, +{ -27, -28}, { -28, -29}, { -29, -30}, { -30, -16}, +}; + +static int16_t vfpu_sin_lut_interval_delta[65537]= +{ + -16384, -16385, -16384, -16383, -16384, -16384, -16385, -16386, + -16387, -16388, -16390, -16391, -16392, -16394, -16394, -16394, + -16396, -16397, -16397, -16399, -16398, -16398, -16398, -16398, + -16399, -16400, -16401, -16402, -16403, -16405, -16406, -16407, + -16408, -16409, -16410, -16412, -16413, -16414, -16416, -16416, + -16417, -16419, -16420, -16421, -16423, -16424, -16425, -16426, + -16427, -16428, -16429, -16430, -16430, -16430, -16431, -16430, + -16431, -16432, -16433, -16432, -16432, -16433, -16432, -16433, + -16433, -16434, -16434, -16433, -16433, -16435, -16435, -16435, + -16435, -16435, -16435, -16435, -16436, -16437, -16438, -16438, + -16438, -16439, -16440, -16441, -16442, -16444, -16444, -16445, + -16447, -16448, -16448, -16450, -16451, -16452, -16454, -16455, + -16456, -16457, -16458, -16459, -16461, -16462, -16463, -16463, + -16465, -16466, -16467, -16468, -16469, -16470, -16472, -16470, + -16471, -16472, -16472, -16473, -16475, -16476, -16477, -16479, + -16480, -16481, -16482, -16483, -16484, -16486, -16486, -16487, + -16489, -16490, -16490, -16489, -16491, -16492, -16493, -16495, + -16496, -16497, -16499, -16500, -16501, -16503, -16504, -16504, + -16506, -16507, -16507, -16509, -16510, -16511, -16513, -16514, + -16515, -16517, -16517, -16518, -16519, -16520, -16520, -16521, + -16523, -16523, -16524, -16526, -16527, -16528, -16530, -16531, + -16531, -16533, -16534, -16534, -16536, -16537, -16537, -16539, + -16540, -16541, -16542, -16543, -16544, -16545, -16547, -16548, + -16549, -16551, -16552, -16552, -16553, -16554, -16555, -16557, + -16558, -16559, -16561, -16561, -16561, -16563, -16564, -16564, + -16566, -16567, -16568, -16569, -16570, -16571, -16572, -16574, + -16575, -16576, -16577, -16578, -16578, -16580, -16581, -16582, + -16584, -16584, -16585, -16586, -16586, -16587, -16589, -16590, + -16591, -16593, -16593, -16593, -16595, -16596, -16597, -16598, + -16598, -16599, -16600, -16602, -16603, -16604, -16606, -16605, + -16606, -16608, -16609, -16610, -16611, -16612, -16613, -16615, + -16616, -16616, -16618, -16619, -16620, -16622, -16622, -16623, + -16624, -16623, -16624, -16625, -16627, -16628, -16629, -16630, + -16631, -16632, -16633, -16633, -16634, -16636, -16637, -16637, + -16639, -16640, -16641, -16642, -16643, -16644, -16645, -16646, + -16647, -16648, -16649, -16650, -16651, -16653, -16653, -16654, + -16656, -16657, -16658, -16659, -16660, -16661, -16663, -16663, + -16663, -16665, -16666, -16667, -16669, -16670, -16671, -16673, + -16674, -16675, -16676, -16677, -16678, -16679, -16680, -16681, + -16682, -16683, -16684, -16685, -16687, -16688, -16688, -16690, + -16691, -16692, -16693, -16693, -16694, -16695, -16696, -16697, + -16699, -16700, -16700, -16701, -16702, -16703, -16704, -16704, + -16705, -16706, -16707, -16708, -16709, -16711, -16710, -16711, + -16713, -16714, -16715, -16717, -16718, -16719, -16720, -16721, + -16721, -16723, -16723, -16724, -16726, -16727, -16728, -16728, + -16730, -16731, -16732, -16734, -16734, -16735, -16736, -16736, + -16737, -16739, -16740, -16740, -16742, -16743, -16743, -16744, + -16745, -16746, -16747, -16748, -16749, -16751, -16752, -16753, + -16754, -16755, -16756, -16757, -16758, -16759, -16760, -16762, + -16761, -16762, -16764, -16764, -16765, -16767, -16767, -16768, + -16770, -16771, -16772, -16773, -16773, -16774, -16776, -16776, + -16777, -16779, -16780, -16780, -16781, -16783, -16784, -16785, + -16787, -16787, -16788, -16789, -16790, -16791, -16793, -16794, + -16795, -16796, -16797, -16798, -16799, -16800, -16801, -16801, + -16802, -16803, -16803, -16804, -16805, -16806, -16808, -16809, + -16809, -16811, -16812, -16813, -16815, -16816, -16816, -16818, + -16819, -16818, -16820, -16819, -16820, -16821, -16821, -16821, + -16823, -16823, -16824, -16825, -16825, -16826, -16826, -16828, + -16829, -16829, -16831, -16831, -16832, -16834, -16833, -16834, + -16836, -16837, -16837, -16838, -16839, -16840, -16842, -16843, + -16844, -16844, -16845, -16844, -16846, -16846, -16847, -16847, + -16848, -16849, -16849, -16851, -16852, -16852, -16853, -16852, + -16853, -16855, -16855, -16855, -16856, -16857, -16857, -16858, + -16859, -16858, -16859, -16860, -16860, -16862, -16863, -16864, + -16866, -16810, -16752, -16695, -16639, -16582, -16526, -16469, + -16412, -16354, -16298, -16240, -16183, -16127, -16071, -16014, + -15957, -15900, -15843, -15788, -15729, -15672, -15616, -15559, + -15501, -15445, -15390, -15333, -15275, -15219, -15164, -15107, + -15050, -14992, -14937, -14881, -14823, -14766, -14710, -14653, + -14596, -14540, -14484, -14428, -14372, -14316, -14259, -14201, + -14144, -14087, -14031, -13973, -13917, -13860, -13803, -13746, + -13688, -13632, -13573, -13517, -13461, -13403, -13346, -13290, + -13232, -13175, -13119, -13062, -13003, -12948, -12891, -12833, + -12778, -12721, -12662, -12606, -12550, -12491, -12434, -12379, + -12323, -12266, -12211, -12153, -12096, -12041, -11982, -11924, + -11869, -11811, -11753, -11699, -11641, -11584, -11528, -11470, + -11414, -11358, -11300, -11244, -11188, -11130, -11074, -11017, + -10961, -10903, -10846, -10789, -10734, -10676, -10621, -10564, + -10506, -10451, -10394, -10336, -10280, -10224, -10167, -10112, + -10054, -9997, -9941, -9884, -9829, -9772, -9716, -9659, + -9603, -9546, -9487, -9430, -9375, -9317, -9262, -9205, + -9148, -9091, -9033, -8976, -8921, -8923, -8924, -8925, + -8927, -8928, -8929, -8931, -8932, -8933, -8934, -8935, + -8936, -8938, -8938, -8939, -8939, -8940, -8941, -8941, + -8943, -8943, -8944, -8945, -8945, -8946, -8948, -8949, + -8949, -8951, -8952, -8952, -8954, -8955, -8956, -8958, + -8959, -8960, -8962, -8963, -8964, -8965, -8967, -8968, + -8969, -8971, -8972, -8973, -8975, -8976, -8977, -8979, + -8980, -8981, -8983, -8984, -8985, -8987, -8988, -8989, + -8990, -8991, -8992, -8994, -8995, -8996, -8997, -8999, + -9000, -9001, -9003, -9004, -9005, -9007, -9008, -9009, + -9011, -9012, -9012, -9014, -9015, -9016, -9018, -9019, + -9020, -9022, -9023, -9024, -9026, -9027, -9028, -9029, + -9031, -9032, -9033, -9034, -9035, -9036, -9038, -9039, + -9040, -9042, -9042, -9043, -9045, -9046, -9047, -9049, + -9050, -9051, -9053, -9054, -9055, -9057, -9058, -9059, + -9061, -9062, -9063, -9064, -9066, -9067, -9068, -9070, + -9071, -9072, -9074, -9075, -9076, -9078, -9079, -9080, + -9081, -9082, -9083, -9085, -9086, -9087, -9089, -9090, + -9091, -9093, -9093, -9094, -9095, -9097, -9098, -9099, + -9101, -9102, -9103, -9105, -9106, -9107, -9109, -9110, + -9110, -9112, -9113, -9114, -9116, -9117, -9118, -9120, + -9121, -9122, -9124, -9125, -9126, -9126, -9127, -9128, + -9129, -9130, -9131, -9132, -9133, -9134, -9135, -9137, + -9138, -9139, -9141, -9142, -9143, -9145, -9146, -9147, + -9149, -9150, -9151, -9153, -9154, -9155, -9155, -9157, + -9158, -9159, -9161, -9162, -9162, -9164, -9165, -9166, + -9168, -9169, -9170, -9172, -9173, -9174, -9174, -9175, + -9176, -9178, -9178, -9179, -9181, -9181, -9182, -9183, + -9185, -9185, -9186, -9188, -9188, -9189, -9191, -9192, + -9193, -9195, -9196, -9197, -9198, -9199, -9200, -9202, + -9203, -9204, -9206, -9207, -9208, -9210, -9211, -9211, + -9212, -9213, -9214, -9215, -9216, -9217, -9218, -9220, + -9221, -9221, -9223, -9224, -9225, -9225, -9226, -9227, + -9228, -9228, -9229, -9231, -9232, -9233, -9235, -9236, + -9237, -9239, -9239, -9240, -9241, -9243, -9244, -9245, + -9246, -9247, -9248, -9250, -9249, -9250, -9252, -9253, + -9254, -9256, -9256, -9257, -9259, -9260, -9261, -9262, + -9263, -9264, -9266, -9267, -9268, -9269, -9271, -9272, + -9273, -9275, -9276, -9276, -9278, -9279, -9280, -9282, + -9283, -9283, -9284, -9285, -9286, -9288, -9289, -9289, + -9290, -9290, -9291, -9293, -9294, -9295, -9296, -9298, + -9298, -9299, -9301, -9302, -9303, -9305, -9306, -9306, + -9308, -9308, -9309, -9311, -9312, -9313, -9315, -9316, + -9316, -9317, -9318, -9319, -9321, -9322, -9323, -9324, + -9326, -9326, -9326, -9327, -9328, -9329, -9331, -9332, + -9333, -9335, -9336, -9336, -9338, -9337, -9337, -9338, + -9338, -9339, -9341, -9342, -9343, -9345, -9346, -9347, + -9349, -9293, -9236, -9181, -9126, -9070, -9014, -8958, + -8901, -8846, -8792, -8737, -8682, -8628, -8573, -8518, + -8464, -8409, -8354, -8300, -8245, -8190, -8136, -8081, + -8026, -7972, -7917, -7862, -7807, -7753, -7698, -7643, + -7589, -7534, -7479, -7425, -7370, -7315, -7261, -7206, + -7151, -7097, -7042, -6987, -6933, -6878, -6823, -6769, + -6712, -6657, -6602, -6546, -6490, -6434, -6378, -6322, + -6267, -6212, -6156, -6101, -6045, -5990, -5934, -5879, + -5823, -5767, -5713, -5658, -5603, -5549, -5494, -5439, + -5385, -5330, -5275, -5221, -5166, -5110, -5053, -4999, + -4942, -4885, -4830, -4774, -4718, -4664, -4609, -4554, + -4500, -4445, -4388, 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-15956, -15958, -15959, -15960, -15962, + -15963, -15964, -15966, -15967, -15968, -15970, -15971, -15972, + -15974, +}; + +static uint8_t vfpu_sin_lut_exceptions[86938]= +{ + 15, 83,128, 26,128, 86, 6, 24, 72, 4,128, 83,128,192, 90,192, + 22, 6, 24, 72, 4, 83, 79, 72, 15, 68,192,128, 83, 8, 79, 15, + 68,128,192, 15, 83, 8, 79,192,128,192, 19, 72, 15, 79, 4,192, + 19, 72, 15, 4, 72, 88, 88, 6, 22, 19,192, 90,128, 4, 70, 86, + 83,128, 26, 90, 4, 70,128, 68, 88,128, 4, 24, 22, 83,128, 26, +192, 24, 22, 22, 83, 22, 83, 8, 83, 8, 19, 72, 19, 72, 83, 22, + 86,192, 0, 88, 24, 26, 4, 90, 70, 72, 22, 86, 26, 6, 72, 4, + 72, 22, 68, 83, 8, 86, 26, 4, 19, 72, 22, 64, 72, 68, 6, 0, + 24, 64, 24, 90, 64, 90, 68, 64, 6, 64, 19, 72, 4, 64, 70, 83, +121, 0, 88, 26, 64, 64, 64, 72, 22, 64, 64, 0, 0, 88, 26, 64, + 86, 64, 24, 0, 22, 0, 64, 0, 64, 0, 72, 70, 83, 0, 88, 0, + 8, 64, 6, 72, 26, 64, 24, 64, 72, 57, 70, 83, 90, 0, 22, 64, + 70, 8,133,134,135, 8,141,142,143, 16,149,150,151, 24,158,159, + 32, 33,166, 39, 40, 41,174, 47, 48, 49, 55, 56, 57, 58, 63,196, + 69, 70, 71, 76, 77, 78,211, 84, 85, 86,219, 92, 93,226,227,100, +101,234,235,108,241,242,115,116,249,250,123, 3, 4, 5, 6, 11, + 12, 13, 14, 19, 20, 21, 26, 27, 28, 29, 34, 35, 36,169, 42, 43, + 44,177, 50, 51,184,185, 58, 59,192, 65,198, 71, 72, 73,206, 79, + 80,213,214, 87, 88,221,222, 95,228,229,102,103,236,237,110,243, +244,245,118,251,252,253, 4, 5, 6, 11, 12, 13, 14, 19, 20, 21, +154, 27, 28, 29,162, 35, 36,169,170, 43, 44,177, 50, 51,184,185, + 58, 59,192, 65,198,199, 72, 73,206,207, 80,213,214, 87, 88,221, +222, 95,228,229,230,103,236,237,238,243,244,245,246,251,252,253, + 0,133, 6, 7, 8,141, 14, 15,148,149, 22, 23,156,157, 30,163, +164, 37, 38,171,172, 45,178,179,180, 53,186,187,188, 67, 68, 69, + 74, 75, 76, 77, 82, 83, 84,217, 90, 91, 92,225, 98, 99,232,105, +106,107,240,113,114,247,248,121,122,255,128,133,134, 7, 8,141, +142, 15,148,149, 22, 23,156,157, 30,163,164,165, 38,171,172,173, +178,179,180, 53,186,187,188, 67, 68, 69, 70, 75, 76, 77, 78, 83, + 84, 85, 90, 91, 92, 93, 98, 99,100,233,106,107,108,241,114,115, +248,249,122,123,128,134,135,136, 9,142,143,144, 17,150,151,152, + 25,159,160, 33, 34,167, 40, 41, 42,175, 48, 49, 50, 56, 57, 58, + 59,196,197, 70, 71,204, 77, 78,211,212, 85, 86,219,220, 93,226, +227,228,101,234,235,236,241,242,243,116,249,250,251, 2, 3, 4, + 5, 10, 11, 12, 13, 18, 19, 20, 25, 26, 27, 28, 33, 34, 35,168, + 41, 42, 43,176, 49, 50,183,184, 57, 58,191,197,198,199, 72,205, +206,207, 80,213,214,215, 88,222,223, 96, 97,230,103,104,105,238, +111,112,113,119,120,121,122,127,132, 5, 6, 7, 12, 13, 14,147, + 20, 21, 22,155, 28, 29,162,163, 36, 37,170,171, 44,177,178, 51, + 52,185,186, 59,192,198,199,200, 73,206,207,208, 81,214,215, 88, + 89,222,223, 96, 97,231,104,105,106,239,112,113,114,119,120,121, +122,127, 0, 1,134, 7, 8, 9,142, 15, 16,149,150, 23, 24,157, + 30, 31,164,165, 38, 39,172,173, 46,179,180,181, 54,187,188,189, + 67, 68, 69, 70, 75, 76, 77, 78, 83, 84, 85,218, 91, 92, 93,226, + 99,100,233,106,107,108,241,114,115,248,249,122,123,128, 1,134, +135, 8, 9,142, 15, 16,149,150, 23, 24,157,158, 31,164,165,166, + 39,172,173,174,179,180,181, 54,187,188,189, 68, 69, 70, 71, 76, + 77, 78,211, 84, 85, 86, 91, 92, 93,226, 99,100,101,234,107,108, +241,242,115,116,249,250,123, 2, 3, 4, 5, 10, 11, 12, 13, 18, + 19, 20,153, 26, 27, 28,161, 34, 35,168, 41, 42, 43,176, 49, 50, +183,184, 57, 58,191,192,197,198, 71, 72,205, 78, 79,212,213, 86, + 87,220,221, 94,227,228,229,102,235,236,237,242,243,244,117,250, +251,252, 3, 4, 5, 6, 11, 12, 13, 14, 19, 20, 21, 26, 27, 28, + 29, 34, 35, 36,169, 42, 43, 44,177, 50, 51,184,185, 58, 59,192, +198,199,200, 73,206,207,208, 81,214,215,216, 89,223, 96, 97, 98, +231,104,105,106,239,112,113,114,120,121,122,123,132, 5, 6, 7, +140, 13, 14,147,148, 21, 22,155,156, 29,162,163,164, 37,170,171, + 44,177,178,179, 52,185,186,187, 66, 67, 68, 69, 74, 75, 76, 81, + 82, 83, 84, 89, 90, 91,224, 97, 98, 99,232,105,106,239,240,113, +114,247,120,121,254,255, 0,133, 6, 7, 8,141, 14, 15,148,149, + 22, 23,156, 29, 30,163,164, 37, 38,171,172, 45,178,179,180, 53, +186,187,188, 68, 69, 70, 71, 76, 77, 78,211, 84, 85, 86,219, 92, + 93,226,227,100,101,234,107,108,241,242,115,116,249,250,123,128, +134,135,136, 9,142,143, 16, 17,150,151, 24, 25,158,159, 32, 33, +167, 40, 41, 42,175, 48, 49, 50, 55, 56, 57, 58, 63,196, 69, 70, + 71,204, 77, 78,211,212, 85, 86,219, 92, 93,226,227,100,101,234, +235,108,241,242,243,116,249,250,251, 3, 4, 5, 6, 11, 12, 13, + 14, 19, 20, 21,154, 27, 28, 29,162, 35, 36,169, 42, 43, 44,177, + 50, 51,184,185, 58, 59,192, 65,198,199, 72, 73,206, 79, 80,213, +214, 87, 88,221,222, 95,228,229,230,103,236,237,110,243,244,245, +118,251,252,253, 4, 5, 6, 7, 12, 13, 14, 19, 20, 21, 22, 27, + 28, 29,162, 35, 36, 37,170, 43, 44,177,178, 51, 52,185, 58, 59, + 66, 67, 68, 69, 74, 75, 76, 77, 82, 83, 84,217, 90, 91, 92, 97, + 98, 99,232,105,106,107,240,113,114,247,248,121,122,255,128,133, + 6, 7, 8,141, 14, 15,148,149, 22, 23,156,157, 30,163,164,165, + 38,171,172, 45,178,179,180, 53,186,187,188, 67, 68, 69, 70, 75, + 76, 77, 82, 83, 84, 85, 90, 91, 92,225, 98, 99,100,233,106,107, +240,241,114,115,248,121,122,255,128,134,135,136, 9,142,143,144, + 17,150,151,152, 25,159, 32, 33, 34,167, 40, 41, 42,175, 48, 49, + 50, 56, 57, 58, 59,196, 69, 70, 71,204, 77, 78,211,212, 85, 86, +219,220, 93,226,227,228,101,234,235,108,241,242,243,116,249,250, +251, 2, 3, 4, 5, 10, 11, 12, 17, 18, 19, 20, 25, 26, 27,160, + 33, 34, 35,168, 41, 42,175,176, 49, 50,183, 56, 57,190,191, 64, + 65,198,199, 72, 73,206,207, 80,213,214, 87, 88,221,222, 95,228, +229,230,103,236,237,238,243,244,245,246,251,252,253, 4, 5, 6, + 7, 12, 13, 14,147, 20, 21, 22,155, 28, 29,162, 35, 36, 37,170, + 43, 44,177,178, 51, 52,185,186, 59,192,198,199, 72, 73,206,207, + 80, 81,214,215, 88, 89,222,223, 96, 97,231,104,105,106,111,112, +113,114,119,120,121,122,127, 0,133,134, 7, 8,141,142, 15,148, +149, 22, 23,156,157, 30,163,164,165, 38,171,172,173,178,179,180, +181,186,187,188, 67, 68, 69, 70, 75, 76, 77, 78, 83, 84, 85,218, + 91, 92, 93, 98, 99,100,233,106,107,108,241,114,115,248,249,122, +123,128, 1,134, 7, 8, 9,142, 15, 16,149,150, 23, 24,157,158, + 31,164,165,166, 39,172,173, 46,179,180,181, 54,187,188,189,196, +197, 70, 71,204,205, 78,211,212, 85, 86,219,220, 93,226,227,228, +101,234,235,236,241,242,243,116,249,250,251, 2, 3, 4, 5, 10, + 11, 12, 13, 18, 19, 20, 25, 26, 27, 28, 33, 34, 35,168, 41, 42, + 43,176, 49, 50,183,184, 57, 58,191, 64,197, 70, 71, 72,205, 78, + 79,212,213, 86, 87,220,221, 94,227,228,101,102,235,236,109,242, +243,244,117,250,251,252,132, 5, 6, 7, 12, 13, 14,147, 20, 21, + 22,155, 28, 29,162,163, 36, 37,170,171, 44,177,178, 51, 52,185, +186, 59,192,198,199,200, 73,206,207,208, 81,214,215, 88, 89,222, +223, 96, 97,231,104,105,106,239,112,113,114,247,120,121,122,127, +132, 5, 6, 7,140, 13, 14,147,148, 21, 22,155,156, 29,162,163, + 36, 37,170,171, 44,177,178,179, 52,185,186,187, 68, 69, 70, 75, + 76, 77, 78, 83, 84, 85,218, 91, 92, 93,226, 99,100,233,234,107, +108,241,114,115,248,249,122,123,128, 1,134,135, 8, 9,142,143, + 16,149,150, 23, 24,157,158, 31,164,165,166, 39,172,173,174,179, +180,181,182,187,188,189, 68, 69, 70, 71, 76, 77, 78,211, 84, 85, + 86,219, 92, 93,226, 99,100,101,234,107,108,241,242,115,116,249, +250,123, 2, 3, 4, 5, 10, 11, 12, 13, 18, 19, 20,153, 26, 27, + 28,161, 34, 35,168, 41, 42, 43,176, 49, 50,183,184, 57, 58,191, +192,197,198, 71, 72,205, 78, 79,212,213, 86, 87,220,221, 94,227, +228,229,102,235,236,237,242,243,244,117,250,251,252, 3, 4, 5, + 6, 11, 12, 13, 14, 19, 20, 21, 26, 27, 28, 29, 34, 35, 36,169, + 42, 43, 44,177, 50, 51,184,185, 58, 59,192,198,199,200, 73,206, +207,208, 81,214,215,216, 89,223,224, 97, 98,231,104,105,106,239, +112,113,114,120,121,122,123,132,133, 6, 7,140, 13, 14,147,148, + 21, 22,155,156, 29,162,163,164, 37,170,171,172,177,178,179, 52, +185,186,187, 68, 69, 70, 71, 76, 77, 78,211, 84, 85, 86, 91, 92, + 93,226, 99,100,101,234,107,108,241,242,115,116,249,122,123,128, +134,135, 8, 9,142,143, 16, 17,150,151, 24, 25,158, 31, 32, 33, + 39, 40, 41, 42, 47, 48, 49, 50, 55, 56, 57, 58, 63,196, 69, 70, + 71, 76, 77, 78,211, 84, 85, 86,219, 92, 93,226,227,100,101,234, +107,108,241,242,115,116,249,250,123, 3, 4, 5, 6, 11, 12, 13, + 18, 19, 20, 21, 26, 27, 28,161, 34, 35, 36,169, 42, 43,176,177, + 50, 51,184, 57, 58,191,192, 65,198, 71, 72, 73,206, 79, 80,213, +214, 87, 88,221, 94, 95,228,229,102,103,236,237,110,243,244,245, +118,251,252,253, 3, 4, 5, 6, 11, 12, 13, 14, 19, 20, 21,154, + 27, 28, 29,162, 35, 36,169, 42, 43, 44,177, 50, 51,184,185, 58, + 59, 66, 67, 68, 69, 74, 75, 76, 81, 82, 83, 84, 89, 90, 91,224, + 97, 98, 99,232,105,106,239,240,113,114,247,120,121,254,255,132, +133, 6, 7,140,141, 14,147,148,149, 22,155,156, 29,162,163,164, + 37,170,171,172,177,178,179,180,185,186,187, 68, 69, 70, 71, 76, + 77, 78,211, 84, 85, 86,219, 92, 93,226, 99,100,101,234,107,108, +241,242,115,116,249,250,123,128,134,135, 8, 9,142,143, 16, 17, +150,151, 24, 25,158,159, 32, 33,167, 40, 41, 42, 47, 48, 49, 50, + 55, 56, 57, 58, 63,196, 69, 70, 71,204, 77, 78,211, 84, 85, 86, +219, 92, 93,226,227,100,101,234,235,108,241,242,243,116,249,250, +123, 3, 4, 5, 6, 11, 12, 13, 14, 19, 20, 21,154, 27, 28, 29, + 34, 35, 36,169, 42, 43, 44,177, 50, 51,184,185, 58, 59,192, 65, +198, 71, 72, 73,206, 79, 80,213,214, 87, 88,221,222, 95,228,229, +230,103,236,237,110,243,244,245,118,251,252,253, 4, 5, 6, 7, + 12, 13, 14, 19, 20, 21, 22, 27, 28, 29,162, 35, 36, 37,170, 43, + 44,177,178, 51, 52,185, 58, 59, 66, 67, 68, 69, 74, 75, 76, 77, + 82, 83, 84,217, 90, 91, 92, 97, 98, 99,232,105,106,107,240,113, +114,247,248,121,122,255, 0,133, 6, 7, 8,141, 14, 15,148,149, + 22, 23,156,157, 30,163,164, 37, 38,171,172, 45,178,179,180, 53, +186,187,188, 67, 68, 69, 74, 75, 76, 77, 82, 83, 84,217, 90, 91, + 92,225, 98, 99,232,233,106,107,240,113,114,247,248,121,122,255, +128,134,135,136, 9,142,143,144, 17,150,151, 24, 25,158,159, 32, + 33,167, 40, 41, 42,175, 48, 49, 50,183, 56, 57, 58, 63,196, 69, + 70, 71,204, 77, 78,211,212, 85, 86,219,220, 93,226,227,100,101, +234,235,108,241,242,243,116,249,250,251, 4, 5, 6, 11, 12, 13, + 14, 19, 20, 21,154, 27, 28, 29,162, 35, 36,169,170, 43, 44,177, + 50, 51,184,185, 58, 59,192, 65,198,199, 72, 73,206,207, 80,213, +214, 87, 88,221,222, 95,228,229,230,103,236,237,238,243,244,245, +246,251,252,253, 4, 5, 6, 7, 12, 13, 14,147, 20, 21, 22,155, + 28, 29,162, 35, 36, 37,170, 43, 44,177,178, 51, 52,185,186, 59, + 66, 67, 68, 69, 74, 75, 76, 77, 82, 83, 84,217, 90, 91, 92,225, + 98, 99,232,105,106,107,240,113,114,247,248,121,122,255,128,133, +134, 7, 8,141, 14, 15,148,149, 22, 23,156,157, 30,163,164,165, + 38,171,172,173,178,179,180, 53,186,187,188,196, 69, 70, 71,204, + 77, 78,211,212, 85, 86,219, 92, 93,226,227,100,101,234,235,108, +241,242,243,116,249,250,251,128,134,135,136, 9,142,143,144, 17, +150,151,152, 25,159,160, 33, 34,167, 40, 41, 42,175, 48, 49, 50, + 56, 57, 58, 59,196,197, 70, 71,204, 77, 78,211,212, 85, 86,219, +220, 93,226,227,228,101,234,235,236,241,242,243,116,249,250,251, + 4, 5, 6, 7, 12, 13, 14,147, 20, 21, 22, 27, 28, 29,162, 35, + 36, 37,170, 43, 44,177,178, 51, 52,185, 58, 59,192,198,199, 72, + 73,206,207, 80, 81,214,215, 88, 89,222,223, 96, 97,103,104,105, +106,111,112,113,114,119,120,121,122,127,132, 5, 6, 7, 12, 13, + 14,147, 20, 21, 22,155, 28, 29,162,163, 36, 37,170, 43, 44,177, +178, 51, 52,185,186, 59, 67, 68, 69, 70, 75, 76, 77, 82, 83, 84, + 85, 90, 91, 92,225, 98, 99,100,233,106,107,240,241,114,115,248, +121,122,255,128, 1,134, 7, 8, 9,142, 15, 16,149,150, 23, 24, +157, 30, 31,164,165, 38, 39,172,173, 46,179,180,181, 54,187,188, +189,196, 69, 70, 71,204, 77, 78,211,212, 85, 86,219,220, 93,226, +227,228,101,234,235,108,241,242,243,116,249,250,251, 2, 3, 4, + 5, 10, 11, 12, 17, 18, 19, 20, 25, 26, 27,160, 33, 34, 35,168, + 41, 42,175,176, 49, 50,183, 56, 57,190,191, 64, 65,198,199, 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0, 64, + 64, 0, 64, 0, 64, 0, 64, 0, 64, 0, + }; From 6b89aadfb5d7104bae2860c30bb682ae83625977 Mon Sep 17 00:00:00 2001 From: fp64 <106717720+fp64@users.noreply.github.com> Date: Sun, 19 Feb 2023 02:30:17 -0500 Subject: [PATCH 02/14] Fix the sign of cos(2*n+1) Also fix the license text. --- Core/MIPS/MIPSVFPUUtils.cpp | 3 +-- Core/MIPS/vfpu_sin_lut.h | 2 +- 2 files changed, 2 insertions(+), 3 deletions(-) diff --git a/Core/MIPS/MIPSVFPUUtils.cpp b/Core/MIPS/MIPSVFPUUtils.cpp index e03badb91b..d6e62adb51 100644 --- a/Core/MIPS/MIPSVFPUUtils.cpp +++ b/Core/MIPS/MIPSVFPUUtils.cpp @@ -993,7 +993,6 @@ float vfpu_sin(float x) { return (sign ? -1.0f : +1.0f) * float(int32_t(ret)) * 3.7252903e-09f; // 0x1p-28f } -// WARNING: not tested. float vfpu_cos(float x) { uint32_t bits; memcpy(&bits, &x, sizeof(x)); @@ -1022,7 +1021,7 @@ float vfpu_cos(float x) { } sign ^= ((significand << 7) & 0x80000000u); significand &= 0x00FFFFFFu; - if(significand > 0x00800000u) { + if(significand >= 0x00800000u) { significand = 0x01000000u - significand; sign ^= 0x80000000u; } diff --git a/Core/MIPS/vfpu_sin_lut.h b/Core/MIPS/vfpu_sin_lut.h index d2bec30211..ba891c86ab 100644 --- a/Core/MIPS/vfpu_sin_lut.h +++ b/Core/MIPS/vfpu_sin_lut.h @@ -1,4 +1,4 @@ -// Copyright (c) 2012- PPSSPP Project. +// Copyright (c) 2023- PPSSPP Project. // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by From 02500a05b7ebda8c6fb09d744f853369d80a9d62 Mon Sep 17 00:00:00 2001 From: fp64 <106717720+fp64@users.noreply.github.com> Date: Thu, 9 Mar 2023 23:23:33 -0500 Subject: [PATCH 03/14] Add more vfpu_*, move tables to assets --- Core/MIPS/MIPSIntVFPU.cpp | 18 +- Core/MIPS/MIPSVFPUUtils.cpp | 547 +- Core/MIPS/MIPSVFPUUtils.h | 10 +- Core/MIPS/vfpu_sin_lut.h | 46687 ----------------- Core/System.cpp | 2 +- assets/vfpu/vfpu_asin_lut65536.dat | Bin 0 -> 1536 bytes assets/vfpu/vfpu_asin_lut_deltas.dat | Bin 0 -> 517448 bytes assets/vfpu/vfpu_asin_lut_indices.dat | Bin 0 -> 798916 bytes assets/vfpu/vfpu_exp2_lut.dat | 4 + assets/vfpu/vfpu_exp2_lut65536.dat | Bin 0 -> 512 bytes assets/vfpu/vfpu_log2_lut.dat | 22 + assets/vfpu/vfpu_log2_lut65536.dat | Bin 0 -> 516 bytes assets/vfpu/vfpu_log2_lut65536_quadratic.dat | Bin 0 -> 512 bytes assets/vfpu/vfpu_rcp_lut.dat | Bin 0 -> 262144 bytes assets/vfpu/vfpu_rsqrt_lut.dat | Bin 0 -> 262144 bytes assets/vfpu/vfpu_sin_lut8192.dat | Bin 0 -> 4100 bytes assets/vfpu/vfpu_sin_lut_delta.dat | Bin 0 -> 262144 bytes assets/vfpu/vfpu_sin_lut_exceptions.dat | Bin 0 -> 86938 bytes assets/vfpu/vfpu_sin_lut_interval_delta.dat | Bin 0 -> 131074 bytes assets/vfpu/vfpu_sqrt_lut.dat | Bin 0 -> 262144 bytes unittest/JitHarness.cpp | 2 +- unittest/UnitTest.cpp | 2 +- 22 files changed, 476 insertions(+), 46818 deletions(-) delete mode 100644 Core/MIPS/vfpu_sin_lut.h create mode 100644 assets/vfpu/vfpu_asin_lut65536.dat create mode 100644 assets/vfpu/vfpu_asin_lut_deltas.dat create mode 100644 assets/vfpu/vfpu_asin_lut_indices.dat create mode 100644 assets/vfpu/vfpu_exp2_lut.dat create mode 100644 assets/vfpu/vfpu_exp2_lut65536.dat create mode 100644 assets/vfpu/vfpu_log2_lut.dat create mode 100644 assets/vfpu/vfpu_log2_lut65536.dat create mode 100644 assets/vfpu/vfpu_log2_lut65536_quadratic.dat create mode 100644 assets/vfpu/vfpu_rcp_lut.dat create mode 100644 assets/vfpu/vfpu_rsqrt_lut.dat create mode 100644 assets/vfpu/vfpu_sin_lut8192.dat create mode 100644 assets/vfpu/vfpu_sin_lut_delta.dat create mode 100644 assets/vfpu/vfpu_sin_lut_exceptions.dat create mode 100644 assets/vfpu/vfpu_sin_lut_interval_delta.dat create mode 100644 assets/vfpu/vfpu_sqrt_lut.dat diff --git a/Core/MIPS/MIPSIntVFPU.cpp b/Core/MIPS/MIPSIntVFPU.cpp index b8bbe25caf..c6585f21f2 100644 --- a/Core/MIPS/MIPSIntVFPU.cpp +++ b/Core/MIPS/MIPSIntVFPU.cpp @@ -629,18 +629,24 @@ namespace MIPSInt // vsat0 changes -0.0 to +0.0, both retain NAN. case 4: if (s[i] <= 0) d[i] = 0; else {if(s[i] > 1.0f) d[i] = 1.0f; else d[i] = s[i];} break; // vsat0 case 5: if (s[i] < -1.0f) d[i] = -1.0f; else {if(s[i] > 1.0f) d[i] = 1.0f; else d[i] = s[i];} break; // vsat1 - case 16: d[i] = 1.0f / s[i]; break; //vrcp + //case 16: d[i] = 1.0f / s[i]; break; //vrcp + case 16: { d[i] = vfpu_rcp(s[i]); } break; //vrcp case 17: d[i] = USE_VFPU_SQRT ? vfpu_rsqrt(s[i]) : 1.0f / sqrtf(s[i]); break; //vrsq case 18: { d[i] = vfpu_sin(s[i]); } break; //vsin case 19: { d[i] = vfpu_cos(s[i]); } break; //vcos - case 20: d[i] = powf(2.0f, s[i]); break; //vexp2 - case 21: d[i] = logf(s[i])/log(2.0f); break; //vlog2 + //case 20: d[i] = powf(2.0f, s[i]); break; //vexp2 + case 20: { d[i] = vfpu_exp2(s[i]); } break; //vexp2 + //case 21: d[i] = logf(s[i])/log(2.0f); break; //vlog2 + case 21: { d[i] = vfpu_log2(s[i]); } break; //vlog2 case 22: d[i] = USE_VFPU_SQRT ? vfpu_sqrt(s[i]) : fabsf(sqrtf(s[i])); break; //vsqrt - case 23: d[i] = (float)(asinf(s[i]) / M_PI_2); break; //vasin - case 24: d[i] = -1.0f / s[i]; break; // vnrcp + //case 23: d[i] = (float)(asinf(s[i]) / M_PI_2); break; //vasin + case 23: { d[i] = vfpu_asin(s[i]); } break; //vasin + //case 24: d[i] = -1.0f / s[i]; break; // vnrcp + case 24: { d[i] = -vfpu_rcp(s[i]); } break; // vnrcp case 26: { d[i] = -vfpu_sin(s[i]); } break; // vnsin - case 28: d[i] = 1.0f / powf(2.0, s[i]); break; // vrexp2 + //case 28: d[i] = 1.0f / powf(2.0, s[i]); break; // vrexp2 + case 28: { d[i] = vfpu_rexp2(s[i]); } break; // vrexp2 default: _dbg_assert_msg_( false, "Invalid VV2Op op type %d", optype); break; diff --git a/Core/MIPS/MIPSVFPUUtils.cpp b/Core/MIPS/MIPSVFPUUtils.cpp index d6e62adb51..e97a476d78 100644 --- a/Core/MIPS/MIPSVFPUUtils.cpp +++ b/Core/MIPS/MIPSVFPUUtils.cpp @@ -22,6 +22,7 @@ #include "Common/BitScan.h" #include "Common/CommonFuncs.h" +#include "Common/File/VFS/VFS.h" #include "Core/Reporting.h" #include "Core/MIPS/MIPS.h" #include "Core/MIPS/MIPSVFPUUtils.h" @@ -791,134 +792,47 @@ float vfpu_dot(const float a[4], const float b[4]) { return result.f; } -// TODO: This is still not completely accurate compared to the PSP's vsqrt. -float vfpu_sqrt(float a) { - float2int val; - val.f = a; - - if ((val.i & 0xff800000) == 0x7f800000) { - if ((val.i & 0x007fffff) != 0) { - val.i = 0x7f800001; - } - return val.f; - } - if ((val.i & 0x7f800000) == 0) { - // Kill any sign. - val.i = 0; - return val.f; - } - if (val.i & 0x80000000) { - val.i = 0x7f800001; - return val.f; - } - - int k = get_exp(val.i); - uint32_t sp = get_mant(val.i); - int less_bits = k & 1; - k >>= 1; - - uint32_t z = 0x00C00000 >> less_bits; - int64_t halfsp = sp >> 1; - halfsp <<= 23 - less_bits; - for (int i = 0; i < 6; ++i) { - z = (z >> 1) + (uint32_t)(halfsp / z); - } - - val.i = ((k + 127) << 23) | ((z << less_bits) & 0x007FFFFF); - // The lower two bits never end up set on the PSP, it seems like. - val.i &= 0xFFFFFFFC; - - return val.f; -} - -static inline uint32_t mant_mul(uint32_t a, uint32_t b) { - uint64_t m = (uint64_t)a * (uint64_t)b; - if (m & 0x007FFFFF) { - m += 0x01437000; - } - return (uint32_t)(m >> 23); -} - -float vfpu_rsqrt(float a) { - float2int val; - val.f = a; - - if (val.i == 0x7f800000) { - return 0.0f; - } - if ((val.i & 0x7fffffff) > 0x7f800000) { - val.i = (val.i & 0x80000000) | 0x7f800001; - return val.f; - } - if ((val.i & 0x7f800000) == 0) { - val.i = (val.i & 0x80000000) | 0x7f800000; - return val.f; - } - if (val.i & 0x80000000) { - val.i = 0xff800001; - return val.f; - } - - int k = get_exp(val.i); - uint32_t sp = get_mant(val.i); - int less_bits = k & 1; - k = -(k >> 1); - - uint32_t z = 0x00800000 >> less_bits; - uint32_t halfsp = sp >> (1 + less_bits); - for (int i = 0; i < 6; ++i) { - uint32_t zsq = mant_mul(z, z); - uint32_t correction = 0x00C00000 - mant_mul(halfsp, zsq); - z = mant_mul(z, correction); - } - - int8_t shift = (int8_t)clz32_nonzero(z) - 8 + less_bits; - if (shift < 1) { - z >>= -shift; - k += -shift; - } else if (shift > 0) { - z <<= shift; - k -= shift; - } - - z >>= less_bits; - - val.i = ((k + 127) << 23) | (z & 0x007FFFFF); - val.i &= 0xFFFFFFFC; - - return val.f; -} - //============================================================================== // The code below attempts to exactly match the output of -// PSP's sin and cos instructions. For the sake of -// making lookup tables smaller (473KB) the code is +// several PSP's VFPU functions. For the sake of +// making lookup tables smaller the code is // somewhat gnarly. -// The key observation is that (ignoring range -// reduction) PSP effectively converts input to 9.23 -// fixed-point, and that output is always representable -// as 4.28 fixed-point (though that is probably not -// what is going on internally). -// The rest is mostly trying to obtain the same result -// with smaller tables (pretty ad-hoc, and almost certainly -// does not match what PSP does internally). -// Lookup tables store deltas from (explicitly computable) -// estimations, to allow to store them in smaller types: -// int8 and int16. +// Lookup tables sometimes store deltas from (explicitly computable) +// estimations, to allow to store them in smaller types. // See https://github.com/hrydgard/ppsspp/issues/16946 for details. -#include "Core/MIPS/vfpu_sin_lut.h" +static uint32_t (*vfpu_sin_lut8192)=nullptr; +static int8_t (*vfpu_sin_lut_delta)[2]=nullptr; +static int16_t (*vfpu_sin_lut_interval_delta)=nullptr; +static uint8_t (*vfpu_sin_lut_exceptions)=nullptr; + +static int8_t (*vfpu_sqrt_lut)[2]=nullptr; + +static int8_t (*vfpu_rsqrt_lut)[2]=nullptr; + +static uint32_t (*vfpu_exp2_lut65536)=nullptr; +static uint8_t (*vfpu_exp2_lut)[2]=nullptr; + +static uint32_t (*vfpu_log2_lut65536)=nullptr; +static uint32_t (*vfpu_log2_lut65536_quadratic)=nullptr; +static uint8_t (*vfpu_log2_lut)[131072][2]=nullptr; + +static int32_t (*vfpu_asin_lut65536)[3]=nullptr; +static uint64_t (*vfpu_asin_lut_deltas)=nullptr; +static uint16_t (*vfpu_asin_lut_indices)=nullptr; + +static int8_t (*vfpu_rcp_lut)[2]=nullptr; // Note: PSP sin/cos output only has 22 significant // binary digits. -static inline uint32_t quantum(uint32_t x) { +static inline uint32_t vfpu_sin_quantum(uint32_t x) { return x < 1u << 22? 1u: 1u << (32 - 22 - clz32_nonzero(x)); } -static inline uint32_t truncate_bits(u32 x) { - return x & -quantum(x); +static inline uint32_t vfpu_sin_truncate_bits(u32 x) { + return x & -vfpu_sin_quantum(x); } static inline uint32_t vfpu_sin_fixed(uint32_t arg) { @@ -932,11 +846,11 @@ static inline uint32_t vfpu_sin_fixed(uint32_t arg) { uint32_t A = L+(((H - L)*(((arg >> 6) & 127) + 0)) >> 7); uint32_t B = L+(((H - L)*(((arg >> 6) & 127) + 1)) >> 7); // Adjust endpoints from deltas, and increase working precision. - uint64_t a = (uint64_t(A) << 5) + uint64_t(vfpu_sin_lut_delta[arg >> 6][0]) * quantum(A); - uint64_t b = (uint64_t(B) << 5) + uint64_t(vfpu_sin_lut_delta[arg >> 6][1]) * quantum(B); + uint64_t a = (uint64_t(A) << 5) + uint64_t(vfpu_sin_lut_delta[arg >> 6][0]) * vfpu_sin_quantum(A); + uint64_t b = (uint64_t(B) << 5) + uint64_t(vfpu_sin_lut_delta[arg >> 6][1]) * vfpu_sin_quantum(B); // Compute approximation via lerp. Is off by at most 1 quantum. uint32_t v = uint32_t(((a * (64 - (arg & 63)) + b * (arg & 63)) >> 6) >> 5); - v=truncate_bits(v); + v=vfpu_sin_truncate_bits(v); // Look up exceptions via binary search. // Note: vfpu_sin_lut_interval_delta stores // deltas from interval estimation. @@ -952,7 +866,7 @@ static inline uint32_t vfpu_sin_fixed(uint32_t arg) { uint32_t b = vfpu_sin_lut_exceptions[m]; uint32_t e = (arg & -128u)+(b & 127u); if(e == arg) { - v += quantum(v) * (b >> 7 ? -1u : +1u); + v += vfpu_sin_quantum(v) * (b >> 7 ? -1u : +1u); break; } else if(e < arg) lo = m + 1; @@ -1036,8 +950,399 @@ void vfpu_sincos(float a, float &s, float &c) { c = vfpu_cos(a); } +// Integer square root of 2^23*x (rounded to zero). +// Input is in 2^23 <= x < 2^25, and representable in float. +static inline uint32_t isqrt23(uint32_t x) { +#if 0 + // Reference version. + int dir=fesetround(FE_TOWARDZERO); + uint32_t ret=uint32_t(int32_t(sqrtf(float(int32_t(x)) * 8388608.0f))); + fesetround(dir); + return ret; +#elif 1 + // Double version. + // Verified to produce correct result for all valid inputs, + // in all rounding modes, both in double and double-extended (x87) + // precision. + // Requires correctly-rounded sqrt (which on any IEEE-754 system + // it should be). + return uint32_t(int32_t(sqrt(double(x) * 8388608.0))); +#else + // Pure integer version, if you don't like floating point. + // Based on code from Hacker's Delight. See isqrt4 in + // https://github.com/hcs0/Hackers-Delight/blob/master/isqrt.c.txt + // Relatively slow. + uint64_t t=uint64_t(x) << 23, m, y, b; + m=0x4000000000000000ull; + y=0; + while(m != 0) // Do 32 times. + { + b=y | m; + y=y >> 1; + if(t >= b) + { + t = t - b; + y = y | m; + } + m = m >> 2; + } + return y; +#endif +} + +// Returns floating-point bitpattern. +static inline uint32_t vfpu_sqrt_fixed(uint32_t x) { + // Endpoints of input. + uint32_t lo =(x + 0u) & -64u; + uint32_t hi = (x + 64u) & -64u; + // Convert input to 9.23 fixed-point. + lo = (lo >= 0x00400000u ? 4u * lo : 0x00800000u + 2u * lo); + hi = (hi >= 0x00400000u ? 4u * hi : 0x00800000u + 2u * hi); + // Estimate endpoints of output. + uint32_t A = 0x3F000000u + isqrt23(lo); + uint32_t B = 0x3F000000u + isqrt23(hi); + // Apply deltas, and increase the working precision. + uint64_t a = (uint64_t(A) << 4) + uint64_t(vfpu_sqrt_lut[x >> 6][0]); + uint64_t b = (uint64_t(B) << 4) + uint64_t(vfpu_sqrt_lut[x >> 6][1]); + uint32_t ret = uint32_t((a + (((b - a) * (x & 63)) >> 6)) >> 4); + // Truncate lower 2 bits. + ret &= -4u; + return ret; +} + +float vfpu_sqrt(float x) { + uint32_t bits; + memcpy(&bits, &x, sizeof(bits)); + if((bits & 0x7FFFFFFFu) <= 0x007FFFFFu) { + // Denormals (and zeroes) get +0, regardless + // of sign. + return +0.0f; + } + if(bits >> 31) { + // Other negatives get NaN. + bits = 0x7F800001u; + memcpy(&x, &bits, sizeof(x)); + return x; + } + if((bits >> 23) == 255u) { + // Inf/NaN gets Inf/NaN. + bits = 0x7F800000u + ((bits & 0x007FFFFFu) != 0u); + memcpy(&x, &bits, sizeof(bits)); + return x; + } + int32_t exponent = int32_t(bits >> 23) - 127; + // Bottom bit of exponent (inverted) + significand (except bottom bit). + uint32_t index = ((bits + 0x00800000u) >> 1) & 0x007FFFFFu; + bits = vfpu_sqrt_fixed(index); + bits += uint32_t(exponent >> 1) << 23; + memcpy(&x, &bits, sizeof(bits)); + return x; +} + +// Returns floor(2^33/sqrt(x)), for 2^22 <= x < 2^24. +static inline uint32_t rsqrt_floor22(uint32_t x) { +#if 1 + // Verified correct in all rounding directions, + // by exhaustive search. + return uint32_t(8589934592.0 / sqrt(double(x))); // 0x1p33 +#else + // Pure integer version, if you don't like floating point. + // Based on code from Hacker's Delight. See isqrt4 in + // https://github.com/hcs0/Hackers-Delight/blob/master/isqrt.c.txt + // Relatively slow. + uint64_t t=uint64_t(x) << 22, m, y, b; + m = 0x4000000000000000ull; + y = 0; + while(m != 0) // Do 32 times. + { + b = y | m; + y = y >> 1; + if(t >= b) + { + t = t - b; + y = y | m; + } + m = m >> 2; + } + y = (1ull << 44) / y; + // Decrement if y > floor(2^33 / sqrt(x)). + // This hack works because exhaustive + // search (on [2^22;2^24]) says it does. + if((y * y >> 3) * x > (1ull << 63) - 3ull * (((y & 7) == 6) << 21)) --y; + return uint32_t(y); +#endif +} + +// Returns floating-point bitpattern. +static inline uint32_t vfpu_rsqrt_fixed(uint32_t x) { + // Endpoints of input. + uint32_t lo = (x + 0u) & -64u; + uint32_t hi = (x + 64u) & -64u; + // Convert input to 10.22 fixed-point. + lo = (lo >= 0x00400000u ? 2u * lo : 0x00400000u + lo); + hi = (hi >= 0x00400000u ? 2u * hi : 0x00400000u + hi); + // Estimate endpoints of output. + uint32_t A = 0x3E800000u + 4u * rsqrt_floor22(lo); + uint32_t B = 0x3E800000u + 4u * rsqrt_floor22(hi); + // Apply deltas, and increase the working precision. + uint64_t a = (uint64_t(A) << 4) + uint64_t(vfpu_rsqrt_lut[x >> 6][0]); + uint64_t b = (uint64_t(B) << 4) + uint64_t(vfpu_rsqrt_lut[x >> 6][1]); + // Evaluate via lerp. + uint32_t ret = uint32_t((a + (((b - a) * (x & 63)) >> 6)) >> 4); + // Truncate lower 2 bits. + ret &= -4u; + return ret; +} + +float vfpu_rsqrt(float x) { + uint32_t bits; + memcpy(&bits, &x, sizeof(bits)); + if((bits & 0x7FFFFFFFu) <= 0x007FFFFFu) { + // Denormals (and zeroes) get Inf of the same sign. + bits = 0x7F800000u | (bits & 0x80000000u); + memcpy(&x, &bits, sizeof(x)); + return x; + } + if(bits >> 31) { + // Other negatives get negative NaN. + bits = 0xFF800001u; + memcpy(&x, &bits, sizeof(x)); + return x; + } + if((bits >> 23) == 255u) { + // Inf gets 0, NaN gets NaN. + bits = ((bits & 0x007FFFFFu) ? 0x7F800001u : 0u); + memcpy(&x, &bits, sizeof(bits)); + return x; + } + int32_t exponent = int32_t(bits >> 23) - 127; + // Bottom bit of exponent (inverted) + significand (except bottom bit). + uint32_t index = ((bits + 0x00800000u) >> 1) & 0x007FFFFFu; + bits = vfpu_rsqrt_fixed(index); + bits -= uint32_t(exponent >> 1) << 23; + memcpy(&x, &bits, sizeof(bits)); + return x; +} + +static inline uint32_t vfpu_asin_quantum(uint32_t x) { + return x<1u<<23? + 1u: + 1u<<(32-23-clz32_nonzero(x)); +} + +static inline uint32_t vfpu_asin_truncate_bits(uint32_t x) { + return x & -vfpu_asin_quantum(x); +} + +// Input is fixed 9.23, output is fixed 2.30. +static inline uint32_t vfpu_asin_approx(uint32_t x) { + const int32_t *C = vfpu_asin_lut65536[x >> 16]; + x &= 0xFFFFu; + return vfpu_asin_truncate_bits(uint32_t((((((int64_t(C[2]) * x) >> 16) + int64_t(C[1])) * x) >> 16) + C[0])); +} + +// Input is fixed 9.23, output is fixed 2.30. +static uint32_t vfpu_asin_fixed(uint32_t x) { + if(x == 0u) return 0u; + if(x == 1u << 23) return 1u << 30; + uint32_t ret = vfpu_asin_approx(x); + uint32_t index = vfpu_asin_lut_indices[x / 21u]; + uint64_t deltas = vfpu_asin_lut_deltas[index]; + return ret + (3u - uint32_t((deltas >> (3u * (x % 21u))) & 7u)) * vfpu_asin_quantum(ret); +} + +float vfpu_asin(float x) { + uint32_t bits; + memcpy(&bits, &x, sizeof(x)); + uint32_t sign = bits & 0x80000000u; + bits = bits & 0x7FFFFFFFu; + if(bits > 0x3F800000u) { + bits = 0x7F800001u ^ sign; + memcpy(&x, &bits, sizeof(x)); + return x; + } + + bits = vfpu_asin_fixed(uint32_t(int32_t(fabsf(x) * 8388608.0f))); // 0x1p23 + x=float(int32_t(bits)) * 9.31322574615478515625e-10f; // 0x1p-30 + if(sign) x = -x; + return x; +} + +static inline uint32_t vfpu_exp2_approx(uint32_t x) { + if(x == 0x00800000u) return 0x00800000u; + uint32_t a=vfpu_exp2_lut65536[x >> 16]; + x &= 0x0000FFFFu; + uint32_t b = uint32_t(((2977151143ull * x) >> 23) + ((1032119999ull * (x * x)) >> 46)); + return (a + uint32_t((uint64_t(a + (1u << 23)) * uint64_t(b)) >> 32)) & -4u; +} + +static inline uint32_t vfpu_exp2_fixed(uint32_t x) { + if(x == 0u) return 0u; + if(x == 0x00800000u) return 0x00800000u; + uint32_t A = vfpu_exp2_approx((x ) & -64u); + uint32_t B = vfpu_exp2_approx((x + 64) & -64u); + uint64_t a = (A<<4)+vfpu_exp2_lut[x >> 6][0]-64u; + uint64_t b = (B<<4)+vfpu_exp2_lut[x >> 6][1]-64u; + uint32_t y = uint32_t((a + (((b - a) * (x & 63)) >> 6)) >> 4); + y &= -4u; + return y; +} + +float vfpu_exp2(float x) { + int32_t bits; + memcpy(&bits, &x, sizeof(bits)); + if((bits & 0x7FFFFFFF) <= 0x007FFFFF) { + // Denormals are treated as 0. + return 1.0f; + } + if(x != x) { + // NaN gets NaN. + bits = 0x7F800001u; + memcpy(&x, &bits, sizeof(x)); + return x; + } + if(x <= -126.0f) { + // Small numbers get 0 (exp2(-126) is smallest positive non-denormal). + // But yes, -126.0f produces +0.0f. + return 0.0f; + } + if(x >= +128.0f) { + // Large numbers get infinity. + bits = 0x7F800000u; + memcpy(&x, &bits, sizeof(x)); + return x; + } + bits = int32_t(x * 0x1p23f); + if(x < 0.0f) --bits; // Yes, really. + bits = int32_t(0x3F800000) + (bits & int32_t(0xFF800000)) + int32_t(vfpu_exp2_fixed(bits & int32_t(0x007FFFFF))); + memcpy(&x, &bits, sizeof(bits)); + return x; +} + +float vfpu_rexp2(float x) { + return vfpu_exp2(-x); +} + +// Input fixed 9.23, output fixed 10.22. +// Returns log2(1+x). +static inline uint32_t vfpu_log2_approx(uint32_t x) { + uint32_t a=vfpu_log2_lut65536[(x >> 16) + 0]; + uint32_t b=vfpu_log2_lut65536[(x >> 16) + 1]; + uint32_t c=vfpu_log2_lut65536_quadratic[x >> 16]; + x &= 0xFFFFu; + uint64_t ret = uint64_t(a) * (0x10000u - x) + uint64_t(b) * x; + uint64_t d = (uint64_t(c) * x * (0x10000u-x)) >> 40; + ret += d; + return uint32_t(ret >> 16); +} + +// Matches PSP output on all known values. +float vfpu_log2(float x) { + uint32_t bits; + memcpy(&bits, &x, sizeof(bits)); + if((bits & 0x7FFFFFFFu) <= 0x007FFFFFu) { + // Denormals (and zeroes) get -inf. + bits = 0xFF800000u; + memcpy(&x, &bits, sizeof(x)); + return x; + } + if(bits & 0x80000000u) { + // Other negatives get NaN. + bits = 0x7F800001u; + memcpy(&x, &bits, sizeof(x)); + return x; + } + if((bits >> 23) == 255u) { + // NaN gets NaN, +inf gets +inf. + bits = 0x7F800000u + ((bits & 0x007FFFFFu) != 0); + memcpy(&x, &bits, sizeof(x)); + return x; + } + uint32_t e = (bits & 0x7F800000u) - 0x3F800000u; + uint32_t i = bits & 0x007FFFFFu; + if(e >> 31 && i >= 0x007FFE00u) { + // Process 1-2^{-14}<=x*2^n<1 (for n>0) separately, + // since the table doesn't give the right answer. + float c = float(int32_t(~e) >> 23); + // Note: if c is 0 the sign of -0 output is correct. + return i < 0x007FFEF7u ? // 1-265*2^{-24} + -3.05175781e-05f - c: + -0.0f - c; + } + int d = (e<0x01000000u ? 0 : 8 - clz32_nonzero(e) - int(e >> 31)); + //assert(d>=0&&d<8); + uint32_t q = 1u << d; + uint32_t A = vfpu_log2_approx((i ) & -64u) & -q; + uint32_t B = vfpu_log2_approx((i + 64) & -64u) & -q; + uint64_t a = (A << 6)+(uint64_t(vfpu_log2_lut[d][i >> 6][0]) - 80ull) * q; + uint64_t b = (B << 6)+(uint64_t(vfpu_log2_lut[d][i >> 6][1]) - 80ull) * q; + uint32_t v = uint32_t((a +(((b - a) * (i & 63)) >> 6)) >> 6); + v &= -q; + bits = e ^ (2u * v); + x = float(int32_t(bits)) * 1.1920928955e-7f; // 0x1p-23f + return x; +} + +static inline uint32_t vfpu_rcp_approx(uint32_t i) { + return 0x3E800000u + (uint32_t((1ull << 47) / ((1ull << 23) + i)) & -4u); +} + +float vfpu_rcp(float x) { + uint32_t bits; + memcpy(&bits, &x, sizeof(bits)); + uint32_t s = bits & 0x80000000u; + uint32_t e = bits & 0x7F800000u; + uint32_t i = bits & 0x007FFFFFu; + if((bits & 0x7FFFFFFFu) > 0x7E800000u) { + bits = (e == 0x7F800000u && i ? s ^ 0x7F800001u : s); + memcpy(&x, &bits, sizeof(x)); + return x; + } + if(e==0u) { + bits = s^0x7F800000u; + memcpy(&x, &bits, sizeof(x)); + return x; + } + uint32_t A = vfpu_rcp_approx((i ) & -64u); + uint32_t B = vfpu_rcp_approx((i + 64) & -64u); + uint64_t a = (uint64_t(A) << 6) + uint64_t(vfpu_rcp_lut[i >> 6][0]) * 4u; + uint64_t b = (uint64_t(B) << 6) + uint64_t(vfpu_rcp_lut[i >> 6][1]) * 4u; + uint32_t v = uint32_t((a+(((b-a)*(i&63))>>6))>>6); + v &= -4u; + bits = s + (0x3F800000u - e) + v; + memcpy(&x, &bits, sizeof(x)); + return x; +} + //============================================================================== -void InitVFPUSinCos() { - // TODO: Could prepare a CORDIC table here. +void InitVFPU() { +// WARNING: this is not endian-safe! + size_t size=0; +#define LOAD(expected,name)\ + if(!name) {\ + const char *filename = "vfpu/" #name ".dat";\ + INFO_LOG(CPU, "Loading '%s'.\n", filename);\ + name=reinterpret_cast(g_VFS.ReadFile(filename, &size));\ + if(size!=(expected))\ + ERROR_LOG(CPU, "Error loading '%s' (size=%u, expected: %u).\n", filename, (unsigned)size, (unsigned)(expected));\ + else\ + INFO_LOG(CPU, "Successfully loaded '%s'.