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implement 14-bit RCP approximation (used in PFRCP instruction) exactl…
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…y macthing AMD HW

based on tables posted in the paper
Analysis of Reciprocal and Square Root Reciprocal Instructions in the AMD K6-2 Implementation of 3DNow!
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Stanislav Shwartsman committed Jan 22, 2025
1 parent 7a9fb4d commit 751d8f8
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187 changes: 183 additions & 4 deletions bochs/cpu/3dnow_rcp.cc
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Original file line number Diff line number Diff line change
Expand Up @@ -30,9 +30,6 @@

extern softfloat_status_t prepare_softfloat_status_word_3dnow(int rounding_mode);

// use 11-bit SSE approximation function, ideally need to use AVX-512 14-bit approximation but it was compiled only under BX_SUPPORT_AVX/BX_SUPPORT_EVEX so far
extern float32 approximate_rcp(float32 a);

// use 11-bit SSE approximation function, ideally need to use AVX-512 14-bit approximation but it was compiled only under BX_SUPPORT_AVX/BX_SUPPORT_EVEX so far
extern float32 approximate_rsqrt(float32 a);

Expand All @@ -43,6 +40,188 @@ extern float32 approximate_rsqrt(float32 a);
#include "softfloat3e/include/softfloat.h"
#include "fpu/softfloat-specialize.h"

