14d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle/* From: @(#)k_tan.c 1.5 04/04/22 SMI */ 24d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle 34d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle/* 44d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle * ==================================================== 54d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle * Copyright 2004 Sun Microsystems, Inc. All Rights Reserved. 64d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle * Copyright (c) 2008 Steven G. Kargl, David Schultz, Bruce D. Evans. 74d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle * 84d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle * Permission to use, copy, modify, and distribute this 94d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle * software is freely granted, provided that this notice 104d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle * is preserved. 114d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle * ==================================================== 124d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle */ 134d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle 144d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle#include <sys/cdefs.h> 154d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle__FBSDID("$FreeBSD$"); 164d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle 174d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle/* 184d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle * ld128 version of k_tan.c. See ../src/k_tan.c for most comments. 194d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle */ 204d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle 214d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle#include "math.h" 224d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle#include "math_private.h" 234d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle 244d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle/* 254d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle * Domain [-0.67434, 0.67434], range ~[-3.37e-36, 1.982e-37] 264d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle * |tan(x)/x - t(x)| < 2**-117.8 (XXX should be ~1e-37) 274d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle * 284d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle * See ../ld80/k_cosl.c for more details about the polynomial. 294d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle */ 304d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravlestatic const long double 314d77c1151c40010d137e4a2fa8629bff4bea72b0Calin JuravleT3 = 0x1.5555555555555555555555555553p-2L, 324d77c1151c40010d137e4a2fa8629bff4bea72b0Calin JuravleT5 = 0x1.1111111111111111111111111eb5p-3L, 334d77c1151c40010d137e4a2fa8629bff4bea72b0Calin JuravleT7 = 0x1.ba1ba1ba1ba1ba1ba1ba1b694cd6p-5L, 344d77c1151c40010d137e4a2fa8629bff4bea72b0Calin JuravleT9 = 0x1.664f4882c10f9f32d6bbe09d8bcdp-6L, 354d77c1151c40010d137e4a2fa8629bff4bea72b0Calin JuravleT11 = 0x1.226e355e6c23c8f5b4f5762322eep-7L, 364d77c1151c40010d137e4a2fa8629bff4bea72b0Calin JuravleT13 = 0x1.d6d3d0e157ddfb5fed8e84e27b37p-9L, 374d77c1151c40010d137e4a2fa8629bff4bea72b0Calin JuravleT15 = 0x1.7da36452b75e2b5fce9ee7c2c92ep-10L, 384d77c1151c40010d137e4a2fa8629bff4bea72b0Calin JuravleT17 = 0x1.355824803674477dfcf726649efep-11L, 394d77c1151c40010d137e4a2fa8629bff4bea72b0Calin JuravleT19 = 0x1.f57d7734d1656e0aceb716f614c2p-13L, 404d77c1151c40010d137e4a2fa8629bff4bea72b0Calin JuravleT21 = 0x1.967e18afcb180ed942dfdc518d6cp-14L, 414d77c1151c40010d137e4a2fa8629bff4bea72b0Calin JuravleT23 = 0x1.497d8eea21e95bc7e2aa79b9f2cdp-15L, 424d77c1151c40010d137e4a2fa8629bff4bea72b0Calin JuravleT25 = 0x1.0b132d39f055c81be49eff7afd50p-16L, 434d77c1151c40010d137e4a2fa8629bff4bea72b0Calin JuravleT27 = 0x1.b0f72d33eff7bfa2fbc1059d90b6p-18L, 444d77c1151c40010d137e4a2fa8629bff4bea72b0Calin JuravleT29 = 0x1.5ef2daf21d1113df38d0fbc00267p-19L, 454d77c1151c40010d137e4a2fa8629bff4bea72b0Calin JuravleT31 = 0x1.1c77d6eac0234988cdaa04c96626p-20L, 464d77c1151c40010d137e4a2fa8629bff4bea72b0Calin JuravleT33 = 0x1.cd2a5a292b180e0bdd701057dfe3p-22L, 474d77c1151c40010d137e4a2fa8629bff4bea72b0Calin JuravleT35 = 0x1.75c7357d0298c01a31d0a6f7d518p-23L, 484d77c1151c40010d137e4a2fa8629bff4bea72b0Calin JuravleT37 = 0x1.2f3190f4718a9a520f98f50081fcp-24L, 494d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravlepio4 = 0x1.921fb54442d18469898cc51701b8p-1L, 504d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravlepio4lo = 0x1.cd129024e088a67cc74020bbea60p-116L; 514d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle 524d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravlestatic const double 534d77c1151c40010d137e4a2fa8629bff4bea72b0Calin JuravleT39 = 0.000000028443389121318352, /* 0x1e8a7592977938.0p-78 */ 544d77c1151c40010d137e4a2fa8629bff4bea72b0Calin JuravleT41 = 0.000000011981013102001973, /* 0x19baa1b1223219.0p-79 */ 554d77c1151c40010d137e4a2fa8629bff4bea72b0Calin JuravleT43 = 0.0000000038303578044958070, /* 0x107385dfb24529.0p-80 */ 564d77c1151c40010d137e4a2fa8629bff4bea72b0Calin JuravleT45 = 0.0000000034664378216909893, /* 0x1dc6c702a05262.0p-81 */ 574d77c1151c40010d137e4a2fa8629bff4bea72b0Calin JuravleT47 = -0.0000000015090641701997785, /* -0x19ecef3569ebb6.0p-82 */ 584d77c1151c40010d137e4a2fa8629bff4bea72b0Calin JuravleT49 = 0.0000000029449552300483952, /* 0x194c0668da786a.0p-81 */ 594d77c1151c40010d137e4a2fa8629bff4bea72b0Calin JuravleT51 = -0.0000000022006995706097711, /* -0x12e763b8845268.0p-81 */ 604d77c1151c40010d137e4a2fa8629bff4bea72b0Calin JuravleT53 = 0.0000000015468200913196612, /* 0x1a92fc98c29554.0p-82 */ 614d77c1151c40010d137e4a2fa8629bff4bea72b0Calin JuravleT55 = -0.00000000061311613386849674, /* -0x151106cbc779a9.0p-83 */ 624d77c1151c40010d137e4a2fa8629bff4bea72b0Calin JuravleT57 = 1.4912469681508012e-10; /* 0x147edbdba6f43a.0p-85 */ 634d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle 644d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravlelong double 654d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle__kernel_tanl(long double x, long double y, int iy) { 664d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle long double z, r, v, w, s; 674d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle long double osign; 684d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle int i; 694d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle 704d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle iy = (iy == 1 ? -1 : 1); /* XXX recover original interface */ 714d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle osign = (x >= 0 ? 1.0 : -1.0); /* XXX slow, probably wrong for -0 */ 724d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle if (fabsl(x) >= 0.67434) { 734d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle if (x < 0) { 744d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle x = -x; 754d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle y = -y; 764d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle } 774d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle z = pio4 - x; 784d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle w = pio4lo - y; 794d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle x = z + w; 804d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle y = 0.0; 814d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle i = 1; 824d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle } else 834d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle i = 0; 844d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle z = x * x; 854d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle w = z * z; 864d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle r = T5 + w * (T9 + w * (T13 + w * (T17 + w * (T21 + 874d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle w * (T25 + w * (T29 + w * (T33 + 884d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle w * (T37 + w * (T41 + w * (T45 + w * (T49 + w * (T53 + 894d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle w * T57)))))))))))); 904d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle v = z * (T7 + w * (T11 + w * (T15 + w * (T19 + w * (T23 + 914d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle w * (T27 + w * (T31 + w * (T35 + 924d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle w * (T39 + w * (T43 + w * (T47 + w * (T51 + w * T55)))))))))))); 934d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle s = z * x; 944d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle r = y + z * (s * (r + v) + y); 954d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle r += T3 * s; 964d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle w = x + r; 974d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle if (i == 1) { 984d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle v = (long double) iy; 994d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle return osign * 1004d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle (v - 2.0 * (x - (w * w / (w + v) - r))); 1014d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle } 1024d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle if (iy == 1) 1034d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle return w; 1044d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle else { 1054d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle /* 1064d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle * if allow error up to 2 ulp, simply return 1074d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle * -1.0 / (x+r) here 1084d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle */ 1094d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle /* compute -1.0 / (x+r) accurately */ 1104d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle long double a, t; 1114d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle z = w; 1124d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle z = z + 0x1p32 - 0x1p32; 1134d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle v = r - (z - x); /* z+v = r+x */ 1144d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle t = a = -1.0 / w; /* a = -1.0/w */ 1154d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle t = t + 0x1p32 - 0x1p32; 1164d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle s = 1.0 + t * z; 1174d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle return t + a * (s + t * v); 1184d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle } 1194d77c1151c40010d137e4a2fa8629bff4bea72b0Calin Juravle} 120