\n", filename);\ + } + LOAD( 1536, vfpu_asin_lut65536); + LOAD( 517448, vfpu_asin_lut_deltas); + LOAD( 798916, vfpu_asin_lut_indices); + LOAD( 512, vfpu_exp2_lut65536); + LOAD( 262144, vfpu_exp2_lut); + LOAD( 516, vfpu_log2_lut65536); + LOAD( 512, vfpu_log2_lut65536_quadratic); + LOAD( 2097152, vfpu_log2_lut); + LOAD( 262144, vfpu_rcp_lut); + LOAD( 262144, vfpu_rsqrt_lut); + LOAD( 4100, vfpu_sin_lut8192); + LOAD( 262144, vfpu_sin_lut_delta); + LOAD( 86938, vfpu_sin_lut_exceptions); + LOAD( 131074, vfpu_sin_lut_interval_delta); + LOAD( 262144, vfpu_sqrt_lut); +#undef LOAD } diff --git a/Core/MIPS/MIPSVFPUUtils.h b/Core/MIPS/MIPSVFPUUtils.h index a137245e8a..a8b2bebd79 100644 --- a/Core/MIPS/MIPSVFPUUtils.h +++ b/Core/MIPS/MIPSVFPUUtils.h @@ -50,9 +50,12 @@ extern float vfpu_sin(float); extern float vfpu_cos(float); extern void vfpu_sincos(float, float&, float&); +/* inline float vfpu_asin(float angle) { return (float)(asinf(angle) / M_PI_2); } +*/ +extern float vfpu_asin(float); inline float vfpu_clamp(float v, float min, float max) { // Note: NAN is preserved, and -0.0 becomes +0.0 if min=+0.0. @@ -63,6 +66,11 @@ float vfpu_dot(const float a[4], const float b[4]); float vfpu_sqrt(float a); float vfpu_rsqrt(float a); +extern float vfpu_exp2(float); +extern float vfpu_rexp2(float); +extern float vfpu_log2(float); +extern float vfpu_rcp(float); + #define VFPU_FLOAT16_EXP_MAX 0x1f #define VFPU_SH_FLOAT16_SIGN 15 #define VFPU_MASK_FLOAT16_SIGN 0x1 @@ -211,4 +219,4 @@ int GetVectorOverlap(int reg1, VectorSize size1, int reg2, VectorSize size2); bool GetVFPUCtrlMask(int reg, u32 *mask); float Float16ToFloat32(unsigned short l); -void InitVFPUSinCos(); +void InitVFPU(); diff --git a/Core/MIPS/vfpu_sin_lut.h b/Core/MIPS/vfpu_sin_lut.h deleted file mode 100644 index ba891c86ab..0000000000 --- a/Core/MIPS/vfpu_sin_lut.h +++ /dev/null @@ -1,46687 +0,0 @@ -// Copyright (c) 2023- PPSSPP Project. - -// This program is free software: you can redistribute it and/or modify -// it under the terms of the GNU General Public License as published by -// the Free Software Foundation, version 2.0 or later versions. - -// This program is distributed in the hope that it will be useful, -// but WITHOUT ANY WARRANTY; without even the implied warranty of -// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -// GNU General Public License 2.0 for more details. - -// A copy of the GPL 2.0 should have been included with the program. -// If not, see http://www.gnu.org/licenses/ - -// Official git repository and contact information can be found at -// https://github.com/hrydgard/ppsspp and http://www.ppsspp.org/. - -//============================================================================== -// WARNING: this is partially automatically generated, -// and only meant to be included inside Core/MIPS/MIPSVFPUUtils.cpp, -// so no header guards. - -static uint32_t vfpu_sin_lut8192[1025]={ - 0, 411778, 823552, 1235322, - 1647089, 2058851, 2470610, 2882365, - 3294116, 3705858, 4117590, 4529310, - 4941018, 5352714, 5764400, 6176074, - 6587736, 6999380, 7411008, 7822616, - 8234204, 8645772, 9057324, 9468852, - 9880364, 10291848, 10703312, 11114744, - 11526152, 11937528, 12348880, 12760204, - 13171504, 13582768, 13994000, 14405196, - 14816360, 15227488, 15638580, 16049636, - 16460660, 16871640, 17282584, 17693480, - 18104336, 18515152, 18925920, 19336648, - 19747336, 20157976, 20568560, 20979104, - 21389592, 21800024, 22210416, 22620752, - 23031040, 23441264, 23851440, 24261560, - 24671616, 25081616, 25491560, 25901448, - 26311272, 26721040, 27130736, 27540368, - 27949936, 28359440, 28768872, 29178240, - 29587544, 29996776, 30405944, 30815024, - 31224040, 31632984, 32041848, 32450640, - 32859360, 33268000, 33676560, 34085040, - 34493440, 34901760, 35310000, 35718144, - 36126224, 36534208, 36942112, 37349920, - 37757648, 38165280, 38572832, 38980288, - 39387648, 39794928, 40202112, 40609184, - 41016176, 41423072, 41829856, 42236544, - 42643152, 43049648, 43456048, 43862336, - 44268528, 44674608, 45080576, 45486448, - 45892224, 46297888, 46703440, 47108880, - 47514208, 47919424, 48324528, 48729504, - 49134384, 49539152, 49943792, 50348320, - 50752720, 51157008, 51561168, 51965216, - 52369152, 52772960, 53176640, 53580192, - 53983616, 54386896, 54790064, 55193120, - 55596032, 55998816, 56401456, 56803984, - 57206368, 57608608, 58010720, 58412688, - 58814528, 59216240, 59617808, 60019216, - 60420496, 60821632, 61222624, 61623472, - 62024176, 62424752, 62825168, 63225424, - 63625536, 64025504, 64425312, 64824976, - 65224496, 65623840, 66023040, 66422080, - 66820992, 67219712, 67618272, 68016704, - 68414976, 68813056, 69211008, 69608768, - 70006368, 70403808, 70801088, 71198176, - 71595136, 71991936, 72388544, 72784960, - 73181216, 73577312, 73973216, 74368960, - 74764544, 75159936, 75555168, 75950208, - 76345056, 76739712, 77134240, 77528544, - 77922688, 78316640, 78710432, 79104000, - 79497408, 79890592, 80283616, 80676448, - 81069088, 81461536, 81853792, 82245856, - 82637760, 83029408, 83420896, 83812192, - 84203296, 84594176, 84984896, 85375360, - 85765664, 86155744, 86545632, 86935328, - 87324800, 87714080, 88103136, 88492000, - 88880672, 89269088, 89657344, 90045344, - 90433184, 90820768, 91208160, 91595328, - 91982272, 92368992, 92755520, 93141824, - 93527904, 93913792, 94299424, 94684832, - 95070048, 95455008, 95839744, 96224288, - 96608576, 96992640, 97376480, 97760096, - 98143488, 98526624, 98909536, 99292224, - 99674688,100056928,100438880,100820640, -101202144,101583424,101964448,102345216, -102725792,103106080,103486176,103865984, -104245568,104624896,105003968,105382816, -105761408,106139776,106517856,106895712, -107273280,107650624,108027712,108404544, -108781120,109157440,109533504,109909312, -110284864,110660128,111035168,111409920, -111784448,112158688,112532672,112906368, -113279808,113652992,114025888,114398560, -114770944,115143040,115514880,115886432, -116257728,116628736,116999488,117369952, -117740128,118110048,118479680,118849024, -119218112,119586912,119955424,120323648, -120691616,121059264,121426656,121793760, -122160576,122527072,122893312,123259264, -123624896,123990272,124355328,124720128, -125084608,125448768,125812672,126176288, -126539584,126902592,127265312,127627712, -127989792,128351616,128713120,129074304, -129435200,129795808,130156096,130516064, -130875744,131235104,131594144,131952896, -132311328,132669440,133027264,133384768, -133741952,134098816,134455360,134811584, -135167552,135523136,135878400,136233408, -136588032,136942336,137296320,137650048, -138003392,138356416,138709120,139061504, -139413568,139765248,140116672,140467712, -140818432,141168832,141518912,141868672, -142218048,142567104,142915840,143264256, -143612288,143960000,144307392,144654464, -145001152,145347520,145693504,146039168, -146384512,146729536,147074176,147418496, -147762432,148105984,148449280,148792192, -149134720,149476928,149818752,150160256, -150501440,150842176,151182656,151522688, -151862464,152201792,152540864,152879488, -153217792,153555648,153893248,154230464, -154567296,154903808,155239936,155575680, -155911040,156246016,156580672,156914944, -157248896,157582400,157915584,158248384, -158580800,158912832,159244544,159575872, -159906816,160237312,160567488,160897344, -161226752,161555776,161884416,162212736, -162540608,162868160,163195264,163521984, -163848384,164174336,164499904,164825088, -165149952,165474368,165798400,166122048, -166445312,166768192,167090624,167412736, -167734400,168055680,168376640,168697088, -169017216,169336896,169656192,169975104, -170293632,170611712,170929408,171246720, -171563648,171880128,172196224,172511872, -172827200,173142080,173456512,173770560, -174084224,174397440,174710272,175022720, -175334720,175646336,175957504,176268288, -176578624,176888576,177198080,177507200, -177815872,178124096,178432000,178739392, -179046400,179352960,179659136,179964864, -180270208,180575104,180879552,181183616, -181487232,181790400,182093184,182395520, -182697408,182998912,183299968,183600512, -183900736,184200448,184499776,184798656, -185097088,185395136,185692672,185989824, -186286528,186582784,186878592,187173952, -187468928,187763392,188057472,188351104, -188644288,188936960,189229248,189521088, -189812480,190103424,190393984,190684032, -190973632,191262784,191551488,191839680, -192127488,192414848,192701760,192988224, -193274176,193559680,193844800,194129408, -194413568,194697280,194980544,195263296, -195545664,195827520,196108928,196389888, -196670336,196950400,197229952,197509056, -197787712,198065856,198343552,198620736, -198897536,199173824,199449664,199724992, -199999936,200274304,200548288,200821760, -201094720,201367296,201639360,201910912, -202182016,202452672,202722816,202992448, -203261696,203530368,203798656,204066432, -204333696,204600512,204866816,205132608, -205398016,205662848,205927296,206191168, -206454592,206717504,206979968,207241920, -207503360,207764352,208024832,208284864, -208544384,208803392,209061952,209319936, -209577536,209834560,210091136,210347200, -210602816,210857856,211112448,211366528, -211620096,211873152,212125760,212377856, -212629440,212880512,213131136,213381248, 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-261547200,261639552,261731328,261822464, -261913024,262002944,262092224,262180864, -262268992,262356416,262443264,262529408, -262615040,262700032,262784384,262868096, -262951232,263033728,263115584,263196864, -263277504,263357504,263436928,263515712, -263593920,263671424,263748352,263824640, -263900352,263975424,264049856,264123648, -264196864,264269440,264341376,264412672, -264483456,264553536,264622976,264691840, -264760064,264827648,264894592,264960960, -265026688,265091776,265156288,265220096, -265283328,265345920,265407936,265469248, -265530048,265590144,265649600,265708480, -265766720,265824320,265881280,265937664, -265993408,266048512,266102976,266156800, -266210048,266262656,266314624,266365952, -266416704,266466752,266516224,266565056, -266613312,266660864,266707840,266754112, -266799872,266844928,266889344,266933184, -266976384,267018944,267060864,267102144, -267142848,267182912,267222272,267261056, -267299264,267336768,267373696,267409920, -267445632,267480640,267515008,267548736, -267581888,267614336,267646208,267677440, -267708096,267738048,267767424,267796160, -267824256,267851648,267878528,267904704, -267930240,267955200,267979520,268003200, -268026240,268048640,268070400,268091584, -268112064,268131968,268151232,268169856, -268187840,268205248,268221952,268238080, -268253504,268268352,268282560,268296128, -268309120,268321408,268333120,268344128, -268354560,268364352,268373504,268382080, -268389952,268397184,268403840,268409856, -268415232,268419968,268424064,268427520, -268430400,268432576,268434176,268435136, -268435456}; - -static int8_t vfpu_sin_lut_delta[131072][2]= -{ -{ 0, -3}, { -3, -6}, { -2, 0}, { -1, -4}, -{ 3, 1}, { 1, -1}, { 7, 4}, { 3, 1}, -{ 7, 8}, { 5, 3}, { 11, 8}, { 7, 7}, -{ 12, 11}, { 10, 8}, { 16, 13}, { 13, 10}, -{ 10, 6}, { 16, 12}, { 12, 10}, { 16, 15}, -{ 15, 11}, { 20, 16}, { 17, 12}, { 22, 19}, -{ 18, 16}, { 24, 22}, { 20, 18}, { 25, 24}, -{ 22, 22}, { 27, 26}, { 24, 24}, { 31, 28}, -{ 28, 25}, { 25, 21}, { 29, 28}, { 27, 25}, -{ 31, 30}, { 30, 26}, { 33, 33}, { 31, 28}, -{ 37, 34}, { 33, 32}, { 31, 28}, { 35, 33}, -{ 33, 31}, { 37, 37}, { 35, 33}, { 39, 39}, -{ 37, 35}, { 43, 40}, { 40, 37}, { 37, 35}, -{ 42, 40}, { 39, 37}, { 45, 42}, { 42, 38}, -{ 46, 45}, { 44, 42}, { 39, 40}, { 46, 43}, -{ 44, 41}, { 49, 44}, { 44, 43}, { 50, 16}, -{ 16, 13}, { 13, 10}, { 19, 14}, { 16, 12}, -{ 20, 18}, { 15, 17}, { 15, 11}, { 18, 18}, -{ 16, 15}, { 22, 19}, { 18, 16}, { 24, 22}, -{ 20, 18}, { 18, 16}, { 24, 21}, { 20, 18}, -{ 25, 24}, { 23, 20}, { 20, 17}, { 24, 24}, -{ 22, 20}, { 27, 25}, { 25, 21}, { 22, 19}, -{ 27, 22}, { 24, 22}, { 29, 26}, { 25, 24}, -{ 22, 22}, { 27, 26}, { 24, 24}, { 31, 28}, -{ 28, 25}, { 25, 21}, { 29, 28}, { 27, 25}, -{ 31, 30}, { 30, 26}, { 27, 22}, { 31, 28}, -{ 29, 26}, { 30, 32}, { 31, 28}, { 27, 26}, -{ 31, 31}, { 29, 28}, { 28, 25}, { 31, 31}, -{ 30, 26}, { 36, 31}, { 32, 29}, { 29, 26}, -{ 33, 33}, { 31, 28}, { 27, 26}, { 30, 32}, -{ 31, 28}, { 28, 25}, { 31, 31}, { 29, 28}, -{ 36, 31}, { 32, 31}, { 30, 26}, { 33, 1}, -{ 0, 29}, { 29, 26}, { 30, 32}, { 31, 28}, -{ 27, 26}, { 31, 31}, { 31, 28}, { 35, 33}, -{ 32, 31}, { 29, 28}, { 36, 31}, { 32, 29}, -{ 29, 26}, { 33, 33}, { 31, 28}, { 27, 26}, -{ 30, 32}, { 31, 28}, { 27, 26}, { 31, 31}, -{ 29, 28}, { 35, 33}, { 32, 31}, { 30, 26}, -{ 27, 22}, { 31, 30}, { 29, 26}, { 25, 24}, -{ 31, 28}, { 27, 26}, { 30, 32}, { 31, 28}, -{ 28, 25}, { 25, 21}, { 29, 28}, { 27, 25}, -{ 24, 22}, { 30, 26}, { 27, 22}, { 24, 21}, -{ 29, 26}, { 25, 24}, { 23, 20}, { 27, 26}, -{ 24, 24}, { 22, 20}, { 28, 25}, { 25, 21}, -{ 22, 19}, { 27, 25}, { 24, 22}, { 20, 18}, -{ 25, 24}, { 24, 21}, { 20, 18}, { 24, 24}, -{ 23, 20}, { 20, 17}, { 16, 15}, { 22, 20}, -{ 20, 16}, { 17, 12}, { 22, 19}, { 18, 16}, -{ 16, 45}, { 52, 50}, { 51, 46}, { 48, 44}, -{ 52, 50}, { 47, 49}, { 47, 43}, { 44, 41}, -{ 48, 47}, { 46, 43}, { 43, 40}, { 49, 44}, -{ 44, 43}, { 42, 40}, { 39, 37}, { 45, 42}, -{ 42, 38}, { 39, 36}, { 44, 42}, { 39, 40}, -{ 37, 35}, { 35, 33}, { 39, 39}, { 37, 35}, -{ 36, 31}, { 40, 37}, { 37, 34}, { 33, 33}, -{ 31, 28}, { 35, 33}, { 33, 32}, { 31, 28}, -{ 35, 33}, { 32, 31}, { 29, 28}, { 27, 25}, -{ 31, 30}, { 30, 26}, { 27, 22}, { 24, 21}, -{ 29, 26}, { 25, 24}, { 23, 20}, { 20, 17}, -{ 24, 24}, { 22, 20}, { 20, 16}, { 25, 21}, -{ 22, 19}, { 18, 16}, { 16, 13}, { 12, 11}, -{ 19, 14}, { 16, 13}, { 13, 10}, { 10, 6}, -{ 14, 13}, { 12, 10}, { 7, 8}, { 5, 3}, -{ 12, 9}, { 7, 7}, { 5, 3}, { 11, 8}, -{ 8, 37}, { 37, 34}, { 33, 32}, { 31, 28}, -{ 35, 33}, { 33, 31}, { 31, 28}, { 28, 25}, -{ 31, 31}, { 29, 28}, { 27, 25}, { 24, 22}, -{ 29, 26}, { 27, 22}, { 24, 21}, { 20, 18}, -{ 15, 17}, { 23, 20}, { 20, 17}, { 16, 15}, -{ 15, 11}, { 20, 48}, { 49, 44}, { 46, 43}, -{ 43, 40}, { 40, 37}, { 44, 43}, { 42, 40}, -{ 39, 37}, { 35, 33}, { 42, 38}, { 39, 36}, -{ 35, 33}, { 32, 31}, { 29, 28}, { 27, 25}, -{ 31, 30}, { 30, 26}, { 27, 22}, { 24, 21}, -{ 29, 26}, { 25, 24}, { 23, 52}, { 52, 49}, -{ 47, 49}, { 54, 52}, { 52, 48}, { 48, 47}, -{ 46, 43}, { 43, 40}, { 48, 45}, { 44, 43}, -{ 42, 40}, { 39, 37}, { 35, 35}, { 33, 32}, -{ 39, 36}, { 35, 33}, { 33, 31}, { 29, 28}, -{ 27, 25}, { 31, 31}, { 30, 26}, { 27, 22}, -{ 24, 53}, { 52, 50}, { 57, 56}, { 55, 52}, -{ 52, 50}, { 47, 49}, { 47, 43}, { 44, 41}, -{ 48, 47}, { 46, 43}, { 43, 40}, { 39, 39}, -{ 37, 35}, { 33, 33}, { 39, 37}, { 37, 34}, -{ 33, 32}, { 31, 28}, { 27, 26}, { 24, 24}, -{ 29, 28}, { 27, 57}, { 57, 53}, { 54, 51}, -{ 50, 48}, { 48, 45}, { 52, 50}, { 51, 46}, -{ 48, 44}, { 45, 42}, { 42, 38}, { 39, 36}, -{ 44, 42}, { 39, 40}, { 37, 35}, { 36, 31}, -{ 32, 29}, { 30, 26}, { 27, 22}, { 24, 21}, -{ 29, 26}, { 25, 24}, { 23, 52}, { 52, 49}, -{ 47, 49}, { 47, 43}, { 44, 41}, { 48, 47}, -{ 46, 43}, { 43, 40}, { 40, 37}, { 37, 35}, -{ 33, 33}, { 31, 28}, { 35, 35}, { 33, 32}, -{ 31, 28}, { 28, 25}, { 24, 24}, { 22, 20}, -{ 20, 16}, { 17, 12}, { 22, 19}, { 18, 16}, -{ 16, 45}, { 45, 42}, { 42, 40}, { 39, 37}, -{ 35, 33}, { 33, 31}, { 31, 28}, { 35, 33}, -{ 32, 31}, { 29, 28}, { 27, 25}, { 24, 22}, -{ 20, 18}, { 18, 16}, { 16, 45}, { 52, 50}, -{ 47, 49}, { 48, 44}, { 44, 42}, { 39, 40}, -{ 37, 35}, { 35, 33}, { 32, 31}, { 30, 26}, -{ 27, 22}, { 31, 30}, { 29, 26}, { 25, 24}, -{ 22, 54}, { 52, 50}, { 47, 49}, { 47, 43}, -{ 44, 42}, { 39, 40}, { 37, 35}, { 36, 31}, -{ 39, 39}, { 37, 35}, { 33, 33}, { 31, 28}, -{ 29, 26}, { 25, 24}, { 23, 52}, { 52, 49}, -{ 47, 49}, { 47, 43}, { 44, 41}, { 39, 39}, -{ 37, 35}, { 43, 40}, { 40, 37}, { 37, 35}, -{ 33, 33}, { 31, 28}, { 27, 26}, { 24, 24}, -{ 23, 52}, { 52, 49}, { 48, 47}, { 46, 43}, -{ 44, 41}, { 39, 39}, { 37, 35}, { 43, 40}, -{ 40, 37}, { 37, 34}, { 33, 32}, { 31, 28}, -{ 27, 26}, { 24, 24}, { 22, 20}, { 18, 50}, -{ 48, 47}, { 46, 43}, { 43, 40}, { 39, 39}, -{ 37, 35}, { 33, 33}, { 31, 28}, { 27, 26}, -{ 25, 24}, { 23, 20}, { 27, 26}, { 24, 24}, -{ 22, 20}, { 20, 48}, { 49, 44}, { 46, 43}, -{ 43, 40}, { 40, 37}, { 37, 34}, { 33, 33}, -{ 31, 28}, { 27, 26}, { 24, 24}, { 22, 20}, -{ 20, 17}, { 16, 15}, { 14, 11}, { 10, 41}, -{ 39, 39}, { 37, 35}, { 33, 33}, { 31, 28}, -{ 29, 26}, { 25, 24}, { 23, 20}, { 20, 17}, -{ 15, 17}, { 15, 11}, { 12, 9}, { 7, 7}, -{ 5, 3}, { 4, 31}, { 32, 29}, { 29, 26}, -{ 25, 24}, { 24, 21}, { 20, 18}, { 15, 17}, -{ 14, 13}, { 12, 10}, { 7, 8}, { 5, 3}, -{ 4, -1}, { 0, -1}, { -2, -6}, { 1, 1}, -{ -8, 21}, { 20, 18}, { 19, 14}, { 16, 12}, -{ 12, 10}, { 7, 8}, { 7, 4}, { 3, 1}, -{ 0, -1}, { -3, 28}, { 27, 25}, { 24, 22}, -{ 20, 18}, { 18, 16}, { 16, 13}, { 13, 10}, -{ 10, 6}, { 7, 4}, { 3, 33}, { 33, 31}, -{ 29, 28}, { 27, 25}, { 25, 21}, { 22, 19}, -{ 18, 16}, { 16, 13}, { 12, 11}, { 10, 40}, -{ 39, 37}, { 35, 33}, { 33, 32}, { 31, 28}, -{ 28, 25}, { 25, 21}, { 22, 19}, { 20, 16}, -{ 17, 44}, { 44, 43}, { 42, 40}, { 40, 37}, -{ 37, 34}, { 33, 32}, { 31, 28}, { 27, 26}, -{ 24, 24}, { 15, 43}, { 44, 41}, { 39, 39}, -{ 37, 35}, { 36, 31}, { 32, 29}, { 29, 26}, -{ 25, 24}, { 24, 21}, { 20, 50}, { 47, 49}, -{ 46, 45}, { 44, 42}, { 39, 40}, { 37, 35}, -{ 36, 31}, { 32, 31}, { 30, 26}, { 27, 22}, -{ 16, 45}, { 45, 42}, { 42, 40}, { 39, 37}, -{ 35, 33}, { 33, 31}, { 31, 28}, { 28, 25}, -{ 25, 21}, { 22, 51}, { 50, 48}, { 49, 44}, -{ 44, 43}, { 42, 40}, { 32, 27}, { 27, 26}, -{ 25, 24}, { 23, 20}, { 20, 49}, { 48, 47}, -{ 47, 43}, { 44, 41}, { 39, 39}, { 37, 35}, -{ 36, 31}, { 32, 29}, { 29, 26}, { 19, 46}, -{ 48, 44}, { 45, 42}, { 42, 38}, { 39, 36}, -{ 35, 33}, { 32, 31}, { 29, 28}, { 27, 25}, -{ 24, 54}, { 52, 52}, { 42, 40}, { 40, 37}, -{ 37, 34}, { 33, 32}, { 31, 28}, { 27, 26}, -{ 24, 24}, { 22, 52}, { 52, 48}, { 48, 47}, -{ 37, 35}, { 36, 31}, { 32, 29}, { 29, 26}, -{ 25, 24}, { 24, 21}, { 20, 50}, { 47, 49}, -{ 39, 36}, { 35, 33}, { 33, 31}, { 29, 28}, -{ 27, 25}, { 24, 22}, { 22, 19}, { 18, 16}, -{ 16, 45}, { 37, 34}, { 33, 32}, { 31, 28}, -{ 27, 26}, { 24, 24}, { 22, 20}, { 18, 50}, -{ 48, 47}, { 37, 35}, { 36, 31}, { 32, 29}, -{ 29, 26}, { 27, 22}, { 24, 21}, { 20, 50}, -{ 42, 38}, { 39, 36}, { 35, 33}, { 33, 31}, -{ 29, 28}, { 27, 25}, { 25, 53}, { 46, 43}, -{ 43, 40}, { 40, 37}, { 37, 34}, { 33, 33}, -{ 31, 28}, { 27, 26}, { 24, 56}, { 47, 43}, -{ 44, 42}, { 39, 40}, { 37, 35}, { 36, 31}, -{ 32, 29}, { 20, 52}, { 50, 48}, { 48, 45}, -{ 45, 42}, { 42, 38}, { 39, 37}, { 27, 26}, -{ 24, 24}, { 22, 52}, { 52, 48}, { 48, 47}, -{ 46, 43}, { 36, 31}, { 32, 29}, { 29, 26}, -{ 25, 56}, { 56, 53}, { 52, 50}, { 42, 38}, -{ 39, 36}, { 35, 33}, { 33, 31}, { 29, 28}, -{ 27, 57}, { 49, 44}, { 44, 43}, { 43, 40}, -{ 40, 37}, { 37, 34}, { 25, 24}, { 23, 52}, -{ 52, 50}, { 47, 49}, { 47, 43}, { 35, 33}, -{ 32, 31}, { 29, 28}, { 27, 25}, { 24, 54}, -{ 52, 50}, { 42, 40}, { 39, 37}, { 37, 34}, -{ 33, 32}, { 31, 28}, { 20, 49}, { 48, 47}, -{ 47, 43}, { 44, 41}, { 39, 39}, { 30, 26}, -{ 27, 22}, { 24, 22}, { 20, 50}, { 42, 40}, -{ 39, 37}, { 35, 33}, { 33, 32}, { 31, 28}, -{ 28, 25}, { 16, 47}, { 46, 43}, { 42, 41}, -{ 39, 39}, { 30, 26}, { 27, 22}, { 24, 21}, -{ 20, 18}, { 19, 46}, { 39, 37}, { 35, 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28, 27}, -{ 35, 34}, { 34, 33}, { 32, 33}, { 32, 31}, -{ 31, 30}, { 29, 29}, { 29, 27}, { 28, 27}, -{ 26, 30}, { 29, 29}, { 36, 37}, { 36, 35}, -{ 35, 34}, { 33, 33}, { 33, 31}, { 32, 31}, -{ 30, 30}, { 29, 29}, { 28, 27}, { 27, 26}, -{ 26, 25}, { 33, 33}, { 33, 31}, { 32, 31}, -{ 30, 34}, { 33, 33}, { 32, 31}, { 31, 30}, -{ 30, 29}, { 29, 28}, { 28, 27}, { 27, 26}, -{ 25, 27}, { 25, 24}, { 24, 23}, { 23, 22}, -{ 29, 27}, { 28, 27}, { 26, 26}, { 25, 25}, -{ 24, 27}, { 27, 26}, { 26, 25}, { 25, 24}, -{ 24, 23}, { 23, 22}, { 21, 23}, { 21, 20}, -{ 20, 19}, { 19, 18}, { 18, 17}, { 16, 17}, -{ 16, 15}, { 15, 14}, { 13, 13}, { 13, 11}, -{ 12, 15}, { 14, 14}, { 13, 13}, { 12, 11}, -{ 11, 10}, { 10, 9}, { 9, 8}, { 8, 7}, -{ 7, 6}, { 5, 7}, { 5, 4}, { 4, 3}, -{ 3, 2}, { 2, 1}, { 0, 1}, { 8, 7}, -{ 0, 3}, { 3, 2}, { 2, 5}, { 5, 4}, -{ 4, 7}, { 7, 6}, { 5, 11}, { 9, 8}, -{ 8, 11}, { 11, 10}, { 10, 13}, { 12, 13}, -{ 12, 15}, { 15, 14}, { 13, 17}, { 17, 15}, -{ 16, 19}, { 18, 18}, { 17, 21}, { 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35}, { 27, 27}, -{ 27, 29}, { 28, 29}, { 27, 30}, { 29, 30}, -{ 30, 31}, { 30, 31}, { 31, 33}, { 31, 34}, -{ 33, 32}, { 33, 34}, { 25, 27}, { 26, 28}, -{ 26, 29}, { 28, 27}, { 29, 28}, { 29, 30}, -{ 30, 30}, { 30, 32}, { 30, 32}, { 32, 32}, -{ 31, 34}, { 25, 25}, { 25, 27}, { 25, 28}, -{ 27, 27}, { 26, 29}, { 28, 28}, { 29, 29}, -{ 29, 29}, { 22, 22}, { 23, 23}, { 23, 23}, -{ 24, 24}, { 24, 26}, { 25, 25}, { 26, 27}, -{ 18, 20}, { 19, 19}, { 20, 20}, { 20, 22}, -{ 21, 22}, { 20, 23}, { 22, 23}, { 23, 24}, -{ 16, 17}, { 16, 17}, { 17, 18}, { 16, 20}, -{ 18, 19}, { 18, 20}, { 19, 21}, { 12, 13}, -{ 11, 15}, { 13, 14}, { 15, 14}, { 14, 16}, -{ 16, 15}, { 8, 9}, { 8, 9}, { 10, 9}, -{ 9, 14}, { 13, 13}, { 14, 16}, { 7, 10}, -{ 10, 11}, { 11, 15}, { 14, 14}, { 16, 16}, -{ 16, 20}, { 12, 12}, { 13, 16}, { 14, 18}, -{ 17, 18}, { 19, 21}, { 21, 22}, { 23, 24}, -{ 15, 20}, { 19, 19}, { 21, 22}, { 21, 24}, -{ 24, 26}, { 19, 19}, { 20, 20}, { 22, 23}, -{ 24, 26}, { 26, 27}, { 20, 20}, { 21, 23}, 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23}, { 22, 21}, { 30, 26}, { 27, 24}, -{ 25, 22}, { 23, 20}, { 29, 25}, { 27, 23}, -{ 25, 21}, { 23, 19}, { 20, 17}, { 26, 23}, -{ 24, 20}, { 22, 18}, { 20, 16}, { 18, 14}, -{ 22, 21}, { 20, 19}, { 19, 16}, { 25, 21}, -{ 23, 20}, { 19, 18}, { 17, 16}, { 15, 14}, -{ 21, 20}, { 19, 18}, { 18, 14}, { 16, 13}, -{ 12, 11}, { 18, 17}, { 16, 15}, { 14, 13}, -{ 12, 11}, { 10, 9}, { 9, 6}, { 13, 12}, -{ 11, 10}, { 9, 8}, { 7, 6}, { 5, 4}, -{ 7, 15}, { 10, 7}, { 6, 5}, { 4, 3}, -{ 2, 1}, { 0, -1}, { -4, 15}, { 0, 8}, -{ 3, 0}, { 1, -2}, { -3, -4}, { 3, 2}, -{ 1, 2}, { 1, 1}, { -7, 9}, { 1, -1}, -{ 0, -1}, { -2, -2}, { 5, 6}, { 5, 5}, -{ 4, 5}, { -3, 12}, { 4, 3}, { 4, 2}, -{ 11, 9}, { 10, 8}, { 8, 9}, { 8, 8}, -{ 0, 16}, { 8, 6}, { 15, 13}, { 14, 13}, -{ 14, 12}, { 12, 12}, { 11, 12}, { 4, 19}, -{ 11, 10}, { 18, 17}, { 18, 16}, { 17, 15}, -{ 15, 16}, { 15, 15}, { 7, 23}, { 15, 13}, -{ 14, 13}, { 21, 20}, { 21, 19}, { 19, 19}, -{ 18, 19}, { 11, 26}, { 18, 17}, { 18, 16}, -{ 17, 15}, { 24, 22}, { 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31, 35}, { 34, 37}, { 29, 32}, -{ 32, 35}, { 34, 38}, { 37, 41}, { 31, 36}, -{ 35, 38}, { 38, 40}, { 33, 36}, { 35, 39}, -{ 38, 42}, { 33, 37}, { 35, 40}, { 39, 42}, -{ 36, 35}, { 38, 39}, { 30, 36}, { 34, 38}, -{ 36, 41}, { 40, 43}, { 35, 37}, { 37, 41}, -{ 39, 45}, { 35, 39}, { 38, 41}, { 33, 36}, -{ 36, 39}, { 39, 41}, { 32, 37}, { 37, 39}, -{ 39, 42}, { 35, 36}, { 36, 41}, { 31, 34}, -{ 33, 38}, { 37, 40}, { 32, 34}, { 33, 38}, -{ 36, 41}, { 31, 37}, { 35, 38}, { 30, 33}, -{ 33, 35}, { 36, 37}, { 31, 32}, { 34, 36}, -{ 28, 32}, { 31, 34}, { 33, 38}, { 28, 33}, -{ 30, 35}, { 27, 28}, { 29, 33}, { 25, 27}, -{ 26, 31}, { 28, 34}, { 23, 29}, { 28, 30}, -{ 21, 26}, { 26, 28}, { 27, 32}, { 23, 24}, -{ 25, 29}, { 19, 24}, { 23, 26}, { 18, 21}, -{ 20, 24}, { 21, 27}, { 21, 19}, { 22, 24}, -{ 16, 19}, { 19, 22}, { 13, 17}, { 15, 21}, -{ 10, 16}, { 13, 17}, { 9, 12}, { 12, 15}, -{ 14, 18}, { 9, 13}, { 11, 17}, { 7, 11}, -{ 9, 13}, { 4, 8}, { 6, 12}, { 3, 4}, -{ 5, 8}, { 0, 3}, { 1, 8}, { -3, 1}, -{ 0, 4}, { -5, -1}, { -3, 1}, { 1, 4}, -{ -4, 0}, { -7, -2}, { -2, 4}, { -6, 2}, -{ 0, 6}, { -3, 2}, { 3, 7}, { -1, 5}, -{ 4, 10}, { 0, 8}, { 5, 12}, { 4, 7}, -{ 9, 14}, { 6, 11}, { 10, 17}, { 8, 13}, -{ 11, 20}, { 9, 17}, { 14, 21}, { 13, 16}, -{ 18, 23}, { 15, 20}, { 10, 17}, { 15, 22}, -{ 14, 19}, { 18, 24}, { 15, 21}, { 20, 27}, -{ 17, 24}, { 23, 28}, { 19, 25}, { 24, 31}, -{ 21, 28}, { 27, 33}, { 24, 30}, { 21, 28}, -{ 26, 33}, { 23, 29}, { 28, 34}, { 25, 32}, -{ 31, 36}, { 28, 33}, { 24, 30}, { 29, 36}, -{ 26, 33}, { 32, 38}, { 29, 35}, { 34, 40}, -{ 31, 38}, { 28, 34}, { 33, 39}, { 30, 36}, -{ 36, 40}, { 33, 38}, { 30, 35}, { 35, 40}, -{ 31, 38}, { 36, 44}, { 34, 40}, { 31, 37}, -{ 36, 43}, { 32, 40}, { 39, 44}, { 35, 41}, -{ 32, 39}, { 38, 43}, { 35, 40}, { 31, 37}, -{ 36, 43}, { 33, 40}, { 39, 45}, { 36, 42}, -{ 32, 39}, { 38, 45}, { 35, 41}, { 32, 38}, -{ 37, 43}, { 34, 41}, { 31, 38}, { 37, 42}, -{ 33, 39}, { 30, 37}, { 35, 42}, { 33, 38}, -{ 38, 44}, { 34, 41}, { 31, 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46}, -{ 36, 45}, { 37, 42}, { 38, 40}, { 43, 49}, -{ 41, 48}, { 40, 47}, { 38, 46}, { 38, 42}, -{ 36, 43}, { 36, 42}, { 41, 49}, { 40, 48}, -{ 39, 47}, { 38, 46}, { 37, 44}, { 43, 51}, -{ 42, 50}, { 41, 49}, { 40, 48}, { 39, 47}, -{ 38, 46}, { 37, 44}, { 34, 45}, { 34, 42}, -{ 41, 49}, { 40, 48}, { 39, 47}, { 37, 45}, -{ 36, 44}, { 35, 43}, { 34, 42}, { 41, 49}, -{ 40, 48}, { 39, 47}, { 37, 45}, { 36, 44}, -{ 35, 43}, { 34, 42}, { 33, 41}, { 31, 40}, -{ 30, 38}, { 29, 37}, { 28, 36}, { 27, 35}, -{ 32, 43}, { 33, 40}, { 31, 40}, { 30, 38}, -{ 29, 37}, { 28, 36}, { 27, 35}, { 25, 34}, -{ 24, 32}, { 23, 31}, { 22, 30}, { 21, 29}, -{ 20, 28}, { 26, 35}, { 25, 34}, { 24, 32}, -{ 23, 31}, { 22, 29}, { 21, 28}, { 20, 27}, -{ 17, 27}, { 17, 25}, { 15, 25}, { 15, 22}, -{ 14, 21}, { 13, 20}, { 13, 18}, { 11, 17}, -{ 8, 17}, { 7, 17}, { 6, 15}, { 4, 13}, -{ 3, 12}, { 4, 10}, { 1, 10}, { 9, 16}, -{ 23, 17}, { 25, 18}, { 25, 19}, { 27, 20}, -{ 27, 21}, { 28, 21}, { 28, 25}, { 31, 24}, -{ 31, 26}, { 32, 26}, { 33, 28}, { 34, 28}, -{ 36, 29}, { 34, 32}, { 38, 30}, { 38, 32}, -{ 39, 32}, { 39, 36}, { 40, 35}, { 43, 35}, -{ 43, 37}, { 45, 37}, { 45, 39}, { 46, 39}, -{ 45, 43}, { 46, 43}, { 49, 43}, { 50, 43}, -{ 51, 44}, { 51, 46}, { 53, 45}, { 52, 49}, -{ 46, 40}, { 48, 41}, { 48, 42}, { 51, 42}, -{ 49, 45}, { 52, 44}, { 52, 46}, { 54, 47}, -{ 53, 50}, { 56, 48}, { 56, 51}, { 57, 51}, -{ 58, 53}, { 51, 45}, { 53, 46}, { 53, 47}, -{ 55, 47}, { 55, 49}, { 55, 50}, { 57, 51}, -{ 57, 52}, { 60, 52}, { 60, 54}, { 54, 46}, -{ 52, 50}, { 56, 47}, { 56, 50}, { 57, 50}, -{ 58, 52}, { 59, 52}, { 61, 52}, { 59, 56}, -{ 54, 47}, { 54, 49}, { 56, 48}, { 55, 52}, -{ 56, 52}, { 59, 52}, { 59, 53}, { 54, 45}, -{ 52, 48}, { 55, 47}, { 55, 49}, { 56, 49}, -{ 56, 53}, { 58, 51}, { 51, 46}, { 52, 45}, -{ 54, 46}, { 54, 48}, { 56, 48}, { 56, 50}, -{ 48, 43}, { 49, 46}, { 50, 45}, { 53, 45}, -{ 53, 47}, { 51, 49}, { 46, 41}, { 49, 40}, -{ 49, 43}, { 50, 43}, { 51, 45}, { 52, 45}, -{ 45, 38}, { 46, 39}, { 45, 40}, { 48, 41}, -{ 48, 42}, { 42, 35}, { 42, 36}, { 44, 37}, -{ 44, 38}, { 47, 37}, { 38, 32}, { 37, 34}, -{ 40, 34}, { 41, 34}, { 34, 28}, { 35, 28}, -{ 36, 30}, { 37, 30}, { 39, 31}, { 31, 25}, -{ 30, 27}, { 33, 27}, { 33, 28}, { 27, 21}, -{ 28, 21}, { 29, 23}, { 29, 24}, { 24, 16}, -{ 24, 18}, { 22, 20}, { 26, 19}, { 26, 20}, -{ 20, 15}, { 23, 18}, { 26, 22}, { 21, 16}, -{ 24, 18}, { 27, 22}, { 28, 25}, { 25, 20}, -{ 27, 23}, { 32, 25}, { 33, 29}, { 29, 23}, -{ 31, 27}, { 35, 29}, { 37, 33}, { 32, 27}, -{ 35, 31}, { 38, 33}, { 33, 29}, { 36, 31}, -{ 40, 34}, { 42, 37}, { 38, 32}, { 40, 35}, -{ 42, 38}, { 37, 35}, { 39, 38}, { 44, 40}, -{ 38, 35}, { 40, 40}, { 43, 42}, { 49, 42}, -{ 42, 39}, { 47, 40}, { 48, 45}, { 43, 40}, -{ 47, 41}, { 49, 45}, { 45, 39}, { 48, 43}, -{ 50, 46}, { 44, 43}, { 47, 45}, { 53, 46}, -{ 46, 42}, { 50, 44}, { 51, 49}, { 48, 42}, -{ 50, 46}, { 53, 48}, { 48, 44}, { 49, 48}, -{ 54, 50}, { 49, 44}, { 53, 47}, { 47, 42}, -{ 51, 45}, { 53, 48}, { 49, 43}, { 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11, 12}, -{ 9, 12}, { 12, 14}, { 15, 14}, { 13, 16}, -{ 16, 19}, { 15, 18}, { 17, 21}, { 21, 22}, -{ 19, 22}, { 21, 27}, { 26, 24}, { 16, 19}, -{ 19, 20}, { 17, 23}, { 20, 23}, { 23, 22}, -{ 22, 24}, { 24, 27}, { 27, 25}, { 26, 28}, -{ 30, 30}, { 27, 30}, { 30, 33}, { 25, 24}, -{ 24, 27}, { 28, 27}, { 26, 29}, { 28, 32}, -{ 32, 30}, { 30, 33}, { 32, 38}, { 31, 37}, -{ 27, 30}, { 26, 29}, { 28, 34}, { 33, 32}, -{ 30, 33}, { 33, 35}, { 37, 35}, { 34, 37}, -{ 37, 39}, { 29, 31}, { 31, 34}, { 34, 33}, -{ 33, 35}, { 38, 37}, { 34, 37}, { 37, 40}, -{ 32, 31}, { 31, 34}, { 34, 36}, { 33, 36}, -{ 35, 39}, { 27, 30}, { 30, 33}, { 34, 32}, -{ 31, 35}, { 34, 37}, { 37, 35}, { 28, 32}, -{ 32, 30}, { 30, 33}, { 32, 38}, { 31, 37}, -{ 34, 37}, { 26, 29}, { 28, 34}, { 33, 32}, -{ 30, 33}, { 33, 35}, { 24, 30}, { 27, 30}, -{ 31, 30}, { 29, 31}, { 26, 24}, { 23, 26}, -{ 26, 28}, { 28, 30}, { 27, 30}, { 30, 32}, -{ 22, 24}, { 24, 27}, { 27, 25}, { 19, 21}, -{ 21, 20}, { 20, 23}, { 25, 24}, { 15, 17}, -{ 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28}, { 44, 39}, -{ 43, 39}, { 44, 37}, { 44, 34}, { 43, 36}, -{ 42, 34}, { 42, 31}, { 41, 31}, { 40, 30}, -{ 39, 32}, { 38, 33}, { 47, 37}, { 38, 32}, -{ 44, 37}, { 45, 37}, { 43, 37}, { 42, 38}, -{ 42, 38}, { 43, 36}, { 42, 36}, { 42, 35}, -{ 42, 32}, { 41, 31}, { 40, 30}, { 40, 29}, -{ 47, 40}, { 47, 37}, { 46, 36}, { 46, 35}, -{ 44, 37}, { 44, 33}, { 42, 36}, { 42, 36}, -{ 41, 37}, { 41, 36}, { 41, 35}, { 41, 34}, -{ 41, 31}, { 39, 32}, { 39, 29}, { 38, 31}, -{ 37, 29}, { 36, 30}, { 36, 29}, { 34, 31}, -{ 35, 30}, { 35, 29}, { 35, 28}, { 35, 24}, -{ 34, 24}, { 33, 23}, { 32, 22}, { 32, 21}, -{ 30, 23}, { 30, 23}, { 28, 24}, { 29, 23}, -{ 28, 23}, { 29, 22}, { 29, 19}, { 28, 17}, -{ 27, 17}, { 25, 18}, { 25, 15}, { 24, 17}, -{ 23, 18}, { 23, 17}, { 22, 17}, { 22, 17}, -{ 14, 4}, { 13, 6}, { 11, 6}, { 11, 6}, -{ 12, 5}, { 12, 4}, { 11, 4}, { 11, 1}, -{ 10, 0}, { 9, 0}, { 8, 1}, { 8, -3}, -{ 0, -7}, { 2, -6}, { 3, -1}, { 5, -1}, -{ 7, -1}, { 9, 1}, { 10, 6}, { 12, 8}, -{ 13, 12}, { 16, 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42}, -{ 8, 44}, { 34, 28}, { 28, 22}, { 22, 15}, -{ 15, 9}, { 9, 53}, { 8, 61}, { 17, 54}, -{ 22, 16}, { 16, 10}, { 10, 4}, { 4, -3}, -{ 25, 51}, { 23, 17}, { 17, 11}, { 11, 4}, -{ 4, -2}, { -2, 31}, { -8, 37}, { 18, 11}, -{ 11, 5}, { 5, -1}, { -1, -7}, { -7, -14}, -{ 5, 43}, { 9, 30}, { 6, 0}, { 0, -7}, -{ -7, -13}, { -13, -19}, { -19, 15}, { 7, 0}, -{ 0, -3}, { -3, -7}, { -7, -11}, { -11, -15}, -{ -15, -18}, { -18, -22}, { 7, 31}, { 6, 2}, -{ 2, -1}, { -1, -5}, { -5, -9}, { -9, 29}, -{ -13, 39}, { 16, 12}, { 12, 8}, { 8, 4}, -{ 4, 1}, { 1, -3}, { -3, -7}, { 23, 45}, -{ 21, 18}, { 18, 14}, { 14, 10}, { 10, 6}, -{ 6, 3}, { 3, 55}, { 12, 58}, { 20, 54}, -{ 23, 20}, { 20, 16}, { 16, 12}, { 12, 8}, -{ 9, 41}, { 5, 47}, { 1, 61}, { 16, 56}, -{ 25, 22}, { 22, 18}, { 18, 14}, { 14, 10}, -{ 11, 39}, { 7, 43}, { 3, 52}, { 31, 27}, -{ 27, 24}, { 24, 20}, { 20, 16}, { 16, 12}, -{ 12, 9}, { 38, 61}, { 37, 33}, { 33, 29}, -{ 29, 26}, { 26, 22}, { 22, 18}, { 18, 14}, -{ 14, 11}, { 11, 7}, { 38, 51}, { 35, 31}, -{ 31, 28}, { 28, 24}, { 24, 20}, { 20, 16}, -{ 16, 13}, { 13, 9}, { 36, 65}, { 37, 33}, -{ 33, 30}, { 30, 26}, { 26, 22}, { 22, 18}, -{ 18, 15}, { 15, 11}, { 11, 7}, { 7, 40}, -{ 35, 32}, { 32, 28}, { 28, 24}, { 24, 20}, -{ 20, 17}, { 17, 13}, { 13, 9}, { 9, 38}, -{ 5, 42}, { 2, 50}, { 30, 26}, { 26, 22}, -{ 22, 19}, { 19, 15}, { 15, 11}, { 11, 7}, -{ 10, 38}, { 4, 44}, { 0, 56}, { 12, 55}, -{ 18, 53}, { 21, 17}, { 17, 13}, { 13, 9}, -{ 9, 6}, { 6, 2}, { 2, -2}, { -2, -6}, -{ -6, -9}, { 20, 48}, { 19, 15}, { 15, 11}, -{ 11, 8}, { 8, 4}, { 4, 0}, { 0, -4}, -{ -4, -7}, { -7, -11}, { -11, -15}, { -15, 31}, -{ -12, 42}, { -1, 37}, { 4, 25}, { 2, -2}, -{ -2, -5}, { -5, -9}, { -9, -13}, { -13, -17}, -{ -17, -20}, { -20, -24}, { -24, -28}, { -28, 8}, -{ -32, 20}, { -24, 30}, { -12, 28}, { -5, 26}, -{ -5, -6}, { -6, -7}, { -7, -8}, { -8, -10}, -{ -10, -11}, { -11, -12}, { -12, -13}, { -13, -15}, -{ -15, -16}, { -16, -17}, { -7, 45}, { 5, 43}, -{ -20, 17}, { -21, 27}, { 10, 9}, { 9, 7}, -{ 7, 6}, { 6, 5}, { 5, 4}, { 4, 2}, -{ 2, 1}, { 1, 0}, { 0, -1}, { -1, -3}, -{ -3, -4}, { -3, 33}, { -5, 44}, { -1, 56}, -{ 13, 54}, { 21, 46}, { 22, 21}, { 21, 19}, -{ 19, 18}, { 18, 17}, { 17, 16}, { 16, 14}, -{ 14, 13}, { 13, 12}, { 12, 11}, { 11, 9}, -{ 9, 8}, { 8, 7}, { 7, 6}, { 6, 52}, -{ 36, 3}, { 3, 2}, { 4, 35}, { 1, 43}, -{ -1, 57}, { 12, 61}, { 22, 59}, { 28, 26}, -{ 26, 25}, { 25, 24}, { 24, 23}, { 23, 21}, -{ 21, 20}, { 20, 19}, { 19, 18}, { 18, 16}, -{ 16, 15}, { 15, 14}, { 14, 13}, { 13, 11}, -{ 11, 10}, { 10, 9}, { 9, 8}, { 8, 6}, -{ 6, 44}, { 37, 3}, { 9, 67}, { 35, 1}, -{ 1, 36}, { 0, 45}, { -1, 60}, { 14, 60}, -{ 23, 58}, { 27, 26}, { 26, 25}, { 6, 54}, -{ 16, 53}, { 22, 21}, { 21, 20}, { 20, 18}, -{ 18, 17}, { 17, 16}, { 16, 15}, { 15, 13}, -{ 13, 12}, { 12, 11}, { 11, 10}, { 10, 8}, -{ 8, 7}, { 7, 6}, { 6, 5}, { 5, 3}, -{ 3, 2}, { 2, 1}, { 1, 0}, { 0, -2}, -{ -2, -3}, { -3, -4}, { -4, -5}, { -5, -7}, -{ -7, -8}, { -8, -9}, { -9, -10}, { -10, -12}, -{ -12, -13}, { -13, -14}, { -14, -15}, { -15, -17}, -{ -17, -18}, { -18, -19}, { -19, -20}, { -20, -22}, -{ -22, -23}, { -23, -24}, { -24, -25}, { -25, -27}, -{ -27, -28}, { -28, -29}, { -29, -30}, { -30, -16}, -}; - -static int16_t vfpu_sin_lut_interval_delta[65537]= -{ - -16384, -16385, -16384, -16383, -16384, -16384, -16385, -16386, - -16387, -16388, -16390, -16391, -16392, -16394, -16394, -16394, - -16396, -16397, -16397, -16399, -16398, -16398, -16398, -16398, - -16399, -16400, -16401, -16402, -16403, -16405, -16406, -16407, - -16408, -16409, -16410, -16412, -16413, -16414, -16416, -16416, - -16417, -16419, -16420, -16421, -16423, -16424, -16425, -16426, - -16427, -16428, -16429, -16430, -16430, -16430, -16431, -16430, - -16431, -16432, -16433, -16432, -16432, -16433, -16432, -16433, - -16433, -16434, -16434, -16433, -16433, -16435, -16435, -16435, - -16435, -16435, -16435, -16435, -16436, -16437, -16438, -16438, - -16438, -16439, -16440, -16441, -16442, -16444, -16444, -16445, - -16447, -16448, -16448, -16450, -16451, -16452, -16454, -16455, - -16456, -16457, -16458, -16459, -16461, -16462, -16463, -16463, - -16465, -16466, -16467, -16468, -16469, -16470, -16472, -16470, - -16471, -16472, -16472, -16473, -16475, -16476, -16477, -16479, - -16480, -16481, -16482, -16483, -16484, -16486, -16486, -16487, - -16489, -16490, -16490, -16489, -16491, -16492, -16493, -16495, - -16496, -16497, -16499, -16500, -16501, -16503, -16504, -16504, - -16506, -16507, -16507, -16509, -16510, -16511, -16513, -16514, - -16515, -16517, -16517, -16518, -16519, -16520, -16520, -16521, - -16523, -16523, -16524, -16526, -16527, -16528, -16530, -16531, - -16531, -16533, -16534, -16534, -16536, -16537, -16537, -16539, - -16540, -16541, -16542, -16543, -16544, -16545, -16547, -16548, - -16549, -16551, -16552, -16552, -16553, -16554, -16555, -16557, - -16558, -16559, -16561, -16561, -16561, -16563, -16564, -16564, - -16566, -16567, -16568, -16569, -16570, -16571, -16572, -16574, - -16575, -16576, -16577, -16578, -16578, -16580, -16581, -16582, - -16584, -16584, -16585, -16586, -16586, -16587, -16589, -16590, - -16591, -16593, -16593, -16593, -16595, -16596, -16597, -16598, - -16598, -16599, -16600, -16602, -16603, -16604, -16606, -16605, - -16606, -16608, -16609, -16610, -16611, -16612, -16613, -16615, - -16616, -16616, -16618, -16619, -16620, -16622, -16622, -16623, - -16624, -16623, -16624, -16625, -16627, -16628, -16629, -16630, - -16631, -16632, -16633, -16633, -16634, -16636, -16637, -16637, - -16639, -16640, -16641, -16642, -16643, -16644, -16645, -16646, - -16647, -16648, -16649, -16650, -16651, -16653, -16653, -16654, - -16656, -16657, -16658, -16659, -16660, -16661, -16663, -16663, - -16663, -16665, -16666, -16667, -16669, -16670, -16671, -16673, - -16674, -16675, -16676, -16677, -16678, -16679, -16680, -16681, - -16682, -16683, -16684, -16685, -16687, -16688, -16688, -16690, - -16691, -16692, -16693, -16693, -16694, -16695, -16696, -16697, - -16699, -16700, -16700, -16701, -16702, -16703, -16704, -16704, - -16705, -16706, -16707, -16708, -16709, -16711, -16710, -16711, - -16713, -16714, -16715, -16717, -16718, -16719, -16720, -16721, - -16721, -16723, -16723, -16724, -16726, -16727, -16728, -16728, - -16730, -16731, -16732, -16734, -16734, -16735, -16736, -16736, - -16737, -16739, -16740, -16740, -16742, -16743, -16743, -16744, - -16745, -16746, -16747, -16748, -16749, -16751, -16752, -16753, - -16754, -16755, -16756, -16757, -16758, -16759, -16760, -16762, - -16761, -16762, -16764, -16764, -16765, -16767, -16767, -16768, - -16770, -16771, -16772, -16773, -16773, -16774, -16776, -16776, - -16777, -16779, -16780, -16780, -16781, -16783, -16784, -16785, - -16787, -16787, -16788, -16789, -16790, -16791, -16793, -16794, - -16795, -16796, -16797, -16798, -16799, -16800, -16801, -16801, - -16802, -16803, -16803, -16804, -16805, -16806, -16808, -16809, - -16809, -16811, -16812, -16813, -16815, -16816, -16816, -16818, - -16819, -16818, -16820, -16819, -16820, -16821, -16821, -16821, - -16823, -16823, -16824, -16825, -16825, -16826, -16826, -16828, - -16829, -16829, -16831, -16831, -16832, -16834, -16833, -16834, - -16836, -16837, -16837, -16838, -16839, -16840, -16842, -16843, - -16844, -16844, -16845, -16844, -16846, -16846, -16847, -16847, - -16848, -16849, -16849, -16851, -16852, -16852, -16853, -16852, - -16853, -16855, -16855, -16855, -16856, -16857, -16857, -16858, - -16859, -16858, -16859, -16860, -16860, -16862, -16863, -16864, - -16866, -16810, -16752, -16695, -16639, -16582, -16526, -16469, - -16412, -16354, -16298, -16240, -16183, -16127, -16071, -16014, - -15957, -15900, -15843, -15788, -15729, -15672, -15616, -15559, - -15501, -15445, -15390, -15333, -15275, -15219, -15164, -15107, - -15050, -14992, -14937, -14881, -14823, -14766, -14710, -14653, - -14596, -14540, -14484, -14428, -14372, -14316, -14259, -14201, - -14144, -14087, -14031, -13973, -13917, -13860, -13803, -13746, - -13688, -13632, -13573, -13517, -13461, -13403, -13346, -13290, - -13232, -13175, -13119, -13062, -13003, -12948, -12891, -12833, - -12778, -12721, -12662, -12606, -12550, -12491, -12434, -12379, - -12323, -12266, -12211, -12153, -12096, -12041, -11982, -11924, - -11869, -11811, -11753, -11699, -11641, -11584, -11528, -11470, - -11414, -11358, -11300, -11244, -11188, -11130, -11074, -11017, - -10961, -10903, -10846, -10789, -10734, -10676, -10621, -10564, - -10506, -10451, -10394, -10336, -10280, -10224, -10167, -10112, - -10054, -9997, -9941, -9884, -9829, -9772, -9716, -9659, - -9603, -9546, -9487, -9430, -9375, -9317, -9262, -9205, - -9148, -9091, -9033, -8976, -8921, -8923, -8924, -8925, - -8927, -8928, -8929, -8931, -8932, -8933, -8934, -8935, - -8936, -8938, -8938, -8939, -8939, -8940, -8941, -8941, - -8943, -8943, -8944, -8945, -8945, -8946, -8948, -8949, - -8949, -8951, -8952, -8952, -8954, -8955, -8956, -8958, - -8959, -8960, -8962, -8963, -8964, -8965, -8967, -8968, - -8969, -8971, -8972, -8973, -8975, -8976, -8977, -8979, - -8980, -8981, -8983, -8984, -8985, -8987, -8988, -8989, - -8990, -8991, -8992, -8994, -8995, -8996, -8997, -8999, - -9000, -9001, -9003, -9004, -9005, -9007, -9008, -9009, - -9011, -9012, -9012, -9014, -9015, -9016, -9018, -9019, - -9020, -9022, -9023, -9024, -9026, -9027, -9028, -9029, - -9031, -9032, -9033, -9034, -9035, -9036, -9038, -9039, - -9040, -9042, -9042, -9043, -9045, -9046, -9047, -9049, - -9050, -9051, -9053, -9054, -9055, -9057, -9058, -9059, - -9061, -9062, -9063, -9064, -9066, -9067, -9068, -9070, - -9071, -9072, -9074, -9075, -9076, -9078, -9079, -9080, - -9081, -9082, -9083, -9085, -9086, -9087, -9089, -9090, - -9091, -9093, -9093, -9094, -9095, -9097, -9098, -9099, - -9101, -9102, -9103, -9105, -9106, -9107, -9109, -9110, - -9110, -9112, -9113, -9114, -9116, -9117, -9118, -9120, - -9121, -9122, -9124, -9125, -9126, -9126, -9127, -9128, - -9129, -9130, -9131, -9132, -9133, -9134, -9135, -9137, - -9138, -9139, -9141, -9142, -9143, -9145, -9146, -9147, - -9149, -9150, -9151, -9153, -9154, -9155, -9155, -9157, - -9158, -9159, -9161, -9162, -9162, -9164, -9165, -9166, - -9168, -9169, -9170, -9172, -9173, -9174, -9174, -9175, - -9176, -9178, -9178, -9179, -9181, -9181, -9182, -9183, - -9185, -9185, -9186, -9188, -9188, -9189, -9191, -9192, - -9193, -9195, -9196, -9197, -9198, -9199, -9200, -9202, - -9203, -9204, -9206, -9207, -9208, -9210, -9211, -9211, - -9212, -9213, -9214, -9215, -9216, -9217, -9218, -9220, - -9221, -9221, -9223, -9224, -9225, -9225, -9226, -9227, - -9228, -9228, -9229, -9231, -9232, -9233, -9235, -9236, - -9237, -9239, -9239, -9240, -9241, -9243, -9244, -9245, - -9246, -9247, -9248, -9250, -9249, -9250, -9252, -9253, - -9254, -9256, -9256, -9257, -9259, -9260, -9261, -9262, - -9263, -9264, -9266, -9267, -9268, -9269, -9271, -9272, - -9273, -9275, -9276, -9276, -9278, -9279, -9280, -9282, - -9283, -9283, -9284, -9285, -9286, -9288, -9289, -9289, - -9290, -9290, -9291, -9293, -9294, -9295, -9296, -9298, - -9298, -9299, -9301, -9302, -9303, -9305, -9306, -9306, - -9308, -9308, -9309, -9311, -9312, -9313, -9315, -9316, - -9316, -9317, -9318, -9319, -9321, -9322, -9323, -9324, - -9326, -9326, -9326, -9327, -9328, -9329, -9331, -9332, - -9333, -9335, -9336, -9336, -9338, -9337, -9337, -9338, - -9338, -9339, -9341, -9342, -9343, -9345, -9346, -9347, - -9349, -9293, -9236, -9181, -9126, -9070, -9014, -8958, - -8901, -8846, -8792, -8737, -8682, -8628, -8573, -8518, - -8464, -8409, -8354, -8300, -8245, -8190, -8136, -8081, - -8026, -7972, -7917, -7862, -7807, -7753, -7698, -7643, - -7589, -7534, -7479, -7425, -7370, -7315, -7261, -7206, - -7151, -7097, -7042, -6987, -6933, -6878, -6823, -6769, - -6712, -6657, -6602, -6546, -6490, -6434, -6378, -6322, - -6267, -6212, -6156, -6101, -6045, -5990, -5934, -5879, - -5823, -5767, -5713, -5658, -5603, -5549, -5494, -5439, - -5385, -5330, -5275, -5221, -5166, -5110, -5053, -4999, - -4942, -4885, -4830, -4774, -4718, -4664, -4609, -4554, - -4500, -4445, -4388, 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24396, 24394, 24393, - 24393, 24392, 24391, 24391, 24390, 24389, 24389, 24387, - 24386, 24385, 24383, 24382, 24381, 24379, 24378, 24377, - 24375, 24375, 24374, 24372, 24371, 24371, 24370, 24369, - 24369, 24368, 24366, 24365, 24364, 24363, 24362, 24361, - 24360, 24359, 24358, 24356, 24356, 24355, 24353, 24353, - 24352, 24350, 24349, 24348, 24347, 24346, 24345, 24345, - 24343, 24342, 24341, 24339, 24339, 24338, 24336, 24335, - 24335, 24333, 24332, 24331, 24330, 24329, 24328, 24326, - 24326, 24326, 24324, 24323, 24322, 24321, 24320, 24319, - 24317, 24316, 24315, 24315, 24313, 24312, 24311, 24309, - 24310, 24309, 24309, 24308, 24308, 24306, 24305, 24304, - 24302, 24302, 24301, 24299, 24298, 24297, 24295, 24294, - 24293, 24291, 24290, 24290, 24289, 24288, 24288, 24288, - 24287, 24286, 24285, 24283, 24282, 24281, 24279, 24278, - 24277, 24275, 24274, 24273, 24271, 24271, 24270, 24269, - 24268, 24268, 24266, 24266, 24266, 24265, 24264, 24263, - 24262, 24260, 24259, 24258, 24256, 24255, 24254, 24252, - 24251, 24250, 24248, 24247, 24247, 24245, 24244, 24243, - 24241, 24242, 24242, 24241, 24240, 24240, 24239, 24238, - 24237, 24237, 24235, 24234, 24233, 24231, 24230, 24229, - 24227, 24226, 24226, 24224, 24224, 24223, 24221, 24220, - 24220, 24218, 24217, 24216, 24214, 24213, 24212, 24212, - 24210, 24209, 24208, 24206, 24205, 24204, 24202, 24202, - 24201, 24199, 24198, 24197, 24195, 24194, 24193, 24191, - 24190, 24190, 24188, 24187, 24186, 24184, 24183, 24182, - 24181, 24180, 24179, 24178, 24176, 24175, 24174, 24172, - 24171, 24170, 24168, 24167, 24166, 24164, 24163, 24162, - 24160, 24159, 24158, 24156, 24155, 24154, 24152, 24151, - 24150, 24148, 24148, 24147, 24146, 24144, 24143, 24142, - 24140, 24139, 24138, 24136, 24135, 24135, 24133, 24133, - 24132, 24130, 24129, 24128, 24126, 24125, 24124, 24122, - 24122, 24121, 24119, 24118, 24117, 24116, 24115, 24115, - 24114, 24112, 24111, 24110, 24108, 24108, 24107, 24105, - 24104, 24103, 24101, 24101, 24100, 24098, 24097, 24096, - 24094, 24093, 24092, 24091, 24090, 24089, 24088, 24086, - 24085, 24084, 24082, 24081, 24080, 24078, 24078, 24077, - 24075, 24074, 24073, 24071, 24070, 24069, 24067, 24066, - 24065, 24063, 24063, 24062, 24061, 24060, 24060, 24059, - 24058, 24057, 24056, 24055, 24054, 24053, 24051, 24050, - 24050, 24048, 24048, 24048, 24047, 24046, 24046, 24045, - 24044, 24044, 24043, 24043, 24042, 24040, 24040, 24039, - 24037, 24036, 24035, 24034, 24032, 24031, 24031, 24029, - 24029, 24029, 24028, 24027, 24026, 24024, 24024, 24024, - 24022, 24021, 24020, 24018, 24018, 24018, 24016, 24015, - 24014, 24012, 24012, 24012, 24011, 24009, 24009, 24008, - 24007, 24007, 24006, 24004, 24004, 24003, 24001, 24000, - 24000, 23998, 23997, 23996, 23994, 23993, 23992, 23991, - 23991, 23990, 23988, 23988, 23987, 23986, 23984, 23983, - 23983, 23981, 23980, 23979, 23977, 23976, 23975, 23973, - 23972, 23973, 23972, 23971, 23970, 23968, 23967, 23966, - 23965, 23965, 23964, 23963, 23962, 23962, 23963, 23961, - 23960, 23959, 23957, 23957, 23956, 23954, 23953, 23952, - 23950, 23949, 23949, 23949, 23949, 23949, 23948, 23947, - 23946, 23944, 23943, 23942, 23940, 23939, 23938, 23937, - 23935, 23934, 23933, 23931, 23931, 23930, 23930, 23930, - 23930, 23930, 23930, 23931, 23930, 23931, 23930, 23930, - 23929, 23928, 23926, 23925, 23924, 23922, 23921, 23920, - 23918, 23917, 23916, 23915, 23913, 23912, 23912, 23910, - 23910, 23909, 23907, 23906, 23905, 23903, 23902, 23901, - 23899, 23898, 23897, 23895, 23894, 23893, 23891, 23890, - 23889, 23887, 23886, 23885, 23884, 23883, 23882, 23882, - 23880, 23880, 23880, 23879, 23880, 23879, 23878, 23877, - 23876, 23874, 23873, 23872, 23870, 23869, 23868, 23867, - 23866, 23865, 23864, 23864, 23864, 23864, 23862, 23861, - 23860, 23858, 23857, 23856, 23854, 23853, 23852, 23850, - 23851, 23850, 23848, 23847, 23847, 23845, 23844, 23843, - 23841, 23840, 23840, 23840, 23839, 23838, 23837, 23835, - 23834, 23834, 23832, 23832, 23832, 23831, 23831, 23830, - 23828, 23827, 23826, 23824, 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-15956, -15958, -15959, -15960, -15962, - -15963, -15964, -15966, -15967, -15968, -15970, -15971, -15972, - -15974, -}; - -static uint8_t vfpu_sin_lut_exceptions[86938]= -{ - 15, 83,128, 26,128, 86, 6, 24, 72, 4,128, 83,128,192, 90,192, - 22, 6, 24, 72, 4, 83, 79, 72, 15, 68,192,128, 83, 8, 79, 15, - 68,128,192, 15, 83, 8, 79,192,128,192, 19, 72, 15, 79, 4,192, - 19, 72, 15, 4, 72, 88, 88, 6, 22, 19,192, 90,128, 4, 70, 86, - 83,128, 26, 90, 4, 70,128, 68, 88,128, 4, 24, 22, 83,128, 26, -192, 24, 22, 22, 83, 22, 83, 8, 83, 8, 19, 72, 19, 72, 83, 22, - 86,192, 0, 88, 24, 26, 4, 90, 70, 72, 22, 86, 26, 6, 72, 4, - 72, 22, 68, 83, 8, 86, 26, 4, 19, 72, 22, 64, 72, 68, 6, 0, - 24, 64, 24, 90, 64, 90, 68, 64, 6, 64, 19, 72, 4, 64, 70, 83, -121, 0, 88, 26, 64, 