From dade876474a63e2b5d9ef92bccc26021322ef5da Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Henrik=20Rydg=C3=A5rd?= Date: Tue, 22 Sep 2026 18:58:55 -0600 Subject: [PATCH] VFPU: Compute vrcp, vrsq, vsqrt and vexp2 without correction tables The four share one quadratic interpolator: 128 segments picked by the top 7 bits of the input, each with a constant, a linear and a squared-term coefficient, and a squarer on the top 10 bits of the rest that rounds t^2 up to a multiple of 256. 128 small coefficient sets per function replace the 1 MB of delta tables. Derived from the output of the table-based code, and bit-exact with it over every 32-bit input. Co-Authored-By: Claude Opus 5.5 (1M context) --- Core/MIPS/MIPSVFPUUtils.cpp | 491 ++++++++++++++++++----------- assets/vfpu/vfpu_exp2_lut.dat | 4 - assets/vfpu/vfpu_exp2_lut65536.dat | Bin 512 -> 0 bytes assets/vfpu/vfpu_rcp_lut.dat | Bin 262144 -> 0 bytes assets/vfpu/vfpu_rsqrt_lut.dat | Bin 262144 -> 0 bytes assets/vfpu/vfpu_sqrt_lut.dat | Bin 262144 -> 0 bytes 6 files changed, 311 insertions(+), 184 deletions(-) delete mode 100644 assets/vfpu/vfpu_exp2_lut.dat delete mode 100644 assets/vfpu/vfpu_exp2_lut65536.dat delete mode 100644 assets/vfpu/vfpu_rcp_lut.dat delete mode 100644 assets/vfpu/vfpu_rsqrt_lut.dat delete mode 100644 assets/vfpu/vfpu_sqrt_lut.dat diff --git a/Core/MIPS/MIPSVFPUUtils.cpp b/Core/MIPS/MIPSVFPUUtils.cpp index 044e00282b..95de4210c4 100644 --- a/Core/MIPS/MIPSVFPUUtils.cpp +++ b/Core/MIPS/MIPSVFPUUtils.cpp @@ -1038,6 +1038,310 @@ uint32_t vrnd_generate(uint32_t *rcx) { // estimations, to allow to store them in smaller types. // See https://github.com/hrydgard/ppsspp/issues/16946 for details. +// rcp, rsqrt, sqrt and exp2 share one quadratic interpolator. The top 7 bits of a 23-bit input +// index pick one of 128 segments with their own coefficients; the other 16 bits, x2, enter the +// linear term in full, while the squared term only sees the top 10 of them, as a distance t from the +// middle of the segment. The squarer rounds t^2 up to a multiple of 256, and the squared term is +// floored separately from the rest. The sum is the significand (implicit bit included) in ulps of the +// segment's exponent, truncated to 22 bits like every VFPU result. Derived from the output of the +// table-based versions this replaces, and bit-exact with them over every input. +struct VFPUSegment { + int32_t c0; // value at x2 = 0, in ulps of 2^(e - 150), implicit bit included + int32_t m; // slope in 2^-17 ulps per step of x2 + int16_t n; // squared term coefficient + int16_t e; // binade whose ulps the segment works in +}; + +// 1/x for x in [1, 2). +static const VFPUSegment vfpu_rcp_segments[128] = { + { 0x0FFFF02, -0x003F80C, 0x07F, 0x7E }, { 0x0FE0300, -0x003E86C, 0x07C, 0x7E }, + { 0x0FC0ECF, -0x003D924, 0x079, 0x7E }, { 0x0FA2241, -0x003CA38, 0x076, 0x7E }, + { 0x0F83D28, -0x003BBA0, 0x074, 0x7E }, { 0x0F65F5C, -0x003AD60, 0x071, 0x7E }, + { 0x0F488B1, -0x0039F6C, 0x06E, 0x7E }, { 0x0F2B8FE, -0x00391C8, 0x06C, 0x7E }, + { 0x0F0F01D, -0x0038470, 0x06A, 0x7E }, { 0x0EF2DE9, -0x0037764, 0x067, 0x7E }, + { 0x0ED723A, -0x0036AA0, 0x065, 0x7E }, { 0x0EBBCED, -0x0035E20, 0x063, 0x7E }, + { 0x0EA0DDF, -0x00351E8, 0x061, 0x7E }, { 0x0E864EE, -0x00345EC, 0x05F, 0x7E }, + { 0x0E6C1FA, -0x0033A34, 0x05D, 0x7E }, { 0x0E524E2, -0x0032EBC, 0x05B, 0x7E }, + { 0x0E38D87, -0x0032380, 0x059, 0x7E }, { 0x0E1FBCA, -0x003187C, 0x057, 0x7E }, + { 0x0E06F8C, -0x0030DB4, 