mirror of
https://github.com/projectPiki/pikmin2.git
synced 2025-01-22 14:04:23 +00:00
finish matching fdlibm files
fdlibm complete!
This commit is contained in:
EpochFlame
parent
46774da475
commit
6b9f925f74
@ -1,226 +0,0 @@
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.include "macros.inc"
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.section .sdata2, "a" # 0x80516360 - 0x80520E40
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.balign 8
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.global lbl_805170F0
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lbl_805170F0:
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.4byte 0x3FF921FB
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.4byte 0x54442D18
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.global lbl_805170F8
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lbl_805170F8:
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.4byte 0x3C91A626
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.4byte 0x33145C07
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.global lbl_80517100
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lbl_80517100:
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.4byte 0x7E37E43C
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.4byte 0x8800759C
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.global lbl_80517108
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lbl_80517108:
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.4byte 0x3FF00000
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.4byte 0x00000000
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.global lbl_80517110
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lbl_80517110:
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.4byte 0x3FC55555
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.4byte 0x55555555
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.global lbl_80517118
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lbl_80517118:
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.4byte 0xBFD4D612
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.4byte 0x03EB6F7D
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.global lbl_80517120
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lbl_80517120:
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.4byte 0x3FC9C155
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.4byte 0x0E884455
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.global lbl_80517128
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lbl_80517128:
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.4byte 0xBFA48228
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.4byte 0xB5688F3B
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.global lbl_80517130
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lbl_80517130:
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.4byte 0x3F49EFE0
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.4byte 0x7501B288
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.global lbl_80517138
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lbl_80517138:
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.4byte 0x3F023DE1
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.4byte 0x0DFDF709
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.global lbl_80517140
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lbl_80517140:
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.4byte 0xC0033A27
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.4byte 0x1C8A2D4B
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.global lbl_80517148
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lbl_80517148:
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.4byte 0x40002AE5
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.4byte 0x9C598AC8
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.global lbl_80517150
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lbl_80517150:
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.4byte 0xBFE6066C
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.4byte 0x1B8D0159
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.global lbl_80517158
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lbl_80517158:
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.4byte 0x3FB3B8C5
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.4byte 0xB12E9282
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.global lbl_80517160
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lbl_80517160:
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.4byte 0x3FE00000
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.4byte 0x00000000
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.global lbl_80517168
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lbl_80517168:
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.4byte 0x40000000
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.4byte 0x00000000
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.global lbl_80517170
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lbl_80517170:
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.4byte 0x3FE921FB
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.4byte 0x54442D18
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.section .text, "ax" # 0x800056C0 - 0x80472F00
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.global __ieee754_asin
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__ieee754_asin:
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/* 800CC3B0 000C92F0 94 21 FF B0 */ stwu r1, -0x50(r1)
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/* 800CC3B4 000C92F4 7C 08 02 A6 */ mflr r0
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/* 800CC3B8 000C92F8 90 01 00 54 */ stw r0, 0x54(r1)
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/* 800CC3BC 000C92FC DB E1 00 40 */ stfd f31, 0x40(r1)
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/* 800CC3C0 000C9300 F3 E1 00 48 */ psq_st f31, 72(r1), 0, qr0
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/* 800CC3C4 000C9304 DB C1 00 30 */ stfd f30, 0x30(r1)
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/* 800CC3C8 000C9308 F3 C1 00 38 */ psq_st f30, 56(r1), 0, qr0
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/* 800CC3CC 000C930C DB A1 00 20 */ stfd f29, 0x20(r1)
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/* 800CC3D0 000C9310 F3 A1 00 28 */ psq_st f29, 40(r1), 0, qr0
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/* 800CC3D4 000C9314 93 E1 00 1C */ stw r31, 0x1c(r1)
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/* 800CC3D8 000C9318 93 C1 00 18 */ stw r30, 0x18(r1)
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/* 800CC3DC 000C931C D8 21 00 08 */ stfd f1, 8(r1)
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/* 800CC3E0 000C9320 3C 00 3F F0 */ lis r0, 0x3ff0
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/* 800CC3E4 000C9324 83 E1 00 08 */ lwz r31, 8(r1)
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/* 800CC3E8 000C9328 57 FE 00 7E */ clrlwi r30, r31, 1
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/* 800CC3EC 000C932C 7C 1E 00 00 */ cmpw r30, r0
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/* 800CC3F0 000C9330 41 80 00 34 */ blt lbl_800CC424
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/* 800CC3F4 000C9334 80 01 00 0C */ lwz r0, 0xc(r1)