64, 64, 72, 22, 64, 64, 0, 0, 88, 26, 64, - 86, 64, 24, 0, 22, 0, 64, 0, 64, 0, 72, 70, 83, 0, 88, 0, - 8, 64, 6, 72, 26, 64, 24, 64, 72, 57, 70, 83, 90, 0, 22, 64, - 70, 8,133,134,135, 8,141,142,143, 16,149,150,151, 24,158,159, - 32, 33,166, 39, 40, 41,174, 47, 48, 49, 55, 56, 57, 58, 63,196, - 69, 70, 71, 76, 77, 78,211, 84, 85, 86,219, 92, 93,226,227,100, -101,234,235,108,241,242,115,116,249,250,123, 3, 4, 5, 6, 11, - 12, 13, 14, 19, 20, 21, 26, 27, 28, 29, 34, 35, 36,169, 42, 43, - 44,177, 50, 51,184,185, 58, 59,192, 65,198, 71, 72, 73,206, 79, - 80,213,214, 87, 88,221,222, 95,228,229,102,103,236,237,110,243, -244,245,118,251,252,253, 4, 5, 6, 11, 12, 13, 14, 19, 20, 21, -154, 27, 28, 29,162, 35, 36,169,170, 43, 44,177, 50, 51,184,185, - 58, 59,192, 65,198,199, 72, 73,206,207, 80,213,214, 87, 88,221, -222, 95,228,229,230,103,236,237,238,243,244,245,246,251,252,253, - 0,133, 6, 7, 8,141, 14, 15,148,149, 22, 23,156,157, 30,163, -164, 37, 38,171,172, 45,178,179,180, 53,186,187,188, 67, 68, 69, - 74, 75, 76, 77, 82, 83, 84,217, 90, 91, 92,225, 98, 99,232,105, -106,107,240,113,114,247,248,121,122,255,128,133,134, 7, 8,141, -142, 15,148,149, 22, 23,156,157, 30,163,164,165, 38,171,172,173, -178,179,180, 53,186,187,188, 67, 68, 69, 70, 75, 76, 77, 78, 83, - 84, 85, 90, 91, 92, 93, 98, 99,100,233,106,107,108,241,114,115, -248,249,122,123,128,134,135,136, 9,142,143,144, 17,150,151,152, - 25,159,160, 33, 34,167, 40, 41, 42,175, 48, 49, 50, 56, 57, 58, - 59,196,197, 70, 71,204, 77, 78,211,212, 85, 86,219,220, 93,226, -227,228,101,234,235,236,241,242,243,116,249,250,251, 2, 3, 4, - 5, 10, 11, 12, 13, 18, 19, 20, 25, 26, 27, 28, 33, 34, 35,168, - 41, 42, 43,176, 49, 50,183,184, 57, 58,191,197,198,199, 72,205, -206,207, 80,213,214,215, 88,222,223, 96, 97,230,103,104,105,238, -111,112,113,119,120,121,122,127,132, 5, 6, 7, 12, 13, 14,147, - 20, 21, 22,155, 28, 29,162,163, 36, 37,170,171, 44,177,178, 51, - 52,185,186, 59,192,198,199,200, 73,206,207,208, 81,214,215, 88, - 89,222,223, 96, 97,231,104,105,106,239,112,113,114,119,120,121, -122,127, 0, 1,134, 7, 8, 9,142, 15, 16,149,150, 23, 24,157, - 30, 31,164,165, 38, 39,172,173, 46,179,180,181, 54,187,188,189, - 67, 68, 69, 70, 75, 76, 77, 78, 83, 84, 85,218, 91, 92, 93,226, - 99,100,233,106,107,108,241,114,115,248,249,122,123,128, 1,134, -135, 8, 9,142, 15, 16,149,150, 23, 24,157,158, 31,164,165,166, - 39,172,173,174,179,180,181, 54,187,188,189, 68, 69, 70, 71, 76, - 77, 78,211, 84, 85, 86, 91, 92, 93,226, 99,100,101,234,107,108, -241,242,115,116,249,250,123, 2, 3, 4, 5, 10, 11, 12, 13, 18, - 19, 20,153, 26, 27, 28,161, 34, 35,168, 41, 42, 43,176, 49, 50, -183,184, 57, 58,191,192,197,198, 71, 72,205, 78, 79,212,213, 86, - 87,220,221, 94,227,228,229,102,235,236,237,242,243,244,117,250, -251,252, 3, 4, 5, 6, 11, 12, 13, 14, 19, 20, 21, 26, 27, 28, - 29, 34, 35, 36,169, 42, 43, 44,177, 50, 51,184,185, 58, 59,192, -198,199,200, 73,206,207,208, 81,214,215,216, 89,223, 96, 97, 98, -231,104,105,106,239,112,113,114,120,121,122,123,132, 5, 6, 7, -140, 13, 14,147,148, 21, 22,155,156, 29,162,163,164, 37,170,171, - 44,177,178,179, 52,185,186,187, 66, 67, 68, 69, 74, 75, 76, 81, - 82, 83, 84, 89, 90, 91,224, 97, 98, 99,232,105,106,239,240,113, -114,247,120,121,254,255, 0,133, 6, 7, 8,141, 14, 15,148,149, - 22, 23,156, 29, 30,163,164, 37, 38,171,172, 45,178,179,180, 53, -186,187,188, 68, 69, 70, 71, 76, 77, 78,211, 84, 85, 86,219, 92, - 93,226,227,100,101,234,107,108,241,242,115,116,249,250,123,128, -134,135,136, 9,142,143, 16, 17,150,151, 24, 25,158,159, 32, 33, -167, 40, 41, 42,175, 48, 49, 50, 55, 56, 57, 58, 63,196, 69, 70, - 71,204, 77, 78,211,212, 85, 86,219, 92, 93,226,227,100,101,234, -235,108,241,242,243,116,249,250,251, 3, 4, 5, 6, 11, 12, 13, - 14, 19, 20, 21,154, 27, 28, 29,162, 35, 36,169, 42, 43, 44,177, - 50, 51,184,185, 58, 59,192, 65,198,199, 72, 73,206, 79, 80,213, -214, 87, 88,221,222, 95,228,229,230,103,236,237,110,243,244,245, -118,251,252,253, 4, 5, 6, 7, 12, 13, 14, 19, 20, 21, 22, 27, - 28, 29,162, 35, 36, 37,170, 43, 44,177,178, 51, 52,185, 58, 59, - 66, 67, 68, 69, 74, 75, 76, 77, 82, 83, 84,217, 90, 91, 92, 97, - 98, 99,232,105,106,107,240,113,114,247,248,121,122,255,128,133, - 6, 7, 8,141, 14, 15,148,149, 22, 23,156,157, 30,163,164,165, - 38,171,172, 45,178,179,180, 53,186,187,188, 67, 68, 69, 70, 75, - 76, 77, 82, 83, 84, 85, 90, 91, 92,225, 98, 99,100,233,106,107, -240,241,114,115,248,121,122,255,128,134,135,136, 9,142,143,144, - 17,150,151,152, 25,159, 32, 33, 34,167, 40, 41, 42,175, 48, 49, - 50, 56, 57, 58, 59,196, 69, 70, 71,204, 77, 78,211,212, 85, 86, -219,220, 93,226,227,228,101,234,235,108,241,242,243,116,249,250, -251, 2, 3, 4, 5, 10, 11, 12, 17, 18, 19, 20, 25, 26, 27,160, - 33, 34, 35,168, 41, 42,175,176, 49, 50,183, 56, 57,190,191, 64, - 65,198,199, 72, 73,206,207, 80,213,214, 87, 88,221,222, 95,228, -229,230,103,236,237,238,243,244,245,246,251,252,253, 4, 5, 6, - 7, 12, 13, 14,147, 20, 21, 22,155, 28, 29,162, 35, 36, 37,170, - 43, 44,177,178, 51, 52,185,186, 59,192,198,199, 72, 73,206,207, - 80, 81,214,215, 88, 89,222,223, 96, 97,231,104,105,106,111,112, -113,114,119,120,121,122,127, 0,133,134, 7, 8,141,142, 15,148, -149, 22, 23,156,157, 30,163,164,165, 38,171,172,173,178,179,180, -181,186,187,188, 67, 68, 69, 70, 75, 76, 77, 78, 83, 84, 85,218, - 91, 92, 93, 98, 99,100,233,106,107,108,241,114,115,248,249,122, -123,128, 1,134, 7, 8, 9,142, 15, 16,149,150, 23, 24,157,158, - 31,164,165,166, 39,172,173, 46,179,180,181, 54,187,188,189,196, -197, 70, 71,204,205, 78,211,212, 85, 86,219,220, 93,226,227,228, -101,234,235,236,241,242,243,116,249,250,251, 2, 3, 4, 5, 10, - 11, 12, 13, 18, 19, 20, 25, 26, 27, 28, 33, 34, 35,168, 41, 42, - 43,176, 49, 50,183,184, 57, 58,191, 64,197, 70, 71, 72,205, 78, - 79,212,213, 86, 87,220,221, 94,227,228,101,102,235,236,109,242, -243,244,117,250,251,252,132, 5, 6, 7, 12, 13, 14,147, 20, 21, - 22,155, 28, 29,162,163, 36, 37,170,171, 44,177,178, 51, 52,185, -186, 59,192,198,199,200, 73,206,207,208, 81,214,215, 88, 89,222, -223, 96, 97,231,104,105,106,239,112,113,114,247,120,121,122,127, -132, 5, 6, 7,140, 13, 14,147,148, 21, 22,155,156, 29,162,163, - 36, 37,170,171, 44,177,178,179, 52,185,186,187, 68, 69, 70, 75, - 76, 77, 78, 83, 84, 85,218, 91, 92, 93,226, 99,100,233,234,107, -108,241,114,115,248,249,122,123,128, 1,134,135, 8, 9,142,143, - 16,149,150, 23, 24,157,158, 31,164,165,166, 39,172,173,174,179, -180,181,182,187,188,189, 68, 69, 70, 71, 76, 77, 78,211, 84, 85, - 86,219, 92, 93,226, 99,100,101,234,107,108,241,242,115,116,249, -250,123, 2, 3, 4, 5, 10, 11, 12, 13, 18, 19, 20,153, 26, 27, - 28,161, 34, 35,168, 41, 42, 43,176, 49, 50,183,184, 57, 58,191, -192,197,198, 71, 72,205, 78, 79,212,213, 86, 87,220,221, 94,227, -228,229,102,235,236,237,242,243,244,117,250,251,252, 3, 4, 5, - 6, 11, 12, 13, 14, 19, 20, 21, 26, 27, 28, 29, 34, 35, 36,169, - 42, 43, 44,177, 50, 51,184,185, 58, 59,192,198,199,200, 73,206, -207,208, 81,214,215,216, 89,223,224, 97, 98,231,104,105,106,239, -112,113,114,120,121,122,123,132,133, 6, 7,140, 13, 14,147,148, - 21, 22,155,156, 29,162,163,164, 37,170,171,172,177,178,179, 52, -185,186,187, 68, 69, 70, 71, 76, 77, 78,211, 84, 85, 86, 91, 92, - 93,226, 99,100,101,234,107,108,241,242,115,116,249,122,123,128, -134,135, 8, 9,142,143, 16, 17,150,151, 24, 25,158, 31, 32, 33, - 39, 40, 41, 42, 47, 48, 49, 50, 55, 56, 57, 58, 63,196, 69, 70, - 71, 76, 77, 78,211, 84, 85, 86,219, 92, 93,226,227,100,101,234, -107,108,241,242,115,116,249,250,123, 3, 4, 5, 6, 11, 12, 13, - 18, 19, 20, 21, 26, 27, 28,161, 34, 35, 36,169, 42, 43,176,177, - 50, 51,184, 57, 58,191,192, 65,198, 71, 72, 73,206, 79, 80,213, -214, 87, 88,221, 94, 95,228,229,102,103,236,237,110,243,244,245, -118,251,252,253, 3, 4, 5, 6, 11, 12, 13, 14, 19, 20, 21,154, - 27, 28, 29,162, 35, 36,169, 42, 43, 44,177, 50, 51,184,185, 58, - 59, 66, 67, 68, 69, 74, 75, 76, 81, 82, 83, 84, 89, 90, 91,224, - 97, 98, 99,232,105,106,239,240,113,114,247,120,121,254,255,132, -133, 6, 7,140,141, 14,147,148,149, 22,155,156, 29,162,163,164, - 37,170,171,172,177,178,179,180,185,186,187, 68, 69, 70, 71, 76, - 77, 78,211, 84, 85, 86,219, 92, 93,226, 99,100,101,234,107,108, -241,242,115,116,249,250,123,128,134,135, 8, 9,142,143, 16, 17, -150,151, 24, 25,158,159, 32, 33,167, 40, 41, 42, 47, 48, 49, 50, - 55, 56, 57, 58, 63,196, 69, 70, 71,204, 77, 78,211, 84, 85, 86, -219, 92, 93,226,227,100,101,234,235,108,241,242,243,116,249,250, -123, 3, 4, 5, 6, 11, 12, 13, 14, 19, 20, 21,154, 27, 28, 29, - 34, 35, 36,169, 42, 43, 44,177, 50, 51,184,185, 58, 59,192, 65, -198, 71, 72, 73,206, 79, 80,213,214, 87, 88,221,222, 95,228,229, -230,103,236,237,110,243,244,245,118,251,252,253, 4, 5, 6, 7, - 12, 13, 14, 19, 20, 21, 22, 27, 28, 29,162, 35, 36, 37,170, 43, - 44,177,178, 51, 52,185, 58, 59, 66, 67, 68, 69, 74, 75, 76, 77, - 82, 83, 84,217, 90, 91, 92, 97, 98, 99,232,105,106,107,240,113, -114,247,248,121,122,255, 0,133, 6, 7, 8,141, 14, 15,148,149, - 22, 23,156,157, 30,163,164, 37, 38,171,172, 45,178,179,180, 53, -186,187,188, 67, 68, 69, 74, 75, 76, 77, 82, 83, 84,217, 90, 91, - 92,225, 98, 99,232,233,106,107,240,113,114,247,248,121,122,255, -128,134,135,136, 9,142,143,144, 17,150,151, 24, 25,158,159, 32, - 33,167, 40, 41, 42,175, 48, 49, 50,183, 56, 57, 58, 63,196, 69, - 70, 71,204, 77, 78,211,212, 85, 86,219,220, 93,226,227,100,101, -234,235,108,241,242,243,116,249,250,251, 4, 5, 6, 11, 12, 13, - 14, 19, 20, 21,154, 27, 28, 29,162, 35, 36,169,170, 43, 44,177, - 50, 51,184,185, 58, 59,192, 65,198,199, 72, 73,206,207, 80,213, -214, 87, 88,221,222, 95,228,229,230,103,236,237,238,243,244,245, -246,251,252,253, 4, 5, 6, 7, 12, 13, 14,147, 20, 21, 22,155, - 28, 29,162, 35, 36, 37,170, 43, 44,177,178, 51, 52,185,186, 59, - 66, 67, 68, 69, 74, 75, 76, 77, 82, 83, 84,217, 90, 91, 92,225, - 98, 99,232,105,106,107,240,113,114,247,248,121,122,255,128,133, -134, 7, 8,141, 14, 15,148,149, 22, 23,156,157, 30,163,164,165, - 38,171,172,173,178,179,180, 53,186,187,188,196, 69, 70, 71,204, - 77, 78,211,212, 85, 86,219, 92, 93,226,227,100,101,234,235,108, -241,242,243,116,249,250,251,128,134,135,136, 9,142,143,144, 17, -150,151,152, 25,159,160, 33, 34,167, 40, 41, 42,175, 48, 49, 50, - 56, 57, 58, 59,196,197, 70, 71,204, 77, 78,211,212, 85, 86,219, -220, 93,226,227,228,101,234,235,236,241,242,243,116,249,250,251, - 4, 5, 6, 7, 12, 13, 14,147, 20, 21, 22, 27, 28, 29,162, 35, - 36, 37,170, 43, 44,177,178, 51, 52,185, 58, 59,192,198,199, 72, - 73,206,207, 80, 81,214,215, 88, 89,222,223, 96, 97,103,104,105, -106,111,112,113,114,119,120,121,122,127,132, 5, 6, 7, 12, 13, - 14,147, 20, 21, 22,155, 28, 29,162,163, 36, 37,170, 43, 44,177, -178, 51, 52,185,186, 59, 67, 68, 69, 70, 75, 76, 77, 82, 83, 84, - 85, 90, 91, 92,225, 98, 99,100,233,106,107,240,241,114,115,248, -121,122,255,128, 1,134, 7, 8, 9,142, 15, 16,149,150, 23, 24, -157, 30, 31,164,165, 38, 39,172,173, 46,179,180,181, 54,187,188, -189,196, 69, 70, 71,204, 77, 78,211,212, 85, 86,219,220, 93,226, -227,228,101,234,235,108,241,242,243,116,249,250,251, 2, 3, 4, - 5, 10, 11, 12, 17, 18, 19, 20, 25, 26, 27,160, 33, 34, 35,168, - 41, 42,175,176, 49, 50,183, 56, 57,190,191, 64, 65,198,199, 72, - 73,206,207, 80,213,214, 87, 88,221,222, 95,228,229,230,103,236, -237,238,243,244,245,246,251,252,253, 4, 5, 6, 7, 12, 13, 14, -147, 20, 21, 22,155, 28, 29,162, 35, 36, 37,170, 43, 44,177,178, - 51, 52,185,186, 59,192,198,199, 72, 73,206,207, 80, 81,214,215, - 88, 89,222,223, 96, 97,231,104,105,106,111,112,113,114,119,120, -121,122,127, 0,133,134, 7, 8,141,142, 15,148,149, 22, 23,156, -157, 30,163,164,165, 38,171,172,173,178,179,180,181,186,187,188, - 67, 68, 69, 70, 75, 76, 77, 78, 83, 84, 85,218, 91, 92, 93, 98, - 99,100,233,106,107,108,241,114,115,248,249,122,123, 2, 3, 4, - 9, 10, 11, 12, 17, 18, 19,152, 25, 26, 27,160, 33, 34,167,168, - 41, 42,175, 48, 49,182,183, 56, 57,190,191,196,197, 70, 71,204, -205, 78,211,212, 85, 86,219,220, 93,226,227,228,101,234,235,236, -241,242,243,244,249,250,251, 2, 3, 4, 5, 10, 11, 12, 13, 18, - 19, 20,153, 26, 27, 28, 33, 34, 35,168, 41, 42, 43,176, 49, 50, -183,184, 57, 58,191,197,198,199, 72,205,206,207, 80,213,214,215, - 88,222,223, 96, 97,230,103,104,105,238,111,112,113,119,120,121, -122,127,132, 5, 6, 7, 12, 13, 14,147, 20, 21, 22,155, 28, 29, -162,163, 36, 37,170,171, 44,177,178, 51, 52,185,186, 59, 67, 68, - 69, 70, 75, 76, 77, 78, 83, 84, 85, 90, 91, 92, 93, 98, 99,100, -233,106,107,108,241,114,115,248,249,122,123,128, 1,134, 7, 8, - 9,142, 15, 16,149,150, 23, 24,157,158, 31,164,165, 38, 39,172, -173, 46,179,180,181, 54,187,188,189, 68, 69, 70, 75, 76, 77, 78, - 83, 84, 85,218, 91, 92, 93,226, 99,100,233,234,107,108,241,114, -115,248,249,122,123, 2, 3, 4, 5, 10, 11, 12, 13, 18, 19, 20, - 25, 26, 27, 28, 33, 34, 35,168, 41, 42, 43,176, 49, 50,183, 56, - 57, 58,191, 64,197, 70, 71, 72,205, 78, 79,212,213, 86, 87,220, - 93, 94,227,228,101,102,235,236,109,242,243,244,117,250,251,252, - 4, 5, 6, 7, 12, 13, 14,147, 20, 21, 22,155, 28, 29,162,163, - 36, 37,170, 43, 44,177,178, 51, 52,185,186, 59,192,198,199,200, - 73,206,207, 80, 81,214,215, 88, 89,222,223, 96, 97,231,104,105, -106,239,112,113,114,119,120,121,122,127, 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0, 64, - 64, 0, 64, 0, 64, 0, 64, 0, 64, 0, - }; diff --git a/Core/System.cpp b/Core/System.cpp index 8303f08a15..a4ba6bf524 100644 --- a/Core/System.cpp +++ b/Core/System.cpp @@ -290,7 +290,7 @@ bool CPU_Init(std::string *errorString) { // likely to collide with any commercial ones. g_CoreParameter.compat.Load(g_paramSFO.GetDiscID()); - InitVFPUSinCos(); + InitVFPU(); if (allowPlugins) HLEPlugins::Init(); diff --git a/assets/vfpu/vfpu_asin_lut65536.dat b/assets/vfpu/vfpu_asin_lut65536.dat new file mode 100644 index 0000000000000000000000000000000000000000..507f51f24bbd5604f7f178dc30e3050b02345ffd GIT binary patch literal 1536 zcmXApdsK{h7{|Zw+gz%dGN#*1qr1{gS1Ik*hF#@sXL+ZYn$nFdSsR;9h00cjgp$o_ z2}Lfkh(xVJVzbrCl5L5@8td4|?jnV*vybDS_x=37=leY0=l7o9`vZV?xg0$|yd&~B zydj=8asYnca@ft#B6k4Eg&YD|pb~SKM;keG6LXs@m?K*`q#FRste-Il$~n040H69` zcDRzm5n`QkE4%Fwhb4UA_Sge9=M)FN0GQw4ZSdO#4n@RgvI`78`jx|MA=S?P-5}&H z)e_sgJM#*kaR@gAMikk+e}_3RMl_Fo2XC{95^coEfeJnxl?XQmT2j*ZsewueL_p-> 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K,‘PrPUP>‘PPaPKK)‘PrPUP=OPaPJJ)‘PrPTP=OP_PJJ)‘PpPTP=O‰P_PJJ'PpPTP;O‰P_PII'PpPSP;O‰P^PII'PnPSP;O†P^PII$‘PnPSP9P†P^PGO$‘PnPRP9P†P\PGO$‘PlPRP9P‚P\PGO!‘PlPRP7P‚P\PFN!‘PlPP7P‚P[PFN!‘PjPP7PP[PFN‘PjPP5PP[PDQ‘PjPP5PP[PDQ‘PjPOO5PPZPDQ‘PhPOO5P|PZPDQPhPOO3P|PZPCOPhPNN3P|PXPCOPfPNN3PzPXPCO‘PfPNN1PzPXPAQ‘PfPMM1PzPWPAQ‘PdPMM1PwPWPAQ‘PdPMM.QwPWP@O‘PdPLL.QwPVP@O‘PbPLL.QtPVP@OPbPLL,QtPVP>QPbPKK,QtPUP>QPaPKK,QrPUP>QPaPKK)QrPUP=OPaPJJ)QrPTP=OP_PJJ)QpPTP=O‰P_PJJ'PpPTP;O‰P_PII'PpPSP;O‰P^PII'PnPSP;O†P^PII$QnPSP9P†P^PGO$QnPRP9P†P\PGO$QlPRP9P‚P\PGO!QlPRP7P‚P\PFN!QlPP7P‚P[PFN!QjPP7PP[PFNQjPP5PP[PDQQjPP5PP[PDQQjPOO5PPZPDQQhPOO5P|PZPDQPhPOO3P|PZPCOPhPNN3P|PXPCOPfPNN3PzPXPCOQfPNN1PzPXPAQQfPMM1PzPWPAQQdPMM1PwPWPAQQdPMM.QwPWP@OQdPLL.QwPVP@O‘PbPLL.QtPVP@OPbPLL,QtPVP>QPbPKK,QtPUP>QPaPKK,QrPUP>QPaPKK)QrPUP=OPaPJJ)QrPTP=OP_PJJ)QpPTP=O‰P_PJJ'PpPTP;O‰P_PII'PpPSP;O‰P^PII'PnPSP;O†P^PII$QnPSP9P†P^PGO$QnPRP9P†P\PGO$QlPRP9P‚P\PGO!‘PlPRP7P‚P\PFN!‘PlPP7P‚P[PFN!‘PjPP7PP[PFN‘PjPP5PP[PDQ‘PjPP5PP[PDQ‘PjPOO5PPZPDQ‘PhPOO5P|PZPDQPhPOO3P|PZPCOPhPNN3P|PXPCOPfPNN3PzPXPCO‘PfPNN1PzPXPAQ‘PfPMM1PzPWPAQ‘PdPMM1PwPWPAQ‘PdPMM.‘PwPWP@O‘PdPLL.‘PwPVP@O‘PbPLL.‘PtPVP@OPbPLL,‘PtPVP>QPbPKK,‘PtPUP>‘PPaPKK,‘PrPUP>‘PPaPKK)‘PrPUP=PPaPJJ)‘PrPTP=PP_PJJ)‘PpPTP=P‰P_PJJ'PpPTP;P‰P_PII'PpPSP;P‰P^PI‰gPnPSP;P†P^PI‰d‘PnPrPTPP}P‰P^PP‰‰d‘PlPRPPwPP[PP„‘[PfPNŽqPwPWPP€PPbPK‹i‘PpPTPP{P†P^PGa‘PlPPPuPPZPPƒW‘PfPMn‘PwPVPP~‘PPaPJŠgPpPSPPyP†P\PFŽa‘PjPOuP|PXPA‘W‘PdPLŒn‘PtPUP>‘PP_PI‰gPnPRP9P‚P[PFŽ^‘PhPOsPzPWPA‘S‘PbPLŒl‘PrPUP=P‰P^PI‰d‘PlPRP7PP[PD‘[PhPNN1PwPWP@PPbPKK)‘PrPTP;P‰P^PGa‘PlPP5PPZPC[PfPMM.‘PwPVP>‘PPaPJJ)‘PpPSP;P†P\PFN!‘PjPOO5P|PXPCW‘PdPLL.‘PtPUP>‘PP_PJJ'PnPSP9P‚P[PFN‘PhPOO3PzPXPAQ‘PbPLL,‘PrPUP=O‰P_PII$‘PnPRP7PP[PDQPhPNN1PzPWP@OPbPKK)‘PrPTP;O‰P^PGO$‘PlPP5PPZPCOPfPMM1PwPVP>QPaPJJ)‘PpPSP;O†P\PGO!‘PjPOO5P|PXPCO‘PdPMM.QtPVP>QP_PJJ'PnPSP9P‚P\PFN‘PhPOO3PzPXPAQ‘PdPLL,QtPUP=O‰P_PII$QnPRP7P‚P[PDQPhPNN1PzPWP@O‘PbPKK,QrPTP;O‰P^PGO$QlPP7PPZPCOPfPMM1PwPVP@OPaPKK)QpPSP;O†P\PGO!QjPP5P|PXPCOQdPMM.QtPVP>QPaPJJ'PnPSP9P‚P\PFNQjPOO3P|PXPAQQdPLL,QtPUP=OP_PII$QnPRP7P‚P[PDQQhPNN3PzPWP@OQbPKK,QrPTP=O‰P^PGO$QlPP7PPZPDQPfPNN1PwPVP@OPaPKK)QpPTP;O†P\PGO!QjPP5P|PZPCOQfPMM.QtPVP>QMaPJJ'PpPSP9P‚P\PFNQjPOO3P|PXPAQQdPLL,QtPUP=OM_PII'PnPRP9P‚P[PDQQhPNN3PzPWPAQQbPKK,QrPTP=OI^PII$QlPRP7PPZPDQPfPNN1PwPWP@OPaPKK)QpPTP;OF^PGO!QlPP5P|PZPCOQfPMM.QwPVP>QMaPJJ'PpPSP9PF\PFN!QjPOO3P|PXPAQQdPLL.QtPUP=OM_PII'PnPRP9P‚P[PFNQhPNN3PzPWPAQQbPLL,QrPTP=OI^PII$QlPRP7PP[PDQPfPNN1PwPWP@OPbPKK)QrPTP;O†P^PGO!QlPP5PPZPCOQfPMM.QwPVP>QPaPJJ)QpPSP9P†P\PFN!QjPOO5P|PXPAQQdPLL.QtPUP>QP_PJJ'PnPRP9P‚P[PFNQhPOO3PzPWPAQ‘PbPLL,QrPUP=O‰P_PII$QlPRP7PP[PDQPhPNN1PwPWP@OPbPKK)QrPTP;O‰P^PGO!QlPP5PPZPCOPfPMM1PwPVP>QPaPJJ)QpPSP;O†P\PFN!‘PjPOO5P|PXPCO‘PdPMM.QtPUP>QP_PJJ'PnPSP9P‚P[PFN‘PhPOO3PzPXPAQ‘PdPLL,‘PrPUP=O‰P_PII$‘PnPRP7PP[PDQPhPNN1PzPWP@O‘PbPKK)‘PrPTP;O‰P^PGO$‘PlPP5PPZPCOPfPMM1PwPVP@OPaPJJ)‘PpPSP;P†P\PGO!‘PjPPRPPwPPZPCW‘PdPLŒl‘PrPTPP{P†P\PFŽ^‘PhPNŽqPwPVP>‘PP_PI‰d‘PlPPPuP|PXPA‘S‘PbPK‹i‘PpPSP9P‚P[PD‘[PfPMn‘PtPUP=P‰P^PGa‘PjPOO3PzPWP@PPaPJŠgPnPRP7PPZPCW‘PdPLL,‘PrPTP;P†P\PFŽ[PfPMM.‘PtPUP=P‰P^PGO!‘PjPOO3PzPWP@PPaPJJ'PnPRP7PPZPCO‘PdPLL,‘PrPTP;P†P\PFN‘PhPNN1PwPVP>‘PP_PII$‘PlPP5P|PXPAQ‘PbPKK)‘PpPSP9P‚P[PDQPfPMM.‘PtPUP=O‰P^PGO!‘PjPOO3PzPWP@OPaPJJ'PnPRP7PPZPCO‘PdPLL,‘PrPTP;O†P\PFN‘PhPNN1PtPUP=O‰P^PGO!‘PjPOO3PzPWP@OPaPJJ'PnPRP7PPZPCO‘PdPLL,‘PrPTP;O†P\PFN‘PhPNN1PwPVP>QP_PII$‘PlPP5P|PXPAQ‘PbPKK)QpPSP9P‚P[PDQPfPMM.QtPUP=O‰P^PGO!‘PjPOO3PzPWP@OPaPJJ'PnPRP7PPZPCO‘PdPLL,QrPTP;O†P\PFN‘PhPNN1PwPVP>QP^PGO!QjPOO3PzPWP@OPaPJJ'PnPRP7PPZPCO‘PdPLL,QrPTP;O†P\PFNQhPNN1PwPVP>QP_PII$QlPP5P|PXPAQ‘PbPKK)QpPSP9P‚P[PDQPfPMM.QtPUP=O‰P^PGO!QjPOO3PzPWP@OPaPJJ'PnPRP7PPZPCO‘PdPLL,QrPTP;O†P\PFNQhPNN1PwPVP>QP_PII$QlPP3PzPWP@OPaPJJ'PnPRP7PPZPCOQdPLL,QrPTP;O†P\PFNQhPNN1PwPVP>QP_PII$QlPP5P|PXPAQ‘PbPKK)QpPSP9P‚P[PDQPfPMM.QtPUP=O‰P^PGO!QjPOO3PzPWP@OPaPJJ'PnPRP7PPZPCO‘PdPLL,QrPTP;O†P\PFNQhPNN1PwPVP>QP_PII$QlPP5P|PXPAQPaPJJ'PnPRP7PPZPCO‘PdPLL,QrPTP;O†P\PFN‘PhPNN1PwPVP>QP_PII$QlPP5P|PXPAQ‘PbPKK)QpPSP9P‚P[PDQPfPMM.QtPUP=O‰P^PGO!‘PjPOO3PzPWP@OPaPJJ'PnPRP7PPZPCO‘PdPLL,‘PrPTP;O†P\PFN‘PhPNN1PwPVP>QP_PII$‘PlPP5P|PXPAQ‘PbPKK)‘PnPRP7PPZPCO‘PdPLL,‘PrPTP;O†P\PFN‘PhPNN1PwPVP>QP_PII$‘PlPP5P|PXPAQ‘PbPKK)‘PpPSP9P‚P[PDQPfPMM.‘PtPUP=O‰P^PGO!‘PjPOO3PzPWP@OPaPJJ'PnPRP7PPZPCO‘PdPLL,‘PrPTP;P†P\PFN‘PhPNN1PwPVP>‘PP_PII$‘PlPP5P|PXPA‘S‘PbPKK)‘PpPSP9P‚PZPCW‘PdPLL,‘PrPTP;P†P\PFŽ^‘PhPNN1PwPVP>‘PP_PI‰d‘PlPP5P|PXPA‘S‘PbPK‹i‘PpPSP9P‚P[PD‘[PfPMM.‘PtPUP=P‰P^PGa‘PjPOO3PzPWP@PPaPJŠgPnPRP7PPZPCW‘PdPLŒl‘PrPTP;P†P\PFŽ^‘PhPNŽqPtPUP=P†P\PD‘[PfPLŒl‘PpPSP9PPZPCS‘PbPJŠgPnPP5P|PWP@PP_PI‰a‘PjPOO1PwPUP=P‰P\PFŽ[PfPMM,‘PrPTP9P‚PZPCW‘PbPKK)‘PnPRP5P|PXP@PPaPII$‘PjPOO3PwPVP=P‰P^PFN‘PhPMM.‘PrPTP;P‚P[PDQ‘PdPKK)‘PpPRP7PPXPAQPaPJJ$‘PlPP3PzPVP>QP^PGO‘PhPNN.‘PtPUP;O†P[PDQPdPLL,‘PpPSP7PPZPAQ‘PbPJJ'PlPP5PzPWP>QP_PGO!‘PjPNN1PtPUP=O†P\PFNPfPLL,‘PrPSP9P‚PZPCO‘PbPKK'PnPP5P|PWP@OP_PII!‘PjPOO1PwPVP=O‰P\PFN‘PfPMM.QrPTP9P‚P[PCO‘PbPKK)QnPRP7P|PXP@OPaPII$QlPOO3PwPVP>Q‰P^PGOQhPMM.QtPTP;O‚P[PDQQdPLL)QpPRP7PPXPAQQaPJJ$QlPP3PzPWP>QM^PGO!QhPNN.QtPUP;O†P\PDQPdPLL,QpPSP9PPZPAQQbPJJ'PnPP5PzPWP@OM_PGO!QjPNN1PwPUP=OF\PFNPfPMM,QrPSP9PBZPCOQbPKK'PnPRP5P<XP@OP_PII$QjPOO1PwPVP=OI^PFNQfPMM.QrPTP;OB[PCOQdPKK)QpPRP7P<XPAQPaPII$QlPOO3P:VP>QI^PGOQhPNN.Q4TP;OF[PDQPdPLL)QpPSP7P?XPAQQaPJJ'PlPP3P:WP>QM_PGO!QhPNN1P4UP=OF\PDQPfPLL,Q0SP9P?ZPCOQbPJJ'PnPP5P<WP@OM_PII!QjPOO1P7UP=OI\PFNPfPMM,Q2TP9PBZPCOQbPKK)QnPRP5P<XP@OPaPII$QjPOO3P7VP=OI^PFNQhPMM.Q2TP;OB[PDQQdPKK)Q0RP7P?XPAQPaPJJ$QlPP3P:VP>QM^PGOQhPNN.Q4UP;OF[PDQPdPLL,Q0SP7P?ZPAQQbPJJ'PlPP5P:WP>QM_PGO!QjPNN1P4UP=OF\PFNPfPLL,QrPSP9PBZPCOQbPKK'PnPP5P<WP@OP_PII!QjPOO1P7VP=OI\PFNQfPMM.QrPTP9PB[PCOQbPKK)QnPRP7P<XP@OPaPII$QlPOO3PwPVP>QI^PGOQhPMM.QtPTP;OB[PDQQdPLL)QpPRP7P?XPAQQaPJJ$QlPP3PzPWP>QM^PGO!QhPNN.QtPUP;OF\PDQPdPLL,QpPSP9PPZPAQQbPJJ'PnPP5PzPWP@OM_PGO!QjPNN1PwPUP=O†P\PFNPfPMM,QrPSP9P‚PZPCOQbPKK'PnPRP5P|PXP@OP_PII$QjPOO1PwPVP=O‰P^PFNQfPMM.QrPTP;O‚P[PCO‘PdPKK)QpPRP7P|PXPAQPaPII$QlPOO3PzPVP>Q‰P^PGO‘PhPNN.QtPTP;O†P[PDQPdPLL)‘PpPSP7PPXPAQ‘PaPJJ'PlPP3PzPWP>QP_PGO!‘PhPNNPPsPwPUP=P†P[PD‘W‘PbPK‹gPlPOO3PwPUP=P†P[PD‘W‘PbPJŠgPlPOO3PwPUP=P†P[PCW‘PbPJŠgPlPOO3PwPUP;P†P[PCW‘PbPJJ'PlPOO1PwPUP;P†P[PCW‘PbPJJ$‘PlPOO1PwPUP;P†P[PCW‘PbPJJ$‘PlPOO1PwPUP;P†P[PCO‘PbPJJ$‘PlPOO1PwPUP;P‚P[PCO‘PbPJJ$‘PlPOO1PtPUP;P‚P[PCO‘PbPJJ$‘PjPOO1PtPUP;O‚P[PCO‘PaPJJ$‘PjPOO1PtPUP;O‚PZPCO‘PaPJJ$‘PjPOO1PtPUP;O‚PZPCO‘PaPJJ$‘PjPOO1PtPTP;O‚PZPCO‘PaPJJ$‘PjPNN1PtPTP;O‚PZPCO‘PaPII$‘PjPNN1PtPTP;O‚PZPAQ‘PaPII$‘PjPNN1PtPTP9P‚PZPAQ‘PaPII$‘PjPNN.QtPTP9P‚PZPAQ‘PaPII$‘PjPNN.QtPTP9P‚PZPAQ‘PaPII!QjPNN.QtPTP9P‚PZPAQPaPII!QjPNN.QtPTP9PPZPAQPaPII!QjPNN.QrPTP9PPZPAQPaPII!QhPNN.QrPTP9PPZPAQP_PII!QhPNN.QrPTP9PPZPAQP_PII!QhPNN.QrPTP9PPXPAQP_PII!QhPNN.QrPSP9PPXPAQP_PII!QhPMM.QrPSP9PPXPAQP_PGO!QhPMM.QrPSP9PPXP@OP_PGO!QhPMM.QrPSP7PPXP@OP_PGO!QhPMM.QrPSP7PPXP@OP_PGO!QhPMM,QrPSP7PPXP@OP_PGOQhPMM,QrPSP7PPXP@OM_PGOQhPMM,QrPSP7P|PXP@OM_PGOQhPMM,QpPSP7P|PXP@OM_PGOQhPMM,QpPSP7P|PXP@OP_PGOQfPMM,QpPSP7P|PXP@OP^PGOQfPMM,QpPSP7P|PWP@OP^PGOQfPMM,QpPRP7P|PWP@OP^PGOQfPLL,QpPRP7P|PWP@OP^PFNQfPLL,QpPRP7P|PWP@OP^PFNQfPLL,QpPRP7P|PWP>QP^PFNQfPLL,QpPRP5P|PWP>QP^PFNQfPLL)QpPRP5P|PWP>QP^PFNPfPLL)QpPRP5P|PWP>Q‰P^PFNPfPLL)QpPRP5PzPWP>Q‰P^PFNPfPLL)QpPRP5PzPWP>Q‰P^PFNPfPLL)QnPRP5PzPWP>Q‰P^PFNPdPLL)‘PnPRP5PzPWP>Q‰P\PFNPdPLL)‘PnPRP5PzPVP>Q‰P\PFNPdPLL)‘PnPP5PzPVP>Q‰P\PFNPdPKK)‘PnPP5PzPVP>Q‰P\PFNPdPKK)‘PnPP5PzPVP>Q‰P\PDQPdPKK)‘PnPP5PzPVP=O‰P\PDQPdPKK)‘PnPP3PzPVP=P‰P\PDQPdPKK'PnPP3PzPVP=P‰P\PDQ‘PdPKK'PnPP3PzPVP=P†P\PDQ‘PdPKK'PnPP3PzPVP=P†P\PD‘W‘PdPKK'PnPP3PwPVP=P†P\PD‘W‘PdPKK'PlPP3PwPVP=P†P\PD‘W‘PbPK‹gPlPP3PwPVP=P†P[PD‘W‘PbPK‹gPlPP3PwPUP=P†P[PD‘W‘PbPK‹gPlPPPqPtPTP9PPXP@PP^PFŽ[PdPK‹d‘PjPNN.‘PrPSP7P|PWP>‘P‰P\PD‘S‘PaPI‰a‘PhPMM,‘PpPRP5PzPVP=P†PZPA‘PP_PG^‘PfPLL)‘PnPP3PwPTP9PPXP@PP^PFNPdPKK'PlPOO.‘PrPSP7P|PWP>‘P‰P\PDQ‘PbPJJ!‘PhPMM,‘PpPRP5PzPVP=O†P[PCO‘P_PGO‘PfPLL)‘PnPP3PwPUP;O‚PXP@OP^PFNPdPKK'PlPOO1PtPSP7P|PWP>Q‰P\PDQ‘PbPJJ$‘PjPNN,‘PpPRP5PzPVP=O†P[PCO‘PaPII‘PfPLL)QnPP3PwPUP;O‚PZPAQP^PFNPdPKK'PlPOO1PtPTP9PPWP>Q‰P\PDQ‘PbPJJ$QjPNN.QrPSP5PzPVP=O†P[PCO‘PaPII!QhPMM)QnPP3PwPUP;O‚PZPAQP_PGOQdPKK'PlPOO1PtPTP9PPXP@OM\PDQQbPJJ$QjPNN.QrPSP7P|PVP=OF[PCOQaPII!QhPMM,QpPRP3PwPUP;OBZPAQP_PGOQfPLL'PlPOO1PtPTP9P?XP@OM^PFNPbPJJ$QjPNN.QrPSP7P<WP>QI[PCOQaPII!QhPMM,QpPRP5P:VP;OBZPAQP_PGOQfPLL)QnPP1P4TP9P?XP@OM^PFNPdPKK$QjPNN.Q2SP7P<WP>QI\PDQQaPII!QhPMM,Q0RP5P:VP=OFZPAQP_PGOQfPLL)QnPP3P7UP9P?XP@OM^PFNPdPKK'PlPOO.Q2SP7P<WP>QI\PDQQbPJJ$QhPMM,Q0RP5P:VP=OF[PCOQ_PGOQfPLL)Q.P3P7UP;OBZP@OM^PFNPdPKK'P,OO1P4TP7P<WP>QI\PDQQbPJJ$QjPNN,Q0RP5P:VP=OF[PCOQaPII!QfPLL)Q.P3P7UP;OBZPAQP^PFNPdPKK'P,OO1P4TP9P?XP>QI\PDQQbPJJ$QjPNN.Q2SP5P:VP=OF[PCOQaPII!QhPMM,Q.P3P7UP;OBZPAQP_PGOQdPKK'PlPOO1P4TP9P?XP@OM^PDQQbPJJ$QjPNN.Q2SP7P<WP=OF[PCOQaPII!QhPMM,QpPRP3P7UP;OBZPAQP_PGOQfPLL)QlPOO1P4TP9P?XP@OM^PFNPbPJJ$QjPNN.QrPSP7P<WP>QI\PCOQaPII!QhPMM,QpPRP5PzPVP;OBZPAQP_PGOQfPLL)QnPP3PtPTP9P?XP@OM^PFNPdPKK'PjPNN.QrPSP7P|PWP>QI\PDQQaPII!QhPMM,QpPRP5PzPVP=O†P[PAQP_PGOQfPLL)QnPP3PwPUP9PPXP@OP^PFNPdPKK'PlPOO1PrPSP7P|PWP>Q‰P\PDQ‘PbPJJ$QhPMM,QpPRP5PzPVP=O†P[PCO‘PaPGO‘PfPLL)QnPP3PwPUP;O‚PZP@OP^PFNPdPKK'PlPOO1PtPTP9P|PWP>Q‰P\PDQ‘PbPJJ$‘PjPNN.QPPqPtPSPPwP|PVPP}P‚PZPP‘PP^PP„‘W‘PbPP‰‰a‘PfPPŒŒi‘PlPOn‘PrPSPPuPzPUPP{P‚PXPP€P‰P\PP„‘S‘PaPP‡^‘PfPK‹gPjPNŽn‘PpPRPPsPwPUPPyPPWPP~‘P‰P[PPƒPP_PG[PdPJŠd‘PjPMl‘PnPPPsPtPTPPwP|PWPP}P†PZPA‘PP^PFŽW‘PbPJŠa‘PhPLŒi‘PnPOqPrPSPPwPzPVP;P‚PZP@PP\PD‘W‘PaPI‰^‘PfPLŒgPlPNŽn‘PrPRPPuPwPUP;PPXP>‘P‰P\PCS‘P_PG^‘PdPK‹d‘PjPNŽl‘PpPP3PwPTP9P|PWP>‘P†P[PA‘PP_PFŽ[PbPJŠd‘PhPMM)‘PnPP1PtPSP7P|PVP=P‚PZPA‘PP^PD‘W‘PbPI‰a‘PfPLL)‘PlPOO.‘PrPSP5PzPUP;P‚PXP@P‰P\PD‘S‘PaPGO‘PfPKK'PjPNN.‘PpPRP3PwPUP9PPWP>‘P‰P[PCPP_PGOPdPJJ$‘PjPMM,‘PnPP3PtPTP7P|PWP=P†PZPA‘PP^PFN‘PbPJJ!‘PhPLL)‘PnPOO1PrPSP7PzPVP;P‚PZP@OP^PDQ‘PaPII!‘PfPLL'PlPOO.‘PrPRP5PzPUP;PPXP@O‰P\PCO‘PaPGO‘PdPKK'PjPNN,‘PpPRP3PwPTP9PPWP>Q†P[PCOP_PFNPdPJJ$‘PhPMM,‘PnPP1PtPTP7P|PVP=O†PZPAQP^PFN‘PbPII!‘PhPLL)‘PlPOO1PrPSP5PzPVP;O‚PXP@OP\PDQ‘PaPII‘PfPKK'PlPNN.‘PpPRP5PwPUP9PPXP>Q‰P[PCO‘P_PGOPdPKK$‘PjPMM,‘PpPP3PtPTP9P|PWP=O†P[PAQP^PFNPbPJJ!‘PhPMM)‘PnPOO1PtPSP7PzPVP=O‚PZP@OP^PDQ‘PaPII!‘PfPLL'PlPOO.‘PrPRP5PzPUP;OPXP@O‰P\PCO‘PaPGO‘PdPKK'PjPNN,‘PpPRP3PwPTP9PPWP>Q†P[PCOP_PFNPdPJJ$‘PhPMM,‘PnPP1PtPTP7P|PVP=O†PZPAQP^PFN‘PbPII!‘PhPLL)‘PlPOO1PrPSP5PzPVP;P‚PXP@OP\PDQ‘PaPII‘PfPLL'PlPNN.‘PrPRP5PwPUP;PPXP>Q‰P\PCO‘P_PGO‘PdPKK$‘PjPNN,‘PpPP3PwPTP9P|PWP>‘P†P[PAQP_PFNPbPJJ$‘PhPMM)‘PnPP1PtPSP7P|PVP=P‚PZPA‘PP^PDQ‘PbPII!‘PfPLL)‘PlPOO.‘PrPSP5PzPUP;P‚PXP@P‰P\PD‘S‘PaPGO‘PfPKK'PjPNN.‘PpPRP3PwPUP9PPWP>‘P‰P[PCPP_PG[PdPJJ$‘PjPMM,‘PnPP3PtPTP7P|PWP=P†PZPA‘PP^PFŽW‘PbPJŠa‘PhPLL)‘PnPOO1PrPSP7PzPVP;P‚PZP@PP\PD‘W‘PaPI‰^‘PfPLŒgPlPNŽn‘PrPRP5PwPUP;PPXP>‘P‰P\PCS‘P_PG^‘PdPK‹d‘PjPNŽl‘PpPPPsPwPTP9P|PWP>‘P†P[PA‘PP_PFŽ[PbPJŠd‘PhPMi‘PnPPPqPtPSPPwP|PVPP}P‚PZPA‘PP^PD‘W‘PbPI‰a‘PfPLŒi‘PlPOn‘PrPSPPuPzPUPP{P‚PXPP€P‰P\PP„‘S‘PaPG^‘PfPK‹gPjPNŽn‘PpPPPsPtPSPPuPwPUPPyP|PVPP}P‚PXPP~‘P†P[PP‘PP\PCS‘P_PFŽW‘PbPI‰^‘PdPJŠd‘PhPLŒgPlPNŽl‘PnPOqPrPRPPsPwPTPPwPzPUP;PPWP=P‚PZP@P‰P[PCPP^PD‘S‘PaPG[PbPJŠa‘PfPK‹d‘PjPMi‘PlPOO.‘PpPP1PtPSP5PwPTP9P|PVP;P‚PXP>‘P†PZPA‘PP\PCS‘P_PFŽW‘PaPII‘PdPJJ$‘PhPLL'PjPNN,‘PnPOO.‘PrPRP3PtPTP7PzPUP9PPWP=P‚PZP@P‰P[PAQP^PDQ‘P_PGOPbPII!‘PfPKK$‘PhPMM)‘PlPNN.‘PpPP1PrPSP5PwPTP9P|PVP;OPXP>Q†PZP@OP\PCOP_PFN‘PaPGO‘PdPJJ!‘PhPLL'PjPMM,‘PnPOO.‘PrPRP3PtPSP7PzPUP9P|PWP=O‚PXP@O‰P[PAQP^PDQ‘P_PGOPbPII‘PfPKK$‘PhPMM)QlPNN,QpPP1PrPRP5PwPTP7P|PVP;OPWP>Q†PZP@OP\PCOP^PFN‘PaPGOQdPJJ!QfPLL'PjPMM)QnPOO.QpPRP3PtPSP5PzPUP9P|PWP=O‚PXP>Q‰P[PAQP^PDQQ_PFNPbPIIQdPKK$QhPLL)QlPNN,QnPP1PrPRP5PwPTP7PzPVP;OPWP>Q†PZP@OI\PCOP^PDQQaPGOPdPJJ!QfPKK'PjPMM)QnPOO.QpPP3PtPSP5PzPUP9P|PVP=OBXP>QF[PAQM\PDQQ_PFNQbPIIQdPKK$QhPLL'PlPNN,QnPP1PrPRP3PwPTP7P:UP;O?WP=OFZP@OI[PCOP^PDQQaPGOPbPJJ!QfPKK$QjPMM)QlPOO.QpPP1PtPSP5P7UP9P<VP;OBXP>QF[PAQM\PCOQ_PFNQaPIIQdPJJ$QhPLL'PjPNN,QnPOO1PrPRP3PtPTP7P:UP;O?WP=OBZP@OI[PAQP^PDQQaPGOPbPII!QfPKK$QjPMM)QlPNN.QpPP1PtPSP5P7TP9P<VP;O?XP>QFZPAQM\PCOP_PFNQaPIIQdPJJ!QhPLL'PjPNN,QnPOO.QrPRP3PtPSP7P:UP9P?WP=OBXP@OI[PAQP^PDQQ_PGOPbPII!QfPKK$QhPMM)QlPNN,QpPP1PrPSP5PwPTP7P|PVP;O?XP>QFZP@OM\PCOP_PFNQaPGOQdPJJ!QfPLL'PjPMM,QnPOO.QpPRP3PtPSP7PzPUP9P|PWP=O‚PXP@OI[PAQM^PDQQ_PFNPbPIIQfPKK$QhPLL)QlPNN,QpPP1PrPRP5PwPTP7PzPVP;OPWP>Q†PZP@O‰P\PCOP^PFNQaPGOPdPJJ!QfPLL'PjPMM)QnPOO.QpPP3PtPSP5PzPUP9P|PVP=O‚PXP>Q‰P[PAQP\PDQ‘P_PFNPbPIIQdPKK$QhPLL'PlPNN,QnPP1PrPRP3PwPTP7PzPVP;OPWP=O†PZP@O‰P\PCOP^PDQ‘PaPGOPbPJJ!‘PfPKK'PjPMM)‘PlPOO.QPPn‘PpPPPqPrPRPPsPtPRPPsPtPSPPuPwPTPPwPzPTPPwPzPUPPyP|PVPP{PPVPP{PPWPP}P‚PXPP~‘P†PXPP~‘P†PZPP€P‰P[PP‘PP[PP‘PP\PPƒPP^PD‘S‘P^PD‘S‘P_PFŽW‘PaPG[PaPG[PbPI‰^‘PdPJŠa‘PdPJŠa‘PfPK‹d‘PhPLŒgPhPLŒgPjPMi‘PlPNŽl‘PlPNŽl‘PnPOn‘PpPPPqPpPPPqPrPRPPsPtPSPPuPtPSP5PwPTP7PzPUP9PzPUP9P|PVP;PPWP=PPWP=P‚PXP>‘P†PZP@P†PZP@P‰P[PA‘PP\PCPP\PCPP^PD‘S‘P_PFŽS‘P_PFŽW‘PaPG[PbPI‰[PbPI‰^‘PdPJJ!‘PfPKK!‘PfPKK$‘PhPLL'PjPMM'PjPMM)‘PlPNN,‘PnPOO,‘PnPOO.‘PpPP1PrPP1PrPRP3PtPSP5PwPSP5PwPTP7PzPUP9P|PUP9P|PVP;PPWP=P‚PWP=P‚PXP>‘P†PZP@O‰PZP@O‰P[PAQP\PCOP\PCOP^PDQ‘P_PFN‘P_PFN‘PaPGOPbPII‘PbPII‘PdPJJ!‘PfPKK$‘PfPKK$‘PhPLL'PjPMM)‘PjPMM)‘PlPNN,‘PnPOO.‘PnPOO.‘PpPP1PrPRP3PrPRP3PtPSP5PwPTP7PwPTP7PzPUP9P|PVP;O|PVP;OPWP=O‚PXP>Q‚PXP>Q†PZP@O‰P[PAQ‰P[PAQP\PCOP^PDQP^PDQ‘P_PFN‘PaPGO‘PaPGOPbPII‘PdPJJ‘PdPJJ!‘PfPKK$‘PhPLL$‘PhPLL'PjPMM)‘PlPNN)‘PlPNN,QnPOO.QpPP.QpPP1PrPRP3PtPRP3PtPSP5PwPTP7PzPTP7PzPUP9P|PVP;OPVP;OPWP=O‚PXP>Q†PXP>Q†PZP@O‰P[PAQP[PAQP\PCOP^PDQ‘P^PDQ‘P_PFN‘PaPGOPaPGOPbPII‘PdPJJ!‘PdPJJ!‘PfPKK$‘PhPLL'PhPLL'PjPMM)QlPNN,QlPNN,QnPOO.QpPP1PpPP1PrPRP3PtPSP5PtPSP5PwPTP7PzPUP9PzPUP9P|PVP;OPWP=OPWP=O‚PXP>Q†PZP@O†PZP@O‰P[PAQP\PCOP\PCOP^PDQ‘P_PFN‘P_PFN‘PaPGOPbPIIPbPII‘PdPJJ!‘PfPKK!‘PfPKK$‘PhPLL'PjPMM'PjPMM)‘PlPNN,‘PnPOO,‘PnPOO.‘PpPP1PrPP1PrPRP3PtPSP5PwPSP5PwPTP7PzPUP9P|PUP9P|PVP;OPWP=O‚PWP=O‚PXP>Q†PZP@O‰PZP@O‰P[PAQP\PCOP\PCOP^PDQ‘P_PFN‘P_PFN‘PaPGOPbPII‘PbPII‘PdPJJ!‘PfPKK$‘PfPKK$‘PhPLL'PjPMM)‘PjPMM)‘PlPNN,‘PnPOO.‘PnPOO.‘PpPP1PrPRP3PrPRP3PtPSP5PwPTP7PwPTP7PzPUP9P|PVP;P|PVP;PPWP=P‚PXP>‘P‚PXP>‘P†PZP@P‰P[PA‘P‰P[PA‘PP\PCPP^PD‘PP^PD‘S‘P_PFŽW‘PaPGW‘PaPG[PbPI‰^‘PdPJŠ^‘PdPJŠa‘PfPK‹d‘PhPLŒd‘PhPLŒgPjPMi‘PlPNŽi‘PlPNŽl‘PnPOn‘PpPPOn‘PpPOn‘PnPOl‘PnPNŽl‘PnPNŽl‘PlPNŽi‘PlPMi‘PlPMi‘PjPMgPjPLŒgPjPLŒgPhPLŒd‘PhPK‹d‘PhPK‹d‘PfPK‹a‘PfPJŠa‘PfPJŠa‘PdPJŠ^‘PdPI‰^‘PdPI‰^‘PbPI‰[PbPG[PbPG[PaPGW‘PaPFŽW‘PaPFŽW‘P_PFŽS‘P_PD‘S‘P_PD‘S‘P^PD‘PP^PCPP^PCPP\PCPP\PA‘PP\PA‘PP[PA‘P‰P[P@P‰P[P@P‰PZP@P†PZP>‘P†PZP>‘P†PXP>‘P‚PXP=P‚PXP=P‚PWP=PPWP;PPWP;PPVP;P|PVP9P|PVP9P|PUP9PzPUP7PzPUP7PzPTP7PwPTP5PwPTP5PwPSP5PtPSP3PtPSP3PtPRP3PrPRP1PrPRP1PrPP1PpPP.‘PpPP.‘PpPOO.‘PnPOO,‘PnPNN,‘PnPNN,‘PlPNN)‘PlPMM)‘PlPMM)‘PjPMM'PjPLL'PjPLL'PhPLL$‘PhPKK$‘PhPKK$‘PfPKK!‘PfPJJ!‘PfPJJ!‘PdPJJ‘PdPII‘PdPII‘PbPIIPbPGOPbPGOPaPGO‘PaPFN‘PaPFN‘P_PFN‘P_PDQ‘P_PDQ‘P^PDQP^PCOP^PCOP\PCOP\PAQP\PAQP[PAQ‰P[P@O‰P[P@O‰PZP@O†PZP>Q†PZP>Q†PXP>Q‚PXP=O‚PXP=O‚PWP=OPWP;OPWP;OPVP;O|PVP9P|PVP9P|PUP9PzPUP7PzPUP7PzPTP7PwPTP5PwPTP5PwPSP5PtPSP3PtPSP3PtPRP3PrPRP1PrPRP1PrPP1PpPP.‘PpPP.‘PpPOO.‘PnPOO,‘PnPOO,‘PnPNN,‘PlPNN)‘PlPNN)‘PlPMM)‘PjPMM'PjPMM'PjPLL'PhPLL$‘PhPLL$‘PhPKK$‘PfPKK!‘PfPKK!‘PfPJJ!‘PdPJJ‘PdPJJ‘PdPII‘PbPIIPbPIIPbPGOPaPGO‘PaPGO‘PaPFN‘P_PFN‘P_PFN‘P_PDQ‘P^PDQP^PDQP^PCOP\PCOP\PCOP\PAQP[PAQ‰P[PAQ‰P[P@O‰PZP@O†PZP@O†PZP>Q†PXP>Q‚PXP>Q‚PXP=O‚PWP=OPWP=PPWP;PPVP;P|PVP;P|PVP9P|PUP9PzPUP9PzPUP7PzPTP7PwPTP7PwPTP5PwPSP5PtPSP5PtPSP3PtPRP3PrPRP3PrPRP1PrPP1PpPP1PpPP.‘PpPOO.‘PnPOO.‘PnPOO,‘PnPNN,‘PlPNN,‘PlPNN)‘PlPMM)‘PjPMM)‘PjPMM'PjPLL'PhPLL'PhPLL$‘PhPKK$‘PfPKK$‘PfPKK!‘PfPJJ!‘PdPJJ!‘PdPJJ‘PdPII‘PbPI‰^‘PbPI‰[PbPG[PaPG[PaPGW‘PaPFŽW‘P_PFŽW‘P_PFŽS‘P_PD‘S‘P^PD‘S‘P^PD‘PP^PCPP\PCPP\PCPP\PA‘PP[PA‘PP[PA‘P‰P[P@P‰PZP@P‰PZP@P†PZP>‘P†PXP>‘P†PXP>‘P‚PXP=P‚PWP=P‚PWP=PPWP;PPVP;PPVP;P|PVP9P|PUP9P|PUPPyPzPUPPwPzPTPPwPzPTPPwPwPTPPuPwPSPPuPwPSPPuPtPSPPsPtPRPPsPtPRPPsPrPRPPqPrPPPqPrPPPqPpPPPn‘PpPOl‘PnPNŽi‘PjPLŒgPhPK‹a‘PfPJŠ^‘PbPG[PaPFŽS‘P_PD‘PP\PA‘PP[P@P†PZP>‘P‚PWP;PPVP9PzPUPPwPwPSPPsPtPRPPqPpPPPn‘PnPNŽi‘PlPMgPhPK‹d‘PfPJŠ^‘PdPI‰[PaPFŽW‘P_PD‘PP^PCPP[P@P‰PZP>‘P‚PXP=PPVP9P|PUP7PwPTP5PtPRP1PrPP.‘PnPNN,‘PlPMM'PjPLL$‘PfPJJ!‘PdPI‰[PbPGW‘P_PD‘S‘P^PCPP\PA‘P‰PZP>‘P†PXP=PPWP;P|PUP7PzPTP5PtPSP3PrPP.‘PpPOO,‘PlPMM)‘PjPLL$‘PhPKK!‘PdPII‘PbPGO‘PaPFN‘P^PCOP\PAQ‰P[P@P†PXP=P‚PWP;P|PVP9PzPTP5PwPSP3PrPRP1PpPOO,‘PnPNN)‘PjPLL'PhPKK!‘PfPJJ‘PbPGOPaPFN‘P_PDQP\PAQP[P@O†PZP>Q‚PWP;OPVP9PzPUP7PwPSP3PtPRP1PpPP.‘PnPNN)‘PlPMM'PhPKK$‘PfPJJ‘PdPIIPaPFN‘P_PDQP^PCOP[P@O‰PZP>Q‚PXP=OPVP9P|PUP7PwPTP5PtPRP1PrPP.‘PnPNN,‘PlPMM'PjPLL$‘PfPJJ!‘PdPIIPbPGO‘P_PDQ‘P^PCOP\PAQ‰PZP>Q†PXP=OPWP;O|PUP7PzPTP5PtPSP3PrPP.QpPOO,QlPMM)‘PjPLL$‘PhPKK!‘PdPII‘PbPGO‘PaPFN‘P^PCOP\PAQ‰P[P@O†PXP=O‚PWP;O|PVP9PzPTP5PwPSP3PrPRP1PpPOO,QnPNN)‘PjPLL'PhPKK!‘PfPJJ‘PbPGOPaPFN‘P_PDQP\PAQP[P@O†PZP>Q‚PWP;OPVP9PzPUP7PwPSP3PtPRP1PpPP.QnPNN)‘PlPMM'PhPKK$‘PfPJJ‘PdPIIPaPFN‘P_PDQP^PCOP[P@O‰PZP>Q‚PXP=OPVP9P|PUP7PwPTP5PtPRP1PrPP.QnPNN,‘PlPMM'PjPLL$‘PfPJJ!‘PdPIIPbPGO‘P_PDQ‘P^PCOP\PAQ‰PZP>Q†PXP=OPWP;O|PUP7PzPTP5PtPSP3PrPP.‘PpPOO,‘PlPMM)‘PjPLL$‘PhPKK!‘PdPII‘PbPGO‘PaPFN‘P^PCOP\PAQ‰P[P@O†PXP=O‚PWP;O|PVP9PzPTP5PwPSP3PrPRP1PpPOO,‘PnPNN)‘PjPLL'PhPKK!‘PfPJJ‘PbPGOPaPFN‘P_PDQP\PAQP[P@O†PZP>‘P‚PWP;PPVP9PzPUP7PwPSP3PtPRP1PpPP.‘PnPNN)‘PlPMM'PhPKK$‘PfPJJ‘PdPIIPaPFN‘P_PD‘PP^PCPP[P@P‰PZP>‘P‚PXP=PPVP9P|PUP7PwPTP5PtPRP1PrPP.‘PnPNN,‘PlPMM'PjPLL$‘PfPJŠa‘PdPI‰[PbPGW‘P_PD‘S‘P^PCPP\PA‘P‰PZP>‘P†PXP=PPWP;P|PUP7PzPTP5PtPSP3PrPPPn‘PpPOl‘PlPMi‘PjPLŒd‘PhPK‹a‘PdPI‰^‘PbPGW‘PaPFŽS‘P^PCPP\PA‘P‰P[P@P†PXP=P‚PWP;P|PVPPyPzPTPPuPwPSPPsPrPRPPqPpPOl‘PlPLŒd‘PfPJŠ^‘PaPFŽS‘P^PCPPZP>‘P‚PWP;P|PTPPuPtPRPPqPnPNŽi‘PjPLŒd‘PdPI‰[PaPFŽS‘P\PA‘P‰PZP>‘P‚PVP9PzPTP5PrPP.‘PnPNN)‘PhPK‹a‘PdPI‰[P_PD‘PP\PA‘P‰PXP=PPVP9PwPSP3PrPP.‘PlPMM'PhPKK!‘PbPGO‘P_PD‘PP[P@P†PXP=P|PUP7PwPSP3PpPOO,‘PlPMM'PfPJJ‘PbPGO‘P^PCOP[P@O‚PWP;P|PUP7PtPRP1PpPOO)‘PjPLL$‘PfPJJPaPFN‘P^PCO‰PZP>Q‚PWP;OzPTP5PtPRP.‘PnPNN)‘PjPLL!‘PdPIIPaPFNP\PAQ‰PZP=OPVP9PzPTP3PrPP.QnPNN'PhPKK!‘PdPII‘P_PDQP\P@O†PXP=OPVP7PwPSP3PrPP,QlPMM'PhPJJQbPGO‘P_PCOP[P@O†PXP;O|PUP7PwPSP1PpPOO,QlPLL$QfPJJQbPFNQ^PCOM[P>Q‚PWP;O|PTP5PtPRP1PpPNN)QjPLL$QfPIIPaPFNQ^PAQIZP>QBVP9PzPTP5PtPP.QnPNN)QjPKK!QdPIIPaPDQP\PAQIXP=O?VP9PzPSP3PrPP.QnPMM'PhPKK!QbPGOQ_PDQP[P@OFXP=O?UP7P7SP3PrPOO,QlPMM'PfPJJQbPGOQ^PCOM[P@OFWP;O<UP7P4RP1P0OO,QjPLL$QfPJJQaPFNQ^PCOMZP>QBWP;O:TP5P4RP1P.NN)QjPLL$QdPIIPaPFNP\PAQIZP>Q?VP9P:TP5P2P.Q.NN)QhPKK!QdPIIQ_PDQP\PAQFXP=O?VP9P7SP3P2P,Q,MM'P(KKQbPGOQ_PDQM[P@OFXP=O<UP7P7SP1P0OO,Q,MM$Q&JJQbPGOQ^PCOM[P>QBWP;O<UP5P4RP1P0OO)Q*LL$QfPJJPaPFNQ^PAQIZP>QBWP9P:TP5P4RP.Q.NN)Q*LL!QdPIIPaPDQP\PAQIZP=O?VP9P:TP3P2P.Q.MM'P(KK!QdPGOQ_PDQP\P@OFXP=O?VP7P7SP3P2OO,Q,MM'PhPJJQbPGOQ_PCOM[P@OFWP;O<UP7P7RP1P0OO,Q,LL$QfPJJQbPFNQ^PCOMZP>QBWP;O<TP5P4RP1P0NN)QjPLL$QdPIIPaPFNQ\PAQIZP>QBVP9P:TP5P4P.QnPNN)QhPKK!QdPIIP_PDQP\PAQIXP=O?VP9P7SP3P2P.QlPMM'PhPKK!QbPGOQ_PDQP[P@OFXP=O<UP7P7SP3PpPOO,QlPMM'PfPJJQbPGOQ^PCOM[P@OBWP;O<UP7PtPRP1PpPOO,QjPLL$QfPJJPaPFNQ^PCOIZP>Q‚PWP;OzPTP5PtPRP1PnPNN)QjPLL!QdPIIPaPFNP\PAQ‰PZP>QPVP9PzPTP3PrPPPOi‘PjPK‹a‘PbPGS‘P\PA‘P†PXPP{P|PTPPuPrPPPl‘PlPLŒd‘PdPI‰W‘P_PCPPZP>‘PPVP7PwPRPPqPnPNŽgPfPJŠ[PaPD‘PP[P@P‚PWP9PzPSP3PpPOi‘PjPK‹a‘PbPGS‘P^PA‘P‰PXP=P|PUP5PrPP,‘PlPLL$‘PdPI‰W‘P_PCPPZP>‘PPVP7PwPRP1PnPNN'PhPJJ‘PaPFŽPP\P@P‚PWP9PzPSP3PpPOO)‘PjPKK!‘PbPGO‘P^PA‘P‰PXP=P|PUP5PtPP.‘PlPMM$‘PfPII‘P_PCOPZP>QPVP7PwPRP1PnPNN'PhPJJ‘PaPFNP\P@O†PWP;OzPTP3PrPOO)‘PjPKK!‘PbPGO‘P^PAQ‰PXP=O|PUP5PtPP.‘PlPMM$‘PfPIIP_PDQP[P>Q‚PVP7PwPRP1PnPNN'PhPJJ‘PaPFNP\P@O†PWP;OzPTP3PrPOO,QjPLL!‘PdPGO‘P^PAQ‰PXP=O|PUP5PtPP.QlPMM$QfPIIP_PDQP[P>Q‚PVP9PwPSP1PpPNN)QhPJJQaPFNP\P@O†PWP;OzPTP3PrPOO,QjPLL!QdPGOQ^PCO‰PZP=OPUP7PtPP.QlPMM$QfPIIP_PDQM[P>Q‚PVP9PwPSP1PpPNN)QhPKKQbPFNQ\PAQFWP;OzPTP3PrPOO,QjPLL!QdPGOQ^PCOIZP=OPUP7PtPRP.QnPMM'PfPJJP_PDQM[P>QBVP9PwPSP1PpPNN)QhPKKQbPFNQ\PAQFXP;O<TP5PrPP,QjPLL!QdPGOQ^PCOIZP=O?UP7PtPRP.QnPMM'PfPJJPaPDQP[P@OBVP9P7SP1PpPNN)QhPKKQbPFNQ\PAQFXP;O<TP5PrPP,QlPLL$QdPIIQ^PCOIZP=O?UP7P4RP.QnPMM'PfPJJPaPDQP[P@OBWP9P:SP3PpPOO)QhPKKQbPFNQ\PAQFXP;O<TP5PrPP,QlPLL$QdPIIQ_PCOMZP>Q?VP7P4RP.QnPMM'PfPJJPaPDQP[P@OBWP9P:SP3PpPOO)QjPKK!QbPGOQ^PAQFXP;O<TP5PrPP,QlPLL$QdPIIQ_PCOMZP>Q?VP7PwPRP1PnPNN'PhPJJPaPDQP[P@OBWP9P:SP3PpPOO)QjPKK!QbPGOQ^PAQIXP=O<UP5PtPP,QlPLL$QdPIIQ_PCOMZP>Q?VP7PwPRP1PnPNN'PhPJJQaPFNP\P@OFWP9PzPSP3PpPOO)QjPKK!QbPGOQ^PAQIXP=O|PUP5PtPP.QlPMM$QfPIIP_PCOMZP>QPVP7PwPRP1PnPNN'PhPJJQaPFNP\P@O†PWP;OzPTP3PrPOO,QjPKK!QbPGOQ^PAQ‰PXP=O|PUP5PtPP.QlPMM$QfPIIP_PDQP[P>Q‚PVP9PwPRP1PnPNN'PhPJJ‘PaPFNP\P@O†PWP;OzPTP3PrPOO,QjPLL!‘PdPGO‘P^PCO‰PXP=O|PUP5PtPPPNŽgPhPPŠŠ[P_PPƒP‰PXPP}P|PTPPsPpPNŽgPhPJŠ[P_PPƒP‰PXPP}P|PTPPsPpPNŽgPhPJŠ[P_PPƒP‰PXPP}P|PTPPsPpPNŽgPhPJŠ[P_PCP‰PXPP{P|PTPPsPpPNŽgPfPJŠ[P_PCP‰PXP;P|PTPPsPpPNŽgPfPJŠ[P_PCP‰PXP;P|PTPPsPpPNŽgPfPJŠ[P_PCP‰PXP;PzPTP3PpPNŽgPfPI‰[P_PCP‰PXP;PzPTP3PpPNŽgPfPI‰[P_PCP‰PXP;PzPTP3PpPNN'PfPI‰[P_PCP‰PXP;PzPTP3PpPNN'PfPII‘P_PCP‰PXP;PzPSP3PpPNN'PfPII‘P_PCP‰PXP;PzPSP3PpPNN'PfPII‘P_PCP‰PXP;PzPSP3PpPNN'PfPII‘P_PCO‰PXP;PzPSP1PpPNN'PfPII‘P^PCO‰PXP;PzPSP1PpPNN'PfPII‘P^PCO‰PXP;OzPSP1PpPNN'PfPII‘P^PCO‰PXP;OzPSP1PnPNN'PfPII‘P^PAQ‰PXP;OzPSP1PnPNN'PfPII‘P^PAQ‰PXP;OzPSP1PnPNN'PfPII‘P^PAQ‰PXP;OzPSP1PnPNN'PfPII‘P^PAQ†PXP;OzPSP1PnPMM'PfPII‘P^PAQ†PXP;OzPSP1PnPMM'PfPII‘P^PAQ†PXP;OzPSP1PnPMM'PfPII‘P^PAQ†PWP;OzPSP1PnPMM$QfPII‘P^PAQ†PWP;OzPSP1PnPMM$QfPII‘P^PAQ†PWP;OzPSP1PnPMM$QfPII‘P^PAQ†PWP;OzPSP1PnPMM$QdPII‘P^PAQ†PWP9PzPSP1PnPMM$QdPII‘P^PAQ†PWP9PzPSP1PnPMM$QdPIIQ^PAQ†PWP9PzPSP1PnPMM$QdPIIQ^PAQ†PWP9PwPSP1PnPMM$QdPGOQ^PAQ†PWP9PwPSP1PnPMM$QdPGOQ^PAQ†PWP9PwPSP1PnPMM$QdPGOQ^PAQ†PWP9PwPRP1PnPMM$QdPGOQ^PAQ†PWP9PwPRP1PnPMM$QdPGOQ^PAQ†PWP9PwPRP1PnPMM$QdPGOQ^PAQ†PWP9PwPRP1PnPMM$QdPGOQ\PAQ†PWP9PwPRP.QnPMM$QdPGO‘P\PAQ†PWP9PwPRP.QnPMM$QdPGO‘P\PAQ†PWP9PwPRP.QnPMM$QdPGO‘P\P@O†PWP9PwPRP.QlPMM$QdPGO‘P\P@O†PWP9PwPRP.QlPMM$QdPGO‘P\P@O†PWP9PwPRP.QlPMM$QdPGO‘P\P@O†PWP9PwPRP.QlPLL$QdPGO‘P\P@O‚PWP9PwPRP.QlPLL$‘PdPGO‘P\P@O‚PWP9PwPRP.QlPLL$‘PdPGO‘P\P@O‚PWP9PwPRP.QlPLL$‘PdPGO‘P\P@O‚PVP9PwPRP.QlPLL!‘PdPGO‘P\P@O‚PVP9PwPRP.‘PlPLL!‘PdPGO‘P\P@O‚PVP9PwPRP.‘PlPLL!‘PdPGO‘P\P@O‚PVP7PwPRP.‘PlPLL!‘PbPGO‘P\P@O‚PVP7PwPRP.‘PlPLL!‘PbPGO‘P\P@O‚PVP7PwPRP.‘PlPLL!‘PbPGO‘P\P@O‚PVP7PwPRPPPi‘PhPJŠ[P^PA‘P†PWPPyPtPPPl‘PjPK‹[P_PCP‰PXP9PwPRPPn‘PlPK‹^‘PaPD‘P‰PXP;PzPSPPn‘PlPLŒa‘PbPD‘PPZP=P|PSP1PnPMd‘PbPFŽPP[P>‘P|PTP3PpPMM$‘PdPGS‘P[P>‘PPUP5PpPNN'PfPI‰S‘P\P@P‚PVP5PrPOO)‘PhPII‘P^PA‘P‚PVP7PtPP)‘PhPJJP_PA‘P†PWP9PwPP,‘PjPKK‘P_PCO‰PXP;PwPRP.‘PlPKK‘PaPDQPXP;PzPSP1PlPLL!‘PbPFNPZP=O|PTP1PnPMM$‘PdPFNP[P>Q|PTP3PpPNN$‘PdPGO‘P\P>QPUP5PrPNN'PfPII‘P\P@O‚PVP7PrPOO)‘PhPII‘P^PAQ†PVP7PtPP,‘PhPJJP_PCO†PWP9PwPRP,QjPKK‘PaPCO‰PXP;OwPRP.QlPLL‘PaPDQPZP;OzPSP1PnPLL!QbPFNPZP=O|PTP3PnPMM$QdPFNP[P>QPTP3PpPNN'PdPGO‘P\P@OPUP5PrPOO'PfPIIQ^P@O‚PVP7PrPOO)QhPJJQ^PAQ†PWP7PtPP,QjPJJP_PCO‰PWP9PwPRP.QjPKKQaPCOIXP;OzPRP.QlPLL!QaPDQMZP=OzPSP1PnPMM!QbPFNP[P=O|PTP3PnPMM$QdPGOP[P>Q?UP3PpPNN'PfPGOQ\P@OBUP5PrPOO)QfPIIQ^P@OBVP7PtPOO)QhPJJP^PAQFWP9PtPP,QjPKKP_PCOIXP9PwPRP.QjPKKQaPDQIXP;O:SP.QlPLL!QbPDQMZP=O<SP1PnPMM$QbPFNP[P=O<TP3PpPMM$QdPGOQ[P>Q?UP5PpPNN'PfPIIQ\P@OBVP5PrPOO)QfPIIQ^PAQBVP7P4P)QhPJJP_PAQFWP9P7P,QjPKKQ_PCOIXP9P7RP.QlPKKQaPDQMXP;O:SP1PlPLL!QbPFNMZP=O<TP1PnPMM$QbPFNP[P>Q<TP3PpPNN$QdPGOQ\P>Q?UP5PrPNN'PfPIIQ\P@OBVP5PrPOO)QhPIIQ^PAQFVP7PtPP,QhPJJP_PCOFWP9P7RP,QjPKKQ_PCOIXP;O7RP.QlPLLQaPDQMZP;O:SP1PnPLL!QbPFNPZP=O<TP1PnPMM$QdPFNP[P>Q?TP3PpPNN'PdPGOQ\P@O?UP5PrPOO'PfPIIQ\P@OBVP7PrPOO)QhPJJQ^PAQFWP7PtPP,QjPJJP_PCOIWP9PwPRP,QjPKKQaPCOIXP;OzPRP.QlPLL!QaPDQMZP=OzPSP1PnPMM!QbPFNPZP=O|PTP3PnPMM$QdPGOP[P>QPUP3PpPNN'PfPGOQ\P@O‚PUP5PrPOO'PfPII‘P^P@O‚PVP7PtPOO)QhPJJP^PAQ†PWP9PtPP,QjPKKP_PCO‰PWP9PwPRP.QjPKK‘PaPDQ‰PXP;OzPSP.QlPLL!‘PbPDQPZP=O|PSP1PPPi‘PfPP‰‰S‘P\PP~‘PPTPPqPnPLŒa‘PaPP„‘P‰PXPPyPtPPPi‘PhPI‰W‘P\PP€PPTPPsPnPMa‘PbPD‘PPXPPyPwPPPl‘PhPJŠW‘P^PP€PPUPPsPpPMd‘PbPFŽPPXPP{PwPRPPl‘PjPJŠ[P^P@P‚PUPPuPpPNŽd‘PdPFŽPPZP;PzPRPPn‘PjPK‹[P^PA‘P‚PVP5PrPNŽgPdPFŽPPZP=PzPSP.‘PlPK‹[P_PA‘P†PVP7PrPOgPdPGPP[P=P|PSP1PlPK‹^‘P_PCP†PWP7PtPOO'PfPGS‘P[P>‘P|PSP1PlPLL‘PaPCP‰PWP7PtPOO)‘PfPI‰S‘P\P>‘P|PTP1PnPLL!‘PaPD‘P‰PWP9PtPP)‘PhPII‘P\P>‘PPTP3PnPMM!‘PbPDQ‰PXP9PwPP,‘PhPJJ‘P\P@OPUP3PpPMM$‘PbPDQPXP;PwPRP,‘PjPJJ‘P^P@O‚PUP5PpPNN$‘PbPFNPZP;OzPRP.‘PjPJJP^PAQ‚PVP5PrPNN$‘PdPFNPZP=OzPSP.‘PjPKKP_PAQ†PVP7PrPNN'PdPGOP[P=OzPSP.‘PlPKK‘P_PCO†PVP7PrPOO'PfPGO‘P[P=O|PSP1PlPLL‘PaPCO†PWP7PtPOO)‘PfPII‘P[P>Q|PTP1PnPLL!‘PaPCO‰PWP9PtPP)QhPII‘P\P>QPTP3PnPMM!‘PaPDQ‰PXP9PwPP,QhPII‘P\P@OPUP3PpPMM!QbPDQPXP;OwPRP,QhPJJ‘P^P@O‚PUP5PpPMM$QbPFNPZP;OzPRP,QjPJJP^PAQ‚PVP5PpPNN$QdPFNPZP;OzPRP.QjPKKP_PAQ‚PVP5PrPNN'PdPGOPZP=OzPSP.QlPKKQ_PAQ†PVP7PrPOO'PfPGOP[P=O|PSP1PlPLLQ_PCO†PWP7PtPOO)QfPGOQ[P>Q|PTP1PnPLLQaPCO‰PWP9PtPP)QfPIIQ\P>QPTP3PnPLL!QaPDQ‰PXP9PwPP)QhPIIQ\P@OPUP3PnPMM!QbPDQPXP;OwPP,QhPJJQ^P@O‚PUP3PpPMM$QbPFNPXP;OwPRP,QjPJJP^P@O‚PUP5PpPNN$QdPFNPZP;OzPRP.QjPKKP^PAQ‚PVP5PrPNN'PdPFNPZP=OzPSP.QlPKKP_PAQ†PVP7PrPOO'PdPGOP[P=O|PSP1PlPKKQ_PCO†PWP7PtPOO'PfPGO‘P[P>Q|PTP1PlPLLQaPCO‰PWP9PtPOO)QfPII‘P\P>QPTP1PnPLL!QaPDQ‰PXP9PtPP)QhPII‘P\P@OPTP3PnPMM!QbPDQ‰PXP9PwPP,QhPJJ‘P\P@OPUP3PpPMM$‘PbPDQPXP;OwPRP,QjPJJ‘P^P@O‚PUP5PpPNN$‘PbPFNPZP;OzPRP.QjPJJP^PAQ‚PVP5PrPNN$‘PdPFNPZP=OzPSP.‘PjPKKP_PAQ†PVP7PrPNN'PdPGOP[P=O|PSP.‘PlPKK‘P_PCO†PWP7PrPOO'PfPGO‘P[P>Q|PSP1PlPLL‘PaPCO‰PWP7PtPOO)‘PfPII‘P\P>Q|PTP1n‘PjPJŠW‘P\P>‘P|PSPPn‘PjPJŠ[P^P@PPTPPqPlPK‹[P^P@P‚PUP3PnPLŒ^‘P_PA‘P‚PUP3PpPMa‘PaPCP†PVP5PpPMa‘PbPD‘P‰PWP7PrPNN$‘PbPD‘P‰PXP9PtPOO'PdPFŽPPXP9PtPP)‘PfPGPPZP;PwPP)‘PfPII‘P[P=PzPRP,‘PhPII‘P[P>‘P|PSP.‘PjPJJ‘P\P>‘P|PSP1PlPKKP^P@OPTP1PlPKK‘P_PAQ‚PUP3PnPLL‘P_PAQ†PVP5PpPMM!‘PaPCO†PVP5PrPNN$‘PbPDQ‰PWP7PrPNN$‘PdPFNPXP9PtPOO'PdPFNPZP;OwPP)‘PfPGOPZP;OwPRP,QhPII‘P[P=OzPRP,QhPJJ‘P\P>Q|PSP.QjPJJ‘P\P@OPTP1PlPKKP^P@OPTP3PnPLLQ_PAQ‚PUP3PnPLL!QaPCO†PVP5PpPMM!QaPCO‰PWP7PrPNN$QbPDQ‰PWP9PtPOO'PdPFNMXP9PtPOO)QfPGOPZP;OwPP)QfPGOQ[P=OzPRP,QhPIIQ[P=O|PSP.QjPJJQ\P>Q|PSP.QlPKKP^P@O?TP1PlPKKP_PAQBUP3PnPLLQ_PAQBVP5PpPMM!QaPCOFVP5PpPNN$QbPDQIWP7PrPNN$QbPFNMXP9P4OO'PdPFNMXP;O7P)QfPGOPZP;O7P,QhPIIQ[P=O:RP,QhPIIQ\P>Q<SP.QjPJJQ\P>Q?TP1PlPKKP^P@O?TP1P.LLQ_PAQBUP3P.LLQaPCOFVP5P0MM!QaPCOFWP7P2NN$QbPDQIWP7P2OO'PdPFNMXP9P4OO'PdPGOPZP;O7P)QfPGOPZP=O:RP,QhPIIQ[P=O:RP.Q*JJQ\P>Q<SP.Q*JJP^P@O?TP1P,KKP^P@OBUP3P.LLQ_PAQBUP3P0MM!QaPCOFVP5P0MM!QbPDQIWP7P2NN$QbPDQIXP9P4OO'PdPFNMXP9P4P)QfPGOPZP;O7P)QfPIIQ[P=O:RP,Q(IIQ\P>Q<SP.Q*JJQ\P>Q<TP1P,KKP^P@O?TP1P,LLQ_PAQBUP3P.LLQ_PCOFVP5P0MM!QaPCOFVP7P2NN$QbPDQIWP7P2NN'PdPFNMXP9P4OO'PdPFNPZP;O7P)QfPGOPZP;O:RP,QhPIIQ[P=O:RP,QjPJJQ\P>Q<SP.QjPJJQ^P@O?TP1PlPKKP^P@O?UP3PnPLLQ_PAQBUP3PnPMM!QaPCOFVP5PpPMM!QaPDQIWP7PrPNN$QbPDQIWP9PtPOO'PdPFNMXP9PtPOO)QfPGOPZP;OwPP)QfPGOQ[P=OzPRP,QhPIIQ[P=O|PSP.QjPJJQ\P>Q|PSP.QlPKKP^P@OPTP1PlPKKP_PAQ‚PUP3PnPLLQ_PAQ‚PVP5PpPMM!QaPCO†PVP5Ppl‘PhPI‰S‘P[PP{PwPPPi‘PfPFŽPPXPPyPtPNŽd‘PbPD‘P‰PVPPuPpPMa‘P_PA‘P‚PUPPsPlPK‹[P^P>‘P|PSPPn‘PjPI‰S‘P[P=PzPPPi‘PfPGPPXP9PtPOgPbPD‘P‰PWP7PpPMa‘PaPCP‚PUP3PnPLŒ[P^P@PPTP.‘PjPJŠW‘P[P=PzPRP,‘PfPGPPZP;PtPOO'PdPFŽP‰PWP7PrPNŽa‘PaPCP†PVP3PnPLŒ^‘P_P@PPTP1PlPJŠW‘P\P>‘P|PRP,‘PhPI‰PPZP;PwPP'PdPFŽPPXP7PrPNN$‘PbPCP†PVP5PpPLL‘P_PA‘P‚PTP1PlPKKP\P>‘P|PSP.‘PhPII‘P[P=PwPP)‘PfPFNPXP9PtPNN$‘PbPDQ‰PVP5PpPMM!‘P_PA‘P‚PUP3PlPKKP^P@P|PSP.‘PjPJJ‘P[P=PzPRP)‘PfPGOPZP9PtPOO'PbPDQ‰PWP7PpPMM!‘PaPCO‚PUP3PnPLLP^P@OPTP.‘PjPJJ‘P\P=OzPRP,‘PhPGOPZP;PwPOO'PdPFNPWP7PrPNN!‘PaPCO†PVP3PnPLL‘P_P@OPTP1PlPJJ‘P\P>Q|PRP,‘PhPII‘PZP;OwPP)‘PdPFNPXP9PrPNN$‘PbPDQ†PVP5PpPLL‘P_PAQ‚PTP1PlPKKP\P>Q|PSP.‘PhPII‘P[P=OwPP)‘PfPGOPXP9PtPOO$‘PbPDQ‰PWP5PpPMM!‘PaPAQ‚PUP3PlPKKP^P@O|PSP.‘PjPJJ‘P[P=OzPRP)‘PfPGOPZP9PtPOO'PdPDQ‰PWP7PrPMM!‘PaPCO†PUP3PnPLL‘P^P@OPTP.‘PjPJJ‘P\P=OzPRP,‘PhPGOPZP;OwPOO'PdPFNPWP7PrPNN$‘PaPCO†PVP5PnPLL‘P_PAQPTP1PlPKK‘P\P>Q|PRP,‘PhPII‘PZP;OwPP)‘PdPFNPXP9PrPNN$‘PbPDQ†PVP5PpPMM‘P_PAQ‚PUP1PlPKKP^P>Q|PSP.‘PjPII‘P[P=OwPP)‘PfPGOPXP9PtPOO$‘PbPDQ‰PWP5PpPMM!‘PaPAQ‚PUP3PnPKKP^P@OPSP.‘PjPJJ‘P[P=OzPRP,‘PfPGOPZP9PtPOO'PdPDQ‰PWP7PrPMM!‘PaPCO†PUP3PnPLL‘P^P@OPTP1PjPJJ‘P\P>‘PzPRP,‘PhPIIPZP;PwPP'PdPFNPWP7PrPNN$‘PaPCP†PVP5PnPLL‘P_PA‘PPTP1PlPKK‘P\P>‘P|PSP,‘PhPII‘P[P;PwPP)‘PfPFŽPPXP9PrPNN$‘PbPD‘P†PVP5PpPMM‘P_PA‘P‚PUP1PlPKKP^P>‘P|PSP.‘PjPI‰S‘P[P=PzPP)‘PfPGPPXP9PtPOO'PbPD‘P‰PWP5PpPMa‘PaPA‘P‚PUP3PnPK‹[P^P@PPSP.‘PjPJŠW‘P[P=PzPRPPl‘PfPGPPZP;PtPOgPdPFŽP‰PWP7PrPNŽa‘PaPCP†PUP3PnPLŒ^‘P^P@PPTPPqPjPJŠW‘P\P>‘PzPRPPl‘PhPI‰PPZP;PwPPPgPdPFŽPPXPPwPrPNŽd‘PbPCP†PVPPuPpPLŒ^‘P_PA‘PPTPPqPlPK‹W‘P\PP~‘P|PSPPl‘PhPGPPXPPyPrPMa‘P_PA‘PPTPPn‘PhPI‰PPZPPyPtPNŽd‘PaPA‘P‚PTPPqPjPJŠS‘PZP;PtPOd‘PbPCP†PUPPqPlPJŠW‘P[P=PwPPPgPbPD‘P†PVP3PnPK‹W‘P\P=PzPPPi‘PdPFŽP‰PVP5PnPLŒ[P^P>‘PzPRP)‘PfPFŽPPWP7PpPLŒ^‘P^P@P|PSP,‘PfPGPPXP7PrPMa‘P_P@PPSP.‘PhPI‰PPXP9PrPNN!‘PaPA‘P‚PTP.‘PjPI‰S‘PZP;PtPNN$‘PaPCP‚PUP1PlPJJ‘P[P;PwPOO'PbPCP†PUP3PlPKK‘P\P=PwPP'PdPDQ‰PVP3PnPKKP\P>‘PzPRP)‘PdPFN‰PWP5PpPLLP^P>‘P|PRP,‘PfPGOPWP7PpPMM‘P_P@O|PSP,‘PhPGOPXP9PrPMM!‘P_PAQPTP.‘PhPIIPZP9PtPNN$‘PaPAQ‚PTP1PjPJJ‘PZP;OtPOO$‘PbPCO†PUP1PlPJJ‘P[P=OwPP'PbPDQ†PVP3PnPKK‘P\P=OzPP)‘PdPFN‰PVP5PnPLLP^P>QzPRP)‘PfPFNPWP7PpPLL‘P^P@O|PSP,‘PfPGOPXP7PrPMM!‘P_P@OPSP.‘PhPIIPXP9PrPNN!‘PaPAQ‚PTP.QjPII‘PZP;OtPNN$‘PaPCO‚PUP1PlPJJ‘P[P;OwPOO'PbPCO†PUP3PlPKK‘P\P=OwPP'PdPDQ‰PVP3PnPKKP\P>QzPRP)QdPFN‰PWP5PpPLLP^P>Q|PRP,QfPGOPWP7PpPMM‘P_P@O|PSP,QhPGOPXP9PrPMM!‘P_PAQPTP.QhPIIPZP9PtPNN$‘PaPAQ‚PTP1PjPJJ‘PZP;OtPOO$‘PbPCO†PUP1PlPJJ‘P[P=OwPP'PbPDQ†PVP3PnPKK‘P\P=OzPP)QdPFN‰PVP5PnPLLP^P>QzPRP)QfPFNPWP7PpPLL‘P^P@O|PSP,QfPGOPXP7PrPMM!‘P_P@OPSP.QhPIIPXP9PrPNN!‘PaPAQ‚PTP.QjPII‘PZP;OtPNN$‘PaPCO‚PUP1PlPJJ‘P[P;OwPOO'PbPCO†PUP3PlPKK‘P\P=OwPP'PdPDQ‰PVP3PnPKKP\P>QzPRP)‘PdPFN‰PWP5PpPLLP^P>Q|PRP,‘PfPGOPWP7PpPMM‘P_P@O|PSP,‘PhPGOPXP9PrPMM!‘P_PAQPTP.‘PhPIIPZP9PtPNN$‘PaPAQ‚PTP1PjPJJ‘PZP;OtPOO$‘PbPCO†PUP1PlPJJ‘P[P=OwPP'PbPDQ†PVP3PnPKK‘P\P=PzPP)‘PdPFN‰PVP5PnPLLP^P>‘PzPRP)‘PfPFNPWP7PpPLL‘P^P@P|PSP,‘PfPGOPXP7PrPMM!‘P_P@PPSP.‘PhPIIPXP9PrPNN!‘PaPA‘P‚PTP.‘PjPII‘PZP;PtPNN$‘PaPCP‚PUP1PlPJJ‘P[P;PwPOO'PbPCP†PUP3PlPK‹W‘P\P=PwPP'PdPD‘P‰PVP3PnPK‹[P\P>‘PzPRP)‘PdPFŽP‰PWP5PpPLŒ[P^P>‘P|PRP,‘PfPGPPWP7PpPM^‘P_P@P|PSPPPd‘PaPP‘PPSPPl‘PfPP†ŽP‰PUPPqPjPP‰‰PPXPPwPpPLŒ[P[PP{PtPNŽa‘P_PP€P|PRPPgPbPCP‚PTPPn‘PhPGPPWPPsPlPJŠS‘PZPPyPrPM^‘P^P=PwPOd‘PaPA‘PPSPPl‘PdPD‘P†PUP1PjPI‰PPXP7PnPK‹W‘P[P;PtPNŽa‘P_P>‘PzPP'PbPCP‚PTP.‘PhPFŽP‰PVP3PlPJJ‘PZP9PrPLLP\P=PwPOO$‘PaPA‘P|PRPOa‘P_P@P|PRPPi‘PdPD‘P†PUPPn‘PhPGPPWPPuPnPK‹W‘PZP9PrPM^‘P^P>‘PzPPPgPaPA‘PPSPPl‘PfPFŽP‰PVP1PjPI‰PPXP7PpPLŒ[P\P;PtPNN!‘P_P@P|PRP)‘PdPCP‚PTP.‘PhPGPPWP5PlPJJ‘PZP9PrPMM‘P^P>‘PwPOO$‘PaPA‘PPSP,‘PfPDQ†PUP1PjPIIPXP7PpPKK‘P[P;PtPNN!‘P_P@P|PP'PbPCO‚PTP.‘PhPGO‰PVP3PlPJJ‘PZP9PrPMMP\P=OwPOO$‘PaPAQPSP)‘PdPDQ†PUP1PjPIIPWP5PnPKK‘P[P;OtPNN!‘P^P>QzPP'PbPCO‚PTP,‘PfPFN‰PVP3PlPJJ‘PZP7PpPLLP\P=OwPOO$‘PaP@O|PRP)QdPDQ†PUP1PhPGOPWP5PnPKK‘P[P;OrPMM‘P^P>QzPP'PbPAQPSP,QfPFN‰PVP3PlPIIPXP7PpPLLP\P=OwPNN!Q_P@O|PRP)QdPDQ‚PTP.QhPGOPWP5PnPKK‘PZP9PrPMMQ^P>QzPP$QaPAQPSP,QfPFN‰PUP1PjPIIPXP7PpPLLP[P;OtPNN!Q_P@O|PRP'PbPCO‚PTP.QhPGOPWP3PlPJJ‘PZP9PrPMMQ^P=OwPOO$QaPAQPSP,QdPDQ†PUP1PjPIIPXP7PnPKK‘P[P;OtPNN!Q_P>QzPP'PbPCO‚PTP.QhPFN‰PVP3PlPJJ‘PZP9PrPLLP\P=OwPOO$QaPAQ|PRP)QdPDQ†PUP1PjPIIPWP5PnPKK‘P[P;OtPMM‘P^P>QzPP'PbPCO‚PSP,QfPFN‰PVP3PlPJJ‘PXP7PpPLLP\P=OwPOO!‘P_P@O|PRP)‘PdPDQ†PUP.QhPGOPWP5PnPKK‘P[P9PrPMM‘P^P>QzPP'PaPAQPSP,‘PfPFN‰PVP3PjPIIPXP7PpPLLP\P;OtPNN!‘P_P@O|PRP)‘PdPCO‚PTP.‘PhPGOPWP5PnPJJ‘PZP9PrPMM‘P^P>‘PwPOO$‘PaPA‘PPSP,‘PfPFN†PUP1PjPIIPXP7PpPKK‘P[P;PtPNN!‘P_P@P|PPhPGOPWP5PnPJJ‘PZP9PrPMM‘P^P>QzPOO$‘PaPAQPSP,QfPFN†PUP1PjPIIPXP7PpPLL‘P[P;OtPNN!‘P_P@O|PRP'PbPCO‚PTP.‘PhPGOPVP3PlPJJ‘PZP9PrPMM‘P\P=PwPOO$‘PaPA‘PPSP)‘PdPD‘P†PUP1PjPIIPXP5PnPKK‘P[P;PtPNN!‘P_P>‘PzPP'PbPCP‚PTP.‘PfPFŽP‰PVP3l‘PdPP„‘P‚PSPPi‘PbPPƒPPRPPgPbPP‘P|PPPd‘PaPP€PzPOd‘P_PP~‘PwPNŽa‘P^PP}PtPNŽ^‘P\PP{PrPM[P[PPyPrPLŒW‘PZP7PpPK‹S‘PXP7PnPJŠPPXP5PlPI‰PPWP3PjPGPPVP1PhPFŽP‰PUP.‘PfPFŽP†PTP,‘PdPD‘P‚PSP)‘PdPCPPRP'PbPA‘P|PP'PaP@PzPP$‘P_P>‘PwPOO!‘P^P=PwPNN‘P\P;PtPMMJŠPPWPPsPjPI‰PPVPPqPjPGP‰PUPPn‘PhPFŽP†PTPPn‘PfPD‘P‚PSPPl‘PdPCPPSPPi‘PbPA‘PPRPPgPaP@P|PPPd‘P_P@PzPOa‘P^P>‘PwPNŽ^‘P^P=PtPM[P\P;PrPLŒ[P[P9PpPK‹W‘PZP7PnPK‹S‘PXP5PlPJŠPPWP3PlPI‰PPVP3PjPGP‰PUP1PhPFŽP†PUP.‘PfPD‘P‚PTP,‘PdPCP‚PSP)‘PbPA‘PPRP'PaPA‘P|PP$‘P_P@PzPOO!‘P_P>‘PwPNN‘P^P=PtPMM‘P\P;PrPMMP[P9PpPLL‘PZP7PpPKK‘PXP5PnPJJPWP5PlPIIPVP3PjPGO‰PVP1PhPFN†PUP.‘PfPDQ†PTP,‘PdPDQ‚PSP)‘PbPCOPRP'PbPAQ|PP$‘PaP@OzPOO$‘P_P>QwPNN!‘P^P=OtPNN‘P\P;OrPMMP[P9PrPLL‘PZP7PpPKK‘PXP7PnPJJPXP5PlPIIPWP3PjPGOPVP1PhPFN‰PUP.QfPFN†PTP,QdPDQ‚PSP)‘PdPCOPRP'PbPAQ|PP'PaP@OzPP$‘P_P>QwPOO!‘P^P=OwPNN‘P\P;OtPMMP[P;OrPLL‘PZP9PpPKK‘PZP7PnPJJPXP5PlPIIPWP3PjPGOPVP1PhPGO‰PUP.QhPFN†PTP,QfPDQ‚PSP,‘PdPCOPRP)‘PbPAQ|PRP'PaP@OzPP$‘P_P>QzPOO!‘P^P=OwPNN‘P\P=OtPMMP[P;OrPLL‘P[P9PpPKK‘PZP7PnPJJ‘PXP5PlPJJPWP3PjPIIPVP1PjPGO‰PUP.‘PhPFN†PTP.‘PfPDQ‚PSP,‘PdPCOPSP)‘PbPAQPRP'PaP@O|PP$‘P_P@OzPOO!‘P^P>‘PwPNN‘P^P=PtPMMP\P;PrPLLP[P9PpPKK‘PZP7PnPKK‘PXP5PlPJJPWP3PlPIIPVP3PjPGO‰PUP1PhPFŽP†PUP.‘PfPD‘P‚PTP,‘PdPCP‚PSP)‘PbPA‘PPRP'PaPA‘P|PP$‘P_P@PzPOO!‘P_P>‘PwPNN‘P^P=PtPM^‘P\P;PrPM[P[P9PpPLŒW‘PZP7PpPK‹S‘PXP5PnPJŠPPWP5PlPI‰PPVPpPKK‘PZP7PnPKK‘PXP5PlPJJPWP3PlPIIPVP3PjPGO‰PUP1PhPFN†PUP.‘PfPD‘P‚PTP,‘PdPCP‚PSP)‘PbPA‘PPRP'PaPA‘P|PP$‘P_P@PzPOO!