util: import public domain code for integer division by a constant

Compilers can use this to generate optimal code for integer division
by a constant.

Additionally, an unsigned division by a uniform that is constant but not
known at compile time can still be optimized by passing 2-4 division
factors to the shader as uniforms and executing one of the fast_udiv*
variants. The signed division algorithm doesn't have this capability.

Reviewed-by: Jason Ekstrand <jason@jlekstrand.net>
Reviewed-by: Marek Olšák <marek.olsak@amd.com>

src/util/Makefile.sources

@@ -11,6 +11,8 @@ MESA_UTIL_FILES := \
 	debug.h \
 	disk_cache.c \
 	disk_cache.h \
+	fast_idiv_by_const.c \
+	fast_idiv_by_const.h \
 	format_r11g11b10f.h \
 	format_rgb9e5.h \
 	format_srgb.h \

src/util/fast_idiv_by_const.c

@@ -0,0 +1,224 @@
+/*
+ * Copyright © 2018 Advanced Micro Devices, Inc.
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining a
+ * copy of this software and associated documentation files (the "Software"),
+ * to deal in the Software without restriction, including without limitation
+ * the rights to use, copy, modify, merge, publish, distribute, sublicense,
+ * and/or sell copies of the Software, and to permit persons to whom the
+ * Software is furnished to do so, subject to the following conditions:
+ *
+ * The above copyright notice and this permission notice (including the next
+ * paragraph) shall be included in all copies or substantial portions of the
+ * Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+ * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.  IN NO EVENT SHALL
+ * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+ * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
+ * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
+ * IN THE SOFTWARE.
+ */
+
+/* Imported from:
+ *   https://raw.githubusercontent.com/ridiculousfish/libdivide/master/divide_by_constants_codegen_reference.c
+ * Paper:
+ *   http://ridiculousfish.com/files/faster_unsigned_division_by_constants.pdf
+ *
+ * The author, ridiculous_fish, wrote:
+ *
+ *  ''Reference implementations of computing and using the "magic number"
+ *    approach to dividing by constants, including codegen instructions.
+ *    The unsigned division incorporates the "round down" optimization per
+ *    ridiculous_fish.
+ *
+ *    This is free and unencumbered software. Any copyright is dedicated
+ *    to the Public Domain.''
+ */
+
+#include "fast_idiv_by_const.h"
+#include "u_math.h"
+#include <limits.h>
+#include <assert.h>
+
+/* uint_t and sint_t can be replaced by different integer types and the code
+ * will work as-is. The only requirement is that sizeof(uintN) == sizeof(intN).
+ */
+
+struct util_fast_udiv_info
+util_compute_fast_udiv_info(uint_t D, unsigned num_bits)
+{
+   /* The numerator must fit in a uint_t */
+   assert(num_bits > 0 && num_bits <= sizeof(uint_t) * CHAR_BIT);
+   assert(D != 0);
+
+   /* The eventual result */
+   struct util_fast_udiv_info result;
+
+   /* Bits in a uint_t */
+   const unsigned UINT_BITS = sizeof(uint_t) * CHAR_BIT;
+
+   /* The extra shift implicit in the difference between UINT_BITS and num_bits
+    */
+   const unsigned extra_shift = UINT_BITS - num_bits;
+
+   /* The initial power of 2 is one less than the first one that can possibly
+    * work.
+    */
+   const uint_t initial_power_of_2 = (uint_t)1 << (UINT_BITS-1);
+
+   /* The remainder and quotient of our power of 2 divided by d */
+   uint_t quotient = initial_power_of_2 / D;
+   uint_t remainder = initial_power_of_2 % D;
+
+   /* ceil(log_2 D) */
+   unsigned ceil_log_2_D;
+
+   /* The magic info for the variant "round down" algorithm */
+   uint_t down_multiplier = 0;
+   unsigned down_exponent = 0;
+   int has_magic_down = 0;
+
+   /* Compute ceil(log_2 D) */
+   ceil_log_2_D = 0;
+   uint_t tmp;
+   for (tmp = D; tmp > 0; tmp >>= 1)
+      ceil_log_2_D += 1;
+
+
+   /* Begin a loop that increments the exponent, until we find a power of 2
+    * that works.
+    */
+   unsigned exponent;
+   for (exponent = 0; ; exponent++) {
+      /* Quotient and remainder is from previous exponent; compute it for this
+       * exponent.