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/* 800CC3F8 000C9338 3C 7E C0 10 */ addis r3, r30, 0xc010
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/* 800CC3FC 000C933C 7C 60 03 79 */ or. r0, r3, r0
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/* 800CC400 000C9340 40 82 00 18 */ bne lbl_800CC418
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/* 800CC404 000C9344 C8 02 8D 98 */ lfd f0, lbl_805170F8@sda21(r2)
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/* 800CC408 000C9348 C8 42 8D 90 */ lfd f2, lbl_805170F0@sda21(r2)
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/* 800CC40C 000C934C FC 00 00 72 */ fmul f0, f0, f1
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/* 800CC410 000C9350 FC 22 00 7A */ fmadd f1, f2, f1, f0
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/* 800CC414 000C9354 48 00 01 A4 */ b lbl_800CC5B8
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lbl_800CC418:
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/* 800CC418 000C9358 3C 60 80 51 */ lis r3, __float_nan@ha
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/* 800CC41C 000C935C C0 23 48 B0 */ lfs f1, __float_nan@l(r3)
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/* 800CC420 000C9360 48 00 01 98 */ b lbl_800CC5B8
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lbl_800CC424:
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/* 800CC424 000C9364 3C 00 3F E0 */ lis r0, 0x3fe0
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/* 800CC428 000C9368 7C 1E 00 00 */ cmpw r30, r0
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/* 800CC42C 000C936C 40 80 00 94 */ bge lbl_800CC4C0
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/* 800CC430 000C9370 3C 00 3E 40 */ lis r0, 0x3e40
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/* 800CC434 000C9374 7C 1E 00 00 */ cmpw r30, r0
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/* 800CC438 000C9378 40 80 00 1C */ bge lbl_800CC454
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/* 800CC43C 000C937C C8 42 8D A0 */ lfd f2, lbl_80517100@sda21(r2)
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/* 800CC440 000C9380 C8 02 8D A8 */ lfd f0, lbl_80517108@sda21(r2)
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/* 800CC444 000C9384 FC 42 08 2A */ fadd f2, f2, f1
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/* 800CC448 000C9388 FC 02 00 40 */ fcmpo cr0, f2, f0
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/* 800CC44C 000C938C 40 81 00 0C */ ble lbl_800CC458
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/* 800CC450 000C9390 48 00 01 68 */ b lbl_800CC5B8
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lbl_800CC454:
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/* 800CC454 000C9394 FF E1 00 72 */ fmul f31, f1, f1
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lbl_800CC458:
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/* 800CC458 000C9398 C8 22 8D D8 */ lfd f1, lbl_80517138@sda21(r2)
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/* 800CC45C 000C939C C8 02 8D D0 */ lfd f0, lbl_80517130@sda21(r2)
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/* 800CC460 000C93A0 C8 42 8D C8 */ lfd f2, lbl_80517128@sda21(r2)
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/* 800CC464 000C93A4 FC 61 07 FA */ fmadd f3, f1, f31, f0
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/* 800CC468 000C93A8 C8 C2 8D C0 */ lfd f6, lbl_80517120@sda21(r2)
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/* 800CC46C 000C93AC C8 22 8D F8 */ lfd f1, lbl_80517158@sda21(r2)
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/* 800CC470 000C93B0 C8 02 8D F0 */ lfd f0, lbl_80517150@sda21(r2)
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/* 800CC474 000C93B4 C8 A2 8D B8 */ lfd f5, lbl_80517118@sda21(r2)
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/* 800CC478 000C93B8 FC FF 10 FA */ fmadd f7, f31, f3, f2
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/* 800CC47C 000C93BC C8 42 8D E8 */ lfd f2, lbl_80517148@sda21(r2)
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/* 800CC480 000C93C0 FC 61 07 FA */ fmadd f3, f1, f31, f0
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/* 800CC484 000C93C4 C8 82 8D B0 */ lfd f4, lbl_80517110@sda21(r2)
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/* 800CC488 000C93C8 C8 22 8D E0 */ lfd f1, lbl_80517140@sda21(r2)
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/* 800CC48C 000C93CC FC DF 31 FA */ fmadd f6, f31, f7, f6
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/* 800CC490 000C93D0 C8 02 8D A8 */ lfd f0, lbl_80517108@sda21(r2)
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/* 800CC494 000C93D4 FC 5F 10 FA */ fmadd f2, f31, f3, f2
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/* 800CC498 000C93D8 C8 E1 00 08 */ lfd f7, 8(r1)
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/* 800CC49C 000C93DC FC 7F 29 BA */ fmadd f3, f31, f6, f5
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/* 800CC4A0 000C93E0 FC 3F 08 BA */ fmadd f1, f31, f2, f1
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/* 800CC4A4 000C93E4 FC 5F 20 FA */ fmadd f2, f31, f3, f4
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/* 800CC4A8 000C93E8 FC 1F 00 7A */ fmadd f0, f31, f1, f0
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/* 800CC4AC 000C93EC FC 3F 00 B2 */ fmul f1, f31, f2
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/* 800CC4B0 000C93F0 FC 01 00 24 */ fdiv f0, f1, f0
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/* 800CC4B4 000C93F4 FC 27 38 3A */ fmadd f1, f7, f0, f7
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/* 800CC4B8 000C93F8 D8 01 00 10 */ stfd f0, 0x10(r1)
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/* 800CC4BC 000C93FC 48 00 00 FC */ b lbl_800CC5B8
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lbl_800CC4C0:
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/* 800CC4C0 000C9400 FC 20 0A 10 */ fabs f1, f1
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/* 800CC4C4 000C9404 C9 22 8D A8 */ lfd f9, lbl_80517108@sda21(r2)
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/* 800CC4C8 000C9408 C8 02 8E 00 */ lfd f0, lbl_80517160@sda21(r2)
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/* 800CC4CC 000C940C C8 E2 8D D8 */ lfd f7, lbl_80517138@sda21(r2)
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/* 800CC4D0 000C9410 FD 09 08 28 */ fsub f8, f9, f1
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/* 800CC4D4 000C9414 C8 62 8D D0 */ lfd f3, lbl_80517130@sda21(r2)
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/* 800CC4D8 000C9418 C8 C2 8D C8 */ lfd f6, lbl_80517128@sda21(r2)
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/* 800CC4DC 000C941C C8 A2 8D C0 */ lfd f5, lbl_80517120@sda21(r2)
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/* 800CC4E0 000C9420 FF E0 02 32 */ fmul f31, f0, f8
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/* 800CC4E4 000C9424 C8 42 8D F8 */ lfd f2, lbl_80517158@sda21(r2)
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/* 800CC4E8 000C9428 C8 02 8D F0 */ lfd f0, lbl_80517150@sda21(r2)
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/* 800CC4EC 000C942C C8 82 8D B8 */ lfd f4, lbl_80517118@sda21(r2)
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/* 800CC4F0 000C9430 C8 22 8D E8 */ lfd f1, lbl_80517148@sda21(r2)