static Bit16u rcp_table1[1024] = {
0xFFBE, 0xFF3E, 0xFEBF, 0xFE40, 0xFDC1, 0xFD42, 0xFCC3, 0xFC45, 0xFBC7, 0xFB49, 0xFACC, 0xFA4F, 0xF9D1, 0xF955, 0xF8D8, 0xF85C, // 0x00 FRACTION MSB[b1..b5]
0xF7E0, 0xF764, 0xF6E8, 0xF66D, 0xF5F2, 0xF577, 0xF4FC, 0xF482, 0xF407, 0xF38D, 0xF314, 0xF29A, 0xF221, 0xF1A8, 0xF12F, 0xF0B7,
0xF03F, 0xEFC6, 0xEF4F, 0xEED7, 0xEE5F, 0xEDE8, 0xED71, 0xECFA, 0xEC84, 0xEC0E, 0xEB97, 0xEB22, 0xEAAC, 0xEA36, 0xE9C1, 0xE94C, // 0x01
0xE8D7, 0xE863, 0xE7EE, 0xE77A, 0xE706, 0xE693, 0xE61F, 0xE5AC, 0xE539, 0xE4C6, 0xE453, 0xE3E1, 0xE36F, 0xE2FD, 0xE28B, 0xE219,
0xE1A8, 0xE136, 0xE0C5, 0xE055, 0xDFE4, 0xDF74, 0xDF04, 0xDE94, 0xDE24, 0xDDB4, 0xDD45, 0xDCD6, 0xDC67, 0xDBF8, 0xDB8A, 0xDB1C, // 0x02
0xDAAD, 0xDA3F, 0xD9D2, 0xD964, 0xD8F7, 0xD88A, 0xD81D, 0xD7B0, 0xD744, 0xD6D7, 0xD66B, 0xD5FF, 0xD593, 0xD528, 0xD4BC, 0xD451,
0xD3E6, 0xD37B, 0xD311, 0xD2A6, 0xD23C, 0xD1D2, 0xD168, 0xD0FF, 0xD095, 0xD02C, 0xCFC3, 0xCF5A, 0xCEF1, 0xCE88, 0xCE20, 0xCDB8, // 0x03
0xCD50, 0xCCE8, 0xCC80, 0xCC19, 0xCBB2, 0xCB4B, 0xCAE4, 0xCA7D, 0xCA16, 0xC9B0, 0xC94A, 0xC8E4, 0xC87E, 0xC818, 0xC7B3, 0xC74D,
0xC6E9, 0xC684, 0xC61F, 0xC5BA, 0xC556, 0xC4F2, 0xC48D, 0xC42A, 0xC3C6, 0xC362, 0xC2FF, 0xC29C, 0xC239, 0xC1D6, 0xC173, 0xC110, // 0x04
0xC0AE, 0xC04C, 0xBFEA, 0xBF88, 0xBF26, 0xBEC5, 0xBE63, 0xBE02, 0xBDA1, 0xBD40, 0xBCDF, 0xBC7F, 0xBC1E, 0xBBBE, 0xBB5E, 0xBAFE,
0xBA9E, 0xBA3E, 0xB9DF, 0xB980, 0xB921, 0xB8C2, 0xB863, 0xB804, 0xB7A6, 0xB747, 0xB6E9, 0xB68B, 0xB62D, 0xB5D0, 0xB572, 0xB515, // 0x05
0xB4B8, 0xB45B, 0xB3FE, 0xB3A1, 0xB344, 0xB2E8, 0xB28C, 0xB230, 0xB1D4, 0xB178, 0xB11C, 0xB0C1, 0xB065, 0xB00A, 0xAFAF, 0xAF54,
0xAEFA, 0xAE9F, 0xAE45, 0xADEB, 0xAD90, 0xAD36, 0xACDC, 0xAC83, 0xAC29, 0xABD0, 0xAB76, 0xAB1D, 0xAAC4, 0xAA6B, 0xAA13, 0xA9BA, // 0x06
0xA962, 0xA909, 0xA8B1, 0xA859, 0xA801, 0xA7AA, 0xA752, 0xA6FB, 0xA6A3, 0xA64C, 0xA5F5, 0xA59E, 0xA548, 0xA4F1, 0xA49B, 0xA444,
0xA3EE, 0xA398, 0xA342, 0xA2EC, 0xA297, 0xA241, 0xA1EC, 0xA197, 0xA141, 0xA0ED, 0xA098, 0xA043, 0x9FEE, 0x9F9A, 0x9F46, 0x9EF2, // 0x07
0x9E9E, 0x9E4A, 0x9DF6, 0x9DA2, 0x9D4F, 0x9CFC, 0x9CA8, 0x9C55, 0x9C02, 0x9BB0, 0x9B5D, 0x9B0A, 0x9AB8, 0x9A66, 0x9A13, 0x99C1,