0x056, 0x7E }, { 0x0DEE8B4, -0x0030324, 0x054, 0x7E }, + { 0x0DD6725, -0x002F8CC, 0x052, 0x7E }, { 0x0DBEAC0, -0x002EEA4, 0x051, 0x7E }, + { 0x0DA7370, -0x002E4B4, 0x04F, 0x7E }, { 0x0D90118, -0x002DAF4, 0x04D, 0x7E }, + { 0x0D7939E, -0x002D168, 0x04C, 0x7E }, { 0x0D62AEB, -0x002C808, 0x04B, 0x7E }, + { 0x0D4C6E9, -0x002BED8, 0x049, 0x7E }, { 0x0D3677D, -0x002B5D4, 0x048, 0x7E }, + { 0x0D20C95, -0x002AD00, 0x046, 0x7E }, { 0x0D0B616, -0x002A454, 0x045, 0x7E }, + { 0x0CF63EF, -0x0029BD4, 0x043, 0x7E }, { 0x0CE1606, -0x0029378, 0x042, 0x7E }, + { 0x0CCCC4B, -0x0028B48, 0x041, 0x7E }, { 0x0CB86A8, -0x002833C, 0x040, 0x7E }, + { 0x0CA450A, -0x0027B58, 0x03F, 0x7E }, { 0x0C90760, -0x0027398, 0x03D, 0x7E }, + { 0x0C7CD94, -0x0026BFC, 0x03C, 0x7E }, { 0x0C69796, -0x0026484, 0x03B, 0x7E }, + { 0x0C56554, -0x0025D2C, 0x03A, 0x7E }, { 0x0C436BE, -0x00255FC, 0x039, 0x7E }, + { 0x0C30BC1, -0x0024EE8, 0x038, 0x7E }, { 0x0C1E44E, -0x00247F4, 0x037, 0x7E }, + { 0x0C0C055, -0x0024120, 0x036, 0x7E }, { 0x0BF9FC6, -0x0023A68, 0x035, 0x7E }, + { 0x0BE8292, -0x00233D0, 0x034, 0x7E }, { 0x0BD68A8, -0x0022D54, 0x034, 0x7E }, + { 0x0BC5200, -0x00226F8, 0x032, 0x7E }, { 0x0BB3E83, -0x00220B4, 0x032, 0x7E }, + { 0x0BA2E2A, -0x0021A8C, 0x031, 0x7E }, { 0x0B920E4, -0x0021480, 0x030, 0x7E }, + { 0x0B816A5, -0x0020E8C, 0x02F, 0x7E }, { 0x0B70F5D, -0x00208B0, 0x02F, 0x7E }, + { 0x0B60B05, -0x00202F0, 0x02E, 0x7E }, { 0x0B5098D, -0x001FD48, 0x02D, 0x7E }, + { 0x0B40AE9, -0x001F7B8, 0x02C, 0x7E }, { 0x0B30F0B, -0x001F23C, 0x02C, 0x7E }, + { 0x0B215ED, -0x001ECDC, 0x02B, 0x7E }, { 0x0B11F80, -0x001E790, 0x02A, 0x7E }, + { 0x0B02BB9, -0x001E258, 0x029, 0x7E }, { 0x0AF3A8C, -0x001DD38, 0x029, 0x7E }, + { 0x0AE4BF1, -0x001D828, 0x028, 0x7E }, { 0x0AD5FDD, -0x001D330, 0x027, 0x7E }, + { 0x0AC7644, -0x001CE4C, 0x027, 0x7E }, { 0x0AB8F1E, -0x001C97C, 0x026, 0x7E }, + { 0x0AAAA5F, -0x001C4C0, 0x026, 0x7E }, { 0x0A9C800, -0x001C014, 0x025, 0x7E }, + { 0x0A8E7F5, -0x001BB78, 0x025, 0x7E }, { 0x0A80A39, -0x001B6F4, 0x024, 0x7E }, + { 0x0A72EBF, -0x001B280, 0x023, 0x7E }, { 0x0A6557E, -0x001AE1C, 0x023, 0x7E }, + { 0x0A57E6F, -0x001A9C8, 0x023, 0x7E }, { 0x0A4A98B, -0x001A588, 0x022, 0x7E }, + { 0x0A3D6C8, -0x001A154, 0x021, 0x7E }, { 0x0A3061C, -0x0019D34, 0x021, 0x7E }, + { 0x0A23783, -0x0019920, 0x020, 0x7E }, { 0x0A16AF1, -0x001951C, 0x020, 0x7E }, + { 0x0A0A063, -0x001912C, 0x01F, 0x7E }, { 0x09FD7CC, -0x0018D44, 0x01F, 0x7E }, + { 0x09F112A, -0x0018970, 0x01E, 0x7E }, { 0x09E4C71, -0x00185A4, 0x01E, 0x7E }, + { 0x09D899D, -0x00181EC, 0x01E, 0x7E }, { 0x09CC8A7, -0x0017E3C, 0x01D, 0x7E }, + { 0x09C0987, -0x0017AA0, 0x01D, 0x7E }, { 0x09B4C36, -0x001770C, 0x01D, 0x7E }, + { 0x09A90B0, -0x0017388, 0x01C, 0x7E }, { 0x099D6EB, -0x0017010, 0x01C, 0x7E }, + { 0x0991EE4, -0x0016CA0, 0x01B, 0x7E }, { 0x0986892, -0x0016940, 0x01B, 0x7E }, + { 0x097B3F0, -0x00165EC, 0x01B, 0x7E }, { 0x09700FA, -0x00162A4, 0x01A, 0x7E }, + { 0x0964FA6, -0x0015F68, 0x01A, 0x7E }, { 0x0959FF3, -0x0015C34, 0x019, 0x7E }, + { 0x094F1D7, -0x001590C, 0x019, 0x7E }, { 0x094454F, -0x00155F4, 0x019, 0x7E }, + { 0x0939A54, -0x00152E0, 0x019, 0x7E }, { 0x092F0E4, -0x0014FDC, 0x018, 0x7E }, + { 0x09248F5, -0x0014CE0, 0x018, 0x7E }, { 0x091A284, -0x00149EC, 0x018, 0x7E }, + { 0x090FD8E, -0x0014704, 0x017, 0x7E }, { 0x0905A0A, -0x0014424, 0x017, 0x7E }, + { 0x08FB7F6, -0x0014150, 0x017, 0x7E }, { 0x08F174E, -0x0013E88, 0x016, 0x7E }, + { 0x08E7809, -0x0013BC4, 0x016, 0x7E }, { 