1/* origin: FreeBSD /usr/src/lib/msun/ld80/k_tanl.c */ 2/* origin: FreeBSD /usr/src/lib/msun/ld128/k_tanl.c */ 3/* 4 * ==================================================== 5 * Copyright 2004 Sun Microsystems, Inc. All Rights Reserved. 6 * Copyright (c) 2008 Steven G. Kargl, David Schultz, Bruce D. Evans. 7 * 8 * Permission to use, copy, modify, and distribute this 9 * software is freely granted, provided that this notice 10 * is preserved. 11 * ==================================================== 12 */ 13 14#include "libm.h" 15 16#if (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384 17#if LDBL_MANT_DIG == 64 18/* 19 * ld80 version of __tan.c. See __tan.c for most comments. 20 */ 21/* 22 * Domain [-0.67434, 0.67434], range ~[-2.25e-22, 1.921e-22] 23 * |tan(x)/x - t(x)| < 2**-71.9 24 * 25 * See __cosl.c for more details about the polynomial. 26 */ 27static const long double T3 = 0.333333333333333333180L, /* 0xaaaaaaaaaaaaaaa5.0p-65 */ 28 T5 = 0.133333333333333372290L, /* 0x88888888888893c3.0p-66 */ 29 T7 = 0.0539682539682504975744L, /* 0xdd0dd0dd0dc13ba2.0p-68 */ 30 pio4 = 0.785398163397448309628L, /* 0xc90fdaa22168c235.0p-64 */ 31 pio4lo = -1.25413940316708300586e-20L; /* -0xece675d1fc8f8cbb.0p-130 */ 32static const double T9 = 0.021869488536312216, /* 0x1664f4882cc1c2.0p-58 */ 33 T11 = 0.0088632355256619590, /* 0x1226e355c17612.0p-59 */ 34 T13 = 0.0035921281113786528, /* 0x1d6d3d185d7ff8.0p-61 */ 35 T15 = 0.0014558334756312418, /* 0x17da354aa3f96b.0p-62 */ 36 T17 = 0.00059003538700862256, /* 0x13559358685b83.0p-63 */ 37 T19 = 0.00023907843576635544, /* 0x1f56242026b5be.0p-65 */ 38 T21 = 0.000097154625656538905, /* 0x1977efc26806f4.0p-66 */ 39 T23 = 0.000038440165747303162, /* 0x14275a09b3ceac.0p-67 */ 40 T25 = 0.000018082171885432524, /* 0x12f5e563e5487e.0p-68 */ 41 T27 = 0.0000024196006108814377, /* 0x144c0d80cc6896.0p-71 */ 42 T29 = 0.0000078293456938132840, /* 0x106b59141a6cb3.0p-69 */ 43 T31 = -0.0000032609076735050182, /* -0x1b5abef3ba4b59.0p-71 */ 44 T33 = 0.0000023261313142559411; /* 0x13835436c0c87f.0p-71 */ 45#define RPOLY(w) \ 46 (T5 + w * (T9 + w * (T13 + w * (T17 + w * (T21 + w * (T25 + w * (T29 + w * T33))))))) 47#define VPOLY(w) (T7 + w * (T11 + w * (T15 + w * (T19 + w * (T23 + w * (T27 + w * T31)))))) 48#elif LDBL_MANT_DIG == 113 49/* 50 * ld128 version of __tan.c. See __tan.c for most comments. 51 */ 52/* 53 * Domain [-0.67434, 0.67434], range ~[-3.37e-36, 1.982e-37] 54 * |tan(x)/x - t(x)| < 2**-117.8 (XXX should be ~1e-37) 55 * 56 * See __cosl.c for more details about the polynomial. 