‘P_P>‘PwPNN‘P^P=PtPM^‘P\P;PrPM[P[P9PpPLŒW‘PZP7PpPK‹S‘PXP5PnPJŠPPWP5PlPI‰PPVPPsPjPGP‰PVPPqPhPFŽP†PUPPn‘PfPD‘P†PTPPl‘PbPA‘P|POa‘P\PP{PpPK‹PPWPPqPhPD‘P‚PSPPgPaP>‘PwPM[PZP7PlPI‰PPUP.‘PdPCP|PPPa‘P^P;PrPLŒS‘PXP3PjPFŽP†PSP)‘PaP@PwPNN‘P[P9PnPJŠPPVP.‘PfPCPPRP$‘P_P=PtPLL‘PXP5PjPGO‰PTP,‘PbPA‘PzPOO‘P\P9PpPKKPWP1PhPDQ‚PRP'P_P>QtPMMPZP7PlPII‰PUP,‘PdPP=PrPLŒS‘PXP3PjPFŽP†PTP)‘PbP@PzPNŽ^‘P[P9PnPJŠPPVP1PfPD‘PPRP$‘P_P=PtPLŒW‘PZP5PlPGP‰PTP,‘PbPA‘PzPOO!‘P\P;PpPKKPWP1PhPD‘P‚PRP'PaP>‘PwPMMPZP7PlPII‰PUP.‘PdPCP|PP!‘P^P;PrPKK‘PXP3PjPFN†PSP)‘PaP@OwPNNP[P9PnPJJPVP.‘PfPCOPP$‘P_P=OtPLL‘PXP5PjPGO†PTP,‘PbPAQzPOO‘P\P9PpPJJPWP1PhPDQ‚PRP'P_P>QtPMM‘PZP7PlPII‰PUP,‘PdPAQ|POO!‘P^P;OrPKK‘PWP3PhPFN‚PSP)‘PaP@OwPNNP[P7PnPIIPUP.QfPCOPP$‘P^P=OrPLL‘PXP5PjPGO†PTP)QbP@OzPNN‘P\P9PpPJJPVP1PfPDQPRP'P_P>QtPMM‘PZP5PlPGO‰PTP,QdPAQ|POO!‘P\P;OpPKKPWP3PhPFN‚PSP'PaP>QwPMMP[P7PnPIIPUP.QdPCO|PP!Q^P=OrPjLL‘PXP3PjPFN†PSP)QbP@OzPNN‘P[P9PnPJJPVP1PfPDQPRP$Q_P=OtPLL‘PXP5PlPGO‰PTP,QbPAQzPOO‘P\P;OpPKKPWP1PhPDQ‚PRP'PaP>QwPMMPZP7PlPII‰PUP.QdPCO|PP!‘P^P;OrPKK‘PWP3PjPFN†PSP)QaP@OwPNNP[P9PnPJJPVP.QfPCOPP$‘P_P=OtPLL‘PXP5PjPGO†PTP)‘PbPAQzPOO‘P\P9PpPJJPVP1PhPDQ‚PRP'P_P>QtPMM‘PZP7PlPII‰PUP,‘PdPAQ|POO!‘P\P;OrPKK‘PWP3PhPFN‚PSP'PaP@OwPNNP[P7PnPIIPUP.‘PfPCOPP$‘P^P=PrPLL‘PXP5PjPGO†PTP)‘PbP@PzPNN‘P[P9PpPJJPVP1PfPD‘PPRP$‘P_P>‘PtPMM‘PZP5PlPGP‰PTP,‘PdPA‘P|POO!‘P\P;PpPK‹PPWP1PhPFŽP‚PSP'PaP>‘PwPM[PZP7PnPI‰PPUP.‘PdPCP|PPPa‘P^P=PrPLŒS‘PX;OrPKK‘PWP3PhPFN‚PSP)‘PaP@OwPNNP[P7PnPIIPUP.‘PfPCOPP$‘P^P=PrPLL‘PXP5PjPGO†PTP)‘PbP@PzPNN‘P\P9PpPJJPVP1PfPD‘PPRP'P_P>‘PtPMW‘PZP5PlPGP‰PTP,‘PdPA‘P|POa‘P\P;PpPK‹PPWP3PhPFŽP‚PSPPgPaP>‘PwPM[P[P7PnPI‰PPUPPn‘PdPCP|PPPa‘P^PP}PrPK‹PPVPPn‘PdP@PwPMW‘PXPPsPhPCP|PO^‘P[P7PjPFŽP‚PRPPd‘P^P;PnPI‰P‰PTP)‘PaP>‘PrPK‹PPVP.‘PdP@PwPMW‘PXP3PhPCP|POO‘P[P7PlPFŽP‚PRP$‘P^P;PpPII‰PTP)‘PaP>‘PrPKKPVP.‘PdPA‘PwPMM‘PXP3PhPDQ|POO‘P[P7PlPFN‚PRP$‘P^P;PpPII‰PTP)‘PaP>QtPKKPVP.‘PdPAQ9PnPI‰P‰PTPPi‘P_P=PrPK‹PPVP.‘PbP@PwPMW‘PXP1PfPCP|POO‘P[P5PjPFŽP‚PRP$‘P^P9PnPI‰P‰PTP)‘P_P=PrPKKPVP.‘PbP@PwPMM‘PXP3PfPCP|POO‘P[P7PjPFN‚PRP$‘P^P9PnPII‰PTP)‘PaP=PrPKKPVP.‘PdP@PwPMM‘PXP3PhPCO|POO‘P[P7PjPFN‚PRP$‘P^P;PnPII‰PTP)‘PaP>QrPKKPVP.‘PdP@OwPMM‘PXP3PhPCO|POO‘P[P7PlPFN‚PRP$‘P^P;OpPII‰PTP)‘PaP>QrPKKPVP.‘PdPAQwPMM‘PXP3PhPDQ|POO‘P[P7PlPFN‚PRP$‘P^P;OpPII‰PTP)‘PaP>QtPKKPVP.QdPAQzPMM‘PXP3PhPDQ|POO‘P[P7PlPGO‚PRP$‘P^P;OpPJJ‰PTP)QaP>QtPKKPVP.QdPAQzPMM‘PXP3PhPDQPOO‘P[P7PlPGO†PRP$Q^P;OpPJJ‰PTP)QaP>QtPLLPVP.QdPAQzPNN‘PXP3PhPDQPP‘P[P7PlPGO†PRP$Q^P;OpPJJPTP)QaP>QtPLL‘PVP.QdPAQzPNN‘PXP3PhPDQPP‘P[P7PlPGO†PSP$Q^P;OpPJJPUP)QaP>QtPLL‘PVP.QdPAQzPNNPXP3PhPDQPP!‘P[P7PlPGO†PSP$‘P^P;OpPJJPUP)QaP>QtPLL‘PWP.QdPAQzPNNPZP3PhPDQPP!‘P[P7PlPGO†PSP'P^P;OpPJJPUP,‘PaP>QtPLL‘PWP.‘PdPAQzPNNPZP3PhPDQPP!‘P\P7PlPGO†PSP'P_P;OpPJJPUP,‘PaP>QtPLL‘PWP1PdPAQzPNNPZP5PhPDQPP!‘P\P7PlPGO†PSP'P_P;PpPJJPUP,‘PbP>‘PtPLL‘PWP1PfPA‘PzPNNPZP5PhPD‘PPP!‘P\P9PlPGP†PSP'P_P=PpPJŠPPUP,‘PbP@PtPLL‘PWP1PfPA‘PzPNNPZP5PjPD‘PPP!‘P\P9PnPGP†PSP'P_P=PpPJŠPPUP,‘PbP@PtPLŒS‘PWP1PfP‰PTP'P_P=OrPKKPVP,‘PbP@OwPMM‘PXP1PfPCO|POO‘PZP5PjPFN‚PRP$‘P\P9PnPII‰PTP)‘P_P=PrPKKPVP.‘PbP@PwPMM‘PXP1PfPCP|POO‘P[P5PjPFŽP‚PRP$‘P^P9PnPI‰P‰PTP)‘P_P=PrPK‹PPVP.‘PbP@PwPMW‘PXP3PfPCP|PO^‘P[P7PjPFŽP‚PRPPd‘P^P9PnPI‰P‰PTPPi‘PaP=PrPK‹PPTPPgP^P9PnPGP‚PPP^‘PZPPsPhPCPzPMS‘PVPPl‘PbP>‘PrPJŠP‰PSPPd‘P^P9PlPFŽPPO^‘PZP3PfPA‘PwPLŒS‘PVP,‘PaP=PpPI‰P‰PSP$‘P\P7PjPD‘PPOOPXP1PdPA‘PwPLLPUP)‘P_P=PpPII†PRP!‘P[P7PjPDQ|PNN‘PWP1PdP@OtPKKPUP)‘P_P;PnPGO‚PRP!‘P[P5PhPCOzPNN‘PWPPPa‘P[P5PjPD‘P|PNŽW‘PWP1PdP@PtPK‹PPTP)‘P_P;PnPGP‚PP!‘P[P5PhPCPzPMM‘PWP.‘PbP>‘PrPK‹PPTP'P^P9PlPGP‚PP‘PZP3PfPCPzPMM‘PVP,‘PaP>‘PrPJJ‰PSP$‘P^P9PlPFNPOOPZP3PfPAQwPLLPVP,‘PaP=PpPII‰PSP$‘P\P7PjPDQPOOPXP1PdP@OwPLLPUP)‘P_P;OpPII†PRP!‘P[P7PjPDQ|PNN‘PWP1PdP@OtPKKPTP)‘P_P;OnPGO‚PP!‘P[P5PhPCOzPNN‘PWP.QbP>QrPKKPTP'P^P9PlPGO‚PP‘PZP3PfPCOzPMM‘PVP,QbP>QrPJJ‰PSP$‘P^P9PlPFNPOOPZP3PfPAQwPLL‘PVP,QaP=OpPII‰PSP$Q\P7PjPDQPOOPXP1PdP@OwPLLPUP)Q_P=OpPII†PRP!Q[P7PjPDQ|PNN‘PWP1PdP@OtPKKPTP)Q_P;OnPGO‚PRP!Q[P5PhPCOzPNN‘PWP.QbP>QrPjKKPTP'P^P9PnPGO‚PPQZP3PhPCOzPMM‘PVP,QbP>QrPJJ‰P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PLLhP$QJJdPQIIbPPFN_PQDQ^PMAQ[PI@OZPB=OWP?;OVP:7PTP75PSPrP1PPpP.QOOlP)QMMjP'PKKfP!QJJdPQGOaPQFN_PQCO\PMAQ[PI>QXPB=OWP?9PUP:7PTP43PRP21PP.,QNN,)QMM($QKKfP!QJJbPPGOaPQDQ^PPCO\PM@OZPF>QXPB;OVP<9PUP:5PSP43PRP2.QOO.,QNN*'PLL($QKK$QIIbPPGO_PQDQ^PPCO[PI@OZPF>QWP?;OVP<7PTP75PSP41PP0.QOO.)QMM*'PLL(!QJJ$QIIbPQFN_PQDQ\PMAQ[PI@OXPB=OWP?;OUP:7PTP75PRP21PP0.QNN,)QMM*$QKK&!QJJdPPGOaPQFN_PPCO\PMAQ[PF>QXPB=OWP<9PUP:7PSP43PRP21POO.,QNN,)QLLhP$QKKfP!QIIbPPGOaPQDQ^PPCO\PI@OZPF>QXP?;OVP<9PUP75PSP43PRPpP.QOOnP,QNNjP'PLLhP$QJJdPQIIbPPFN_PQDQ^PPAQ[PI@OZPF=OWPP;OVP|P7PTPwP5PSPrP1PPpP.QOOlP)QMMjP'PLLfP!QJJdPQIIaPQFN_P‘PDQ\PPAQ[P‰P>QXP‚P=OWPP9PUPzP7PTPwP3PRPrP1PPpP,QNNlP)‘PMMjP$‘PKKfP!‘PJJbPPGOaP‘PFN^PPCOPPPnPPi‘PLŒPfPPa‘PI‰PaPPS‘PCP\PPP‰PP~‘PWPPP|PPyPTPPPtPPqPPPPnPPi‘PLŒPfPPa‘PI‰PaPPS‘PCP\PPP‰P>‘PWPPP|P9PTPPPtP1PPPPnPPi‘PLŒPfPPa‘PI‰PaPPS‘PCP\PPP‰P>‘PWPPP|P9PTPPPtP1PPPPnP)‘PLŒPfP!‘PI‰PaPPS‘PCP\PPP‰P>‘PWPPP|P9PTPPPtP1PPPPnP)‘PLŒPfP!‘PI‰PaP‘PCP\P‰P>‘PWPPP|P9PTPPPtP1PPPPnP)‘PLŒPfP!‘PI‰PaP‘PCP\P‰P>‘PWP|P9PTPtP1PPPPnP)‘PLŒPfP!‘PI‰PaP‘PCP\P‰P>‘PWP|P9PTPtP1PPnP)‘PLŒPfP!‘PI‰PaP‘PCP\P‰P>‘PWP|P9PTPtP1PPnP)‘PLLfP!‘PI‰PaP‘PCP\P‰P>‘PWP|P9PTPtP1PPnP)‘PLLfP!‘PIIaP‘PCP\P‰P>‘PWP|P9PTPtP1PPnP)‘PLLfP!‘PIIaP‘PCO\P‰P>‘PWP|P9PTPtP1PPnP)‘PLLfP!‘PIIaP‘PCO\P‰P>QWP|P9PTPtP1PPnP)‘PLLfP!‘PIIaP‘PCO\P‰P>QWP|P9PTPtP1PPnP)‘PLLfP!‘PIIaP‘PCO\P‰P>QWP|P9PTPtP1PPnP)‘PLLfP!‘PIIaP‘PCO\P‰P>QWP|P9PTPtP1PPnP)‘PLLfP!‘PIIaP‘PCO\P‰P>QWP|P9PTPtP1PPnP)‘PLLfP!‘PIIaP‘PCO\P‰P>QWP|P9PTPtP1PPnP)‘PLLfP!‘PIIaP‘PCO\P‰P>QWP|P9PTPtP1PPnP)‘PLLfP!‘PIIaP‘PCO\P‰P>QWP|P9PTPtP1PPnP)‘PLLfP!‘PIIaP‘PCO\P‰P>QWP|P9PTPtP1PPnP)‘PLLfP!‘PIIaP‘PCO\P‰P>QWP|P9PTPtP1PPnP)‘PLLfP!‘PIIaP‘PCO\P‰P>‘PWP|P9PTPtP1PPnP)‘PLLfP!‘PIIaP‘PCO\P‰P>‘PWP|P9PTPtP1PPnP)‘PLLfP!‘PIIaP‘PCP\P‰P>‘PWP|P9PTPtP1PPnP)‘PLLfP!‘PI‰PaP‘PCP\P‰P>‘PWP|P9PTPtP1PPnP)‘PLŒPfP!‘PI‰PaP‘PCP\P‰P>‘PWP|P9PTPtP1PPPPnP)‘PLŒPfP!‘PI‰PaP‘PCP\P‰P>‘PWP|P9PTPPPtP1PPPPnP)‘PLŒPfP!‘PI‰PaP‘PCP\P‰P>‘PWPPP|P9PTPPPtP1PPPPnP)‘PLŒPfP!‘PI‰PaP‘PCP\PPP‰P>‘PWPPP|P9PTPPPtP1PPPPnP)‘PLŒPfP!‘PI‰PaPPS‘PCP\PPP‰P>‘PWPPP|P9PTPPPtP1PPPPnPPi‘PLŒPfPPa‘PI‰PaPPS‘PCP\PPP‰P>‘PWPPP|P9PTPPPtPPqPPPPnPPi‘PLŒPfPPa‘PI‰PaPPS‘PCP\PPP‰P>‘PWPPP|PPyPTPPPtPPqPPPPlPPd‘PJŠPaPPS‘PA‘PZPPPPPyPSPPPrPPl‘PMPfPP^‘PFŽP^PPP‰P>‘PVPPPzP3PPPPlPPgPJŠPbPPS‘PCPZPPP‚P9PTPPPrP.‘PMPhPP^‘PGP^PPPP>‘PWPPPzP5PPPPnP'PK‹PbPPW‘PCP[PPP‚P;PTPPPtP.‘PNŽPhP!‘PGP_PP@PWPPP|P5PRPPPnP)‘PK‹PdP‘PD‘P[P†P;PUPPPtP1PNŽPjP!‘PI‰P_PP@PXP|P7PRPPPpP)‘PLŒPdPPD‘P\P†P=PUPwP1POPjP$‘PI‰PaPPA‘PXPP7PSPpP,‘PLLfPPFŽP\P‰P=PVPwP3POOlP$‘PJJaP‘PA‘PZPP9PSPrP,‘PMMfP‘PFN^P‰P>‘PVPzP3PPlP$‘PJJaP‘PAQZPP9PSPrP,‘PMMfP‘PFN^P‰P>QVPzP3PPlP'PJJbP‘PCOZP‚P9PTPrP.‘PMMhP‘PGO^PP>QWPzP5PPnP'PKKbP‘PCO[P‚P;OTPtP.‘PNNhP!‘PGO_PP@OWP|P5PRPnP)‘PKKdP‘PDQ[P†P;OUPtP1PNNjP!‘PII_PP@OXP|P7PRPpP)QLLdPPDQ\P†P=OUPwP1POOjP$QIIaPPAQXPP7PSPpP,QLLfPPFN\P‰P=OVPwP3POOlP$QJJaP‘PAQZPP9PSPrP,QMMfP‘PFN^P‰P>QVPzP3PPlP$QJJaP‘PAQZPP9PSPrP,QMMfPQFN^P‰P>QVPzP3PPlP'PJJbP‘PCOZP‚P9PTPrP.QMMhPQGO^PP>QWPzP5PPnP'PKKbP‘PCO[P‚P;OTPtP.QNNhP!QGO_PP@OWP|P5PRPnP)QKKdP‘PDQ[P†P;OUPtP1PNNjP!QII_PP@OXP|P7PRPpP)QLLdPPDQ\P†P=OUPwP1POOjP$‘PIIaPPAQXPP7PSPpP,QLLfPPFN\P‰P=OVPwP3POOlP$‘PJJaP‘PAQZPP9PSPrP,‘PMMfP‘PFN^P‰P>QVPzP3PPlP$‘PJJaP‘PAQZPP9PSPrP,‘PMMfP‘PFN^P‰P>QVPzP3PPlP'PJJbP‘PCOZP‚P9PTPrP.‘PMMhP‘PGO^PP>‘PWPzP5PPnP'PKKbP‘PCP[P‚P;PTPtP.‘PNNhP!‘PGO_PP@PWP|P5PRPnP)‘PKKdP‘PD‘P[P†P;PUPtP1PNNjP!‘PI‰P_PP@PXP|P7PRPpP)‘PLŒPdPPD‘P\P†P=PUPwP1POPjP$‘PI‰PaPPA‘PXPP7PSPPPpP,‘PLŒPfPPFŽP\P‰P=PVPPPwP3POPlP$‘PJŠPaP‘PA‘PZPPPP9PSPPPrP,‘PMPfP‘PFŽP^PPP‰P>‘PVPPPzP3PPPwPPPPlPPd‘PP‰‰P^PPP‰PP}PUPPPtPPl‘PLŒPdPPW‘PP‘PXPPP|PPuPPPPjPPa‘PGP^PPP†PP{PTPPPrPPi‘PK‹PbPPS‘PA‘PWPPPzPPsPOPhPP^‘PFŽP\PPP†P9PSPPPpPPi‘PJŠPaPPPP@PVPPPwP1PNŽPhPP[PD‘P[PPP‚P7PRPPPnPPgPJŠP_PPPP>‘PVPPPtP.‘PMPfPPW‘PCPZPPPP7PPPPlP$‘PI‰P^PPP‰P=PUPPPtP,‘PLŒPdP‘PA‘PXPPP|P5PPPPjP!‘PGP^P†P;PTPPPrP)‘PK‹PbP‘PA‘PWPPPzP3POPhP‘PFŽP\P†P9PSPPPpP)‘PJŠPaPP@PVPwP1PNŽPhPPD‘P[P‚P7PRPnP'PJŠP_PP>‘PVPtP.‘PMPfP‘PCPZPP7PPlP$‘PI‰P^P‰P=PUPtP,‘PLLdP‘PA‘PXP|P5PPjP!‘PGO^P†P;PTPrP)‘PKKbP‘PA‘PWPzP3POOhP‘PFN\P†P9PSPpP)‘PJJaPP@OVPwP1PNNhPPDQ[P‚P7PRPnP'PJJ_PP>QVPtP.‘PMMfP‘PCOZPP7PPlP$‘PII^P‰P=OUPtP,‘PLLdP‘PAQXP|P5PPjP!‘PGO^P†P;OTPrP)‘PKKbP‘PAQWPzP3POOhP‘PFN\P†P9PSPpP)‘PJJaPP@OVPwP1PNNhPPDQ[P‚P7PRPnP'PJJ_PP>QVPtP.QMMfP‘PCOZPP7PPlP$‘PII^P‰P=OUPtP,QLLdP‘PAQXP|P5PPjP!‘PGO^P†P;OTPrP)QKKbP‘PAQWPzP3POOhP‘PFN\P†P9PSPpP)QJJaPP@OVPwP1PNNhPPDQ[P‚P7PRPnP'PJJ_PP>QVPtP.QMMfP‘PCOZPP7PPlP$‘PII^P‰P=OUPtP,QLLdP‘PAQXP|P5PPjP!‘PGO^P†P;OTPrP)QKKbP‘PAQWPzP3POOhP‘PFN\P†P9PSPpP)‘PJJaPP@OVPwP1PNNhPPDQ[P‚P7PRPnP'PJJ_PP>QVPtP.‘PMMfP‘PCOZPP7PPlP$‘PII^P‰P=OUPtP,‘PLLdP‘PAQXP|P5PPjP!‘PGO^P†P;OTPrP)‘PKKbP‘PAQWPzP3POOhP‘PFN\P†P9PSPpP)‘PJJaPP@PVPwP1PNNhPPDQ[P‚P7PRPnP'PJJ_PP>‘PVPtP.‘PMMfP‘PCPZPP7PPlP$‘PI‰P^P‰P=PUPtP,‘PLLdP‘PA‘PXP|P5PPjP!‘PGP^P†P;PTPrP)‘PK‹PbP‘PA‘PWPzP3POPhP‘PFŽP\P†P9PSPpP)‘PJŠPaPP@PVPwP1PNŽPhPPD‘P[P‚P7PRPPPnP'PJŠP_PP>‘PVPPPtP.‘PMPfP‘PCPZPPPP[PPPPPuPOPhPP[PPƒPXPPP|PPsPNŽPfPPW‘PA‘PWPPPzPPqPMPdPPS‘P@PVPPPtPPn‘PLŒPbPPPP>‘PUPPPrPPl‘PK‹PaPPPP=PTPPPpPPgPJŠP_PPP‰P;PSPPPnPPd‘PI‰P^PPP†P9PRPPPlPPa‘PFŽP\PPP‚P7PPPPjPP^‘PD‘P[PPPP5POPhPP[PCPXPPP|P3PNŽPfPPW‘PA‘PWPPPwP1PMPdP‘P@PVPPPtP.‘PLŒPbPP>‘PUPPPrP)‘PK‹PaPP=PTPPPpP'PJŠP_P‰P;PSPPPnP$‘PGP^P†P9PRPPPlP!‘PFŽ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‘PAQTPjP‘P=OPfPP7PNNaP‚P1PKK\PzP,‘PGOXPtP$‘PCOUPnPP>QSPhPP9POObP†P5PLL^PP.QIIZPwP'PDQWPpP‘PAQTPjP‘P=OPdPP7PMMaP‚P1PJJ\PzP)QGOXPrP$QCOUPlPP>QRPhPP9POObP†P3PLL^P|P.QIIZPtP'PDQVPpPQ@OTPjPQ;OPdPI7PMM_P‚P1PJJ[PzP)QFNXPrP!QCOUPlPQ>QRPfPP9PNNbPF3PKK^P|P,QIIZPtP'PDQVPnPQ@OSPjPQ;OPdPI5PMM_P?1PJJ[PwP)QFNWPrP!QAQUPlPQ=ORPfPM9PNNaPF3PKK\P<,QGOZPtP$QDQVPnPP@OSPhPQ;OOOdPI5PLL_P?.QJJ[P7)QFNWPpP!QAQTPlPQ=OPfPM7PNNaPB3PKK\P:,QGOXPtP$QCOVPnPP>QSPhPP;OOObPI5PLL^P?.QII[PwP'PFNWPpPQAQTPjPQ=OPfPM7PMMaPB1PKK\PzP)QGOXPrP$QCOUPnPP>QRPhPP9POObPF5PLL^P|P.QIIZPwP'PDQWPpPQ@OTPjPQ=OPdPP7PMM_P‚P1PJJ\PzP)QGOXPrP!QCOUPlPP>QRPhPP9PNNbP†P3PLL^P|P,QIIZPtP'PDQVPpP‘P@OSPjP‘P;OPdP‰P7PMM_PP1PJJ[PzP)QFNXPrP!‘PAQUPlP‘P>QRPfPP9PNNaP†P3PKK^P|P,‘PIIZPtP$‘PDQVPnP‘P@OSPhP‘P;OOOdP‰P5PMM_PP.‘PJJ[PwP)‘PFNWPrP!‘PAQTPlP‘P=PRPfPP9PNNaP‚P3PKK\P|P,‘PGOZPtP$‘PCPVPnPPPPbPPP†P1PJŠP[PPPtP$‘PA‘PTPPPjPPPP9PNŽP_PPPP,‘PGPXPPPpP‘P>‘PRPPPfP‰P5PLŒP\PPPzP'PD‘PVPPPlP‘P;POPbP‚P1PJŠPZPtP!‘PA‘PTPPPhPP7PMP_P|P,‘PGPWPpPP>‘PRPPPdP‰P3PK‹P\PwP'PD‘PUPlP‘P;POOaP‚P.‘PI‰PZPrP!‘PA‘PSPhPP7PMM^P|P)‘PFŽPWPnPP>‘PPdP†P3PKK[PwP$‘PCOUPjP‘P;PNNaPP.‘PIIXPrP‘P@OSPfPP7PLL^PzP)‘PFNVPnP‘P=OPbP†P3PJJ[PtP$‘PCOTPjPP9PNN_PP.QGOXPpP‘P@ORPfPP5PLL\PzP)QDQVPlP‘P=OOObP†P1PJJZPtP$QAQTPhPP9PMM_PP,QGOWPpPQ>QRPdP‰P5PKK\PzP'PDQUPlPQ;OOOaP‚P1PIIZPtP!QAQSPhPP7PMM^P|P,QFNWPpPP>QPdPI3PKK[PwP'PCOUPlPQ;ONNaPB.QIIXPrP!Q@OSPhPM7PLL^P<)QFNVPnPP=OPdPF3PJJ[P7$QCOTPjPQ9PNNaP?.QGOXP2Q@ORPfPM5PLL^P:)QDQVPnPQ=OPbPF1PJJ[P4$QAQTPjPP9PNN_P?,QGOXP0Q>QRPfPI5PLL\P:'PDQVP,Q;OOObPB1PJJZP4!QAQTPhPP7PMM_P<,QGOWP0P>QRPdPI3PKK\P7'PDQUPlPQ;OOOaPB.QIIZP2!QAQSPhPM7PMM^P<)QFNWP.P>QPdPF3PKK[P7$QCOUPjPQ;ONNaP?.QIIXP2Q@OSPfPM7PLL^P:)QFNVPnPQ=OPbPF3PJJ[PtP$QCOTPjPP9PNN_P?.QGOXPpPQ@ORPfPM5PLL\PzP)QDQVPlPQ=OOObPF1PJJZPtP$QAQTPhPP9PMM_PP,QGOWPpPQ>QRPdP‰P5PKK\PzP'PDQUPlPQ;OOOaP‚P1PIIZPtP!QAQSPhPP7PMM^P|P,QFNWPpPP>QPdP‰P3PKK[PwP'PCOUPlP‘P;ONNaP‚P.QIIXPrP!‘P@OSPhPP7PLL^P|P)‘PFNVPnPP=OPdP†P3PJJ[PwP$‘PCOTPjP‘P9PNNaPP.‘PGOXPrP‘P@ORPfPP5PLL^PzP)‘PDQVPnP‘P=PPWPPPnPPW‘PP{PNŽP_PPP|PPi‘PP„‘PUPPPjPPPPPwPK‹P[PPPtPPa‘PP€PRPPPdPPP†PPqPI‰PXPPPpPP[PP}PNŽP_PPP|PPi‘PD‘PUPPPjPPPPPwPLŒP\PPPwPPd‘P@PRPPPdPPP†PPqPI‰PXPPPpPP[P=POPaPPPPPi‘PD‘PUPPPjPPPP7PLŒP\PPPwPPd‘PA‘PSPPPfPPP‰P1PI‰PXPPPpPP[P=POPaPPPP,‘PFŽPVPPPlPPPP7PLŒP\PPPwP$‘PA‘PSPPPfPPP‰P3PJŠPZPPPrPP=POPaPPPP,‘PFŽPVPPPlP‘P9PMP^PPPwP$‘PA‘PSPPPfP‰P3PJŠPZPPPrP‘P>‘PPPPaPP,‘PFŽPVPPPlP‘P9PMP^PzP'PCPTPPPfP‰P3PJŠPZPrP‘P>‘PPPPbP‚P.‘PGPVPlP‘P9PMP^PzP'PCPTPhPP5PJŠPZPrP‘P>‘PPbP‚P.‘PGPWPnP‘P;PMM^PzP'PCPTPhPP5PKK[PtP!‘P>‘PPbP‚P.‘PGPWPnP‘P;PNN_P|P'PCPTPhPP5PKK[PtP!‘P@PRPdP†P.‘PGOWPnP‘P;PNN_P|P)‘PDQUPjPP5PKK[PtP!‘P@PRPdP†P1PIIXPnP‘P;PNN_P|P)‘PDQUPjPP7PLL\PtP!‘P@ORPdP†P1PIIXPpPP=OOO_P|P)‘PDQUPjPP7PLL\PwP$‘PAQSPdP†P1PIIXPpPP=OOOaPP,‘PFNUPjPP7PLL\PwP$‘PAQSPfP‰P3PIIXPpPP=OOOaPP,‘PFNVPlP‘P9PLL\PwP$‘PAQSPfP‰P3PJJZPrP‘P=OOOaPP,‘PFNVPlP‘P9PMM^PzP$‘PAQSPfP‰P3PJJZPrP‘P>QPbP‚P,‘PFNVPlP‘P9PMM^PzP'PCOTPhP‰P3PJJZPrP‘P>QPbP‚P.‘PGOWPlP‘P9PMM^PzP'PCOTPhPP5PKK[PrP‘P>QPbP‚P.‘PGOWPnP‘P;PNN^PzP'PCOTPhPP5PKK[PtP!‘P@PRPbP‚P.‘PGOWPnP‘P;PNN_P|P)‘PDQTPhPP5PKK[PtP!‘P@PRPdP†P1PGOWPnP‘P;PNN_P|P)‘PD‘PUPjPP7PKK[PtP!‘P@PRPdP†P1PI‰PXPpPP;PNN_P|P)‘PD‘PUPjPP7PLŒP\PwP!‘P@PRPdP†P1PI‰PXPpPP=POPaPP)‘PD‘PUPjPP7PLŒP\PwP$‘PA‘PSPPPfP†P1PI‰PXPpPP=POPaPP,‘PFŽPVPPPjPP7PLŒP\PwP$‘PA‘PSPPPfP‰P3PJŠPZPPPpPP=POPaPP,‘PFŽPVPPPlP‘P9PMP\PPPwP$‘PA‘PSPPPfP‰P3PJŠPZPPPrP‘P>‘PPPl‘PP†ŽPUPPPhPPP‰PPsPP‰‰PWPPPlPPPPPwPK‹PZPPPpPP[PP{PMP\PPPtPPa‘PP~‘POP_PPP|PPgPA‘PRPPPdPPP‚PPl‘PD‘PTPPPhPPP‰PPqPGPWPPPlPPPP5PJŠPZPPPpPPW‘P9PMP\PPPtPP^‘P=POP_PPPzPPd‘PA‘PRPPPbPPPP,‘PD‘PTPPPfPPP†P1PGPVPPPjPPPP5PJŠPXPPPnP‘P9PLŒP[PPPtP‘P=PNŽP^PPPzP$‘P@PPPPbPPPP)‘PCPTPPPfP†P.‘PFŽPVPPPjPP3PJŠPXPPPnP‘P7PLŒP[PPPrPP=PNŽP^PwP!‘P@PPPPaP|P)‘PCPSPPPdP†P.‘PFŽPUPPPhPP3PI‰PWPnP‘P7PK‹PZPrPP;PMP^PwP!‘P>‘PPPPaP|P'PA‘PSPdP‚P,‘PFŽPUPhP‰P1PI‰PWPlPP7PK‹PZPpP‘P;PMM\PtP!‘P>‘POO_P|P'PA‘PRPbP‚P,‘PD‘PTPhP‰P1PGOVPlPP5PJJZPpP‘P9PLL\PtP‘P=POO_PzP$‘PA‘PRPbPP)‘PDQTPfP†P1PGOVPjPP5PJJXPnP‘P9PLL[PrP‘P=PNN^PzP$‘P@OPbPP)‘PCOSPfP†P.‘PFNVPjPP3PIIXPnP‘P7PLL[PrPP;ONN^PwP!‘P@OPaP|P)‘PCOSPdP‚P.‘PFNUPhPP3PIIWPlP‘P7PKKZPrPP;OMM\PwP!‘P>QOOaP|P'PAQSPdP‚P,‘PDQUPhP‰P1PIIWPlPP5PKKZPpP‘P;OMM\PtP‘P>QOO_PzP'PAQRPbP‚P,‘PDQTPfP‰P1PGOVPlPP5PJJXPpP‘P9PLL\PtP‘P=ONN_PzP$‘P@ORPbPP)‘PDQTPfP†P.‘PGOVPjPP5PJJXPnP‘P9PLL[PrP‘P=ONN^PwP$‘P@OPaPP)‘PCOSPfP†P.‘PFNUPjPP3PIIXPnP‘P7PKK[PrPP;ONN^PwP!‘P>QPaP|P'PCOSPdP‚P.‘PFNUPhP‰P3PIIWPlP‘P7PKKZPpPP;PMM\PwP!‘P>QOOaP|P'PAQRPdP‚P,‘PDQUPhP‰P1PGOWPlPP5PKKZPpP‘P9PMM\PtP‘P>‘POO_PzP'PA‘PRPbPP,‘PD‘PTPfP‰P1PGPVPjPP5PJJXPpP‘P9PLL[PtP‘P=PNN_PzP$‘P@PRPbPP)‘PCPTPfP†P.‘PGPVPjPP3PJŠPXPnP‘P9PLŒP[PrPP=PNŽP^PwP$‘P@PPPPaPP)‘PCPSPPPdP†P.‘PFŽPUPPPjPP3PI‰PWPPPnP‘P7PK‹P[PrPP;PMP^PwP!‘P>‘PPPPaP|P'PCPSPPPdP‚PWPPPjPPPPPqPGPUPPPhPPP†PPn‘PD‘PTPPPdPPP‚PPi‘PCPSPPPbPPPPPgPA‘PPPPaPPPzPPd‘P>‘POP^PPPwPP^‘P=PMP\PPPrPP[P9PLŒPZPPPpPPS‘P7PJŠPXPPPnPPPP5PI‰PWPPPjPPPP1PGPUPPPhPPP†P.‘PD‘PTPPPdPPP‚P)‘PCPRPPPbPPP|P'P@PPPP_PPPzP$‘P>‘POP^PPPwP‘P=PMP\PPPrPP9PLŒPZPPPpP‘P7PJŠPXPPPlPP3PI‰PVPPPjP‰P1PFŽPUPPPhP†P.‘PD‘PTPPPdP‚P)‘PCPRPPPbP|P'P@PPPP_PzP!‘P>‘PNŽP^PtP‘P;PMP[PrPP9PLŒPZPpP‘P7PJŠPXPlPP3PI‰PVPjP‰P1PFŽPUPfP†P,‘PD‘PSPdPP)‘PCPRPbP|P'P@PP_PzP!‘P>‘PNN^PtP‘P;PMM[PrP‘P9PKKZPnP‘P5PJJWPlPP3PIIVPjP‰P1PF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K,‘PrPUP>‘PPaPKK)‘PrPUP=OPaPJJ)‘PrPTP=OP_PJJ)‘PpPTP=O‰P_PJJ'PpPTP;O‰P_PII'PpPSP;O‰P^PII'PnPSP;O†P^PII$‘PnPSP9P†P^PGO$‘PnPRP9P†P\PGO$‘PlPRP9P‚P\PGO!‘PlPRP7P‚P\PFN!‘PlPP7P‚P[PFN!‘PjPP7PP[PFN‘PjPP5PP[PDQ‘PjPP5PP[PDQ‘PjPOO5PPZPDQ‘PhPOO5P|PZPDQPhPOO3P|PZPCOPhPNN3P|PXPCOPfPNN3PzPXPCO‘PfPNN1PzPXPAQ‘PfPMM1PzPWPAQ‘PdPMM1PwPWPAQ‘PdPMM.QwPWP@O‘PdPLL.QwPVP@O‘PbPLL.QtPVP@OPbPLL,QtPVP>QPbPKK,QtPUP>QPaPKK,QrPUP>QPaPKK)QrPUP=OPaPJJ)QrPTP=OP_PJJ)QpPTP=O‰P_PJJ'PpPTP;O‰P_PII'PpPSP;O‰P^PII'PnPSP;O†P^PII$QnPSP9P†P^PGO$QnPRP9P†P\PGO$QlPRP9P‚P\PGO!QlPRP7P‚P\PFN!QlPP7P‚P[PFN!QjPP7PP[PFNQjPP5PP[PDQQjPP5PP[PDQQjPOO5PPZPDQQhPOO5P|PZPDQPhPOO3P|PZPCOPhPNN3P|PXPCOPfPNN3PzPXPCOQfPNN1PzPXPAQQfPMM1PzPWPAQQdPMM1PwPWPAQQdPMM.QwPWP@OQdPLL.QwPVP@O‘PbPLL.QtPVP@OPbPLL,QtPVP>QPbPKK,QtPUP>QPaPKK,QrPUP>QPaPKK)QrPUP=OPaPJJ)QrPTP=OP_PJJ)QpPTP=O‰P_PJJ'PpPTP;O‰P_PII'PpPSP;O‰P^PII'PnPSP;O†P^PII$QnPSP9P†P^PGO$QnPRP9P†P\PGO$QlPRP9P‚P\PGO!‘PlPRP7P‚P\PFN!‘PlPP7P‚P[PFN!‘PjPP7PP[PFN‘PjPP5PP[PDQ‘PjPP5PP[PDQ‘PjPOO5PPZPDQ‘PhPOO5P|PZPDQPhPOO3P|PZPCOPhPNN3P|PXPCOPfPNN3PzPXPCO‘PfPNN1PzPXPAQ‘PfPMM1PzPWPAQ‘PdPMM1PwPWPAQ‘PdPMM.‘PwPWP@O‘PdPLL.‘PwPVP@O‘PbPLL.‘PtPVP@OPbPLL,‘PtPVP>QPbPKK,‘PtPUP>‘PPaPKK,‘PrPUP>‘PPaPKK)‘PrPUP=PPaPJJ)‘PrPTP=PP_PJJ)‘PpPTP=P‰P_PJJ'PpPTP;P‰P_PII'PpPSP;P‰P^PI‰gPnPSP;P†P^PI‰d‘PnPrPTPP}P‰P^PP‰‰d‘PlPRPPwPP[PP„‘[PfPNŽqPwPWPP€PPbPK‹i‘PpPTPP{P†P^PGa‘PlPPPuPPZPPƒW‘PfPMn‘PwPVPP~‘PPaPJŠgPpPSPPyP†P\PFŽa‘PjPOuP|PXPA‘W‘PdPLŒn‘PtPUP>‘PP_PI‰gPnPRP9P‚P[PFŽ^‘PhPOsPzPWPA‘S‘PbPLŒl‘PrPUP=P‰P^PI‰d‘PlPRP7PP[PD‘[PhPNN1PwPWP@PPbPKK)‘PrPTP;P‰P^PGa‘PlPP5PPZPC[PfPMM.‘PwPVP>‘PPaPJJ)‘PpPSP;P†P\PFN!‘PjPOO5P|PXPCW‘PdPLL.‘PtPUP>‘PP_PJJ'PnPSP9P‚P[PFN‘PhPOO3PzPXPAQ‘PbPLL,‘PrPUP=O‰P_PII$‘PnPRP7PP[PDQPhPNN1PzPWP@OPbPKK)‘PrPTP;O‰P^PGO$‘PlPP5PPZPCOPfPMM1PwPVP>QPaPJJ)‘PpPSP;O†P\PGO!‘PjPOO5P|PXPCO‘PdPMM.QtPVP>QP_PJJ'PnPSP9P‚P\PFN‘PhPOO3PzPXPAQ‘PdPLL,QtPUP=O‰P_PII$QnPRP7P‚P[PDQPhPNN1PzPWP@O‘PbPKK,QrPTP;O‰P^PGO$QlPP7PPZPCOPfPMM1PwPVP@OPaPKK)QpPSP;O†P\PGO!QjPP5P|PXPCOQdPMM.QtPVP>QPaPJJ'PnPSP9P‚P\PFNQjPOO3P|PXPAQQdPLL,QtPUP=OP_PII$QnPRP7P‚P[PDQQhPNN3PzPWP@OQbPKK,QrPTP=O‰P^PGO$QlPP7PPZPDQPfPNN1PwPVP@OPaPKK)QpPTP;O†P\PGO!QjPP5P|PZPCOQfPMM.QtPVP>QMaPJJ'PpPSP9P‚P\PFNQjPOO3P|PXPAQQdPLL,QtPUP=OM_PII'PnPRP9P‚P[PDQQhPNN3PzPWPAQQbPKK,QrPTP=OI^PII$QlPRP7PPZPDQPfPNN1PwPWP@OPaPKK)QpPTP;OF^PGO!QlPP5P|PZPCOQfPMM.QwPVP>QMaPJJ'PpPSP9PF\PFN!QjPOO3P|PXPAQQdPLL.QtPUP=OM_PII'PnPRP9P‚P[PFNQhPNN3PzPWPAQQbPLL,QrPTP=OI^PII$QlPRP7PP[PDQPfPNN1PwPWP@OPbPKK)QrPTP;O†P^PGO!QlPP5PPZPCOQfPMM.QwPVP>QPaPJJ)QpPSP9P†P\PFN!QjPOO5P|PXPAQQdPLL.QtPUP>QP_PJJ'PnPRP9P‚P[PFNQhPOO3PzPWPAQ‘PbPLL,QrPUP=O‰P_PII$QlPRP7PP[PDQPhPNN1PwPWP@OPbPKK)QrPTP;O‰P^PGO!QlPP5PPZPCOPfPMM1PwPVP>QPaPJJ)QpPSP;O†P\PFN!‘PjPOO5P|PXPCO‘PdPMM.QtPUP>QP_PJJ'PnPSP9P‚P[PFN‘PhPOO3PzPXPAQ‘PdPLL,‘PrPUP=O‰P_PII$‘PnPRP7PP[PDQPhPNN1PzPWP@O‘PbPKK)‘PrPTP;O‰P^PGO$‘PlPP5PPZPCOPfPMM1PwPVP@OPaPJJ)‘PpPSP;P†P\PGO!‘PjPPRPPwPPZPCW‘PdPLŒl‘PrPTPP{P†P\PFŽ^‘PhPNŽqPwPVP>‘PP_PI‰d‘PlPPPuP|PXPA‘S‘PbPK‹i‘PpPSP9P‚P[PD‘[PfPMn‘PtPUP=P‰P^PGa‘PjPOO3PzPWP@PPaPJŠgPnPRP7PPZPCW‘PdPLL,‘PrPTP;P†P\PFŽ[PfPMM.‘PtPUP=P‰P^PGO!‘PjPOO3PzPWP@PPaPJJ'PnPRP7PPZPCO‘PdPLL,‘PrPTP;P†P\PFN‘PhPNN1PwPVP>‘PP_PII$‘PlPP5P|PXPAQ‘PbPKK)‘PpPSP9P‚P[PDQPfPMM.‘PtPUP=O‰P^PGO!‘PjPOO3PzPWP@OPaPJJ'PnPRP7PPZPCO‘PdPLL,‘PrPTP;O†P\PFN‘PhPNN1PtPUP=O‰P^PGO!‘PjPOO3PzPWP@OPaPJJ'PnPRP7PPZPCO‘PdPLL,‘PrPTP;O†P\PFN‘PhPNN1PwPVP>QP_PII$‘PlPP5P|PXPAQ‘PbPKK)QpPSP9P‚P[PDQPfPMM.QtPUP=O‰P^PGO!‘PjPOO3PzPWP@OPaPJJ'PnPRP7PPZPCO‘PdPLL,QrPTP;O†P\PFN‘PhPNN1PwPVP>QP^PGO!QjPOO3PzPWP@OPaPJJ'PnPRP7PPZPCO‘PdPLL,QrPTP;O†P\PFNQhPNN1PwPVP>QP_PII$QlPP5P|PXPAQ‘PbPKK)QpPSP9P‚P[PDQPfPMM.QtPUP=O‰P^PGO!QjPOO3PzPWP@OPaPJJ'PnPRP7PPZPCO‘PdPLL,QrPTP;O†P\PFNQhPNN1PwPVP>QP_PII$QlPP3PzPWP@OPaPJJ'PnPRP7PPZPCOQdPLL,QrPTP;O†P\PFNQhPNN1PwPVP>QP_PII$QlPP5P|PXPAQ‘PbPKK)QpPSP9P‚P[PDQPfPMM.QtPUP=O‰P^PGO!QjPOO3PzPWP@OPaPJJ'PnPRP7PPZPCO‘PdPLL,QrPTP;O†P\PFNQhPNN1PwPVP>QP_PII$QlPP5P|PXPAQPaPJJ'PnPRP7PPZPCO‘PdPLL,QrPTP;O†P\PFN‘PhPNN1PwPVP>QP_PII$QlPP5P|PXPAQ‘PbPKK)QpPSP9P‚P[PDQPfPMM.QtPUP=O‰P^PGO!‘PjPOO3PzPWP@OPaPJJ'PnPRP7PPZPCO‘PdPLL,‘PrPTP;O†P\PFN‘PhPNN1PwPVP>QP_PII$‘PlPP5P|PXPAQ‘PbPKK)‘PnPRP7PPZPCO‘PdPLL,‘PrPTP;O†P\PFN‘PhPNN1PwPVP>QP_PII$‘PlPP5P|PXPAQ‘PbPKK)‘PpPSP9P‚P[PDQPfPMM.‘PtPUP=O‰P^PGO!‘PjPOO3PzPWP@OPaPJJ'PnPRP7PPZPCO‘PdPLL,‘PrPTP;P†P\PFN‘PhPNN1PwPVP>‘PP_PII$‘PlPP5P|PXPA‘S‘PbPKK)‘PpPSP9P‚PZPCW‘PdPLL,‘PrPTP;P†P\PFŽ^‘PhPNN1PwPVP>‘PP_PI‰d‘PlPP5P|PXPA‘S‘PbPK‹i‘PpPSP9P‚P[PD‘[PfPMM.‘PtPUP=P‰P^PGa‘PjPOO3PzPWP@PPaPJŠgPnPRP7PPZPCW‘PdPLŒl‘PrPTP;P†P\PFŽ^‘PhPNŽqPtPUP=P†P\PD‘[PfPLŒl‘PpPSP9PPZPCS‘PbPJŠgPnPP5P|PWP@PP_PI‰a‘PjPOO1PwPUP=P‰P\PFŽ[PfPMM,‘PrPTP9P‚PZPCW‘PbPKK)‘PnPRP5P|PXP@PPaPII$‘PjPOO3PwPVP=P‰P^PFN‘PhPMM.‘PrPTP;P‚P[PDQ‘PdPKK)‘PpPRP7PPXPAQPaPJJ$‘PlPP3PzPVP>QP^PGO‘PhPNN.‘PtPUP;O†P[PDQPdPLL,‘PpPSP7PPZPAQ‘PbPJJ'PlPP5PzPWP>QP_PGO!‘PjPNN1PtPUP=O†P\PFNPfPLL,‘PrPSP9P‚PZPCO‘PbPKK'PnPP5P|PWP@OP_PII!‘PjPOO1PwPVP=O‰P\PFN‘PfPMM.QrPTP9P‚P[PCO‘PbPKK)QnPRP7P|PXP@OPaPII$QlPOO3PwPVP>Q‰P^PGOQhPMM.QtPTP;O‚P[PDQQdPLL)QpPRP7PPXPAQQaPJJ$QlPP3PzPWP>QM^PGO!QhPNN.QtPUP;O†P\PDQPdPLL,QpPSP9PPZPAQQbPJJ'PnPP5PzPWP@OM_PGO!QjPNN1PwPUP=OF\PFNPfPMM,QrPSP9PBZPCOQbPKK'PnPRP5P<XP@OP_PII$QjPOO1PwPVP=OI^PFNQfPMM.QrPTP;OB[PCOQdPKK)QpPRP7P<XPAQPaPII$QlPOO3P:VP>QI^PGOQhPNN.Q4TP;OF[PDQPdPLL)QpPSP7P?XPAQQaPJJ'PlPP3P:WP>QM_PGO!QhPNN1P4UP=OF\PDQPfPLL,Q0SP9P?ZPCOQbPJJ'PnPP5P<WP@OM_PII!QjPOO1P7UP=OI\PFNPfPMM,Q2TP9PBZPCOQbPKK)QnPRP5P<XP@OPaPII$QjPOO3P7VP=OI^PFNQhPMM.Q2TP;OB[PDQQdPKK)Q0RP7P?XPAQPaPJJ$QlPP3P:VP>QM^PGOQhPNN.Q4UP;OF[PDQPdPLL,Q0SP7P?ZPAQQbPJJ'PlPP5P:WP>QM_PGO!QjPNN1P4UP=OF\PFNPfPLL,QrPSP9PBZPCOQbPKK'PnPP5P<WP@OP_PII!QjPOO1P7VP=OI\PFNQfPMM.QrPTP9PB[PCOQbPKK)QnPRP7P<XP@OPaPII$QlPOO3PwPVP>QI^PGOQhPMM.QtPTP;OB[PDQQdPLL)QpPRP7P?XPAQQaPJJ$QlPP3PzPWP>QM^PGO!QhPNN.QtPUP;OF\PDQPdPLL,QpPSP9PPZPAQQbPJJ'PnPP5PzPWP@OM_PGO!QjPNN1PwPUP=O†P\PFNPfPMM,QrPSP9P‚PZPCOQbPKK'PnPRP5P|PXP@OP_PII$QjPOO1PwPVP=O‰P^PFNQfPMM.QrPTP;O‚P[PCO‘PdPKK)QpPRP7P|PXPAQPaPII$QlPOO3PzPVP>Q‰P^PGO‘PhPNN.QtPTP;O†P[PDQPdPLL)‘PpPSP7PPXPAQ‘PaPJJ'PlPP3PzPWP>QP_PGO!‘PhPNNPPsPwPUP=P†P[PD‘W‘PbPK‹gPlPOO3PwPUP=P†P[PD‘W‘PbPJŠgPlPOO3PwPUP=P†P[PCW‘PbPJŠgPlPOO3PwPUP;P†P[PCW‘PbPJJ'PlPOO1PwPUP;P†P[PCW‘PbPJJ$‘PlPOO1PwPUP;P†P[PCW‘PbPJJ$‘PlPOO1PwPUP;P†P[PCO‘PbPJJ$‘PlPOO1PwPUP;P‚P[PCO‘PbPJJ$‘PlPOO1PtPUP;P‚P[PCO‘PbPJJ$‘PjPOO1PtPUP;O‚P[PCO‘PaPJJ$‘PjPOO1PtPUP;O‚PZPCO‘PaPJJ$‘PjPOO1PtPUP;O‚PZPCO‘PaPJJ$‘PjPOO1PtPTP;O‚PZPCO‘PaPJJ$‘PjPNN1PtPTP;O‚PZPCO‘PaPII$‘PjPNN1PtPTP;O‚PZPAQ‘PaPII$‘PjPNN1PtPTP9P‚PZPAQ‘PaPII$‘PjPNN.QtPTP9P‚PZPAQ‘PaPII$‘PjPNN.QtPTP9P‚PZPAQ‘PaPII!QjPNN.QtPTP9P‚PZPAQPaPII!QjPNN.QtPTP9PPZPAQPaPII!QjPNN.QrPTP9PPZPAQPaPII!QhPNN.QrPTP9PPZPAQP_PII!QhPNN.QrPTP9PPZPAQP_PII!QhPNN.QrPTP9PPXPAQP_PII!QhPNN.QrPSP9PPXPAQP_PII!QhPMM.QrPSP9PPXPAQP_PGO!QhPMM.QrPSP9PPXP@OP_PGO!QhPMM.QrPSP7PPXP@OP_PGO!QhPMM.QrPSP7PPXP@OP_PGO!QhPMM,QrPSP7PPXP@OP_PGOQhPMM,QrPSP7PPXP@OM_PGOQhPMM,QrPSP7P|PXP@OM_PGOQhPMM,QpPSP7P|PXP@OM_PGOQhPMM,QpPSP7P|PXP@OP_PGOQfPMM,QpPSP7P|PXP@OP^PGOQfPMM,QpPSP7P|PWP@OP^PGOQfPMM,QpPRP7P|PWP@OP^PGOQfPLL,QpPRP7P|PWP@OP^PFNQfPLL,QpPRP7P|PWP@OP^PFNQfPLL,QpPRP7P|PWP>QP^PFNQfPLL,QpPRP5P|PWP>QP^PFNQfPLL)QpPRP5P|PWP>QP^PFNPfPLL)QpPRP5P|PWP>Q‰P^PFNPfPLL)QpPRP5PzPWP>Q‰P^PFNPfPLL)QpPRP5PzPWP>Q‰P^PFNPfPLL)QnPRP5PzPWP>Q‰P^PFNPdPLL)‘PnPRP5PzPWP>Q‰P\PFNPdPLL)‘PnPRP5PzPVP>Q‰P\PFNPdPLL)‘PnPP5PzPVP>Q‰P\PFNPdPKK)‘PnPP5PzPVP>Q‰P\PFNPdPKK)‘PnPP5PzPVP>Q‰P\PDQPdPKK)‘PnPP5PzPVP=O‰P\PDQPdPKK)‘PnPP3PzPVP=P‰P\PDQPdPKK'PnPP3PzPVP=P‰P\PDQ‘PdPKK'PnPP3PzPVP=P†P\PDQ‘PdPKK'PnPP3PzPVP=P†P\PD‘W‘PdPKK'PnPP3PwPVP=P†P\PD‘W‘PdPKK'PlPP3PwPVP=P†P\PD‘W‘PbPK‹gPlPP3PwPVP=P†P[PD‘W‘PbPK‹gPlPP3PwPUP=P†P[PD‘W‘PbPK‹gPlPPPqPtPTP9PPXP@PP^PFŽ[PdPK‹d‘PjPNN.‘PrPSP7P|PWP>‘P‰P\PD‘S‘PaPI‰a‘PhPMM,‘PpPRP5PzPVP=P†PZPA‘PP_PG^‘PfPLL)‘PnPP3PwPTP9PPXP@PP^PFNPdPKK'PlPOO.‘PrPSP7P|PWP>‘P‰P\PDQ‘PbPJJ!‘PhPMM,‘PpPRP5PzPVP=O†P[PCO‘P_PGO‘PfPLL)‘PnPP3PwPUP;O‚PXP@OP^PFNPdPKK'PlPOO1PtPSP7P|PWP>Q‰P\PDQ‘PbPJJ$‘PjPNN,‘PpPRP5PzPVP=O†P[PCO‘PaPII‘PfPLL)QnPP3PwPUP;O‚PZPAQP^PFNPdPKK'PlPOO1PtPTP9PPWP>Q‰P\PDQ‘PbPJJ$QjPNN.QrPSP5PzPVP=O†P[PCO‘PaPII!QhPMM)QnPP3PwPUP;O‚PZPAQP_PGOQdPKK'PlPOO1PtPTP9PPXP@OM\PDQQbPJJ$QjPNN.QrPSP7P|PVP=OF[PCOQaPII!QhPMM,QpPRP3PwPUP;OBZPAQP_PGOQfPLL'PlPOO1PtPTP9P?XP@OM^PFNPbPJJ$QjPNN.QrPSP7P<WP>QI[PCOQaPII!QhPMM,QpPRP5P:VP;OBZPAQP_PGOQfPLL)QnPP1P4TP9P?XP@OM^PFNPdPKK$QjPNN.Q2SP7P<WP>QI\PDQQaPII!QhPMM,Q0RP5P:VP=OFZPAQP_PGOQfPLL)QnPP3P7UP9P?XP@OM^PFNPdPKK'PlPOO.Q2SP7P<WP>QI\PDQQbPJJ$QhPMM,Q0RP5P:VP=OF[PCOQ_PGOQfPLL)Q.P3P7UP;OBZP@OM^PFNPdPKK'P,OO1P4TP7P<WP>QI\PDQQbPJJ$QjPNN,Q0RP5P:VP=OF[PCOQaPII!QfPLL)Q.P3P7UP;OBZPAQP^PFNPdPKK'P,OO1P4TP9P?XP>QI\PDQQbPJJ$QjPNN.Q2SP5P:VP=OF[PCOQaPII!QhPMM,Q.P3P7UP;OBZPAQP_PGOQdPKK'PlPOO1P4TP9P?XP@OM^PDQQbPJJ$QjPNN.Q2SP7P<WP=OF[PCOQaPII!QhPMM,QpPRP3P7UP;OBZPAQP_PGOQfPLL)QlPOO1P4TP9P?XP@OM^PFNPbPJJ$QjPNN.QrPSP7P<WP>QI\PCOQaPII!QhPMM,QpPRP5PzPVP;OBZPAQP_PGOQfPLL)QnPP3PtPTP9P?XP@OM^PFNPdPKK'PjPNN.QrPSP7P|PWP>QI\PDQQaPII!QhPMM,QpPRP5PzPVP=O†P[PAQP_PGOQfPLL)QnPP3PwPUP9PPXP@OP^PFNPdPKK'PlPOO1PrPSP7P|PWP>Q‰P\PDQ‘PbPJJ$QhPMM,QpPRP5PzPVP=O†P[PCO‘PaPGO‘PfPLL)QnPP3PwPUP;O‚PZP@OP^PFNPdPKK'PlPOO1PtPTP9P|PWP>Q‰P\PDQ‘PbPJJ$‘PjPNN.QPPqPtPSPPwP|PVPP}P‚PZPP‘PP^PP„‘W‘PbPP‰‰a‘PfPPŒŒi‘PlPOn‘PrPSPPuPzPUPP{P‚PXPP€P‰P\PP„‘S‘PaPP‡^‘PfPK‹gPjPNŽn‘PpPRPPsPwPUPPyPPWPP~‘P‰P[PPƒPP_PG[PdPJŠd‘PjPMl‘PnPPPsPtPTPPwP|PWPP}P†PZPA‘PP^PFŽW‘PbPJŠa‘PhPLŒi‘PnPOqPrPSPPwPzPVP;P‚PZP@PP\PD‘W‘PaPI‰^‘PfPLŒgPlPNŽn‘PrPRPPuPwPUP;PPXP>‘P‰P\PCS‘P_PG^‘PdPK‹d‘PjPNŽl‘PpPP3PwPTP9P|PWP>‘P†P[PA‘PP_PFŽ[PbPJŠd‘PhPMM)‘PnPP1PtPSP7P|PVP=P‚PZPA‘PP^PD‘W‘PbPI‰a‘PfPLL)‘PlPOO.‘PrPSP5PzPUP;P‚PXP@P‰P\PD‘S‘PaPGO‘PfPKK'PjPNN.‘PpPRP3PwPUP9PPWP>‘P‰P[PCPP_PGOPdPJJ$‘PjPMM,‘PnPP3PtPTP7P|PWP=P†PZPA‘PP^PFN‘PbPJJ!‘PhPLL)‘PnPOO1PrPSP7PzPVP;P‚PZP@OP^PDQ‘PaPII!‘PfPLL'PlPOO.‘PrPRP5PzPUP;PPXP@O‰P\PCO‘PaPGO‘PdPKK'PjPNN,‘PpPRP3PwPTP9PPWP>Q†P[PCOP_PFNPdPJJ$‘PhPMM,‘PnPP1PtPTP7P|PVP=O†PZPAQP^PFN‘PbPII!‘PhPLL)‘PlPOO1PrPSP5PzPVP;O‚PXP@OP\PDQ‘PaPII‘PfPKK'PlPNN.‘PpPRP5PwPUP9PPXP>Q‰P[PCO‘P_PGOPdPKK$‘PjPMM,‘PpPP3PtPTP9P|PWP=O†P[PAQP^PFNPbPJJ!‘PhPMM)‘PnPOO1PtPSP7PzPVP=O‚PZP@OP^PDQ‘PaPII!‘PfPLL'PlPOO.‘PrPRP5PzPUP;OPXP@O‰P\PCO‘PaPGO‘PdPKK'PjPNN,‘PpPRP3PwPTP9PPWP>Q†P[PCOP_PFNPdPJJ$‘PhPMM,‘PnPP1PtPTP7P|PVP=O†PZPAQP^PFN‘PbPII!‘PhPLL)‘PlPOO1PrPSP5PzPVP;P‚PXP@OP\PDQ‘PaPII‘PfPLL'PlPNN.‘PrPRP5PwPUP;PPXP>Q‰P\PCO‘P_PGO‘PdPKK$‘PjPNN,‘PpPP3PwPTP9P|PWP>‘P†P[PAQP_PFNPbPJJ$‘PhPMM)‘PnPP1PtPSP7P|PVP=P‚PZPA‘PP^PDQ‘PbPII!‘PfPLL)‘PlPOO.‘PrPSP5PzPUP;P‚PXP@P‰P\PD‘S‘PaPGO‘PfPKK'PjPNN.‘PpPRP3PwPUP9PPWP>‘P‰P[PCPP_PG[PdPJJ$‘PjPMM,‘PnPP3PtPTP7P|PWP=P†PZPA‘PP^PFŽW‘PbPJŠa‘PhPLL)‘PnPOO1PrPSP7PzPVP;P‚PZP@PP\PD‘W‘PaPI‰^‘PfPLŒgPlPNŽn‘PrPRP5PwPUP;PPXP>‘P‰P\PCS‘P_PG^‘PdPK‹d‘PjPNŽl‘PpPPPsPwPTP9P|PWP>‘P†P[PA‘PP_PFŽ[PbPJŠd‘PhPMi‘PnPPPqPtPSPPwP|PVPP}P‚PZPA‘PP^PD‘W‘PbPI‰a‘PfPLŒi‘PlPOn‘PrPSPPuPzPUPP{P‚PXPP€P‰P\PP„‘S‘PaPG^‘PfPK‹gPjPNŽn‘PpPPPsPtPSPPuPwPUPPyP|PVPP}P‚PXPP~‘P†P[PP‘PP\PCS‘P_PFŽW‘PbPI‰^‘PdPJŠd‘PhPLŒgPlPNŽl‘PnPOqPrPRPPsPwPTPPwPzPUP;PPWP=P‚PZP@P‰P[PCPP^PD‘S‘PaPG[PbPJŠa‘PfPK‹d‘PjPMi‘PlPOO.‘PpPP1PtPSP5PwPTP9P|PVP;P‚PXP>‘P†PZPA‘PP\PCS‘P_PFŽW‘PaPII‘PdPJJ$‘PhPLL'PjPNN,‘PnPOO.‘PrPRP3PtPTP7PzPUP9PPWP=P‚PZP@P‰P[PAQP^PDQ‘P_PGOPbPII!‘PfPKK$‘PhPMM)‘PlPNN.‘PpPP1PrPSP5PwPTP9P|PVP;OPXP>Q†PZP@OP\PCOP_PFN‘PaPGO‘PdPJJ!‘PhPLL'PjPMM,‘PnPOO.‘PrPRP3PtPSP7PzPUP9P|PWP=O‚PXP@O‰P[PAQP^PDQ‘P_PGOPbPII‘PfPKK$‘PhPMM)QlPNN,QpPP1PrPRP5PwPTP7P|PVP;OPWP>Q†PZP@OP\PCOP^PFN‘PaPGOQdPJJ!QfPLL'PjPMM)QnPOO.QpPRP3PtPSP5PzPUP9P|PWP=O‚PXP>Q‰P[PAQP^PDQQ_PFNPbPIIQdPKK$QhPLL)QlPNN,QnPP1PrPRP5PwPTP7PzPVP;OPWP>Q†PZP@OI\PCOP^PDQQaPGOPdPJJ!QfPKK'PjPMM)QnPOO.QpPP3PtPSP5PzPUP9P|PVP=OBXP>QF[PAQM\PDQQ_PFNQbPIIQdPKK$QhPLL'PlPNN,QnPP1PrPRP3PwPTP7P:UP;O?WP=OFZP@OI[PCOP^PDQQaPGOPbPJJ!QfPKK$QjPMM)QlPOO.QpPP1PtPSP5P7UP9P<VP;OBXP>QF[PAQM\PCOQ_PFNQaPIIQdPJJ$QhPLL'PjPNN,QnPOO1PrPRP3PtPTP7P:UP;O?WP=OBZP@OI[PAQP^PDQQaPGOPbPII!QfPKK$QjPMM)QlPNN.QpPP1PtPSP5P7TP9P<VP;O?XP>QFZPAQM\PCOP_PFNQaPIIQdPJJ!QhPLL'PjPNN,QnPOO.QrPRP3PtPSP7P:UP9P?WP=OBXP@OI[PAQP^PDQQ_PGOPbPII!QfPKK$QhPMM)QlPNN,QpPP1PrPSP5PwPTP7P|PVP;O?XP>QFZP@OM\PCOP_PFNQaPGOQdPJJ!QfPLL'PjPMM,QnPOO.QpPRP3PtPSP7PzPUP9P|PWP=O‚PXP@OI[PAQM^PDQQ_PFNPbPIIQfPKK$QhPLL)QlPNN,QpPP1PrPRP5PwPTP7PzPVP;OPWP>Q†PZP@O‰P\PCOP^PFNQaPGOPdPJJ!QfPLL'PjPMM)QnPOO.QpPP3PtPSP5PzPUP9P|PVP=O‚PXP>Q‰P[PAQP\PDQ‘P_PFNPbPIIQdPKK$QhPLL'PlPNN,QnPP1PrPRP3PwPTP7PzPVP;OPWP=O†PZP@O‰P\PCOP^PDQ‘PaPGOPbPJJ!‘PfPKK'PjPMM)‘PlPOO.QPPn‘PpPPPqPrPRPPsPtPRPPsPtPSPPuPwPTPPwPzPTPPwPzPUPPyP|PVPP{PPVPP{PPWPP}P‚PXPP~‘P†PXPP~‘P†PZPP€P‰P[PP‘PP[PP‘PP\PPƒPP^PD‘S‘P^PD‘S‘P_PFŽW‘PaPG[PaPG[PbPI‰^‘PdPJŠa‘PdPJŠa‘PfPK‹d‘PhPLŒgPhPLŒgPjPMi‘PlPNŽl‘PlPNŽl‘PnPOn‘PpPPPqPpPPPqPrPRPPsPtPSPPuPtPSP5PwPTP7PzPUP9PzPUP9P|PVP;PPWP=PPWP=P‚PXP>‘P†PZP@P†PZP@P‰P[PA‘PP\PCPP\PCPP^PD‘S‘P_PFŽS‘P_PFŽW‘PaPG[PbPI‰[PbPI‰^‘PdPJJ!‘PfPKK!‘PfPKK$‘PhPLL'PjPMM'PjPMM)‘PlPNN,‘PnPOO,‘PnPOO.‘PpPP1PrPP1PrPRP3PtPSP5PwPSP5PwPTP7PzPUP9P|PUP9P|PVP;PPWP=P‚PWP=P‚PXP>‘P†PZP@O‰PZP@O‰P[PAQP\PCOP\PCOP^PDQ‘P_PFN‘P_PFN‘PaPGOPbPII‘PbPII‘PdPJJ!‘PfPKK$‘PfPKK$‘PhPLL'PjPMM)‘PjPMM)‘PlPNN,‘PnPOO.‘PnPOO.‘PpPP1PrPRP3PrPRP3PtPSP5PwPTP7PwPTP7PzPUP9P|PVP;O|PVP;OPWP=O‚PXP>Q‚PXP>Q†PZP@O‰P[PAQ‰P[PAQP\PCOP^PDQP^PDQ‘P_PFN‘PaPGO‘PaPGOPbPII‘PdPJJ‘PdPJJ!‘PfPKK$‘PhPLL$‘PhPLL'PjPMM)‘PlPNN)‘PlPNN,QnPOO.QpPP.QpPP1PrPRP3PtPRP3PtPSP5PwPTP7PzPTP7PzPUP9P|PVP;OPVP;OPWP=O‚PXP>Q†PXP>Q†PZP@O‰P[PAQP[PAQP\PCOP^PDQ‘P^PDQ‘P_PFN‘PaPGOPaPGOPbPII‘PdPJJ!‘PdPJJ!‘PfPKK$‘PhPLL'PhPLL'PjPMM)QlPNN,QlPNN,QnPOO.QpPP1PpPP1PrPRP3PtPSP5PtPSP5PwPTP7PzPUP9PzPUP9P|PVP;OPWP=OPWP=O‚PXP>Q†PZP@O†PZP@O‰P[PAQP\PCOP\PCOP^PDQ‘P_PFN‘P_PFN‘PaPGOPbPIIPbPII‘PdPJJ!‘PfPKK!‘PfPKK$‘PhPLL'PjPMM'PjPMM)‘PlPNN,‘PnPOO,‘PnPOO.‘PpPP1PrPP1PrPRP3PtPSP5PwPSP5PwPTP7PzPUP9P|PUP9P|PVP;OPWP=O‚PWP=O‚PXP>Q†PZP@O‰PZP@O‰P[PAQP\PCOP\PCOP^PDQ‘P_PFN‘P_PFN‘PaPGOPbPII‘PbPII‘PdPJJ!‘PfPKK$‘PfPKK$‘PhPLL'PjPMM)‘PjPMM)‘PlPNN,‘PnPOO.‘PnPOO.‘PpPP1PrPRP3PrPRP3PtPSP5PwPTP7PwPTP7PzPUP9P|PVP;P|PVP;PPWP=P‚PXP>‘P‚PXP>‘P†PZP@P‰P[PA‘P‰P[PA‘PP\PCPP^PD‘PP^PD‘S‘P_PFŽW‘PaPGW‘PaPG[PbPI‰^‘PdPJŠ^‘PdPJŠa‘PfPK‹d‘PhPLŒd‘PhPLŒgPjPMi‘PlPNŽi‘PlPNŽl‘PnPOn‘PpPPOn‘PpPOn‘PnPOl‘PnPNŽl‘PnPNŽl‘PlPNŽi‘PlPMi‘PlPMi‘PjPMgPjPLŒgPjPLŒgPhPLŒd‘PhPK‹d‘PhPK‹d‘PfPK‹a‘PfPJŠa‘PfPJŠa‘PdPJŠ^‘PdPI‰^‘PdPI‰^‘PbPI‰[PbPG[PbPG[PaPGW‘PaPFŽW‘PaPFŽW‘P_PFŽS‘P_PD‘S‘P_PD‘S‘P^PD‘PP^PCPP^PCPP\PCPP\PA‘PP\PA‘PP[PA‘P‰P[P@P‰P[P@P‰PZP@P†PZP>‘P†PZP>‘P†PXP>‘P‚PXP=P‚PXP=P‚PWP=PPWP;PPWP;PPVP;P|PVP9P|PVP9P|PUP9PzPUP7PzPUP7PzPTP7PwPTP5PwPTP5PwPSP5PtPSP3PtPSP3PtPRP3PrPRP1PrPRP1PrPP1PpPP.‘PpPP.‘PpPOO.‘PnPOO,‘PnPNN,‘PnPNN,‘PlPNN)‘PlPMM)‘PlPMM)‘PjPMM'PjPLL'PjPLL'PhPLL$‘PhPKK$‘PhPKK$‘PfPKK!‘PfPJJ!‘PfPJJ!‘PdPJJ‘PdPII‘PdPII‘PbPIIPbPGOPbPGOPaPGO‘PaPFN‘PaPFN‘P_PFN‘P_PDQ‘P_PDQ‘P^PDQP^PCOP^PCOP\PCOP\PAQP\PAQP[PAQ‰P[P@O‰P[P@O‰PZP@O†PZP>Q†PZP>Q†PXP>Q‚PXP=O‚PXP=O‚PWP=OPWP;OPWP;OPVP;O|PVP9P|PVP9P|PUP9PzPUP7PzPUP7PzPTP7PwPTP5PwPTP5PwPSP5PtPSP3PtPSP3PtPRP3PrPRP1PrPRP1PrPP1PpPP.‘PpPP.‘PpPOO.‘PnPOO,‘PnPOO,‘PnPNN,‘PlPNN)‘PlPNN)‘PlPMM)‘PjPMM'PjPMM'PjPLL'PhPLL$‘PhPLL$‘PhPKK$‘PfPKK!‘PfPKK!‘PfPJJ!‘PdPJJ‘PdPJJ‘PdPII‘PbPIIPbPIIPbPGOPaPGO‘PaPGO‘PaPFN‘P_PFN‘P_PFN‘P_PDQ‘P^PDQP^PDQP^PCOP\PCOP\PCOP\PAQP[PAQ‰P[PAQ‰P[P@O‰PZP@O†PZP@O†PZP>Q†PXP>Q‚PXP>Q‚PXP=O‚PWP=OPWP=PPWP;PPVP;P|PVP;P|PVP9P|PUP9PzPUP9PzPUP7PzPTP7PwPTP7PwPTP5PwPSP5PtPSP5PtPSP3PtPRP3PrPRP3PrPRP1PrPP1PpPP1PpPP.‘PpPOO.‘PnPOO.‘PnPOO,‘PnPNN,‘PlPNN,‘PlPNN)‘PlPMM)‘PjPMM)‘PjPMM'PjPLL'PhPLL'PhPLL$‘PhPKK$‘PfPKK$‘PfPKK!‘PfPJJ!‘PdPJJ!‘PdPJJ‘PdPII‘PbPI‰^‘PbPI‰[PbPG[PaPG[PaPGW‘PaPFŽW‘P_PFŽW‘P_PFŽS‘P_PD‘S‘P^PD‘S‘P^PD‘PP^PCPP\PCPP\PCPP\PA‘PP[PA‘PP[PA‘P‰P[P@P‰PZP@P‰PZP@P†PZP>‘P†PXP>‘P†PXP>‘P‚PXP=P‚PWP=P‚PWP=PPWP;PPVP;PPVP;P|PVP9P|PUP9P|PUPPyPzPUPPwPzPTPPwPzPTPPwPwPTPPuPwPSPPuPwPSPPuPtPSPPsPtPRPPsPtPRPPsPrPRPPqPrPPPqPrPPPqPpPPPn‘PpPOl‘PnPNŽi‘PjPLŒgPhPK‹a‘PfPJŠ^‘PbPG[PaPFŽS‘P_PD‘PP\PA‘PP[P@P†PZP>‘P‚PWP;PPVP9PzPUPPwPwPSPPsPtPRPPqPpPPPn‘PnPNŽi‘PlPMgPhPK‹d‘PfPJŠ^‘PdPI‰[PaPFŽW‘P_PD‘PP^PCPP[P@P‰PZP>‘P‚PXP=PPVP9P|PUP7PwPTP5PtPRP1PrPP.‘PnPNN,‘PlPMM'PjPLL$‘PfPJJ!‘PdPI‰[PbPGW‘P_PD‘S‘P^PCPP\PA‘P‰PZP>‘P†PXP=PPWP;P|PUP7PzPTP5PtPSP3PrPP.‘PpPOO,‘PlPMM)‘PjPLL$‘PhPKK!‘PdPII‘PbPGO‘PaPFN‘P^PCOP\PAQ‰P[P@P†PXP=P‚PWP;P|PVP9PzPTP5PwPSP3PrPRP1PpPOO,‘PnPNN)‘PjPLL'PhPKK!‘PfPJJ‘PbPGOPaPFN‘P_PDQP\PAQP[P@O†PZP>Q‚PWP;OPVP9PzPUP7PwPSP3PtPRP1PpPP.‘PnPNN)‘PlPMM'PhPKK$‘PfPJJ‘PdPIIPaPFN‘P_PDQP^PCOP[P@O‰PZP>Q‚PXP=OPVP9P|PUP7PwPTP5PtPRP1PrPP.‘PnPNN,‘PlPMM'PjPLL$‘PfPJJ!‘PdPIIPbPGO‘P_PDQ‘P^PCOP\PAQ‰PZP>Q†PXP=OPWP;O|PUP7PzPTP5PtPSP3PrPP.QpPOO,QlPMM)‘PjPLL$‘PhPKK!‘PdPII‘PbPGO‘PaPFN‘P^PCOP\PAQ‰P[P@O†PXP=O‚PWP;O|PVP9PzPTP5PwPSP3PrPRP1PpPOO,QnPNN)‘PjPLL'PhPKK!‘PfPJJ‘PbPGOPaPFN‘P_PDQP\PAQP[P@O†PZP>Q‚PWP;OPVP9PzPUP7PwPSP3PtPRP1PpPP.QnPNN)‘PlPMM'PhPKK$‘PfPJJ‘PdPIIPaPFN‘P_PDQP^PCOP[P@O‰PZP>Q‚PXP=OPVP9P|PUP7PwPTP5PtPRP1PrPP.QnPNN,‘PlPMM'PjPLL$‘PfPJJ!‘PdPIIPbPGO‘P_PDQ‘P^PCOP\PAQ‰PZP>Q†PXP=OPWP;O|PUP7PzPTP5PtPSP3PrPP.‘PpPOO,‘PlPMM)‘PjPLL$‘PhPKK!‘PdPII‘PbPGO‘PaPFN‘P^PCOP\PAQ‰P[P@O†PXP=O‚PWP;O|PVP9PzPTP5PwPSP3PrPRP1PpPOO,‘PnPNN)‘PjPLL'PhPKK!‘PfPJJ‘PbPGOPaPFN‘P_PDQP\PAQP[P@O†PZP>‘P‚PWP;PPVP9PzPUP7PwPSP3PtPRP1PpPP.‘PnPNN)‘PlPMM'PhPKK$‘PfPJJ‘PdPIIPaPFN‘P_PD‘PP^PCPP[P@P‰PZP>‘P‚PXP=PPVP9P|PUP7PwPTP5PtPRP1PrPP.‘PnPNN,‘PlPMM'PjPLL$‘PfPJŠa‘PdPI‰[PbPGW‘P_PD‘S‘P^PCPP\PA‘P‰PZP>‘P†PXP=PPWP;P|PUP7PzPTP5PtPSP3PrPPPn‘PpPOl‘PlPMi‘PjPLŒd‘PhPK‹a‘PdPI‰^‘PbPGW‘PaPFŽS‘P^PCPP\PA‘P‰P[P@P†PXP=P‚PWP;P|PVPPyPzPTPPuPwPSPPsPrPRPPqPpPOl‘PlPLŒd‘PfPJŠ^‘PaPFŽS‘P^PCPPZP>‘P‚PWP;P|PTPPuPtPRPPqPnPNŽi‘PjPLŒd‘PdPI‰[PaPFŽS‘P\PA‘P‰PZP>‘P‚PVP9PzPTP5PrPP.‘PnPNN)‘PhPK‹a‘PdPI‰[P_PD‘PP\PA‘P‰PXP=PPVP9PwPSP3PrPP.‘PlPMM'PhPKK!‘PbPGO‘P_PD‘PP[P@P†PXP=P|PUP7PwPSP3PpPOO,‘PlPMM'PfPJJ‘PbPGO‘P^PCOP[P@O‚PWP;P|PUP7PtPRP1PpPOO)‘PjPLL$‘PfPJJPaPFN‘P^PCO‰PZP>Q‚PWP;OzPTP5PtPRP.‘PnPNN)‘PjPLL!‘PdPIIPaPFNP\PAQ‰PZP=OPVP9PzPTP3PrPP.QnPNN'PhPKK!‘PdPII‘P_PDQP\P@O†PXP=OPVP7PwPSP3PrPP,QlPMM'PhPJJQbPGO‘P_PCOP[P@O†PXP;O|PUP7PwPSP1PpPOO,QlPLL$QfPJJQbPFNQ^PCOM[P>Q‚PWP;O|PTP5PtPRP1PpPNN)QjPLL$QfPIIPaPFNQ^PAQIZP>QBVP9PzPTP5PtPP.QnPNN)QjPKK!QdPIIPaPDQP\PAQIXP=O?VP9PzPSP3PrPP.QnPMM'PhPKK!QbPGOQ_PDQP[P@OFXP=O?UP7P7SP3PrPOO,QlPMM'PfPJJQbPGOQ^PCOM[P@OFWP;O<UP7P4RP1P0OO,QjPLL$QfPJJQaPFNQ^PCOMZP>QBWP;O:TP5P4RP1P.NN)QjPLL$QdPIIPaPFNP\PAQIZP>Q?VP9P:TP5P2P.Q.NN)QhPKK!QdPIIQ_PDQP\PAQFXP=O?VP9P7SP3P2P,Q,MM'P(KKQbPGOQ_PDQM[P@OFXP=O<UP7P7SP1P0OO,Q,MM$Q&JJQbPGOQ^PCOM[P>QBWP;O<UP5P4RP1P0OO)Q*LL$QfPJJPaPFNQ^PAQIZP>QBWP9P:TP5P4RP.Q.NN)Q*LL!QdPIIPaPDQP\PAQIZP=O?VP9P:TP3P2P.Q.MM'P(KK!QdPGOQ_PDQP\P@OFXP=O?VP7P7SP3P2OO,Q,MM'PhPJJQbPGOQ_PCOM[P@OFWP;O<UP7P7RP1P0OO,Q,LL$QfPJJQbPFNQ^PCOMZP>QBWP;O<TP5P4RP1P0NN)QjPLL$QdPIIPaPFNQ\PAQIZP>QBVP9P:TP5P4P.QnPNN)QhPKK!QdPIIP_PDQP\PAQIXP=O?VP9P7SP3P2P.QlPMM'PhPKK!QbPGOQ_PDQP[P@OFXP=O<UP7P7SP3PpPOO,QlPMM'PfPJJQbPGOQ^PCOM[P@OBWP;O<UP7PtPRP1PpPOO,QjPLL$QfPJJPaPFNQ^PCOIZP>Q‚PWP;OzPTP5PtPRP1PnPNN)QjPLL!QdPIIPaPFNP\PAQ‰PZP>QPVP9PzPTP3PrPPPOi‘PjPK‹a‘PbPGS‘P\PA‘P†PXPP{P|PTPPuPrPPPl‘PlPLŒd‘PdPI‰W‘P_PCPPZP>‘PPVP7PwPRPPqPnPNŽgPfPJŠ[PaPD‘PP[P@P‚PWP9PzPSP3PpPOi‘PjPK‹a‘PbPGS‘P^PA‘P‰PXP=P|PUP5PrPP,‘PlPLL$‘PdPI‰W‘P_PCPPZP>‘PPVP7PwPRP1PnPNN'PhPJJ‘PaPFŽPP\P@P‚PWP9PzPSP3PpPOO)‘PjPKK!‘PbPGO‘P^PA‘P‰PXP=P|PUP5PtPP.‘PlPMM$‘PfPII‘P_PCOPZP>QPVP7PwPRP1PnPNN'PhPJJ‘PaPFNP\P@O†PWP;OzPTP3PrPOO)‘PjPKK!‘PbPGO‘P^PAQ‰PXP=O|PUP5PtPP.‘PlPMM$‘PfPIIP_PDQP[P>Q‚PVP7PwPRP1PnPNN'PhPJJ‘PaPFNP\P@O†PWP;OzPTP3PrPOO,QjPLL!‘PdPGO‘P^PAQ‰PXP=O|PUP5PtPP.QlPMM$QfPIIP_PDQP[P>Q‚PVP9PwPSP1PpPNN)QhPJJQaPFNP\P@O†PWP;OzPTP3PrPOO,QjPLL!QdPGOQ^PCO‰PZP=OPUP7PtPP.QlPMM$QfPIIP_PDQM[P>Q‚PVP9PwPSP1PpPNN)QhPKKQbPFNQ\PAQFWP;OzPTP3PrPOO,QjPLL!QdPGOQ^PCOIZP=OPUP7PtPRP.QnPMM'PfPJJP_PDQM[P>QBVP9PwPSP1PpPNN)QhPKKQbPFNQ\PAQFXP;O<TP5PrPP,QjPLL!QdPGOQ^PCOIZP=O?UP7PtPRP.QnPMM'PfPJJPaPDQP[P@OBVP9P7SP1PpPNN)QhPKKQbPFNQ\PAQFXP;O<TP5PrPP,QlPLL$QdPIIQ^PCOIZP=O?UP7P4RP.QnPMM'PfPJJPaPDQP[P@OBWP9P:SP3PpPOO)QhPKKQbPFNQ\PAQFXP;O<TP5PrPP,QlPLL$QdPIIQ_PCOMZP>Q?VP7P4RP.QnPMM'PfPJJPaPDQP[P@OBWP9P:SP3PpPOO)QjPKK!QbPGOQ^PAQFXP;O<TP5PrPP,QlPLL$QdPIIQ_PCOMZP>Q?VP7PwPRP1PnPNN'PhPJJPaPDQP[P@OBWP9P:SP3PpPOO)QjPKK!QbPGOQ^PAQIXP=O<UP5PtPP,QlPLL$QdPIIQ_PCOMZP>Q?VP7PwPRP1PnPNN'PhPJJQaPFNP\P@OFWP9PzPSP3PpPOO)QjPKK!QbPGOQ^PAQIXP=O|PUP5PtPP.QlPMM$QfPIIP_PCOMZP>QPVP7PwPRP1PnPNN'PhPJJQaPFNP\P@O†PWP;OzPTP3PrPOO,QjPKK!QbPGOQ^PAQ‰PXP=O|PUP5PtPP.QlPMM$QfPIIP_PDQP[P>Q‚PVP9PwPRP1PnPNN'PhPJJ‘PaPFNP\P@O†PWP;OzPTP3PrPOO,QjPLL!‘PdPGO‘P^PCO‰PXP=O|PUP5PtPPPNŽgPhPPŠŠ[P_PPƒP‰PXPP}P|PTPPsPpPNŽgPhPJŠ[P_PPƒP‰PXPP}P|PTPPsPpPNŽgPhPJŠ[P_PPƒP‰PXPP}P|PTPPsPpPNŽgPhPJŠ[P_PCP‰PXPP{P|PTPPsPpPNŽgPfPJŠ[P_PCP‰PXP;P|PTPPsPpPNŽgPfPJŠ[P_PCP‰PXP;P|PTPPsPpPNŽgPfPJŠ[P_PCP‰PXP;PzPTP3PpPNŽgPfPI‰[P_PCP‰PXP;PzPTP3PpPNŽgPfPI‰[P_PCP‰PXP;PzPTP3PpPNN'PfPI‰[P_PCP‰PXP;PzPTP3PpPNN'PfPII‘P_PCP‰PXP;PzPSP3PpPNN'PfPII‘P_PCP‰PXP;PzPSP3PpPNN'PfPII‘P_PCP‰PXP;PzPSP3PpPNN'PfPII‘P_PCO‰PXP;PzPSP1PpPNN'PfPII‘P^PCO‰PXP;PzPSP1PpPNN'PfPII‘P^PCO‰PXP;OzPSP1PpPNN'PfPII‘P^PCO‰PXP;OzPSP1PnPNN'PfPII‘P^PAQ‰PXP;OzPSP1PnPNN'PfPII‘P^PAQ‰PXP;OzPSP1PnPNN'PfPII‘P^PAQ‰PXP;OzPSP1PnPNN'PfPII‘P^PAQ†PXP;OzPSP1PnPMM'PfPII‘P^PAQ†PXP;OzPSP1PnPMM'PfPII‘P^PAQ†PXP;OzPSP1PnPMM'PfPII‘P^PAQ†PWP;OzPSP1PnPMM$QfPII‘P^PAQ†PWP;OzPSP1PnPMM$QfPII‘P^PAQ†PWP;OzPSP1PnPMM$QfPII‘P^PAQ†PWP;OzPSP1PnPMM$QdPII‘P^PAQ†PWP9PzPSP1PnPMM$QdPII‘P^PAQ†PWP9PzPSP1PnPMM$QdPIIQ^PAQ†PWP9PzPSP1PnPMM$QdPIIQ^PAQ†PWP9PwPSP1PnPMM$QdPGOQ^PAQ†PWP9PwPSP1PnPMM$QdPGOQ^PAQ†PWP9PwPSP1PnPMM$QdPGOQ^PAQ†PWP9PwPRP1PnPMM$QdPGOQ^PAQ†PWP9PwPRP1PnPMM$QdPGOQ^PAQ†PWP9PwPRP1PnPMM$QdPGOQ^PAQ†PWP9PwPRP1PnPMM$QdPGOQ\PAQ†PWP9PwPRP.QnPMM$QdPGO‘P\PAQ†PWP9PwPRP.QnPMM$QdPGO‘P\PAQ†PWP9PwPRP.QnPMM$QdPGO‘P\P@O†PWP9PwPRP.QlPMM$QdPGO‘P\P@O†PWP9PwPRP.QlPMM$QdPGO‘P\P@O†PWP9PwPRP.QlPMM$QdPGO‘P\P@O†PWP9PwPRP.QlPLL$QdPGO‘P\P@O‚PWP9PwPRP.QlPLL$‘PdPGO‘P\P@O‚PWP9PwPRP.QlPLL$‘PdPGO‘P\P@O‚PWP9PwPRP.QlPLL$‘PdPGO‘P\P@O‚PVP9PwPRP.QlPLL!‘PdPGO‘P\P@O‚PVP9PwPRP.‘PlPLL!‘PdPGO‘P\P@O‚PVP9PwPRP.‘PlPLL!‘PdPGO‘P\P@O‚PVP7PwPRP.‘PlPLL!‘PbPGO‘P\P@O‚PVP7PwPRP.‘PlPLL!‘PbPGO‘P\P@O‚PVP7PwPRP.‘PlPLL!‘PbPGO‘P\P@O‚PVP7PwPRPPPi‘PhPJŠ[P^PA‘P†PWPPyPtPPPl‘PjPK‹[P_PCP‰PXP9PwPRPPn‘PlPK‹^‘PaPD‘P‰PXP;PzPSPPn‘PlPLŒa‘PbPD‘PPZP=P|PSP1PnPMd‘PbPFŽPP[P>‘P|PTP3PpPMM$‘PdPGS‘P[P>‘PPUP5PpPNN'PfPI‰S‘P\P@P‚PVP5PrPOO)‘PhPII‘P^PA‘P‚PVP7PtPP)‘PhPJJP_PA‘P†PWP9PwPP,‘PjPKK‘P_PCO‰PXP;PwPRP.‘PlPKK‘PaPDQPXP;PzPSP1PlPLL!‘PbPFNPZP=O|PTP1PnPMM$‘PdPFNP[P>Q|PTP3PpPNN$‘PdPGO‘P\P>QPUP5PrPNN'PfPII‘P\P@O‚PVP7PrPOO)‘PhPII‘P^PAQ†PVP7PtPP,‘PhPJJP_PCO†PWP9PwPRP,QjPKK‘PaPCO‰PXP;OwPRP.QlPLL‘PaPDQPZP;OzPSP1PnPLL!QbPFNPZP=O|PTP3PnPMM$QdPFNP[P>QPTP3PpPNN'PdPGO‘P\P@OPUP5PrPOO'PfPIIQ^P@O‚PVP7PrPOO)QhPJJQ^PAQ†PWP7PtPP,QjPJJP_PCO‰PWP9PwPRP.QjPKKQaPCOIXP;OzPRP.QlPLL!QaPDQMZP=OzPSP1PnPMM!QbPFNP[P=O|PTP3PnPMM$QdPGOP[P>Q?UP3PpPNN'PfPGOQ\P@OBUP5PrPOO)QfPIIQ^P@OBVP7PtPOO)QhPJJP^PAQFWP9PtPP,QjPKKP_PCOIXP9PwPRP.QjPKKQaPDQIXP;O:SP.QlPLL!QbPDQMZP=O<SP1PnPMM$QbPFNP[P=O<TP3PpPMM$QdPGOQ[P>Q?UP5PpPNN'PfPIIQ\P@OBVP5PrPOO)QfPIIQ^PAQBVP7P4P)QhPJJP_PAQFWP9P7P,QjPKKQ_PCOIXP9P7RP.QlPKKQaPDQMXP;O:SP1PlPLL!QbPFNMZP=O<TP1PnPMM$QbPFNP[P>Q<TP3PpPNN$QdPGOQ\P>Q?UP5PrPNN'PfPIIQ\P@OBVP5PrPOO)QhPIIQ^PAQFVP7PtPP,QhPJJP_PCOFWP9P7RP,QjPKKQ_PCOIXP;O7RP.QlPLLQaPDQMZP;O:SP1PnPLL!QbPFNPZP=O<TP1PnPMM$QdPFNP[P>Q?TP3PpPNN'PdPGOQ\P@O?UP5PrPOO'PfPIIQ\P@OBVP7PrPOO)QhPJJQ^PAQFWP7PtPP,QjPJJP_PCOIWP9PwPRP,QjPKKQaPCOIXP;OzPRP.QlPLL!QaPDQMZP=OzPSP1PnPMM!QbPFNPZP=O|PTP3PnPMM$QdPGOP[P>QPUP3PpPNN'PfPGOQ\P@O‚PUP5PrPOO'PfPII‘P^P@O‚PVP7PtPOO)QhPJJP^PAQ†PWP9PtPP,QjPKKP_PCO‰PWP9PwPRP.QjPKK‘PaPDQ‰PXP;OzPSP.QlPLL!‘PbPDQPZP=O|PSP1PPPi‘PfPP‰‰S‘P\PP~‘PPTPPqPnPLŒa‘PaPP„‘P‰PXPPyPtPPPi‘PhPI‰W‘P\PP€PPTPPsPnPMa‘PbPD‘PPXPPyPwPPPl‘PhPJŠW‘P^PP€PPUPPsPpPMd‘PbPFŽPPXPP{PwPRPPl‘PjPJŠ[P^P@P‚PUPPuPpPNŽd‘PdPFŽPPZP;PzPRPPn‘PjPK‹[P^PA‘P‚PVP5PrPNŽgPdPFŽPPZP=PzPSP.‘PlPK‹[P_PA‘P†PVP7PrPOgPdPGPP[P=P|PSP1PlPK‹^‘P_PCP†PWP7PtPOO'PfPGS‘P[P>‘P|PSP1PlPLL‘PaPCP‰PWP7PtPOO)‘PfPI‰S‘P\P>‘P|PTP1PnPLL!‘PaPD‘P‰PWP9PtPP)‘PhPII‘P\P>‘PPTP3PnPMM!‘PbPDQ‰PXP9PwPP,‘PhPJJ‘P\P@OPUP3PpPMM$‘PbPDQPXP;PwPRP,‘PjPJJ‘P^P@O‚PUP5PpPNN$‘PbPFNPZP;OzPRP.‘PjPJJP^PAQ‚PVP5PrPNN$‘PdPFNPZP=OzPSP.‘PjPKKP_PAQ†PVP7PrPNN'PdPGOP[P=OzPSP.‘PlPKK‘P_PCO†PVP7PrPOO'PfPGO‘P[P=O|PSP1PlPLL‘PaPCO†PWP7PtPOO)‘PfPII‘P[P>Q|PTP1PnPLL!‘PaPCO‰PWP9PtPP)QhPII‘P\P>QPTP3PnPMM!‘PaPDQ‰PXP9PwPP,QhPII‘P\P@OPUP3PpPMM!QbPDQPXP;OwPRP,QhPJJ‘P^P@O‚PUP5PpPMM$QbPFNPZP;OzPRP,QjPJJP^PAQ‚PVP5PpPNN$QdPFNPZP;OzPRP.QjPKKP_PAQ‚PVP5PrPNN'PdPGOPZP=OzPSP.QlPKKQ_PAQ†PVP7PrPOO'PfPGOP[P=O|PSP1PlPLLQ_PCO†PWP7PtPOO)QfPGOQ[P>Q|PTP1PnPLLQaPCO‰PWP9PtPP)QfPIIQ\P>QPTP3PnPLL!QaPDQ‰PXP9PwPP)QhPIIQ\P@OPUP3PnPMM!QbPDQPXP;OwPP,QhPJJQ^P@O‚PUP3PpPMM$QbPFNPXP;OwPRP,QjPJJP^P@O‚PUP5PpPNN$QdPFNPZP;OzPRP.QjPKKP^PAQ‚PVP5PrPNN'PdPFNPZP=OzPSP.QlPKKP_PAQ†PVP7PrPOO'PdPGOP[P=O|PSP1PlPKKQ_PCO†PWP7PtPOO'PfPGO‘P[P>Q|PTP1PlPLLQaPCO‰PWP9PtPOO)QfPII‘P\P>QPTP1PnPLL!QaPDQ‰PXP9PtPP)QhPII‘P\P@OPTP3PnPMM!QbPDQ‰PXP9PwPP,QhPJJ‘P\P@OPUP3PpPMM$‘PbPDQPXP;OwPRP,QjPJJ‘P^P@O‚PUP5PpPNN$‘PbPFNPZP;OzPRP.QjPJJP^PAQ‚PVP5PrPNN$‘PdPFNPZP=OzPSP.‘PjPKKP_PAQ†PVP7PrPNN'PdPGOP[P=O|PSP.‘PlPKK‘P_PCO†PWP7PrPOO'PfPGO‘P[P>Q|PSP1PlPLL‘PaPCO‰PWP7PtPOO)‘PfPII‘P\P>Q|PTP1n‘PjPJŠW‘P\P>‘P|PSPPn‘PjPJŠ[P^P@PPTPPqPlPK‹[P^P@P‚PUP3PnPLŒ^‘P_PA‘P‚PUP3PpPMa‘PaPCP†PVP5PpPMa‘PbPD‘P‰PWP7PrPNN$‘PbPD‘P‰PXP9PtPOO'PdPFŽPPXP9PtPP)‘PfPGPPZP;PwPP)‘PfPII‘P[P=PzPRP,‘PhPII‘P[P>‘P|PSP.‘PjPJJ‘P\P>‘P|PSP1PlPKKP^P@OPTP1PlPKK‘P_PAQ‚PUP3PnPLL‘P_PAQ†PVP5PpPMM!‘PaPCO†PVP5PrPNN$‘PbPDQ‰PWP7PrPNN$‘PdPFNPXP9PtPOO'PdPFNPZP;OwPP)‘PfPGOPZP;OwPRP,QhPII‘P[P=OzPRP,QhPJJ‘P\P>Q|PSP.QjPJJ‘P\P@OPTP1PlPKKP^P@OPTP3PnPLLQ_PAQ‚PUP3PnPLL!QaPCO†PVP5PpPMM!QaPCO‰PWP7PrPNN$QbPDQ‰PWP9PtPOO'PdPFNMXP9PtPOO)QfPGOPZP;OwPP)QfPGOQ[P=OzPRP,QhPIIQ[P=O|PSP.QjPJJQ\P>Q|PSP.QlPKKP^P@O?TP1PlPKKP_PAQBUP3PnPLLQ_PAQBVP5PpPMM!QaPCOFVP5PpPNN$QbPDQIWP7PrPNN$QbPFNMXP9P4OO'PdPFNMXP;O7P)QfPGOPZP;O7P,QhPIIQ[P=O:RP,QhPIIQ\P>Q<SP.QjPJJQ\P>Q?TP1PlPKKP^P@O?TP1P.LLQ_PAQBUP3P.LLQaPCOFVP5P0MM!QaPCOFWP7P2NN$QbPDQIWP7P2OO'PdPFNMXP9P4OO'PdPGOPZP;O7P)QfPGOPZP=O:RP,QhPIIQ[P=O:RP.Q*JJQ\P>Q<SP.Q*JJP^P@O?TP1P,KKP^P@OBUP3P.LLQ_PAQBUP3P0MM!QaPCOFVP5P0MM!QbPDQIWP7P2NN$QbPDQIXP9P4OO'PdPFNMXP9P4P)QfPGOPZP;O7P)QfPIIQ[P=O:RP,Q(IIQ\P>Q<SP.Q*JJQ\P>Q<TP1P,KKP^P@O?TP1P,LLQ_PAQBUP3P.LLQ_PCOFVP5P0MM!QaPCOFVP7P2NN$QbPDQIWP7P2NN'PdPFNMXP9P4OO'PdPFNPZP;O7P)QfPGOPZP;O:RP,QhPIIQ[P=O:RP,QjPJJQ\P>Q<SP.QjPJJQ^P@O?TP1PlPKKP^P@O?UP3PnPLLQ_PAQBUP3PnPMM!QaPCOFVP5PpPMM!QaPDQIWP7PrPNN$QbPDQIWP9PtPOO'PdPFNMXP9PtPOO)QfPGOPZP;OwPP)QfPGOQ[P=OzPRP,QhPIIQ[P=O|PSP.QjPJJQ\P>Q|PSP.QlPKKP^P@OPTP1PlPKKP_PAQ‚PUP3PnPLLQ_PAQ‚PVP5PpPMM!QaPCO†PVP5Ppl‘PhPI‰S‘P[PP{PwPPPi‘PfPFŽPPXPPyPtPNŽd‘PbPD‘P‰PVPPuPpPMa‘P_PA‘P‚PUPPsPlPK‹[P^P>‘P|PSPPn‘PjPI‰S‘P[P=PzPPPi‘PfPGPPXP9PtPOgPbPD‘P‰PWP7PpPMa‘PaPCP‚PUP3PnPLŒ[P^P@PPTP.‘PjPJŠW‘P[P=PzPRP,‘PfPGPPZP;PtPOO'PdPFŽP‰PWP7PrPNŽa‘PaPCP†PVP3PnPLŒ^‘P_P@PPTP1PlPJŠW‘P\P>‘P|PRP,‘PhPI‰PPZP;PwPP'PdPFŽPPXP7PrPNN$‘PbPCP†PVP5PpPLL‘P_PA‘P‚PTP1PlPKKP\P>‘P|PSP.‘PhPII‘P[P=PwPP)‘PfPFNPXP9PtPNN$‘PbPDQ‰PVP5PpPMM!‘P_PA‘P‚PUP3PlPKKP^P@P|PSP.‘PjPJJ‘P[P=PzPRP)‘PfPGOPZP9PtPOO'PbPDQ‰PWP7PpPMM!‘PaPCO‚PUP3PnPLLP^P@OPTP.‘PjPJJ‘P\P=OzPRP,‘PhPGOPZP;PwPOO'PdPFNPWP7PrPNN!‘PaPCO†PVP3PnPLL‘P_P@OPTP1PlPJJ‘P\P>Q|PRP,‘PhPII‘PZP;OwPP)‘PdPFNPXP9PrPNN$‘PbPDQ†PVP5PpPLL‘P_PAQ‚PTP1PlPKKP\P>Q|PSP.‘PhPII‘P[P=OwPP)‘PfPGOPXP9PtPOO$‘PbPDQ‰PWP5PpPMM!‘PaPAQ‚PUP3PlPKKP^P@O|PSP.‘PjPJJ‘P[P=OzPRP)‘PfPGOPZP9PtPOO'PdPDQ‰PWP7PrPMM!‘PaPCO†PUP3PnPLL‘P^P@OPTP.‘PjPJJ‘P\P=OzPRP,‘PhPGOPZP;OwPOO'PdPFNPWP7PrPNN$‘PaPCO†PVP5PnPLL‘P_PAQPTP1PlPKK‘P\P>Q|PRP,‘PhPII‘PZP;OwPP)‘PdPFNPXP9PrPNN$‘PbPDQ†PVP5PpPMM‘P_PAQ‚PUP1PlPKKP^P>Q|PSP.‘PjPII‘P[P=OwPP)‘PfPGOPXP9PtPOO$‘PbPDQ‰PWP5PpPMM!‘PaPAQ‚PUP3PnPKKP^P@OPSP.‘PjPJJ‘P[P=OzPRP,‘PfPGOPZP9PtPOO'PdPDQ‰PWP7PrPMM!‘PaPCO†PUP3PnPLL‘P^P@OPTP1PjPJJ‘P\P>‘PzPRP,‘PhPIIPZP;PwPP'PdPFNPWP7PrPNN$‘PaPCP†PVP5PnPLL‘P_PA‘PPTP1PlPKK‘P\P>‘P|PSP,‘PhPII‘P[P;PwPP)‘PfPFŽPPXP9PrPNN$‘PbPD‘P†PVP5PpPMM‘P_PA‘P‚PUP1PlPKKP^P>‘P|PSP.‘PjPI‰S‘P[P=PzPP)‘PfPGPPXP9PtPOO'PbPD‘P‰PWP5PpPMa‘PaPA‘P‚PUP3PnPK‹[P^P@PPSP.‘PjPJŠW‘P[P=PzPRPPl‘PfPGPPZP;PtPOgPdPFŽP‰PWP7PrPNŽa‘PaPCP†PUP3PnPLŒ^‘P^P@PPTPPqPjPJŠW‘P\P>‘PzPRPPl‘PhPI‰PPZP;PwPPPgPdPFŽPPXPPwPrPNŽd‘PbPCP†PVPPuPpPLŒ^‘P_PA‘PPTPPqPlPK‹W‘P\PP~‘P|PSPPl‘PhPGPPXPPyPrPMa‘P_PA‘PPTPPn‘PhPI‰PPZPPyPtPNŽd‘PaPA‘P‚PTPPqPjPJŠS‘PZP;PtPOd‘PbPCP†PUPPqPlPJŠW‘P[P=PwPPPgPbPD‘P†PVP3PnPK‹W‘P\P=PzPPPi‘PdPFŽP‰PVP5PnPLŒ[P^P>‘PzPRP)‘PfPFŽPPWP7PpPLŒ^‘P^P@P|PSP,‘PfPGPPXP7PrPMa‘P_P@PPSP.‘PhPI‰PPXP9PrPNN!‘PaPA‘P‚PTP.‘PjPI‰S‘PZP;PtPNN$‘PaPCP‚PUP1PlPJJ‘P[P;PwPOO'PbPCP†PUP3PlPKK‘P\P=PwPP'PdPDQ‰PVP3PnPKKP\P>‘PzPRP)‘PdPFN‰PWP5PpPLLP^P>‘P|PRP,‘PfPGOPWP7PpPMM‘P_P@O|PSP,‘PhPGOPXP9PrPMM!‘P_PAQPTP.‘PhPIIPZP9PtPNN$‘PaPAQ‚PTP1PjPJJ‘PZP;OtPOO$‘PbPCO†PUP1PlPJJ‘P[P=OwPP'PbPDQ†PVP3PnPKK‘P\P=OzPP)‘PdPFN‰PVP5PnPLLP^P>QzPRP)‘PfPFNPWP7PpPLL‘P^P@O|PSP,‘PfPGOPXP7PrPMM!‘P_P@OPSP.‘PhPIIPXP9PrPNN!‘PaPAQ‚PTP.QjPII‘PZP;OtPNN$‘PaPCO‚PUP1PlPJJ‘P[P;OwPOO'PbPCO†PUP3PlPKK‘P\P=OwPP'PdPDQ‰PVP3PnPKKP\P>QzPRP)QdPFN‰PWP5PpPLLP^P>Q|PRP,QfPGOPWP7PpPMM‘P_P@O|PSP,QhPGOPXP9PrPMM!‘P_PAQPTP.QhPIIPZP9PtPNN$‘PaPAQ‚PTP1PjPJJ‘PZP;OtPOO$‘PbPCO†PUP1PlPJJ‘P[P=OwPP'PbPDQ†PVP3PnPKK‘P\P=OzPP)QdPFN‰PVP5PnPLLP^P>QzPRP)QfPFNPWP7PpPLL‘P^P@O|PSP,QfPGOPXP7PrPMM!‘P_P@OPSP.QhPIIPXP9PrPNN!‘PaPAQ‚PTP.QjPII‘PZP;OtPNN$‘PaPCO‚PUP1PlPJJ‘P[P;OwPOO'PbPCO†PUP3PlPKK‘P\P=OwPP'PdPDQ‰PVP3PnPKKP\P>QzPRP)‘PdPFN‰PWP5PpPLLP^P>Q|PRP,‘PfPGOPWP7PpPMM‘P_P@O|PSP,‘PhPGOPXP9PrPMM!‘P_PAQPTP.‘PhPIIPZP9PtPNN$‘PaPAQ‚PTP1PjPJJ‘PZP;OtPOO$‘PbPCO†PUP1PlPJJ‘P[P=OwPP'PbPDQ†PVP3PnPKK‘P\P=PzPP)‘PdPFN‰PVP5PnPLLP^P>‘PzPRP)‘PfPFNPWP7PpPLL‘P^P@P|PSP,‘PfPGOPXP7PrPMM!‘P_P@PPSP.‘PhPIIPXP9PrPNN!‘PaPA‘P‚PTP.‘PjPII‘PZP;PtPNN$‘PaPCP‚PUP1PlPJJ‘P[P;PwPOO'PbPCP†PUP3PlPK‹W‘P\P=PwPP'PdPD‘P‰PVP3PnPK‹[P\P>‘PzPRP)‘PdPFŽP‰PWP5PpPLŒ[P^P>‘P|PRP,‘PfPGPPWP7PpPM^‘P_P@P|PSPPPd‘PaPP‘PPSPPl‘PfPP†ŽP‰PUPPqPjPP‰‰PPXPPwPpPLŒ[P[PP{PtPNŽa‘P_PP€P|PRPPgPbPCP‚PTPPn‘PhPGPPWPPsPlPJŠS‘PZPPyPrPM^‘P^P=PwPOd‘PaPA‘PPSPPl‘PdPD‘P†PUP1PjPI‰PPXP7PnPK‹W‘P[P;PtPNŽa‘P_P>‘PzPP'PbPCP‚PTP.‘PhPFŽP‰PVP3PlPJJ‘PZP9PrPLLP\P=PwPOO$‘PaPA‘P|PRPOa‘P_P@P|PRPPi‘PdPD‘P†PUPPn‘PhPGPPWPPuPnPK‹W‘PZP9PrPM^‘P^P>‘PzPPPgPaPA‘PPSPPl‘PfPFŽP‰PVP1PjPI‰PPXP7PpPLŒ[P\P;PtPNN!‘P_P@P|PRP)‘PdPCP‚PTP.‘PhPGPPWP5PlPJJ‘PZP9PrPMM‘P^P>‘PwPOO$‘PaPA‘PPSP,‘PfPDQ†PUP1PjPIIPXP7PpPKK‘P[P;PtPNN!‘P_P@P|PP'PbPCO‚PTP.‘PhPGO‰PVP3PlPJJ‘PZP9PrPMMP\P=OwPOO$‘PaPAQPSP)‘PdPDQ†PUP1PjPIIPWP5PnPKK‘P[P;OtPNN!‘P^P>QzPP'PbPCO‚PTP,‘PfPFN‰PVP3PlPJJ‘PZP7PpPLLP\P=OwPOO$‘PaP@O|PRP)QdPDQ†PUP1PhPGOPWP5PnPKK‘P[P;OrPMM‘P^P>QzPP'PbPAQPSP,QfPFN‰PVP3PlPIIPXP7PpPLLP\P=OwPNN!Q_P@O|PRP)QdPDQ‚PTP.QhPGOPWP5PnPKK‘PZP9PrPMMQ^P>QzPP$QaPAQPSP,QfPFN‰PUP1PjPIIPXP7PpPLLP[P;OtPNN!Q_P@O|PRP'PbPCO‚PTP.QhPGOPWP3PlPJJ‘PZP9PrPMMQ^P=OwPOO$QaPAQPSP,QdPDQ†PUP1PjPIIPXP7PnPKK‘P[P;OtPNN!Q_P>QzPP'PbPCO‚PTP.QhPFN‰PVP3PlPJJ‘PZP9PrPLLP\P=OwPOO$QaPAQ|PRP)QdPDQ†PUP1PjPIIPWP5PnPKK‘P[P;OtPMM‘P^P>QzPP'PbPCO‚PSP,QfPFN‰PVP3PlPJJ‘PXP7PpPLLP\P=OwPOO!‘P_P@O|PRP)‘PdPDQ†PUP.QhPGOPWP5PnPKK‘P[P9PrPMM‘P^P>QzPP'PaPAQPSP,‘PfPFN‰PVP3PjPIIPXP7PpPLLP\P;OtPNN!‘P_P@O|PRP)‘PdPCO‚PTP.‘PhPGOPWP5PnPJJ‘PZP9PrPMM‘P^P>‘PwPOO$‘PaPA‘PPSP,‘PfPFN†PUP1PjPIIPXP7PpPKK‘P[P;PtPNN!‘P_P@P|PPhPGOPWP5PnPJJ‘PZP9PrPMM‘P^P>QzPOO$‘PaPAQPSP,QfPFN†PUP1PjPIIPXP7PpPLL‘P[P;OtPNN!‘P_P@O|PRP'PbPCO‚PTP.‘PhPGOPVP3PlPJJ‘PZP9PrPMM‘P\P=PwPOO$‘PaPA‘PPSP)‘PdPD‘P†PUP1PjPIIPXP5PnPKK‘P[P;PtPNN!‘P_P>‘PzPP'PbPCP‚PTP.‘PfPFŽP‰PVP3l‘PdPP„‘P‚PSPPi‘PbPPƒPPRPPgPbPP‘P|PPPd‘PaPP€PzPOd‘P_PP~‘PwPNŽa‘P^PP}PtPNŽ^‘P\PP{PrPM[P[PPyPrPLŒW‘PZP7PpPK‹S‘PXP7PnPJŠPPXP5PlPI‰PPWP3PjPGPPVP1PhPFŽP‰PUP.‘PfPFŽP†PTP,‘PdPD‘P‚PSP)‘PdPCPPRP'PbPA‘P|PP'PaP@PzPP$‘P_P>‘PwPOO!‘P^P=PwPNN‘P\P;PtPMMJŠPPWPPsPjPI‰PPVPPqPjPGP‰PUPPn‘PhPFŽP†PTPPn‘PfPD‘P‚PSPPl‘PdPCPPSPPi‘PbPA‘PPRPPgPaP@P|PPPd‘P_P@PzPOa‘P^P>‘PwPNŽ^‘P^P=PtPM[P\P;PrPLŒ[P[P9PpPK‹W‘PZP7PnPK‹S‘PXP5PlPJŠPPWP3PlPI‰PPVP3PjPGP‰PUP1PhPFŽP†PUP.‘PfPD‘P‚PTP,‘PdPCP‚PSP)‘PbPA‘PPRP'PaPA‘P|PP$‘P_P@PzPOO!‘P_P>‘PwPNN‘P^P=PtPMM‘P\P;PrPMMP[P9PpPLL‘PZP7PpPKK‘PXP5PnPJJPWP5PlPIIPVP3PjPGO‰PVP1PhPFN†PUP.‘PfPDQ†PTP,‘PdPDQ‚PSP)‘PbPCOPRP'PbPAQ|PP$‘PaP@OzPOO$‘P_P>QwPNN!‘P^P=OtPNN‘P\P;OrPMMP[P9PrPLL‘PZP7PpPKK‘PXP7PnPJJPXP5PlPIIPWP3PjPGOPVP1PhPFN‰PUP.QfPFN†PTP,QdPDQ‚PSP)‘PdPCOPRP'PbPAQ|PP'PaP@OzPP$‘P_P>QwPOO!‘P^P=OwPNN‘P\P;OtPMMP[P;OrPLL‘PZP9PpPKK‘PZP7PnPJJPXP5PlPIIPWP3PjPGOPVP1PhPGO‰PUP.QhPFN†PTP,QfPDQ‚PSP,‘PdPCOPRP)‘PbPAQ|PRP'PaP@OzPP$‘P_P>QzPOO!‘P^P=OwPNN‘P\P=OtPMMP[P;OrPLL‘P[P9PpPKK‘PZP7PnPJJ‘PXP5PlPJJPWP3PjPIIPVP1PjPGO‰PUP.‘PhPFN†PTP.‘PfPDQ‚PSP,‘PdPCOPSP)‘PbPAQPRP'PaP@O|PP$‘P_P@OzPOO!‘P^P>‘PwPNN‘P^P=PtPMMP\P;PrPLLP[P9PpPKK‘PZP7PnPKK‘PXP5PlPJJPWP3PlPIIPVP3PjPGO‰PUP1PhPFŽP†PUP.‘PfPD‘P‚PTP,‘PdPCP‚PSP)‘PbPA‘PPRP'PaPA‘P|PP$‘P_P@PzPOO!‘P_P>‘PwPNN‘P^P=PtPM^‘P\P;PrPM[P[P9PpPLŒW‘PZP7PpPK‹S‘PXP5PnPJŠPPWP5PlPI‰PPVPpPKK‘PZP7PnPKK‘PXP5PlPJJPWP3PlPIIPVP3PjPGO‰PUP1PhPFN†PUP.‘PfPD‘P‚PTP,‘PdPCP‚PSP)‘PbPA‘PPRP'PaPA‘P|PP$‘P_P@PzPOO!‘P_P>‘PwPNN‘P^P=PtPM^‘P\P;PrPM[P[P9PpPLŒW‘PZP7PpPK‹S‘PXP5PnPJŠPPWP5PlPI‰PPVPPsPjPGP‰PVPPqPhPFŽP†PUPPn‘PfPD‘P†PTPPl‘PbPA‘P|POa‘P\PP{PpPK‹PPWPPqPhPD‘P‚PSPPgPaP>‘PwPM[PZP7PlPI‰PPUP.‘PdPCP|PPPa‘P^P;PrPLŒS‘PXP3PjPFŽP†PSP)‘PaP@PwPNN‘P[P9PnPJŠPPVP.