0x08DDA26, -0x001390C, 0x016, 0x7E }, + { 0x08D3DA1, -0x001365C, 0x015, 0x7E }, { 0x08CA272, -0x00133B4, 0x015, 0x7E }, + { 0x08C0897, -0x0013118, 0x015, 0x7E }, { 0x08B700C, -0x0012E80, 0x014, 0x7E }, + { 0x08AD8CB, -0x0012BF4, 0x014, 0x7E }, { 0x08A42D0, -0x001296C, 0x014, 0x7E }, + { 0x089AE19, -0x00126F0, 0x014, 0x7E }, { 0x0891A9F, -0x0012478, 0x014, 0x7E }, + { 0x0888861, -0x001220C, 0x014, 0x7E }, { 0x087F75B, -0x0011FA8, 0x013, 0x7E }, + { 0x0876785, -0x0011D48, 0x013, 0x7E }, { 0x086D8E1, -0x0011AF4, 0x012, 0x7E }, + { 0x0864B66, -0x00118A4, 0x012, 0x7E }, { 0x085BF13, -0x001165C, 0x012, 0x7E }, + { 0x08533E4, -0x0011418, 0x012, 0x7E }, { 0x084A9D6, -0x00111E0, 0x012, 0x7E }, + { 0x08420E4, -0x0010FAC, 0x012, 0x7E }, { 0x083990E, -0x0010D80, 0x011, 0x7E }, + { 0x083124D, -0x0010B5C, 0x011, 0x7E }, { 0x0828C9E, -0x001093C, 0x011, 0x7E }, + { 0x08207FF, -0x0010724, 0x011, 0x7E }, { 0x081846C, -0x0010510, 0x011, 0x7E }, + { 0x08101E4, -0x0010304, 0x010, 0x7E }, { 0x0808061, -0x0010100, 0x010, 0x7E }, +}; + +// 1/sqrt(x) for x in [1, 4), indexed by the bottom exponent bit and the top 22 mantissa bits. +static const VFPUSegment vfpu_rsqrt_segments[128] = { + { 0x0FFFE88, -0x003F428, 0x0BC, 0x7E }, { 0x0FE0482, -0x003DD10, 0x0B5, 0x7E }, + { 0x0FC1608, -0x003C6D4, 0x0AE, 0x7E }, { 0x0FA32AB, -0x003B16C, 0x0A7, 0x7E }, + { 0x0F859FE, -0x0039CCC, 0x0A2, 0x7E }, { 0x0F68BA4, -0x00388E8, 0x09C, 0x7E }, + { 0x0F4C73B, -0x00375B8, 0x096, 0x7E }, { 0x0F30C68, -0x0036334, 0x091, 0x7E }, + { 0x0F15AD7, -0x0035154, 0x08C, 0x7E }, { 0x0EFB237, -0x003400C, 0x087, 0x7E }, + { 0x0EE1238, -0x0032F5C, 0x083, 0x7E }, { 0x0EC7A94, -0x0031F34, 0x07E, 0x7E }, + { 0x0EAEB01, -0x0030F94, 0x07A, 0x7E }, { 0x0E9633C, -0x0030078, 0x077, 0x7E }, + { 0x0E7E307, -0x002F1D4, 0x073, 0x7E }, { 0x0E66A24, -0x002E3A8, 0x06F, 0x7E }, + { 0x0E4F856, -0x002D5E8, 0x06C, 0x7E }, { 0x0E38D67, -0x002C898, 0x069, 0x7E }, + { 0x0E22923, -0x002BBAC, 0x065, 0x7E }, { 0x0E0CB52, -0x002AF24, 0x062, 0x7E }, + { 0x0DF73C3, -0x002A2FC, 0x060, 0x7E }, { 0x0DE224B, -0x002972C, 0x05D, 0x7E }, + { 0x0DCD6BA, -0x0028BB4, 0x05A, 0x7E }, { 0x0DB90E5, -0x0028090, 0x057, 0x7E }, + { 0x0DA50A0, -0x00275BC, 0x055, 0x7E }, { 0x0D915C5, -0x0026B38, 0x053, 0x7E }, + { 0x0D7E02D, -0x00260FC, 0x051, 0x7E }, { 0x0D6AFB5, -0x0025708, 0x04E, 0x7E }, + { 0x0D58435, -0x0024D54, 0x04C, 0x7E }, { 0x0D45D8E, -0x00243E8, 0x04A, 0x7E }, + { 0x0D33B9E, -0x0023ABC, 0x048, 0x7E }, { 0x0D21E44, -0x00231C8, 0x046, 0x7E }, + { 0x0D10562, -0x0022914, 0x045, 0x7E }, { 0x0CFF0DC, -0x0022098, 0x043, 0x7E }, + { 0x0CEE094, -0x0021850, 0x041, 0x7E }, { 0x0CDD46F, -0x0021040, 0x03F, 0x7E }, + { 0x0CCCC51, -0x0020864, 0x03E, 0x7E }, { 0x0CBC823, -0x00200B8, 0x03C, 0x7E }, + { 0x0CAC7C9, -0x001F938, 0x03B, 0x7E }, { 0x0C9CB30, -0x001F1EC, 0x039, 0x7E }, + { 0x0C8D23B, -0x001EACC, 0x038, 0x7E }, { 0x0C7DCD9, -0x001E3D4, 0x036, 0x7E }, + { 0x0C6EAEE, -0x001DD08, 0x036, 0x7E }, { 0x0C5FC6E, -0x001D664, 0x034, 0x7E }, + { 0x0C5113D, -0x001CFE8, 0x033, 0x7E }, { 0x0C4294B, -0x001C990, 0x032, 0x7E }, + { 0x0C34486, -0x001C35C, 0x030, 0x7E }, { 0x0C262D7, -0x001BD50, 0x030, 0x7E }, + { 0x0C18433, -0x001B760, 0x02E, 0x7E }, { 0x0C0A882, -0x001B198, 0x02E, 0x7E }, + { 0x0BFCFB8, -0x001ABEC, 0x02D, 0x7E }, { 0x0BEF9C6, -0x001A660, 0x02B, 0x7E }, + { 0x0BE2695, -0x001A0F4, 0x02B, 0x7E }, { 0x0BD561D, -0x0019BA4, 0x02A, 0x7E }, + { 0x0BC884D, -0x0019670, 0x029, 0x7E }, { 0x0BBBD17, -0x0019158, 0x028, 0x7E }, + { 