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/* 800CC4F4 000C9434 FC E7 1F FA */ fmadd f7, f7, f31, f3
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/* 800CC4F8 000C9438 C8 62 8D B0 */ lfd f3, lbl_80517110@sda21(r2)
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/* 800CC4FC 000C943C FC 42 07 FA */ fmadd f2, f2, f31, f0
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/* 800CC500 000C9440 C8 02 8D E0 */ lfd f0, lbl_80517140@sda21(r2)
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/* 800CC504 000C9444 D9 01 00 10 */ stfd f8, 0x10(r1)
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/* 800CC508 000C9448 FC DF 31 FA */ fmadd f6, f31, f7, f6
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/* 800CC50C 000C944C FC 3F 08 BA */ fmadd f1, f31, f2, f1
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/* 800CC510 000C9450 FC 5F 29 BA */ fmadd f2, f31, f6, f5
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/* 800CC514 000C9454 FC 1F 00 7A */ fmadd f0, f31, f1, f0
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/* 800CC518 000C9458 FC 3F 20 BA */ fmadd f1, f31, f2, f4
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/* 800CC51C 000C945C FF BF 48 3A */ fmadd f29, f31, f0, f9
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/* 800CC520 000C9460 FC 1F 18 7A */ fmadd f0, f31, f1, f3
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/* 800CC524 000C9464 FC 20 F8 90 */ fmr f1, f31
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/* 800CC528 000C9468 FF DF 00 32 */ fmul f30, f31, f0
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/* 800CC52C 000C946C 48 00 37 91 */ bl sqrt
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/* 800CC530 000C9470 3C 60 3F EF */ lis r3, 0x3FEF3333@ha
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/* 800CC534 000C9474 38 03 33 33 */ addi r0, r3, 0x3FEF3333@l
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/* 800CC538 000C9478 7C 1E 00 00 */ cmpw r30, r0
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/* 800CC53C 000C947C 41 80 00 28 */ blt lbl_800CC564
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/* 800CC540 000C9480 FC 9E E8 24 */ fdiv f4, f30, f29
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/* 800CC544 000C9484 C8 42 8E 08 */ lfd f2, lbl_80517168@sda21(r2)
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/* 800CC548 000C9488 C8 02 8D 98 */ lfd f0, lbl_805170F8@sda21(r2)
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/* 800CC54C 000C948C C8 62 8D 90 */ lfd f3, lbl_805170F0@sda21(r2)
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/* 800CC550 000C9490 FC 21 09 3A */ fmadd f1, f1, f4, f1
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/* 800CC554 000C9494 D8 81 00 10 */ stfd f4, 0x10(r1)
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/* 800CC558 000C9498 FC 02 00 78 */ fmsub f0, f2, f1, f0
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/* 800CC55C 000C949C FC 23 00 28 */ fsub f1, f3, f0
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/* 800CC560 000C94A0 48 00 00 48 */ b lbl_800CC5A8
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lbl_800CC564:
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/* 800CC564 000C94A4 D8 21 00 10 */ stfd f1, 0x10(r1)
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/* 800CC568 000C94A8 38 00 00 00 */ li r0, 0
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/* 800CC56C 000C94AC C8 E2 8E 08 */ lfd f7, lbl_80517168@sda21(r2)
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/* 800CC570 000C94B0 FC BE E8 24 */ fdiv f5, f30, f29
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/* 800CC574 000C94B4 90 01 00 14 */ stw r0, 0x14(r1)
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/* 800CC578 000C94B8 C8 02 8D 98 */ lfd f0, lbl_805170F8@sda21(r2)
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/* 800CC57C 000C94BC C9 01 00 10 */ lfd f8, 0x10(r1)
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/* 800CC580 000C94C0 C8 42 8E 10 */ lfd f2, lbl_80517170@sda21(r2)
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/* 800CC584 000C94C4 FC 88 FA 3C */ fnmsub f4, f8, f8, f31
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/* 800CC588 000C94C8 FC 61 40 2A */ fadd f3, f1, f8
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/* 800CC58C 000C94CC FC C7 00 72 */ fmul f6, f7, f1
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/* 800CC590 000C94D0 FC 24 18 24 */ fdiv f1, f4, f3
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/* 800CC594 000C94D4 FC 27 00 7C */ fnmsub f1, f7, f1, f0
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/* 800CC598 000C94D8 FC 07 12 3C */ fnmsub f0, f7, f8, f2
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/* 800CC59C 000C94DC FC 26 09 78 */ fmsub f1, f6, f5, f1
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/* 800CC5A0 000C94E0 FC 01 00 28 */ fsub f0, f1, f0
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/* 800CC5A4 000C94E4 FC 22 00 28 */ fsub f1, f2, f0
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lbl_800CC5A8:
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/* 800CC5A8 000C94E8 2C 1F 00 00 */ cmpwi r31, 0
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/* 800CC5AC 000C94EC 40 81 00 08 */ ble lbl_800CC5B4
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/* 800CC5B0 000C94F0 48 00 00 08 */ b lbl_800CC5B8
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lbl_800CC5B4:
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/* 800CC5B4 000C94F4 FC 20 08 50 */ fneg f1, f1
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lbl_800CC5B8:
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/* 800CC5B8 000C94F8 E3 E1 00 48 */ psq_l f31, 72(r1), 0, qr0
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/* 800CC5BC 000C94FC CB E1 00 40 */ lfd f31, 0x40(r1)
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/* 800CC5C0 000C9500 E3 C1 00 38 */ psq_l f30, 56(r1), 0, qr0
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/* 800CC5C4 000C9504 CB C1 00 30 */ lfd f30, 0x30(r1)
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/* 800CC5C8 000C9508 E3 A1 00 28 */ psq_l f29, 40(r1), 0, qr0
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/* 800CC5CC 000C950C CB A1 00 20 */ lfd f29, 0x20(r1)
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/* 800CC5D0 000C9510 83 E1 00 1C */ lwz r31, 0x1c(r1)
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/* 800CC5D4 000C9514 80 01 00 54 */ lwz r0, 0x54(r1)
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/* 800CC5D8 000C9518 83 C1 00 18 */ lwz r30, 0x18(r1)
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/* 800CC5DC 000C951C 7C 08 03 A6 */ mtlr r0
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/* 800CC5E0 000C9520 38 21 00 50 */ addi r1, r1, 0x50
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/* 800CC5E4 000C9524 4E 80 00 20 */ blr
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@ -1,170 +0,0 @@
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.include "macros.inc"
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.section .sdata2, "a" # 0x80516360 - 0x80520E40
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.balign 8
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.global lbl_805175E8
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lbl_805175E8:
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.4byte 0x3FF00000
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.4byte 0x00000000
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.section .text, "ax" # 0x800056C0 - 0x80472F00
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.global __ieee754_sqrt
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__ieee754_sqrt:
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/* 800CFA2C 000CC96C 94 21 FF E0 */ stwu r1, -0x20(r1)
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/* 800CFA30 000CC970 D8 21 00 08 */ stfd f1, 8(r1)
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/* 800CFA34 000CC974 80 C1 00 08 */ lwz r6, 8(r1)
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/* 800CFA38 000CC978 80 01 00 0C */ lwz r0, 0xc(r1)
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/* 800CFA3C 000CC97C 54 C3 00 56 */ rlwinm r3, r6, 0, 1, 0xb
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/* 800CFA40 000CC980 3C 63 80 10 */ addis r3, r3, 0x8010
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/* 800CFA44 000CC984 28 03 00 00 */ cmplwi r3, 0
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/* 800CFA48 000CC988 40 82 00 14 */ bne lbl_800CFA5C
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/* 800CFA4C 000CC98C FC 21 08 7A */ fmadd f1, f1, f1, f1
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/* 800CFA50 000CC990 38 00 00 21 */ li r0, 0x21
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/* 800CFA54 000CC994 90 0D 8C C0 */ stw r0, errno@sda21(r13)
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/* 800CFA58 000CC998 48 00 01 F0 */ b lbl_800CFC48
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lbl_800CFA5C:
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/* 800CFA5C 000CC99C 2C 06 00 00 */ cmpwi r6, 0
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/* 800CFA60 000CC9A0 41 81 00 30 */ bgt lbl_800CFA90
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/* 800CFA64 000CC9A4 54 C3 00 7E */ clrlwi r3, r6, 1
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/* 800CFA68 000CC9A8 7C 03 1B 79 */ or. r3, r0, r3
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/* 800CFA6C 000CC9AC 40 82 00 08 */ bne lbl_800CFA74
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/* 800CFA70 000CC9B0 48 00 01 D8 */ b lbl_800CFC48
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lbl_800CFA74:
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/* 800CFA74 000CC9B4 2C 06 00 00 */ cmpwi r6, 0
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/* 800CFA78 000CC9B8 40 80 00 18 */ bge lbl_800CFA90
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/* 800CFA7C 000CC9BC 3C 60 80 51 */ lis r3, __float_nan@ha
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/* 800CFA80 000CC9C0 38 00 00 21 */ li r0, 0x21
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/* 800CFA84 000CC9C4 90 0D 8C C0 */ stw r0, errno@sda21(r13)
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/* 800CFA88 000CC9C8 C0 23 48 B0 */ lfs f1, __float_nan@l(r3)
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/* 800CFA8C 000CC9CC 48 00 01 BC */ b lbl_800CFC48
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lbl_800CFA90:
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/* 800CFA90 000CC9D0 7C C3 A6 71 */ srawi. r3, r6, 0x14
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/* 800CFA94 000CC9D4 40 82 00 50 */ bne lbl_800CFAE4
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/* 800CFA98 000CC9D8 48 00 00 14 */ b lbl_800CFAAC
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lbl_800CFA9C:
|
||||
/* 800CFA9C 000CC9DC 54 04 AA FE */ srwi r4, r0, 0xb
|
||||
/* 800CFAA0 000CC9E0 54 00 A8 14 */ slwi r0, r0, 0x15
|
||||
/* 800CFAA4 000CC9E4 7C C6 23 78 */ or r6, r6, r4
|
||||
/* 800CFAA8 000CC9E8 38 63 FF EB */ addi r3, r3, -21
|
||||
lbl_800CFAAC:
|
||||
/* 800CFAAC 000CC9EC 2C 06 00 00 */ cmpwi r6, 0
|
||||
/* 800CFAB0 000CC9F0 41 82 FF EC */ beq lbl_800CFA9C
|
||||
/* 800CFAB4 000CC9F4 38 E0 00 00 */ li r7, 0
|
||||
/* 800CFAB8 000CC9F8 48 00 00 0C */ b lbl_800CFAC4
|
||||
lbl_800CFABC:
|
||||
/* 800CFABC 000CC9FC 54 C6 08 3C */ slwi r6, r6, 1
|
||||
/* 800CFAC0 000CCA00 38 E7 00 01 */ addi r7, r7, 1
|
||||
lbl_800CFAC4:
|
||||
/* 800CFAC4 000CCA04 54 C4 02 D7 */ rlwinm. r4, r6, 0, 0xb, 0xb
|
||||
/* 800CFAC8 000CCA08 41 82 FF F4 */ beq lbl_800CFABC
|
||||
/* 800CFACC 000CCA0C 20 87 00 20 */ subfic r4, r7, 0x20
|
||||
/* 800CFAD0 000CCA10 38 A7 FF FF */ addi r5, r7, -1
|
||||
/* 800CFAD4 000CCA14 7C 04 24 30 */ srw r4, r0, r4
|
||||
/* 800CFAD8 000CCA18 7C 00 38 30 */ slw r0, r0, r7
|
||||
/* 800CFADC 000CCA1C 7C 65 18 50 */ subf r3, r5, r3
|
||||
/* 800CFAE0 000CCA20 7C C6 23 78 */ or r6, r6, r4
|
||||
lbl_800CFAE4:
|
||||
/* 800CFAE4 000CCA24 38 83 FC 01 */ addi r4, r3, -1023
|
||||
/* 800CFAE8 000CCA28 54 C5 03 3E */ clrlwi r5, r6, 0xc
|
||||
/* 800CFAEC 000CCA2C 54 84 07 FF */ clrlwi. r4, r4, 0x1f
|
||||
/* 800CFAF0 000CCA30 64 A5 00 10 */ oris r5, r5, 0x10
|
||||
/* 800CFAF4 000CCA34 41 82 00 14 */ beq lbl_800CFB08
|
||||
/* 800CFAF8 000CCA38 54 04 0F FE */ srwi r4, r0, 0x1f
|
||||
/* 800CFAFC 000CCA3C 7C 00 02 14 */ add r0, r0, r0
|
||||
/* 800CFB00 000CCA40 7C 84 2A 14 */ add r4, r4, r5
|
||||
/* 800CFB04 000CCA44 7C A5 22 14 */ add r5, r5, r4
|
||||
lbl_800CFB08:
|
||||
/* 800CFB08 000CCA48 54 04 0F FE */ srwi r4, r0, 0x1f
|
||||
/* 800CFB0C 000CCA4C 7C 00 02 14 */ add r0, r0, r0
|
||||
/* 800CFB10 000CCA50 7C 84 2A 14 */ add r4, r4, r5
|
||||
/* 800CFB14 000CCA54 39 20 00 00 */ li r9, 0
|
||||
/* 800CFB18 000CCA58 7C A5 22 14 */ add r5, r5, r4
|
||||
/* 800CFB1C 000CCA5C 39 60 00 00 */ li r11, 0
|
||||
/* 800CFB20 000CCA60 39 40 00 00 */ li r10, 0
|
||||
/* 800CFB24 000CCA64 39 80 00 00 */ li r12, 0
|
||||
/* 800CFB28 000CCA68 3C C0 00 20 */ lis r6, 0x20
|
||||
/* 800CFB2C 000CCA6C 48 00 00 30 */ b lbl_800CFB5C
|
||||
lbl_800CFB30:
|
||||
/* 800CFB30 000CCA70 7C 8B 32 14 */ add r4, r11, r6
|
||||
/* 800CFB34 000CCA74 7C 04 28 00 */ cmpw r4, r5
|
||||
/* 800CFB38 000CCA78 41 81 00 10 */ bgt lbl_800CFB48
|
||||
/* 800CFB3C 000CCA7C 7D 64 32 14 */ add r11, r4, r6
|
||||
/* 800CFB40 000CCA80 7C A4 28 50 */ subf r5, r4, r5
|
||||
/* 800CFB44 000CCA84 7D 8C 32 14 */ add r12, r12, r6
|
||||
lbl_800CFB48:
|
||||
/* 800CFB48 000CCA88 54 04 0F FE */ srwi r4, r0, 0x1f
|
||||
/* 800CFB4C 000CCA8C 7C 00 02 14 */ add r0, r0, r0
|
||||
/* 800CFB50 000CCA90 7C 84 2A 14 */ add r4, r4, r5
|
||||
/* 800CFB54 000CCA94 54 C6 F8 7E */ srwi r6, r6, 1
|
||||
/* 800CFB58 000CCA98 7C A5 22 14 */ add r5, r5, r4
|
||||
lbl_800CFB5C:
|
||||
/* 800CFB5C 000CCA9C 28 06 00 00 */ cmplwi r6, 0
|
||||
/* 800CFB60 000CCAA0 40 82 FF D0 */ bne lbl_800CFB30
|
||||
/* 800CFB64 000CCAA4 3C C0 80 00 */ lis r6, 0x8000
|
||||
/* 800CFB68 000CCAA8 48 00 00 6C */ b lbl_800CFBD4
|
||||
lbl_800CFB6C:
|
||||
/* 800CFB6C 000CCAAC 7C 0B 28 00 */ cmpw r11, r5
|
||||
/* 800CFB70 000CCAB0 7D 67 5B 78 */ mr r7, r11
|
||||
/* 800CFB74 000CCAB4 7D 09 32 14 */ add r8, r9, r6
|
||||
/* 800CFB78 000CCAB8 41 80 00 10 */ blt lbl_800CFB88
|
||||
/* 800CFB7C 000CCABC 40 82 00 44 */ bne lbl_800CFBC0
|
||||
/* 800CFB80 000CCAC0 7C 08 00 40 */ cmplw r8, r0
|
||||
/* 800CFB84 000CCAC4 41 81 00 3C */ bgt lbl_800CFBC0
|
||||
lbl_800CFB88:
|
||||
/* 800CFB88 000CCAC8 55 04 00 00 */ rlwinm r4, r8, 0, 0, 0
|
||||
/* 800CFB8C 000CCACC 7D 28 32 14 */ add r9, r8, r6
|
||||