‘PfPCPPRP$‘P_P=PtPLL‘PXP5PjPGO‰PTP,‘PbPA‘PzPOO‘P\P9PpPKKPWP1PhPDQ‚PRP'P_P>QtPMMPZP7PlPII‰PUP,‘PdPP=PrPLŒS‘PXP3PjPFŽP†PTP)‘PbP@PzPNŽ^‘P[P9PnPJŠPPVP1PfPD‘PPRP$‘P_P=PtPLŒW‘PZP5PlPGP‰PTP,‘PbPA‘PzPOO!‘P\P;PpPKKPWP1PhPD‘P‚PRP'PaP>‘PwPMMPZP7PlPII‰PUP.‘PdPCP|PP!‘P^P;PrPKK‘PXP3PjPFN†PSP)‘PaP@OwPNNP[P9PnPJJPVP.‘PfPCOPP$‘P_P=OtPLL‘PXP5PjPGO†PTP,‘PbPAQzPOO‘P\P9PpPJJPWP1PhPDQ‚PRP'P_P>QtPMM‘PZP7PlPII‰PUP,‘PdPAQ|POO!‘P^P;OrPKK‘PWP3PhPFN‚PSP)‘PaP@OwPNNP[P7PnPIIPUP.QfPCOPP$‘P^P=OrPLL‘PXP5PjPGO†PTP)QbP@OzPNN‘P\P9PpPJJPVP1PfPDQPRP'P_P>QtPMM‘PZP5PlPGO‰PTP,QdPAQ|POO!‘P\P;OpPKKPWP3PhPFN‚PSP'PaP>QwPMMP[P7PnPIIPUP.QdPCO|PP!Q^P=OrPjLL‘PXP3PjPFN†PSP)QbP@OzPNN‘P[P9PnPJJPVP1PfPDQPRP$Q_P=OtPLL‘PXP5PlPGO‰PTP,QbPAQzPOO‘P\P;OpPKKPWP1PhPDQ‚PRP'PaP>QwPMMPZP7PlPII‰PUP.QdPCO|PP!‘P^P;OrPKK‘PWP3PjPFN†PSP)QaP@OwPNNP[P9PnPJJPVP.QfPCOPP$‘P_P=OtPLL‘PXP5PjPGO†PTP)‘PbPAQzPOO‘P\P9PpPJJPVP1PhPDQ‚PRP'P_P>QtPMM‘PZP7PlPII‰PUP,‘PdPAQ|POO!‘P\P;OrPKK‘PWP3PhPFN‚PSP'PaP@OwPNNP[P7PnPIIPUP.‘PfPCOPP$‘P^P=PrPLL‘PXP5PjPGO†PTP)‘PbP@PzPNN‘P[P9PpPJJPVP1PfPD‘PPRP$‘P_P>‘PtPMM‘PZP5PlPGP‰PTP,‘PdPA‘P|POO!‘P\P;PpPK‹PPWP1PhPFŽP‚PSP'PaP>‘PwPM[PZP7PnPI‰PPUP.‘PdPCP|PPPa‘P^P=PrPLŒS‘PX;OrPKK‘PWP3PhPFN‚PSP)‘PaP@OwPNNP[P7PnPIIPUP.‘PfPCOPP$‘P^P=PrPLL‘PXP5PjPGO†PTP)‘PbP@PzPNN‘P\P9PpPJJPVP1PfPD‘PPRP'P_P>‘PtPMW‘PZP5PlPGP‰PTP,‘PdPA‘P|POa‘P\P;PpPK‹PPWP3PhPFŽP‚PSPPgPaP>‘PwPM[P[P7PnPI‰PPUPPn‘PdPCP|PPPa‘P^PP}PrPK‹PPVPPn‘PdP@PwPMW‘PXPPsPhPCP|PO^‘P[P7PjPFŽP‚PRPPd‘P^P;PnPI‰P‰PTP)‘PaP>‘PrPK‹PPVP.‘PdP@PwPMW‘PXP3PhPCP|POO‘P[P7PlPFŽP‚PRP$‘P^P;PpPII‰PTP)‘PaP>‘PrPKKPVP.‘PdPA‘PwPMM‘PXP3PhPDQ|POO‘P[P7PlPFN‚PRP$‘P^P;PpPII‰PTP)‘PaP>QtPKKPVP.‘PdPAQ9PnPI‰P‰PTPPi‘P_P=PrPK‹PPVP.‘PbP@PwPMW‘PXP1PfPCP|POO‘P[P5PjPFŽP‚PRP$‘P^P9PnPI‰P‰PTP)‘P_P=PrPKKPVP.‘PbP@PwPMM‘PXP3PfPCP|POO‘P[P7PjPFN‚PRP$‘P^P9PnPII‰PTP)‘PaP=PrPKKPVP.‘PdP@PwPMM‘PXP3PhPCO|POO‘P[P7PjPFN‚PRP$‘P^P;PnPII‰PTP)‘PaP>QrPKKPVP.‘PdP@OwPMM‘PXP3PhPCO|POO‘P[P7PlPFN‚PRP$‘P^P;OpPII‰PTP)‘PaP>QrPKKPVP.‘PdPAQwPMM‘PXP3PhPDQ|POO‘P[P7PlPFN‚PRP$‘P^P;OpPII‰PTP)‘PaP>QtPKKPVP.QdPAQzPMM‘PXP3PhPDQ|POO‘P[P7PlPGO‚PRP$‘P^P;OpPJJ‰PTP)QaP>QtPKKPVP.QdPAQzPMM‘PXP3PhPDQPOO‘P[P7PlPGO†PRP$Q^P;OpPJJ‰PTP)QaP>QtPLLPVP.QdPAQzPNN‘PXP3PhPDQPP‘P[P7PlPGO†PRP$Q^P;OpPJJPTP)QaP>QtPLL‘PVP.QdPAQzPNN‘PXP3PhPDQPP‘P[P7PlPGO†PSP$Q^P;OpPJJPUP)QaP>QtPLL‘PVP.QdPAQzPNNPXP3PhPDQPP!‘P[P7PlPGO†PSP$‘P^P;OpPJJPUP)QaP>QtPLL‘PWP.QdPAQzPNNPZP3PhPDQPP!‘P[P7PlPGO†PSP'P^P;OpPJJPUP,‘PaP>QtPLL‘PWP.‘PdPAQzPNNPZP3PhPDQPP!‘P\P7PlPGO†PSP'P_P;OpPJJPUP,‘PaP>QtPLL‘PWP1PdPAQzPNNPZP5PhPDQPP!‘P\P7PlPGO†PSP'P_P;PpPJJPUP,‘PbP>‘PtPLL‘PWP1PfPA‘PzPNNPZP5PhPD‘PPP!‘P\P9PlPGP†PSP'P_P=PpPJŠPPUP,‘PbP@PtPLL‘PWP1PfPA‘PzPNNPZP5PjPD‘PPP!‘P\P9PnPGP†PSP'P_P=PpPJŠPPUP,‘PbP@PtPLŒS‘PWP1PfP‰PTP'P_P=OrPKKPVP,‘PbP@OwPMM‘PXP1PfPCO|POO‘PZP5PjPFN‚PRP$‘P\P9PnPII‰PTP)‘P_P=PrPKKPVP.‘PbP@PwPMM‘PXP1PfPCP|POO‘P[P5PjPFŽP‚PRP$‘P^P9PnPI‰P‰PTP)‘P_P=PrPK‹PPVP.‘PbP@PwPMW‘PXP3PfPCP|PO^‘P[P7PjPFŽP‚PRPPd‘P^P9PnPI‰P‰PTPPi‘PaP=PrPK‹PPTPPgP^P9PnPGP‚PPP^‘PZPPsPhPCPzPMS‘PVPPl‘PbP>‘PrPJŠP‰PSPPd‘P^P9PlPFŽPPO^‘PZP3PfPA‘PwPLŒS‘PVP,‘PaP=PpPI‰P‰PSP$‘P\P7PjPD‘PPOOPXP1PdPA‘PwPLLPUP)‘P_P=PpPII†PRP!‘P[P7PjPDQ|PNN‘PWP1PdP@OtPKKPUP)‘P_P;PnPGO‚PRP!‘P[P5PhPCOzPNN‘PWPPPa‘P[P5PjPD‘P|PNŽW‘PWP1PdP@PtPK‹PPTP)‘P_P;PnPGP‚PP!‘P[P5PhPCPzPMM‘PWP.‘PbP>‘PrPK‹PPTP'P^P9PlPGP‚PP‘PZP3PfPCPzPMM‘PVP,‘PaP>‘PrPJJ‰PSP$‘P^P9PlPFNPOOPZP3PfPAQwPLLPVP,‘PaP=PpPII‰PSP$‘P\P7PjPDQPOOPXP1PdP@OwPLLPUP)‘P_P;OpPII†PRP!‘P[P7PjPDQ|PNN‘PWP1PdP@OtPKKPTP)‘P_P;OnPGO‚PP!‘P[P5PhPCOzPNN‘PWP.QbP>QrPKKPTP'P^P9PlPGO‚PP‘PZP3PfPCOzPMM‘PVP,QbP>QrPJJ‰PSP$‘P^P9PlPFNPOOPZP3PfPAQwPLL‘PVP,QaP=OpPII‰PSP$Q\P7PjPDQPOOPXP1PdP@OwPLLPUP)Q_P=OpPII†PRP!Q[P7PjPDQ|PNN‘PWP1PdP@OtPKKPTP)Q_P;OnPGO‚PRP!Q[P5PhPCOzPNN‘PWP.QbP>QrPjKKPTP'P^P9PnPGO‚PPQZP3PhPCOzPMM‘PVP,QbP>QrPJJ‰P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PLLhP$QJJdPQIIbPPFN_PQDQ^PMAQ[PI@OZPB=OWP?;OVP:7PTP75PSPrP1PPpP.QOOlP)QMMjP'PKKfP!QJJdPQGOaPQFN_PQCO\PMAQ[PI>QXPB=OWP?9PUP:7PTP43PRP21PP.,QNN,)QMM($QKKfP!QJJbPPGOaPQDQ^PPCO\PM@OZPF>QXPB;OVP<9PUP:5PSP43PRP2.QOO.,QNN*'PLL($QKK$QIIbPPGO_PQDQ^PPCO[PI@OZPF>QWP?;OVP<7PTP75PSP41PP0.QOO.)QMM*'PLL(!QJJ$QIIbPQFN_PQDQ\PMAQ[PI@OXPB=OWP?;OUP:7PTP75PRP21PP0.QNN,)QMM*$QKK&!QJJdPPGOaPQFN_PPCO\PMAQ[PF>QXPB=OWP<9PUP:7PSP43PRP21POO.,QNN,)QLLhP$QKKfP!QIIbPPGOaPQDQ^PPCO\PI@OZPF>QXP?;OVP<9PUP75PSP43PRPpP.QOOnP,QNNjP'PLLhP$QJJdPQIIbPPFN_PQDQ^PPAQ[PI@OZPF=OWPP;OVP|P7PTPwP5PSPrP1PPpP.QOOlP)QMMjP'PLLfP!QJJdPQIIaPQFN_P‘PDQ\PPAQ[P‰P>QXP‚P=OWPP9PUPzP7PTPwP3PRPrP1PPpP,QNNlP)‘PMMjP$‘PKKfP!‘PJJbPPGOaP‘PFN^PPCOPPPnPPi‘PLŒPfPPa‘PI‰PaPPS‘PCP\PPP‰PP~‘PWPPP|PPyPTPPPtPPqPPPPnPPi‘PLŒPfPPa‘PI‰PaPPS‘PCP\PPP‰P>‘PWPPP|P9PTPPPtP1PPPPnPPi‘PLŒPfPPa‘PI‰PaPPS‘PCP\PPP‰P>‘PWPPP|P9PTPPPtP1PPPPnP)‘PLŒPfP!‘PI‰PaPPS‘PCP\PPP‰P>‘PWPPP|P9PTPPPtP1PPPPnP)‘PLŒPfP!‘PI‰PaP‘PCP\P‰P>‘PWPPP|P9PTPPPtP1PPPPnP)‘PLŒPfP!‘PI‰PaP‘PCP\P‰P>‘PWP|P9PTPtP1PPPPnP)‘PLŒPfP!‘PI‰PaP‘PCP\P‰P>‘PWP|P9PTPtP1PPnP)‘PLŒPfP!‘PI‰PaP‘PCP\P‰P>‘PWP|P9PTPtP1PPnP)‘PLLfP!‘PI‰PaP‘PCP\P‰P>‘PWP|P9PTPtP1PPnP)‘PLLfP!‘PIIaP‘PCP\P‰P>‘PWP|P9PTPtP1PPnP)‘PLLfP!‘PIIaP‘PCO\P‰P>‘PWP|P9PTPtP1PPnP)‘PLLfP!‘PIIaP‘PCO\P‰P>QWP|P9PTPtP1PPnP)‘PLLfP!‘PIIaP‘PCO\P‰P>QWP|P9PTPtP1PPnP)‘PLLfP!‘PIIaP‘PCO\P‰P>QWP|P9PTPtP1PPnP)‘PLLfP!‘PIIaP‘PCO\P‰P>QWP|P9PTPtP1PPnP)‘PLLfP!‘PIIaP‘PCO\P‰P>QWP|P9PTPtP1PPnP)‘PLLfP!‘PIIaP‘PCO\P‰P>QWP|P9PTPtP1PPnP)‘PLLfP!‘PIIaP‘PCO\P‰P>QWP|P9PTPtP1PPnP)‘PLLfP!‘PIIaP‘PCO\P‰P>QWP|P9PTPtP1PPnP)‘PLLfP!‘PIIaP‘PCO\P‰P>QWP|P9PTPtP1PPnP)‘PLLfP!‘PIIaP‘PCO\P‰P>QWP|P9PTPtP1PPnP)‘PLLfP!‘PIIaP‘PCO\P‰P>‘PWP|P9PTPtP1PPnP)‘PLLfP!‘PIIaP‘PCO\P‰P>‘PWP|P9PTPtP1PPnP)‘PLLfP!‘PIIaP‘PCP\P‰P>‘PWP|P9PTPtP1PPnP)‘PLLfP!‘PI‰PaP‘PCP\P‰P>‘PWP|P9PTPtP1PPnP)‘PLŒPfP!‘PI‰PaP‘PCP\P‰P>‘PWP|P9PTPtP1PPPPnP)‘PLŒPfP!‘PI‰PaP‘PCP\P‰P>‘PWP|P9PTPPPtP1PPPPnP)‘PLŒPfP!‘PI‰PaP‘PCP\P‰P>‘PWPPP|P9PTPPPtP1PPPPnP)‘PLŒPfP!‘PI‰PaP‘PCP\PPP‰P>‘PWPPP|P9PTPPPtP1PPPPnP)‘PLŒPfP!‘PI‰PaPPS‘PCP\PPP‰P>‘PWPPP|P9PTPPPtP1PPPPnPPi‘PLŒPfPPa‘PI‰PaPPS‘PCP\PPP‰P>‘PWPPP|P9PTPPPtPPqPPPPnPPi‘PLŒPfPPa‘PI‰PaPPS‘PCP\PPP‰P>‘PWPPP|PPyPTPPPtPPqPPPPlPPd‘PJŠPaPPS‘PA‘PZPPPPPyPSPPPrPPl‘PMPfPP^‘PFŽP^PPP‰P>‘PVPPPzP3PPPPlPPgPJŠPbPPS‘PCPZPPP‚P9PTPPPrP.‘PMPhPP^‘PGP^PPPP>‘PWPPPzP5PPPPnP'PK‹PbPPW‘PCP[PPP‚P;PTPPPtP.‘PNŽPhP!‘PGP_PP@PWPPP|P5PRPPPnP)‘PK‹PdP‘PD‘P[P†P;PUPPPtP1PNŽPjP!‘PI‰P_PP@PXP|P7PRPPPpP)‘PLŒPdPPD‘P\P†P=PUPwP1POPjP$‘PI‰PaPPA‘PXPP7PSPpP,‘PLLfPPFŽP\P‰P=PVPwP3POOlP$‘PJJaP‘PA‘PZPP9PSPrP,‘PMMfP‘PFN^P‰P>‘PVPzP3PPlP$‘PJJaP‘PAQZPP9PSPrP,‘PMMfP‘PFN^P‰P>QVPzP3PPlP'PJJbP‘PCOZP‚P9PTPrP.‘PMMhP‘PGO^PP>QWPzP5PPnP'PKKbP‘PCO[P‚P;OTPtP.‘PNNhP!‘PGO_PP@OWP|P5PRPnP)‘PKKdP‘PDQ[P†P;OUPtP1PNNjP!‘PII_PP@OXP|P7PRPpP)QLLdPPDQ\P†P=OUPwP1POOjP$QIIaPPAQXPP7PSPpP,QLLfPPFN\P‰P=OVPwP3POOlP$QJJaP‘PAQZPP9PSPrP,QMMfP‘PFN^P‰P>QVPzP3PPlP$QJJaP‘PAQZPP9PSPrP,QMMfPQFN^P‰P>QVPzP3PPlP'PJJbP‘PCOZP‚P9PTPrP.QMMhPQGO^PP>QWPzP5PPnP'PKKbP‘PCO[P‚P;OTPtP.QNNhP!QGO_PP@OWP|P5PRPnP)QKKdP‘PDQ[P†P;OUPtP1PNNjP!QII_PP@OXP|P7PRPpP)QLLdPPDQ\P†P=OUPwP1POOjP$‘PIIaPPAQXPP7PSPpP,QLLfPPFN\P‰P=OVPwP3POOlP$‘PJJaP‘PAQZPP9PSPrP,‘PMMfP‘PFN^P‰P>QVPzP3PPlP$‘PJJaP‘PAQZPP9PSPrP,‘PMMfP‘PFN^P‰P>QVPzP3PPlP'PJJbP‘PCOZP‚P9PTPrP.‘PMMhP‘PGO^PP>‘PWPzP5PPnP'PKKbP‘PCP[P‚P;PTPtP.‘PNNhP!‘PGO_PP@PWP|P5PRPnP)‘PKKdP‘PD‘P[P†P;PUPtP1PNNjP!‘PI‰P_PP@PXP|P7PRPpP)‘PLŒPdPPD‘P\P†P=PUPwP1POPjP$‘PI‰PaPPA‘PXPP7PSPPPpP,‘PLŒPfPPFŽP\P‰P=PVPPPwP3POPlP$‘PJŠPaP‘PA‘PZPPPP9PSPPPrP,‘PMPfP‘PFŽP^PPP‰P>‘PVPPPzP3PPPwPPPPlPPd‘PP‰‰P^PPP‰PP}PUPPPtPPl‘PLŒPdPPW‘PP‘PXPPP|PPuPPPPjPPa‘PGP^PPP†PP{PTPPPrPPi‘PK‹PbPPS‘PA‘PWPPPzPPsPOPhPP^‘PFŽP\PPP†P9PSPPPpPPi‘PJŠPaPPPP@PVPPPwP1PNŽPhPP[PD‘P[PPP‚P7PRPPPnPPgPJŠP_PPPP>‘PVPPPtP.‘PMPfPPW‘PCPZPPPP7PPPPlP$‘PI‰P^PPP‰P=PUPPPtP,‘PLŒPdP‘PA‘PXPPP|P5PPPPjP!‘PGP^P†P;PTPPPrP)‘PK‹PbP‘PA‘PWPPPzP3POPhP‘PFŽP\P†P9PSPPPpP)‘PJŠPaPP@PVPwP1PNŽPhPPD‘P[P‚P7PRPnP'PJŠP_PP>‘PVPtP.‘PMPfP‘PCPZPP7PPlP$‘PI‰P^P‰P=PUPtP,‘PLLdP‘PA‘PXP|P5PPjP!‘PGO^P†P;PTPrP)‘PKKbP‘PA‘PWPzP3POOhP‘PFN\P†P9PSPpP)‘PJJaPP@OVPwP1PNNhPPDQ[P‚P7PRPnP'PJJ_PP>QVPtP.‘PMMfP‘PCOZPP7PPlP$‘PII^P‰P=OUPtP,‘PLLdP‘PAQXP|P5PPjP!‘PGO^P†P;OTPrP)‘PKKbP‘PAQWPzP3POOhP‘PFN\P†P9PSPpP)‘PJJaPP@OVPwP1PNNhPPDQ[P‚P7PRPnP'PJJ_PP>QVPtP.QMMfP‘PCOZPP7PPlP$‘PII^P‰P=OUPtP,QLLdP‘PAQXP|P5PPjP!‘PGO^P†P;OTPrP)QKKbP‘PAQWPzP3POOhP‘PFN\P†P9PSPpP)QJJaPP@OVPwP1PNNhPPDQ[P‚P7PRPnP'PJJ_PP>QVPtP.QMMfP‘PCOZPP7PPlP$‘PII^P‰P=OUPtP,QLLdP‘PAQXP|P5PPjP!‘PGO^P†P;OTPrP)QKKbP‘PAQWPzP3POOhP‘PFN\P†P9PSPpP)‘PJJaPP@OVPwP1PNNhPPDQ[P‚P7PRPnP'PJJ_PP>QVPtP.‘PMMfP‘PCOZPP7PPlP$‘PII^P‰P=OUPtP,‘PLLdP‘PAQXP|P5PPjP!‘PGO^P†P;OTPrP)‘PKKbP‘PAQWPzP3POOhP‘PFN\P†P9PSPpP)‘PJJaPP@PVPwP1PNNhPPDQ[P‚P7PRPnP'PJJ_PP>‘PVPtP.‘PMMfP‘PCPZPP7PPlP$‘PI‰P^P‰P=PUPtP,‘PLLdP‘PA‘PXP|P5PPjP!‘PGP^P†P;PTPrP)‘PK‹PbP‘PA‘PWPzP3POPhP‘PFŽP\P†P9PSPpP)‘PJŠPaPP@PVPwP1PNŽPhPPD‘P[P‚P7PRPPPnP'PJŠP_PP>‘PVPPPtP.‘PMPfP‘PCPZPPPP[PPPPPuPOPhPP[PPƒPXPPP|PPsPNŽPfPPW‘PA‘PWPPPzPPqPMPdPPS‘P@PVPPPtPPn‘PLŒPbPPPP>‘PUPPPrPPl‘PK‹PaPPPP=PTPPPpPPgPJŠP_PPP‰P;PSPPPnPPd‘PI‰P^PPP†P9PRPPPlPPa‘PFŽP\PPP‚P7PPPPjPP^‘PD‘P[PPPP5POPhPP[PCPXPPP|P3PNŽPfPPW‘PA‘PWPPPwP1PMPdP‘P@PVPPPtP.‘PLŒPbPP>‘PUPPPrP)‘PK‹PaPP=PTPPPpP'PJŠP_P‰P;PSPPPnP$‘PGP^P†P9PRPPPlP!‘PFŽ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‘PAQTPjP‘P=OPfPP7PNNaP‚P1PKK\PzP,‘PGOXPtP$‘PCOUPnPP>QSPhPP9POObP†P5PLL^PP.QIIZPwP'PDQWPpP‘PAQTPjP‘P=OPdPP7PMMaP‚P1PJJ\PzP)QGOXPrP$QCOUPlPP>QRPhPP9POObP†P3PLL^P|P.QIIZPtP'PDQVPpPQ@OTPjPQ;OPdPI7PMM_P‚P1PJJ[PzP)QFNXPrP!QCOUPlPQ>QRPfPP9PNNbPF3PKK^P|P,QIIZPtP'PDQVPnPQ@OSPjPQ;OPdPI5PMM_P?1PJJ[PwP)QFNWPrP!QAQUPlPQ=ORPfPM9PNNaPF3PKK\P<,QGOZPtP$QDQVPnPP@OSPhPQ;OOOdPI5PLL_P?.QJJ[P7)QFNWPpP!QAQTPlPQ=OPfPM7PNNaPB3PKK\P:,QGOXPtP$QCOVPnPP>QSPhPP;OOObPI5PLL^P?.QII[PwP'PFNWPpPQAQTPjPQ=OPfPM7PMMaPB1PKK\PzP)QGOXPrP$QCOUPnPP>QRPhPP9POObPF5PLL^P|P.QIIZPwP'PDQWPpPQ@OTPjPQ=OPdPP7PMM_P‚P1PJJ\PzP)QGOXPrP!QCOUPlPP>QRPhPP9PNNbP†P3PLL^P|P,QIIZPtP'PDQVPpP‘P@OSPjP‘P;OPdP‰P7PMM_PP1PJJ[PzP)QFNXPrP!‘PAQUPlP‘P>QRPfPP9PNNaP†P3PKK^P|P,‘PIIZPtP$‘PDQVPnP‘P@OSPhP‘P;OOOdP‰P5PMM_PP.‘PJJ[PwP)‘PFNWPrP!‘PAQTPlP‘P=PRPfPP9PNNaP‚P3PKK\P|P,‘PGOZPtP$‘PCPVPnPPPPbPPP†P1PJŠP[PPPtP$‘PA‘PTPPPjPPPP9PNŽP_PPPP,‘PGPXPPPpP‘P>‘PRPPPfP‰P5PLŒP\PPPzP'PD‘PVPPPlP‘P;POPbP‚P1PJŠPZPtP!‘PA‘PTPPPhPP7PMP_P|P,‘PGPWPpPP>‘PRPPPdP‰P3PK‹P\PwP'PD‘PUPlP‘P;POOaP‚P.‘PI‰PZPrP!‘PA‘PSPhPP7PMM^P|P)‘PFŽPWPnPP>‘PPdP†P3PKK[PwP$‘PCOUPjP‘P;PNNaPP.‘PIIXPrP‘P@OSPfPP7PLL^PzP)‘PFNVPnP‘P=OPbP†P3PJJ[PtP$‘PCOTPjPP9PNN_PP.QGOXPpP‘P@ORPfPP5PLL\PzP)QDQVPlP‘P=OOObP†P1PJJZPtP$QAQTPhPP9PMM_PP,QGOWPpPQ>QRPdP‰P5PKK\PzP'PDQUPlPQ;OOOaP‚P1PIIZPtP!QAQSPhPP7PMM^P|P,QFNWPpPP>QPdPI3PKK[PwP'PCOUPlPQ;ONNaPB.QIIXPrP!Q@OSPhPM7PLL^P<)QFNVPnPP=OPdPF3PJJ[P7$QCOTPjPQ9PNNaP?.QGOXP2Q@ORPfPM5PLL^P:)QDQVPnPQ=OPbPF1PJJ[P4$QAQTPjPP9PNN_P?,QGOXP0Q>QRPfPI5PLL\P:'PDQVP,Q;OOObPB1PJJZP4!QAQTPhPP7PMM_P<,QGOWP0P>QRPdPI3PKK\P7'PDQUPlPQ;OOOaPB.QIIZP2!QAQSPhPM7PMM^P<)QFNWP.P>QPdPF3PKK[P7$QCOUPjPQ;ONNaP?.QIIXP2Q@OSPfPM7PLL^P:)QFNVPnPQ=OPbPF3PJJ[PtP$QCOTPjPP9PNN_P?.QGOXPpPQ@ORPfPM5PLL\PzP)QDQVPlPQ=OOObPF1PJJZPtP$QAQTPhPP9PMM_PP,QGOWPpPQ>QRPdP‰P5PKK\PzP'PDQUPlPQ;OOOaP‚P1PIIZPtP!QAQSPhPP7PMM^P|P,QFNWPpPP>QPdP‰P3PKK[PwP'PCOUPlP‘P;ONNaP‚P.QIIXPrP!‘P@OSPhPP7PLL^P|P)‘PFNVPnPP=OPdP†P3PJJ[PwP$‘PCOTPjP‘P9PNNaPP.‘PGOXPrP‘P@ORPfPP5PLL^PzP)‘PDQVPnP‘P=PPWPPPnPPW‘PP{PNŽP_PPP|PPi‘PP„‘PUPPPjPPPPPwPK‹P[PPPtPPa‘PP€PRPPPdPPP†PPqPI‰PXPPPpPP[PP}PNŽP_PPP|PPi‘PD‘PUPPPjPPPPPwPLŒP\PPPwPPd‘P@PRPPPdPPP†PPqPI‰PXPPPpPP[P=POPaPPPPPi‘PD‘PUPPPjPPPP7PLŒP\PPPwPPd‘PA‘PSPPPfPPP‰P1PI‰PXPPPpPP[P=POPaPPPP,‘PFŽPVPPPlPPPP7PLŒP\PPPwP$‘PA‘PSPPPfPPP‰P3PJŠPZPPPrPP=POPaPPPP,‘PFŽPVPPPlP‘P9PMP^PPPwP$‘PA‘PSPPPfP‰P3PJŠPZPPPrP‘P>‘PPPPaPP,‘PFŽPVPPPlP‘P9PMP^PzP'PCPTPPPfP‰P3PJŠPZPrP‘P>‘PPPPbP‚P.‘PGPVPlP‘P9PMP^PzP'PCPTPhPP5PJŠPZPrP‘P>‘PPbP‚P.‘PGPWPnP‘P;PMM^PzP'PCPTPhPP5PKK[PtP!‘P>‘PPbP‚P.‘PGPWPnP‘P;PNN_P|P'PCPTPhPP5PKK[PtP!‘P@PRPdP†P.‘PGOWPnP‘P;PNN_P|P)‘PDQUPjPP5PKK[PtP!‘P@PRPdP†P1PIIXPnP‘P;PNN_P|P)‘PDQUPjPP7PLL\PtP!‘P@ORPdP†P1PIIXPpPP=OOO_P|P)‘PDQUPjPP7PLL\PwP$‘PAQSPdP†P1PIIXPpPP=OOOaPP,‘PFNUPjPP7PLL\PwP$‘PAQSPfP‰P3PIIXPpPP=OOOaPP,‘PFNVPlP‘P9PLL\PwP$‘PAQSPfP‰P3PJJZPrP‘P=OOOaPP,‘PFNVPlP‘P9PMM^PzP$‘PAQSPfP‰P3PJJZPrP‘P>QPbP‚P,‘PFNVPlP‘P9PMM^PzP'PCOTPhP‰P3PJJZPrP‘P>QPbP‚P.‘PGOWPlP‘P9PMM^PzP'PCOTPhPP5PKK[PrP‘P>QPbP‚P.‘PGOWPnP‘P;PNN^PzP'PCOTPhPP5PKK[PtP!‘P@PRPbP‚P.‘PGOWPnP‘P;PNN_P|P)‘PDQTPhPP5PKK[PtP!‘P@PRPdP†P1PGOWPnP‘P;PNN_P|P)‘PD‘PUPjPP7PKK[PtP!‘P@PRPdP†P1PI‰PXPpPP;PNN_P|P)‘PD‘PUPjPP7PLŒP\PwP!‘P@PRPdP†P1PI‰PXPpPP=POPaPP)‘PD‘PUPjPP7PLŒP\PwP$‘PA‘PSPPPfP†P1PI‰PXPpPP=POPaPP,‘PFŽPVPPPjPP7PLŒP\PwP$‘PA‘PSPPPfP‰P3PJŠPZPPPpPP=POPaPP,‘PFŽPVPPPlP‘P9PMP\PPPwP$‘PA‘PSPPPfP‰P3PJŠPZPPPrP‘P>‘PPPl‘PP†ŽPUPPPhPPP‰PPsPP‰‰PWPPPlPPPPPwPK‹PZPPPpPP[PP{PMP\PPPtPPa‘PP~‘POP_PPP|PPgPA‘PRPPPdPPP‚PPl‘PD‘PTPPPhPPP‰PPqPGPWPPPlPPPP5PJŠPZPPPpPPW‘P9PMP\PPPtPP^‘P=POP_PPPzPPd‘PA‘PRPPPbPPPP,‘PD‘PTPPPfPPP†P1PGPVPPPjPPPP5PJŠPXPPPnP‘P9PLŒP[PPPtP‘P=PNŽP^PPPzP$‘P@PPPPbPPPP)‘PCPTPPPfP†P.‘PFŽPVPPPjPP3PJŠPXPPPnP‘P7PLŒP[PPPrPP=PNŽP^PwP!‘P@PPPPaP|P)‘PCPSPPPdP†P.‘PFŽPUPPPhPP3PI‰PWPnP‘P7PK‹PZPrPP;PMP^PwP!‘P>‘PPPPaP|P'PA‘PSPdP‚P,‘PFŽPUPhP‰P1PI‰PWPlPP7PK‹PZPpP‘P;PMM\PtP!‘P>‘POO_P|P'PA‘PRPbP‚P,‘PD‘PTPhP‰P1PGOVPlPP5PJJZPpP‘P9PLL\PtP‘P=POO_PzP$‘PA‘PRPbPP)‘PDQTPfP†P1PGOVPjPP5PJJXPnP‘P9PLL[PrP‘P=PNN^PzP$‘P@OPbPP)‘PCOSPfP†P.‘PFNVPjPP3PIIXPnP‘P7PLL[PrPP;ONN^PwP!‘P@OPaP|P)‘PCOSPdP‚P.‘PFNUPhPP3PIIWPlP‘P7PKKZPrPP;OMM\PwP!‘P>QOOaP|P'PAQSPdP‚P,‘PDQUPhP‰P1PIIWPlPP5PKKZPpP‘P;OMM\PtP‘P>QOO_PzP'PAQRPbP‚P,‘PDQTPfP‰P1PGOVPlPP5PJJXPpP‘P9PLL\PtP‘P=ONN_PzP$‘P@ORPbPP)‘PDQTPfP†P.‘PGOVPjPP5PJJXPnP‘P9PLL[PrP‘P=ONN^PwP$‘P@OPaPP)‘PCOSPfP†P.‘PFNUPjPP3PIIXPnP‘P7PKK[PrPP;ONN^PwP!‘P>QPaP|P'PCOSPdP‚P.‘PFNUPhP‰P3PIIWPlP‘P7PKKZPpPP;PMM\PwP!‘P>QOOaP|P'PAQRPdP‚P,‘PDQUPhP‰P1PGOWPlPP5PKKZPpP‘P9PMM\PtP‘P>‘POO_PzP'PA‘PRPbPP,‘PD‘PTPfP‰P1PGPVPjPP5PJJXPpP‘P9PLL[PtP‘P=PNN_PzP$‘P@PRPbPP)‘PCPTPfP†P.‘PGPVPjPP3PJŠPXPnP‘P9PLŒP[PrPP=PNŽP^PwP$‘P@PPPPaPP)‘PCPSPPPdP†P.‘PFŽPUPPPjPP3PI‰PWPPPnP‘P7PK‹P[PrPP;PMP^PwP!‘P>‘PPPPaP|P'PCPSPPPdP‚PWPPPjPPPPPqPGPUPPPhPPP†PPn‘PD‘PTPPPdPPP‚PPi‘PCPSPPPbPPPPPgPA‘PPPPaPPPzPPd‘P>‘POP^PPPwPP^‘P=PMP\PPPrPP[P9PLŒPZPPPpPPS‘P7PJŠPXPPPnPPPP5PI‰PWPPPjPPPP1PGPUPPPhPPP†P.‘PD‘PTPPPdPPP‚P)‘PCPRPPPbPPP|P'P@PPPP_PPPzP$‘P>‘POP^PPPwP‘P=PMP\PPPrPP9PLŒPZPPPpP‘P7PJŠPXPPPlPP3PI‰PVPPPjP‰P1PFŽPUPPPhP†P.‘PD‘PTPPPdP‚P)‘PCPRPPPbP|P'P@PPPP_PzP!‘P>‘PNŽP^PtP‘P;PMP[PrPP9PLŒPZPpP‘P7PJŠPXPlPP3PI‰PVPjP‰P1PFŽPUPfP†P,‘PD‘PSPdPP)‘PCPRPbP|P'P@PP_PzP!‘P>‘PNN^PtP‘P;PMM[PrP‘P9PKKZPnP‘P5PJJWPlPP3PIIVPjP‰P1PF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zcS?RH(?54CekL2Kd!UGWWIC~ui+iDUsWC(nzVn~`O~zYo8Y%7#2P{d~WxY`e8nnuK zjR*cpQnR>qpL;%vy}6eEz*_U)73cEbEyg6-4FA`D&A$KXe!UMQEE4F8Z^?SztHq)2 zI>U^!HuqIy?iH_d+}$fm@(HuB%Md;`KUk#SC7fZAYf<#b&1YU@mu<9PHC=xV*Bwem zowx17RE~=7vCor_oL*ZX@e<@L8vk%=2dDmitES^|TH;3;WCe(V7r)E(>|I}nv`p? zyZGGqli_aN%dT6*%)Wj>JXz7qn z*|W%=>%cu>{=;9!`LFyfr%wi#tscII=Cr7p8^K@e`44}!xsRuBkvZ3a=QD**d*Q$O z{>}9ZNAh4eIK4<*(Zo+u`f5Cr}l*oxl8($_rnX9oe!j) zL|q@>;G$1@l^ZLl=e|bmMb=s7a3Z_YMAn5Bzwj9szGTlXF2ZUJJ^bxcIJKp>bb9aD##~m@uNdaioEZ` dd#l-pQF-1qCQ$dCc#2l|h Date: Fri, 10 Mar 2023 01:11:54 -0500 Subject: [PATCH 11/14] Fix tabs vs spaces, tweak comments, error on BE --- Core/MIPS/MIPSVFPUUtils.cpp | 104 +++++++++++++++++++----------------- 1 file changed, 54 insertions(+), 50 deletions(-) diff --git a/Core/MIPS/MIPSVFPUUtils.cpp b/Core/MIPS/MIPSVFPUUtils.cpp index e97a476d78..ca4f4c889b 100644 --- a/Core/MIPS/MIPSVFPUUtils.cpp +++ b/Core/MIPS/MIPSVFPUUtils.cpp @@ -801,6 +801,7 @@ float vfpu_dot(const float a[4], const float b[4]) { // estimations, to allow to store them in smaller types. // See https://github.com/hrydgard/ppsspp/issues/16946 for details. +// Lookup tables. static uint32_t (*vfpu_sin_lut8192)=nullptr; static int8_t (*vfpu_sin_lut_delta)[2]=nullptr; static int16_t (*vfpu_sin_lut_interval_delta)=nullptr; @@ -1098,7 +1099,7 @@ float vfpu_rsqrt(float x) { uint32_t bits; memcpy(&bits, &x, sizeof(bits)); if((bits & 0x7FFFFFFFu) <= 0x007FFFFFu) { - // Denormals (and zeroes) get Inf of the same sign. + // Denormals (and zeroes) get inf of the same sign. bits = 0x7F800000u | (bits & 0x80000000u); memcpy(&x, &bits, sizeof(x)); return x; @@ -1110,7 +1111,7 @@ float vfpu_rsqrt(float x) { return x; } if((bits >> 23) == 255u) { - // Inf gets 0, NaN gets NaN. + // inf gets 0, NaN gets NaN. bits = ((bits & 0x007FFFFFu) ? 0x7F800001u : 0u); memcpy(&x, &bits, sizeof(bits)); return x; @@ -1238,53 +1239,53 @@ static inline uint32_t vfpu_log2_approx(uint32_t x) { // Matches PSP output on all known values. float vfpu_log2(float x) { - uint32_t bits; - memcpy(&bits, &x, sizeof(bits)); - if((bits & 0x7FFFFFFFu) <= 0x007FFFFFu) { - // Denormals (and zeroes) get -inf. - bits = 0xFF800000u; - memcpy(&x, &bits, sizeof(x)); - return x; - } - if(bits & 0x80000000u) { - // Other negatives get NaN. - bits = 0x7F800001u; - memcpy(&x, &bits, sizeof(x)); - return x; - } - if((bits >> 23) == 255u) { - // NaN gets NaN, +inf gets +inf. - bits = 0x7F800000u + ((bits & 0x007FFFFFu) != 0); - memcpy(&x, &bits, sizeof(x)); - return x; - } - uint32_t e = (bits & 0x7F800000u) - 0x3F800000u; - uint32_t i = bits & 0x007FFFFFu; - if(e >> 31 && i >= 0x007FFE00u) { - // Process 1-2^{-14}<=x*2^n<1 (for n>0) separately, - // since the table doesn't give the right answer. - float c = float(int32_t(~e) >> 23); - // Note: if c is 0 the sign of -0 output is correct. - return i < 0x007FFEF7u ? // 1-265*2^{-24} - -3.05175781e-05f - c: - -0.0f - c; - } - int d = (e<0x01000000u ? 0 : 8 - clz32_nonzero(e) - int(e >> 31)); - //assert(d>=0&&d<8); - uint32_t q = 1u << d; - uint32_t A = vfpu_log2_approx((i ) & -64u) & -q; - uint32_t B = vfpu_log2_approx((i + 64) & -64u) & -q; - uint64_t a = (A << 6)+(uint64_t(vfpu_log2_lut[d][i >> 6][0]) - 80ull) * q; - uint64_t b = (B << 6)+(uint64_t(vfpu_log2_lut[d][i >> 6][1]) - 80ull) * q; - uint32_t v = uint32_t((a +(((b - a) * (i & 63)) >> 6)) >> 6); - v &= -q; - bits = e ^ (2u * v); - x = float(int32_t(bits)) * 1.1920928955e-7f; // 0x1p-23f - return x; + uint32_t bits; + memcpy(&bits, &x, sizeof(bits)); + if((bits & 0x7FFFFFFFu) <= 0x007FFFFFu) { + // Denormals (and zeroes) get -inf. + bits = 0xFF800000u; + memcpy(&x, &bits, sizeof(x)); + return x; + } + if(bits & 0x80000000u) { + // Other negatives get NaN. + bits = 0x7F800001u; + memcpy(&x, &bits, sizeof(x)); + return x; + } + if((bits >> 23) == 255u) { + // NaN gets NaN, +inf gets +inf. + bits = 0x7F800000u + ((bits & 0x007FFFFFu) != 0); + memcpy(&x, &bits, sizeof(x)); + return x; + } + uint32_t e = (bits & 0x7F800000u) - 0x3F800000u; + uint32_t i = bits & 0x007FFFFFu; + if(e >> 31 && i >= 0x007FFE00u) { + // Process 1-2^{-14}<=x*2^n<1 (for n>0) separately, + // since the table doesn't give the right answer. + float c = float(int32_t(~e) >> 23); + // Note: if c is 0 the sign of -0 output is correct. + return i < 0x007FFEF7u ? // 1-265*2^{-24} + -3.05175781e-05f - c: + -0.0f - c; + } + int d = (e < 0x01000000u ? 0 : 8 - clz32_nonzero(e) - int(e >> 31)); + //assert(d >= 0 && d < 8); + uint32_t q = 1u << d; + uint32_t A = vfpu_log2_approx((i ) & -64u) & -q; + uint32_t B = vfpu_log2_approx((i + 64) & -64u) & -q; + uint64_t a = (A << 6)+(uint64_t(vfpu_log2_lut[d][i >> 6][0]) - 80ull) * q; + uint64_t b = (B << 6)+(uint64_t(vfpu_log2_lut[d][i >> 6][1]) - 80ull) * q; + uint32_t v = uint32_t((a +(((b - a) * (i & 63)) >> 6)) >> 6); + v &= -q; + bits = e ^ (2u * v); + x = float(int32_t(bits)) * 1.1920928955e-7f; // 0x1p-23f + return x; } static inline uint32_t vfpu_rcp_approx(uint32_t i) { - return 0x3E800000u + (uint32_t((1ull << 47) / ((1ull << 23) + i)) & -4u); + return 0x3E800000u + (uint32_t((1ull << 47) / ((1ull << 23) + i)) & -4u); } float vfpu_rcp(float x) { @@ -1317,17 +1318,20 @@ float vfpu_rcp(float x) { //============================================================================== void InitVFPU() { -// WARNING: this is not endian-safe! +#if COMMON_BIG_ENDIAN + // Tables are little-endian. +#error Byteswap for VFPU tables not implemented +#endif size_t size=0; #define LOAD(expected,name)\ if(!name) {\ const char *filename = "vfpu/" #name ".dat";\ - INFO_LOG(CPU, "Loading '%s'.\n", filename);\ + INFO_LOG(CPU, "Loading '%s'...", filename);\ name=reinterpret_cast(g_VFS.ReadFile(filename, &size));\ if(size!=(expected))\ - ERROR_LOG(CPU, "Error loading '%s' (size=%u, expected: %u).\n", filename, (unsigned)size, (unsigned)(expected));\ + ERROR_LOG(CPU, "Error loading '%s' (size=%u, expected: %u)", filename, (unsigned)size, (unsigned)(expected));\ else\ - INFO_LOG(CPU, "Successfully loaded '%s'.\n", filename);\ + INFO_LOG(CPU, "Successfully loaded '%s'", filename);\ } LOAD( 1536, vfpu_asin_lut65536); LOAD( 517448, vfpu_asin_lut_deltas); From 0619572f978339a9e19a1a9aa51916dd01cb827b Mon Sep 17 00:00:00 2001 From: fp64 <106717720+fp64@users.noreply.github.com> Date: Fri, 10 Mar 2023 05:22:09 -0500 Subject: [PATCH 12/14] Fix CMakeLists.txt --- CMakeLists.txt | 7 +++++++ 1 file changed, 7 insertions(+) diff --git a/CMakeLists.txt b/CMakeLists.txt index 9056de3389..19a7ae89c5 100644 --- a/CMakeLists.txt +++ b/CMakeLists.txt @@ -368,6 +368,10 @@ if(NOT MSVC) if(X86 OR X86_64) # enable sse2 code generation add_definitions(-msse2) + if(NOT X86_64 AND NOT CLANG) + add_definitions(-mfpmath=sse) + # add_definitions(-mstackrealign) + endif() endif() if(IOS) @@ -2355,6 +2359,7 @@ set(NativeAssets assets/lang assets/shaders assets/themes + assets/vfpu assets/Roboto-Condensed.ttf assets/7z.png assets/compat.ini @@ -2465,6 +2470,7 @@ if(TargetBin) file(GLOB_RECURSE SHADER_FILES assets/shaders/*) file(GLOB_RECURSE THEME_FILE assets/themes/*) file(GLOB_RECURSE DEBUGGER_FILES assets/debugger/*) + file(GLOB_RECURSE VFPU_FILES assets/vfpu/*) if(NOT IOS) set_source_files_properties(${BigFontAssets} PROPERTIES MACOSX_PACKAGE_LOCATION "Resources/assets") @@ -2474,6 +2480,7 @@ if(TargetBin) set_source_files_properties(${SHADER_FILES} PROPERTIES MACOSX_PACKAGE_LOCATION "Resources/assets/shaders") set_source_files_properties(${THEME_FILE} PROPERTIES MACOSX_PACKAGE_LOCATION "Resources/assets/themes") set_source_files_properties(${DEBUGGER_FILES} PROPERTIES MACOSX_PACKAGE_LOCATION "Resources/assets/debugger") + set_source_files_properties(${VFPU_FILES} PROPERTIES MACOSX_PACKAGE_LOCATION "Resources/assets/vfpu") endif() if(IOS) From c49c45a10692022d447c34ea95d16dc1993c9810 Mon Sep 17 00:00:00 2001 From: fp64 <106717720+fp64@users.noreply.github.com> Date: Fri, 10 Mar 2023 09:01:00 -0500 Subject: [PATCH 13/14] Add VFS registration during unittest --- unittest/UnitTest.cpp | 5 +++++ 1 file changed, 5 insertions(+) diff --git a/unittest/UnitTest.cpp b/unittest/UnitTest.cpp index 1789b97ad0..e8718d6680 100644 --- a/unittest/UnitTest.cpp +++ b/unittest/UnitTest.cpp @@ -58,6 +58,8 @@ #include "Common/CPUDetect.h" #include "Common/Log.h" #include "Core/Config.h" +#include "Common/File/VFS/VFS.h" +#include "Common/File/VFS/DirectoryReader.h" #include "Core/FileSystems/ISOFileSystem.h" #include "Core/MemMap.h" #include "Core/MIPS/MIPSVFPUUtils.h" @@ -352,6 +354,9 @@ bool TestTinySet() { bool TestVFPUSinCos() { float sine, cosine; + // Needed for VFPU tables. + // There might be a better place to invoke it, but whatever. + g_VFS.Register("", new DirectoryReader(Path("assets"))); InitVFPU(); vfpu_sincos(0.0f, sine, cosine); EXPECT_EQ_FLOAT(sine, 0.0f); From 38fc21a2c07aadc758f67001b4e3ddc6bb7b7cfd Mon Sep 17 00:00:00 2001 From: fp64 <106717720+fp64@users.noreply.github.com> Date: Sun, 12 Mar 2023 05:11:59 -0400 Subject: [PATCH 14/14] Implement load-on-demand of vfpu tables --- Core/MIPS/MIPSIntVFPU.cpp | 6 --- Core/MIPS/MIPSVFPUUtils.cpp | 99 ++++++++++++++++++++++++++----------- Core/MIPS/MIPSVFPUUtils.h | 6 +-- 3 files changed, 70 insertions(+), 41 deletions(-) diff --git a/Core/MIPS/MIPSIntVFPU.cpp b/Core/MIPS/MIPSIntVFPU.cpp index c6585f21f2..5e40a1e434 100644 --- a/Core/MIPS/MIPSIntVFPU.cpp +++ b/Core/MIPS/MIPSIntVFPU.cpp @@ -629,23 +629,17 @@ namespace MIPSInt // vsat0 changes -0.0 to +0.0, both retain NAN. case 4: if (s[i] <= 0) d[i] = 0; else {if(s[i] > 1.0f) d[i] = 1.0f; else d[i] = s[i];} break; // vsat0 case 5: if (s[i] < -1.0f) d[i] = -1.0f; else {if(s[i] > 1.0f) d[i] = 1.0f; else d[i] = s[i];} break; // vsat1 - //case 16: d[i] = 1.0f / s[i]; break; //vrcp case 16: { d[i] = vfpu_rcp(s[i]); } break; //vrcp case 17: d[i] = USE_VFPU_SQRT ? vfpu_rsqrt(s[i]) : 1.0f / sqrtf(s[i]); break; //vrsq case 18: { d[i] = vfpu_sin(s[i]); } break; //vsin case 19: { d[i] = vfpu_cos(s[i]); } break; //vcos - //case 20: d[i] = powf(2.0f, s[i]); break; //vexp2 case 20: { d[i] = vfpu_exp2(s[i]); } break; //vexp2 - //case 21: d[i] = logf(s[i])/log(2.0f); break; //vlog2 case 21: { d[i] = vfpu_log2(s[i]); } break; //vlog2 case 22: d[i] = USE_VFPU_SQRT ? vfpu_sqrt(s[i]) : fabsf(sqrtf(s[i])); break; //vsqrt - //case 23: d[i] = (float)(asinf(s[i]) / M_PI_2); break; //vasin case 23: { d[i] = vfpu_asin(s[i]); } break; //vasin - //case 24: d[i] = -1.0f / s[i]; break; // vnrcp case 24: { d[i] = -vfpu_rcp(s[i]); } break; // vnrcp case 26: { d[i] = -vfpu_sin(s[i]); } break; // vnsin - //case 28: d[i] = 1.0f / powf(2.0, s[i]); break; // vrexp2 case 28: { d[i] = vfpu_rexp2(s[i]); } break; // vrexp2 default: _dbg_assert_msg_( false, "Invalid VV2Op op type %d", optype); diff --git a/Core/MIPS/MIPSVFPUUtils.cpp b/Core/MIPS/MIPSVFPUUtils.cpp index ca4f4c889b..d5d622f752 100644 --- a/Core/MIPS/MIPSVFPUUtils.cpp +++ b/Core/MIPS/MIPSVFPUUtils.cpp @@ -802,6 +802,7 @@ float vfpu_dot(const float a[4], const float b[4]) { // See https://github.com/hrydgard/ppsspp/issues/16946 for details. // Lookup tables. +// Note: these are never unloaded, and stay till program termination. static uint32_t (*vfpu_sin_lut8192)=nullptr; static int8_t (*vfpu_sin_lut_delta)[2]=nullptr; static int16_t (*vfpu_sin_lut_interval_delta)=nullptr; @@ -824,6 +825,30 @@ static uint16_t (*vfpu_asin_lut_indices)=nullptr; static int8_t (*vfpu_rcp_lut)[2]=nullptr; +template +static inline bool load_vfpu_table(T *&ptr,const char *filename, size_t expected_size) { +#if COMMON_BIG_ENDIAN + // Tables are little-endian. +#error Byteswap for VFPU tables not implemented +#endif + if(ptr) return true; // Already loaded. + size_t size = 0u; + INFO_LOG(CPU, "Loading '%s'...", filename); + ptr = reinterpret_cast(g_VFS.ReadFile(filename, &size)); + if(!ptr || size != expected_size) + { + ERROR_LOG(CPU, "Error loading '%s' (size=%u, expected: %u)", filename, (unsigned)size, (unsigned)expected_size); + if(ptr) delete[] ptr; + ptr = nullptr; + return false; + } + INFO_LOG(CPU, "Successfully loaded '%s'", filename); + return true; +} + +#define LOAD_TABLE(name, expected_size)\ + load_vfpu_table(name,"vfpu/" #name ".dat",expected_size) + // Note: PSP sin/cos output only has 22 significant // binary digits. static inline uint32_t vfpu_sin_quantum(uint32_t x) { @@ -877,6 +902,11 @@ static inline uint32_t vfpu_sin_fixed(uint32_t arg) { } float vfpu_sin(float x) { + static bool loaded = + LOAD_TABLE(vfpu_sin_lut8192, 4100)&& + LOAD_TABLE(vfpu_sin_lut_delta, 262144)&& + LOAD_TABLE(vfpu_sin_lut_interval_delta, 131074)&& + LOAD_TABLE(vfpu_sin_lut_exceptions, 86938); uint32_t bits; memcpy(&bits, &x, sizeof(x)); uint32_t sign = bits & 0x80000000u; @@ -909,6 +939,11 @@ float vfpu_sin(float x) { } float vfpu_cos(float x) { + static bool loaded = + LOAD_TABLE(vfpu_sin_lut8192, 4100)&& + LOAD_TABLE(vfpu_sin_lut_delta, 262144)&& + LOAD_TABLE(vfpu_sin_lut_interval_delta, 131074)&& + LOAD_TABLE(vfpu_sin_lut_exceptions, 86938); uint32_t bits; memcpy(&bits, &x, sizeof(x)); bits &= 0x7FFFFFFFu; @@ -1012,6 +1047,8 @@ static inline uint32_t vfpu_sqrt_fixed(uint32_t x) { } float vfpu_sqrt(float x) { + static bool loaded = + LOAD_TABLE(vfpu_sqrt_lut, 262144); uint32_t bits; memcpy(&bits, &x, sizeof(bits)); if((bits & 0x7FFFFFFFu) <= 0x007FFFFFu) { @@ -1096,6 +1133,8 @@ static inline uint32_t vfpu_rsqrt_fixed(uint32_t x) { } float vfpu_rsqrt(float x) { + static bool loaded = + LOAD_TABLE(vfpu_rsqrt_lut, 262144); uint32_t bits; memcpy(&bits, &x, sizeof(bits)); if((bits & 0x7FFFFFFFu) <= 0x007FFFFFu) { @@ -1153,6 +1192,10 @@ static uint32_t vfpu_asin_fixed(uint32_t x) { } float vfpu_asin(float x) { + static bool loaded = + LOAD_TABLE(vfpu_asin_lut65536, 1536)&& + LOAD_TABLE(vfpu_asin_lut_indices, 798916)&& + LOAD_TABLE(vfpu_asin_lut_deltas, 517448); uint32_t bits; memcpy(&bits, &x, sizeof(x)); uint32_t sign = bits & 0x80000000u; @@ -1190,6 +1233,9 @@ static inline uint32_t vfpu_exp2_fixed(uint32_t x) { } float vfpu_exp2(float x) { + static bool loaded = + LOAD_TABLE(vfpu_exp2_lut65536, 512)&& + LOAD_TABLE(vfpu_exp2_lut, 262144); int32_t bits; memcpy(&bits, &x, sizeof(bits)); if((bits & 0x7FFFFFFF) <= 0x007FFFFF) { @@ -1239,6 +1285,10 @@ static inline uint32_t vfpu_log2_approx(uint32_t x) { // Matches PSP output on all known values. float vfpu_log2(float x) { + static bool loaded = + LOAD_TABLE(vfpu_log2_lut65536, 516)&& + LOAD_TABLE(vfpu_log2_lut65536_quadratic, 512)&& + LOAD_TABLE(vfpu_log2_lut, 2097152); uint32_t bits; memcpy(&bits, &x, sizeof(bits)); if((bits & 0x7FFFFFFFu) <= 0x007FFFFFu) { @@ -1289,6 +1339,8 @@ static inline uint32_t vfpu_rcp_approx(uint32_t i) { } float vfpu_rcp(float x) { + static bool loaded = + LOAD_TABLE(vfpu_rcp_lut, 262144); uint32_t bits; memcpy(&bits, &x, sizeof(bits)); uint32_t s = bits & 0x80000000u; @@ -1318,35 +1370,22 @@ float vfpu_rcp(float x) { //============================================================================== void InitVFPU() { -#if COMMON_BIG_ENDIAN - // Tables are little-endian. -#error Byteswap for VFPU tables not implemented +#if 0 + // Load all in advance. + LOAD_TABLE(vfpu_asin_lut65536 , 1536); + LOAD_TABLE(vfpu_asin_lut_deltas , 517448); + LOAD_TABLE(vfpu_asin_lut_indices , 798916); + LOAD_TABLE(vfpu_exp2_lut65536 , 512); + LOAD_TABLE(vfpu_exp2_lut , 262144); + LOAD_TABLE(vfpu_log2_lut65536 , 516); + LOAD_TABLE(vfpu_log2_lut65536_quadratic, 512); + LOAD_TABLE(vfpu_log2_lut , 2097152); + LOAD_TABLE(vfpu_rcp_lut , 262144); + LOAD_TABLE(vfpu_rsqrt_lut , 262144); + LOAD_TABLE(vfpu_sin_lut8192 , 4100); + LOAD_TABLE(vfpu_sin_lut_delta , 262144); + LOAD_TABLE(vfpu_sin_lut_exceptions , 86938); + LOAD_TABLE(vfpu_sin_lut_interval_delta , 131074); + LOAD_TABLE(vfpu_sqrt_lut , 262144); #endif - size_t size=0; -#define LOAD(expected,name)\ - if(!name) {\ - const char *filename = "vfpu/" #name ".dat";\ - INFO_LOG(CPU, "Loading '%s'...", filename);\ - name=reinterpret_cast(g_VFS.ReadFile(filename, &size));\ - if(size!=(expected))\ - ERROR_LOG(CPU, "Error loading '%s' (size=%u, expected: %u)", filename, (unsigned)size, (unsigned)(expected));\ - else\ - INFO_LOG(CPU, "Successfully loaded '%s'", filename);\ - } - LOAD( 1536, vfpu_asin_lut65536); - LOAD( 517448, vfpu_asin_lut_deltas); - LOAD( 798916, vfpu_asin_lut_indices); - LOAD( 512, vfpu_exp2_lut65536); - LOAD( 262144, vfpu_exp2_lut); - LOAD( 516, vfpu_log2_lut65536); - LOAD( 512, vfpu_log2_lut65536_quadratic); - LOAD( 2097152, vfpu_log2_lut); - LOAD( 262144, vfpu_rcp_lut); - LOAD( 262144, vfpu_rsqrt_lut); - LOAD( 4100, vfpu_sin_lut8192); - LOAD( 262144, vfpu_sin_lut_delta); - LOAD( 86938, vfpu_sin_lut_exceptions); - LOAD( 131074, vfpu_sin_lut_interval_delta); - LOAD( 262144, vfpu_sqrt_lut); -#undef LOAD } diff --git a/Core/MIPS/MIPSVFPUUtils.h b/Core/MIPS/MIPSVFPUUtils.h index a8b2bebd79..1b03ca390a 100644 --- a/Core/MIPS/MIPSVFPUUtils.h +++ b/Core/MIPS/MIPSVFPUUtils.h @@ -42,6 +42,7 @@ inline int Xpose(int v) { // Final Fantasy III (#2921 ) // Hitman Reborn 2 (#12900) // Cho Aniki Zero (#13705) +// Hajime no Ippo (#13671) // Dissidia Duodecim Final Fantasy (#6710 ) // // Messing around with the modulo functions? try https://www.desmos.com/calculator. @@ -50,11 +51,6 @@ extern float vfpu_sin(float); extern float vfpu_cos(float); extern void vfpu_sincos(float, float&, float&); -/* -inline float vfpu_asin(float angle) { - return (float)(asinf(angle) / M_PI_2); -} -*/ extern float vfpu_asin(float); inline float vfpu_clamp(float v, float min, float max) {

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zcS?RH(?54CekL2Kd!UGWWIC~ui+iDUsWC(nzVn~`O~zYo8Y%7#2P{d~WxY`e8nnuK zjR*cpQnR>qpL;%vy}6eEz*_U)73cEbEyg6-4FA`D&A$KXe!UMQEE4F8Z^?SztHq)2 zI>U^!HuqIy?iH_d+}$fm@(HuB%Md;`KUk#SC7fZAYf<#b&1YU@mu<9PHC=xV*Bwem zowx17RE~=7vCor_oL*ZX@e<@L8vk%=2dDmitES^|TH;3;WCe(V7r)E(>|I}nv`p? zyZGGqli_aN%dT6*%)Wj>JXz7qn z*|W%=>%cu>{=;9!`LFyfr%wi#tscII=Cr7p8^K@e`44}!xsRuBkvZ3a=QD**d*Q$O z{>}9ZNAh4eIK4<*(Zo+u`f5Cr}l*oxl8($_rnX9oe!j) zL|q@>;G$1@l^ZLl=e|bmMb=s7a3Z_YMAn5Bzwj9szGTlXF2ZUJJ^bxcIJKp>bb9aD##~m@uNdaioEZ` dd#l-pQF-1qCQ$dCc#2l|h Date: Fri, 10 Mar 2023 01:11:54 -0500 Subject: [PATCH 04/14] Fix tabs vs spaces, tweak comments, error on BE --- Core/MIPS/MIPSVFPUUtils.cpp | 104 +++++++++++++++++++----------------- 1 file changed, 54 insertions(+), 50 deletions(-) diff --git a/Core/MIPS/MIPSVFPUUtils.cpp b/Core/MIPS/MIPSVFPUUtils.cpp index e97a476d78..ca4f4c889b 100644 --- a/Core/MIPS/MIPSVFPUUtils.cpp +++ b/Core/MIPS/MIPSVFPUUtils.cpp @@ -801,6 +801,7 @@ float vfpu_dot(const float a[4], const float b[4]) { // estimations, to allow to store them in smaller types. // See https://github.com/hrydgard/ppsspp/issues/16946 for details. +// Lookup tables. static uint32_t (*vfpu_sin_lut8192)=nullptr; static int8_t (*vfpu_sin_lut_delta)[2]=nullptr; static int16_t (*vfpu_sin_lut_interval_delta)=nullptr; @@ -1098,7 +1099,7 @@ float vfpu_rsqrt(float x) { uint32_t bits; memcpy(&bits, &x, sizeof(bits)); if((bits & 0x7FFFFFFFu) <= 0x007FFFFFu) { - // Denormals (and zeroes) get Inf of the same sign. + // Denormals (and zeroes) get inf of the same sign. bits = 0x7F800000u | (bits & 0x80000000u); memcpy(&x, &bits, sizeof(x)); return x; @@ -1110,7 +1111,7 @@ float vfpu_rsqrt(float x) { return x; } if((bits >> 23) == 255u) { - // Inf gets 0, NaN gets NaN. + // inf gets 0, NaN gets NaN. bits = ((bits & 0x007FFFFFu) ? 0x7F800001u : 0u); memcpy(&x, &bits, sizeof(bits)); return x; @@ -1238,53 +1239,53 @@ static inline uint32_t vfpu_log2_approx(uint32_t x) { // Matches PSP output on all known values. float vfpu_log2(float x) { - uint32_t bits; - memcpy(&bits, &x, sizeof(bits)); - if((bits & 0x7FFFFFFFu) <= 0x007FFFFFu) { - // Denormals (and zeroes) get -inf. - bits = 0xFF800000u; - memcpy(&x, &bits, sizeof(x)); - return x; - } - if(bits & 0x80000000u) { - // Other negatives get NaN. - bits = 0x7F800001u; - memcpy(&x, &bits, sizeof(x)); - return x; - } - if((bits >> 23) == 255u) { - // NaN gets NaN, +inf gets +inf. - bits = 0x7F800000u + ((bits & 0x007FFFFFu) != 0); - memcpy(&x, &bits, sizeof(x)); - return x; - } - uint32_t e = (bits & 0x7F800000u) - 0x3F800000u; - uint32_t i = bits & 0x007FFFFFu; - if(e >> 31 && i >= 0x007FFE00u) { - // Process 1-2^{-14}<=x*2^n<1 (for n>0) separately, - // since the table doesn't give the right answer. - float c = float(int32_t(~e) >> 23); - // Note: if c is 0 the sign of -0 output is correct. - return i < 0x007FFEF7u ? // 1-265*2^{-24} - -3.05175781e-05f - c: - -0.0f - c; - } - int d = (e<0x01000000u ? 0 : 8 - clz32_nonzero(e) - int(e >> 31)); - //assert(d>=0&&d<8); - uint32_t q = 1u << d; - uint32_t A = vfpu_log2_approx((i ) & -64u) & -q; - uint32_t B = vfpu_log2_approx((i + 64) & -64u) & -q; - uint64_t a = (A << 6)+(uint64_t(vfpu_log2_lut[d][i >> 6][0]) - 80ull) * q; - uint64_t b = (B << 6)+(uint64_t(vfpu_log2_lut[d][i >> 6][1]) - 80ull) * q; - uint32_t v = uint32_t((a +(((b - a) * (i & 63)) >> 6)) >> 6); - v &= -q; - bits = e ^ (2u * v); - x = float(int32_t(bits)) * 1.1920928955e-7f; // 0x1p-23f - return x; + uint32_t bits; + memcpy(&bits, &x, sizeof(bits)); + if((bits & 0x7FFFFFFFu) <= 0x007FFFFFu) { + // Denormals (and zeroes) get -inf. + bits = 0xFF800000u; + memcpy(&x, &bits, sizeof(x)); + return x; + } + if(bits & 0x80000000u) { + // Other negatives get NaN. + bits = 0x7F800001u; + memcpy(&x, &bits, sizeof(x)); + return x; + } + if((bits >> 23) == 255u) { + // NaN gets NaN, +inf gets +inf. + bits = 0x7F800000u + ((bits & 0x007FFFFFu) != 0); + memcpy(&x, &bits, sizeof(x)); + return x; + } + uint32_t e = (bits & 0x7F800000u) - 0x3F800000u; + uint32_t i = bits & 0x007FFFFFu; + if(e >> 31 && i >= 0x007FFE00u) { + // Process 1-2^{-14}<=x*2^n<1 (for n>0) separately, + // since the table doesn't give the right answer. + float c = float(int32_t(~e) >> 23); + // Note: if c is 0 the sign of -0 output is correct. + return i < 0x007FFEF7u ? // 1-265*2^{-24} + -3.05175781e-05f - c: + -0.0f - c; + } + int d = (e < 0x01000000u ? 0 : 8 - clz32_nonzero(e) - int(e >> 31)); + //assert(d >= 0 && d < 8); + uint32_t q = 1u << d; + uint32_t A = vfpu_log2_approx((i ) & -64u) & -q; + uint32_t B = vfpu_log2_approx((i + 64) & -64u) & -q; + uint64_t a = (A << 6)+(uint64_t(vfpu_log2_lut[d][i >> 6][0]) - 80ull) * q; + uint64_t b = (B << 6)+(uint64_t(vfpu_log2_lut[d][i >> 6][1]) - 80ull) * q; + uint32_t v = uint32_t((a +(((b - a) * (i & 63)) >> 6)) >> 6); + v &= -q; + bits = e ^ (2u * v); + x = float(int32_t(bits)) * 1.1920928955e-7f; // 0x1p-23f + return x; } static inline uint32_t vfpu_rcp_approx(uint32_t i) { - return 0x3E800000u + (uint32_t((1ull << 47) / ((1ull << 23) + i)) & -4u); + return 0x3E800000u + (uint32_t((1ull << 47) / ((1ull << 23) + i)) & -4u); } float vfpu_rcp(float x) { @@ -1317,17 +1318,20 @@ float vfpu_rcp(float x) { //============================================================================== void InitVFPU() { -// WARNING: this is not endian-safe! +#if COMMON_BIG_ENDIAN + // Tables are little-endian. +#error Byteswap for VFPU tables not implemented +#endif size_t size=0; #define LOAD(expected,name)\ if(!name) {\ const char *filename = "vfpu/" #name ".dat";\ - INFO_LOG(CPU, "Loading '%s'.\n", filename);\ + INFO_LOG(CPU, "Loading '%s'...", filename);\ name=reinterpret_cast(g_VFS.ReadFile(filename, &size));\ if(size!=(expected))\ - ERROR_LOG(CPU, "Error loading '%s' (size=%u, expected: %u).\n", filename, (unsigned)size, (unsigned)(expected));\ + ERROR_LOG(CPU, "Error loading '%s' (size=%u, expected: %u)", filename, (unsigned)size, (unsigned)(expected));\ else\ - INFO_LOG(CPU, "Successfully loaded '%s'.\n", filename);\ + INFO_LOG(CPU, "Successfully loaded '%s'", filename);\ } LOAD( 1536, vfpu_asin_lut65536); LOAD( 517448, vfpu_asin_lut_deltas); From 1c41078487e2e3d169121fedad39b1db4ae26414 Mon Sep 17 00:00:00 2001 From: fp64 <106717720+fp64@users.noreply.github.com> Date: Fri, 10 Mar 2023 05:22:09 -0500 Subject: [PATCH 05/14] Fix CMakeLists.txt --- CMakeLists.txt | 7 +++++++ 1 file changed, 7 insertions(+) diff --git a/CMakeLists.txt b/CMakeLists.txt index 25505d597c..1d0c86dcce 100644 --- a/CMakeLists.txt +++ b/CMakeLists.txt @@ -368,6 +368,10 @@ if(NOT MSVC) if(X86 OR X86_64) # enable sse2 code generation add_definitions(-msse2) + if(NOT X86_64 AND NOT CLANG) + add_definitions(-mfpmath=sse) + # add_definitions(-mstackrealign) + endif() endif() if(IOS) @@ -2353,6 +2357,7 @@ set(NativeAssets assets/lang assets/shaders assets/themes + assets/vfpu assets/Roboto-Condensed.ttf assets/7z.png assets/compat.ini @@ -2463,6 +2468,7 @@ if(TargetBin) file(GLOB_RECURSE SHADER_FILES assets/shaders/*) file(GLOB_RECURSE THEME_FILE assets/themes/*) file(GLOB_RECURSE DEBUGGER_FILES assets/debugger/*) + file(GLOB_RECURSE VFPU_FILES assets/vfpu/*) if(NOT IOS) set_source_files_properties(${BigFontAssets} PROPERTIES MACOSX_PACKAGE_LOCATION "Resources/assets") @@ -2472,6 +2478,7 @@ if(TargetBin) set_source_files_properties(${SHADER_FILES} PROPERTIES MACOSX_PACKAGE_LOCATION "Resources/assets/shaders") set_source_files_properties(${THEME_FILE} PROPERTIES MACOSX_PACKAGE_LOCATION "Resources/assets/themes") set_source_files_properties(${DEBUGGER_FILES} PROPERTIES MACOSX_PACKAGE_LOCATION "Resources/assets/debugger") + set_source_files_properties(${VFPU_FILES} PROPERTIES MACOSX_PACKAGE_LOCATION "Resources/assets/vfpu") endif() if(IOS) From 03b0d2e3aed87a0903047dfc07a7dbd284d860ce Mon Sep 17 00:00:00 2001 From: fp64 <106717720+fp64@users.noreply.github.com> Date: Fri, 10 Mar 2023 09:01:00 -0500 Subject: [PATCH 06/14] Add VFS registration during unittest --- unittest/UnitTest.cpp | 5 +++++ 1 file changed, 5 insertions(+) diff --git a/unittest/UnitTest.cpp b/unittest/UnitTest.cpp index 1789b97ad0..e8718d6680 100644 --- a/unittest/UnitTest.cpp +++ b/unittest/UnitTest.cpp @@ -58,6 +58,8 @@ #include "Common/CPUDetect.h" #include "Common/Log.h" #include "Core/Config.h" +#include "Common/File/VFS/VFS.h" +#include "Common/File/VFS/DirectoryReader.h" #include "Core/FileSystems/ISOFileSystem.h" #include "Core/MemMap.h" #include "Core/MIPS/MIPSVFPUUtils.h" @@ -352,6 +354,9 @@ bool TestTinySet() { bool TestVFPUSinCos() { float sine, cosine; + // Needed for VFPU tables. + // There might be a better place to invoke it, but whatever. + g_VFS.Register("", new DirectoryReader(Path("assets"))); InitVFPU(); vfpu_sincos(0.0f, sine, cosine); EXPECT_EQ_FLOAT(sine, 0.0f); From 098e07fc33d28cc54345ae77d99661275be025c5 Mon Sep 17 00:00:00 2001 From: fp64 <106717720+fp64@users.noreply.github.com> Date: Sun, 12 Mar 2023 05:11:59 -0400 Subject: [PATCH 07/14] Implement load-on-demand of vfpu tables --- Core/MIPS/MIPSIntVFPU.cpp | 6 --- Core/MIPS/MIPSVFPUUtils.cpp | 99 ++++++++++++++++++++++++++----------- Core/MIPS/MIPSVFPUUtils.h | 6 +-- 3 files changed, 70 insertions(+), 41 deletions(-) diff --git a/Core/MIPS/MIPSIntVFPU.cpp b/Core/MIPS/MIPSIntVFPU.cpp index c6585f21f2..5e40a1e434 100644 --- a/Core/MIPS/MIPSIntVFPU.cpp +++ b/Core/MIPS/MIPSIntVFPU.cpp @@ -629,23 +629,17 @@ namespace MIPSInt // vsat0 changes -0.0 to +0.0, both retain NAN. case 4: if (s[i] <= 0) d[i] = 0; else {if(s[i] > 1.0f) d[i] = 1.0f; else d[i] = s[i];} break; // vsat0 case 5: if (s[i] < -1.0f) d[i] = -1.0f; else {if(s[i] > 1.0f) d[i] = 1.0f; else d[i] = s[i];} break; // vsat1 - //case 16: d[i] = 1.0f / s[i]; break; //vrcp case 16: { d[i] = vfpu_rcp(s[i]); } break; //vrcp case 17: d[i] = USE_VFPU_SQRT ? vfpu_rsqrt(s[i]) : 1.0f / sqrtf(s[i]); break; //vrsq case 18: { d[i] = vfpu_sin(s[i]); } break; //vsin case 19: { d[i] = vfpu_cos(s[i]); } break; //vcos - //case 20: d[i] = powf(2.0f, s[i]); break; //vexp2 case 20: { d[i] = vfpu_exp2(s[i]); } break; //vexp2 - //case 21: d[i] = logf(s[i])/log(2.0f); break; //vlog2 case 21: { d[i] = vfpu_log2(s[i]); } break; //vlog2 case 22: d[i] = USE_VFPU_SQRT ? vfpu_sqrt(s[i]) : fabsf(sqrtf(s[i])); break; //vsqrt - //case 23: d[i] = (float)(asinf(s[i]) / M_PI_2); break; //vasin case 23: { d[i] = vfpu_asin(s[i]); } break; //vasin - //case 24: d[i] = -1.0f / s[i]; break; // vnrcp case 24: { d[i] = -vfpu_rcp(s[i]); } break; // vnrcp case 26: { d[i] = -vfpu_sin(s[i]); } break; // vnsin - //case 28: d[i] = 1.0f / powf(2.0, s[i]); break; // vrexp2 case 28: { d[i] = vfpu_rexp2(s[i]); } break; // vrexp2 default: _dbg_assert_msg_( false, "Invalid VV2Op op type %d", optype); diff --git a/Core/MIPS/MIPSVFPUUtils.cpp b/Core/MIPS/MIPSVFPUUtils.cpp index ca4f4c889b..d5d622f752 100644 --- a/Core/MIPS/MIPSVFPUUtils.cpp +++ b/Core/MIPS/MIPSVFPUUtils.cpp @@ -802,6 +802,7 @@ float vfpu_dot(const float a[4], const float b[4]) { // See https://github.com/hrydgard/ppsspp/issues/16946 for details. // Lookup tables. +// Note: these are never unloaded, and stay till program termination. static uint32_t (*vfpu_sin_lut8192)=nullptr; static int8_t (*vfpu_sin_lut_delta)[2]=nullptr; static int16_t (*vfpu_sin_lut_interval_delta)=nullptr; @@ -824,6 +825,30 @@ static uint16_t (*vfpu_asin_lut_indices)=nullptr; static int8_t (*vfpu_rcp_lut)[2]=nullptr; +template +static inline bool load_vfpu_table(T *&ptr,const char *filename, size_t expected_size) { +#if COMMON_BIG_ENDIAN + // Tables are little-endian. +#error Byteswap for VFPU tables not implemented +#endif + if(ptr) return true; // Already loaded. + size_t size = 0u; + INFO_LOG(CPU, "Loading '%s'...", filename); + ptr = reinterpret_cast(g_VFS.ReadFile(filename, &size)); + if(!ptr || size != expected_size) + { + ERROR_LOG(CPU, "Error loading '%s' (size=%u, expected: %u)", filename, (unsigned)size, (unsigned)expected_size); + if(ptr) delete[] ptr; + ptr = nullptr; + return false; + } + INFO_LOG(CPU, "Successfully loaded '%s'", filename); + return true; +} + +#define LOAD_TABLE(name, expected_size)\ + load_vfpu_table(name,"vfpu/" #name ".dat",expected_size) + // Note: PSP sin/cos output only has 22 significant // binary digits. static inline uint32_t vfpu_sin_quantum(uint32_t x) { @@ -877,6 +902,11 @@ static inline uint32_t vfpu_sin_fixed(uint32_t arg) { } float vfpu_sin(float x) { + static bool loaded = + LOAD_TABLE(vfpu_sin_lut8192, 4100)&& + LOAD_TABLE(vfpu_sin_lut_delta, 262144)&& + LOAD_TABLE(vfpu_sin_lut_interval_delta, 131074)&& + LOAD_TABLE(vfpu_sin_lut_exceptions, 86938); uint32_t bits; memcpy(&bits, &x, sizeof(x)); uint32_t sign = bits & 0x80000000u; @@ -909,6 +939,11 @@ float vfpu_sin(float x) { } float vfpu_cos(float x) { + static bool loaded = + LOAD_TABLE(vfpu_sin_lut8192, 4100)&& + LOAD_TABLE(vfpu_sin_lut_delta, 262144)&& + LOAD_TABLE(vfpu_sin_lut_interval_delta, 131074)&& + LOAD_TABLE(vfpu_sin_lut_exceptions, 86938); uint32_t bits; memcpy(&bits, &x, sizeof(x)); bits &= 0x7FFFFFFFu; @@ -1012,6 +1047,8 @@ static inline uint32_t vfpu_sqrt_fixed(uint32_t x) { } float vfpu_sqrt(float x) { + static bool loaded = + LOAD_TABLE(vfpu_sqrt_lut, 262144); uint32_t bits; memcpy(&bits, &x, sizeof(bits)); if((bits & 0x7FFFFFFFu) <= 0x007FFFFFu) { @@ -1096,6 +1133,8 @@ static inline uint32_t vfpu_rsqrt_fixed(uint32_t x) { } float vfpu_rsqrt(float x) { + static bool loaded = + LOAD_TABLE(vfpu_rsqrt_lut, 262144); uint32_t bits; memcpy(&bits, &x, sizeof(bits)); if((bits & 0x7FFFFFFFu) <= 0x007FFFFFu) { @@ -1153,6 +1192,10 @@ static uint32_t vfpu_asin_fixed(uint32_t x) { } float vfpu_asin(float x) { + static bool loaded = + LOAD_TABLE(vfpu_asin_lut65536, 1536)&& + LOAD_TABLE(vfpu_asin_lut_indices, 798916)&& + LOAD_TABLE(vfpu_asin_lut_deltas, 517448); uint32_t bits; memcpy(&bits, &x, sizeof(x)); uint32_t sign = bits & 0x80000000u; @@ -1190,6 +1233,9 @@ static inline uint32_t vfpu_exp2_fixed(uint32_t x) { } float vfpu_exp2(float x) { + static bool loaded = + LOAD_TABLE(vfpu_exp2_lut65536, 512)&& + LOAD_TABLE(vfpu_exp2_lut, 262144); int32_t bits; memcpy(&bits, &x, sizeof(bits)); if((bits & 0x7FFFFFFF) <= 0x007FFFFF) { @@ -1239,6 +1285,10 @@ static inline uint32_t vfpu_log2_approx(uint32_t x) { // Matches PSP output on all known values. float vfpu_log2(float x) { + static bool loaded = + LOAD_TABLE(vfpu_log2_lut65536, 516)&& + LOAD_TABLE(vfpu_log2_lut65536_quadratic, 512)&& + LOAD_TABLE(vfpu_log2_lut, 2097152); uint32_t bits; memcpy(&bits, &x, sizeof(bits)); if((bits & 0x7FFFFFFFu) <= 0x007FFFFFu) { @@ -1289,6 +1339,8 @@ static inline uint32_t vfpu_rcp_approx(uint32_t i) { } float vfpu_rcp(float x) { + static bool loaded = + LOAD_TABLE(vfpu_rcp_lut, 262144); uint32_t bits; memcpy(&bits, &x, sizeof(bits)); uint32_t s = bits & 0x80000000u; @@ -1318,35 +1370,22 @@ float vfpu_rcp(float x) { //============================================================================== void InitVFPU() { -#if COMMON_BIG_ENDIAN - // Tables are little-endian. -#error Byteswap for VFPU tables not implemented +#if 0 + // Load all in advance. + LOAD_TABLE(vfpu_asin_lut65536 , 1536); + LOAD_TABLE(vfpu_asin_lut_deltas , 517448); + LOAD_TABLE(vfpu_asin_lut_indices , 798916); + LOAD_TABLE(vfpu_exp2_lut65536 , 512); + LOAD_TABLE(vfpu_exp2_lut , 262144); + LOAD_TABLE(vfpu_log2_lut65536 , 516); + LOAD_TABLE(vfpu_log2_lut65536_quadratic, 512); + LOAD_TABLE(vfpu_log2_lut , 2097152); + LOAD_TABLE(vfpu_rcp_lut , 262144); + LOAD_TABLE(vfpu_rsqrt_lut , 262144); + LOAD_TABLE(vfpu_sin_lut8192 , 4100); + LOAD_TABLE(vfpu_sin_lut_delta , 262144); + LOAD_TABLE(vfpu_sin_lut_exceptions , 86938); + LOAD_TABLE(vfpu_sin_lut_interval_delta , 131074); + LOAD_TABLE(vfpu_sqrt_lut , 262144); #endif - size_t size=0; -#define LOAD(expected,name)\ - if(!name) {\ - const char *filename = "vfpu/" #name ".dat";\ - INFO_LOG(CPU, "Loading '%s'...", filename);\ - name=reinterpret_cast(g_VFS.ReadFile(filename, &size));\ - if(size!