0x0BAF46C, -0x0018C5C, 0x027, 0x7E }, { 0x0BA2E40, -0x001877C, 0x026, 0x7E }, + { 0x0B96A84, -0x00182B0, 0x025, 0x7E }, { 0x0B8A92B, -0x0017E00, 0x025, 0x7E }, + { 0x0B7EA2C, -0x0017968, 0x024, 0x7E }, { 0x0B72D79, -0x00174E8, 0x023, 0x7E }, + { 0x0B67306, -0x0017080, 0x022, 0x7E }, { 0x0B5BAC5, -0x0016C2C, 0x022, 0x7E }, + { 0x0B503E9, -0x002CBB4, 0x085, 0x7E }, { 0x0B39E19, -0x002BB5C, 0x080, 0x7E }, + { 0x0B24072, -0x002ABA8, 0x07C, 0x7E }, { 0x0B0EAA8, -0x0029C84, 0x077, 0x7E }, + { 0x0AF9C6D, -0x0028DEC, 0x073, 0x7E }, { 0x0AE557E, -0x0027FE0, 0x06F, 0x7E }, + { 0x0AD1596, -0x002724C, 0x06B, 0x7E }, { 0x0ABDC78, -0x0026534, 0x067, 0x7E }, + { 0x0AAA9E5, -0x0025890, 0x063, 0x7E }, { 0x0A97DA2, -0x0024C58, 0x060, 0x7E }, + { 0x0A8577B, -0x0024088, 0x05D, 0x7E }, { 0x0A7373C, -0x0023520, 0x05A, 0x7E }, + { 0x0A61CB1, -0x0022A14, 0x057, 0x7E }, { 0x0A507AD, -0x0021F64, 0x054, 0x7E }, + { 0x0A3F800, -0x0021508, 0x051, 0x7E }, { 0x0A2ED7F, -0x0020B04, 0x04F, 0x7E }, + { 0x0A1E801, -0x002014C, 0x04D, 0x7E }, { 0x0A0E761, -0x001F7E0, 0x04A, 0x7E }, + { 0x09FEB74, -0x001EEC0, 0x048, 0x7E }, { 0x09EF418, -0x001E5E0, 0x046, 0x7E }, + { 0x09E012B, -0x001DD48, 0x044, 0x7E }, { 0x09D128A, -0x001D4F0, 0x042, 0x7E }, + { 0x09C2816, -0x001CCD4, 0x040, 0x7E }, { 0x09B41B0, -0x001C4F4, 0x03E, 0x7E }, + { 0x09A5F38, -0x001BD4C, 0x03D, 0x7E }, { 0x0998096, -0x001B5D8, 0x03B, 0x7E }, + { 0x098A5AD, -0x001AE9C, 0x039, 0x7E }, { 0x097CE60, -0x001A794, 0x038, 0x7E }, + { 0x096FA9A, -0x001A0B8, 0x036, 0x7E }, { 0x0962A3F, -0x0019A0C, 0x035, 0x7E }, + { 0x0955D3C, -0x0019390, 0x033, 0x7E }, { 0x0949375, -0x0018D3C, 0x032, 0x7E }, + { 0x093CCD8, -0x0018714, 0x031, 0x7E }, { 0x093094F, -0x0018114, 0x030, 0x7E }, + { 0x09248C7, -0x0017B3C, 0x02F, 0x7E }, { 0x0918B2B, -0x0017588, 0x02E, 0x7E }, + { 0x090D06B, -0x0016FF8, 0x02C, 0x7E }, { 0x0901870, -0x0016A88, 0x02B, 0x7E }, + { 0x08F632D, -0x0016540, 0x02A, 0x7E }, { 0x08EB08E, -0x0016014, 0x029, 0x7E }, + { 0x08E0085, -0x0015B0C, 0x028, 0x7E }, { 0x08D5301, -0x0015620, 0x027, 0x7E }, + { 0x08CA7F3, -0x0015150, 0x026, 0x7E }, { 0x08BFF4D, -0x0014C9C, 0x025, 0x7E }, + { 0x08B58FE, -0x0014808, 0x025, 0x7E }, { 0x08AB4FE, -0x001438C, 0x023, 0x7E }, + { 0x08A1337, -0x0013F28, 0x023, 0x7E }, { 0x08973A4, -0x0013AE0, 0x022, 0x7E }, + { 0x088D635, -0x00136B0, 0x021, 0x7E }, { 0x0883ADC, -0x0013298, 0x021, 0x7E }, + { 0x087A192, -0x0012E94, 0x020, 0x7E }, { 0x0870A49, -0x0012AA8, 0x01F, 0x7E }, + { 0x08674F6, -0x00126D4, 0x01E, 0x7E }, { 0x085E18B, -0x0012310, 0x01E, 0x7E }, + { 0x0855004, -0x0011F64, 0x01D, 0x7E }, { 0x084C051, -0x0011BCC, 0x01D, 0x7E }, + { 0x084326D, -0x0011844, 0x01C, 0x7E }, { 0x083A64A, -0x00114D0, 0x01C, 0x7E }, + { 0x0831BE4, -0x0011170, 0x01B, 0x7E }, { 0x082932E, -0x0010E20, 0x01A, 0x7E }, + { 0x0820C1E, -0x0010AE0, 0x01A, 0x7E }, { 0x08186B0, -0x00107B0, 0x019, 0x7E }, + { 0x08102D8, -0x0010490, 0x019, 0x7E }, { 0x0808091, -0x0010180, 0x018, 0x7E }, +}; + +// sqrt(x) for x in [1, 4), indexed like rsqrt. +static const VFPUSegment vfpu_sqrt_segments[128] = { + { 0x0800040, 0x001FE04, -0x020, 0x7F }, { 0x080FF40, 0x001FA1C, -0x01F, 0x7F }, + { 0x081FC4E, 0x001F648, -0x01F, 0x7F }, { 0x082F770, 0x001F290, -0x01E, 0x7F }, + { 0x083F0B5, 0x001EEE8, -0x01D, 0x7F }, { 0x084E828, 0x001EB54, -0x01D, 0x7F }, + { 0x085DDD0, 0x001E7D4, -0x01C, 0x7F }, { 0x086D1BA, 0x001E468, -0x01C, 0x7F }, + { 0x087C3EC, 0x001E110, -0x01B, 0x7F }, { 0x088B471, 0x001DDC8, -0x01A, 0x7F }, + { 