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