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 "cdefs-compat.h" 15 //__FBSDID("$FreeBSD: src/lib/msun/ld128/k_tanl.c,v 1.1 2008/02/17 07:32:31 das Exp $"); 16 17 /* 18 * ld128 version of k_tan.c. See ../src/k_tan.c for most comments. 19 */ 20 21 #include <openlibm_math.h> 22 23 #include "math_private.h" 24 25 /* 26 * Domain [-0.67434, 0.67434], range ~[-3.37e-36, 1.982e-37] 27 * |tan(x)/x - t(x)| < 2**-117.8 (XXX should be ~1e-37) 28 * 29 * See ../ld80/k_cosl.c for more details about the polynomial. 30 */ 31 static const long double 32 T3 = 0x1.5555555555555555555555555553p-2L, 33 T5 = 0x1.1111111111111111111111111eb5p-3L, 34 T7 = 0x1.ba1ba1ba1ba1ba1ba1ba1b694cd6p-5L, 35 T9 = 0x1.664f4882c10f9f32d6bbe09d8bcdp-6L, 36 T11 = 0x1.226e355e6c23c8f5b4f5762322eep-7L, 37 T13 = 0x1.d6d3d0e157ddfb5fed8e84e27b37p-9L, 38 T15 = 0x1.7da36452b75e2b5fce9ee7c2c92ep-10L, 39 T17 = 0x1.355824803674477dfcf726649efep-11L, 40 T19 = 0x1.f57d7734d1656e0aceb716f614c2p-13L, 41 T21 = 0x1.967e18afcb180ed942dfdc518d6cp-14L, 42 T23 = 0x1.497d8eea21e95bc7e2aa79b9f2cdp-15L, 43 T25 = 0x1.0b132d39f055c81be49eff7afd50p-16L, 44 T27 = 0x1.b0f72d33eff7bfa2fbc1059d90b6p-18L, 45 T29 = 0x1.5ef2daf21d1113df38d0fbc00267p-19L, 46 T31 = 0x1.1c77d6eac0234988cdaa04c96626p-20L, 47 T33 = 0x1.cd2a5a292b180e0bdd701057dfe3p-22L, 48 T35 = 0x1.75c7357d0298c01a31d0a6f7d518p-23L, 49 T37 = 0x1.2f3190f4718a9a520f98f50081fcp-24L, 50 pio4 = 0x1.921fb54442d18469898cc51701b8p-1L, 51 pio4lo = 0x1.cd129024e088a67cc74020bbea60p-116L; 52 53 static const double 54 T39 = 0.000000028443389121318352, /* 0x1e8a7592977938.0p-78 */ 55 T41 = 0.000000011981013102001973, /* 0x19baa1b1223219.0p-79 */ 56 T43 = 0.0000000038303578044958070, /* 0x107385dfb24529.0p-80 */ 57 T45 = 0.0000000034664378216909893, /* 0x1dc6c702a05262.0p-81 */ 58 T47 = -0.0000000015090641701997785, /* -0x19ecef3569ebb6.0p-82 */ 59 T49 = 0.0000000029449552300483952, /* 0x194c0668da786a.0p-81 */ 60 T51 = -0.0000000022006995706097711, /* -0x12e763b8845268.0p-81 */ 61 T53 = 0.0000000015468200913196612, /* 0x1a92fc98c29554.0p-82 */ 62 T55 = -0.00000000061311613386849674, /* -0x151106cbc779a9.0p-83 */ 63 T57 = 1.4912469681508012e-10; /* 0x147edbdba6f43a.0p-85 */ 64 65 DLLEXPORT long double 66 __kernel_tanl(long double x, long double y, int iy) { 67 long double z, r, v, w, s; 68 long double osign; 69 int i; 70 71 iy = (iy == 1 ? -1 : 1); /* XXX recover original interface */ 72 osign = (x >= 0 ? 1.0 : -1.0); /* XXX slow, probably wrong for -0 */ 73 if (fabsl(x) >= 0.67434) { 74 if (x < 0) { 75 x = -x; 76 y = -y; 77 } 78 z = pio4 - x; 79 w = pio4lo - y; 80 x = z + w; 81 y = 0.0; 82 i = 1; 83 } else 84 i = 0; 85 z = x * x; 86 w = z * z; 87 r = T5 + w * (T9 + w * (T13 + w * (T17 + w * (T21 + 88 w * (T25 + w * (T29 + w * (T33 + 89 w * (T37 + w * (T41 + w * (T45 + w * (T49 + w * (T53 + 90 w * T57)))))))))))); 91 v = z * (T7 + w * (T11 + w * (T15 + w * (T19 + w * (T23 + 92 w * (T27 + w * (T31 + w * (T35 + 93 w * (T39 + w * (T43 + w * (T47 + w * (T51 + w * T55)))))))))))); 94 s = z * x; 95 r = y + z * (s * (r + v) + y); 96 r += T3 * s; 97 w = x + r; 98 if (i == 1) { 99 v = (long double) iy; 100 return osign * 101 (v - 2.0 * (x - (w * w / (w + v) - r))); 102 } 103 if (iy == 1) 104 return w; 105 else { 106 /* 107 * if allow error up to 2 ulp, simply return 108 * -1.0 / (x+r) here 109 */ 110 /* compute -1.0 / (x+r) accurately */ 111 long double a, t; 112 z = w; 113 z = z + 0x1p32 - 0x1p32; 114 v = r - (z - x); /* z+v = r+x */ 115 t = a = -1.0 / w; /* a = -1.0/w */ 116 t = t + 0x1p32 - 0x1p32; 117 s = 1.0 + t * z; 118 return t + a * (s + t * v); 119 } 120 } 121