0x089A352, 0x001DA90, -0x019, 0x7F }, { 0x08A9099, 0x001D768, -0x019, 0x7F }, + { 0x08B7C4A, 0x001D450, -0x018, 0x7F }, { 0x08C6671, 0x001D148, -0x018, 0x7F }, + { 0x08D4F14, 0x001CE50, -0x018, 0x7F }, { 0x08E3639, 0x001CB64, -0x017, 0x7F }, + { 0x08F1BEB, 0x001C888, -0x017, 0x7F }, { 0x090002C, 0x001C5B8, -0x016, 0x7F }, + { 0x090E308, 0x001C2F4, -0x016, 0x7F }, { 0x091C482, 0x001C040, -0x016, 0x7F }, + { 0x092A4A0, 0x001BD98, -0x015, 0x7F }, { 0x093836B, 0x001BAFC, -0x015, 0x7F }, + { 0x09460E8, 0x001B868, -0x015, 0x7F }, { 0x0953D1A, 0x001B5E4, -0x014, 0x7F }, + { 0x096180B, 0x001B368, -0x014, 0x7F }, { 0x096F1BC, 0x001B0F8, -0x013, 0x7F }, + { 0x097CA37, 0x001AE94, -0x013, 0x7F }, { 0x098A180, 0x001AC34, -0x013, 0x7F }, + { 0x0997798, 0x001A9E4, -0x012, 0x7F }, { 0x09A4C89, 0x001A79C, -0x012, 0x7F }, + { 0x09B2056, 0x001A55C, -0x012, 0x7F }, { 0x09BF303, 0x001A324, -0x012, 0x7F }, + { 0x09CC493, 0x001A0F8, -0x011, 0x7F }, { 0x09D950E, 0x0019ED4, -0x011, 0x7F }, + { 0x09E6477, 0x0019CB4, -0x011, 0x7F }, { 0x09F32D1, 0x0019AA4, -0x011, 0x7F }, + { 0x0A00022, 0x0019894, -0x011, 0x7F }, { 0x0A0CC6A, 0x0019690, -0x010, 0x7F }, + { 0x0A197B2, 0x0019494, -0x010, 0x7F }, { 0x0A261FC, 0x00192A0, -0x010, 0x7F }, + { 0x0A32B49, 0x00190B0, -0x00F, 0x7F }, { 0x0A3F3A1, 0x0018EC8, -0x00F, 0x7F }, + { 0x0A4BB05, 0x0018CE8, -0x00F, 0x7F }, { 0x0A58178, 0x0018B10, -0x00F, 0x7F }, + { 0x0A646FF, 0x001893C, -0x00F, 0x7F }, { 0x0A70B9B, 0x0018770, -0x00E, 0x7F }, + { 0x0A7CF52, 0x00185A8, -0x00E, 0x7F }, { 0x0A89226, 0x00183E8, -0x00E, 0x7F }, + { 0x0A95419, 0x0018230, -0x00E, 0x7F }, { 0x0AA1530, 0x0018078, -0x00E, 0x7F }, + { 0x0AAD56A, 0x0017ECC, -0x00D, 0x7F }, { 0x0AB94CF, 0x0017D20, -0x00D, 0x7F }, + { 0x0AC535F, 0x0017B80, -0x00D, 0x7F }, { 0x0AD111E, 0x00179E0, -0x00D, 0x7F }, + { 0x0ADCE0D, 0x0017848, -0x00D, 0x7F }, { 0x0AE8A2E, 0x00176B4, -0x00C, 0x7F }, + { 0x0AF4587, 0x0017524, -0x00C, 0x7F }, { 0x0B0001A, 0x0017398, -0x00D, 0x7F }, + { 0x0B0B9E6, 0x0017214, -0x00D, 0x7F }, { 0x0B172EE, 0x0017094, -0x00C, 0x7F }, + { 0x0B22B38, 0x0016F18, -0x00C, 0x7F }, { 0x0B2E2C4, 0x0016DA0, -0x00C, 0x7F }, + { 0x0B39994, 0x0016C30, -0x00C, 0x7F }, { 0x0B44FAB, 0x0016AC0, -0x00C, 0x7F }, + { 0x0B5054D, 0x002D148, -0x02D, 0x7F }, { 0x0B66DEE, 0x002CBC0, -0x02C, 0x7F }, + { 0x0B7D3CB, 0x002C658, -0x02B, 0x7F }, { 0x0B936F5, 0x002C110, -0x02A, 0x7F }, + { 0x0BA977A, 0x002BBE8, -0x029, 0x7F }, { 0x0BBF56B, 0x002B6D8, -0x028, 0x7F }, + { 0x0BD50D5, 0x002B1E4, -0x027, 0x7F }, { 0x0BEA9C5, 0x002AD10, -0x026, 0x7F }, + { 0x0C0004C, 0x002A850, -0x026, 0x7F }, { 0x0C15472, 0x002A3AC, -0x025, 0x7F }, + { 0x0C2A646, 0x0029F20, -0x024, 0x7F }, { 0x0C3F5D5, 0x0029AA8, -0x024, 0x7F }, + { 0x0C54327, 0x002964C, -0x023, 0x7F }, { 0x0C68E4A, 0x0029200, -0x022, 0x7F }, + { 0x0C7D74A, 0x0028DCC, -0x022, 0x7F }, { 0x0C91E2E, 0x00289AC, -0x021, 0x7F }, + { 0x0CA6302, 0x00285A0, -0x020, 0x7F }, { 0x0CBA5D0, 0x00281A8, -0x01F, 0x7F }, + { 0x0CCE6A3, 0x0027DC0, -0x01F, 0x7F }, { 0x0CE2581, 0x00279EC, -0x01E, 0x7F }, + { 0x0CF6276, 0x0027628, -0x01E, 0x7F }, { 0x0D09D88, 0x0027278, -0x01D, 0x7F }, + { 0x0D1D6C3, 0x0026ED4, -0x01D, 0x7F }, { 0x0D30E2D, 0x0026B44, -0x01D, 0x7F }, + { 0x0D443CD, 0x00267C0, -0x01C, 0x7F }, { 0x0D577AD, 0x002644C, -0x01C, 0x7F }, + { 0x0D6A9D1, 0x00260EC, -0x01B, 0x7F }, { 0x0D7DA44, 0x0025D94, -0x01A, 0x7F }, + { 0x0D9090D, 0x0025A4C, -0x01A, 0x7F }, { 0x0DA3632, 0x0025710, -0x01A, 0x7F }, + { 0x0DB61B8, 0x00253E4, -0x019, 