0x996F, 0x991E, 0x98CC, 0x987A, 0x9829, 0x97D8, 0x9787, 0x9736, 0x96E5, 0x9694, 0x9643, 0x95F3, 0x95A2, 0x9552, 0x9502, 0x94B2, // 0x08
0x9462, 0x9412, 0x93C2, 0x9373, 0x9323, 0x92D4, 0x9285, 0x9236, 0x91E7, 0x9198, 0x9149, 0x90FB, 0x90AC, 0x905E, 0x9010, 0x8FC2,
0x8F74, 0x8F26, 0x8ED8, 0x8E8B, 0x8E3D, 0x8DF0, 0x8DA3, 0x8D56, 0x8D08, 0x8CBC, 0x8C6F, 0x8C22, 0x8BD6, 0x8B89, 0x8B3D, 0x8AF1, // 0x09
0x8AA4, 0x8A58, 0x8A0D, 0x89C1, 0x8975, 0x892A, 0x88DE, 0x8893, 0x8848, 0x87FD, 0x87B2, 0x8767, 0x871C, 0x86D1, 0x8687, 0x863C,
0x85F2, 0x85A8, 0x855E, 0x8514, 0x84CA, 0x8481, 0x8437, 0x83ED, 0x83A4, 0x835B, 0x8311, 0x82C8, 0x827F, 0x8236, 0x81EE, 0x81A5, // 0x0A
0x815C, 0x8114, 0x80CC, 0x8083, 0x803B, 0x7FF3, 0x7FAB, 0x7F63, 0x7F1C, 0x7ED4, 0x7E8D, 0x7E45, 0x7DFE, 0x7DB7, 0x7D70, 0x7D29,
0x7CE1, 0x7C9A, 0x7C54, 0x7C0D, 0x7BC7, 0x7B80, 0x7B3A, 0x7AF4, 0x7AAE, 0x7A68, 0x7A22, 0x79DC, 0x7996, 0x7951, 0x790B, 0x78C6, // 0x0B
0x7881, 0x783C, 0x77F6, 0x77B2, 0x776D, 0x7728, 0x76E3, 0x769F, 0x765A, 0x7616, 0x75D1, 0x758D, 0x7549, 0x7505, 0x74C1, 0x747E,
0x743A, 0x73F7, 0x73B3, 0x7370, 0x732C, 0x72E9, 0x72A6, 0x7263, 0x7220, 0x71DD, 0x719B, 0x7158, 0x7115, 0x70D3, 0x7090, 0x704E, // 0x0C
0x700C, 0x6FCA, 0x6F88, 0x6F46, 0x6F04, 0x6EC2, 0x6E81, 0x6E3F, 0x6DFE, 0x6DBC, 0x6D7B, 0x6D3A, 0x6CF9, 0x6CB8, 0x6C77, 0x6C36,
0x6BF5, 0x6BB4, 0x6B74, 0x6B33, 0x6AF3, 0x6AB3, 0x6A73, 0x6A33, 0x69F2, 0x69B3, 0x6973, 0x6933, 0x68F3, 0x68B4, 0x6874, 0x6835, // 0x0D
0x67F6, 0x67B6, 0x6777, 0x6738, 0x66F9, 0x66BA, 0x667B, 0x663D, 0x65FE, 0x65C0, 0x6581, 0x6543, 0x6505, 0x64C6, 0x6488, 0x644A,
0x640D, 0x63CF, 0x6391, 0x6354, 0x6316, 0x62D8, 0x629B, 0x625E, 0x6220, 0x61E3, 0x61A6, 0x6169, 0x612C, 0x60EF, 0x60B2, 0x6076, // 0x0E
0x6039, 0x5FFD, 0x5FC0, 0x5F84, 0x5F48, 0x5F0B, 0x5ECF, 0x5E93, 0x5E57, 0x5E1B, 0x5DDF, 0x5DA4, 0x5D68, 0x5D2C, 0x5CF1, 0x5CB6,
0x5C7A, 0x5C3F, 0x5C04, 0x5BC8, 0x5B8D, 0x5B53, 0x5B18, 0x5ADD, 0x5AA2, 0x5A68, 0x5A2D, 0x59F2, 0x59B8, 0x597E, 0x5944, 0x5909, // 0x0F
0x58CF, 0x5895, 0x585B, 0x5821, 0x57E8, 0x57AE, 0x5774, 0x573B, 0x5701, 0x56C8, 0x568F, 0x5655, 0x561C, 0x55E3, 0x55AA, 0x5571,