57 */ 58static const long double T3 = 0x1.5555555555555555555555555553p-2L, 59 T5 = 0x1.1111111111111111111111111eb5p-3L, 60 T7 = 0x1.ba1ba1ba1ba1ba1ba1ba1b694cd6p-5L, 61 T9 = 0x1.664f4882c10f9f32d6bbe09d8bcdp-6L, 62 T11 = 0x1.226e355e6c23c8f5b4f5762322eep-7L, 63 T13 = 0x1.d6d3d0e157ddfb5fed8e84e27b37p-9L, 64 T15 = 0x1.7da36452b75e2b5fce9ee7c2c92ep-10L, 65 T17 = 0x1.355824803674477dfcf726649efep-11L, 66 T19 = 0x1.f57d7734d1656e0aceb716f614c2p-13L, 67 T21 = 0x1.967e18afcb180ed942dfdc518d6cp-14L, 68 T23 = 0x1.497d8eea21e95bc7e2aa79b9f2cdp-15L, 69 T25 = 0x1.0b132d39f055c81be49eff7afd50p-16L, 70 T27 = 0x1.b0f72d33eff7bfa2fbc1059d90b6p-18L, 71 T29 = 0x1.5ef2daf21d1113df38d0fbc00267p-19L, 72 T31 = 0x1.1c77d6eac0234988cdaa04c96626p-20L, 73 T33 = 0x1.cd2a5a292b180e0bdd701057dfe3p-22L, 74 T35 = 0x1.75c7357d0298c01a31d0a6f7d518p-23L, 75 T37 = 0x1.2f3190f4718a9a520f98f50081fcp-24L, 76 pio4 = 0x1.921fb54442d18469898cc51701b8p-1L, 77 pio4lo = 0x1.cd129024e088a67cc74020bbea60p-116L; 78static const double T39 = 0.000000028443389121318352, /* 0x1e8a7592977938.0p-78 */ 79 T41 = 0.000000011981013102001973, /* 0x19baa1b1223219.0p-79 */ 80 T43 = 0.0000000038303578044958070, /* 0x107385dfb24529.0p-80 */ 81 T45 = 0.0000000034664378216909893, /* 0x1dc6c702a05262.0p-81 */ 82 T47 = -0.0000000015090641701997785, /* -0x19ecef3569ebb6.0p-82 */ 83 T49 = 0.0000000029449552300483952, /* 0x194c0668da786a.0p-81 */ 84 T51 = -0.0000000022006995706097711, /* -0x12e763b8845268.0p-81 */ 85 T53 = 0.0000000015468200913196612, /* 0x1a92fc98c29554.0p-82 */ 86 T55 = -0.00000000061311613386849674, /* -0x151106cbc779a9.0p-83 */ 87 T57 = 1.4912469681508012e-10; /* 0x147edbdba6f43a.0p-85 */ 88#define RPOLY(w) \ 89 (T5 + \ 90 w * (T9 + \ 91 w * (T13 + \ 92 w * (T17 + \ 93 w * (T21 + \ 94 w * (T25 + \ 95 w * (T29 + \ 96 w * (T33 + \ 97 w * (T37 + \ 98 w * (T41 + \ 99 w * (T45 + \ 100 w * (T49 + w * (T53 + w * T57))))))))))))) 101#define VPOLY(w) \ 102 (T7 + \ 103 w * (T11 + \ 104 w * (T15 + \ 105 w * (T19 + \ 106 w * (T23 + \ 107 w * (T27 + \ 108 w * (T31 + \ 109 w * (T35 + \ 110 w * (T39 + \ 111 w * (T43 + w * (T47 + w * (T51 + w * T55)))))))))))) 112#endif 113 114long double __tanl(long double x, long double y, int odd) { 115 long double z, r, v, w, s, a, t; 116 int big, sign; 117 118 big = fabsl(x) >= 0.67434; 119 if (big) { 120 sign = 0; 121 if (x < 0) { 122 sign = 1; 123 x = -x; 124 y = -y; 125 } 126 x = (pio4 - x) + (pio4lo - y); 127 y = 0.0; 128 } 129 z = x * x; 130 w = z * z; 131 r = RPOLY(w); 132 v = z * VPOLY(w); 133 s = z * x; 134 r = y + z * (s * (r + v) + y) + T3 * s; 135 w = x + r; 136 if (big) { 137 s = 1 - 2 * odd; 138 v = s - 2.0 * (x + (r - w * w / (w + s))); 139 return sign ? -v : v; 140 } 141 if (!odd) 142 return w; 143 /* 144 * if allow error up to 2 ulp, simply return 145 * -1.0 / (x+r) here 146 */ 147 /* compute -1.0 / (x+r) accurately */ 148 z = w; 149 z = z + 0x1p32 - 0x1p32; 150 v = r - (z - x); /* z+v = r+x */ 151 t = a = -1.0 / w; /* a = -1.0/w */ 152 t = t + 0x1p32 - 0x1p32; 153 s = 1.0 + t * z; 154 return t + a * (s + t * v); 155} 156#endif 157