| Calin Juravle | 4d77c11 | 2014-03-14 17:56:46 +0000 | [diff] [blame^] | 1 | /* From: @(#)k_tan.c 1.5 04/04/22 SMI */ |
| 2 | |
| 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 <sys/cdefs.h> |
| 15 | __FBSDID("$FreeBSD$"); |
| 16 | |
| 17 | /* |
| 18 | * ld128 version of k_tan.c. See ../src/k_tan.c for most comments. |
| 19 | */ |
| 20 | |
| 21 | #include "math.h" |
| 22 | #include "math_private.h" |
| 23 | |
| 24 | /* |
| 25 | * Domain [-0.67434, 0.67434], range ~[-3.37e-36, 1.982e-37] |
| 26 | * |tan(x)/x - t(x)| < 2**-117.8 (XXX should be ~1e-37) |
| 27 | * |
| 28 | * See ../ld80/k_cosl.c for more details about the polynomial. |
| 29 | */ |
| 30 | static const long double |
| 31 | T3 = 0x1.5555555555555555555555555553p-2L, |
| 32 | T5 = 0x1.1111111111111111111111111eb5p-3L, |
| 33 | T7 = 0x1.ba1ba1ba1ba1ba1ba1ba1b694cd6p-5L, |
| 34 | T9 = 0x1.664f4882c10f9f32d6bbe09d8bcdp-6L, |
| 35 | T11 = 0x1.226e355e6c23c8f5b4f5762322eep-7L, |
| 36 | T13 = 0x1.d6d3d0e157ddfb5fed8e84e27b37p-9L, |
| 37 | T15 = 0x1.7da36452b75e2b5fce9ee7c2c92ep-10L, |
| 38 | T17 = 0x1.355824803674477dfcf726649efep-11L, |
| 39 | T19 = 0x1.f57d7734d1656e0aceb716f614c2p-13L, |
| 40 | T21 = 0x1.967e18afcb180ed942dfdc518d6cp-14L, |
| 41 | T23 = 0x1.497d8eea21e95bc7e2aa79b9f2cdp-15L, |
| 42 | T25 = 0x1.0b132d39f055c81be49eff7afd50p-16L, |
| 43 | T27 = 0x1.b0f72d33eff7bfa2fbc1059d90b6p-18L, |
| 44 | T29 = 0x1.5ef2daf21d1113df38d0fbc00267p-19L, |
| 45 | T31 = 0x1.1c77d6eac0234988cdaa04c96626p-20L, |
| 46 | T33 = 0x1.cd2a5a292b180e0bdd701057dfe3p-22L, |
| 47 | T35 = 0x1.75c7357d0298c01a31d0a6f7d518p-23L, |
| 48 | T37 = 0x1.2f3190f4718a9a520f98f50081fcp-24L, |
| 49 | pio4 = 0x1.921fb54442d18469898cc51701b8p-1L, |
| 50 | pio4lo = 0x1.cd129024e088a67cc74020bbea60p-116L; |
| 51 | |
| 52 | static const double |
| 53 | T39 = 0.000000028443389121318352, /* 0x1e8a7592977938.0p-78 */ |
| 54 | T41 = 0.000000011981013102001973, /* 0x19baa1b1223219.0p-79 */ |
| 55 | T43 = 0.0000000038303578044958070, /* 0x107385dfb24529.0p-80 */ |
| 56 | T45 = 0.0000000034664378216909893, /* 0x1dc6c702a05262.0p-81 */ |
| 57 | T47 = -0.0000000015090641701997785, /* -0x19ecef3569ebb6.0p-82 */ |
| 58 | T49 = 0.0000000029449552300483952, /* 0x194c0668da786a.0p-81 */ |
| 59 | T51 = -0.0000000022006995706097711, /* -0x12e763b8845268.0p-81 */ |
| 60 | T53 = 0.0000000015468200913196612, /* 0x1a92fc98c29554.0p-82 */ |
| 61 | T55 = -0.00000000061311613386849674, /* -0x151106cbc779a9.0p-83 */ |
| 62 | T57 = 1.4912469681508012e-10; /* 0x147edbdba6f43a.0p-85 */ |
| 63 | |
| 64 | long double |
| 65 | __kernel_tanl(long double x, long double y, int iy) { |
| 66 | long double z, r, v, w, s; |
| 67 | long double osign; |
| 68 | int i; |
| 69 | |
| 70 | iy = (iy == 1 ? -1 : 1); /* XXX recover original interface */ |
| 71 | osign = (x >= 0 ? 1.0 : -1.0); /* XXX slow, probably wrong for -0 */ |
| 72 | if (fabsl(x) >= 0.67434) { |
| 73 | if (x < 0) { |
| 74 | x = -x; |
| 75 | y = -y; |
| 76 | } |
| 77 | z = pio4 - x; |
| 78 | w = pio4lo - y; |
| 79 | x = z + w; |
| 80 | y = 0.0; |
| 81 | i = 1; |
| 82 | } else |
| 83 | i = 0; |
| 84 | z = x * x; |
| 85 | w = z * z; |
| 86 | r = T5 + w * (T9 + w * (T13 + w * (T17 + w * (T21 + |
| 87 | w * (T25 + w * (T29 + w * (T33 + |
| 88 | w * (T37 + w * (T41 + w * (T45 + w * (T49 + w * (T53 + |
| 89 | w * T57)))))))))))); |
| 90 | v = z * (T7 + w * (T11 + w * (T15 + w * (T19 + w * (T23 + |
| 91 | w * (T27 + w * (T31 + w * (T35 + |
| 92 | w * (T39 + w * (T43 + w * (T47 + w * (T51 + w * T55)))))))))))); |
| 93 | s = z * x; |
| 94 | r = y + z * (s * (r + v) + y); |
| 95 | r += T3 * s; |
| 96 | w = x + r; |
| 97 | if (i == 1) { |
| 98 | v = (long double) iy; |
| 99 | return osign * |
| 100 | (v - 2.0 * (x - (w * w / (w + v) - r))); |
| 101 | } |
| 102 | if (iy == 1) |
| 103 | return w; |
| 104 | else { |
| 105 | /* |
| 106 | * if allow error up to 2 ulp, simply return |
| 107 | * -1.0 / (x+r) here |
| 108 | */ |
| 109 | /* compute -1.0 / (x+r) accurately */ |
| 110 | long double a, t; |
| 111 | z = w; |
| 112 | z = z + 0x1p32 - 0x1p32; |
| 113 | v = r - (z - x); /* z+v = r+x */ |
| 114 | t = a = -1.0 / w; /* a = -1.0/w */ |
| 115 | t = t + 0x1p32 - 0x1p32; |
| 116 | s = 1.0 + t * z; |
| 117 | return t + a * (s + t * v); |
| 118 | } |
| 119 | } |