0x5538, 0x54FF, 0x54C6, 0x548E, 0x5455, 0x541D, 0x53E4, 0x53AC, 0x5373, 0x533B, 0x5303, 0x52CB, 0x5293, 0x525B, 0x5223, 0x51EB, // 0x10
0x51B4, 0x517C, 0x5144, 0x510D, 0x50D5, 0x509E, 0x5067, 0x5030, 0x4FF8, 0x4FC1, 0x4F8A, 0x4F53, 0x4F1D, 0x4EE6, 0x4EAF, 0x4E78,
0x4E42, 0x4E0B, 0x4DD5, 0x4D9E, 0x4D68, 0x4D32, 0x4CFC, 0x4CC5, 0x4C8F, 0x4C59, 0x4C24, 0x4BEE, 0x4BB8, 0x4B82, 0x4B4D, 0x4B17, // 0x11
0x4AE2, 0x4AAC, 0x4A77, 0x4A42, 0x4A0C, 0x49D7, 0x49A2, 0x496D, 0x4938, 0x4903, 0x48CE, 0x489A, 0x4865, 0x4830, 0x47FC, 0x47C7,
0x4793, 0x475E, 0x472A, 0x46F6, 0x46C2, 0x468E, 0x465A, 0x4626, 0x45F2, 0x45BE, 0x458A, 0x4556, 0x4523, 0x44EF, 0x44BC, 0x4488, // 0x12
0x4455, 0x4421, 0x43EE, 0x43BB, 0x4388, 0x4355, 0x4322, 0x42EF, 0x42BC, 0x4289, 0x4256, 0x4224, 0x41F1, 0x41BE, 0x418C, 0x4159,
0x4127, 0x40F5, 0x40C2, 0x4090, 0x405E, 0x402C, 0x3FFA, 0x3FC8, 0x3F96, 0x3F64, 0x3F32, 0x3F01, 0x3ECF, 0x3E9D, 0x3E6C, 0x3E3A, // 0x13
0x3E09, 0x3DD8, 0x3DA6, 0x3D75, 0x3D44, 0x3D13, 0x3CE2, 0x3CB1, 0x3C80, 0x3C4F, 0x3C1E, 0x3BED, 0x3BBD, 0x3B8C, 0x3B5B, 0x3B2B,
0x3AFB, 0x3ACA, 0x3A9A, 0x3A69, 0x3A39, 0x3A09, 0x39D9, 0x39A9, 0x3979, 0x3949, 0x3919, 0x38E9, 0x38B9, 0x388A, 0x385A, 0x382A, // 0x14
0x37FB, 0x37CB, 0x379C, 0x376C, 0x373D, 0x370E, 0x36DF, 0x36AF, 0x3680, 0x3651, 0x3622, 0x35F3, 0x35C5, 0x3596, 0x3567, 0x3538,
0x350A, 0x34DB, 0x34AD, 0x347E, 0x3450, 0x3421, 0x33F3, 0x33C5, 0x3396, 0x3368, 0x333A, 0x330C, 0x32DE, 0x32B0, 0x3282, 0x3254, // 0x15
0x3227, 0x31F9, 0x31CB, 0x319D, 0x3170, 0x3142, 0x3115, 0x30E7, 0x30BA, 0x308D, 0x305F, 0x3032, 0x3005, 0x2FD8, 0x2FAB, 0x2F7E,
0x2F51, 0x2F24, 0x2EF7, 0x2ECB, 0x2E9E, 0x2E71, 0x2E45, 0x2E18, 0x2DEB, 0x2DBF, 0x2D93, 0x2D66, 0x2D3A, 0x2D0E, 0x2CE1, 0x2CB5, // 0x16
0x2C89, 0x2C5D, 0x2C31, 0x2C05, 0x2BD9, 0x2BAD, 0x2B81, 0x2B56, 0x2B2A, 0x2AFE, 0x2AD3, 0x2AA7, 0x2A7B, 0x2A50, 0x2A25, 0x29F9,
0x29CE, 0x29A3, 0x2978, 0x294C, 0x2921, 0x28F6, 0x28CB, 0x28A0, 0x2875, 0x284A, 0x281F, 0x27F5, 0x27CA, 0x279F, 0x2775, 0x274A, // 0x17
0x271F, 0x26F5, 0x26CA, 0x26A0, 0x2676, 0x264B, 0x2621, 0x25F7, 0x25CD, 0x25A3, 0x2578, 0x254E, 0x2524, 0x24FB, 0x24D1, 0x24A7,