0x7F }, { 0x0DC8BA9, 0x00250C0, -0x019, 0x7F }, + { 0x0DDB407, 0x0024DB0, -0x018, 0x7F }, { 0x0DEDADE, 0x0024AA4, -0x018, 0x7F }, + { 0x0E00030, 0x00247A8, -0x018, 0x7F }, { 0x0E12404, 0x00244B8, -0x018, 0x7F }, + { 0x0E2465E, 0x00241D4, -0x017, 0x7F }, { 0x0E36747, 0x0023EF8, -0x017, 0x7F }, + { 0x0E486C3, 0x0023C28, -0x017, 0x7F }, { 0x0E5A4D5, 0x0023964, -0x016, 0x7F }, + { 0x0E6C186, 0x00236A8, -0x016, 0x7F }, { 0x0E7DCD8, 0x00233F8, -0x015, 0x7F }, + { 0x0E8F6D3, 0x0023150, -0x015, 0x7F }, { 0x0EA0F7A, 0x0022EB4, -0x015, 0x7F }, + { 0x0EB26D3, 0x0022C1C, -0x015, 0x7F }, { 0x0EC3CE1, 0x0022990, -0x015, 0x7F }, + { 0x0ED51A7, 0x0022710, -0x014, 0x7F }, { 0x0EE652F, 0x0022494, -0x014, 0x7F }, + { 0x0EF7777, 0x0022224, -0x013, 0x7F }, { 0x0F08888, 0x0021FB8, -0x013, 0x7F }, + { 0x0F19864, 0x0021D58, -0x013, 0x7F }, { 0x0F2A710, 0x0021B00, -0x013, 0x7F }, + { 0x0F3B490, 0x00218AC, -0x013, 0x7F }, { 0x0F4C0E6, 0x0021664, -0x013, 0x7F }, + { 0x0F5CC16, 0x0021424, -0x012, 0x7F }, { 0x0F6D627, 0x00211E8, -0x012, 0x7F }, + { 0x0F7DF1A, 0x0020FB0, -0x012, 0x7F }, { 0x0F8E6F0, 0x0020D88, -0x011, 0x7F }, + { 0x0F9EDB3, 0x0020B60, -0x011, 0x7F }, { 0x0FAF362, 0x0020940, -0x011, 0x7F }, + { 0x0FBF801, 0x0020728, -0x011, 0x7F }, { 0x0FCFB94, 0x0020514, -0x011, 0x7F }, + { 0x0FDFE1C, 0x0020308, -0x010, 0x7F }, { 0x0FEFF9F, 0x0020104, -0x010, 0x7F }, +}; + +// exp2(x) for x in [0, 1). +static const VFPUSegment vfpu_exp2_segments[128] = { + { 0x07FFFE2, 0x00163DC, 0x00F, 0x7F }, { 0x080B1CF, 0x00165CC, 0x00F, 0x7F }, + { 0x08164B4, 0x00167BC, 0x00F, 0x7F }, { 0x0821891, 0x00169B0, 0x00F, 0x7F }, + { 0x082CD67, 0x0016BA4, 0x010, 0x7F }, { 0x0838339, 0x0016DA0, 0x010, 0x7F }, + { 0x0843A0B, 0x0016F9C, 0x00F, 0x7F }, { 0x084F1D8, 0x001719C, 0x00F, 0x7F }, + { 0x085AAA3, 0x001739C, 0x010, 0x7F }, { 0x0866471, 0x00175A4, 0x010, 0x7F }, + { 0x0871F42, 0x00177A8, 0x010, 0x7F }, { 0x087DB15, 0x00179B4, 0x010, 0x7F }, + { 0x08897EF, 0x0017BC0, 0x010, 0x7F }, { 0x08955CE, 0x0017DD0, 0x010, 0x7F }, + { 0x08A14B5, 0x0017FE4, 0x010, 0x7F }, { 0x08AD4A6, 0x00181F8, 0x010, 0x7F }, + { 0x08B95A0, 0x0018410, 0x011, 0x7F }, { 0x08C57AA, 0x001862C, 0x010, 0x7F }, + { 0x08D1ABF, 0x001884C, 0x010, 0x7F }, { 0x08DDEE2, 0x0018A6C, 0x011, 0x7F }, + { 0x08EA418, 0x0018C90, 0x011, 0x7F }, { 0x08F6A5F, 0x0018EB8, 0x011, 0x7F }, + { 0x09031BA, 0x00190E4, 0x011, 0x7F }, { 0x090FA2B, 0x001930C, 0x011, 0x7F }, + { 0x091C3B1, 0x0019540, 0x011, 0x7F }, { 0x0928E50, 0x0019774, 0x011, 0x7F }, + { 0x0935A09, 0x00199A8, 0x011, 0x7F }, { 0x09426DD, 0x0019BE4, 0x011, 0x7F }, + { 0x094F4CC, 0x0019E20, 0x012, 0x7F }, { 0x095C3DB, 0x001A05C, 0x012, 0x7F }, + { 0x0969409, 0x001A2A0, 0x012, 0x7F }, { 0x0976559, 0x001A4E8, 0x012, 0x7F }, + { 0x09837CC, 0x001A730, 0x012, 0x7F }, { 0x0990B64, 0x001A97C, 0x012, 0x7F }, + { 0x099E022, 0x001ABCC, 0x012, 0x7F }, { 0x09AB607, 0x001AE20, 0x012, 0x7F }, + { 0x09B8D16, 0x001B074, 0x012, 0x7F }, { 0x09C654F, 0x001B2D0, 0x012, 0x7F }, + { 0x09D3EB4, 0x001B528, 0x013, 0x7F }, { 0x09E1948, 0x001B788, 0x013, 0x7F }, + { 0x09EF50C, 0x001B9EC, 0x013, 0x7F }, { 0x09FD202, 0x001BC54, 0x013, 0x7F }, + { 0x0A0B02B, 0x001BEBC, 0x013, 0x7F }, { 0x0A18F89, 0x001C128, 0x013, 0x7F }, + { 0x0A2701D, 0x001C398, 0x013, 0x7F }, { 0x0A351E9, 0x001C610, 0x013, 0x7F }, + { 0x0A434EE, 0x001C884, 0x014, 0x7F }, { 0x0A51930, 0x001CB00, 0x014, 0x7F }, + { 0x0A5FEAF, 0x001CD7C, 0x014, 0x7F }, { 0x0A6E56D, 0x001D000, 0x014, 0x7F }, + { 0x0A7CD6C, 