=(expected))\ - ERROR_LOG(CPU, "Error loading '%s' (size=%u, expected: %u)", filename, (unsigned)size, (unsigned)(expected));\ - else\ - INFO_LOG(CPU, "Successfully loaded '%s'", filename);\ - } - LOAD( 1536, vfpu_asin_lut65536); - LOAD( 517448, vfpu_asin_lut_deltas); - LOAD( 798916, vfpu_asin_lut_indices); - LOAD( 512, vfpu_exp2_lut65536); - LOAD( 262144, vfpu_exp2_lut); - LOAD( 516, vfpu_log2_lut65536); - LOAD( 512, vfpu_log2_lut65536_quadratic); - LOAD( 2097152, vfpu_log2_lut); - LOAD( 262144, vfpu_rcp_lut); - LOAD( 262144, vfpu_rsqrt_lut); - LOAD( 4100, vfpu_sin_lut8192); - LOAD( 262144, vfpu_sin_lut_delta); - LOAD( 86938, vfpu_sin_lut_exceptions); - LOAD( 131074, vfpu_sin_lut_interval_delta); - LOAD( 262144, vfpu_sqrt_lut); -#undef LOAD } diff --git a/Core/MIPS/MIPSVFPUUtils.h b/Core/MIPS/MIPSVFPUUtils.h index a8b2bebd79..1b03ca390a 100644 --- a/Core/MIPS/MIPSVFPUUtils.h +++ b/Core/MIPS/MIPSVFPUUtils.h @@ -42,6 +42,7 @@ inline int Xpose(int v) { // Final Fantasy III (#2921 ) // Hitman Reborn 2 (#12900) // Cho Aniki Zero (#13705) +// Hajime no Ippo (#13671) // Dissidia Duodecim Final Fantasy (#6710 ) // // Messing around with the modulo functions? try https://www.desmos.com/calculator. @@ -50,11 +51,6 @@ extern float vfpu_sin(float); extern float vfpu_cos(float); extern void vfpu_sincos(float, float&, float&); -/* -inline float vfpu_asin(float angle) { - return (float)(asinf(angle) / M_PI_2); -} -*/ extern float vfpu_asin(float); inline float vfpu_clamp(float v, float min, float max) { From 3661bb27cebb424e0ed2dcc89e634e4695e3bd47 Mon Sep 17 00:00:00 2001 From: fp64 <106717720+fp64@users.noreply.github.com> Date: Fri, 17 Feb 2023 22:52:01 -0500 Subject: [PATCH 08/14] Implement sin/cos as per #16946 --- Core/MIPS/MIPSVFPUUtils.cpp | 297 +- Core/MIPS/MIPSVFPUUtils.h | 18 +- Core/MIPS/vfpu_sin_lut.h | 46687 ++++++++++++++++++++++++++++++++++ 3 files changed, 46829 insertions(+), 173 deletions(-) create mode 100644 Core/MIPS/vfpu_sin_lut.h diff --git a/Core/MIPS/MIPSVFPUUtils.cpp b/Core/MIPS/MIPSVFPUUtils.cpp index b60cd7c97c..e03badb91b 100644 --- a/Core/MIPS/MIPSVFPUUtils.cpp +++ b/Core/MIPS/MIPSVFPUUtils.cpp @@ -29,13 +29,6 @@ #define V(i) (currentMIPS->v[voffset[i]]) #define VI(i) (currentMIPS->vi[voffset[i]]) -// Flushes the angle to 0 if exponent smaller than this in vfpu_sin/vfpu_cos/vfpu_sincos. -// Was measured to be around 0x68, but GTA on Mac is somehow super sensitive -// to the shape of the sine curve which seem to be very slightly different. -// -// So setting a lower value. -#define PRECISION_EXP_THRESHOLD 0x65 - union float2int { uint32_t i; float f; @@ -896,176 +889,156 @@ float vfpu_rsqrt(float a) { return val.f; } -float vfpu_sin(float a) { - float2int val; - val.f = a; +//============================================================================== +// The code below attempts to exactly match the output of +// PSP's sin and cos instructions. For the sake of +// making lookup tables smaller (473KB) the code is +// somewhat gnarly. +// The key observation is that (ignoring range +// reduction) PSP effectively converts input to 9.23 +// fixed-point, and that output is always representable +// as 4.28 fixed-point (though that is probably not +// what is going on internally). +// The rest is mostly trying to obtain the same result +// with smaller tables (pretty ad-hoc, and almost certainly +// does not match what PSP does internally). +// Lookup tables store deltas from (explicitly computable) +// estimations, to allow to store them in smaller types: +// int8 and int16. +// See https://github.com/hrydgard/ppsspp/issues/16946 for details. - int32_t k = get_uexp(val.i); - if (k == 255) { - val.i = (val.i & 0xFF800001) | 1; - return val.f; - } +#include "Core/MIPS/vfpu_sin_lut.h" - if (k < PRECISION_EXP_THRESHOLD) { - val.i &= 0x80000000; - return val.f; - } - - // Okay, now modulus by 4 to begin with (identical wave every 4.) - int32_t mantissa = get_mant(val.i); - if (k > 0x80) { - const uint8_t over = k & 0x1F; - mantissa = (mantissa << over) & 0x00FFFFFF; - k = 0x80; - } - // This subtracts off the 2. If we do, flip sign to inverse the wave. - if (k == 0x80 && mantissa >= (1 << 23)) { - val.i ^= 0x80000000; - mantissa -= 1 << 23; - } - - int8_t norm_shift = mantissa == 0 ? 32 : (int8_t)clz32_nonzero(mantissa) - 8; - mantissa <<= norm_shift; - k -= norm_shift; - - if (k <= 0 || mantissa == 0) { - val.i &= 0x80000000; - return val.f; - } - - // This is the value with modulus applied. - val.i = (val.i & 0x80000000) | (k << 23) | (mantissa & ~(1 << 23)); - val.f = (float)sin((double)val.f * M_PI_2); - val.i &= 0xFFFFFFFC; - return val.f; +// Note: PSP sin/cos output only has 22 significant +// binary digits. +static inline uint32_t quantum(uint32_t x) { + return x < 1u << 22? + 1u: + 1u << (32 - 22 - clz32_nonzero(x)); } -float vfpu_cos(float a) { - float2int val; - val.f = a; - bool negate = false; +static inline uint32_t truncate_bits(u32 x) { + return x & -quantum(x); +} - int32_t k = get_uexp(val.i); - if (k == 255) { - // Note: unlike sin, cos always returns +NAN. - val.i = (val.i & 0x7F800001) | 1; - return val.f; +static inline uint32_t vfpu_sin_fixed(uint32_t arg) { + // Handle endpoints. + if(arg == 0u) return 0u; + if(arg == 0x00800000) return 0x10000000; + // Get endpoints for 8192-wide interval. + uint32_t L = vfpu_sin_lut8192[(arg >> 13) + 0]; + uint32_t H = vfpu_sin_lut8192[(arg >> 13) + 1]; + // Approximate endpoints for 64-wide interval via lerp. + uint32_t A = L+(((H - L)*(((arg >> 6) & 127) + 0)) >> 7); + uint32_t B = L+(((H - L)*(((arg >> 6) & 127) + 1)) >> 7); + // Adjust endpoints from deltas, and increase working precision. + uint64_t a = (uint64_t(A) << 5) + uint64_t(vfpu_sin_lut_delta[arg >> 6][0]) * quantum(A); + uint64_t b = (uint64_t(B) << 5) + uint64_t(vfpu_sin_lut_delta[arg >> 6][1]) * quantum(B); + // Compute approximation via lerp. Is off by at most 1 quantum. + uint32_t v = uint32_t(((a * (64 - (arg & 63)) + b * (arg & 63)) >> 6) >> 5); + v=truncate_bits(v); + // Look up exceptions via binary search. + // Note: vfpu_sin_lut_interval_delta stores + // deltas from interval estimation. + uint32_t lo = ((169u * ((arg >> 7) + 0)) >> 7)+uint32_t(vfpu_sin_lut_interval_delta[(arg >> 7) + 0]) + 16384u; + uint32_t hi = ((169u * ((arg >> 7) + 1)) >> 7)+uint32_t(vfpu_sin_lut_interval_delta[(arg >> 7) + 1]) + 16384u; + while(lo < hi) { + uint32_t m = (lo + hi) / 2; + // Note: vfpu_sin_lut_exceptions stores + // index&127 (for each initial interval the + // upper bits of index are the same, namely + // arg&-128), plus direction (0 for +1, and + // 128 for -1). + uint32_t b = vfpu_sin_lut_exceptions[m]; + uint32_t e = (arg & -128u)+(b & 127u); + if(e == arg) { + v += quantum(v) * (b >> 7 ? -1u : +1u); + break; + } + else if(e < arg) lo = m + 1; + else hi = m; } + return v; +} - if (k < PRECISION_EXP_THRESHOLD) - return 1.0f; - - // Okay, now modulus by 4 to begin with (identical wave every 4.) - int32_t mantissa = get_mant(val.i); - if (k > 0x80) { - const uint8_t over = k & 0x1F; - mantissa = (mantissa << over) & 0x00FFFFFF; - k = 0x80; +float vfpu_sin(float x) { + uint32_t bits; + memcpy(&bits, &x, sizeof(x)); + uint32_t sign = bits & 0x80000000u; + uint32_t exponent = (bits >> 23) & 0xFFu; + uint32_t significand = (bits & 0x007FFFFFu) | 0x00800000u; + if(exponent == 0xFFu) { + // NOTE: this bitpattern is a signaling + // NaN on x86, so maybe just return + // a normal qNaN? + float y; + bits=sign ^ 0x7F800001u; + memcpy(&y, &bits, sizeof(y)); + return y; } - // This subtracts off the 2. If we do, negate the result value. - if (k == 0x80 && mantissa >= (1 << 23)) { - mantissa -= 1 << 23; - negate = true; + if(exponent < 0x7Fu) { + if(exponent < 0x7Fu-23u) significand = 0u; + else significand >>= (0x7F - exponent); } - - int8_t norm_shift = mantissa == 0 ? 32 : (int8_t)clz32_nonzero(mantissa) - 8; - mantissa <<= norm_shift; - k -= norm_shift; - - if (k <= 0 || mantissa == 0) - return negate ? -1.0f : 1.0f; - - // This is the value with modulus applied. - val.i = (val.i & 0x80000000) | (k << 23) | (mantissa & ~(1 << 23)); - if (val.f == 1.0f || val.f == -1.0f) { - return negate ? 0.0f : -0.0f; + else if(exponent > 0x7Fu) { + // There is weirdness for large exponents. + if(exponent - 0x7Fu >= 25u && exponent - 0x7Fu < 32u) significand = 0u; + else if((exponent & 0x9Fu) == 0x9Fu) significand = 0u; + else significand <<= (exponent - 0x7Fu); } - val.f = (float)cos((double)val.f * M_PI_2); - val.i &= 0xFFFFFFFC; - return negate ? -val.f : val.f; + sign ^= ((significand << 7) & 0x80000000u); + significand &= 0x00FFFFFFu; + if(significand > 0x00800000u) significand = 0x01000000u - significand; + uint32_t ret = vfpu_sin_fixed(significand); + return (sign ? -1.0f : +1.0f) * float(int32_t(ret)) * 3.7252903e-09f; // 0x1p-28f +} + +// WARNING: not tested. +float vfpu_cos(float x) { + uint32_t bits; + memcpy(&bits, &x, sizeof(x)); + bits &= 0x7FFFFFFFu; + uint32_t sign = 0u; + uint32_t exponent = (bits >> 23) & 0xFFu; + uint32_t significand = (bits & 0x007FFFFFu) | 0x00800000u; + if(exponent == 0xFFu) { + // NOTE: this bitpattern is a signaling + // NaN on x86, so maybe just return + // a normal qNaN? + float y; + bits = sign ^ 0x7F800001u; + memcpy(&y, &bits, sizeof(y)); + return y; + } + if(exponent < 0x7Fu) { + if(exponent < 0x7Fu - 23u) significand = 0u; + else significand >>= (0x7F - exponent); + } + else if(exponent > 0x7Fu) { + // There is weirdness for large exponents. + if(exponent - 0x7Fu >= 25u && exponent - 0x7Fu < 32u) significand = 0u; + else if((exponent & 0x9Fu) == 0x9Fu) significand = 0u; + else significand <<= (exponent - 0x7Fu); + } + sign ^= ((significand << 7) & 0x80000000u); + significand &= 0x00FFFFFFu; + if(significand > 0x00800000u) { + significand = 0x01000000u - significand; + sign ^= 0x80000000u; + } + uint32_t ret = vfpu_sin_fixed(0x00800000u - significand); + return (sign ? -1.0f : +1.0f) * float(int32_t(ret)) * 3.7252903e-09f; // 0x1p-28f } void vfpu_sincos(float a, float &s, float &c) { - float2int val; - val.f = a; - // For sin, negate the input, for cos negate the output. - bool negate = false; - - int32_t k = get_uexp(val.i); - if (k == 255) { - val.i = (val.i & 0xFF800001) | 1; - s = val.f; - val.i &= 0x7F800001; - c = val.f; - return; - } - - if (k < PRECISION_EXP_THRESHOLD) { - val.i &= 0x80000000; - s = val.f; - c = 1.0f; - return; - } - - // Okay, now modulus by 4 to begin with (identical wave every 4.) - int32_t mantissa = get_mant(val.i); - if (k > 0x80) { - const uint8_t over = k & 0x1F; - mantissa = (mantissa << over) & 0x00FFFFFF; - k = 0x80; - } - // This subtracts off the 2. If we do, flip signs. - if (k == 0x80 && mantissa >= (1 << 23)) { - mantissa -= 1 << 23; - negate = true; - } - - int8_t norm_shift = mantissa == 0 ? 32 : (int8_t)clz32_nonzero(mantissa) - 8; - mantissa <<= norm_shift; - k -= norm_shift; - - if (k <= 0 || mantissa == 0) { - val.i &= 0x80000000; - if (negate) - val.i ^= 0x80000000; - s = val.f; - c = negate ? -1.0f : 1.0f; - return; - } - - // This is the value with modulus applied. - val.i = (val.i & 0x80000000) | (k << 23) | (mantissa & ~(1 << 23)); - float2int i_sine, i_cosine; - if (val.f == 1.0f) { - i_sine.f = negate ? -1.0f : 1.0f; - i_cosine.f = negate ? 0.0f : -0.0f; - } else if (val.f == -1.0f) { - i_sine.f = negate ? 1.0f : -1.0f; - i_cosine.f = negate ? 0.0f : -0.0f; - } else if (negate) { - i_sine.f = (float)sin((double)-val.f * M_PI_2); - i_cosine.f = -(float)cos((double)val.f * M_PI_2); - } else { - double angle = (double)val.f * M_PI_2; -#if defined(__linux__) - double d_sine; - double d_cosine; - sincos(angle, &d_sine, &d_cosine); - i_sine.f = (float)d_sine; - i_cosine.f = (float)d_cosine; -#else - i_sine.f = (float)sin(angle); - i_cosine.f = (float)cos(angle); -#endif - } - - i_sine.i &= 0xFFFFFFFC; - i_cosine.i &= 0xFFFFFFFC; - s = i_sine.f; - c = i_cosine.f; - return ; + // Just invoke both sin and cos. + // Suboptimal but whatever. + s = vfpu_sin(a); + c = vfpu_cos(a); } +//============================================================================== + void InitVFPUSinCos() { // TODO: Could prepare a CORDIC table here. } diff --git a/Core/MIPS/MIPSVFPUUtils.h b/Core/MIPS/MIPSVFPUUtils.h index 6506a0664d..a137245e8a 100644 --- a/Core/MIPS/MIPSVFPUUtils.h +++ b/Core/MIPS/MIPSVFPUUtils.h @@ -35,18 +35,14 @@ inline int Xpose(int v) { #endif // The VFPU uses weird angles where 4.0 represents a full circle. This makes it possible to return -// exact 1.0/-1.0 values at certain angles. We currently just scale, and special case the cardinal directions. +// exact 1.0/-1.0 values at certain angles. // -// Stepping down to [0, 2pi) helps, but we also check common exact-result values. -// TODO: cos(1) and sin(2) should be -0.0, but doing that gives wrong results (possibly from floorf.) -// -// We also try an alternative solution, computing things in double precision, multiplying the input by pi/2. -// This fixes #12900 (Hitman Reborn 2) but breaks #13705 (Cho Aniki Zero) and #13671 (Hajime no Ippo). -// #2921 is still fine. So the alt solution (vfpu_sin_double etc) are behind a compat flag. -// -// A better solution would be to tailor some sine approximation for the 0..90 degrees range, compute -// modulo manually and mirror that around the circle. Also correctly special casing for inf/nan inputs -// and just trying to match it as closely as possible to the real PSP. +// The current code attempts to match VFPU sin/cos exactly. +// Possibly affected games: +// Final Fantasy III (#2921 ) +// Hitman Reborn 2 (#12900) +// Cho Aniki Zero (#13705) +// Dissidia Duodecim Final Fantasy (#6710 ) // // Messing around with the modulo functions? try https://www.desmos.com/calculator. diff --git a/Core/MIPS/vfpu_sin_lut.h b/Core/MIPS/vfpu_sin_lut.h new file mode 100644 index 0000000000..d2bec30211 --- /dev/null +++ b/Core/MIPS/vfpu_sin_lut.h @@ -0,0 +1,46687 @@ +// Copyright (c) 2012- PPSSPP Project. + +// This program is free software: you can redistribute it and/or modify +// it under the terms of the GNU General Public License as published by +// the Free Software Foundation, version 2.0 or later versions. + +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License 2.0 for more details. + +// A copy of the GPL 2.0 should have been included with the program. +// If not, see http://www.gnu.org/licenses/ + +// Official git repository and contact information can be found at +// https://github.com/hrydgard/ppsspp and http://www.ppsspp.org/. + +//============================================================================== +// WARNING: this is partially automatically generated, +// and only meant to be included inside Core/MIPS/MIPSVFPUUtils.cpp, +// so no header guards. + +static uint32_t vfpu_sin_lut8192[1025]={ + 0, 411778, 823552, 1235322, + 1647089, 2058851, 2470610, 2882365, + 3294116, 3705858, 4117590, 4529310, + 4941018, 5352714, 5764400, 6176074, + 6587736, 6999380, 7411008, 7822616, + 8234204, 8645772, 9057324, 9468852, + 9880364, 10291848, 10703312, 11114744, + 11526152, 11937528, 12348880, 12760204, + 13171504, 13582768, 13994000, 14405196, + 14816360, 15227488, 15638580, 16049636, + 16460660, 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25}, { 31, 31}, { 29, 28}, +{ 36, 31}, { 32, 31}, { 30, 26}, { 33, 1}, +{ 0, 29}, { 29, 26}, { 30, 32}, { 31, 28}, +{ 27, 26}, { 31, 31}, { 31, 28}, { 35, 33}, +{ 32, 31}, { 29, 28}, { 36, 31}, { 32, 29}, +{ 29, 26}, { 33, 33}, { 31, 28}, { 27, 26}, +{ 30, 32}, { 31, 28}, { 27, 26}, { 31, 31}, +{ 29, 28}, { 35, 33}, { 32, 31}, { 30, 26}, +{ 27, 22}, { 31, 30}, { 29, 26}, { 25, 24}, +{ 31, 28}, { 27, 26}, { 30, 32}, { 31, 28}, +{ 28, 25}, { 25, 21}, { 29, 28}, { 27, 25}, +{ 24, 22}, { 30, 26}, { 27, 22}, { 24, 21}, +{ 29, 26}, { 25, 24}, { 23, 20}, { 27, 26}, +{ 24, 24}, { 22, 20}, { 28, 25}, { 25, 21}, +{ 22, 19}, { 27, 25}, { 24, 22}, { 20, 18}, +{ 25, 24}, { 24, 21}, { 20, 18}, { 24, 24}, +{ 23, 20}, { 20, 17}, { 16, 15}, { 22, 20}, +{ 20, 16}, { 17, 12}, { 22, 19}, { 18, 16}, +{ 16, 45}, { 52, 50}, { 51, 46}, { 48, 44}, +{ 52, 50}, { 47, 49}, { 47, 43}, { 44, 41}, +{ 48, 47}, { 46, 43}, { 43, 40}, { 49, 44}, +{ 44, 43}, { 42, 40}, { 39, 37}, { 45, 42}, +{ 42, 38}, { 39, 36}, { 44, 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49}, { 54, 52}, { 52, 48}, { 48, 47}, +{ 46, 43}, { 43, 40}, { 48, 45}, { 44, 43}, +{ 42, 40}, { 39, 37}, { 35, 35}, { 33, 32}, +{ 39, 36}, { 35, 33}, { 33, 31}, { 29, 28}, +{ 27, 25}, { 31, 31}, { 30, 26}, { 27, 22}, +{ 24, 53}, { 52, 50}, { 57, 56}, { 55, 52}, +{ 52, 50}, { 47, 49}, { 47, 43}, { 44, 41}, +{ 48, 47}, { 46, 43}, { 43, 40}, { 39, 39}, +{ 37, 35}, { 33, 33}, { 39, 37}, { 37, 34}, +{ 33, 32}, { 31, 28}, { 27, 26}, { 24, 24}, +{ 29, 28}, { 27, 57}, { 57, 53}, { 54, 51}, +{ 50, 48}, { 48, 45}, { 52, 50}, { 51, 46}, +{ 48, 44}, { 45, 42}, { 42, 38}, { 39, 36}, +{ 44, 42}, { 39, 40}, { 37, 35}, { 36, 31}, +{ 32, 29}, { 30, 26}, { 27, 22}, { 24, 21}, +{ 29, 26}, { 25, 24}, { 23, 52}, { 52, 49}, +{ 47, 49}, { 47, 43}, { 44, 41}, { 48, 47}, +{ 46, 43}, { 43, 40}, { 40, 37}, { 37, 35}, +{ 33, 33}, { 31, 28}, { 35, 35}, { 33, 32}, +{ 31, 28}, { 28, 25}, { 24, 24}, { 22, 20}, +{ 20, 16}, { 17, 12}, { 22, 19}, { 18, 16}, +{ 16, 45}, { 45, 42}, { 42, 40}, { 39, 37}, +{ 35, 33}, { 33, 31}, { 31, 28}, { 35, 33}, +{ 32, 31}, { 29, 28}, { 27, 25}, { 24, 22}, +{ 20, 18}, { 18, 16}, { 16, 45}, { 52, 50}, +{ 47, 49}, { 48, 44}, { 44, 42}, { 39, 40}, +{ 37, 35}, { 35, 33}, { 32, 31}, { 30, 26}, +{ 27, 22}, { 31, 30}, { 29, 26}, { 25, 24}, +{ 22, 54}, { 52, 50}, { 47, 49}, { 47, 43}, +{ 44, 42}, { 39, 40}, { 37, 35}, { 36, 31}, +{ 39, 39}, { 37, 35}, { 33, 33}, { 31, 28}, +{ 29, 26}, { 25, 24}, { 23, 52}, { 52, 49}, +{ 47, 49}, { 47, 43}, { 44, 41}, { 39, 39}, +{ 37, 35}, { 43, 40}, { 40, 37}, { 37, 35}, +{ 33, 33}, { 31, 28}, { 27, 26}, { 24, 24}, +{ 23, 52}, { 52, 49}, { 48, 47}, { 46, 43}, +{ 44, 41}, { 39, 39}, { 37, 35}, { 43, 40}, +{ 40, 37}, { 37, 34}, { 33, 32}, { 31, 28}, +{ 27, 26}, { 24, 24}, { 22, 20}, { 18, 50}, +{ 48, 47}, { 46, 43}, { 43, 40}, { 39, 39}, +{ 37, 35}, { 33, 33}, { 31, 28}, { 27, 26}, +{ 25, 24}, { 23, 20}, { 27, 26}, { 24, 24}, +{ 22, 20}, { 20, 48}, { 49, 44}, { 46, 43}, +{ 43, 40}, { 40, 37}, { 37, 34}, { 33, 33}, +{ 31, 28}, { 27, 26}, { 24, 24}, { 22, 20}, +{ 20, 17}, { 16, 15}, { 14, 11}, { 10, 41}, +{ 39, 39}, { 37, 35}, { 33, 33}, { 31, 28}, +{ 29, 26}, { 25, 24}, { 23, 20}, { 20, 17}, +{ 15, 17}, { 15, 11}, { 12, 9}, { 7, 7}, +{ 5, 3}, { 4, 31}, { 32, 29}, { 29, 26}, +{ 25, 24}, { 24, 21}, { 20, 18}, { 15, 17}, +{ 14, 13}, { 12, 10}, { 7, 8}, { 5, 3}, +{ 4, -1}, { 0, -1}, { -2, -6}, { 1, 1}, +{ -8, 21}, { 20, 18}, { 19, 14}, { 16, 12}, +{ 12, 10}, { 7, 8}, { 7, 4}, { 3, 1}, +{ 0, -1}, { -3, 28}, { 27, 25}, { 24, 22}, +{ 20, 18}, { 18, 16}, { 16, 13}, { 13, 10}, +{ 10, 6}, { 7, 4}, { 3, 33}, { 33, 31}, +{ 29, 28}, { 27, 25}, { 25, 21}, { 22, 19}, +{ 18, 16}, { 16, 13}, { 12, 11}, { 10, 40}, +{ 39, 37}, { 35, 33}, { 33, 32}, { 31, 28}, +{ 28, 25}, { 25, 21}, { 22, 19}, { 20, 16}, +{ 17, 44}, { 44, 43}, { 42, 40}, { 40, 37}, +{ 37, 34}, { 33, 32}, { 31, 28}, { 27, 26}, +{ 24, 24}, { 15, 43}, { 44, 41}, { 39, 39}, +{ 37, 35}, { 36, 31}, { 32, 29}, { 29, 26}, +{ 25, 24}, { 24, 21}, { 20, 50}, { 47, 49}, +{ 46, 45}, { 44, 42}, { 39, 40}, { 37, 35}, +{ 36, 31}, { 32, 31}, { 30, 26}, { 27, 22}, +{ 16, 45}, { 45, 42}, { 42, 40}, { 39, 37}, +{ 35, 33}, { 33, 31}, { 31, 28}, { 28, 25}, +{ 25, 21}, { 22, 51}, { 50, 48}, { 49, 44}, +{ 44, 43}, { 42, 40}, { 32, 27}, { 27, 26}, +{ 25, 24}, { 23, 20}, { 20, 49}, { 48, 47}, +{ 47, 43}, { 44, 41}, { 39, 39}, { 37, 35}, +{ 36, 31}, { 32, 29}, { 29, 26}, { 19, 46}, +{ 48, 44}, { 45, 42}, { 42, 38}, { 39, 36}, +{ 35, 33}, { 32, 31}, { 29, 28}, { 27, 25}, +{ 24, 54}, { 52, 52}, { 42, 40}, { 40, 37}, +{ 37, 34}, { 33, 32}, { 31, 28}, { 27, 26}, +{ 24, 24}, { 22, 52}, { 52, 48}, { 48, 47}, +{ 37, 35}, { 36, 31}, { 32, 29}, { 29, 26}, +{ 25, 24}, { 24, 21}, { 20, 50}, { 47, 49}, +{ 39, 36}, { 35, 33}, { 33, 31}, { 29, 28}, +{ 27, 25}, { 24, 22}, { 22, 19}, { 18, 16}, +{ 16, 45}, { 37, 34}, { 33, 32}, { 31, 28}, +{ 27, 26}, { 24, 24}, { 22, 20}, { 18, 50}, +{ 48, 47}, { 37, 35}, { 36, 31}, { 32, 29}, +{ 29, 26}, { 27, 22}, { 24, 21}, { 20, 50}, +{ 42, 38}, { 39, 36}, { 35, 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33}, +{ 33, 31}, { 29, 28}, { 20, 16}, { 16, 15}, +{ 14, 43}, { 43, 40}, { 40, 37}, { 29, 26}, +{ 25, 24}, { 24, 21}, { 20, 18}, { 10, 6}, +{ 7, 36}, { 35, 33}, { 33, 31}, { 22, 20}, +{ 20, 16}, { 17, 12}, { 12, 11}, { 11, 8}, +{ 0, 29}, { 29, 26}, { 25, 24}, { 16, 12}, +{ 12, 10}, { 7, 8}, { 7, 36}, { 28, 25}, +{ 25, 21}, { 22, 19}, { 18, 16}, { 7, 7}, +{ 5, 35}, { 33, 33}, { 31, 28}, { 27, 26}, +{ 15, 17}, { 16, 12}, { 12, 42}, { 33, 31}, +{ 29, 28}, { 27, 25}, { 25, 21}, { 14, 11}, +{ 11, 40}, { 40, 37}, { 37, 34}, { 25, 24}, +{ 22, 22}, { 20, 18}, { 15, 49}, { 39, 36}, +{ 35, 33}, { 32, 31}, { 22, 19}, { 20, 16}, +{ 17, 44}, { 44, 43}, { 33, 33}, { 31, 28}, +{ 29, 26}, { 19, 14}, { 16, 44}, { 44, 42}, +{ 39, 40}, { 32, 26}, { 28, 25}, { 25, 21}, +{ 14, 43}, { 43, 40}, { 40, 37}, { 37, 35}, +{ 25, 24}, { 24, 21}, { 20, 50}, { 42, 38}, +{ 39, 36}, { 35, 33}, { 33, 31}, { 22, 20}, +{ 20, 48}, { 49, 44}, { 37, 35}, { 33, 33}, +{ 32, 29}, { 20, 18}, { 19, 14}, { 16, 44}, +{ 35, 33}, { 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23, 50}, { 32, 40}, { 29, 48}, +{ 16, 47}, { 25, 35}, { 24, 42}, { 10, 41}, +{ 18, 44}, { 27, 3}, { 24, 42}, { 12, 39}, +{ 20, 30}, { 29, 5}, { 22, 45}, { 14, 38}, +{ 22, -1}, { 17, 39}, { 7, 33}, { 16, -8}, +{ 13, 31}, { 1, 28}, { 9, 19}, { 18, -6}, +{ 11, 34}, { 3, 27}, { 11, -12}, { 6, 28}, +{ -4, 23}, { 5, -19}, { 2, 20}, { -10, 17}, +{ -2, 8}, { -3, 15}, { -17, 14}, { -8, 16}, +{ 0, -21}, { -2, 21}, { -10, 19}, { 1, -20}, +{ 1, 22}, { -9, 23}, { 3, 14}, { 4, 22}, +{ -8, 25}, { 5, 16}, { 6, 25}, { -7, 29}, +{ 7, 18}, { 9, 23}, { 15, 36}, { 5, 37}, +{ 11, 22}, { -5, 38}, { 6, 41}, { 19, 30}, +{ 20, 39}, { 7, 43}, { 21, 32}, { 23, 37}, +{ 8, 48}, { 19, 35}, { 25, 40}, { 9, 52}, +{ 20, 37}, { 27, 38}, { 14, 53}, { 21, 39}, +{ 29, 40}, { 19, 53}, { 23, 41}, { 31, 42}, +{ 21, 55}, { 23, 44}, { 33, 44}, { 25, 56}, +{ 24, 47}, { 35, 14}, { 14, 45}, { 25, 50}, +{ 36, 15}, { 15, 48}, { 26, 39}, { 37, 16}, +{ 16, 51}, { 27, 41}, { 31, 48}, { 17, 55}, +{ 28, 43}, { 33, 47}, { 18, 60}, { 29, 45}, +{ 35, 50}, { 21, 62}, { 30, 47}, { 38, 45}, +{ 24, 63}, { 31, 10}, { 25, 52}, { 29, 63}, +{ 32, 11}, { 28, 53}, { 22, 49}, { 33, 12}, +{ 31, 54}, { 23, 52}, { 34, 13}, { 34, 55}, +{ 24, 55}, { 30, 41}, { 37, 55}, { 27, 41}, +{ 32, 43}, { 17, 58}, { 26, 44}, { 34, 41}, +{ 22, 59}, { 27, 46}, { 36, 41}, { 17, 42}, +{ 28, 7}, { 25, 49}, { 18, 45}, { 29, 8}, +{ 27, 50}, { 19, 48}, { 23, 40}, { 9, 49}, +{ 20, 35}, { 26, 37}, { 10, 53}, { 23, 37}, +{ 28, 39}, { 11, 33}, { 22, 1}, { 14, 44}, +{ 12, 36}, { 23, 2}, { 2, 34}, { 14, 25}, +{ 15, 33}, { 3, 38}, { 16, 27}, { 17, 36}, +{ 4, 22}, { 12, 23}, { 0, 37}, { 6, 24}, +{ 14, 25}, { -5, 21}, { 6, -15}, { 3, 27}, +{ -4, 24}, { 7, -14}, { -14, 24}, { 0, 11}, +{ 2, 16}, { -13, 29}, { -4, 7}, { -14, 20}, +{ -12, 9}, { -2, 9}, { -22, 6}, { -11, 12}, +{ 0, -18}, { 13, 27}, { 2, 41}, { 9, -10}, +{ 20, 34}, { 4, 32}, { 17, -1}, { 16, 44}, +{ 12, -6}, { 25, 39}, { 7, 46}, { 21, 2}, +{ 28, 45}, { 16, -3}, { 28, 42}, { 20, 55}, +{ 24, 6}, { 36, 50}, { 19, 1}, { 32, 46}, +{ 33, 59}, { 28, 9}, { 40, 54}, { 23, 4}, +{ 35, 49}, { 44, 61}, { 31, 13}, { 44, 58}, +{ 26, 8}, { 39, 53}, { 52, 66}, { 35, 16}, +{ 47, 61}, { 30, 11}, { 42, 56}, { 25, 52}, +{ 38, 20}, { 51, 65}, { 35, 48}, { 47, 28}, +{ 28, 65}, { 42, 23}, { 47, 68}, { 37, 18}, +{ 49, 63}, { 37, 77}, { 45, 27}, { 57, 63}, +{ 40, 22}, { 53, 67}, { 35, 17}, { 48, 62}, +{ 61, 75}, { 44, 25}, { 56, 70}, { 39, 20}, +{ 52, 34}, { 34, 66}, { 47, 29}, { 51, 74}, +{ 42, 24}, { 55, 69}, { 37, 19}, { 50, 64}, +{ 35, 48}, { 46, 27}, { 58, 72}, { 41, 22}, +{ 53, 67}, { 37, 57}, { 49, 31}, { 41, 76}, +{ 44, 26}, { 57, 55}, { 39, 21}, { 52, 66}, +{ 34, 16}, { 47, 61}, { 29, 56}, { 43, 24}, +{ 39, 70}, { 38, 19}, { 50, 64}, { 33, 69}, +{ 46, 28}, { 52, 71}, { 41, 23}, { 54, 68}, +{ 36, 18}, { 49, 63}, { 31, 49}, { 45, 26}, +{ 26, 70}, { 40, 21}, { 49, 63}, { 35, 16}, +{ 47, 61}, { 30, 11}, { 42, 56}, { 25, 46}, +{ 38, 20}, { 27, 65}, { 33, 15}, { 45, 51}, +{ 28, 10}, { 41, 55}, { 23, 5}, { 36, 50}, +{ 18, 44}, { 32, 13}, { 13, -5}, { 26, 40}, +{ 39, 53}, { 22, 3}, { 12, 49}, { 17, -2}, +{ 29, 32}, { 12, -7}, { 24, 38}, { 7, -12}, +{ 19, 33}, { 2, 28}, { 15, -3}, { 12, 42}, +{ 10, -8}, { 23, 37}, { 5, -13}, { 18, 32}, +{ 0, -16}, { 15, 31}, { 0, -16}, { 15, 31}, +{ 0, -16}, { 15, 31}, { 0, 30}, { 16, 0}, +{ 17, 47}, { 16, 0}, { 31, 47}, { 16, 0}, +{ 13, 48}, { 16, 0}, { 31, 47}, { 16, 0}, +{ 31, 47}, { 16, 0}, { 31, 47}, { 16, 47}, +{ 32, 16}, { 34, 63}, { 32, 16}, { 16, 44}, +{ 32, 16}, { 31, 63}, { 32, 16}, { 17, 40}, +{ 32, 16}, { 25, 64}, { 32, 16}, { 47, 53}, +{ 32, 16}, { 47, 63}, { 32, 16}, { 45, 61}, +{ 32, 16}, { 47, 63}, { 32, 16}, { 47, 63}, +{ 32, 57}, { 48, 32}, { 32, 16}, { 47, 63}, +{ 32, 54}, { 48, 32}, { 32, 16}, { 47, 63}, +{ 32, 52}, { 48, 32}, { 32, 79}, { 48, 32}, +{ 32, 50}, { 48, 32}, { 32, 72}, { 48, 32}, +{ 56, 80}, { 48, 32}, { 32, 68}, { 48, 32}, +{ 54, 78}, { 48, 32}, { 32, 63}, { 48, 32}, +{ 50, 79}, { 48, 32}, { 32, 59}, { 48, 32}, +{ 45, 80}, { 48, 32}, { 33, 56}, { 48, 32}, +{ 41, 80}, { 48, 32}, { 34, 53}, { 48, 32}, +{ 34, 80}, { 48, 32}, { 32, 51}, { 48, 32}, +{ 32, 75}, { 48, 32}, { 33, 49}, { 48, 32}, +{ 32, 16}, { 47, 63}, { 32, 16}, { 47, 63}, +{ 32, 65}, { 48, 32}, { 32, 16}, { 45, 61}, +{ 32, 16}, { 47, 63}, { 32, 16}, { 47, 63}, +{ 32, 16}, { 47, 63}, { 32, 16}, { 40, 64}, +{ 32, 16}, { 47, 63}, { 32, 16}, { 37, 63}, +{ 32, 16}, { 16, 47}, { 32, 16}, { 34, 63}, +{ 32, 16}, { 16, 43}, { 32, 16}, { 16, 0}, +{ 31, 47}, { 16, 40}, { 32, 16}, { 16, 0}, +{ 22, 46}, { 16, 0}, { 31, 47}, { 16, 0}, +{ 19, 47}, { 16, 0}, { 0, 28}, { 16, 0}, +{ 0, -16}, { 15, 31}, { 1, 24}, { 16, 0}, +{ 0, -13}, { 10, 36}, { 5, -8}, { 23, 42}, +{ 10, -3}, { 16, 47}, { 15, 2}, { 2, 33}, +{ 20, 7}, { 7, -7}, { 24, 43}, { 12, 40}, +{ 30, 17}, { 17, 3}, { 27, 53}, { 22, 8}, +{ 8, 45}, { 27, 13}, { 34, 62}, { 32, 18}, +{ 18, 51}, { 37, 23}, { 23, 10}, { 37, 56}, +{ 28, 15}, { 46, 65}, { 33, 20}, { 45, 67}, +{ 38, 25}, { 25, 62}, { 43, 30}, { 30, 16}, +{ 46, 65}, { 35, 21}, { 52, 71}, { 40, 26}, +{ 29, 47}, { 45, 31}, { 31, 77}, { 50, 36}, +{ 37, 55}, { 55, 41}, { 41, 28}, { 37, 77}, +{ 46, 33}, { 34, 56}, { 51, 38}, { 38, 24}, +{ 55, 74}, { 43, 29}, { 60, 79}, { 48, 34}, +{ 49, 85}, { 53, 39}, { 39, 67}, { 58, 44}, +{ 44, 31}, { 54, 80}, { 49, 36}, { 36, 72}, +{ 54, 41}, { 41, 27}, { 57, 70}, { 46, 32}, +{ 32, 81}, { 51, 37}, { 39, 57}, { 56, 42}, +{ 42, 29}, { 60, 79}, { 47, 34}, { 34, 60}, +{ 52, 39}, { 39, 25}, { 56, 75}, { 44, 30}, +{ 61, 80}, { 49, 35}, { 53, 85}, { 54, 40}, +{ 40, 27}, { 58, 77}, { 45, 32}, { 57, 82}, +{ 50, 37}, { 37, 76}, { 55, 42}, { 42, 28}, +{ 59, 67}, { 47, 33}, { 33, 20}, { 51, 70}, +{ 38, 25}, { 56, 75}, { 43, 30}, { 45, 80}, +{ 48, 35}, { 35, 21}, { 52, 71}, { 40, 26}, +{ 26, 13}, { 44, 63}, { 31, 18}, { 22, 68}, +{ 36, 23}, { 23, 45}, { 41, 28}, { 28, 14}, +{ 31, 64}, { 33, 19}, { 19, 48}, { 38, 24}, +{ 24, 11}, { 35, 59}, { 29, 16}, { 16, 52}, +{ 34, 21}, { 21, 7}, { 37, 56}, { 26, 12}, +{ 12, -1}, { 30, 49}, { 17, 4}, { 4, 33}, +{ 22, 9}, { 9, -5}, { 20, 44}, { 14, 0}, +{ 0, 42}, { 21, 10}, { 10, -1}, { 29, 50}, +{ 19, 8}, { 8, -3}, { 28, 49}, { 18, 6}, +{ 6, 39}, { 27, 16}, { 16, 5}, { 30, 57}, +{ 25, 14}, { 14, 57}, { 35, 24}, { 24, 12}, +{ 12, 39}, { 33, 22}, { 22, 11}, { 30, 63}, +{ 31, 20}, { 20, 54}, { 41, 30}, { 30, 18}, +{ 45, 70}, { 39, 28}, { 28, 17}, { 28, 69}, +{ 37, 26}, { 27, 53}, { 47, 36}, { 36, 24}, +{ 24, 13}, { 44, 65}, { 34, 23}, { 23, 75}, +{ 43, 32}, { 32, 55}, { 53, 42}, { 42, 30}, +{ 30, 19}, { 50, 71}, { 40, 29}, { 29, 68}, +{ 49, 38}, { 38, 27}, { 27, 53}, { 48, 36}, +{ 36, 25}, { 44, 77}, { 46, 35}, { 35, 23}, +{ 54, 75}, { 44, 33}, { 33, 54}, { 54, 42}, +{ 42, 31}, { 31, 20}, { 51, 72}, { 41, 29}, +{ 29, 67}, { 50, 39}, { 39, 28}, { 57, 73}, +{ 48, 37}, { 37, 26}, { 41, 78}, { 47, 35}, +{ 35, 24}, { 24, 67}, { 45, 34}, { 34, 22}, +{ 53, 74}, { 43, 32}, { 32, 21}, { 41, 73}, +{ 41, 30}, { 30, 19}, { 19, 70}, { 40, 28}, +{ 28, 51}, { 49, 38}, { 38, 27}, { 27, 15}, +{ 40, 67}, { 36, 25}, { 25, 14}, { 21, 66}, +{ 34, 23}, { 24, 48}, { 44, 33}, { 33, 21}, +{ 21, 10}, { 39, 55}, { 31, 20}, { 20, 8}, +{ 23, 60}, { 29, 18}, { 18, 7}, { 7, 48}, +{ 27, 16}, { 16, 5}, { 35, 56}, { 26, 14}, +{ 14, 3}, { 23, 55}, { 24, 13}, { 13, 1}, +{ 1, 51}, { 22, 11}, { 11, 0}, { 0, 29}, +{ 20, 9}, { 9, -2}, { -2, -13}, { 18, 23}, +{ 7, -4}, { -4, -15}, { 5, 38}, { 6, -6}, +{ -6, -17}, { -17, 34}, { 4, -7}, { -7, -19}, +{ -19, 12}, { 2, -9}, { -9, -20}, { 4, 30}, +{ 0, -8}, { -8, -17}, { -17, -25}, { -4, 30}, +{ -2, -10}, { -10, -19}, { -19, 37}, { 5, -4}, +{ -4, -12}, { -12, 22}, { 11, 3}, { 3, -6}, +{ -5, 18}, { 18, 9}, { 9, 1}, { 1, -8}, +{ 15, 45}, { 16, 7}, { 7, -1}, { 1, 54}, +{ 22, 14}, { 14, 5}, { 5, 41}, { 29, 20}, +{ 20, 12}, { 13, 36}, { 35, 27}, { 27, 18}, +{ 18, 10}, { 10, 1}, { 32, 56}, { 25, 16}, +{ 16, 8}, { 27, 63}, { 31, 23}, { 23, 14}, +{ 14, 68}, { 38, 29}, { 29, 21}, { 21, 12}, +{ 12, 59}, { 36, 27}, { 27, 19}, { 19, 49}, +{ 42, 34}, { 34, 25}, { 25, 17}, { 47, 63}, +{ 40, 32}, { 32, 23}, { 23, 15}, { 42, 70}, +{ 38, 30}, { 30, 21}, { 34, 77}, { 38, 65}, +{ 36, 28}, { 28, 19}, { 28, 75}, { 43, 34}, +{ 34, 26}, { 26, 65}, { 49, 41}, { 41, 32}, +{ 32, 24}, { 24, 59}, { 47, 39}, { 39, 30}, +{ 31, 54}, { 23, 53}, { 45, 37}, { 37, 28}, +{ 28, 20}, { 51, 59}, { 43, 35}, { 35, 26}, +{ 26, 18}, { 47, 66}, { 41, 33}, { 33, 24}, +{ 24, 16}, { 42, 69}, { 39, 31}, { 31, 22}, +{ 34, 77}, { 46, 37}, { 37, 29}, { 29, 20}, +{ 26, 75}, { 44, 35}, { 35, 27}, { 27, 18}, +{ 18, 72}, { 42, 33}, { 33, 25}, { 25, 16}, +{ 16, 65}, { 40, 31}, { 31, 23}, { 23, 14}, +{ 14, 57}, { 38, 29}, { 29, 21}, { 21, 12}, +{ 12, 51}, { 36, 27}, { 27, 19}, { 19, 10}, +{ 10, 46}, { 34, 25}, { 25, 17}, { 17, 8}, +{ 8, 40}, { 32, 23}, { 23, 15}, { 15, 6}, +{ 6, 36}, { 30, 21}, { 21, 13}, { 13, 4}, +{ 4, 31}, { -4, 32}, { 19, 11}, { 11, 2}, +{ 2, -6}, { -6, 26}, { 17, 9}, { 9, 0}, +{ 0, -6}, { -5, 26}, { 20, 14}, { 14, 7}, +{ 7, 1}, { 1, 31}, { -5, 34}, { 21, 14}, +{ 14, 8}, { 8, 2}, { 3, 37}, { 28, 21}, +{ 21, 15}, { 15, 9}, { 9, 42}, { 35, 28}, +{ 28, 22}, { 22, 16}, { 16, 10}, { 10, 50}, +{ 35, 29}, { 29, 23}, { 23, 17}, { 17, 10}, +{ 10, 63}, { 36, 30}, { 30, 24}, { 24, 17}, +{ 17, 64}, { 20, 69}, { 37, 31}, { 31, 24}, +{ 24, 18}, { 20, 76}, { 30, 70}, { 38, 31}, +{ 31, 25}, { 25, 19}, { 34, 76}, { 39, 68}, +{ 38, 32}, { 32, 26}, { 26, 20}, { 43, 76}, +{ 44, 70}, { 39, 33}, { 33, 27}, { 27, 20}, +{ 50, 70}, { 46, 40}, { 40, 34}, { 34, 27}, +{ 27, 55}, { 21, 57}, { 47, 41}, { 41, 34}, +{ 34, 28}, { 29, 60}, { 22, 67}, { 48, 41}, +{ 41, 35}, { 35, 29}, { 29, 23}, { 23, 80}, +{ 34, 73}, { 42, 36}, { 36, 30}, { 30, 23}, +{ 36, 81}, { 42, 73}, { 43, 37}, { 37, 30}, +{ 30, 24}, { 24, 18}, { 48, 74}, { 44, 37}, +{ 37, 31}, { 31, 25}, { 27, 53}, { 19, 56}, +{ 44, 38}, { 38, 32}, { 32, 26}, { 26, 19}, +{ 19, 67}, { 23, 71}, { 39, 33}, { 33, 26}, +{ 26, 20}, { 20, 14}, { 14, 8}, { 37, 58}, +{ 33, 27}, { 27, 21}, { 21, 15}, { 15, 42}, +{ 8, 44}, { 34, 28}, { 28, 22}, { 22, 15}, +{ 15, 9}, { 9, 53}, { 8, 61}, { 17, 54}, +{ 22, 16}, { 16, 10}, { 10, 4}, { 4, -3}, +{ 25, 51}, { 23, 17}, { 17, 11}, { 11, 4}, +{ 4, -2}, { -2, 31}, { -8, 37}, { 18, 11}, +{ 11, 5}, { 5, -1}, { -1, -7}, { -7, -14}, +{ 5, 43}, { 9, 30}, { 6, 0}, { 0, -7}, +{ -7, -13}, { -13, -19}, { -19, 15}, { 7, 0}, +{ 0, -3}, { -3, -7}, { -7, -11}, { -11, -15}, +{ -15, -18}, { -18, -22}, { 7, 31}, { 6, 2}, +{ 2, -1}, { -1, -5}, { -5, -9}, { -9, 29}, +{ -13, 39}, { 16, 12}, { 12, 8}, { 8, 4}, +{ 4, 1}, { 1, -3}, { -3, -7}, { 23, 45}, +{ 21, 18}, { 18, 14}, { 14, 10}, { 10, 6}, +{ 6, 3}, { 3, 55}, { 12, 58}, { 20, 54}, +{ 23, 20}, { 20, 16}, { 16, 12}, { 12, 8}, +{ 9, 41}, { 5, 47}, { 1, 61}, { 16, 56}, +{ 25, 22}, { 22, 18}, { 18, 14}, { 14, 10}, +{ 11, 39}, { 7, 43}, { 3, 52}, { 31, 27}, +{ 27, 24}, { 24, 20}, { 20, 16}, { 16, 12}, +{ 12, 9}, { 38, 61}, { 37, 33}, { 33, 29}, +{ 29, 26}, { 26, 22}, { 22, 18}, { 18, 14}, +{ 14, 11}, { 11, 7}, { 38, 51}, { 35, 31}, +{ 31, 28}, { 28, 24}, { 24, 20}, { 20, 16}, +{ 16, 13}, { 13, 9}, { 36, 65}, { 37, 33}, +{ 33, 30}, { 30, 26}, { 26, 22}, { 22, 18}, +{ 18, 15}, { 15, 11}, { 11, 7}, { 7, 40}, +{ 35, 32}, { 32, 28}, { 28, 24}, { 24, 20}, +{ 20, 17}, { 17, 13}, { 13, 9}, { 9, 38}, +{ 5, 42}, { 2, 50}, { 30, 26}, { 26, 22}, +{ 22, 19}, { 19, 15}, { 15, 11}, { 11, 7}, +{ 10, 38}, { 4, 44}, { 0, 56}, { 12, 55}, +{ 18, 53}, { 21, 17}, { 17, 13}, { 13, 9}, +{ 9, 6}, { 6, 2}, { 2, -2}, { -2, -6}, +{ -6, -9}, { 20, 48}, { 19, 15}, { 15, 11}, +{ 11, 8}, { 8, 4}, { 4, 0}, { 0, -4}, +{ -4, -7}, { -7, -11}, { -11, -15}, { -15, 31}, +{ -12, 42}, { -1, 37}, { 4, 25}, { 2, -2}, +{ -2, -5}, { -5, -9}, { -9, -13}, { -13, -17}, +{ -17, -20}, { -20, -24}, { -24, -28}, { -28, 8}, +{ -32, 20}, { -24, 30}, { -12, 28}, { -5, 26}, +{ -5, -6}, { -6, -7}, { -7, -8}, { -8, -10}, +{ -10, -11}, { -11, -12}, { -12, -13}, { -13, -15}, +{ -15, -16}, { -16, -17}, { -7, 45}, { 5, 43}, +{ -20, 17}, { -21, 27}, { 10, 9}, { 9, 7}, +{ 7, 6}, { 6, 5}, { 5, 4}, { 4, 2}, +{ 2, 1}, { 1, 0}, { 0, -1}, { -1, -3}, +{ -3, -4}, { -3, 33}, { -5, 44}, { -1, 56}, +{ 13, 54}, { 21, 46}, { 22, 21}, { 21, 19}, +{ 19, 18}, { 18, 17}, { 17, 16}, { 16, 14}, +{ 14, 13}, { 13, 12}, { 12, 11}, { 11, 9}, +{ 9, 8}, { 8, 7}, { 7, 6}, { 6, 52}, +{ 36, 3}, { 3, 2}, { 4, 35}, { 1, 43}, +{ -1, 57}, { 12, 61}, { 22, 59}, { 28, 26}, +{ 26, 25}, { 25, 24}, { 24, 23}, { 23, 21}, +{ 21, 20}, { 20, 19}, { 19, 18}, { 18, 16}, +{ 16, 15}, { 15, 14}, { 14, 13}, { 13, 11}, +{ 11, 10}, { 10, 9}, { 9, 8}, { 8, 6}, +{ 6, 44}, { 37, 3}, { 9, 67}, { 35, 1}, +{ 1, 36}, { 0, 45}, { -1, 60}, { 14, 60}, +{ 23, 58}, { 27, 26}, { 26, 25}, { 6, 54}, +{ 16, 53}, { 22, 21}, { 21, 20}, { 20, 18}, +{ 18, 17}, { 17, 16}, { 16, 15}, { 15, 13}, +{ 13, 12}, { 12, 11}, { 11, 10}, { 10, 8}, +{ 8, 7}, { 7, 6}, { 6, 5}, { 5, 3}, +{ 3, 2}, { 2, 1}, { 1, 0}, { 0, -2}, +{ -2, -3}, { -3, -4}, { -4, -5}, { -5, -7}, +{ -7, -8}, { -8, -9}, { -9, -10}, { -10, -12}, +{ -12, -13}, { -13, -14}, { -14, -15}, { -15, -17}, +{ -17, -18}, { -18, -19}, { -19, -20}, { -20, -22}, +{ -22, -23}, { -23, -24}, { -24, -25}, { -25, -27}, +{ -27, -28}, { -28, -29}, { -29, -30}, { -30, -16}, +}; + +static int16_t vfpu_sin_lut_interval_delta[65537]= +{ + -16384, -16385, -16384, -16383, -16384, -16384, -16385, -16386, + -16387, -16388, -16390, -16391, -16392, -16394, -16394, -16394, + -16396, -16397, -16397, -16399, -16398, -16398, -16398, -16398, + -16399, -16400, -16401, -16402, -16403, -16405, -16406, -16407, + -16408, -16409, -16410, -16412, -16413, -16414, -16416, -16416, + -16417, -16419, -16420, -16421, -16423, -16424, -16425, -16426, + -16427, -16428, -16429, -16430, -16430, -16430, -16431, -16430, + -16431, -16432, -16433, -16432, -16432, -16433, -16432, -16433, + -16433, -16434, -16434, -16433, -16433, -16435, -16435, -16435, + -16435, -16435, -16435, -16435, -16436, -16437, -16438, -16438, + -16438, -16439, -16440, -16441, -16442, -16444, -16444, -16445, + -16447, 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-15956, -15958, -15959, -15960, -15962, + -15963, -15964, -15966, -15967, -15968, -15970, -15971, -15972, + -15974, +}; + +static uint8_t vfpu_sin_lut_exceptions[86938]= +{ + 15, 83,128, 26,128, 86, 6, 24, 72, 4,128, 83,128,192, 90,192, + 22, 6, 24, 72, 4, 83, 79, 72, 15, 68,192,128, 83, 8, 79, 15, + 68,128,192, 15, 83, 8, 79,192,128,192, 19, 72, 15, 79, 4,192, + 19, 72, 15, 4, 72, 88, 88, 6, 22, 19,192, 90,128, 4, 70, 86, + 83,128, 26, 90, 4, 70,128, 68, 88,128, 4, 24, 22, 83,128, 26, +192, 24, 22, 22, 83, 22, 83, 8, 83, 8, 19, 72, 19, 72, 83, 22, + 86,192, 0, 88, 24, 26, 4, 90, 70, 72, 22, 86, 26, 6, 72, 4, + 72, 22, 68, 83, 8, 86, 26, 4, 19, 72, 22, 64, 72, 68, 6, 0, + 24, 64, 24, 90, 64, 90, 68, 64, 6, 64, 19, 72, 4, 64, 70, 83, +121, 0, 88, 26, 64, 64, 64, 72, 22, 64, 64, 0, 0, 88, 26, 64, + 86, 64, 24, 0, 22, 0, 64, 0, 64, 0, 72, 70, 83, 0, 88, 0, + 8, 64, 6, 72, 26, 64, 24, 64, 72, 57, 70, 83, 90, 0, 22, 64, + 70, 8,133,134,135, 8,141,142,143, 16,149,150,151, 24,158,159, + 32, 33,166, 39, 40, 41,174, 47, 48, 49, 55, 56, 57, 58, 63,196, + 69, 70, 71, 76, 77, 78,211, 84, 85, 86,219, 92, 93,226,227,100, +101,234,235,108,241,242,115,116,249,250,123, 3, 4, 5, 6, 11, + 12, 13, 14, 19, 20, 21, 26, 27, 28, 29, 34, 35, 36,169, 42, 43, + 44,177, 50, 51,184,185, 58, 59,192, 65,198, 71, 72, 73,206, 79, + 80,213,214, 87, 88,221,222, 95,228,229,102,103,236,237,110,243, +244,245,118,251,252,253, 4, 5, 6, 11, 12, 13, 14, 19, 20, 21, +154, 27, 28, 29,162, 35, 36,169,170, 43, 44,177, 50, 51,184,185, + 58, 59,192, 65,198,199, 72, 73,206,207, 80,213,214, 87, 88,221, +222, 95,228,229,230,103,236,237,238,243,244,245,246,251,252,253, + 0,133, 6, 7, 8,141, 14, 15,148,149, 22, 23,156,157, 30,163, +164, 37, 38,171,172, 45,178,179,180, 53,186,187,188, 67, 68, 69, + 74, 75, 76, 77, 82, 83, 84,217, 90, 91, 92,225, 98, 99,232,105, +106,107,240,113,114,247,248,121,122,255,128,133,134, 7, 8,141, +142, 15,148,149, 22, 23,156,157, 30,163,164,165, 38,171,172,173, +178,179,180, 53,186,187,188, 67, 68, 69, 70, 75, 76, 77, 78, 83, + 84, 85, 90, 91, 92, 93, 98, 99,100,233,106,107,108,241,114,115, +248,249,122,123,128,134,135,136, 9,142,143,144, 17,150,151,152, + 25,159,160, 33, 34,167, 40, 41, 42,175, 48, 49, 50, 56, 57, 58, + 59,196,197, 70, 71,204, 77, 78,211,212, 85, 86,219,220, 93,226, +227,228,101,234,235,236,241,242,243,116,249,250,251, 2, 3, 4, + 5, 10, 11, 12, 13, 18, 19, 20, 25, 26, 27, 28, 33, 34, 35,168, + 41, 42, 43,176, 49, 50,183,184, 57, 58,191,197,198,199, 72,205, +206,207, 80,213,214,215, 88,222,223, 96, 97,230,103,104,105,238, +111,112,113,119,120,121,122,127,132, 5, 6, 7, 12, 13, 14,147, + 20, 21, 22,155, 28, 29,162,163, 36, 37,170,171, 44,177,178, 51, + 52,185,186, 59,192,198,199,200, 73,206,207,208, 81,214,215, 88, + 89,222,223, 96, 97,231,104,105,106,239,112,113,114,119,120,121, +122,127, 0, 1,134, 7, 8, 9,142, 15, 16,149,150, 23, 24,157, + 30, 31,164,165, 38, 39,172,173, 46,179,180,181, 54,187,188,189, + 67, 68, 69, 70, 75, 76, 77, 78, 83, 84, 85,218, 91, 92, 93,226, + 99,100,233,106,107,108,241,114,115,248,249,122,123,128, 1,134, +135, 8, 9,142, 15, 16,149,150, 23, 24,157,158, 31,164,165,166, + 39,172,173,174,179,180,181, 54,187,188,189, 68, 69, 70, 71, 76, + 77, 78,211, 84, 85, 86, 91, 92, 93,226, 99,100,101,234,107,108, +241,242,115,116,249,250,123, 2, 3, 4, 5, 10, 11, 12, 13, 18, + 19, 20,153, 26, 27, 28,161, 34, 35,168, 41, 42, 43,176, 49, 50, +183,184, 57, 58,191,192,197,198, 71, 72,205, 78, 79,212,213, 86, + 87,220,221, 94,227,228,229,102,235,236,237,242,243,244,117,250, +251,252, 3, 4, 5, 6, 11, 12, 13, 14, 19, 20, 21, 26, 27, 28, + 29, 34, 35, 36,169, 42, 43, 44,177, 50, 51,184,185, 58, 59,192, +198,199,200, 73,206,207,208, 81,214,215,216, 89,223, 96, 97, 98, +231,104,105,106,239,112,113,114,120,121,122,123,132, 5, 6, 7, +140, 13, 14,147,148, 21, 22,155,156, 29,162,163,164, 37,170,171, + 44,177,178,179, 52,185,186,187, 66, 67, 68, 69, 74, 75, 76, 81, + 82, 83, 84, 89, 90, 91,224, 97, 98, 99,232,105,106,239,240,113, +114,247,120,121,254,255, 0,133, 6, 7, 8,141, 14, 15,148,149, + 22, 23,156, 29, 30,163,164, 37, 38,171,172, 45,178,179,180, 53, +186,187,188, 68, 69, 70, 71, 76, 77, 78,211, 84, 85, 86,219, 92, + 93,226,227,100,101,234,107,108,241,242,115,116,249,250,123,128, +134,135,136, 9,142,143, 16, 17,150,151, 24, 25,158,159, 32, 33, +167, 40, 41, 42,175, 48, 49, 50, 55, 56, 57, 58, 63,196, 69, 70, + 71,204, 77, 78,211,212, 85, 86,219, 92, 93,226,227,100,101,234, +235,108,241,242,243,116,249,250,251, 3, 4, 5, 6, 11, 12, 13, + 14, 19, 20, 21,154, 27, 28, 29,162, 35, 36,169, 42, 43, 44,177, + 50, 51,184,185, 58, 59,192, 65,198,199, 72, 73,206, 79, 80,213, +214, 87, 88,221,222, 95,228,229,230,103,236,237,110,243,244,245, +118,251,252,253, 4, 5, 6, 7, 12, 13, 14, 19, 20, 21, 22, 27, + 28, 29,162, 35, 36, 37,170, 43, 44,177,178, 51, 52,185, 58, 59, + 66, 67, 68, 69, 74, 75, 76, 77, 82, 83, 84,217, 90, 91, 92, 97, + 98, 99,232,105,106,107,240,113,114,247,248,121,122,255,128,133, + 6, 7, 8,141, 14, 15,148,149, 22, 23,156,157, 30,163,164,165, + 38,171,172, 45,178,179,180, 53,186,187,188, 67, 68, 69, 70, 75, + 76, 77, 82, 83, 84, 85, 90, 91, 92,225, 98, 99,100,233,106,107, +240,241,114,115,248,121,122,255,128,134,135,136, 9,142,143,144, + 17,150,151,152, 25,159, 32, 33, 34,167, 40, 41, 42,175, 48, 49, + 50, 56, 57, 58, 59,196, 69, 70, 71,204, 77, 78,211,212, 85, 86, +219,220, 93,226,227,228,101,234,235,108,241,242,243,116,249,250, +251, 2, 3, 4, 5, 10, 11, 12, 17, 18, 19, 20, 25, 26, 27,160, + 33, 34, 35,168, 41, 42,175,176, 49, 50,183, 56, 57,190,191, 64, + 65,198,199, 72, 73,206,207, 80,213,214, 87, 88,221,222, 95,228, +229,230,103,236,237,238,243,244,245,246,251,252,253, 4, 5, 6, + 7, 12, 13, 14,147, 20, 21, 22,155, 28, 29,162, 35, 36, 37,170, + 43, 44,177,178, 51, 52,185,186, 59,192,198,199, 72, 73,206,207, + 80, 81,214,215, 88, 89,222,223, 96, 97,231,104,105,106,111,112, +113,114,119,120,121,122,127, 0,133,134, 7, 8,141,142, 15,148, +149, 22, 23,156,157, 30,163,164,165, 38,171,172,173,178,179,180, +181,186,187,188, 67, 68, 69, 70, 75, 76, 77, 78, 83, 84, 85,218, + 91, 92, 93, 98, 99,100,233,106,107,108,241,114,115,248,249,122, +123,128, 1,134, 7, 8, 9,142, 15, 16,149,150, 23, 24,157,158, + 31,164,165,166, 39,172,173, 46,179,180,181, 54,187,188,189,196, +197, 70, 71,204,205, 78,211,212, 85, 86,219,220, 93,226,227,228, +101,234,235,236,241,242,243,116,249,250,251, 2, 3, 4, 5, 10, + 11, 12, 13, 18, 19, 20, 25, 26, 27, 28, 33, 34, 35,168, 41, 42, + 43,176, 49, 50,183,184, 57, 58,191, 64,197, 70, 71, 72,205, 78, + 79,212,213, 86, 87,220,221, 94,227,228,101,102,235,236,109,242, +243,244,117,250,251,252,132, 5, 6, 7, 12, 13, 14,147, 20, 21, + 22,155, 28, 29,162,163, 36, 37,170,171, 44,177,178, 51, 52,185, +186, 59,192,198,199,200, 73,206,207,208, 81,214,215, 88, 89,222, +223, 96, 97,231,104,105,106,239,112,113,114,247,120,121,122,127, +132, 5, 6, 7,140, 13, 14,147,148, 21, 22,155,156, 29,162,163, + 36, 37,170,171, 44,177,178,179, 52,185,186,187, 68, 69, 70, 75, + 76, 77, 78, 83, 84, 85,218, 91, 92, 93,226, 99,100,233,234,107, +108,241,114,115,248,249,122,123,128, 1,134,135, 8, 9,142,143, + 16,149,150, 23, 24,157,158, 31,164,165,166, 39,172,173,174,179, +180,181,182,187,188,189, 68, 69, 70, 71, 76, 77, 78,211, 84, 85, + 86,219, 92, 93,226, 99,100,101,234,107,108,241,242,115,116,249, +250,123, 2, 3, 4, 5, 10, 11, 12, 13, 18, 19, 20,153, 26, 27, + 28,161, 34, 35,168, 41, 42, 43,176, 49, 50,183,184, 57, 58,191, +192,197,198, 71, 72,205, 78, 79,212,213, 86, 87,220,221, 94,227, +228,229,102,235,236,237,242,243,244,117,250,251,252, 3, 4, 5, + 6, 11, 12, 13, 14, 19, 20, 21, 26, 27, 28, 29, 34, 35, 36,169, + 42, 43, 44,177, 50, 51,184,185, 58, 59,192,198,199,200, 73,206, +207,208, 81,214,215,216, 89,223,224, 97, 98,231,104,105,106,239, +112,113,114,120,121,122,123,132,133, 6, 7,140, 13, 14,147,148, + 21, 22,155,156, 29,162,163,164, 37,170,171,172,177,178,179, 52, +185,186,187, 68, 69, 70, 71, 76, 77, 78,211, 84, 85, 86, 91, 92, + 93,226, 99,100,101,234,107,108,241,242,115,116,249,122,123,128, +134,135, 8, 9,142,143, 16, 17,150,151, 24, 25,158, 31, 32, 33, + 39, 40, 41, 42, 47, 48, 49, 50, 55, 56, 57, 58, 63,196, 69, 70, + 71, 76, 77, 78,211, 84, 85, 86,219, 92, 93,226,227,100,101,234, +107,108,241,242,115,116,249,250,123, 3, 4, 5, 6, 11, 12, 