0x247C, 0x2453, 0x2429, 0x23FF, 0x23D6, 0x23AC, 0x2382, 0x2359, 0x2330, 0x2306, 0x22DD, 0x22B4, 0x228A, 0x2261, 0x2238, 0x220F, // 0x18
0x21E6, 0x21BD, 0x2194, 0x216B, 0x2142, 0x2119, 0x20F0, 0x20C8, 0x209F, 0x2076, 0x204E, 0x2025, 0x1FFD, 0x1FD4, 0x1FAC, 0x1F83,
0x1F5B, 0x1F33, 0x1F0B, 0x1EE3, 0x1EBA, 0x1E92, 0x1E6A, 0x1E42, 0x1E1A, 0x1DF2, 0x1DCA, 0x1DA2, 0x1D7B, 0x1D53, 0x1D2B, 0x1D03, // 0x19
0x1CDC, 0x1CB4, 0x1C8D, 0x1C65, 0x1C3E, 0x1C16, 0x1BEF, 0x1BC8, 0x1BA0, 0x1B79, 0x1B52, 0x1B2B, 0x1B03, 0x1ADC, 0x1AB5, 0x1A8E,
0x1A68, 0x1A41, 0x1A1A, 0x19F3, 0x19CC, 0x19A5, 0x197F, 0x1958, 0x1931, 0x190B, 0x18E4, 0x18BE, 0x1897, 0x1871, 0x184B, 0x1824, // 0x1A
0x17FE, 0x17D8, 0x17B1, 0x178B, 0x1765, 0x173F, 0x1719, 0x16F3, 0x16CD, 0x16A7, 0x1681, 0x165B, 0x1635, 0x1610, 0x15EA, 0x15C4,
0x159E, 0x1578, 0x1553, 0x152D, 0x1508, 0x14E2, 0x14BD, 0x1498, 0x1472, 0x144D, 0x1428, 0x1402, 0x13DD, 0x13B8, 0x1393, 0x136E, // 0x1B
0x1349, 0x1324, 0x12FF, 0x12DA, 0x12B5, 0x1290, 0x126C, 0x1247, 0x1222, 0x11FD, 0x11D9, 0x11B4, 0x1190, 0x116B, 0x1147, 0x1122,
0x10FE, 0x10DA, 0x10B6, 0x1091, 0x106D, 0x1049, 0x1025, 0x1000, 0x0FDC, 0x0FB8, 0x0F94, 0x0F70, 0x0F4C, 0x0F28, 0x0F04, 0x0EE1, // 0x1C
0x0EBD, 0x0E99, 0x0E75, 0x0E52, 0x0E2E, 0x0E0A, 0x0DE7, 0x0DC3, 0x0DA0, 0x0D7C, 0x0D59, 0x0D35, 0x0D12, 0x0CEF, 0x0CCB, 0x0CA8,
0x0C85, 0x0C62, 0x0C3F, 0x0C1C, 0x0BF9, 0x0BD6, 0x0BB3, 0x0B90, 0x0B6D, 0x0B4A, 0x0B27, 0x0B04, 0x0AE1, 0x0ABF, 0x0A9C, 0x0A79, // 0x1D
0x0A57, 0x0A34, 0x0A11, 0x09EF, 0x09CC, 0x09AA, 0x0987, 0x0965, 0x0943, 0x0920, 0x08FE, 0x08DC, 0x08B9, 0x0897, 0x0875, 0x0853,
0x0830, 0x080E, 0x07EC, 0x07CA, 0x07A8, 0x0786, 0x0764, 0x0743, 0x0721, 0x06FF, 0x06DD, 0x06BB, 0x069A, 0x0678, 0x0656, 0x0635, // 0x1E
0x0613, 0x05F2, 0x05D0, 0x05AF, 0x058D, 0x056C, 0x054B, 0x0529, 0x0508, 0x04E7, 0x04C6, 0x04A4, 0x0483, 0x0462, 0x0441, 0x0420,
0x03FF, 0x03DF, 0x03BE, 0x039D, 0x037C, 0x035B, 0x033A, 0x0319, 0x02F8, 0x02D8, 0x02B7, 0x0296, 0x0276, 0x0255, 0x0235, 0x0214, // 0x1F
0x01F4, 0x01D3, 0x01B3, 0x0192, 0x0172, 0x0151, 0x0131, 0x0111, 0x00F1, 0x00D0, 0x00B0, 0x0090, 0x0070, 0x0050, 0x0030, 0x0010
};