0x001D284, 0x014, 0x7F }, { 0x0A8B6AD, 0x001D50C, 0x014, 0x7F }, + { 0x0A9A133, 0x001D798, 0x014, 0x7F }, { 0x0AA8CFE, 0x001DA28, 0x014, 0x7F }, + { 0x0AB7A12, 0x001DCBC, 0x014, 0x7F }, { 0x0AC686D, 0x001DF50, 0x015, 0x7F }, + { 0x0AD5817, 0x001E1EC, 0x014, 0x7F }, { 0x0AE490C, 0x001E48C, 0x014, 0x7F }, + { 0x0AF3B4F, 0x001E72C, 0x015, 0x7F }, { 0x0B02EE4, 0x001E9D0, 0x015, 0x7F }, + { 0x0B123CC, 0x001EC78, 0x015, 0x7F }, { 0x0B21A08, 0x001EF24, 0x015, 0x7F }, + { 0x0B3119A, 0x001F1D8, 0x015, 0x7F }, { 0x0B40A85, 0x001F488, 0x015, 0x7F }, + { 0x0B504C9, 0x001F744, 0x015, 0x7F }, { 0x0B60068, 0x001F9FC, 0x016, 0x7F }, + { 0x0B6FD66, 0x001FCBC, 0x016, 0x7F }, { 0x0B7FBC4, 0x001FF80, 0x016, 0x7F }, + { 0x0B8FB83, 0x0020248, 0x016, 0x7F }, { 0x0B9FCA6, 0x0020514, 0x016, 0x7F }, + { 0x0BAFF2F, 0x00207E0, 0x016, 0x7F }, { 0x0BC031E, 0x0020AB4, 0x016, 0x7F }, + { 0x0BD0876, 0x0020D88, 0x017, 0x7F }, { 0x0BE0F3A, 0x0021064, 0x017, 0x7F }, + { 0x0BF176C, 0x0021344, 0x017, 0x7F }, { 0x0C0210D, 0x0021624, 0x017, 0x7F }, + { 0x0C12C1F, 0x002190C, 0x017, 0x7F }, { 0x0C238A4, 0x0021BF8, 0x017, 0x7F }, + { 0x0C3469F, 0x0021EE4, 0x017, 0x7F }, { 0x0C45611, 0x00221D8, 0x017, 0x7F }, + { 0x0C566FC, 0x00224D0, 0x017, 0x7F }, { 0x0C67961, 0x00227C8, 0x018, 0x7F }, + { 0x0C78D47, 0x0022AC8, 0x017, 0x7F }, { 0x0C8A2A8, 0x0022DCC, 0x018, 0x7F }, + { 0x0C9B98E, 0x00230D0, 0x018, 0x7F }, { 0x0CAD1F6, 0x00233E0, 0x018, 0x7F }, + { 0x0CBEBE5, 0x00236F0, 0x018, 0x7F }, { 0x0CD075A, 0x0023A00, 0x019, 0x7F }, + { 0x0CE245C, 0x0023D1C, 0x018, 0x7F }, { 0x0CF42E7, 0x0024038, 0x019, 0x7F }, + { 0x0D06302, 0x0024358, 0x019, 0x7F }, { 0x0D184AD, 0x0024680, 0x019, 0x7F }, + { 0x0D2A7EC, 0x00249A8, 0x019, 0x7F }, { 0x0D3CCBF, 0x0024CD4, 0x019, 0x7F }, + { 0x0D4F329, 0x0025008, 0x019, 0x7F }, { 0x0D61B2C, 0x0025340, 0x019, 0x7F }, + { 0x0D744C9, 0x0025678, 0x01A, 0x7F }, { 0x0D87005, 0x00259BC, 0x01A, 0x7F }, + { 0x0D99CE2, 0x0025CFC, 0x01A, 0x7F }, { 0x0DACB60, 0x0026048, 0x01A, 0x7F }, + { 0x0DBFB84, 0x0026394, 0x01A, 0x7F }, { 0x0DD2D4E, 0x00266E8, 0x01A, 0x7F }, + { 0x0DE60BF, 0x0026A3C, 0x01B, 0x7F }, { 0x0DF95DD, 0x0026D98, 0x01B, 0x7F }, + { 0x0E0CCA9, 0x00270F8, 0x01B, 0x7F }, { 0x0E20525, 0x002745C, 0x01B, 0x7F }, + { 0x0E33F53, 0x00277C8, 0x01B, 0x7F }, { 0x0E47B37, 0x0027B34, 0x01B, 0x7F }, + { 0x0E5B8CF, 0x0027EA8, 0x01C, 0x7F }, { 0x0E6F825, 0x0028220, 0x01B, 0x7F }, + { 0x0E83932, 0x002859C, 0x01C, 0x7F }, { 0x0E97C00, 0x0028920, 0x01C, 0x7F }, + { 0x0EAC08F, 0x0028CA4, 0x01C, 0x7F }, { 0x0EC06E1, 0x0029030, 0x01C, 0x7F }, + { 0x0ED4EF8, 0x00293C0, 0x01C, 0x7F }, { 0x0EE98D6, 0x0029754, 0x01D, 0x7F }, + { 0x0EFE480, 0x0029AF0, 0x01D, 0x7F }, { 0x0F131F7, 0x0029E8C, 0x01D, 0x7F }, + { 0x0F2813D, 0x002A234, 0x01D, 0x7F }, { 0x0F3D256, 0x002A5DC, 0x01D, 0x7F }, + { 0x0F52543, 0x002A988, 0x01D, 0x7F }, { 0x0F67A07, 0x002AD3C, 0x01D, 0x7F }, + { 0x0F7D0A5, 0x002B0F8, 0x01D, 0x7F }, { 0x0F9291E, 0x002B4B4, 0x01E, 0x7F }, + { 0x0FA8377, 0x002B874, 0x01E, 0x7F }, { 0x0FBDFB1, 0x002BC40, 0x01E, 0x7F }, + { 0x0FD3DD0, 0x002C00C, 0x01E, 0x7F }, { 0x0FE9DD5, 0x002C3E0, 0x01E, 0x7F }, +}; + +// The squarer only sees the top 10 bits of x2, as a distance from the middle of the segment. +static inline int32_t vfpu_square(uint32_t x2) { + const int32_t t = abs(int32_t(x2 >> 6) - 512); + return (t * t + 255) >> 8; +} + +// The untruncated result, in ulps of 2^(seg.e - 150). +static inline int32_t vfpu_interp(const VFPUSegment &seg, uint32_t x2) { + return