13, + 18, 19, 20, 21, 26, 27, 28,161, 34, 35, 36,169, 42, 43,176,177, + 50, 51,184, 57, 58,191,192, 65,198, 71, 72, 73,206, 79, 80,213, +214, 87, 88,221, 94, 95,228,229,102,103,236,237,110,243,244,245, +118,251,252,253, 3, 4, 5, 6, 11, 12, 13, 14, 19, 20, 21,154, + 27, 28, 29,162, 35, 36,169, 42, 43, 44,177, 50, 51,184,185, 58, + 59, 66, 67, 68, 69, 74, 75, 76, 81, 82, 83, 84, 89, 90, 91,224, + 97, 98, 99,232,105,106,239,240,113,114,247,120,121,254,255,132, +133, 6, 7,140,141, 14,147,148,149, 22,155,156, 29,162,163,164, + 37,170,171,172,177,178,179,180,185,186,187, 68, 69, 70, 71, 76, + 77, 78,211, 84, 85, 86,219, 92, 93,226, 99,100,101,234,107,108, +241,242,115,116,249,250,123,128,134,135, 8, 9,142,143, 16, 17, +150,151, 24, 25,158,159, 32, 33,167, 40, 41, 42, 47, 48, 49, 50, + 55, 56, 57, 58, 63,196, 69, 70, 71,204, 77, 78,211, 84, 85, 86, +219, 92, 93,226,227,100,101,234,235,108,241,242,243,116,249,250, +123, 3, 4, 5, 6, 11, 12, 13, 14, 19, 20, 21,154, 27, 28, 29, + 34, 35, 36,169, 42, 43, 44,177, 50, 51,184,185, 58, 59,192, 65, +198, 71, 72, 73,206, 79, 80,213,214, 87, 88,221,222, 95,228,229, +230,103,236,237,110,243,244,245,118,251,252,253, 4, 5, 6, 7, + 12, 13, 14, 19, 20, 21, 22, 27, 28, 29,162, 35, 36, 37,170, 43, + 44,177,178, 51, 52,185, 58, 59, 66, 67, 68, 69, 74, 75, 76, 77, + 82, 83, 84,217, 90, 91, 92, 97, 98, 99,232,105,106,107,240,113, +114,247,248,121,122,255, 0,133, 6, 7, 8,141, 14, 15,148,149, + 22, 23,156,157, 30,163,164, 37, 38,171,172, 45,178,179,180, 53, +186,187,188, 67, 68, 69, 74, 75, 76, 77, 82, 83, 84,217, 90, 91, + 92,225, 98, 99,232,233,106,107,240,113,114,247,248,121,122,255, +128,134,135,136, 9,142,143,144, 17,150,151, 24, 25,158,159, 32, + 33,167, 40, 41, 42,175, 48, 49, 50,183, 56, 57, 58, 63,196, 69, + 70, 71,204, 77, 78,211,212, 85, 86,219,220, 93,226,227,100,101, +234,235,108,241,242,243,116,249,250,251, 4, 5, 6, 11, 12, 13, + 14, 19, 20, 21,154, 27, 28, 29,162, 35, 36,169,170, 43, 44,177, + 50, 51,184,185, 58, 59,192, 65,198,199, 72, 73,206,207, 80,213, +214, 87, 88,221,222, 95,228,229,230,103,236,237,238,243,244,245, +246,251,252,253, 4, 5, 6, 7, 12, 13, 14,147, 20, 21, 22,155, + 28, 29,162, 35, 36, 37,170, 43, 44,177,178, 51, 52,185,186, 59, + 66, 67, 68, 69, 74, 75, 76, 77, 82, 83, 84,217, 90, 91, 92,225, + 98, 99,232,105,106,107,240,113,114,247,248,121,122,255,128,133, +134, 7, 8,141, 14, 15,148,149, 22, 23,156,157, 30,163,164,165, + 38,171,172,173,178,179,180, 53,186,187,188,196, 69, 70, 71,204, + 77, 78,211,212, 85, 86,219, 92, 93,226,227,100,101,234,235,108, +241,242,243,116,249,250,251,128,134,135,136, 9,142,143,144, 17, +150,151,152, 25,159,160, 33, 34,167, 40, 41, 42,175, 48, 49, 50, + 56, 57, 58, 59,196,197, 70, 71,204, 77, 78,211,212, 85, 86,219, +220, 93,226,227,228,101,234,235,236,241,242,243,116,249,250,251, + 4, 5, 6, 7, 12, 13, 14,147, 20, 21, 22, 27, 28, 29,162, 35, + 36, 37,170, 43, 44,177,178, 51, 52,185, 58, 59,192,198,199, 72, + 73,206,207, 80, 81,214,215, 88, 89,222,223, 96, 97,103,104,105, +106,111,112,113,114,119,120,121,122,127,132, 5, 6, 7, 12, 13, + 14,147, 20, 21, 22,155, 28, 29,162,163, 36, 37,170, 43, 44,177, +178, 51, 52,185,186, 59, 67, 68, 69, 70, 75, 76, 77, 82, 83, 84, + 85, 90, 91, 92,225, 98, 99,100,233,106,107,240,241,114,115,248, +121,122,255,128, 1,134, 7, 8, 9,142, 15, 16,149,150, 23, 24, +157, 30, 31,164,165, 38, 39,172,173, 46,179,180,181, 54,187,188, +189,196, 69, 70, 71,204, 77, 78,211,212, 85, 86,219,220, 93,226, +227,228,101,234,235,108,241,242,243,116,249,250,251, 2, 3, 4, + 5, 10, 11, 12, 17, 18, 19, 20, 25, 26, 27,160, 33, 34, 35,168, + 41, 42,175,176, 49, 50,183, 56, 57,190,191, 64, 65,198,199, 72, + 73,206,207, 80,213,214, 87, 88,221,222, 95,228,229,230,103,236, +237,238,243,244,245,246,251,252,253, 4, 5, 6, 7, 12, 13, 14, +147, 20, 21, 22,155, 28, 29,162, 35, 36, 37,170, 43, 44,177,178, + 51, 52,185,186, 59,192,198,199, 72, 73,206,207, 80, 81,214,215, + 88, 89,222,223, 96, 97,231,104,105,106,111,112,113,114,119,120, +121,122,127, 0,133,134, 7, 8,141,142, 15,148,149, 22, 23,156, +157, 30,163,164,165, 38,171,172,173,178,179,180,181,186,187,188, + 67, 68, 69, 70, 75, 76, 77, 78, 83, 84, 85,218, 91, 92, 93, 98, + 99,100,233,106,107,108,241,114,115,248,249,122,123, 2, 3, 4, + 9, 10, 11, 12, 17, 18, 19,152, 25, 26, 27,160, 33, 34,167,168, + 41, 42,175, 48, 49,182,183, 56, 57,190,191,196,197, 70, 71,204, +205, 78,211,212, 85, 86,219,220, 93,226,227,228,101,234,235,236, +241,242,243,244,249,250,251, 2, 3, 4, 5, 10, 11, 12, 13, 18, + 19, 20,153, 26, 27, 28, 33, 34, 35,168, 41, 42, 43,176, 49, 50, +183,184, 57, 58,191,197,198,199, 72,205,206,207, 80,213,214,215, + 88,222,223, 96, 97,230,103,104,105,238,111,112,113,119,120,121, +122,127,132, 5, 6, 7, 12, 13, 14,147, 20, 21, 22,155, 28, 29, +162,163, 36, 37,170,171, 44,177,178, 51, 52,185,186, 59, 67, 68, + 69, 70, 75, 76, 77, 78, 83, 84, 85, 90, 91, 92, 93, 98, 99,100, +233,106,107,108,241,114,115,248,249,122,123,128, 1,134, 7, 8, + 9,142, 15, 16,149,150, 23, 24,157,158, 31,164,165, 38, 39,172, +173, 46,179,180,181, 54,187,188,189, 68, 69, 70, 75, 76, 77, 78, + 83, 84, 85,218, 91, 92, 93,226, 99,100,233,234,107,108,241,114, +115,248,249,122,123, 2, 3, 4, 5, 10, 11, 12, 13, 18, 19, 20, + 25, 26, 27, 28, 33, 34, 35,168, 41, 42, 43,176, 49, 50,183, 56, + 57, 58,191, 64,197, 70, 71, 72,205, 78, 79,212,213, 86, 87,220, + 93, 94,227,228,101,102,235,236,109,242,243,244,117,250,251,252, + 4, 5, 6, 7, 12, 13, 14,147, 20, 21, 22,155, 28, 29,162,163, + 36, 37,170, 43, 44,177,178, 51, 52,185,186, 59,192,198,199,200, + 73,206,207, 80, 81,214,215, 88, 89,222,223, 96, 97,231,104,105, +106,239,112,113,114,119,120,121,122,127, 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64, 64, 65, + 4,191, 64, 0, 66, 0, 0, 0, 0, 33, 64, 66, 0, 0, 64, 99, + 0, 64, 65, 0, 6, 97, 0, 64, 64, 0, 6, 64,255, 0, 64, 64, + 0, 64, 0, 64,255, 0, 64, 0, 64, 0, 64, 6, 64, 0, 64, 0, + 64, 0, 64, 64, 66, 0, 64, 0, 64, 0, 0, 4, 8, 64, 0, 64, + 73, 0, 1, 64, 99, 0, 4, 64, 0, 64, 73, 0, 1, 64, 0, 64, + 66, 0, 64, 0, 64, 0, 0, 0, 64, 0, 64, 64, 0, 64, 64, 0, + 64, 62, 0, 1, 64, 0, 64, 0, 64, 0, 64, 0, 64, 0, 64, 0, + 64, 0,192,128,192,128,192,128,192, 8,250, 8,192,192,128, 72, +186,192,128, 72,128,192,128, 72,192,128, 72,128,192,128,192,186, +192,128,192, 8,128,192,128,250,192,128, 72,186,128,192, 8,128, +192, 8,128,128,192, 8,128, 72, 8,186,250,192, 8,192,128,192, +128,192,192,192,128,192,128,192,128,192,250, 8, 72, 0, 64, 64, + 64, 64, 0, 64, 64, 0, 0, 64, 0, 0, 0, 64, 0, 0, 64, 64, + 64, 0, 64, 64, 64, 64, 64, 0, 0, 0, 0, 64, 64, 0, 0, 64, + 0, 64, 0, 0, 64, 64, 0, 64, 0, 64, 0, 0, 64, 0, 0, 0, + 64, 64, 64, 0, 0, 64, 0,192, 73, 9,128,128, 73,128, 73,192, +192, 9, 73,128,192,128,192,192,128,192,128, 73,192,192,128,192, + 9, 73,128, 73,192,128,128,192,128,128,128,192,192,128,128,128, +192,192,128, 9, 9,128,128,128,128, 9,192,192, 73, 9,192,192, +192, 9,192,192, 73, 9, 9,192, 73,192, 9,128,128,192, 0, 64, + 0, 64, 0, 64, 0, 0, 64, 0, 0, 0, 0, 0, 0, 64, 64, 64, + 0, 0, 64, 0, 0, 0, 0, 0, 64, 0, 0, 64, 0, 64, 64, 0, + 64, 0, 0, 64, 64, 0, 0, 64, 64, 64, 0, 0, 0, 0, 0, 64, + 0, 0, 64, 0, 0, 0, 0,128, 74,128, 74,128,192, 61, 68,192, + 13,128,128,128,192, 10,192,128,128,192, 74,128, 66,192,128, 63, +192, 74,128,128,192,192,128,128,192,192,128,192,192,127,192,128, +192,128, 74,128, 74,192,128,192,128,192,128,192, 10, 29,192,128, + 68, 10,128, 68,192, 10,128,192, 11,128, 63, 74, 3, 10, 75,192, +192, 74, 64, 2, 68, 77, 64, 0, 0, 64, 0, 64, 64, 0, 59, 59, + 59, 0, 0, 15, 64, 64, 0, 64, 0, 64, 64, 0, 0, 0, 64, 0, + 64, 0, 64, 64, 0, 64, 64, 0, 64, 64, 0, 64, 0, 64, 64, 68, + 0, 60, 0, 64, 0, 0, 64, 64, 59, 0, 0, 64,129, 0, 64, 64, +192, 80, 32,192, 77,128,128, 11,192,128, 11,192,128, 11,192,128, +192,128,128,192,128,192, 11,192, 11,192,128, 5, 11,192,128,128, +192, 11,192,128, 75,128,192, 75,128,128,192, 72, 75,128, 11,192, +128,128,192, 11,192,128,128,192,192, 79, 6,128,128,128,192,192, + 75,192,192, 75,128,128, 14,192,128, 79, 11, 80, 77,192,128, 11, + 11, 7, 82,192, 0, 6, 64, 0, 0, 0, 64, 0, 64, 0, 64, 6, + 64, 0, 8, 0, 79, 64, 0, 64, 0, 64, 0, 3, 64, 0, 0, 64, + 64, 0, 64, 64, 0, 14, 64, 64, 64, 64, 0, 0, 0, 64, 64, 0, + 64, 64, 0, 64, 0, 64, 0, 64, 0, 64, 64, 64, 0, 0, 0, 64, + 64, 7, 0, 0, 64, 64,192,192,192,191,128,128,128,128, 67,192, + 76,253,192,192,192,192,192,192,192,192,192,192,192,192, 3,192, +192,192,192,192,192, 76, 67,128,128,128,128,128, 3,192,192,192, +192,128,128,128,128,128, 12,128,192,128,128, 3,192,128, 12,128, + 76,253,128,190, 75,252, 74,128,253,128,190, 75,255, 12,192,128, +192,192, 74, 67, 11,191, 76,192, 2,189,128,192,128, 67,192, 11, +192, 3,192,128,192,192,128, 49, 10, 11,182, 3,114, 67,192,253, + 65,255, 49, 1,191, 3, 50, 2, 49, 2, 64, 64, 0,246, 64, 0, + 50, 64, 3, 0, 0,113, 64, 64, 0, 64,114, 0, 64,253, 10, 64, + 0, 0, 3, 0, 64, 0, 49, 74, 0, 64, 0, 64,191, 64, 0, 64, + 0, 0, 64, 0, 64, 0, 64, 67, 0, 0, 64, 0, 64, 0, 64,113, + 49, 64, 0, 64, 0, 64, 0, 64, 0, 64, 0, 64, 0, 3, 64, 0, + 64, 0, 64, 0, 64, 0,191, 64, 0, 0, 0, 64, 67, 64, 0,128, +192,128,192,128,128,192,128,192,192,128,192, 14, 83,128,192,128, +128,128,192,128,192, 14,192, 14,128,192,128,192,128, 69,192, 14, +128,192,128, 71,128,192, 13,192,128,192, 7, 66, 14,192,128, 91, +192,128,192,192,128, 13,192, 77,192,128,192, 14,192,128,128, 78, + 7, 21,192, 2, 16,192, 15, 68, 16, 83, 80, 64, 0, 64, 7, 0, + 14, 0, 0, 64, 64, 64, 64, 0, 0, 0, 0, 14, 15, 0, 0, 0, + 0, 0, 16, 64, 8, 64, 64, 0, 0, 83, 14, 64, 0, 0, 64, 0, + 7, 64, 83, 64, 0, 64, 64, 0, 64, 0, 7, 64, 83, 64, 80, 0, + 64, 0, 0, 64, 0, 64, 0, 64, 0, 64, 64, 0, 64, 0, 64, 0, + 7, 64, 83, 0, 64, 0, 64, 0, 64, 0, 64, 0, 64, 0, 0, 7, + 64, 0, 16,192,192,128,128,192,192,128,128,192,192,128, 16,128, +128,128,192,192,192,192,192,192,192,192,192,192,128,128,128, 14, +192,192,192,128,192,128,128,192,128,192, 13, 80,192,128,128,128, +128,192,192, 16, 80,128,192,128,128,192, 84,192,128,128,128,192, +128,128,128,192, 64, 64, 0, 0, 0, 64, 64, 0, 64, 64, 64, 64, + 0, 0, 64, 64, 64, 64, 64, 64, 64, 64, 0, 64, 0, 64, 0, 64, + 0, 64, 64, 0, 0, 0, 64, 64, 0, 64, 64, 64, 64, 64, 64, 64, + 0, 0, 0, 64, 64, 0, 0, 64, 64, 0, 64, 64, 0, 85,192,128, +192,101, 25,128,192, 5,192,128,192, 37,192,128,128,192,128,192, +128,192,128,192, 18, 83, 2, 5,192,128,192,192,128, 69,192,192, +128, 83,128,192, 18, 25,128, 67,192, 17, 82,192,128,128,192,128, +128,192, 19,128, 83, 66, 19,247, 82,128,128,128,128, 83, 82, 20, + 19, 19, 18, 22, 7,192,192,192, 84,128,192, 69,128,128, 2,192, + 4, 83, 89, 0, 5, 89, 0, 69, 0, 19, 22, 25, 0, 69, 64, 64, + 0, 0, 64, 64, 22, 0, 89, 0, 0, 0, 0, 64, 68, 64, 0, 0, + 64, 64, 89, 0, 64, 0, 64, 90, 0, 7, 64, 0, 64, 64, 64, 0, + 64, 25, 64, 0, 64, 64, 0, 0, 64, 64, 69, 0, 0, 64, 64, 0, + 64, 0, 64, 64, 64, 0, 64, 0, 4, 0, 64, 64, 64, 0, 64, 0, +128, 86, 21,192,128, 85,128,192,128,192,128, 22, 85, 21,192,128, +192,128,192, 21,192,128,192,128,192, 23, 86, 21, 85,128,192,128, +192,128,128,192,184,128,192,128,192, 22, 86, 21, 89,128,192,128, + 86, 22,184,192, 22,192,192, 23,128, 86, 85,192,192,128,128,128, +192, 21, 86,192, 86, 27,192,192, 21, 69, 64, 0, 0, 27, 64, 69, + 0, 64, 0,248, 64, 0, 64, 64, 64, 0, 0, 64, 0, 64, 0, 0, + 0, 0, 64, 64, 0, 64, 0, 64, 0, 0, 0, 64, 64, 0, 0, 0, + 64, 64, 64, 0, 0, 64, 0, 0, 0, 0, 0, 0,248, 64, 64, 64, + 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 0, 0, 0, 0, 0, 0, + 64, 64,192,192,192,192,192, 94,128,128,128, 1,192, 92,192,128, + 28, 31,192, 94,128,128,128,192,192,128,128, 33,192, 94,128,192, + 92, 27,192,128, 94,192, 29,192, 27,128,192, 31,192,192,128, 30, +192,128,128,192,192,128, 30,128, 91, 96, 68,128,192, 93,192,192, +192,128, 93, 94,192,128,128,192, 32, 4,128,128,128,192,128, 1, + 95, 94, 68,128,192,128, 29, 92, 98,128,192,192, 68,128, 98, 3, + 30, 31, 30, 64, 67, 0, 64, 0, 3, 0, 64, 31, 64, 30, 0, 64, + 64,222, 0, 67, 0, 0, 4, 64, 64, 98, 64, 0, 0, 0, 0, 4, + 64, 64, 64, 67, 0, 64, 67, 64, 0, 64, 0, 64,193, 0, 64, 0, + 64,193, 0, 64, 0, 64, 96, 0, 0, 64, 0, 0, 4, 64, 0,129, + 64, 64, 0, 64, 0, 0,222, 0, 64, 0, 64, 0, 64, 0, 64, 0, + 4, 64, 0, 64, 0, 64, 0, 64, 73, 1, 1, 73, 1, 1, 65, 1, + 65, 31, 65, 1, 65, 1, 1,128, 1, 1, 65, 83,192, 83, 65, 1, + 69, 13,192, 13, 65, 1, 1, 65, 65, 1, 65, 9, 65, 1, 65, 16, + 9, 78, 1, 71, 1, 1, 71, 1, 67, 1, 67, 12, 1, 1, 1, 1, + 5, 32, 67, 12, 1, 1, 32, 67, 1, 1, 1, 1, 1, 65, 65, 65, + 1, 65, 1, 1, 1, 1, 65, 65, 13, 69, 13, 1, 65, 1, 65, 9, + 65, 71, 19, 5, 5, 19, 5, 60, 1, 77, 67, 1, 73, 73, 69, 69, + 64, 69, 65, 65, 64, 69, 65, 64, 69, 65, 69, 65, 69, 65, 0, 0, + 9, 9, 65, 64, 71, 0, 0, 64, 0,253, 0, 64, 0, 12, 19, 64, + 12, 60, 64, 0, 64, 64, 0, 0, 64, 69, 0, 64, 64, 0, 0, 64, + 69, 64, 69, 83, 0, 13, 83, 0, 13, 0, 13, 13, 13, 0, 0, 0, + 0, 64, 0, 9, 16, 64, 0, 9, 0, 64, 0, 5, 64, 64,253, 0, + 0, 64, 0, 64, 0, 64, 67, 0, 19, 64, 64, 0, 0, 64, 64, 0, + 64, 64, 64, 0, 64, 64, 0, 64, 0, 0, 0, 14, 65,192, 65, 56, + 1, 1,128, 65, 1, 1, 65, 61, 1, 65, 61, 1, 65,126,192, 65, + 1, 65,128, 65, 1,125, 65, 1,128, 1, 65, 1, 1, 1,192, 65, +120, 65, 1,126, 1, 1, 1, 1,128,128, 1, 1,124, 65, 62, 65, +127, 1, 1, 54,192, 1, 64, 64, 0, 65, 64, 0, 64, 0, 0, 64, + 0, 0, 64, 64, 64, 64, 0, 64, 0, 64, 64, 0, 64, 0, 64, 64, + 64, 64, 64, 64, 1, 64, 64, 64, 0, 0, 0, 64, 64, 0, 0, 0, + 0, 64, 0, 64, 0, 64, 0, 0, 64, 0, 64, 0, 64, 0, 0, 64, + 0, 64, 64, 64, 0, 64, 0, 0, 64, 0, 0, 64, 64, 0, 0, 0, + 64, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, + 1, 65, 65, 65, 1, 1, 1, 1, 65, 65, 65, 65, 65, 65, 65, 65, + 65, 65, 65, 1, 1, 65, 1, 1, 1, 1, 1, 1, 1, 65, 65, 1, + 1, 64, 64, 64, 0, 64, 0, 64, 0, 64, 0, 0, 64, 64, 64, 0, + 0, 64, 0, 64, 0, 0, 64, 64, 0, 64, 64, 0, 0, 64, 64, 0, + 64, 0, 0, 64, 0, 0, 64, 0, 64, 64, 0, 64, 0, 64, 0, 64, + 64, 0, 64, 0, 64, 0, 64, 0, 64, 0, + }; From ee98603fe7437388f56ffef813c146f73d9d63c7 Mon Sep 17 00:00:00 2001 From: fp64 <106717720+fp64@users.noreply.github.com> Date: Sun, 19 Feb 2023 02:30:17 -0500 Subject: [PATCH 09/14] Fix the sign of cos(2*n+1) Also fix the license text. --- Core/MIPS/MIPSVFPUUtils.cpp | 3 +-- Core/MIPS/vfpu_sin_lut.h | 2 +- 2 files changed, 2 insertions(+), 3 deletions(-) diff --git a/Core/MIPS/MIPSVFPUUtils.cpp b/Core/MIPS/MIPSVFPUUtils.cpp index e03badb91b..d6e62adb51 100644 --- a/Core/MIPS/MIPSVFPUUtils.cpp +++ b/Core/MIPS/MIPSVFPUUtils.cpp @@ -993,7 +993,6 @@ float vfpu_sin(float x) { return (sign ? -1.0f : +1.0f) * float(int32_t(ret)) * 3.7252903e-09f; // 0x1p-28f } -// WARNING: not tested. float vfpu_cos(float x) { uint32_t bits; memcpy(&bits, &x, sizeof(x)); @@ -1022,7 +1021,7 @@ float vfpu_cos(float x) { } sign ^= ((significand << 7) & 0x80000000u); significand &= 0x00FFFFFFu; - if(significand > 0x00800000u) { + if(significand >= 0x00800000u) { significand = 0x01000000u - significand; sign ^= 0x80000000u; } diff --git a/Core/MIPS/vfpu_sin_lut.h b/Core/MIPS/vfpu_sin_lut.h index d2bec30211..ba891c86ab 100644 --- a/Core/MIPS/vfpu_sin_lut.h +++ b/Core/MIPS/vfpu_sin_lut.h @@ -1,4 +1,4 @@ -// Copyright (c) 2012- PPSSPP Project. +// Copyright (c) 2023- PPSSPP Project. // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by From 67bb17eba3f677ad16124934d59a4b7f02c8c67e Mon Sep 17 00:00:00 2001 From: fp64 <106717720+fp64@users.noreply.github.com> Date: Thu, 9 Mar 2023 23:23:33 -0500 Subject: [PATCH 10/14] Add more vfpu_*, move tables to assets --- Core/MIPS/MIPSIntVFPU.cpp | 18 +- Core/MIPS/MIPSVFPUUtils.cpp | 547 +- Core/MIPS/MIPSVFPUUtils.h | 10 +- Core/MIPS/vfpu_sin_lut.h | 46687 ----------------- Core/System.cpp | 2 +- assets/vfpu/vfpu_asin_lut65536.dat | Bin 0 -> 1536 bytes assets/vfpu/vfpu_asin_lut_deltas.dat | Bin 0 -> 517448 bytes assets/vfpu/vfpu_asin_lut_indices.dat | Bin 0 -> 798916 bytes assets/vfpu/vfpu_exp2_lut.dat | 4 + assets/vfpu/vfpu_exp2_lut65536.dat | Bin 0 -> 512 bytes assets/vfpu/vfpu_log2_lut.dat | 22 + assets/vfpu/vfpu_log2_lut65536.dat | Bin 0 -> 516 bytes assets/vfpu/vfpu_log2_lut65536_quadratic.dat | Bin 0 -> 512 bytes assets/vfpu/vfpu_rcp_lut.dat | Bin 0 -> 262144 bytes assets/vfpu/vfpu_rsqrt_lut.dat | Bin 0 -> 262144 bytes assets/vfpu/vfpu_sin_lut8192.dat | Bin 0 -> 4100 bytes assets/vfpu/vfpu_sin_lut_delta.dat | Bin 0 -> 262144 bytes assets/vfpu/vfpu_sin_lut_exceptions.dat | Bin 0 -> 86938 bytes assets/vfpu/vfpu_sin_lut_interval_delta.dat | Bin 0 -> 131074 bytes assets/vfpu/vfpu_sqrt_lut.dat | Bin 0 -> 262144 bytes unittest/JitHarness.cpp | 2 +- unittest/UnitTest.cpp | 2 +- 22 files changed, 476 insertions(+), 46818 deletions(-) delete mode 100644 Core/MIPS/vfpu_sin_lut.h create mode 100644 assets/vfpu/vfpu_asin_lut65536.dat create mode 100644 assets/vfpu/vfpu_asin_lut_deltas.dat create mode 100644 assets/vfpu/vfpu_asin_lut_indices.dat create mode 100644 assets/vfpu/vfpu_exp2_lut.dat create mode 100644 assets/vfpu/vfpu_exp2_lut65536.dat create mode 100644 assets/vfpu/vfpu_log2_lut.dat create mode 100644 assets/vfpu/vfpu_log2_lut65536.dat create mode 100644 assets/vfpu/vfpu_log2_lut65536_quadratic.dat create mode 100644 assets/vfpu/vfpu_rcp_lut.dat create mode 100644 assets/vfpu/vfpu_rsqrt_lut.dat create mode 100644 assets/vfpu/vfpu_sin_lut8192.dat create mode 100644 assets/vfpu/vfpu_sin_lut_delta.dat create mode 100644 assets/vfpu/vfpu_sin_lut_exceptions.dat create mode 100644 assets/vfpu/vfpu_sin_lut_interval_delta.dat create mode 100644 assets/vfpu/vfpu_sqrt_lut.dat diff --git a/Core/MIPS/MIPSIntVFPU.cpp b/Core/MIPS/MIPSIntVFPU.cpp index b8bbe25caf..c6585f21f2 100644 --- a/Core/MIPS/MIPSIntVFPU.cpp +++ b/Core/MIPS/MIPSIntVFPU.cpp @@ -629,18 +629,24 @@ namespace MIPSInt // vsat0 changes -0.0 to +0.0, both retain NAN. case 4: if (s[i] <= 0) d[i] = 0; else {if(s[i] > 1.0f) d[i] = 1.0f; else d[i] = s[i];} break; // vsat0 case 5: if (s[i] < -1.0f) d[i] = -1.0f; else {if(s[i] > 1.0f) d[i] = 1.0f; else d[i] = s[i];} break; // vsat1 - case 16: d[i] = 1.0f / s[i]; break; //vrcp + //case 16: d[i] = 1.0f / s[i]; break; //vrcp + case 16: { d[i] = vfpu_rcp(s[i]); } break; //vrcp case 17: d[i] = USE_VFPU_SQRT ? vfpu_rsqrt(s[i]) : 1.0f / sqrtf(s[i]); break; //vrsq case 18: { d[i] = vfpu_sin(s[i]); } break; //vsin case 19: { d[i] = vfpu_cos(s[i]); } break; //vcos - case 20: d[i] = powf(2.0f, s[i]); break; //vexp2 - case 21: d[i] = logf(s[i])/log(2.0f); break; //vlog2 + //case 20: d[i] = powf(2.0f, s[i]); break; //vexp2 + case 20: { d[i] = vfpu_exp2(s[i]); } break; //vexp2 + //case 21: d[i] = logf(s[i])/log(2.0f); break; //vlog2 + case 21: { d[i] = vfpu_log2(s[i]); } break; //vlog2 case 22: d[i] = USE_VFPU_SQRT ? vfpu_sqrt(s[i]) : fabsf(sqrtf(s[i])); break; //vsqrt - case 23: d[i] = (float)(asinf(s[i]) / M_PI_2); break; //vasin - case 24: d[i] = -1.0f / s[i]; break; // vnrcp + //case 23: d[i] = (float)(asinf(s[i]) / M_PI_2); break; //vasin + case 23: { d[i] = vfpu_asin(s[i]); } break; //vasin + //case 24: d[i] = -1.0f / s[i]; break; // vnrcp + case 24: { d[i] = -vfpu_rcp(s[i]); } break; // vnrcp case 26: { d[i] = -vfpu_sin(s[i]); } break; // vnsin - case 28: d[i] = 1.0f / powf(2.0, s[i]); break; // vrexp2 + //case 28: d[i] = 1.0f / powf(2.0, s[i]); break; // vrexp2 + case 28: { d[i] = vfpu_rexp2(s[i]); } break; // vrexp2 default: _dbg_assert_msg_( false, "Invalid VV2Op op type %d", optype); break; diff --git a/Core/MIPS/MIPSVFPUUtils.cpp b/Core/MIPS/MIPSVFPUUtils.cpp index d6e62adb51..e97a476d78 100644 --- a/Core/MIPS/MIPSVFPUUtils.cpp +++ b/Core/MIPS/MIPSVFPUUtils.cpp @@ -22,6 +22,7 @@ #include "Common/BitScan.h" #include "Common/CommonFuncs.h" +#include "Common/File/VFS/VFS.h" #include "Core/Reporting.h" #include "Core/MIPS/MIPS.h" #include "Core/MIPS/MIPSVFPUUtils.h" @@ -791,134 +792,47 @@ float vfpu_dot(const float a[4], const float b[4]) { return result.f; } -// TODO: This is still not completely accurate compared to the PSP's vsqrt. -float vfpu_sqrt(float a) { - float2int val; - val.f = a; - - if ((val.i & 0xff800000) == 0x7f800000) { - if ((val.i & 0x007fffff) != 0) { - val.i = 0x7f800001; - } - return val.f; - } - if ((val.i & 0x7f800000) == 0) { - // Kill any sign. - val.i = 0; - return val.f; - } - if (val.i & 0x80000000) { - val.i = 0x7f800001; - return val.f; - } - - int k = get_exp(val.i); - uint32_t sp = get_mant(val.i); - int less_bits = k & 1; - k >>= 1; - - uint32_t z = 0x00C00000 >> less_bits; - int64_t halfsp = sp >> 1; - halfsp <<= 23 - less_bits; - for (int i = 0; i < 6; ++i) { - z = (z >> 1) + (uint32_t)(halfsp / z); - } - - val.i = ((k + 127) << 23) | ((z << less_bits) & 0x007FFFFF); - // The lower two bits never end up set on the PSP, it seems like. - val.i &= 0xFFFFFFFC; - - return val.f; -} - -static inline uint32_t mant_mul(uint32_t a, uint32_t b) { - uint64_t m = (uint64_t)a * (uint64_t)b; - if (m & 0x007FFFFF) { - m += 0x01437000; - } - return (uint32_t)(m >> 23); -} - -float vfpu_rsqrt(float a) { - float2int val; - val.f = a; - - if (val.i == 0x7f800000) { - return 0.0f; - } - if ((val.i & 0x7fffffff) > 0x7f800000) { - val.i = (val.i & 0x80000000) | 0x7f800001; - return val.f; - } - if ((val.i & 0x7f800000) == 0) { - val.i = (val.i & 0x80000000) | 0x7f800000; - return val.f; - } - if (val.i & 0x80000000) { - val.i = 0xff800001; - return val.f; - } - - int k = get_exp(val.i); - uint32_t sp = get_mant(val.i); - int less_bits = k & 1; - k = -(k >> 1); - - uint32_t z = 0x00800000 >> less_bits; - uint32_t halfsp = sp >> (1 + less_bits); - for (int i = 0; i < 6; ++i) { - uint32_t zsq = mant_mul(z, z); - uint32_t correction = 0x00C00000 - mant_mul(halfsp, zsq); - z = mant_mul(z, correction); - } - - int8_t shift = (int8_t)clz32_nonzero(z) - 8 + less_bits; - if (shift < 1) { - z >>= -shift; - k += -shift; - } else if (shift > 0) { - z <<= shift; - k -= shift; - } - - z >>= less_bits; - - val.i = ((k + 127) << 23) | (z & 0x007FFFFF); - val.i &= 0xFFFFFFFC; - - return val.f; -} - //============================================================================== // The code below attempts to exactly match the output of -// PSP's sin and cos instructions. For the sake of -// making lookup tables smaller (473KB) the code is +// several PSP's VFPU functions. For the sake of +// making lookup tables smaller the code is // somewhat gnarly. -// The key observation is that (ignoring range -// reduction) PSP effectively converts input to 9.23 -// fixed-point, and that output is always representable -// as 4.28 fixed-point (though that is probably not -// what is going on internally). -// The rest is mostly trying to obtain the same result -// with smaller tables (pretty ad-hoc, and almost certainly -// does not match what PSP does internally). -// Lookup tables store deltas from (explicitly computable) -// estimations, to allow to store them in smaller types: -// int8 and int16. +// Lookup tables sometimes store deltas from (explicitly computable) +// estimations, to allow to store them in smaller types. // See https://github.com/hrydgard/ppsspp/issues/16946 for details. -#include "Core/MIPS/vfpu_sin_lut.h" +static uint32_t (*vfpu_sin_lut8192)=nullptr; +static int8_t (*vfpu_sin_lut_delta)[2]=nullptr; +static int16_t (*vfpu_sin_lut_interval_delta)=nullptr; +static uint8_t (*vfpu_sin_lut_exceptions)=nullptr; + +static int8_t (*vfpu_sqrt_lut)[2]=nullptr; + +static int8_t (*vfpu_rsqrt_lut)[2]=nullptr; + +static uint32_t (*vfpu_exp2_lut65536)=nullptr; +static uint8_t (*vfpu_exp2_lut)[2]=nullptr; + +static uint32_t (*vfpu_log2_lut65536)=nullptr; +static uint32_t (*vfpu_log2_lut65536_quadratic)=nullptr; +static uint8_t (*vfpu_log2_lut)[131072][2]=nullptr; + +static int32_t (*vfpu_asin_lut65536)[3]=nullptr; +static uint64_t (*vfpu_asin_lut_deltas)=nullptr; +static uint16_t (*vfpu_asin_lut_indices)=nullptr; + +static int8_t (*vfpu_rcp_lut)[2]=nullptr; // Note: PSP sin/cos output only has 22 significant // binary digits. -static inline uint32_t quantum(uint32_t x) { +static inline uint32_t vfpu_sin_quantum(uint32_t x) { return x < 1u << 22? 1u: 1u << (32 - 22 - clz32_nonzero(x)); } -static inline uint32_t truncate_bits(u32 x) { - return x & -quantum(x); +static inline uint32_t vfpu_sin_truncate_bits(u32 x) { + return x & -vfpu_sin_quantum(x); } static inline uint32_t vfpu_sin_fixed(uint32_t arg) { @@ -932,11 +846,11 @@ static inline uint32_t vfpu_sin_fixed(uint32_t arg) { uint32_t A = L+(((H - L)*(((arg >> 6) & 127) + 0)) >> 7); uint32_t B = L+(((H - L)*(((arg >> 6) & 127) + 1)) >> 7); // Adjust endpoints from deltas, and increase working precision. - uint64_t a = (uint64_t(A) << 5) + uint64_t(vfpu_sin_lut_delta[arg >> 6][0]) * quantum(A); - uint64_t b = (uint64_t(B) << 5) + uint64_t(vfpu_sin_lut_delta[arg >> 6][1]) * quantum(B); + uint64_t a = (uint64_t(A) << 5) + uint64_t(vfpu_sin_lut_delta[arg >> 6][0]) * vfpu_sin_quantum(A); + uint64_t b = (uint64_t(B) << 5) + uint64_t(vfpu_sin_lut_delta[arg >> 6][1]) * vfpu_sin_quantum(B); // Compute approximation via lerp. Is off by at most 1 quantum. uint32_t v = uint32_t(((a * (64 - (arg & 63)) + b * (arg & 63)) >> 6) >> 5); - v=truncate_bits(v); + v=vfpu_sin_truncate_bits(v); // Look up exceptions via binary search. // Note: vfpu_sin_lut_interval_delta stores // deltas from interval estimation. @@ -952,7 +866,7 @@ static inline uint32_t vfpu_sin_fixed(uint32_t arg) { uint32_t b = vfpu_sin_lut_exceptions[m]; uint32_t e = (arg & -128u)+(b & 127u); if(e == arg) { - v += quantum(v) * (b >> 7 ? -1u : +1u); + v += vfpu_sin_quantum(v) * (b >> 7 ? -1u : +1u); break; } else if(e < arg) lo = m + 1; @@ -1036,8 +950,399 @@ void vfpu_sincos(float a, float &s, float &c) { c = vfpu_cos(a); } +// Integer square root of 2^23*x (rounded to zero). +// Input is in 2^23 <= x < 2^25, and representable in float. +static inline uint32_t isqrt23(uint32_t x) { +#if 0 + // Reference version. + int dir=fesetround(FE_TOWARDZERO); + uint32_t ret=uint32_t(int32_t(sqrtf(float(int32_t(x)) * 8388608.0f))); + fesetround(dir); + return ret; +#elif 1 + // Double version. + // Verified to produce correct result for all valid inputs, + // in all rounding modes, both in double and double-extended (x87) + // precision. + // Requires correctly-rounded sqrt (which on any IEEE-754 system + // it should be). + return uint32_t(int32_t(sqrt(double(x) * 8388608.0))); +#else + // Pure integer version, if you don't like floating point. + // Based on code from Hacker's Delight. See isqrt4 in + // https://github.com/hcs0/Hackers-Delight/blob/master/isqrt.c.txt + // Relatively slow. + uint64_t t=uint64_t(x) << 23, m, y, b; + m=0x4000000000000000ull; + y=0; + while(m != 0) // Do 32 times. + { + b=y | m; + y=y >> 1; + if(t >= b) + { + t = t - b; + y = y | m; + } + m = m >> 2; + } + return y; +#endif +} + +// Returns floating-point bitpattern. +static inline uint32_t vfpu_sqrt_fixed(uint32_t x) { + // Endpoints of input. + uint32_t lo =(x + 0u) & -64u; + uint32_t hi = (x + 64u) & -64u; + // Convert input to 9.23 fixed-point. + lo = (lo >= 0x00400000u ? 4u * lo : 0x00800000u + 2u * lo); + hi = (hi >= 0x00400000u ? 4u * hi : 0x00800000u + 2u * hi); + // Estimate endpoints of output. + uint32_t A = 0x3F000000u + isqrt23(lo); + uint32_t B = 0x3F000000u + isqrt23(hi); + // Apply deltas, and increase the working precision. + uint64_t a = (uint64_t(A) << 4) + uint64_t(vfpu_sqrt_lut[x >> 6][0]); + uint64_t b = (uint64_t(B) << 4) + uint64_t(vfpu_sqrt_lut[x >> 6][1]); + uint32_t ret = uint32_t((a + (((b - a) * (x & 63)) >> 6)) >> 4); + // Truncate lower 2 bits. + ret &= -4u; + return ret; +} + +float vfpu_sqrt(float x) { + uint32_t bits; + memcpy(&bits, &x, sizeof(bits)); + if((bits & 0x7FFFFFFFu) <= 0x007FFFFFu) { + // Denormals (and zeroes) get +0, regardless + // of sign. + return +0.0f; + } + if(bits >> 31) { + // Other negatives get NaN. + bits = 0x7F800001u; + memcpy(&x, &bits, sizeof(x)); + return x; + } + if((bits >> 23) == 255u) { + // Inf/NaN gets Inf/NaN. + bits = 0x7F800000u + ((bits & 0x007FFFFFu) != 0u); + memcpy(&x, &bits, sizeof(bits)); + return x; + } + int32_t exponent = int32_t(bits >> 23) - 127; + // Bottom bit of exponent (inverted) + significand (except bottom bit). + uint32_t index = ((bits + 0x00800000u) >> 1) & 0x007FFFFFu; + bits = vfpu_sqrt_fixed(index); + bits += uint32_t(exponent >> 1) << 23; + memcpy(&x, &bits, sizeof(bits)); + return x; +} + +// Returns floor(2^33/sqrt(x)), for 2^22 <= x < 2^24. +static inline uint32_t rsqrt_floor22(uint32_t x) { +#if 1 + // Verified correct in all rounding directions, + // by exhaustive search. + return uint32_t(8589934592.0 / sqrt(double(x))); // 0x1p33 +#else + // Pure integer version, if you don't like floating point. + // Based on code from Hacker's Delight. See isqrt4 in + // https://github.com/hcs0/Hackers-Delight/blob/master/isqrt.c.txt + // Relatively slow. + uint64_t t=uint64_t(x) << 22, m, y, b; + m = 0x4000000000000000ull; + y = 0; + while(m != 0) // Do 32 times. + { + b = y | m; + y = y >> 1; + if(t >= b) + { + t = t - b; + y = y | m; + } + m = m >> 2; + } + y = (1ull << 44) / y; + // Decrement if y > floor(2^33 / sqrt(x)). + // This hack works because exhaustive + // search (on [2^22;2^24]) says it does. + if((y * y >> 3) * x > (1ull << 63) - 3ull * (((y & 7) == 6) << 21)) --y; + return uint32_t(y); +#endif +} + +// Returns floating-point bitpattern. +static inline uint32_t vfpu_rsqrt_fixed(uint32_t x) { + // Endpoints of input. + uint32_t lo = (x + 0u) & -64u; + uint32_t hi = (x + 64u) & -64u; + // Convert input to 10.22 fixed-point. + lo = (lo >= 0x00400000u ? 2u * lo : 0x00400000u + lo); + hi = (hi >= 0x00400000u ? 2u * hi : 0x00400000u + hi); + // Estimate endpoints of output. + uint32_t A = 0x3E800000u + 4u * rsqrt_floor22(lo); + uint32_t B = 0x3E800000u + 4u * rsqrt_floor22(hi); + // Apply deltas, and increase the working precision. + uint64_t a = (uint64_t(A) << 4) + uint64_t(vfpu_rsqrt_lut[x >> 6][0]); + uint64_t b = (uint64_t(B) << 4) + uint64_t(vfpu_rsqrt_lut[x >> 6][1]); + // Evaluate via lerp. + uint32_t ret = uint32_t((a + (((b - a) * (x & 63)) >> 6)) >> 4); + // Truncate lower 2 bits. + ret &= -4u; + return ret; +} + +float vfpu_rsqrt(float x) { + uint32_t bits; + memcpy(&bits, &x, sizeof(bits)); + if((bits & 0x7FFFFFFFu) <= 0x007FFFFFu) { + // Denormals (and zeroes) get Inf of the same sign. + bits = 0x7F800000u | (bits & 0x80000000u); + memcpy(&x, &bits, sizeof(x)); + return x; + } + if(bits >> 31) { + // Other negatives get negative NaN. + bits = 0xFF800001u; + memcpy(&x, &bits, sizeof(x)); + return x; + } + if((bits >> 23) == 255u) { + // Inf gets 0, NaN gets NaN. + bits = ((bits & 0x007FFFFFu) ? 0x7F800001u : 0u); + memcpy(&x, &bits, sizeof(bits)); + return x; + } + int32_t exponent = int32_t(bits >> 23) - 127; + // Bottom bit of exponent (inverted) + significand (except bottom bit). + uint32_t index = ((bits + 0x00800000u) >> 1) & 0x007FFFFFu; + bits = vfpu_rsqrt_fixed(index); + bits -= uint32_t(exponent >> 1) << 23; + memcpy(&x, &bits, sizeof(bits)); + return x; +} + +static inline uint32_t vfpu_asin_quantum(uint32_t x) { + return x<1u<<23? + 1u: + 1u<<(32-23-clz32_nonzero(x)); +} + +static inline uint32_t vfpu_asin_truncate_bits(uint32_t x) { + return x & -vfpu_asin_quantum(x); +} + +// Input is fixed 9.23, output is fixed 2.30. +static inline uint32_t vfpu_asin_approx(uint32_t x) { + const int32_t *C = vfpu_asin_lut65536[x >> 16]; + x &= 0xFFFFu; + return vfpu_asin_truncate_bits(uint32_t((((((int64_t(C[2]) * x) >> 16) + int64_t(C[1])) * x) >> 16) + C[0])); +} + +// Input is fixed 9.23, output is fixed 2.30. +static uint32_t vfpu_asin_fixed(uint32_t x) { + if(x == 0u) return 0u; + if(x == 1u << 23) return 1u << 30; + uint32_t ret = vfpu_asin_approx(x); + uint32_t index = vfpu_asin_lut_indices[x / 21u]; + uint64_t deltas = vfpu_asin_lut_deltas[index]; + return ret + (3u - uint32_t((deltas >> (3u * (x % 21u))) & 7u)) * vfpu_asin_quantum(ret); +} + +float vfpu_asin(float x) { + uint32_t bits; + memcpy(&bits, &x, sizeof(x)); + uint32_t sign = bits & 0x80000000u; + bits = bits & 0x7FFFFFFFu; + if(bits > 0x3F800000u) { + bits = 0x7F800001u ^ sign; + memcpy(&x, &bits, sizeof(x)); + return x; + } + + bits = vfpu_asin_fixed(uint32_t(int32_t(fabsf(x) * 8388608.0f))); // 0x1p23 + x=float(int32_t(bits)) * 9.31322574615478515625e-10f; // 0x1p-30 + if(sign) x = -x; + return x; +} + +static inline uint32_t vfpu_exp2_approx(uint32_t x) { + if(x == 0x00800000u) return 0x00800000u; + uint32_t a=vfpu_exp2_lut65536[x >> 16]; + x &= 0x0000FFFFu; + uint32_t b = uint32_t(((2977151143ull * x) >> 23) + ((1032119999ull * (x * x)) >> 46)); + return (a + uint32_t((uint64_t(a + (1u << 23)) * uint64_t(b)) >> 32)) & -4u; +} + +static inline uint32_t vfpu_exp2_fixed(uint32_t x) { + if(x == 0u) return 0u; + if(x == 0x00800000u) return 0x00800000u; + uint32_t A = vfpu_exp2_approx((x ) & -64u); + uint32_t B = vfpu_exp2_approx((x + 64) & -64u); + uint64_t a = (A<<4)+vfpu_exp2_lut[x >> 6][0]-64u; + uint64_t b = (B<<4)+vfpu_exp2_lut[x >> 6][1]-64u; + uint32_t y = uint32_t((a + (((b - a) * (x & 63)) >> 6)) >> 4); + y &= -4u; + return y; +} + +float vfpu_exp2(float x) { + int32_t bits; + memcpy(&bits, &x, sizeof(bits)); + if((bits & 0x7FFFFFFF) <= 0x007FFFFF) { + // Denormals are treated as 0. + return 1.0f; + } + if(x != x) { + // NaN gets NaN. + bits = 0x7F800001u; + memcpy(&x, &bits, sizeof(x)); + return x; + } + if(x <= -126.0f) { + // Small numbers get 0 (exp2(-126) is smallest positive non-denormal). + // But yes, -126.0f produces +0.0f. + return 0.0f; + } + if(x >= +128.0f) { + // Large numbers get infinity. + bits = 0x7F800000u; + memcpy(&x, &bits, sizeof(x)); + return x; + } + bits = int32_t(x * 0x1p23f); + if(x < 0.0f) --bits; // Yes, really. + bits = int32_t(0x3F800000) + (bits & int32_t(0xFF800000)) + int32_t(vfpu_exp2_fixed(bits & int32_t(0x007FFFFF))); + memcpy(&x, &bits, sizeof(bits)); + return x; +} + +float vfpu_rexp2(float x) { + return vfpu_exp2(-x); +} + +// Input fixed 9.23, output fixed 10.22. +// Returns log2(1+x). +static inline uint32_t vfpu_log2_approx(uint32_t x) { + uint32_t a=vfpu_log2_lut65536[(x >> 16) + 0]; + uint32_t b=vfpu_log2_lut65536[(x >> 16) + 1]; + uint32_t c=vfpu_log2_lut65536_quadratic[x >> 16]; + x &= 0xFFFFu; + uint64_t ret = uint64_t(a) * (0x10000u - x) + uint64_t(b) * x; + uint64_t d = (uint64_t(c) * x * (0x10000u-x)) >> 40; + ret += d; + return uint32_t(ret >> 16); +} + +// Matches PSP output on all known values. +float vfpu_log2(float x) { + uint32_t bits; + memcpy(&bits, &x, sizeof(bits)); + if((bits & 0x7FFFFFFFu) <= 0x007FFFFFu) { + // Denormals (and zeroes) get -inf. + bits = 0xFF800000u; + memcpy(&x, &bits, sizeof(x)); + return x; + } + if(bits & 0x80000000u) { + // Other negatives get NaN. + bits = 0x7F800001u; + memcpy(&x, &bits, sizeof(x)); + return x; + } + if((bits >> 23) == 255u) { + // NaN gets NaN, +inf gets +inf. + bits = 0x7F800000u + ((bits & 0x007FFFFFu) != 0); + memcpy(&x, &bits, sizeof(x)); + return x; + } + uint32_t e = (bits & 0x7F800000u) - 0x3F800000u; + uint32_t i = bits & 0x007FFFFFu; + if(e >> 31 && i >= 0x007FFE00u) { + // Process 1-2^{-14}<=x*2^n<1 (for n>0) separately, + // since the table doesn't give the right answer. + float c = float(int32_t(~e) >> 23); + // Note: if c is 0 the sign of -0 output is correct. + return i < 0x007FFEF7u ? // 1-265*2^{-24} + -3.05175781e-05f - c: + -0.0f - c; + } + int d = (e<0x01000000u ? 0 : 8 - clz32_nonzero(e) - int(e >> 31)); + //assert(d>=0&&d<8); + uint32_t q = 1u << d; + uint32_t A = vfpu_log2_approx((i ) & -64u) & -q; + uint32_t B = vfpu_log2_approx((i + 64) & -64u) & -q; + uint64_t a = (A << 6)+(uint64_t(vfpu_log2_lut[d][i >> 6][0]) - 80ull) * q; + uint64_t b = (B << 6)+(uint64_t(vfpu_log2_lut[d][i >> 6][1]) - 80ull) * q; + uint32_t v = uint32_t((a +(((b - a) * (i & 63)) >> 6)) >> 6); + v &= -q; + bits = e ^ (2u * v); + x = float(int32_t(bits)) * 1.1920928955e-7f; // 0x1p-23f + return x; +} + +static inline uint32_t vfpu_rcp_approx(uint32_t i) { + return 0x3E800000u + (uint32_t((1ull << 47) / ((1ull << 23) + i)) & -4u); +} + +float vfpu_rcp(float x) { + uint32_t bits; + memcpy(&bits, &x, sizeof(bits)); + uint32_t s = bits & 0x80000000u; + uint32_t e = bits & 0x7F800000u; + uint32_t i = bits & 0x007FFFFFu; + if((bits & 0x7FFFFFFFu) > 0x7E800000u) { + bits = (e == 0x7F800000u && i ? s ^ 0x7F800001u : s); + memcpy(&x, &bits, sizeof(x)); + return x; + } + if(e==0u) { + bits = s^0x7F800000u; + memcpy(&x, &bits, sizeof(x)); + return x; + } + uint32_t A = vfpu_rcp_approx((i ) & -64u); + uint32_t B = vfpu_rcp_approx((i + 64) & -64u); + uint64_t a = (uint64_t(A) << 6) + uint64_t(vfpu_rcp_lut[i >> 6][0]) * 4u; + uint64_t b = (uint64_t(B) << 6) + uint64_t(vfpu_rcp_lut[i >> 6][1]) * 4u; + uint32_t v = uint32_t((a+(((b-a)*(i&63))>>6))>>6); + v &= -4u; + bits = s + (0x3F800000u - e) + v; + memcpy(&x, &bits, sizeof(x)); + return x; +} + //============================================================================== -void InitVFPUSinCos() { - // TODO: Could prepare a CORDIC table here. +void InitVFPU() { +// WARNING: this is not endian-safe! + size_t size=0; +#define LOAD(expected,name)\ + if(!name) {\ + const char *filename = "vfpu/" #name ".dat";\ + INFO_LOG(CPU, "Loading '%s'.\n", filename);\ + name=reinterpret_cast(g_VFS.ReadFile(filename, &size));\ + if(size!=(expected))\ + ERROR_LOG(CPU, "Error loading '%s' (size=%u, expected: %u).\n", filename, (unsigned)size, (unsigned)(expected));\ + else\ + INFO_LOG(CPU, "Successfully loaded '%s'.\n", filename);\ + } + LOAD( 1536, vfpu_asin_lut65536); + LOAD( 517448, vfpu_asin_lut_deltas); + LOAD( 798916, vfpu_asin_lut_indices); + LOAD( 512, vfpu_exp2_lut65536); + LOAD( 262144, vfpu_exp2_lut); + LOAD( 516, vfpu_log2_lut65536); + LOAD( 512, vfpu_log2_lut65536_quadratic); + LOAD( 2097152, vfpu_log2_lut); + LOAD( 262144, vfpu_rcp_lut); + LOAD( 262144, vfpu_rsqrt_lut); + LOAD( 4100, vfpu_sin_lut8192); + LOAD( 262144, vfpu_sin_lut_delta); + LOAD( 86938, vfpu_sin_lut_exceptions); + LOAD( 131074, vfpu_sin_lut_interval_delta); + LOAD( 262144, vfpu_sqrt_lut); +#undef LOAD } diff --git a/Core/MIPS/MIPSVFPUUtils.h b/Core/MIPS/MIPSVFPUUtils.h index a137245e8a..a8b2bebd79 100644 --- a/Core/MIPS/MIPSVFPUUtils.h +++ b/Core/MIPS/MIPSVFPUUtils.h @@ -50,9 +50,12 @@ extern float vfpu_sin(float); extern float vfpu_cos(float); extern void vfpu_sincos(float, float&, float&); +/* inline float vfpu_asin(float angle) { return (float)(asinf(angle) / M_PI_2); } +*/ +extern float vfpu_asin(float); inline float vfpu_clamp(float v, float min, float max) { // Note: NAN is preserved, and -0.0 becomes +0.0 if min=+0.0. @@ -63,6 +66,11 @@ float vfpu_dot(const float a[4], const float b[4]); float vfpu_sqrt(float a); float vfpu_rsqrt(float a); +extern float vfpu_exp2(float); +extern float vfpu_rexp2(float); +extern float vfpu_log2(float); +extern float vfpu_rcp(float); + #define VFPU_FLOAT16_EXP_MAX 0x1f #define VFPU_SH_FLOAT16_SIGN 15 #define VFPU_MASK_FLOAT16_SIGN 0x1 @@ -211,4 +219,4 @@ int GetVectorOverlap(int reg1, VectorSize size1, int reg2, VectorSize size2); bool GetVFPUCtrlMask(int reg, u32 *mask); float Float16ToFloat32(unsigned short l); -void InitVFPUSinCos(); +void InitVFPU(); diff --git a/Core/MIPS/vfpu_sin_lut.h b/Core/MIPS/vfpu_sin_lut.h deleted file mode 100644 index ba891c86ab..0000000000 --- a/Core/MIPS/vfpu_sin_lut.h +++ /dev/null @@ -1,46687 +0,0 @@ -// Copyright (c) 2023- PPSSPP Project. - -// This program is free software: you can redistribute it and/or modify -// it under the terms of the GNU General Public License as published by -// the Free Software Foundation, version 2.0 or later versions. - -// This program is distributed in the hope that it will be useful, -// but WITHOUT ANY WARRANTY; without even the implied warranty of -// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -// GNU General Public License 2.0 for more details. - -// A copy of the GPL 2.0 should have been included with the program. -// If not, see http://www.gnu.org/licenses/ - -// Official git repository and contact information can be found at -// https://github.com/hrydgard/ppsspp and http://www.ppsspp.org/. - -//============================================================================== -// WARNING: this is partially automatically generated, -// and only meant to be included inside Core/MIPS/MIPSVFPUUtils.cpp, -// so no header guards. - -static uint32_t vfpu_sin_lut8192[1025]={ - 0, 411778, 823552, 1235322, - 1647089, 2058851, 2470610, 2882365, - 3294116, 3705858, 4117590, 4529310, - 4941018, 5352714, 5764400, 6176074, - 6587736, 6999380, 7411008, 7822616, - 8234204, 8645772, 9057324, 9468852, - 9880364, 10291848, 10703312, 11114744, - 11526152, 11937528, 12348880, 12760204, - 13171504, 13582768, 13994000, 14405196, - 14816360, 15227488, 15638580, 16049636, - 16460660, 16871640, 17282584, 17693480, - 18104336, 18515152, 18925920, 19336648, - 19747336, 20157976, 20568560, 20979104, - 21389592, 21800024, 22210416, 22620752, - 23031040, 23441264, 23851440, 24261560, - 24671616, 25081616, 25491560, 25901448, - 26311272, 26721040, 27130736, 27540368, - 27949936, 28359440, 28768872, 29178240, - 29587544, 29996776, 30405944, 30815024, - 31224040, 31632984, 32041848, 32450640, - 32859360, 33268000, 33676560, 34085040, - 34493440, 34901760, 35310000, 35718144, - 36126224, 36534208, 36942112, 37349920, - 37757648, 38165280, 38572832, 38980288, - 39387648, 39794928, 40202112, 40609184, - 41016176, 41423072, 41829856, 42236544, - 42643152, 43049648, 43456048, 43862336, - 44268528, 44674608, 45080576, 45486448, - 45892224, 46297888, 46703440, 47108880, - 47514208, 47919424, 48324528, 48729504, - 49134384, 49539152, 49943792, 50348320, - 50752720, 51157008, 51561168, 51965216, - 52369152, 52772960, 53176640, 53580192, - 53983616, 54386896, 54790064, 55193120, - 55596032, 55998816, 56401456, 56803984, - 57206368, 57608608, 58010720, 58412688, - 58814528, 59216240, 59617808, 60019216, - 60420496, 60821632, 61222624, 61623472, - 62024176, 62424752, 62825168, 63225424, - 63625536, 64025504, 64425312, 64824976, - 65224496, 65623840, 66023040, 66422080, - 66820992, 67219712, 67618272, 68016704, - 68414976, 68813056, 69211008, 69608768, - 70006368, 70403808, 70801088, 71198176, - 71595136, 71991936, 72388544, 72784960, - 73181216, 73577312, 73973216, 74368960, - 74764544, 75159936, 75555168, 75950208, - 76345056, 76739712, 77134240, 77528544, - 77922688, 78316640, 78710432, 79104000, - 79497408, 79890592, 80283616, 80676448, - 81069088, 81461536, 81853792, 82245856, - 82637760, 83029408, 83420896, 83812192, - 84203296, 84594176, 84984896, 85375360, - 85765664, 86155744, 86545632, 86935328, - 87324800, 87714080, 88103136, 88492000, - 88880672, 89269088, 89657344, 90045344, - 90433184, 90820768, 91208160, 91595328, - 91982272, 92368992, 92755520, 93141824, - 93527904, 93913792, 94299424, 94684832, - 95070048, 95455008, 95839744, 96224288, - 96608576, 96992640, 97376480, 97760096, - 98143488, 98526624, 98909536, 99292224, - 