/* 800CFB90 000CCAD0 3C 84 80 00 */ addis r4, r4, 0x8000
|
||||
/* 800CFB94 000CCAD4 28 04 00 00 */ cmplwi r4, 0
|
||||
/* 800CFB98 000CCAD8 40 82 00 10 */ bne lbl_800CFBA8
|
||||
/* 800CFB9C 000CCADC 55 24 00 01 */ rlwinm. r4, r9, 0, 0, 0
|
||||
/* 800CFBA0 000CCAE0 40 82 00 08 */ bne lbl_800CFBA8
|
||||
/* 800CFBA4 000CCAE4 39 6B 00 01 */ addi r11, r11, 1
|
||||
lbl_800CFBA8:
|
||||
/* 800CFBA8 000CCAE8 7C 00 40 40 */ cmplw r0, r8
|
||||
/* 800CFBAC 000CCAEC 7C A7 28 50 */ subf r5, r7, r5
|
||||
/* 800CFBB0 000CCAF0 40 80 00 08 */ bge lbl_800CFBB8
|
||||
/* 800CFBB4 000CCAF4 38 A5 FF FF */ addi r5, r5, -1
|
||||
lbl_800CFBB8:
|
||||
/* 800CFBB8 000CCAF8 7C 08 00 50 */ subf r0, r8, r0
|
||||
/* 800CFBBC 000CCAFC 7D 4A 32 14 */ add r10, r10, r6
|
||||
lbl_800CFBC0:
|
||||
/* 800CFBC0 000CCB00 54 04 0F FE */ srwi r4, r0, 0x1f
|
||||
/* 800CFBC4 000CCB04 7C 00 02 14 */ add r0, r0, r0
|
||||
/* 800CFBC8 000CCB08 7C 84 2A 14 */ add r4, r4, r5
|
||||
/* 800CFBCC 000CCB0C 54 C6 F8 7E */ srwi r6, r6, 1
|
||||
/* 800CFBD0 000CCB10 7C A5 22 14 */ add r5, r5, r4
|
||||
lbl_800CFBD4:
|
||||
/* 800CFBD4 000CCB14 28 06 00 00 */ cmplwi r6, 0
|
||||
/* 800CFBD8 000CCB18 40 82 FF 94 */ bne lbl_800CFB6C
|
||||
/* 800CFBDC 000CCB1C 7C A0 03 79 */ or. r0, r5, r0
|
||||
/* 800CFBE0 000CCB20 41 82 00 30 */ beq lbl_800CFC10
|
||||
/* 800CFBE4 000CCB24 C8 02 92 88 */ lfd f0, lbl_805175E8@sda21(r2)
|
||||
/* 800CFBE8 000CCB28 3C 0A 00 01 */ addis r0, r10, 1
|
||||
/* 800CFBEC 000CCB2C 28 00 FF FF */ cmplwi r0, 0xffff
|
||||
/* 800CFBF0 000CCB30 D8 01 00 10 */ stfd f0, 0x10(r1)
|
||||
/* 800CFBF4 000CCB34 D8 01 00 10 */ stfd f0, 0x10(r1)
|
||||
/* 800CFBF8 000CCB38 40 82 00 10 */ bne lbl_800CFC08
|
||||
/* 800CFBFC 000CCB3C 39 40 00 00 */ li r10, 0
|
||||
/* 800CFC00 000CCB40 39 8C 00 01 */ addi r12, r12, 1
|
||||
/* 800CFC04 000CCB44 48 00 00 0C */ b lbl_800CFC10
|
||||
lbl_800CFC08:
|
||||
/* 800CFC08 000CCB48 55 40 07 FE */ clrlwi r0, r10, 0x1f
|
||||
/* 800CFC0C 000CCB4C 7D 4A 02 14 */ add r10, r10, r0
|
||||
lbl_800CFC10:
|
||||
/* 800CFC10 000CCB50 55 80 07 FE */ clrlwi r0, r12, 0x1f
|
||||
/* 800CFC14 000CCB54 7D 84 0E 70 */ srawi r4, r12, 1
|
||||
/* 800CFC18 000CCB58 2C 00 00 01 */ cmpwi r0, 1
|
||||
/* 800CFC1C 000CCB5C 55 45 F8 7E */ srwi r5, r10, 1
|
||||
/* 800CFC20 000CCB60 3C 84 3F E0 */ addis r4, r4, 0x3fe0
|
||||
/* 800CFC24 000CCB64 40 82 00 08 */ bne lbl_800CFC2C
|
||||
/* 800CFC28 000CCB68 64 A5 80 00 */ oris r5, r5, 0x8000
|
||||
lbl_800CFC2C:
|
||||
/* 800CFC2C 000CCB6C 38 03 FC 01 */ addi r0, r3, -1023
|
||||
/* 800CFC30 000CCB70 90 A1 00 14 */ stw r5, 0x14(r1)
|
||||
/* 800CFC34 000CCB74 7C 00 0E 70 */ srawi r0, r0, 1
|
||||
/* 800CFC38 000CCB78 54 00 A0 16 */ slwi r0, r0, 0x14
|
||||
/* 800CFC3C 000CCB7C 7C 84 02 14 */ add r4, r4, r0
|
||||
/* 800CFC40 000CCB80 90 81 00 10 */ stw r4, 0x10(r1)
|
||||
/* 800CFC44 000CCB84 C8 21 00 10 */ lfd f1, 0x10(r1)
|
||||
lbl_800CFC48:
|
||||
/* 800CFC48 000CCB88 38 21 00 20 */ addi r1, r1, 0x20
|
||||
/* 800CFC4C 000CCB8C 4E 80 00 20 */ blr
|
||||
@ -306,7 +306,7 @@ DOLPHIN:=\
|
||||
$(BUILD_DIR)/asm/Dolphin/strtoul.o\
|
||||
$(BUILD_DIR)/src/Dolphin/wchar_io.o\
|
||||
$(BUILD_DIR)/src/Dolphin/uart_console_io_gcn.o\
|
||||
$(BUILD_DIR)/asm/Dolphin/e_asin.o\
|
||||
$(BUILD_DIR)/src/Dolphin/e_asin.o\
|
||||
$(BUILD_DIR)/src/Dolphin/e_atan2.o\
|
||||
$(BUILD_DIR)/src/Dolphin/e_exp.o\
|
||||
$(BUILD_DIR)/src/Dolphin/e_fmod.o\
|
||||
@ -334,7 +334,7 @@ DOLPHIN:=\
|
||||
$(BUILD_DIR)/src/Dolphin/w_fmod.o\
|
||||
$(BUILD_DIR)/src/Dolphin/w_log10.o\
|
||||
$(BUILD_DIR)/src/Dolphin/w_pow.o\
|
||||
$(BUILD_DIR)/asm/Dolphin/e_sqrt.o\
|
||||
$(BUILD_DIR)/src/Dolphin/e_sqrt.o\
|
||||
$(BUILD_DIR)/src/Dolphin/math_ppc.o\
|
||||
$(BUILD_DIR)/src/Dolphin/w_sqrt.o\
|
||||
$(BUILD_DIR)/asm/Dolphin/extras.o\
|
||||
|
||||
@ -42,6 +42,8 @@
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
#include "Dolphin/float.h"
|
||||
#include "Dolphin/math.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double
|
||||
@ -79,7 +81,7 @@ double __ieee754_asin(x) double x;
|
||||
if (((ix - 0x3ff00000) | __LO(x)) == 0)
|
||||
/* asin(1)=+-pi/2 with inexact */
|
||||
return x * pio2_hi + x * pio2_lo;
|
||||
return (x - x) / (x - x); /* asin(|x|>1) is NaN */
|
||||
return __float_nan; /* asin(|x|>1) is NaN */
|
||||
} else if (ix < 0x3fe00000) { /* |x|<0.5 */
|
||||
if (ix < 0x3e400000) { /* if |x| < 2**-27 */
|
||||
if (huge + x > one)
|
||||
@ -92,7 +94,7 @@ double __ieee754_asin(x) double x;
|
||||
return x + x * w;
|
||||
}
|
||||
/* 1> |x|>= 0.5 */
|
||||
w = one - __fabs(x);
|
||||
w = one - fabs(x);
|
||||
t = w * 0.5;
|
||||
p = t * (pS0 + t * (pS1 + t * (pS2 + t * (pS3 + t * (pS4 + t * pS5)))));
|
||||
q = one + t * (qS1 + t * (qS2 + t * (qS3 + t * qS4)));
|
||||
|
||||
@ -1,194 +1,468 @@
|
||||
|
||||
|
||||
/*
|
||||
* --INFO--
|
||||
* Address: 800CFA2C
|
||||
* Size: 000224
|
||||
*/
|
||||
void __ieee754_sqrt(void)
|
||||
|
||||
/* @(#)e_sqrt.c 1.3 95/01/18 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/* __ieee754_sqrt(x)
|
||||
* Return correctly rounded sqrt.
|
||||
* ------------------------------------------
|
||||
* | Use the hardware sqrt if you have one |
|
||||
* ------------------------------------------
|
||||
* Method:
|
||||
* Bit by bit method using integer arithmetic. (Slow, but portable)
|
||||
* 1. Normalization
|
||||
* Scale x to y in [1,4) with even powers of 2:
|
||||
* find an integer k such that 1 <= (y=x*2^(2k)) < 4, then
|
||||
* sqrt(x) = 2^k * sqrt(y)
|
||||
* 2. Bit by bit computation
|
||||
* Let q = sqrt(y) truncated to i bit after binary point (q = 1),
|
||||
* i 0
|
||||
* i+1 2
|
||||
* s = 2*q , and y = 2 * ( y - q ). (1)
|
||||
* i i i i
|
||||
*
|
||||
* To compute q from q , one checks whether
|
||||
* i+1 i
|
||||
*
|
||||
* -(i+1) 2
|
||||
* (q + 2 ) <= y. (2)
|
||||
* i
|
||||
* -(i+1)
|
||||
* If (2) is false, then q = q ; otherwise q = q + 2 .
|
||||
* i+1 i i+1 i
|
||||
*
|
||||
* With some algebric manipulation, it is not difficult to see
|
||||
* that (2) is equivalent to
|
||||
* -(i+1)
|
||||
* s + 2 <= y (3)
|
||||
* i i
|
||||
*
|
||||
* The advantage of (3) is that s and y can be computed by
|
||||
* i i
|
||||
* the following recurrence formula:
|
||||
* if (3) is false
|
||||
*
|
||||
* s = s , y = y ; (4)
|
||||
* i+1 i i+1 i
|
||||
*
|
||||
* otherwise,
|
||||
* -i -(i+1)
|
||||
* s = s + 2 , y = y - s - 2 (5)
|
||||
* i+1 i i+1 i i
|
||||
*
|
||||
* One may easily use induction to prove (4) and (5).
|
||||
* Note. Since the left hand side of (3) contain only i+2 bits,
|
||||
* it does not necessary to do a full (53-bit) comparison
|
||||
* in (3).
|
||||
* 3. Final rounding
|
||||
* After generating the 53 bits result, we compute one more bit.
|
||||
* Together with the remainder, we can decide whether the
|
||||
* result is exact, bigger than 1/2ulp, or less than 1/2ulp
|
||||
* (it will never equal to 1/2ulp).
|
||||
* The rounding mode can be detected by checking whether
|
||||
* huge + tiny is equal to huge, and whether huge - tiny is
|
||||
* equal to huge for some floating point number "huge" and "tiny".
|
||||
*
|
||||
* Special cases:
|
||||
* sqrt(+-0) = +-0 ... exact
|
||||
* sqrt(inf) = inf
|
||||
* sqrt(-ve) = NaN ... with invalid signal
|
||||
* sqrt(NaN) = NaN ... with invalid signal for signaling NaN
|
||||
*
|
||||
* Other methods : see the appended file at the end of the program below.