seg.c0 + int32_t(((int64_t)seg.m * x2) >> 17) + ((seg.n * vfpu_square(x2)) >> 9); +} + +// Float bits of a result in [2^(e-127), 2^(e-126)], truncated to 22 bits. The top of that range +// carries into the exponent, which gives exactly the next power of two. +static inline uint32_t vfpu_interp_bits(const VFPUSegment *segments, uint32_t index) { + const VFPUSegment &seg = segments[index >> 16]; + return ((uint32_t(seg.e - 1) << 23) + uint32_t(vfpu_interp(seg, index & 0xFFFF))) & ~3u; +} + // Lookup tables. // Note: these are never unloaded, and stay till program termination. static uint32_t *vfpu_sin_lut8192=nullptr; @@ -1045,13 +1349,6 @@ 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; @@ -1060,8 +1357,6 @@ 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; - template static inline bool load_vfpu_table(T *&ptr, const char *filename, size_t expected_size) { #if COMMON_BIG_ENDIAN @@ -1226,71 +1521,7 @@ 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) { - static bool loaded = - LOAD_TABLE(vfpu_sqrt_lut, 262144); - if (!loaded) - return vfpu_sqrt_fallback(x); uint32_t bits; memcpy(&bits, &x, sizeof(bits)); if((bits & 0x7FFFFFFFu) <= 0x007FFFFFu) { @@ -1313,72 +1544,13 @@ float vfpu_sqrt(float 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 = vfpu_interp_bits(vfpu_sqrt_segments, 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) { - static bool loaded = - LOAD_TABLE(vfpu_rsqrt_lut, 262144); - if (!loaded) - return vfpu_rsqrt_fallback(x); uint32_t bits; memcpy(&bits, &x, sizeof(bits)); if((bits & 0x7FFFFFFFu) <= 0x007FFFFFu) { @@ -1402,7 +1574,7 @@ float vfpu_rsqrt(float 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 = vfpu_interp_bits(vfpu_rsqrt_segments, index); bits -= uint32_t(exponent >> 1) << 23; memcpy(&x, &bits, sizeof(bits)); return x; @@ -1459,32 +1631,7 @@ float vfpu_asin(float 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) { - static bool loaded = - LOAD_TABLE(vfpu_exp2_lut65536, 512)&& - LOAD_TABLE(vfpu_exp2_lut, 262144); - if (!loaded) - return vfpu_exp2_fallback(x); int32_t bits; memcpy(&bits, &x, sizeof(bits)); if((bits & 0x7FFFFFFF) <= 0x007FFFFF) { @@ -1510,7 +1657,10 @@ float vfpu_exp2(float 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))); + // The fraction's exp2 is in [1, 2), so its significand bits are the offset from 1.0. + const uint32_t frac = bits & 0x007FFFFF; + const int32_t significand = frac == 0 ? 0 : int32_t(vfpu_interp_bits(vfpu_exp2_segments, frac) - 0x3F800000u); + bits = int32_t(0x3F800000) + (bits & int32_t(0xFF800000)) + significand; memcpy(&x, &bits, sizeof(bits)); return x; } @@ -1585,15 +1735,7 @@ float vfpu_log2(float x) { 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) { - static bool loaded = - LOAD_TABLE(vfpu_rcp_lut, 262144); - if (!loaded) - return vfpu_rcp_fallback(x); uint32_t bits; memcpy(&bits, &x, sizeof(bits)); uint32_t s = bits & 0x80000000u; @@ -1609,13 +1751,7 @@ float vfpu_rcp(float x) { 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; + bits = s + (0x3F800000u - e) + vfpu_interp_bits(vfpu_rcp_segments, i); memcpy(&x, &bits, sizeof(x)); return x; } @@ -1628,17 +1764,12 @@ void InitVFPU() { 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 } diff --git a/assets/vfpu/vfpu_exp2_lut.dat b/assets/vfpu/vfpu_exp2_lut.dat deleted file mode 100644 index dcf5449722..0000000000 --- a/assets/vfpu/vfpu_exp2_lut.dat +++ /dev/null @@ -1,4 +0,0 @@ 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