+       */
+      if (remainder >= D - remainder) {
+         /* Doubling remainder will wrap around D */
+         quotient = quotient * 2 + 1;
+         remainder = remainder * 2 - D;
+      } else {
+         /* Remainder will not wrap */
+         quotient = quotient * 2;
+         remainder = remainder * 2;
+      }
+
+      /* We're done if this exponent works for the round_up algorithm.
+       * Note that exponent may be larger than the maximum shift supported,
+       * so the check for >= ceil_log_2_D is critical.
+       */
+      if ((exponent + extra_shift >= ceil_log_2_D) ||
+          (D - remainder) <= ((uint_t)1 << (exponent + extra_shift)))
+         break;
+
+      /* Set magic_down if we have not set it yet and this exponent works for
+       * the round_down algorithm
+       */
+      if (!has_magic_down &&
+          remainder <= ((uint_t)1 << (exponent + extra_shift))) {
+         has_magic_down = 1;
+         down_multiplier = quotient;
+         down_exponent = exponent;
+      }
+   }
+
+   if (exponent < ceil_log_2_D) {
+      /* magic_up is efficient */
+      result.multiplier = quotient + 1;
+      result.pre_shift = 0;
+      result.post_shift = exponent;
+      result.increment = 0;
+   } else if (D & 1) {
+      /* Odd divisor, so use magic_down, which must have been set */
+      assert(has_magic_down);
+      result.multiplier = down_multiplier;
+      result.pre_shift = 0;
+      result.post_shift = down_exponent;
+      result.increment = 1;
+   } else {
+      /* Even divisor, so use a prefix-shifted dividend */
+      unsigned pre_shift = 0;
+      uint_t shifted_D = D;
+      while ((shifted_D & 1) == 0) {
+         shifted_D >>= 1;
+         pre_shift += 1;
+      }
+      result = util_compute_fast_udiv_info(shifted_D, num_bits - pre_shift);
+      /* expect no increment or pre_shift in this path */
+      assert(result.increment == 0 && result.pre_shift == 0);
+      result.pre_shift = pre_shift;
+   }
+   return result;
+}
+
+struct util_fast_sdiv_info
+util_compute_fast_sdiv_info(sint_t D)
+{
+   /* D must not be zero. */
+   assert(D != 0);
+   /* The result is not correct for these divisors. */
+   assert(D != 1 && D != -1);
+
+   /* Our result */
+   struct util_fast_sdiv_info result;
+
+   /* Bits in an sint_t */
+   const unsigned SINT_BITS = sizeof(sint_t) * CHAR_BIT;
+
+   /* Absolute value of D (we know D is not the most negative value since
+    * that's a power of 2)
+    */
+   const uint_t abs_d = (D < 0 ? -D : D);
+
+   /* The initial power of 2 is one less than the first one that can possibly
+    * work */
+   /* "two31" in Warren */
+   unsigned exponent = SINT_BITS - 1;
+   const uint_t initial_power_of_2 = (uint_t)1 << exponent;
+
+   /* Compute the absolute value of our "test numerator,"
+    * which is the largest dividend whose remainder with d is d-1.
+    * This is called anc in Warren.
+    */
+   const uint_t tmp = initial_power_of_2 + (D < 0);
+   const uint_t abs_test_numer = tmp - 1 - tmp % abs_d;
+
+   /* Initialize our quotients and remainders (q1, r1, q2, r2 in Warren) */
+   uint_t quotient1 = initial_power_of_2 / abs_test_numer;
+   uint_t remainder1 = initial_power_of_2 % abs_test_numer;
+   uint_t quotient2 = initial_power_of_2 / abs_d;
+   uint_t remainder2 = initial_power_of_2 % abs_d;
+   uint_t delta;
+
+   /* Begin our loop */
+   do {
+      /* Update the exponent */
+      exponent++;
+
+      /* Update quotient1 and remainder1 */
+      quotient1 *= 2;
+      remainder1 *= 2;
+      if (remainder1 >= abs_test_numer) {
+         quotient1 += 1;
+         remainder1 -= abs_test_numer;
+      }
+
+      /* Update quotient2 and remainder2 */
+      quotient2 *= 2;
+      remainder2 *= 2;
+      if (remainder2 >= abs_d) {
+         quotient2 += 1;
+         remainder2 -= abs_d;
+      }
+
+      /* Keep going as long as (2**exponent) / abs_d <= delta */
+      delta = abs_d - remainder2;
+   } while (quotient1 < delta || (quotient1 == delta && remainder1 == 0));
+
+   result.multiplier = quotient2 + 1;
+   if (D < 0) result.multiplier = -result.multiplier;
+   result.shift = exponent - SINT_BITS;
+   return result;
+}