|
||||
*---------------
|
||||
*/
|
||||
|
||||
#include "fdlibm.h"
|
||||
#include "errno.h"
|
||||
#include "Dolphin/float.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double one = 1.0, tiny = 1.0e-300;
|
||||
#else
|
||||
static double one = 1.0, tiny = 1.0e-300;
|
||||
#endif
|
||||
|
||||
#ifdef __STDC__
|
||||
double __ieee754_sqrt(double x)
|
||||
#else
|
||||
double __ieee754_sqrt(x) double x;
|
||||
#endif
|
||||
{
|
||||
/*
|
||||
.loc_0x0:
|
||||
stwu r1, -0x20(r1)
|
||||
stfd f1, 0x8(r1)
|
||||
lwz r6, 0x8(r1)
|
||||
lwz r0, 0xC(r1)
|
||||
rlwinm r3,r6,0,1,11
|
||||
subis r3, r3, 0x7FF0
|
||||
cmplwi r3, 0
|
||||
bne- .loc_0x30
|
||||
fmadd f1, f1, f1, f1
|
||||
li r0, 0x21
|
||||
stw r0, -0x7340(r13)
|
||||
b .loc_0x21C
|
||||
double z;
|
||||
int sign = (int)0x80000000;
|
||||
unsigned r, t1, s1, ix1, q1;
|
||||
int ix0, s0, q, m, t, i;
|
||||
|
||||
.loc_0x30:
|
||||
cmpwi r6, 0
|
||||
bgt- .loc_0x64
|
||||
rlwinm r3,r6,0,1,31
|
||||
or. r3, r0, r3
|
||||
bne- .loc_0x48
|
||||
b .loc_0x21C
|
||||
ix0 = __HI(x); /* high word of x */
|
||||
ix1 = __LO(x); /* low word of x */
|
||||
|
||||
.loc_0x48:
|
||||
cmpwi r6, 0
|
||||
bge- .loc_0x64
|
||||
lis r3, 0x8051
|
||||
li r0, 0x21
|
||||
stw r0, -0x7340(r13)
|
||||
lfs f1, 0x48B0(r3)
|
||||
b .loc_0x21C
|
||||
/* take care of Inf and NaN */
|
||||
if ((ix0 & 0x7ff00000) == 0x7ff00000) {
|
||||
errno = 33;
|
||||
return x * x + x; /* sqrt(NaN)=NaN, sqrt(+inf)=+inf
|
||||
sqrt(-inf)=sNaN */
|
||||
}
|
||||
/* take care of zero */
|
||||
if (ix0 <= 0) {
|
||||
if (((ix0 & (~sign)) | ix1) == 0)
|
||||
return x; /* sqrt(+-0) = +-0 */
|
||||
else if (ix0 < 0) {
|
||||
errno = 33;
|
||||
return __float_nan;
|
||||
} /* sqrt(-ve) = sNaN */
|
||||
}
|
||||
/* normalize x */
|
||||
m = (ix0 >> 20);
|
||||
if (m == 0) { /* subnormal x */
|
||||
while (ix0 == 0) {
|
||||
m -= 21;
|
||||
ix0 |= (ix1 >> 11);
|
||||
ix1 <<= 21;
|
||||
}
|
||||
for (i = 0; (ix0 & 0x00100000) == 0; i++)
|
||||
ix0 <<= 1;
|
||||
m -= i - 1;
|
||||
ix0 |= (ix1 >> (32 - i));
|
||||
ix1 <<= i;
|
||||
}
|
||||
m -= 1023; /* unbias exponent */
|
||||
ix0 = (ix0 & 0x000fffff) | 0x00100000;
|
||||
if (m & 1) { /* odd m, double x to make it even */
|
||||
ix0 += ix0 + ((ix1 & sign) >> 31);
|
||||
ix1 += ix1;
|
||||
}
|
||||
m >>= 1; /* m = [m/2] */
|
||||
|
||||
.loc_0x64:
|
||||
srawi. r3, r6, 0x14
|
||||
bne- .loc_0xB8
|
||||
b .loc_0x80
|
||||
/* generate sqrt(x) bit by bit */
|
||||
ix0 += ix0 + ((ix1 & sign) >> 31);
|
||||
ix1 += ix1;
|
||||
q = q1 = s0 = s1 = 0; /* [q,q1] = sqrt(x) */
|
||||
r = 0x00200000; /* r = moving bit from right to left */
|
||||
|
||||
.loc_0x70:
|
||||
rlwinm r4,r0,21,11,31
|
||||
rlwinm r0,r0,21,0,10
|
||||
or r6, r6, r4
|
||||
subi r3, r3, 0x15
|
||||
while (r != 0) {
|
||||
t = s0 + r;
|
||||
if (t <= ix0) {
|
||||
s0 = t + r;
|
||||
ix0 -= t;
|
||||
q += r;
|
||||
}
|
||||
ix0 += ix0 + ((ix1 & sign) >> 31);
|
||||
ix1 += ix1;
|
||||
r >>= 1;
|
||||
}
|
||||
|
||||
.loc_0x80:
|
||||
cmpwi r6, 0
|
||||
beq+ .loc_0x70
|
||||
li r7, 0
|
||||
b .loc_0x98
|
||||
r = sign;
|
||||
while (r != 0) {
|
||||
t1 = s1 + r;
|
||||
t = s0;
|
||||
if ((t < ix0) || ((t == ix0) && (t1 <= ix1))) {
|
||||
s1 = t1 + r;
|
||||
if (((t1 & sign) == sign) && (s1 & sign) == 0)
|
||||
s0 += 1;
|
||||
ix0 -= t;
|
||||
if (ix1 < t1)
|
||||
ix0 -= 1;
|
||||
ix1 -= t1;
|
||||
q1 += r;
|
||||
}
|
||||
ix0 += ix0 + ((ix1 & sign) >> 31);
|
||||
ix1 += ix1;
|
||||
r >>= 1;
|
||||
}
|
||||
|
||||
.loc_0x90:
|
||||
rlwinm r6,r6,1,0,30
|
||||
addi r7, r7, 0x1
|
||||
|
||||
.loc_0x98:
|
||||
rlwinm. r4,r6,0,11,11
|
||||
beq+ .loc_0x90
|
||||
subfic r4, r7, 0x20
|
||||
subi r5, r7, 0x1
|
||||
srw r4, r0, r4
|
||||
slw r0, r0, r7
|
||||
sub r3, r3, r5
|
||||
or r6, r6, r4
|
||||
|
||||
.loc_0xB8:
|
||||
subi r4, r3, 0x3FF
|
||||
rlwinm r5,r6,0,12,31
|
||||
rlwinm. r4,r4,0,31,31
|
||||
oris r5, r5, 0x10
|
||||
beq- .loc_0xDC
|
||||
rlwinm r4,r0,1,31,31
|
||||
add r0, r0, r0
|
||||
add r4, r4, r5
|
||||
add r5, r5, r4
|
||||
|
||||
.loc_0xDC:
|
||||
rlwinm r4,r0,1,31,31
|
||||
add r0, r0, r0
|
||||
add r4, r4, r5
|
||||
li r9, 0
|
||||
add r5, r5, r4
|
||||
li r11, 0
|
||||
li r10, 0
|
||||
li r12, 0
|
||||
lis r6, 0x20
|
||||
b .loc_0x130
|
||||
|
||||
.loc_0x104:
|
||||
add r4, r11, r6
|
||||
cmpw r4, r5
|
||||
bgt- .loc_0x11C
|
||||
add r11, r4, r6
|
||||
sub r5, r5, r4
|
||||
add r12, r12, r6
|
||||
|
||||
.loc_0x11C:
|
||||
rlwinm r4,r0,1,31,31
|
||||
add r0, r0, r0
|
||||
add r4, r4, r5
|
||||
rlwinm r6,r6,31,1,31
|
||||
add r5, r5, r4
|
||||
|
||||
.loc_0x130:
|
||||
cmplwi r6, 0
|
||||
bne+ .loc_0x104
|
||||
lis r6, 0x8000
|
||||
b .loc_0x1A8
|
||||
|
||||
.loc_0x140:
|
||||
cmpw r11, r5
|
||||
mr r7, r11
|
||||
add r8, r9, r6
|
||||
blt- .loc_0x15C
|
||||
bne- .loc_0x194
|
||||
cmplw r8, r0
|
||||
bgt- .loc_0x194
|
||||
|
||||
.loc_0x15C:
|
||||
rlwinm r4,r8,0,0,0
|
||||
add r9, r8, r6
|
||||
subis r4, r4, 0x8000
|
||||
cmplwi r4, 0
|
||||
bne- .loc_0x17C
|
||||
rlwinm. r4,r9,0,0,0
|
||||
bne- .loc_0x17C
|
||||
addi r11, r11, 0x1
|
||||
|
||||
.loc_0x17C:
|
||||
cmplw r0, r8
|
||||
sub r5, r5, r7
|
||||
bge- .loc_0x18C
|
||||
subi r5, r5, 0x1
|
||||
|
||||
.loc_0x18C:
|
||||
sub r0, r0, r8
|
||||
add r10, r10, r6
|
||||
|
||||
.loc_0x194:
|
||||
rlwinm r4,r0,1,31,31
|
||||
add r0, r0, r0
|
||||
add r4, r4, r5
|
||||
rlwinm r6,r6,31,1,31
|
||||
add r5, r5, r4
|
||||
|
||||
.loc_0x1A8:
|
||||
cmplwi r6, 0
|
||||
bne+ .loc_0x140
|
||||
or. r0, r5, r0
|
||||
beq- .loc_0x1E4
|
||||
lfd f0, -0x6D78(r2)
|
||||
addis r0, r10, 0x1
|
||||
cmplwi r0, 0xFFFF
|
||||