99674688,100056928,100438880,100820640, -101202144,101583424,101964448,102345216, -102725792,103106080,103486176,103865984, -104245568,104624896,105003968,105382816, -105761408,106139776,106517856,106895712, -107273280,107650624,108027712,108404544, -108781120,109157440,109533504,109909312, -110284864,110660128,111035168,111409920, -111784448,112158688,112532672,112906368, -113279808,113652992,114025888,114398560, -114770944,115143040,115514880,115886432, -116257728,116628736,116999488,117369952, -117740128,118110048,118479680,118849024, -119218112,119586912,119955424,120323648, -120691616,121059264,121426656,121793760, -122160576,122527072,122893312,123259264, -123624896,123990272,124355328,124720128, -125084608,125448768,125812672,126176288, -126539584,126902592,127265312,127627712, -127989792,128351616,128713120,129074304, -129435200,129795808,130156096,130516064, -130875744,131235104,131594144,131952896, -132311328,132669440,133027264,133384768, -133741952,134098816,134455360,134811584, -135167552,135523136,135878400,136233408, -136588032,136942336,137296320,137650048, -138003392,138356416,138709120,139061504, -139413568,139765248,140116672,140467712, -140818432,141168832,141518912,141868672, -142218048,142567104,142915840,143264256, -143612288,143960000,144307392,144654464, -145001152,145347520,145693504,146039168, -146384512,146729536,147074176,147418496, -147762432,148105984,148449280,148792192, -149134720,149476928,149818752,150160256, -150501440,150842176,151182656,151522688, -151862464,152201792,152540864,152879488, -153217792,153555648,153893248,154230464, -154567296,154903808,155239936,155575680, -155911040,156246016,156580672,156914944, -157248896,157582400,157915584,158248384, -158580800,158912832,159244544,159575872, -159906816,160237312,160567488,160897344, -161226752,161555776,161884416,162212736, -162540608,162868160,163195264,163521984, -163848384,164174336,164499904,164825088, -165149952,165474368,165798400,166122048, -166445312,166768192,167090624,167412736, -167734400,168055680,168376640,168697088, -169017216,169336896,169656192,169975104, -170293632,170611712,170929408,171246720, -171563648,171880128,172196224,172511872, -172827200,173142080,173456512,173770560, -174084224,174397440,174710272,175022720, -175334720,175646336,175957504,176268288, -176578624,176888576,177198080,177507200, -177815872,178124096,178432000,178739392, -179046400,179352960,179659136,179964864, -180270208,180575104,180879552,181183616, -181487232,181790400,182093184,182395520, -182697408,182998912,183299968,183600512, -183900736,184200448,184499776,184798656, -185097088,185395136,185692672,185989824, -186286528,186582784,186878592,187173952, -187468928,187763392,188057472,188351104, -188644288,188936960,189229248,189521088, -189812480,190103424,190393984,190684032, -190973632,191262784,191551488,191839680, -192127488,192414848,192701760,192988224, -193274176,193559680,193844800,194129408, -194413568,194697280,194980544,195263296, -195545664,195827520,196108928,196389888, -196670336,196950400,197229952,197509056, -197787712,198065856,198343552,198620736, -198897536,199173824,199449664,199724992, -199999936,200274304,200548288,200821760, -201094720,201367296,201639360,201910912, -202182016,202452672,202722816,202992448, -203261696,203530368,203798656,204066432, -204333696,204600512,204866816,205132608, -205398016,205662848,205927296,206191168, -206454592,206717504,206979968,207241920, -207503360,207764352,208024832,208284864, -208544384,208803392,209061952,209319936, -209577536,209834560,210091136,210347200, -210602816,210857856,211112448,211366528, -211620096,211873152,212125760,212377856, -212629440,212880512,213131136,213381248, -213630848,213879872,214128448,214376512, -214624128,214871168,215117760,215363776, -215609344,215854400,216098944,216342976, -216586496,216829504,217072000,217313920, -217555392,217796352,218036800,218276736, -218516224,218755072,218993472,219231360, -219468736,219705536,219941888,220177728, -220412992,220647744,220882048,221115776, -221348992,221581696,221813824,222045504, -222276608,222507200,222737280,222966848, -223195904,223424384,223652416,223879808, -224106752,224333184,224559040,224784384, -225009216,225233472,225457216,225680448, -225903168,226125312,226346944,226568064, -226788608,227008640,227228160,227447104, -227665536,227883456,228100800,228317632, -228533888,228749632,228964864,229179520, -229393664,229607232,229820288,230032768, -230244736,230456192,230667072,230877376, -231087168,231296448,231505152,231713280, -231920896,232128000,232334528,232540480, -232745920,232950784,233155136,233358912, -233562176,233764864,233966976,234168576, -234369600,234570112,234770048,234969408, -235168256,235366528,235564224,235761408, -235958016,236154048,236349568,236544512, -236738944,236932736,237126016,237318720, -237510912,237702464,237893504,238083968, -238273920,238463296,238652096,238840320, -239028032,239215104,239401664,239587648, -239773056,239957888,240142208,240325888, -240509056,240691648,240873664,241055168, -241236096,241416384,241596160,241775360, -241953984,242132032,242309504,242486400, -242662784,242838528,243013696,243188352, -243362432,243535872,243708800,243881152, -244052928,244224128,244394688,244564736, -244734208,244903104,245071424,245239104, -245406272,245572864,245738880,245904320, -246069184,246233408,246397120,246560192, -246722752,246884672,247046016,247206784, -247367040,247526656,247685696,247844096, -248001984,248159296,248315968,248472064, -248627648,248782592,248936960,249090688, -249243904,249396544,249548544,249699968, -249850816,250001088,250150720,250299840, 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-261547200,261639552,261731328,261822464, -261913024,262002944,262092224,262180864, -262268992,262356416,262443264,262529408, -262615040,262700032,262784384,262868096, -262951232,263033728,263115584,263196864, -263277504,263357504,263436928,263515712, -263593920,263671424,263748352,263824640, -263900352,263975424,264049856,264123648, -264196864,264269440,264341376,264412672, -264483456,264553536,264622976,264691840, -264760064,264827648,264894592,264960960, -265026688,265091776,265156288,265220096, -265283328,265345920,265407936,265469248, -265530048,265590144,265649600,265708480, -265766720,265824320,265881280,265937664, -265993408,266048512,266102976,266156800, -266210048,266262656,266314624,266365952, -266416704,266466752,266516224,266565056, -266613312,266660864,266707840,266754112, -266799872,266844928,266889344,266933184, -266976384,267018944,267060864,267102144, -267142848,267182912,267222272,267261056, -267299264,267336768,267373696,267409920, -267445632,267480640,267515008,267548736, -267581888,267614336,267646208,267677440, -267708096,267738048,267767424,267796160, -267824256,267851648,267878528,267904704, -267930240,267955200,267979520,268003200, -268026240,268048640,268070400,268091584, -268112064,268131968,268151232,268169856, -268187840,268205248,268221952,268238080, -268253504,268268352,268282560,268296128, -268309120,268321408,268333120,268344128, -268354560,268364352,268373504,268382080, -268389952,268397184,268403840,268409856, -268415232,268419968,268424064,268427520, -268430400,268432576,268434176,268435136, -268435456}; - -static int8_t vfpu_sin_lut_delta[131072][2]= -{ -{ 0, -3}, { -3, -6}, { -2, 0}, { -1, -4}, -{ 3, 1}, { 1, -1}, { 7, 4}, { 3, 1}, -{ 7, 8}, { 5, 3}, { 11, 8}, { 7, 7}, -{ 12, 11}, { 10, 8}, { 16, 13}, { 13, 10}, -{ 10, 6}, { 16, 12}, { 12, 10}, { 16, 15}, -{ 15, 11}, { 20, 16}, { 17, 12}, { 22, 19}, -{ 18, 16}, { 24, 22}, { 20, 18}, { 25, 24}, -{ 22, 22}, { 27, 26}, { 24, 24}, { 31, 28}, -{ 28, 25}, { 25, 21}, { 29, 28}, { 27, 25}, -{ 31, 30}, { 30, 26}, { 33, 33}, { 31, 28}, -{ 37, 34}, { 33, 32}, { 31, 28}, { 35, 33}, -{ 33, 31}, { 37, 37}, { 35, 33}, { 39, 39}, -{ 37, 35}, { 43, 40}, { 40, 37}, { 37, 35}, -{ 42, 40}, { 39, 37}, { 45, 42}, { 42, 38}, -{ 46, 45}, { 44, 42}, { 39, 40}, { 46, 43}, -{ 44, 41}, { 49, 44}, { 44, 43}, { 50, 16}, -{ 16, 13}, { 13, 10}, { 19, 14}, { 16, 12}, -{ 20, 18}, { 15, 17}, { 15, 11}, { 18, 18}, -{ 16, 15}, { 22, 19}, { 18, 16}, { 24, 22}, -{ 20, 18}, { 18, 16}, { 24, 21}, { 20, 18}, -{ 25, 24}, { 23, 20}, { 20, 17}, { 24, 24}, -{ 22, 20}, { 27, 25}, { 25, 21}, { 22, 19}, -{ 27, 22}, { 24, 22}, { 29, 26}, { 25, 24}, -{ 22, 22}, { 27, 26}, { 24, 24}, { 31, 28}, -{ 28, 25}, { 25, 21}, { 29, 28}, { 27, 25}, -{ 31, 30}, { 30, 26}, { 27, 22}, { 31, 28}, -{ 29, 26}, { 30, 32}, { 31, 28}, { 27, 26}, -{ 31, 31}, { 29, 28}, { 28, 25}, { 31, 31}, -{ 30, 26}, { 36, 31}, { 32, 29}, { 29, 26}, -{ 33, 33}, { 31, 28}, { 27, 26}, { 30, 32}, -{ 31, 28}, { 28, 25}, { 31, 31}, { 29, 28}, -{ 36, 31}, { 32, 31}, { 30, 26}, { 33, 1}, -{ 0, 29}, { 29, 26}, { 30, 32}, { 31, 28}, -{ 27, 26}, { 31, 31}, { 31, 28}, { 35, 33}, -{ 32, 31}, { 29, 28}, { 36, 31}, { 32, 29}, -{ 29, 26}, { 33, 33}, { 31, 28}, { 27, 26}, -{ 30, 32}, { 31, 28}, { 27, 26}, { 31, 31}, -{ 29, 28}, { 35, 33}, { 32, 31}, { 30, 26}, -{ 27, 22}, { 31, 30}, { 29, 26}, { 25, 24}, -{ 31, 28}, { 27, 26}, { 30, 32}, { 31, 28}, -{ 28, 25}, { 25, 21}, { 29, 28}, { 27, 25}, -{ 24, 22}, { 30, 26}, { 27, 22}, { 24, 21}, -{ 29, 26}, { 25, 24}, { 23, 20}, { 27, 26}, -{ 24, 24}, { 22, 20}, { 28, 25}, { 25, 21}, -{ 22, 19}, { 27, 25}, { 24, 22}, { 20, 18}, -{ 25, 24}, { 24, 21}, { 20, 18}, { 24, 24}, -{ 23, 20}, { 20, 17}, { 16, 15}, { 22, 20}, -{ 20, 16}, { 17, 12}, { 22, 19}, { 18, 16}, -{ 16, 45}, { 52, 50}, { 51, 46}, { 48, 44}, -{ 52, 50}, { 47, 49}, { 47, 43}, { 44, 41}, -{ 48, 47}, { 46, 43}, { 43, 40}, { 49, 44}, -{ 44, 43}, { 42, 40}, { 39, 37}, { 45, 42}, -{ 42, 38}, { 39, 36}, { 44, 42}, { 39, 40}, -{ 37, 35}, { 35, 33}, { 39, 39}, { 37, 35}, -{ 36, 31}, { 40, 37}, { 37, 34}, { 33, 33}, -{ 31, 28}, { 35, 33}, { 33, 32}, { 31, 28}, -{ 35, 33}, { 32, 31}, { 29, 28}, { 27, 25}, -{ 31, 30}, { 30, 26}, { 27, 22}, { 24, 21}, -{ 29, 26}, { 25, 24}, { 23, 20}, { 20, 17}, -{ 24, 24}, { 22, 20}, { 20, 16}, { 25, 21}, -{ 22, 19}, { 18, 16}, { 16, 13}, { 12, 11}, -{ 19, 14}, { 16, 13}, { 13, 10}, { 10, 6}, -{ 14, 13}, { 12, 10}, { 7, 8}, { 5, 3}, -{ 12, 9}, { 7, 7}, { 5, 3}, { 11, 8}, -{ 8, 37}, { 37, 34}, { 33, 32}, { 31, 28}, -{ 35, 33}, { 33, 31}, { 31, 28}, { 28, 25}, -{ 31, 31}, { 29, 28}, { 27, 25}, { 24, 22}, -{ 29, 26}, { 27, 22}, { 24, 21}, { 20, 18}, -{ 15, 17}, { 23, 20}, { 20, 17}, { 16, 15}, -{ 15, 11}, { 20, 48}, { 49, 44}, { 46, 43}, -{ 43, 40}, { 40, 37}, { 44, 43}, { 42, 40}, -{ 39, 37}, { 35, 33}, { 42, 38}, { 39, 36}, -{ 35, 33}, { 32, 31}, { 29, 28}, { 27, 25}, -{ 31, 30}, { 30, 26}, { 27, 22}, { 24, 21}, -{ 29, 26}, { 25, 24}, { 23, 52}, { 52, 49}, -{ 47, 49}, { 54, 52}, { 52, 48}, { 48, 47}, -{ 46, 43}, { 43, 40}, { 48, 45}, { 44, 43}, -{ 42, 40}, { 39, 37}, { 35, 35}, { 33, 32}, -{ 39, 36}, { 35, 33}, { 33, 31}, { 29, 28}, -{ 27, 25}, { 31, 31}, { 30, 26}, { 27, 22}, -{ 24, 53}, { 52, 50}, { 57, 56}, { 55, 52}, -{ 52, 50}, { 47, 49}, { 47, 43}, { 44, 41}, -{ 48, 47}, { 46, 43}, { 43, 40}, { 39, 39}, -{ 37, 35}, { 33, 33}, { 39, 37}, { 37, 34}, -{ 33, 32}, { 31, 28}, { 27, 26}, { 24, 24}, -{ 29, 28}, { 27, 57}, { 57, 53}, { 54, 51}, -{ 50, 48}, { 48, 45}, { 52, 50}, { 51, 46}, -{ 48, 44}, { 45, 42}, { 42, 38}, { 39, 36}, -{ 44, 42}, { 39, 40}, { 37, 35}, { 36, 31}, -{ 32, 29}, { 30, 26}, { 27, 22}, { 24, 21}, -{ 29, 26}, { 25, 24}, { 23, 52}, { 52, 49}, -{ 47, 49}, { 47, 43}, { 44, 41}, { 48, 47}, -{ 46, 43}, { 43, 40}, { 40, 37}, { 37, 35}, -{ 33, 33}, { 31, 28}, { 35, 35}, { 33, 32}, -{ 31, 28}, { 28, 25}, { 24, 24}, { 22, 20}, -{ 20, 16}, { 17, 12}, { 22, 19}, { 18, 16}, -{ 16, 45}, { 45, 42}, { 42, 40}, { 39, 37}, -{ 35, 33}, { 33, 31}, { 31, 28}, { 35, 33}, -{ 32, 31}, { 29, 28}, { 27, 25}, { 24, 22}, -{ 20, 18}, { 18, 16}, { 16, 45}, { 52, 50}, -{ 47, 49}, { 48, 44}, { 44, 42}, { 39, 40}, -{ 37, 35}, { 35, 33}, { 32, 31}, { 30, 26}, -{ 27, 22}, { 31, 30}, { 29, 26}, { 25, 24}, -{ 22, 54}, { 52, 50}, { 47, 49}, { 47, 43}, -{ 44, 42}, { 39, 40}, { 37, 35}, { 36, 31}, -{ 39, 39}, { 37, 35}, { 33, 33}, { 31, 28}, -{ 29, 26}, { 25, 24}, { 23, 52}, { 52, 49}, -{ 47, 49}, { 47, 43}, { 44, 41}, { 39, 39}, -{ 37, 35}, { 43, 40}, { 40, 37}, { 37, 35}, -{ 33, 33}, { 31, 28}, { 27, 26}, { 24, 24}, -{ 23, 52}, { 52, 49}, { 48, 47}, { 46, 43}, -{ 44, 41}, { 39, 39}, { 37, 35}, { 43, 40}, -{ 40, 37}, { 37, 34}, { 33, 32}, { 31, 28}, -{ 27, 26}, { 24, 24}, { 22, 20}, { 18, 50}, -{ 48, 47}, { 46, 43}, { 43, 40}, { 39, 39}, -{ 37, 35}, { 33, 33}, { 31, 28}, { 27, 26}, -{ 25, 24}, { 23, 20}, { 27, 26}, { 24, 24}, -{ 22, 20}, { 20, 48}, { 49, 44}, { 46, 43}, -{ 43, 40}, { 40, 37}, { 37, 34}, { 33, 33}, -{ 31, 28}, { 27, 26}, { 24, 24}, { 22, 20}, -{ 20, 17}, { 16, 15}, { 14, 11}, { 10, 41}, -{ 39, 39}, { 37, 35}, { 33, 33}, { 31, 28}, -{ 29, 26}, { 25, 24}, { 23, 20}, { 20, 17}, -{ 15, 17}, { 15, 11}, { 12, 9}, { 7, 7}, -{ 5, 3}, { 4, 31}, { 32, 29}, { 29, 26}, -{ 25, 24}, { 24, 21}, { 20, 18}, { 15, 17}, -{ 14, 13}, { 12, 10}, { 7, 8}, { 5, 3}, -{ 4, -1}, { 0, -1}, { -2, -6}, { 1, 1}, -{ -8, 21}, { 20, 18}, { 19, 14}, { 16, 12}, -{ 12, 10}, { 7, 8}, { 7, 4}, { 3, 1}, -{ 0, -1}, { -3, 28}, { 27, 25}, { 24, 22}, -{ 20, 18}, { 18, 16}, { 16, 13}, { 13, 10}, -{ 10, 6}, { 7, 4}, { 3, 33}, { 33, 31}, -{ 29, 28}, { 27, 25}, { 25, 21}, { 22, 19}, -{ 18, 16}, { 16, 13}, { 12, 11}, { 10, 40}, -{ 39, 37}, { 35, 33}, { 33, 32}, { 31, 28}, -{ 28, 25}, { 25, 21}, { 22, 19}, { 20, 16}, -{ 17, 44}, { 44, 43}, { 42, 40}, { 40, 37}, -{ 37, 34}, { 33, 32}, { 31, 28}, { 27, 26}, -{ 24, 24}, { 15, 43}, { 44, 41}, { 39, 39}, -{ 37, 35}, { 36, 31}, { 32, 29}, { 29, 26}, -{ 25, 24}, { 24, 21}, { 20, 50}, { 47, 49}, -{ 46, 45}, { 44, 42}, { 39, 40}, { 37, 35}, -{ 36, 31}, { 32, 31}, { 30, 26}, { 27, 22}, -{ 16, 45}, { 45, 42}, { 42, 40}, { 39, 37}, -{ 35, 33}, { 33, 31}, { 31, 28}, { 28, 25}, -{ 25, 21}, { 22, 51}, { 50, 48}, { 49, 44}, -{ 44, 43}, { 42, 40}, { 32, 27}, { 27, 26}, -{ 25, 24}, { 23, 20}, { 20, 49}, { 48, 47}, -{ 47, 43}, { 44, 41}, { 39, 39}, { 37, 35}, -{ 36, 31}, { 32, 29}, { 29, 26}, { 19, 46}, -{ 48, 44}, { 45, 42}, { 42, 38}, { 39, 36}, -{ 35, 33}, { 32, 31}, { 29, 28}, { 27, 25}, -{ 24, 54}, { 52, 52}, { 42, 40}, { 40, 37}, -{ 37, 34}, { 33, 32}, { 31, 28}, { 27, 26}, -{ 24, 24}, { 22, 52}, { 52, 48}, { 48, 47}, -{ 37, 35}, { 36, 31}, { 32, 29}, { 29, 26}, -{ 25, 24}, { 24, 21}, { 20, 50}, { 47, 49}, -{ 39, 36}, { 35, 33}, { 33, 31}, { 29, 28}, -{ 27, 25}, { 24, 22}, { 22, 19}, { 18, 16}, -{ 16, 45}, { 37, 34}, { 33, 32}, { 31, 28}, -{ 27, 26}, { 24, 24}, { 22, 20}, { 18, 50}, -{ 48, 47}, { 37, 35}, { 36, 31}, { 32, 29}, -{ 29, 26}, { 27, 22}, { 24, 21}, { 20, 50}, -{ 42, 38}, { 39, 36}, { 35, 33}, { 33, 31}, -{ 29, 28}, { 27, 25}, { 25, 53}, { 46, 43}, -{ 43, 40}, { 40, 37}, { 37, 34}, { 33, 33}, -{ 31, 28}, { 27, 26}, { 24, 56}, { 47, 43}, -{ 44, 42}, { 39, 40}, { 37, 35}, { 36, 31}, -{ 32, 29}, { 20, 52}, { 50, 48}, { 48, 45}, -{ 45, 42}, { 42, 38}, { 39, 37}, { 27, 26}, -{ 24, 24}, { 22, 52}, { 52, 48}, { 48, 47}, -{ 46, 43}, { 36, 31}, { 32, 29}, { 29, 26}, -{ 25, 56}, { 56, 53}, { 52, 50}, { 42, 38}, -{ 39, 36}, { 35, 33}, { 33, 31}, { 29, 28}, -{ 27, 57}, { 49, 44}, { 44, 43}, { 43, 40}, -{ 40, 37}, { 37, 34}, { 25, 24}, { 23, 52}, -{ 52, 50}, { 47, 49}, { 47, 43}, { 35, 33}, -{ 32, 31}, { 29, 28}, { 27, 25}, { 24, 54}, -{ 52, 50}, { 42, 40}, { 39, 37}, { 37, 34}, -{ 33, 32}, { 31, 28}, { 20, 49}, { 48, 47}, -{ 47, 43}, { 44, 41}, { 39, 39}, { 30, 26}, -{ 27, 22}, { 24, 22}, { 20, 50}, { 42, 40}, -{ 39, 37}, { 35, 33}, { 33, 32}, { 31, 28}, -{ 28, 25}, { 16, 47}, { 46, 43}, { 42, 41}, -{ 39, 39}, { 30, 26}, { 27, 22}, { 24, 21}, -{ 20, 18}, { 19, 46}, { 39, 37}, { 35, 33}, -{ 33, 31}, { 29, 28}, { 20, 16}, { 16, 15}, -{ 14, 43}, { 43, 40}, { 40, 37}, { 29, 26}, -{ 25, 24}, { 24, 21}, { 20, 18}, { 10, 6}, -{ 7, 36}, { 35, 33}, { 33, 31}, { 22, 20}, -{ 20, 16}, { 17, 12}, { 12, 11}, { 11, 8}, -{ 0, 29}, { 29, 26}, { 25, 24}, { 16, 12}, -{ 12, 10}, { 7, 8}, { 7, 36}, { 28, 25}, -{ 25, 21}, { 22, 19}, { 18, 16}, { 7, 7}, -{ 5, 35}, { 33, 33}, { 31, 28}, { 27, 26}, -{ 15, 17}, { 16, 12}, { 12, 42}, { 33, 31}, -{ 29, 28}, { 27, 25}, { 25, 21}, { 14, 11}, -{ 11, 40}, { 40, 37}, { 37, 34}, { 25, 24}, -{ 22, 22}, { 20, 18}, { 15, 49}, { 39, 36}, -{ 35, 33}, { 32, 31}, { 22, 19}, { 20, 16}, -{ 17, 44}, { 44, 43}, { 33, 33}, { 31, 28}, -{ 29, 26}, { 19, 14}, { 16, 44}, { 44, 42}, -{ 39, 40}, { 32, 26}, { 28, 25}, { 25, 21}, -{ 14, 43}, { 43, 40}, { 40, 37}, { 37, 35}, -{ 25, 24}, { 24, 21}, { 20, 50}, { 42, 38}, -{ 39, 36}, { 35, 33}, { 33, 31}, { 22, 20}, -{ 20, 48}, { 49, 44}, { 37, 35}, { 33, 33}, -{ 32, 29}, { 20, 18}, { 19, 14}, { 16, 44}, -{ 35, 33}, { 33, 31}, { 31, 28}, { 28, 25}, -{ 16, 15}, { 14, 43}, { 43, 40}, { 32, 29}, -{ 29, 26}, { 27, 22}, { 16, 13}, { 13, 42}, -{ 42, 38}, { 31, 28}, { 27, 26}, { 24, 24}, -{ 15, 11}, { 12, 41}, { 39, 39}, { 30, 26}, -{ 27, 22}, { 24, 22}, { 12, 11}, { 10, 40}, -{ 39, 37}, { 27, 26}, { 24, 24}, { 22, 20}, -{ 20, 17}, { 7, 40}, { 37, 35}, { 27, 25}, -{ 24, 22}, { 20, 20}, { 10, 8}, { 8, 37}, -{ 37, 34}, { 33, 32}, { 23, 20}, { 20, 17}, -{ 7, 8}, { 5, 37}, { 35, 33}, { 25, 21}, -{ 22, 19}, { 18, 16}, { 8, 5}, { 5, 35}, -{ 33, 33}, { 24, 21}, { 20, 18}, { 15, 17}, -{ 7, 4}, { 3, 33}, { 24, 24}, { 22, 20}, -{ 20, 16}, { 7, 7}, { 5, 3}, { 1, 1}, -{ -8, 21}, { 20, 18}, { 19, 14}, { 7, 5}, -{ 3, 1}, { -8, 24}, { 22, 20}, { 18, 18}, -{ 7, 8}, { 5, 3}, { 4, 31}, { 24, 22}, -{ 20, 18}, { 18, 16}, { 7, 5}, { 5, 34}, -{ 25, 24}, { 23, 20}, { 20, 17}, { 7, 8}, -{ 5, 35}, { 35, 33}, { 25, 21}, { 22, 19}, -{ 11, 8}, { 8, 37}, { 37, 34}, { 25, 24}, -{ 22, 22}, { 13, 10}, { 10, 38}, { 39, 36}, -{ 28, 25}, { 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20, 19}, -{ 19, 22}, { 22, 21}, { 21, 24}, { 24, 23}, -{ 23, 26}, { 25, 27}, { 25, 28}, { 28, 27}, -{ 27, 30}, { 30, 29}, { 28, 33}, { 32, 31}, -{ 31, 34}, { 33, 33}, { 33, 35}, { 27, 26}, -{ 25, 31}, { 29, 28}, { 28, 31}, { 31, 30}, -{ 30, 33}, { 32, 33}, { 32, 35}, { 35, 34}, -{ 33, 37}, { 37, 35}, { 36, 39}, { 38, 38}, -{ 37, 41}, { 40, 39}, { 31, 34}, { 34, 33}, -{ 32, 37}, { 36, 35}, { 35, 38}, { 37, 37}, -{ 37, 39}, { 40, 39}, { 38, 42}, { 41, 41}, -{ 40, 43}, { 35, 34}, { 34, 37}, { 36, 37}, -{ 36, 39}, { 39, 38}, { 37, 41}, { 41, 39}, -{ 40, 43}, { 42, 42}, { 41, 45}, { 37, 37}, -{ 37, 39}, { 40, 39}, { 38, 42}, { 41, 41}, -{ 40, 43}, { 43, 42}, { 42, 45}, { 45, 44}, -{ 36, 39}, { 39, 38}, { 37, 41}, { 41, 39}, -{ 40, 43}, { 42, 42}, { 41, 45}, { 36, 35}, -{ 35, 38}, { 38, 37}, { 36, 41}, { 40, 39}, -{ 39, 42}, { 41, 41}, { 34, 37}, { 36, 37}, -{ 36, 39}, { 39, 38}, { 37, 41}, { 41, 39}, -{ 40, 43}, { 33, 35}, { 33, 36}, { 36, 35}, -{ 35, 38}, { 38, 37}, { 36, 41}, { 31, 30}, 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32, 26}, { 26, 26}, -{ 31, 30}, { 36, 34}, { 33, 28}, { 38, 32}, -{ 33, 33}, { 37, 37}, { 35, 29}, { 32, 27}, -{ 36, 34}, { 39, 39}, { 36, 34}, { 41, 35}, -{ 38, 35}, { 42, 40}, { 37, 36}, { 42, 40}, -{ 40, 34}, { 35, 35}, { 38, 40}, { 43, 43}, -{ 41, 35}, { 46, 40}, { 42, 40}, { 38, 36}, -{ 42, 39}, { 40, 34}, { 44, 42}, { 39, 39}, -{ 44, 42}, { 41, 38}, { 45, 43}, { 41, 41}, -{ 45, 45}, { 43, 37}, { 40, 37}, { 44, 42}, -{ 39, 38}, { 44, 42}, { 42, 36}, { 46, 44}, -{ 40, 42}, { 38, 33}, { 43, 37}, { 40, 37}, -{ 44, 42}, { 40, 38}, { 44, 41}, { 42, 36}, -{ 37, 37}, { 41, 41}, { 39, 33}, { 43, 40}, -{ 40, 38}, { 36, 33}, { 40, 38}, { 38, 32}, -{ 42, 39}, { 36, 36}, { 34, 29}, { 39, 33}, -{ 35, 34}, { 39, 39}, { 35, 33}, { 33, 28}, -{ 37, 34}, { 32, 32}, { 30, 24}, { 34, 32}, -{ 31, 29}, { 35, 34}, { 31, 29}, { 29, 23}, -{ 33, 31}, { 27, 29}, { 25, 20}, { 30, 24}, -{ 27, 24}, { 31, 29}, { 27, 25}, { 24, 19}, -{ 20, 19}, { 22, 24}, { 21, 15}, { 26, 20}, -{ 22, 21}, { 17, 17}, { 15, 9}, { 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11, 12}, -{ 9, 12}, { 12, 14}, { 15, 14}, { 13, 16}, -{ 16, 19}, { 15, 18}, { 17, 21}, { 21, 22}, -{ 19, 22}, { 21, 27}, { 26, 24}, { 16, 19}, -{ 19, 20}, { 17, 23}, { 20, 23}, { 23, 22}, -{ 22, 24}, { 24, 27}, { 27, 25}, { 26, 28}, -{ 30, 30}, { 27, 30}, { 30, 33}, { 25, 24}, -{ 24, 27}, { 28, 27}, { 26, 29}, { 28, 32}, -{ 32, 30}, { 30, 33}, { 32, 38}, { 31, 37}, -{ 27, 30}, { 26, 29}, { 28, 34}, { 33, 32}, -{ 30, 33}, { 33, 35}, { 37, 35}, { 34, 37}, -{ 37, 39}, { 29, 31}, { 31, 34}, { 34, 33}, -{ 33, 35}, { 38, 37}, { 34, 37}, { 37, 40}, -{ 32, 31}, { 31, 34}, { 34, 36}, { 33, 36}, -{ 35, 39}, { 27, 30}, { 30, 33}, { 34, 32}, -{ 31, 35}, { 34, 37}, { 37, 35}, { 28, 32}, -{ 32, 30}, { 30, 33}, { 32, 38}, { 31, 37}, -{ 34, 37}, { 26, 29}, { 28, 34}, { 33, 32}, -{ 30, 33}, { 33, 35}, { 24, 30}, { 27, 30}, -{ 31, 30}, { 29, 31}, { 26, 24}, { 23, 26}, -{ 26, 28}, { 28, 30}, { 27, 30}, { 30, 32}, -{ 22, 24}, { 24, 27}, { 27, 25}, { 19, 21}, -{ 21, 20}, { 20, 23}, { 25, 24}, { 15, 17}, -{ 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28}, { 44, 39}, -{ 43, 39}, { 44, 37}, { 44, 34}, { 43, 36}, -{ 42, 34}, { 42, 31}, { 41, 31}, { 40, 30}, -{ 39, 32}, { 38, 33}, { 47, 37}, { 38, 32}, -{ 44, 37}, { 45, 37}, { 43, 37}, { 42, 38}, -{ 42, 38}, { 43, 36}, { 42, 36}, { 42, 35}, -{ 42, 32}, { 41, 31}, { 40, 30}, { 40, 29}, -{ 47, 40}, { 47, 37}, { 46, 36}, { 46, 35}, -{ 44, 37}, { 44, 33}, { 42, 36}, { 42, 36}, -{ 41, 37}, { 41, 36}, { 41, 35}, { 41, 34}, -{ 41, 31}, { 39, 32}, { 39, 29}, { 38, 31}, -{ 37, 29}, { 36, 30}, { 36, 29}, { 34, 31}, -{ 35, 30}, { 35, 29}, { 35, 28}, { 35, 24}, -{ 34, 24}, { 33, 23}, { 32, 22}, { 32, 21}, -{ 30, 23}, { 30, 23}, { 28, 24}, { 29, 23}, -{ 28, 23}, { 29, 22}, { 29, 19}, { 28, 17}, -{ 27, 17}, { 25, 18}, { 25, 15}, { 24, 17}, -{ 23, 18}, { 23, 17}, { 22, 17}, { 22, 17}, -{ 14, 4}, { 13, 6}, { 11, 6}, { 11, 6}, -{ 12, 5}, { 12, 4}, { 11, 4}, { 11, 1}, -{ 10, 0}, { 9, 0}, { 8, 1}, { 8, -3}, -{ 0, -7}, { 2, -6}, { 3, -1}, { 5, -1}, -{ 7, -1}, { 9, 1}, { 10, 6}, { 12, 8}, -{ 13, 12}, { 16, 14}, { 19, 14}, { 22, 14}, -{ 23, 16}, { 16, 12}, { 17, 15}, { 20, 17}, -{ 23, 17}, { 25, 20}, { 27, 19}, { 28, 23}, -{ 30, 23}, { 32, 24}, { 27, 19}, { 29, 21}, -{ 30, 23}, { 32, 24}, { 34, 26}, { 28, 23}, -{ 30, 24}, { 32, 27}, { 34, 26}, { 35, 30}, -{ 37, 30}, { 39, 34}, { 41, 36}, { 36, 28}, -{ 37, 30}, { 39, 31}, { 41, 33}, { 42, 37}, -{ 37, 31}, { 39, 34}, { 41, 33}, { 42, 37}, -{ 44, 40}, { 39, 34}, { 41, 33}, { 43, 35}, -{ 44, 37}, { 46, 38}, { 41, 34}, { 43, 35}, -{ 44, 38}, { 46, 41}, { 48, 40}, { 42, 37}, -{ 45, 37}, { 46, 41}, { 48, 40}, { 42, 37}, -{ 44, 39}, { 46, 41}, { 48, 41}, { 50, 42}, -{ 43, 40}, { 46, 40}, { 47, 44}, { 49, 44}, -{ 52, 44}, { 43, 42}, { 46, 44}, { 50, 43}, -{ 52, 44}, { 44, 40}, { 45, 43}, { 47, 45}, -{ 43, 35}, { 44, 37}, { 45, 42}, { 48, 43}, -{ 42, 38}, { 45, 37}, { 46, 38}, { 48, 40}, -{ 43, 35}, { 45, 37}, { 46, 39}, { 40, 36}, -{ 42, 38}, { 45, 37}, { 37, 33}, { 38, 37}, -{ 40, 39}, { 44, 39}, { 37, 29}, { 39, 35}, -{ 40, 37}, { 36, 28}, { 37, 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50}, { 19, 1}, { 32, 46}, -{ 33, 59}, { 28, 9}, { 40, 54}, { 23, 4}, -{ 35, 49}, { 44, 61}, { 31, 13}, { 44, 58}, -{ 26, 8}, { 39, 53}, { 52, 66}, { 35, 16}, -{ 47, 61}, { 30, 11}, { 42, 56}, { 25, 52}, -{ 38, 20}, { 51, 65}, { 35, 48}, { 47, 28}, -{ 28, 65}, { 42, 23}, { 47, 68}, { 37, 18}, -{ 49, 63}, { 37, 77}, { 45, 27}, { 57, 63}, -{ 40, 22}, { 53, 67}, { 35, 17}, { 48, 62}, -{ 61, 75}, { 44, 25}, { 56, 70}, { 39, 20}, -{ 52, 34}, { 34, 66}, { 47, 29}, { 51, 74}, -{ 42, 24}, { 55, 69}, { 37, 19}, { 50, 64}, -{ 35, 48}, { 46, 27}, { 58, 72}, { 41, 22}, -{ 53, 67}, { 37, 57}, { 49, 31}, { 41, 76}, -{ 44, 26}, { 57, 55}, { 39, 21}, { 52, 66}, -{ 34, 16}, { 47, 61}, { 29, 56}, { 43, 24}, -{ 39, 70}, { 38, 19}, { 50, 64}, { 33, 69}, -{ 46, 28}, { 52, 71}, { 41, 23}, { 54, 68}, -{ 36, 18}, { 49, 63}, { 31, 49}, { 45, 26}, -{ 26, 70}, { 40, 21}, { 49, 63}, { 35, 16}, -{ 47, 61}, { 30, 11}, { 42, 56}, { 25, 46}, -{ 38, 20}, { 27, 65}, { 33, 15}, { 45, 51}, -{ 28, 10}, { 41, 55}, { 23, 5}, { 36, 50}, -{ 18, 44}, { 32, 13}, { 13, -5}, { 26, 40}, -{ 39, 53}, { 22, 3}, { 12, 49}, { 17, -2}, -{ 29, 32}, { 12, -7}, { 24, 38}, { 7, -12}, -{ 19, 33}, { 2, 28}, { 15, -3}, { 12, 42}, -{ 10, -8}, { 23, 37}, { 5, -13}, { 18, 32}, -{ 0, -16}, { 15, 31}, { 0, -16}, { 15, 31}, -{ 0, -16}, { 15, 31}, { 0, 30}, { 16, 0}, -{ 17, 47}, { 16, 0}, { 31, 47}, { 16, 0}, -{ 13, 48}, { 16, 0}, { 31, 47}, { 16, 0}, -{ 31, 47}, { 16, 0}, { 31, 47}, { 16, 47}, -{ 32, 16}, { 34, 63}, { 32, 16}, { 16, 44}, -{ 32, 16}, { 31, 63}, { 32, 16}, { 17, 40}, -{ 32, 16}, { 25, 64}, { 32, 16}, { 47, 53}, -{ 32, 16}, { 47, 63}, { 32, 16}, { 45, 61}, -{ 32, 16}, { 47, 63}, { 32, 16}, { 47, 63}, -{ 32, 57}, { 48, 32}, { 32, 16}, { 47, 63}, -{ 32, 54}, { 48, 32}, { 32, 16}, { 47, 63}, -{ 32, 52}, { 48, 32}, { 32, 79}, { 48, 32}, -{ 32, 50}, { 48, 32}, { 32, 72}, { 48, 32}, -{ 56, 80}, { 48, 32}, { 32, 68}, { 48, 32}, -{ 54, 78}, { 48, 32}, { 32, 63}, { 48, 32}, -{ 50, 79}, { 48, 32}, { 32, 59}, { 48, 32}, -{ 45, 80}, { 48, 32}, { 33, 56}, { 48, 32}, -{ 41, 80}, { 48, 32}, { 34, 53}, { 48, 32}, -{ 34, 80}, { 48, 32}, { 32, 51}, { 48, 32}, -{ 32, 75}, { 48, 32}, { 33, 49}, { 48, 32}, -{ 32, 16}, { 47, 63}, { 32, 16}, { 47, 63}, -{ 32, 65}, { 48, 32}, { 32, 16}, { 45, 61}, -{ 32, 16}, { 47, 63}, { 32, 16}, { 47, 63}, -{ 32, 16}, { 47, 63}, { 32, 16}, { 40, 64}, -{ 32, 16}, { 47, 63}, { 32, 16}, { 37, 63}, -{ 32, 16}, { 16, 47}, { 32, 16}, { 34, 63}, -{ 32, 16}, { 16, 43}, { 32, 16}, { 16, 0}, -{ 31, 47}, { 16, 40}, { 32, 16}, { 16, 0}, -{ 22, 46}, { 16, 0}, { 31, 47}, { 16, 0}, -{ 19, 47}, { 16, 0}, { 0, 28}, { 16, 0}, -{ 0, -16}, { 15, 31}, { 1, 24}, { 16, 0}, -{ 0, -13}, { 10, 36}, { 5, -8}, { 23, 42}, -{ 10, -3}, { 16, 47}, { 15, 2}, { 2, 33}, -{ 20, 7}, { 7, -7}, { 24, 43}, { 12, 40}, -{ 30, 17}, { 17, 3}, { 27, 53}, { 22, 8}, -{ 8, 45}, { 27, 13}, { 34, 62}, { 32, 18}, -{ 18, 51}, { 37, 23}, { 23, 10}, { 37, 56}, -{ 28, 15}, { 46, 65}, { 33, 20}, { 45, 67}, -{ 38, 25}, { 25, 62}, { 43, 30}, { 30, 16}, -{ 46, 65}, { 35, 21}, { 52, 71}, { 40, 26}, -{ 29, 47}, { 45, 31}, { 31, 77}, { 50, 36}, -{ 37, 55}, { 55, 41}, { 41, 28}, { 37, 77}, -{ 46, 33}, { 34, 56}, { 51, 38}, { 38, 24}, -{ 55, 74}, { 43, 29}, { 60, 79}, { 48, 34}, -{ 49, 85}, { 53, 39}, { 39, 67}, { 58, 44}, -{ 44, 31}, { 54, 80}, { 49, 36}, { 36, 72}, -{ 54, 41}, { 41, 27}, { 57, 70}, { 46, 32}, -{ 32, 81}, { 51, 37}, { 39, 57}, { 56, 42}, -{ 42, 29}, { 60, 79}, { 47, 34}, { 34, 60}, -{ 52, 39}, { 39, 25}, { 56, 75}, { 44, 30}, -{ 61, 80}, { 49, 35}, { 53, 85}, { 54, 40}, -{ 40, 27}, { 58, 77}, { 45, 32}, { 57, 82}, -{ 50, 37}, { 37, 76}, { 55, 42}, { 42, 28}, -{ 59, 67}, { 47, 33}, { 33, 20}, { 51, 70}, -{ 38, 25}, { 56, 75}, { 43, 30}, { 45, 80}, -{ 48, 35}, { 35, 21}, { 52, 71}, { 40, 26}, -{ 26, 13}, { 44, 63}, { 31, 18}, { 22, 68}, -{ 36, 23}, { 23, 45}, { 41, 28}, { 28, 14}, -{ 31, 64}, { 33, 19}, { 19, 48}, { 38, 24}, -{ 24, 11}, { 35, 59}, { 29, 16}, { 16, 52}, -{ 34, 21}, { 21, 7}, { 37, 56}, { 26, 12}, -{ 12, -1}, { 30, 49}, { 17, 4}, { 4, 33}, -{ 22, 9}, { 9, -5}, { 20, 44}, { 14, 0}, -{ 0, 42}, { 21, 10}, { 10, -1}, { 29, 50}, -{ 19, 8}, { 8, -3}, { 28, 49}, { 18, 6}, -{ 6, 39}, { 27, 16}, { 16, 5}, { 30, 57}, -{ 25, 14}, { 14, 57}, { 35, 24}, { 24, 12}, -{ 12, 39}, { 33, 22}, { 22, 11}, { 30, 63}, -{ 31, 20}, { 20, 54}, { 41, 30}, { 30, 18}, -{ 45, 70}, { 39, 28}, { 28, 17}, { 28, 69}, -{ 37, 26}, { 27, 53}, { 47, 36}, { 36, 24}, -{ 24, 13}, { 44, 65}, { 34, 23}, { 23, 75}, -{ 43, 32}, { 32, 55}, { 53, 42}, { 42, 30}, -{ 30, 19}, { 50, 71}, { 40, 29}, { 29, 68}, -{ 49, 38}, { 38, 27}, { 27, 53}, { 48, 36}, -{ 36, 25}, { 44, 77}, { 46, 35}, { 35, 23}, -{ 54, 75}, { 44, 33}, { 33, 54}, { 54, 42}, -{ 42, 31}, { 31, 20}, { 51, 72}, { 41, 29}, -{ 29, 67}, { 50, 39}, { 39, 28}, { 57, 73}, -{ 48, 37}, { 37, 26}, { 41, 78}, { 47, 35}, -{ 35, 24}, { 24, 67}, { 45, 34}, { 34, 22}, -{ 53, 74}, { 43, 32}, { 32, 21}, { 41, 73}, -{ 41, 30}, { 30, 19}, { 19, 70}, { 40, 28}, -{ 28, 51}, { 49, 38}, { 38, 27}, { 27, 15}, -{ 40, 67}, { 36, 25}, { 25, 14}, { 21, 66}, -{ 34, 23}, { 24, 48}, { 44, 33}, { 33, 21}, -{ 21, 10}, { 39, 55}, { 31, 20}, { 20, 8}, -{ 23, 60}, { 29, 18}, { 18, 7}, { 7, 48}, -{ 27, 16}, { 16, 5}, { 35, 56}, { 26, 14}, -{ 14, 3}, { 23, 55}, { 24, 13}, { 13, 1}, -{ 1, 51}, { 22, 11}, { 11, 0}, { 0, 29}, -{ 20, 9}, { 9, -2}, { -2, -13}, { 18, 23}, -{ 7, -4}, { -4, -15}, { 5, 38}, { 6, -6}, -{ -6, -17}, { -17, 34}, { 4, -7}, { -7, -19}, -{ -19, 12}, { 2, -9}, { -9, -20}, { 4, 30}, -{ 0, -8}, { -8, -17}, { -17, -25}, { -4, 30}, -{ -2, -10}, { -10, -19}, { -19, 37}, { 5, -4}, -{ -4, -12}, { -12, 22}, { 11, 3}, { 3, -6}, -{ -5, 18}, { 18, 9}, { 9, 1}, { 1, -8}, -{ 15, 45}, { 16, 7}, { 7, -1}, { 1, 54}, -{ 22, 14}, { 14, 5}, { 5, 41}, { 29, 20}, -{ 20, 12}, { 13, 36}, { 35, 27}, { 27, 18}, -{ 18, 10}, { 10, 1}, { 32, 56}, { 25, 16}, -{ 16, 8}, { 27, 63}, { 31, 23}, { 23, 14}, -{ 14, 68}, { 38, 29}, { 29, 21}, { 21, 12}, -{ 12, 59}, { 36, 27}, { 27, 19}, { 19, 49}, -{ 42, 34}, { 34, 25}, { 25, 17}, { 47, 63}, -{ 40, 32}, { 32, 23}, { 23, 15}, { 42, 70}, -{ 38, 30}, { 30, 21}, { 34, 77}, { 38, 65}, -{ 36, 28}, { 28, 19}, { 28, 75}, { 43, 34}, -{ 34, 26}, { 26, 65}, { 49, 41}, { 41, 32}, -{ 32, 24}, { 24, 59}, { 47, 39}, { 39, 30}, -{ 31, 54}, { 23, 53}, { 45, 37}, { 37, 28}, -{ 28, 20}, { 51, 59}, { 43, 35}, { 35, 26}, -{ 26, 18}, { 47, 66}, { 41, 33}, { 33, 24}, -{ 24, 16}, { 42, 69}, { 39, 31}, { 31, 22}, -{ 34, 77}, { 46, 37}, { 37, 29}, { 29, 20}, -{ 26, 75}, { 44, 35}, { 35, 27}, { 27, 18}, -{ 18, 72}, { 42, 33}, { 33, 25}, { 25, 16}, -{ 16, 65}, { 40, 31}, { 31, 23}, { 23, 14}, -{ 14, 57}, { 38, 29}, { 29, 21}, { 21, 12}, -{ 12, 51}, { 36, 27}, { 27, 19}, { 19, 10}, -{ 10, 46}, { 34, 25}, { 25, 17}, { 17, 8}, -{ 8, 40}, { 32, 23}, { 23, 15}, { 15, 6}, -{ 6, 36}, { 30, 21}, { 21, 13}, { 13, 4}, -{ 4, 31}, { -4, 32}, { 19, 11}, { 11, 2}, -{ 2, -6}, { -6, 26}, { 17, 9}, { 9, 0}, -{ 0, -6}, { -5, 26}, { 20, 14}, { 14, 7}, -{ 7, 1}, { 1, 31}, { -5, 34}, { 21, 14}, -{ 14, 8}, { 8, 2}, { 3, 37}, { 28, 21}, -{ 21, 15}, { 15, 9}, { 9, 42}, { 35, 28}, -{ 28, 22}, { 22, 16}, { 16, 10}, { 10, 50}, -{ 35, 29}, { 29, 23}, { 23, 17}, { 17, 10}, -{ 10, 63}, { 36, 30}, { 30, 24}, { 24, 17}, -{ 17, 64}, { 20, 69}, { 37, 31}, { 31, 24}, -{ 24, 18}, { 20, 76}, { 30, 70}, { 38, 31}, -{ 31, 25}, { 25, 19}, { 34, 76}, { 39, 68}, -{ 38, 32}, { 32, 26}, { 26, 20}, { 43, 76}, -{ 44, 70}, { 39, 33}, { 33, 27}, { 27, 20}, -{ 50, 70}, { 46, 40}, { 40, 34}, { 34, 27}, -{ 27, 55}, { 21, 57}, { 47, 41}, { 41, 34}, -{ 34, 28}, { 29, 60}, { 22, 67}, { 48, 41}, -{ 41, 35}, { 35, 29}, { 29, 23}, { 23, 80}, -{ 34, 73}, { 42, 36}, { 36, 30}, { 30, 23}, -{ 36, 81}, { 42, 73}, { 43, 37}, { 37, 30}, -{ 30, 24}, { 24, 18}, { 48, 74}, { 44, 37}, -{ 37, 31}, { 31, 25}, { 27, 53}, { 19, 56}, -{ 44, 38}, { 38, 32}, { 32, 26}, { 26, 19}, -{ 19, 67}, { 23, 71}, { 39, 33}, { 33, 26}, -{ 26, 20}, { 20, 14}, { 14, 8}, { 37, 58}, -{ 33, 27}, { 27, 21}, { 21, 15}, { 15, 42}, -{ 8, 44}, { 34, 28}, { 28, 22}, { 22, 15}, -{ 15, 9}, { 9, 53}, { 8, 61}, { 17, 54}, -{ 22, 16}, { 16, 10}, { 10, 4}, { 4, -3}, -{ 25, 51}, { 23, 17}, { 17, 11}, { 11, 4}, -{ 4, -2}, { -2, 31}, { -8, 37}, { 18, 11}, -{ 11, 5}, { 5, -1}, { -1, -7}, { -7, -14}, -{ 5, 43}, { 9, 30}, { 6, 0}, { 0, -7}, -{ -7, -13}, { -13, -19}, { -19, 15}, { 7, 0}, -{ 0, -3}, { -3, -7}, { -7, -11}, { -11, -15}, -{ -15, -18}, { -18, -22}, { 7, 31}, { 6, 2}, -{ 2, -1}, { -1, -5}, { -5, -9}, { -9, 29}, -{ -13, 39}, { 16, 12}, { 12, 8}, { 8, 4}, -{ 4, 1}, { 1, -3}, { -3, -7}, { 23, 45}, -{ 21, 18}, { 18, 14}, { 14, 10}, { 10, 6}, -{ 6, 3}, { 3, 55}, { 12, 58}, { 20, 54}, -{ 23, 20}, { 20, 16}, { 16, 12}, { 12, 8}, -{ 9, 41}, { 5, 47}, { 1, 61}, { 16, 56}, -{ 25, 22}, { 22, 18}, { 18, 14}, { 14, 10}, -{ 11, 39}, { 7, 43}, { 3, 52}, { 31, 27}, -{ 27, 24}, { 24, 20}, { 20, 16}, { 16, 12}, -{ 12, 9}, { 38, 61}, { 37, 33}, { 33, 29}, -{ 29, 26}, { 26, 22}, { 22, 18}, { 18, 14}, -{ 14, 11}, { 11, 7}, { 38, 51}, { 35, 31}, -{ 31, 28}, { 28, 24}, { 24, 20}, { 20, 16}, -{ 16, 13}, { 13, 9}, { 36, 65}, { 37, 33}, -{ 33, 30}, { 30, 26}, { 26, 22}, { 22, 18}, -{ 18, 15}, { 15, 11}, { 11, 7}, { 7, 40}, -{ 35, 32}, { 32, 28}, { 28, 24}, { 24, 20}, -{ 20, 17}, { 17, 13}, { 13, 9}, { 9, 38}, -{ 5, 42}, { 2, 50}, { 30, 26}, { 26, 22}, -{ 22, 19}, { 19, 15}, { 15, 11}, { 11, 7}, -{ 10, 38}, { 4, 44}, { 0, 56}, { 12, 55}, -{ 18, 53}, { 21, 17}, { 17, 13}, { 13, 9}, -{ 9, 6}, { 6, 2}, { 2, -2}, { -2, -6}, -{ -6, -9}, { 20, 48}, { 19, 15}, { 15, 11}, -{ 11, 8}, { 8, 4}, { 4, 0}, { 0, -4}, -{ -4, -7}, { -7, -11}, { -11, -15}, { -15, 31}, -{ -12, 42}, { -1, 37}, { 4, 25}, { 2, -2}, -{ -2, -5}, { -5, -9}, { -9, -13}, { -13, -17}, -{ -17, -20}, { -20, -24}, { -24, -28}, { -28, 8}, -{ -32, 20}, { -24, 30}, { -12, 28}, { -5, 26}, -{ -5, -6}, { -6, -7}, { -7, -8}, { -8, -10}, -{ -10, -11}, { -11, -12}, { -12, -13}, { -13, -15}, -{ -15, -16}, { -16, -17}, { -7, 45}, { 5, 43}, -{ -20, 17}, { -21, 27}, { 10, 9}, { 9, 7}, -{ 7, 6}, { 6, 5}, { 5, 4}, { 4, 2}, -{ 2, 1}, { 1, 0}, { 0, -1}, { -1, -3}, -{ -3, -4}, { -3, 33}, { -5, 44}, { -1, 56}, -{ 13, 54}, { 21, 46}, { 22, 21}, { 21, 19}, -{ 19, 18}, { 18, 17}, { 17, 16}, { 16, 14}, -{ 14, 13}, { 13, 12}, { 12, 11}, { 11, 9}, -{ 9, 8}, { 8, 7}, { 7, 6}, { 6, 52}, -{ 36, 3}, { 3, 2}, { 4, 35}, { 1, 43}, -{ -1, 57}, { 12, 61}, { 22, 59}, { 28, 26}, -{ 26, 25}, { 25, 24}, { 24, 23}, { 23, 21}, -{ 21, 20}, { 20, 19}, { 19, 18}, { 18, 16}, -{ 16, 15}, { 15, 14}, { 14, 13}, { 13, 11}, -{ 11, 10}, { 10, 9}, { 9, 8}, { 8, 6}, -{ 6, 44}, { 37, 3}, { 9, 67}, { 35, 1}, -{ 1, 36}, { 0, 45}, { -1, 60}, { 14, 60}, -{ 23, 58}, { 27, 26}, { 26, 25}, { 6, 54}, -{ 16, 53}, { 22, 21}, { 21, 20}, { 20, 18}, -{ 18, 17}, { 17, 16}, { 16, 15}, { 15, 13}, -{ 13, 12}, { 12, 11}, { 11, 10}, { 10, 8}, -{ 8, 7}, { 7, 6}, { 6, 5}, { 5, 3}, -{ 3, 2}, { 2, 1}, { 1, 0}, { 0, -2}, -{ -2, -3}, { -3, -4}, { -4, -5}, { -5, -7}, -{ -7, -8}, { -8, -9}, { -9, -10}, { -10, -12}, -{ -12, -13}, { -13, -14}, { -14, -15}, { -15, -17}, -{ -17, -18}, { -18, -19}, { -19, -20}, { -20, -22}, -{ -22, -23}, { -23, -24}, { -24, -25}, { -25, -27}, -{ -27, -28}, { -28, -29}, { -29, -30}, { -30, -16}, -}; - -static int16_t vfpu_sin_lut_interval_delta[65537]= -{ - -16384, -16385, -16384, -16383, -16384, -16384, -16385, -16386, - -16387, -16388, -16390, -16391, -16392, -16394, -16394, -16394, - -16396, -16397, -16397, -16399, -16398, -16398, -16398, -16398, - -16399, -16400, -16401, -16402, -16403, -16405, -16406, -16407, - -16408, -16409, -16410, -16412, -16413, -16414, -16416, -16416, - -16417, -16419, -16420, -16421, -16423, -16424, -16425, -16426, - -16427, -16428, -16429, -16430, -16430, -16430, -16431, -16430, - -16431, -16432, -16433, -16432, -16432, -16433, -16432, -16433, - -16433, -16434, -16434, -16433, -16433, -16435, -16435, -16435, - -16435, -16435, -16435, -16435, -16436, -16437, -16438, -16438, - -16438, -16439, -16440, -16441, -16442, -16444, -16444, -16445, - -16447, 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20151, 20151, 20149, 20149, 20148, 20146, 20146, 20145, - 20144, 20143, 20143, 20141, 20141, 20141, 20139, 20139, - 20138, 20137, 20136, 20136, 20134, 20134, 20133, 20133, - 20131, 20131, 20130, 20129, 20129, 20128, 20127, 20126, - 20127, 20125, 20124, 20123, 20121, 20121, 20121, 20119, - 20119, 20118, 20118, 20118, 20118, 20117, 20116, 20116, - 20114, 20113, 20113, 20112, 20110, 20109, 20109, 20107, - 20107, 20106, 20105, 20104, 20104, 20102, 20101, 20100, - 20098, 20098, 20097, 20096, 20095, 20095, 20093, 20093, - 20092, 20091, 20090, 20089, 20089, 20087, 20087, 20086, - 20084, 20083, 20082, 20081, 20080, 20080, 20078, 20077, - 20076, 20074, 20074, 20073, 20072, 20071, 20070, 20068, - 20067, 20067, 20065, 20065, 20064, 20064, 20062, 20061, - 20060, 20058, 20057, 20057, 20055, 20055, 20054, 20053, - 20052, 20051, 20049, 20048, 20047, 20046, 20045, 20045, - 20043, 20042, 20041, 20039, 20038, 20037, 20036, 20034, - 20034, 20033, 20031, 20031, 20030, 20029, 20028, 20027, - 20025, 20024, 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-14901, -14903, -14903, -14904, -14905, - -14906, -14907, -14908, -14909, -14910, -14910, -14912, -14913, - -14914, -14916, -14917, -14917, -14919, -14920, -14921, -14922, - -14923, -14924, -14925, -14926, -14927, -14928, -14929, -14930, - -14931, -14931, -14932, -14933, -14933, -14934, -14935, -14937, - -14938, -14939, -14941, -14941, -14942, -14944, -14945, -14945, - -14947, -14948, -14949, -14950, -14951, -14952, -14953, -14953, - -14954, -14956, -14957, -14957, -14959, -14960, -14961, -14961, - -14963, -14964, -14965, -14967, -14967, -14968, -14970, -14971, - -14971, -14972, -14973, -14974, -14976, -14977, -14977, -14979, - -14980, -14981, -14983, -14984, -14985, -14986, -14987, -14988, - -14990, -14991, -14992, -14993, -14995, -14996, -14997, -14999, - -15000, -15000, -15002, -15003, -15004, -15006, -15007, -15008, - -15010, -15011, -15012, -15014, -15015, -15016, -15018, -15019, - -15020, -15021, -15021, -15021, -15022, -15024, -15025, -15026, - -15028, -15029, -15030, -15032, 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-15311, -15312, - -15312, -15314, -15314, -15315, -15315, -15317, -15318, -15319, - -15320, -15321, -15322, -15323, -15324, -15324, -15326, -15326, - -15327, -15328, -15329, -15329, -15331, -15331, -15331, -15333, - -15333, -15334, -15335, -15336, -15336, -15337, -15339, -15340, - -15341, -15342, -15343, -15344, -15346, -15347, -15347, -15348, - -15349, -15350, -15352, -15352, -15352, -15354, -15354, -15354, - -15356, -15356, -15357, -15358, -15358, -15359, -15359, -15360, - -15361, -15361, -15362, -15363, -15363, -15365, -15366, -15367, - -15369, -15370, -15370, -15371, -15372, -15372, -15373, -15374, - -15375, -15377, -15378, -15379, -15380, -15380, -15381, -15381, - -15382, -15383, -15383, -15385, -15386, -15387, -15388, -15388, - -15389, -15390, -15391, -15392, -15394, -15394, -15394, -15395, - -15396, -15396, -15398, -15399, -15400, -15401, -15401, -15401, - -15403, -15404, -15405, -15406, -15408, -15409, -15410, -15412, - -15412, -15413, -15415, -15416, -15416, -15417, -15418, -15419, - -15421, -15421, -15421, -15423, -15424, -15425, -15427, -15427, - -15428, -15430, -15431, -15431, -15431, -15433, -15434, -15435, - -15437, -15438, -15438, -15439, -15440, -15441, -15443, -15444, - -15445, -15447, -15447, -15448, -15450, -15451, -15452, -15454, - -15455, -15455, -15456, -15457, -15458, -15459, -15461, -15462, - -15463, -15464, -15465, -15466, -15467, -15467, -15468, -15470, - -15471, -15471, -15472, -15472, -15473, -15475, -15475, -15476, - -15477, -15477, -15477, -15479, -15480, -15481, -15482, -15484, - -15485, -15485, -15487, -15487, -15487, -15489, -15489, -15490, - -15491, -15492, -15493, -15495, -15496, -15497, -15499, -15500, - -15501, -15503, -15504, -15505, -15507, -15508, -15509, -15510, - -15512, -15513, -15514, -15515, -15515, -15516, -15518, -15518, - -15518, -15519, -15520, -15520, -15522, -15523, -15524, -15526, - -15527, -15527, -15529, -15530, -15530, -15532, -15533, -15533, - -15535, -15536, -15537, -15538, -15540, -15541, -15541, -15543, - -15544, -15545, -15547, -15548, -15549, -15551, -15552, -15553, - -15555, -15556, -15556, -15558, -15559, -15560, -15562, -15563, - -15564, -15565, -15565, -15566, -15567, -15569, -15570, -15571, - -15573, -15574, -15575, -15577, -15578, -15579, -15580, -15580, - -15581, -15583, -15584, -15585, -15587, -15588, -15589, -15591, - -15592, -15593, -15594, -15595, -15596, -15597, -15599, -15600, - -15601, -15603, -15604, -15605, -15607, -15608, -15609, -15611, - -15612, -15613, -15615, -15616, -15617, -15619, -15620, -15621, - -15623, -15624, -15625, -15627, -15628, -15629, -15630, -15632, - -15633, -15633, -15635, -15636, -15637, -15638, -15639, -15640, - -15642, -15643, -15644, -15645, -15646, -15647, -15649, -15650, - -15651, -15653, -15654, -15655, -15657, -15657, -15658, -15659, - -15661, -15662, -15663, -15665, -15666, -15667, -15669, -15670, - -15671, -15673, -15674, -15675, -15677, -15678, -15679, -15681, - -15682, -15683, -15685, -15686, -15687, -15689, -15690, -15691, - -15693, -15694, -15695, -15696, -15698, -15699, -15700, -15702, - -15703, -15704, -15706, -15707, -15708, -15710, -15711, -15712, - -15714, -15715, -15716, -15718, -15719, -15720, -15722, -15723, - -15724, -15726, -15727, -15728, -15728, -15730, -15731, -15732, - -15734, -15735, -15736, -15737, -15738, -15739, -15741, -15742, - -15743, -15745, -15746, -15747, -15749, -15750, -15751, -15753, - -15754, -15755, -15757, -15758, -15759, -15760, -15762, -15763, - -15764, -15766, -15767, -15768, -15770, -15770, -15771, -15773, - -15774, -15775, -15777, -15778, -15778, -15780, -15781, -15782, - -15784, -15785, -15786, -15788, -15789, -15790, -15791, -15792, - -15793, -15794, -15795, -15796, -15796, -15798, -15799, -15799, - -15801, -15802, -15803, -15804, -15805, -15806, -15807, -15808, - -15809, -15810, -15811, -15811, -15813, -15814, -15815, -15816, - -15817, -15818, -15819, -15820, -15821, -15822, -15824, -15825, - -15826, -15827, -15828, -15829, -15829, -15830, -15831, -15833, - -15834, -15835, -15836, -15837, -15838, -15839, -15840, -15841, - -15843, -15844, -15845, -15846, -15848, -15849, -15850, -15851, - -15852, -15853, -15855, -15856, -15857, -15859, -15858, -15859, - -15861, -15861, -15860, -15862, -15863, -15863, -15864, -15865, - -15866, -15868, -15869, -15870, -15871, -15873, -15874, -15875, - -15877, -15878, -15879, -15881, -15882, -15883, -15885, -15886, - -15887, -15889, -15890, -15889, -15891, -15892, -15893, -15894, - -15893, -15893, -15895, -15896, -15897, -15898, -15900, -15901, - -15902, -15904, -15905, -15904, -15905, -15906, -15907, -15909, - -15910, -15909, -15909, -15910, -15911, -15913, -15914, -15915, - -15916, -15915, -15916, -15918, -15919, -15920, -15921, -15923, - -15922, -15921, -15923, -15924, -15925, -15927, -15928, -15929, - -15931, -15932, -15932, -15932, -15932, -15933, -15935, -15936, - -15937, -15939, -15940, -15941, -15943, -15944, -15945, -15945, - -15945, -15945, -15945, -15946, -15947, -15948, -15950, -15951, - -15952, -15954, -15955, -15956, -15958, -15959, -15960, -15962, - -15963, -15964, -15966, -15967, -15968, -15970, -15971, -15972, - -15974, -}; - -static uint8_t vfpu_sin_lut_exceptions[86938]= -{ - 15, 83,128, 26,128, 86, 6, 24, 72, 4,128, 83,128,192, 90,192, - 22, 6, 24, 72, 4, 83, 79, 72, 15, 68,192,128, 83, 8, 79, 15, - 68,128,192, 15, 83, 8, 79,192,128,192, 19, 72, 15, 79, 4,192, - 19, 72, 15, 4, 72, 88, 88, 6, 22, 19,192, 90,128, 4, 70, 86, - 83,128, 26, 90, 4, 70,128, 68, 88,128, 4, 24, 22, 83,128, 26, -192, 24, 22, 22, 83, 22, 83, 8, 83, 8, 19, 72, 19, 72, 83, 22, - 86,192, 0, 88, 24, 26, 4, 90, 70, 72, 22, 86, 26, 6, 72, 4, - 72, 22, 68, 83, 8, 86, 26, 4, 19, 72, 22, 64, 72, 68, 6, 0, - 24, 64, 24, 90, 64, 90, 68, 64, 6, 64, 19, 72, 4, 64, 70, 83, -121, 0, 88, 26, 64, 64, 64, 72, 22, 64, 64, 0, 0, 88, 26, 64, - 86, 64, 24, 0, 22, 0, 64, 0, 64, 0, 72, 70, 83, 0, 88, 0, - 8, 64, 6, 72, 26, 64, 24, 64, 72, 57, 70, 83, 90, 0, 22, 64, - 70, 8,133,134,135, 8,141,142,143, 16,149,150,151, 24,158,159, - 32, 33,166, 39, 40, 41,174, 47, 48, 49, 55, 56, 57, 58, 63,196, - 69, 70, 71, 76, 77, 78,211, 84, 85, 86,219, 92, 93,226,227,100, -101,234,235,108,241,242,115,116,249,250,123, 3, 4, 5, 6, 11, - 12, 13, 14, 19, 20, 21, 26, 27, 28, 29, 34, 35, 36,169, 42, 43, - 44,177, 50, 51,184,185, 58, 59,192, 65,198, 71, 72, 73,206, 79, - 80,213,214, 87, 88,221,222, 95,228,229,102,103,236,237,110,243, -244,245,118,251,252,253, 4, 5, 6, 11, 12, 13, 14, 19, 20, 21, -154, 27, 28, 29,162, 35, 36,169,170, 43, 44,177, 50, 51,184,185, - 58, 59,192, 65,198,199, 72, 73,206,207, 80,213,214, 87, 88,221, -222, 95,228,229,230,103,236,237,238,243,244,245,246,251,252,253, - 0,133, 6, 7, 8,141, 14, 15,148,149, 22, 23,156,157, 30,163, -164, 37, 38,171,172, 45,178,179,180, 53,186,187,188, 67, 68, 69, - 74, 75, 76, 77, 82, 83, 84,217, 90, 91, 92,225, 98, 99,232,105, -106,107,240,113,114,247,248,121,122,255,128,133,134, 7, 8,141, -142, 15,148,149, 22, 23,156,157, 30,163,164,165, 38,171,172,173, -178,179,180, 53,186,187,188, 67, 68, 69, 70, 75, 76, 77, 78, 83, - 84, 85, 90, 91, 92, 93, 98, 99,100,233,106,107,108,241,114,115, -248,249,122,123,128,134,135,136, 9,142,143,144, 17,150,151,152, - 25,159,160, 33, 34,167, 40, 41, 42,175, 48, 49, 50, 56, 57, 58, - 59,196,197, 70, 71,204, 77, 78,211,212, 85, 86,219,220, 93,226, -227,228,101,234,235,236,241,242,243,116,249,250,251, 2, 3, 4, - 5, 10, 11, 12, 13, 18, 19, 20, 25, 26, 27, 28, 33, 34, 35,168, - 41, 42, 43,176, 49, 50,183,184, 57, 58,191,197,198,199, 72,205, -206,207, 80,213,214,215, 88,222,223, 96, 97,230,103,104,105,238, -111,112,113,119,120,121,122,127,132, 5, 6, 7, 12, 13, 14,147, - 20, 21, 22,155, 28, 29,162,163, 36, 37,170,171, 44,177,178, 51, - 52,185,186, 59,192,198,199,200, 73,206,207,208, 81,214,215, 88, - 89,222,223, 96, 97,231,104,105,106,239,112,113,114,119,120,121, -122,127, 0, 1,134, 7, 8, 9,142, 15, 16,149,150, 23, 24,157, - 30, 31,164,165, 38, 39,172,173, 46,179,180,181, 54,187,188,189, - 67, 68, 69, 70, 75, 76, 77, 78, 83, 84, 85,218, 91, 92, 93,226, - 99,100,233,106,107,108,241,114,115,248,249,122,123,128, 1,134, -135, 8, 9,142, 15, 16,149,150, 23, 24,157,158, 31,164,165,166, - 39,172,173,174,179,180,181, 54,187,188,189, 68, 69, 70, 71, 76, - 77, 78,211, 84, 85, 86, 91, 92, 93,226, 99,100,101,234,107,108, -241,242,115,116,249,250,123, 2, 3, 4, 5, 10, 11, 12, 13, 18, - 19, 20,153, 26, 27, 28,161, 34, 35,168, 41, 42, 43,176, 49, 50, -183,184, 57, 58,191,192,197,198, 71, 72,205, 78, 79,212,213, 86, - 87,220,221, 94,227,228,229,102,235,236,237,242,243,244,117,250, -251,252, 3, 4, 5, 6, 11, 12, 13, 14, 19, 20, 21, 26, 27, 28, - 29, 34, 35, 36,169, 42, 43, 44,177, 50, 51,184,185, 58, 59,192, -198,199,200, 73,206,207,208, 81,214,215,216, 89,223, 96, 97, 98, -231,104,105,106,239,112,113,114,120,121,122,123,132, 5, 6, 7, -140, 13, 14,147,148, 21, 22,155,156, 29,162,163,164, 37,170,171, - 44,177,178,179, 52,185,186,187, 66, 67, 68, 69, 74, 75, 76, 81, - 82, 83, 84, 89, 90, 91,224, 97, 98, 99,232,105,106,239,240,113, 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64, 25, 64, 0, 64, 64, 0, 0, 64, 64, 69, 0, 0, 64, 64, 0, - 64, 0, 64, 64, 64, 0, 64, 0, 4, 0, 64, 64, 64, 0, 64, 0, -128, 86, 21,192,128, 85,128,192,128,192,128, 22, 85, 21,192,128, -192,128,192, 21,192,128,192,128,192, 23, 86, 21, 85,128,192,128, -192,128,128,192,184,128,192,128,192, 22, 86, 21, 89,128,192,128, - 86, 22,184,192, 22,192,192, 23,128, 86, 85,192,192,128,128,128, -192, 21, 86,192, 86, 27,192,192, 21, 69, 64, 0, 0, 27, 64, 69, - 0, 64, 0,248, 64, 0, 64, 64, 64, 0, 0, 64, 0, 64, 0, 0, - 0, 0, 64, 64, 0, 64, 0, 64, 0, 0, 0, 64, 64, 0, 0, 0, - 64, 64, 64, 0, 0, 64, 0, 0, 0, 0, 0, 0,248, 64, 64, 64, - 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 0, 0, 0, 0, 0, 0, - 64, 64,192,192,192,192,192, 94,128,128,128, 1,192, 92,192,128, - 28, 31,192, 94,128,128,128,192,192,128,128, 33,192, 94,128,192, - 92, 27,192,128, 94,192, 29,192, 27,128,192, 31,192,192,128, 30, -192,128,128,192,192,128, 30,128, 91, 96, 68,128,192, 93,192,192, -192,128, 93, 94,192,128,128,192, 32, 4,128,128,128,192,128, 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0, 64, - 64, 0, 64, 0, 64, 0, 64, 0, 64, 0, - }; diff --git a/Core/System.cpp b/Core/System.cpp index 8303f08a15..a4ba6bf524 100644 --- a/Core/System.cpp +++ b/Core/System.cpp @@ -290,7 +290,7 @@ bool CPU_Init(std::string *errorString) { // likely to collide with any commercial ones. g_CoreParameter.compat.Load(g_paramSFO.GetDiscID()); - InitVFPUSinCos(); + InitVFPU(); if (allowPlugins) HLEPlugins::Init(); diff --git a/assets/vfpu/vfpu_asin_lut65536.dat b/assets/vfpu/vfpu_asin_lut65536.dat new file mode 100644 index 0000000000000000000000000000000000000000..507f51f24bbd5604f7f178dc30e3050b02345ffd GIT binary patch literal 1536 zcmXApdsK{h7{|Zw+gz%dGN#*1qr1{gS1Ik*hF#@sXL+ZYn$nFdSsR;9h00cjgp$o_ z2}Lfkh(xVJVzbrCl5L5@8td4|?jnV*vybDS_x=37=leY0=l7o9`vZV?xg0$|yd&~B zydj=8asYnca@ft#B6k4Eg&YD|pb~SKM;keG6LXs@m?K*`q#FRste-Il$~n040H69` zcDRzm5n`QkE4%Fwhb4UA_Sge9=M)FN0GQw4ZSdO#4n@RgvI`78`jx|MA=S?P-5}&H z)e_sgJM#*kaR@gAMikk+e}_3RMl_Fo2XC{95^coEfeJnxl?XQmT2j*ZsewueL_p-> 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