// correction table
static Bit8s rcp_table2[1024] = {
62, 58, 54, 50, 46, 43, 39, 35, 31, 27, 23, 19, 15, 12, 8, 4,
0, -4, -8, -12, -16, -20, -23, -27, -31, -35, -39, -43, -47, -51, -54, -58,
58, 54, 51, 47, 43, 40, 36, 32, 29, 25, 21, 18, 14, 10, 7, 3,
0, -4, -8, -11, -15, -19, -22, -26, -30, -33, -37, -41, -44, -48, -52, -55,
55, 52, 48, 45, 41, 38, 34, 31, 27, 24, 21, 17, 14, 10, 7, 3,
0, -4, -7, -10, -14, -17, -21, -24, -28, -31, -35, -38, -41, -45, -48, -52,
52, 49, 45, 42, 39, 36, 32, 29, 26, 23, 19, 16, 13, 10, 6, 3,
0, -3, -7, -10, -13, -16, -20, -23, -26, -29, -33, -36, -39, -42, -46, -49,
49, 46, 43, 40, 37, 34, 31, 27, 24, 21, 18, 15, 12, 9, 6, 3,
0, -3, -6, -9, -13, -16, -19, -22, -25, -28, -31, -34, -37, -40, -43, -46,
47, 44, 41, 38, 35, 32, 30, 27, 24, 21, 18, 15, 12, 9, 6, 3,
0, -3, -5, -8, -11, -14, -17, -20, -23, -26, -29, -32, -35, -38, -40, -43,
44, 41, 38, 36, 33, 30, 27, 25, 22, 19, 16, 14, 11, 8, 5, 3,
0, -3, -6, -9, -11, -14, -17, -20, -22, -25, -28, -31, -33, -36, -39, -42,
42, 39, 37, 34, 31, 29, 26, 24, 21, 18, 16, 13, 10, 8, 5, 3,
0, -3, -5, -8, -11, -13, -16, -18, -21, -24, -26, -29, -32, -34, -37, -39,
40, 37, 35, 33, 30, 28, 25, 23, 20, 18, 15, 13, 10, 8, 5, 3,
0, -2, -5, -7, -10, -12, -15, -17, -20, -22, -25, -27, -30, -32, -35, -37,
38, 36, 33, 31, 28, 26, 24, 21, 19, 17, 14, 12, 9, 7, 5, 2,
0, -2, -5, -7, -10, -12, -14, -17, -19, -21, -24, -26, -29, -31, -33, -36,
36, 34, 31, 29, 27, 25, 22, 20, 18, 16, 13, 11, 9, 6, 4, 2,
0, -3, -5, -7, -9, -12, -14, -16, -18, -21, -23, -25, -28, -30, -32, -34,
35, 33, 31, 28, 26, 24, 22, 20, 18, 16, 13, 11, 9, 7, 5, 3,
0, -2, -4, -6, -8, -10, -13, -15, -17, -19, -21, -23, -26, -28, -30, -32,
33, 31, 29, 27, 25, 23, 21, 19, 16, 14, 12, 10, 8, 6, 4, 2,
0, -2, -4, -6, -8, -10, -13, -15, -17, -19, -21, -23, -25, -27, -29, -31,
32, 30, 28, 26, 24, 22, 20, 18, 16, 14, 12, 10, 8, 6, 4, 2,
0, -2, -4, -6, -8, -10, -12, -14, -16, -17, -19, -21, -23, -25, -27, -29,
30, 28, 26, 24, 22, 21, 19, 17, 15, 13, 11, 9, 7, 5, 3, 2,
0, -2, -4, -6, -8, -10, -12, -14, -15, -17, -19, -21, -23, -25, -27, -29,
29, 27, 25, 24, 22, 20, 18, 16, 14, 13, 11, 9, 7, 5, 4, 2,
0, -2, -4, -6, -7, -9, -11, -13, -15, -16, -18, -20, -22, -24, -25, -27,
28, 26, 25, 23, 21, 19, 18, 16, 14, 12, 11, 9, 7, 5, 4, 2,
0, -2, -3, -5, -7, -9, -10, -12, -14, -16, -17, -19, -21, -23, -24, -26,
27, 25, 24, 22, 20, 19, 17, 15, 14, 12, 10, 9, 7, 5, 4, 2,
0, -1, -3, -5, -6, -8, -10, -11, -13, -15, -16, -18, -20, -21, -23, -25,
26, 24, 23, 21, 20, 18, 16, 15, 13, 12, 10, 8, 7, 5, 4, 2,
0, -1, -3, -5, -6, -8, -9, -11, -13, -14, -16, -17, -19, -21, -22, -24,
25, 23, 22, 20, 19, 17, 16, 14, 13, 11, 10, 8, 6, 5, 3, 2,
0, -1, -3, -4, -6, -7, -9, -11, -12, -14, -15, -17, -18, -20, -21, -23,
24, 23, 21, 20, 18, 17, 15, 14, 12, 11, 9, 8, 6, 5, 3, 2,
0, -1, -3, -4, -6, -7, -9, -10, -12, -13, -15, -16, -18, -19, -21, -22,
23, 22, 20, 19, 17, 16, 14, 13, 12, 10, 9, 7, 6, 4, 3, 2,
0, -1, -3, -4, -6, -7, -8, -10, -11, -13, -14, -16, -17, -19, -20, -21,
22, 21, 19, 18, 16, 15, 14, 12, 11, 10, 8, 7, 5, 4, 3, 1,
0, -1, -3, -4, -6, -7, -8, -10, -11, -12, -14, -15, -17, -18, -19, -21,
21, 20, 18, 17, 16, 14, 13, 12, 10, 9, 8, 6, 5, 4, 2, 1,
0, -2, -3, -4, -6, -7, -8, -10, -11, -12, -14, -15, -16, -18, -19, -20,
21, 20, 18, 17, 16, 15, 13, 12, 11, 9, 8, 7, 6, 4, 3, 2,
0, -1, -2, -3, -5, -6, -7, -9, -10, -11, -12, -14, -15, -16, -18, -19,
20, 19, 18, 16, 15, 14, 13, 11, 10, 9, 8, 6, 5, 4, 3, 1,
0, -1, -2, -4, -5, -6, -7, -9, -10, -11, -12, -13, -15, -16, -17, -18,
19, 18, 17, 15, 14, 13, 12, 11, 9, 8, 7, 6, 5, 3, 2, 1,
0, -1, -3, -4, -5, -6, -7, -9, -10, -11, -12, -13, -15, -16, -17, -18,
19, 18, 17, 16, 14, 13, 12, 11, 10, 9, 7, 6, 5, 4, 3, 2,
0, -1, -2, -3, -4, -5, -6, -8, -9, -10, -11, -12, -13, -15, -16, -17,
18, 17, 16, 15, 14, 12, 11, 10, 9, 8, 7, 6, 5, 3, 2, 1,
0, -1, -2, -3, -4, -6, -7, -8, -9, -10, -11, -12, -13, -14, -16, -17,
17, 16, 15, 14, 13, 12, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1,
0, -1, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14, -15, -17,
17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 5, 4, 3, 2, 1,
0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14, -16,
16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1,
0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14, -15
};