stfd f0, 0x10(r1)
|
||||
stfd f0, 0x10(r1)
|
||||
bne- .loc_0x1DC
|
||||
li r10, 0
|
||||
addi r12, r12, 0x1
|
||||
b .loc_0x1E4
|
||||
|
||||
.loc_0x1DC:
|
||||
rlwinm r0,r10,0,31,31
|
||||
add r10, r10, r0
|
||||
|
||||
.loc_0x1E4:
|
||||
rlwinm r0,r12,0,31,31
|
||||
srawi r4, r12, 0x1
|
||||
cmpwi r0, 0x1
|
||||
rlwinm r5,r10,31,1,31
|
||||
addis r4, r4, 0x3FE0
|
||||
bne- .loc_0x200
|
||||
oris r5, r5, 0x8000
|
||||
|
||||
.loc_0x200:
|
||||
subi r0, r3, 0x3FF
|
||||
stw r5, 0x14(r1)
|
||||
srawi r0, r0, 0x1
|
||||
rlwinm r0,r0,20,0,11
|
||||
add r4, r4, r0
|
||||
stw r4, 0x10(r1)
|
||||
lfd f1, 0x10(r1)
|
||||
|
||||
.loc_0x21C:
|
||||
addi r1, r1, 0x20
|
||||
blr
|
||||
*/
|
||||
/* use floating add to find out rounding direction */
|
||||
if ((ix0 | ix1) != 0) {
|
||||
z = one - tiny; /* trigger inexact flag */
|
||||
if (z >= one) {
|
||||
z = one + tiny;
|
||||
if (q1 == (unsigned)0xffffffff) {
|
||||
q1 = 0;
|
||||
q += 1;
|
||||
} else if (z > one) {
|
||||
if (q1 == (unsigned)0xfffffffe)
|
||||
q += 1;
|
||||
q1 += 2;
|
||||
} else
|
||||
q1 += (q1 & 1);
|
||||
}
|
||||
}
|
||||
ix0 = (q >> 1) + 0x3fe00000;
|
||||
ix1 = q1 >> 1;
|
||||
if ((q & 1) == 1)
|
||||
ix1 |= sign;
|
||||
ix0 += (m << 20);
|
||||
__HI(z) = ix0;
|
||||
__LO(z) = ix1;
|
||||
return z;
|
||||
}
|
||||
|
||||
/*
|
||||
Other methods (use floating-point arithmetic)
|
||||
-------------
|
||||
(This is a copy of a drafted paper by Prof W. Kahan
|
||||
and K.C. Ng, written in May, 1986)
|
||||
|
||||
Two algorithms are given here to implement sqrt(x)
|
||||
(IEEE double precision arithmetic) in software.
|
||||
Both supply sqrt(x) correctly rounded. The first algorithm (in
|
||||
Section A) uses newton iterations and involves four divisions.
|
||||
The second one uses reciproot iterations to avoid division, but
|
||||
requires more multiplications. Both algorithms need the ability
|
||||
to chop results of arithmetic operations instead of round them,
|
||||
and the INEXACT flag to indicate when an arithmetic operation
|
||||
is executed exactly with no roundoff error, all part of the
|
||||
standard (IEEE 754-1985). The ability to perform shift, add,
|
||||
subtract and logical AND operations upon 32-bit words is needed
|
||||
too, though not part of the standard.
|
||||
|
||||
A. sqrt(x) by Newton Iteration
|
||||
|
||||
(1) Initial approximation
|
||||
|
||||
Let x0 and x1 be the leading and the trailing 32-bit words of
|
||||
a floating point number x (in IEEE double format) respectively
|
||||
|
||||
1 11 52 ...widths
|
||||
------------------------------------------------------
|
||||
x: |s| e | f |
|
||||
------------------------------------------------------
|
||||
msb lsb msb lsb ...order
|
||||
|
||||
|
||||
------------------------ ------------------------
|
||||
x0: |s| e | f1 | x1: | f2 |
|
||||
------------------------ ------------------------
|
||||
|
||||
By performing shifts and subtracts on x0 and x1 (both regarded
|
||||
as integers), we obtain an 8-bit approximation of sqrt(x) as
|
||||
follows.
|
||||
|
||||
k := (x0>>1) + 0x1ff80000;
|
||||
y0 := k - T1[31&(k>>15)]. ... y ~ sqrt(x) to 8 bits
|
||||
Here k is a 32-bit integer and T1[] is an integer array containing
|
||||
correction terms. Now magically the floating value of y (y's
|
||||
leading 32-bit word is y0, the value of its trailing word is 0)
|
||||
approximates sqrt(x) to almost 8-bit.
|
||||
|
||||
Value of T1:
|
||||
static int T1[32]= {
|
||||
0, 1024, 3062, 5746, 9193, 13348, 18162, 23592,
|
||||
29598, 36145, 43202, 50740, 58733, 67158, 75992, 85215,
|
||||
83599, 71378, 60428, 50647, 41945, 34246, 27478, 21581,
|
||||
16499, 12183, 8588, 5674, 3403, 1742, 661, 130,};
|
||||
|
||||
(2) Iterative refinement
|
||||
|
||||
Apply Heron's rule three times to y, we have y approximates
|
||||
sqrt(x) to within 1 ulp (Unit in the Last Place):
|
||||
|
||||
y := (y+x/y)/2 ... almost 17 sig. bits
|
||||
y := (y+x/y)/2 ... almost 35 sig. bits
|
||||
y := y-(y-x/y)/2 ... within 1 ulp
|
||||
|
||||
|
||||
Remark 1.
|
||||
Another way to improve y to within 1 ulp is:
|
||||
|
||||
y := (y+x/y) ... almost 17 sig. bits to 2*sqrt(x)
|
||||
y := y - 0x00100006 ... almost 18 sig. bits to sqrt(x)
|
||||
|
||||
2
|
||||
(x-y )*y
|
||||
y := y + 2* ---------- ...within 1 ulp
|
||||
2
|
||||
3y + x
|
||||
|
||||
|
||||
This formula has one division fewer than the one above; however,
|
||||
it requires more multiplications and additions. Also x must be
|
||||
scaled in advance to avoid spurious overflow in evaluating the
|
||||
expression 3y*y+x. Hence it is not recommended uless division
|
||||
is slow. If division is very slow, then one should use the
|
||||
reciproot algorithm given in section B.
|
||||
|
||||
(3) Final adjustment
|
||||
|
||||
By twiddling y's last bit it is possible to force y to be
|
||||
correctly rounded according to the prevailing rounding mode
|
||||
as follows. Let r and i be copies of the rounding mode and
|
||||
inexact flag before entering the square root program. Also we
|
||||
use the expression y+-ulp for the next representable floating
|
||||
numbers (up and down) of y. Note that y+-ulp = either fixed
|
||||
point y+-1, or multiply y by nextafter(1,+-inf) in chopped
|
||||
mode.
|
||||
|
||||
I := FALSE; ... reset INEXACT flag I
|
||||
R := RZ; ... set rounding mode to round-toward-zero
|
||||
z := x/y; ... chopped quotient, possibly inexact
|
||||
If(not I) then { ... if the quotient is exact
|
||||
if(z=y) {
|
||||
I := i; ... restore inexact flag
|
||||
R := r; ... restore rounded mode
|
||||
return sqrt(x):=y.