src/util/fast_idiv_by_const.h

@@ -0,0 +1,137 @@
+/*
+ * Copyright © 2018 Advanced Micro Devices, Inc.
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining a
+ * copy of this software and associated documentation files (the "Software"),
+ * to deal in the Software without restriction, including without limitation
+ * the rights to use, copy, modify, merge, publish, distribute, sublicense,
+ * and/or sell copies of the Software, and to permit persons to whom the
+ * Software is furnished to do so, subject to the following conditions:
+ *
+ * The above copyright notice and this permission notice (including the next
+ * paragraph) shall be included in all copies or substantial portions of the
+ * Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+ * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.  IN NO EVENT SHALL
+ * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+ * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
+ * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
+ * IN THE SOFTWARE.
+ */
+
+#ifndef FAST_IDIV_BY_CONST_H
+#define FAST_IDIV_BY_CONST_H
+
+/* Imported from:
+ *   https://raw.githubusercontent.com/ridiculousfish/libdivide/master/divide_by_constants_codegen_reference.c
+ */
+
+#include <inttypes.h>
+#include <limits.h>
+#include <assert.h>
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+/* You can set these to different types to get different precision. */
+typedef int32_t sint_t;
+typedef uint32_t uint_t;
+
+/* Computes "magic info" for performing signed division by a fixed integer D.
+ * The type 'sint_t' is assumed to be defined as a signed integer type large
+ * enough to hold both the dividend and the divisor.
+ * Here >> is arithmetic (signed) shift, and >>> is logical shift.
+ *
+ * To emit code for n/d, rounding towards zero, use the following sequence:
+ *
+ *   m = compute_signed_magic_info(D)
+ *   emit("result = (m.multiplier * n) >> SINT_BITS");
+ *   if d > 0 and m.multiplier < 0: emit("result += n")
+ *   if d < 0 and m.multiplier > 0: emit("result -= n")
+ *   if m.post_shift > 0: emit("result >>= m.shift")
+ *   emit("result += (result < 0)")
+ *
+ * The shifts by SINT_BITS may be "free" if the high half of the full multiply
+ * is put in a separate register.
+ *
+ * The final add can of course be implemented via the sign bit, e.g.
+ *    result += (result >>> (SINT_BITS - 1))
+ * or
+ *    result -= (result >> (SINT_BITS - 1))
+ *
+ * This code is heavily indebted to Hacker's Delight by Henry Warren.
+ * See http://www.hackersdelight.org/HDcode/magic.c.txt
+ * Used with permission from http://www.hackersdelight.org/permissions.htm
+ */
+
+struct util_fast_sdiv_info {
+   sint_t multiplier; /* the "magic number" multiplier */
+   unsigned shift; /* shift for the dividend after multiplying */
+};
+
+struct util_fast_sdiv_info
+util_compute_fast_sdiv_info(sint_t D);
+
+/* Computes "magic info" for performing unsigned division by a fixed positive
+ * integer D. The type 'uint_t' is assumed to be defined as an unsigned
+ * integer type large enough to hold both the dividend and the divisor.
+ * num_bits can be set appropriately if n is known to be smaller than
+ * the largest uint_t; if this is not known then pass
+ * "(sizeof(uint_t) * CHAR_BIT)" for num_bits.
+ *
+ * Assume we have a hardware register of width UINT_BITS, a known constant D
+ * which is not zero and not a power of 2, and a variable n of width num_bits
+ * (which may be up to UINT_BITS). To emit code for n/d, use one of the two
+ * following sequences (here >>> refers to a logical bitshift):
+ *
+ *   m = compute_unsigned_magic_info(D, num_bits)
+ *   if m.pre_shift > 0: emit("n >>>= m.pre_shift")
+ *   if m.increment: emit("n = saturated_increment(n)")
+ *   emit("result = (m.multiplier * n) >>> UINT_BITS")
+ *   if m.post_shift > 0: emit("result >>>= m.post_shift")
+ *
+ * or
+ *
+ *   m = compute_unsigned_magic_info(D, num_bits)
+ *   if m.pre_shift > 0: emit("n >>>= m.pre_shift")
+ *   emit("result = m.multiplier * n")
+ *   if m.increment: emit("result = result + m.multiplier")
+ *   emit("result >>>= UINT_BITS")
+ *   if m.post_shift > 0: emit("result >>>= m.post_shift")
+ *
+ * The shifts by UINT_BITS may be "free" if the high half of the full multiply
+ * is put in a separate register.
+ *
+ * saturated_increment(n) means "increment n unless it would wrap to 0," i.e.
+ *   if n == (1 << UINT_BITS)-1: result = n
+ *   else: result = n+1
+ * A common way to implement this is with the carry bit. For example, on x86:
+ *   add 1
+ *   sbb 0
+ *
+ * Some invariants:
+ *   1: At least one of pre_shift and increment is zero
+ *   2: multiplier is never zero
+ *
+ * This code incorporates the "round down" optimization per ridiculous_fish.
+ */
+
+struct util_fast_udiv_info {
+   uint_t multiplier; /* the "magic number" multiplier */
+   unsigned pre_shift; /* shift for the dividend before multiplying */
+   unsigned post_shift; /* shift for the dividend after multiplying */
+   int increment; /* 0 or 1; if set then increment the numerator, using one of
+                     the two strategies */
+};
+
+struct util_fast_udiv_info
+util_compute_fast_udiv_info(uint_t D, unsigned num_bits);
+
+#ifdef __cplusplus
+} /* extern C */
+#endif
+
+#endif /* FAST_IDIV_BY_CONST_H */

src/util/meson.build

@@ -35,6 +35,8 @@ files_mesa_util = files(
   'debug.h',
   'disk_cache.c',
   'disk_cache.h',
+  'fast_idiv_by_const.c',
+  'fast_idiv_by_const.h',
   'format_r11g11b10f.h',
   'format_rgb9e5.h',
   'format_srgb.h',