// approximate reciprocal of scalar single precision FP with 14-bit precision
float32 approximate_rcp_3dnow(float32 op)
{
softfloat_class_t op_class = f32_class(op);
bool sign = f32_sign(op);

// Note that NaN handling is not documented in 3Dnow! manuals
// The manual doesn't specify what result going to be if argument is NaN (undefined behavior)
// This implementation choose IEEE-754 behavior which might not necessary match actual AMD's hardware
switch(op_class) {
case softfloat_zero: // return maximum normal value with sign of the argument
case softfloat_denormal:
return packFloat32(sign, 0x7F, 0x7FFFFF);

case softfloat_negative_inf: // this is that actual AMD hardware returns
case softfloat_positive_inf:
return packFloat32(sign, 0x7F, 0x7FFE00);

case softfloat_SNaN:
case softfloat_QNaN:
return convert_to_QNaN(op);

case softfloat_normalized:
break;
}

Bit32u fraction = f32_fraction(op);
Bit16s exp = f32_exp(op);

exp = 2 * FLOAT32_EXP_BIAS - 1 - exp;

/* check for underflow */
if (exp <= 0)
return packFloat32(sign, 0, 0);

// Approximate 1/(1.b1b2b3..bn) with T1(b1..bk..bm) + T2(b1..bk,bm+1..bn)

// Table 1 is indexed with bits[b1..b5][b6...b10]
// Table 2 is indexed with bits[b1..b5][b11..b15]

Bit32u fraction_b1_b5 = (fraction >> 18) & 0x01F;
Bit32u fraction_b1_b10 = (fraction >> 13) & 0x3FF;
Bit32u fraction_b11_b15 = (fraction >> 8) & 0x01F;

return packFloat32(sign, exp, Bit32u(int(rcp_table1[fraction_b1_b10]) + int(rcp_table2[(fraction_b1_b5 << 5) | fraction_b11_b15])) << 7);
}

void BX_CPP_AttrRegparmN(1) BX_CPU_C::PFRCP_PqQq(bxInstruction_c *i)
{
#if BX_CPU_LEVEL >= 5
Expand Down Expand Up @@ -73,7 +252,7 @@ void BX_CPP_AttrRegparmN(1) BX_CPU_C::PFRCP_PqQq(bxInstruction_c *i)
else {
// Note that Inf/NaN handling is not documented in 3Dnow! manuals
// This implementation choose IEEE-754 behavior which might not necessary match actual AMD's hardware
op = approximate_rcp(op);
op = approximate_rcp_3dnow(op);
}

MMXUD0(dst) = op;
Expand Down
2 changes: 1 addition & 1 deletion bochs/cpu/sse_rcp.cc
View file
Original file line number Diff line number Diff line change
Expand Up @@ -26,7 +26,7 @@
#include "cpu.h"
#define LOG_THIS BX_CPU_THIS_PTR

#if BX_CPU_LEVEL >= 6 || BX_SUPPORT_3DNOW
#if BX_CPU_LEVEL >= 6

#include "softfloat3e/include/softfloat.h"
#include "fpu/softfloat-specialize.h"
Expand Down

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