|
||||
} else {
|
||||
z := z - ulp; ... special rounding
|
||||
}
|
||||
}
|
||||
i := TRUE; ... sqrt(x) is inexact
|
||||
If (r=RN) then z=z+ulp ... rounded-to-nearest
|
||||
If (r=RP) then { ... round-toward-+inf
|
||||
y = y+ulp; z=z+ulp;
|
||||
}
|
||||
y := y+z; ... chopped sum
|
||||
y0:=y0-0x00100000; ... y := y/2 is correctly rounded.
|
||||
I := i; ... restore inexact flag
|
||||
R := r; ... restore rounded mode
|
||||
return sqrt(x):=y.
|
||||
|
||||
(4) Special cases
|
||||
|
||||
Square root of +inf, +-0, or NaN is itself;
|
||||
Square root of a negative number is NaN with invalid signal.
|
||||
|
||||
|
||||
B. sqrt(x) by Reciproot Iteration
|
||||
|
||||
(1) Initial approximation
|
||||
|
||||
Let x0 and x1 be the leading and the trailing 32-bit words of
|
||||
a floating point number x (in IEEE double format) respectively
|
||||
(see section A). By performing shifs and subtracts on x0 and y0,
|
||||
we obtain a 7.8-bit approximation of 1/sqrt(x) as follows.
|
||||
|
||||
k := 0x5fe80000 - (x0>>1);
|
||||
y0:= k - T2[63&(k>>14)]. ... y ~ 1/sqrt(x) to 7.8 bits
|
||||
|
||||
Here k is a 32-bit integer and T2[] is an integer array
|
||||
containing correction terms. Now magically the floating
|
||||
value of y (y's leading 32-bit word is y0, the value of
|
||||
its trailing word y1 is set to zero) approximates 1/sqrt(x)
|
||||
to almost 7.8-bit.
|
||||
|
||||
Value of T2:
|
||||
static int T2[64]= {
|
||||
0x1500, 0x2ef8, 0x4d67, 0x6b02, 0x87be, 0xa395, 0xbe7a, 0xd866,
|
||||
0xf14a, 0x1091b,0x11fcd,0x13552,0x14999,0x15c98,0x16e34,0x17e5f,
|
||||
0x18d03,0x19a01,0x1a545,0x1ae8a,0x1b5c4,0x1bb01,0x1bfde,0x1c28d,
|
||||
0x1c2de,0x1c0db,0x1ba73,0x1b11c,0x1a4b5,0x1953d,0x18266,0x16be0,
|
||||
0x1683e,0x179d8,0x18a4d,0x19992,0x1a789,0x1b445,0x1bf61,0x1c989,
|
||||
0x1d16d,0x1d77b,0x1dddf,0x1e2ad,0x1e5bf,0x1e6e8,0x1e654,0x1e3cd,
|
||||
0x1df2a,0x1d635,0x1cb16,0x1be2c,0x1ae4e,0x19bde,0x1868e,0x16e2e,
|
||||
0x1527f,0x1334a,0x11051,0xe951, 0xbe01, 0x8e0d, 0x5924, 0x1edd,};
|
||||
|
||||
(2) Iterative refinement
|
||||
|
||||
Apply Reciproot iteration three times to y and multiply the
|
||||
result by x to get an approximation z that matches sqrt(x)
|
||||
to about 1 ulp. To be exact, we will have
|
||||
-1ulp < sqrt(x)-z<1.0625ulp.
|
||||
|
||||
... set rounding mode to Round-to-nearest
|
||||
y := y*(1.5-0.5*x*y*y) ... almost 15 sig. bits to 1/sqrt(x)
|
||||
y := y*((1.5-2^-30)+0.5*x*y*y)... about 29 sig. bits to 1/sqrt(x)
|
||||
... special arrangement for better accuracy
|
||||
z := x*y ... 29 bits to sqrt(x), with z*y<1
|
||||
z := z + 0.5*z*(1-z*y) ... about 1 ulp to sqrt(x)
|
||||
|
||||
Remark 2. The constant 1.5-2^-30 is chosen to bias the error so that
|
||||
(a) the term z*y in the final iteration is always less than 1;
|
||||
(b) the error in the final result is biased upward so that
|
||||
-1 ulp < sqrt(x) - z < 1.0625 ulp
|
||||
instead of |sqrt(x)-z|<1.03125ulp.
|
||||
|
||||
(3) Final adjustment
|
||||
|
||||
By twiddling y's last bit it is possible to force y to be
|
||||
correctly rounded according to the prevailing rounding mode
|
||||
as follows. Let r and i be copies of the rounding mode and
|
||||
inexact flag before entering the square root program. Also we
|
||||
use the expression y+-ulp for the next representable floating
|
||||
numbers (up and down) of y. Note that y+-ulp = either fixed
|
||||
point y+-1, or multiply y by nextafter(1,+-inf) in chopped
|
||||
mode.
|
||||
|
||||
R := RZ; ... set rounding mode to round-toward-zero
|
||||
switch(r) {
|
||||
case RN: ... round-to-nearest
|
||||
if(x<= z*(z-ulp)...chopped) z = z - ulp; else
|
||||
if(x<= z*(z+ulp)...chopped) z = z; else z = z+ulp;
|
||||
break;
|
||||
case RZ:case RM: ... round-to-zero or round-to--inf
|
||||
R:=RP; ... reset rounding mod to round-to-+inf
|
||||
if(x<z*z ... rounded up) z = z - ulp; else
|
||||
if(x>=(z+ulp)*(z+ulp) ...rounded up) z = z+ulp;
|
||||
break;
|
||||
case RP: ... round-to-+inf
|
||||
if(x>(z+ulp)*(z+ulp)...chopped) z = z+2*ulp; else
|
||||
if(x>z*z ...chopped) z = z+ulp;
|
||||
break;
|
||||
}
|
||||
|
||||
Remark 3. The above comparisons can be done in fixed point. For
|
||||
example, to compare x and w=z*z chopped, it suffices to compare
|
||||
x1 and w1 (the trailing parts of x and w), regarding them as
|
||||
two's complement integers.
|
||||
|
||||
...Is z an exact square root?
|
||||
To determine whether z is an exact square root of x, let z1 be the
|
||||
trailing part of z, and also let x0 and x1 be the leading and
|
||||
trailing parts of x.
|
||||
|
||||
If ((z1&0x03ffffff)!=0) ... not exact if trailing 26 bits of z!=0
|
||||
I := 1; ... Raise Inexact flag: z is not exact
|
||||
else {
|
||||
j := 1 - [(x0>>20)&1] ... j = logb(x) mod 2
|
||||
k := z1 >> 26; ... get z's 25-th and 26-th
|
||||
fraction bits
|
||||
I := i or (k&j) or ((k&(j+j+1))!=(x1&3));
|
||||
}
|
||||
R:= r ... restore rounded mode
|
||||
return sqrt(x):=z.
|
||||
|
||||
If multiplication is cheaper then the foregoing red tape, the
|
||||
Inexact flag can be evaluated by
|
||||
|
||||
I := i;
|
||||
I := (z*z!=x) or I.
|
||||
|
||||
Note that z*z can overwrite I; this value must be sensed if it is
|
||||
True.
|
||||
|
||||
Remark 4. If z*z = x exactly, then bit 25 to bit 0 of z1 must be
|
||||
zero.
|
||||
|
||||
--------------------
|
||||
z1: | f2 |
|
||||
--------------------
|
||||
bit 31 bit 0
|
||||
|
||||
Further more, bit 27 and 26 of z1, bit 0 and 1 of x1, and the odd
|
||||
or even of logb(x) have the following relations:
|
||||
|
||||
-------------------------------------------------
|
||||
bit 27,26 of z1 bit 1,0 of x1 logb(x)
|
||||
-------------------------------------------------
|
||||
00 00 odd and even
|
||||
01 01 even
|
||||
10 10 odd
|
||||
10 00 even
|
||||
11 01 even
|
||||
-------------------------------------------------
|
||||
|
||||
(4) Special cases (see (4) of Section A).
|
||||
|
||||
*/
|
||||
|
||||
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Reference in New Issue
Block a user