1/* from: FreeBSD: head/lib/msun/src/s_tanhl.c XXX */ 2 3/* @(#)s_tanh.c 5.1 93/09/24 */ 4/* 5 * ==================================================== 6 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 7 * 8 * Developed at SunPro, a Sun Microsystems, Inc. business. 9 * Permission to use, copy, modify, and distribute this 10 * software is freely granted, provided that this notice 11 * is preserved. 12 * ==================================================== 13 */ 14 15#include <sys/cdefs.h> 16/* 17 * See s_tanh.c for complete comments. 18 * 19 * Converted to long double by Bruce D. Evans. 20 */ 21 22#include <float.h> 23#ifdef __i386__ 24#include <ieeefp.h> 25#endif 26 27#include "math.h" 28#include "math_private.h" 29#include "fpmath.h" 30#include "k_expl.h" 31 32#if LDBL_MAX_EXP != 0x4000 33/* We also require the usual expsign encoding. */ 34#error "Unsupported long double format" 35#endif 36 37#define BIAS (LDBL_MAX_EXP - 1) 38 39static const volatile double tiny = 1.0e-300; 40static const double one = 1.0; 41#if LDBL_MANT_DIG == 64 42/* 43 * Domain [-0.25, 0.25], range ~[-1.6304e-22, 1.6304e-22]: 44 * |tanh(x)/x - t(x)| < 2**-72.3 45 */ 46static const union IEEEl2bits 47T3u = LD80C(0xaaaaaaaaaaaaaa9f, -2, -3.33333333333333333017e-1L); 48#define T3 T3u.e 49static const double 50T5 = 1.3333333333333314e-1, /* 0x1111111111110a.0p-55 */ 51T7 = -5.3968253968210485e-2, /* -0x1ba1ba1ba1a1a1.0p-57 */ 52T9 = 2.1869488531393817e-2, /* 0x1664f488172022.0p-58 */ 53T11 = -8.8632352345964591e-3, /* -0x1226e34bc138d5.0p-59 */ 54T13 = 3.5921169709993771e-3, /* 0x1d6d371d3e400f.0p-61 */ 55T15 = -1.4555786415756001e-3, /* -0x17d923aa63814d.0p-62 */ 56T17 = 5.8645267876296793e-4, /* 0x13378589b85aa7.0p-63 */ 57T19 = -2.1121033571392224e-4; /* -0x1baf0af80c4090.0p-65 */ 58#elif LDBL_MANT_DIG == 113 59/* 60 * Domain [-0.25, 0.25], range ~[-2.4211e-37, 2.4211e-37]: 61 * |tanh(x)/x - t(x)| < 2**121.6 62 */ 63static const long double 64T3 = -3.33333333333333333333333333333332980e-1L, /* -0x1555555555555555555555555554e.0p-114L */ 65T5 = 1.33333333333333333333333333332707260e-1L, /* 0x1111111111111111111111110ab7b.0p-115L */ 66T7 = -5.39682539682539682539682535723482314e-2L, /* -0x1ba1ba1ba1ba1ba1ba1ba17b5fc98.0p-117L */ 67T9 = 2.18694885361552028218693591149061717e-2L, /* 0x1664f4882c10f9f32d6b1a12a25e5.0p-118L */ 68T11 = -8.86323552990219656883762347736381851e-3L, /* -0x1226e355e6c23c8f5a5a0f386cb4d.0p-119L */ 69T13 = 3.59212803657248101358314398220822722e-3L, /* 0x1d6d3d0e157ddfb403ad3637442c6.0p-121L */ 70T15 = -1.45583438705131796512568010348874662e-3L; /* -0x17da36452b75e150c44cc34253b34.0p-122L */ 71static const double 72T17 = 5.9002744094556621e-4, /* 0x1355824803668e.0p-63 */ 73T19 = -2.3912911424260516e-4, /* -0x1f57d7734c8dde.0p-65 */ 74T21 = 9.6915379535512898e-5, /* 0x1967e18ad6a6ca.0p-66 */ 75T23 = -3.9278322983156353e-5, /* -0x1497d8e6b75729.0p-67 */ 76T25 = 1.5918887220143869e-5, /* 0x10b1319998cafa.0p-68 */ 77T27 = -6.4514295231630956e-6, /* -0x1b0f2b71b218eb.0p-70 */ 78T29 = 2.6120754043964365e-6, /* 0x15e963a3cf3a39.0p-71 */ 79T31 = -1.0407567231003314e-6, /* -0x1176041e656869.0p-72 */ 80T33 = 3.4744117554063574e-7; /* 0x1750fe732cab9c.0p-74 */ 81#endif /* LDBL_MANT_DIG == 64 */ 82 83static inline long double 84divl(long double a, long double b, long double c, long double d, 85 long double e, long double f) 86{ 87 long double inv, r; 88 float fr, fw; 89 90 _2sumF(a, c); 91 b = b + c; 92 _2sumF(d, f); 93 e = e + f; 94 95 inv = 1 / (d + e); 96 97 r = (a + b) * inv; 98 fr = r; 99 r = fr; 100 101 fw = d + e; 102 e = d - fw + e; 103 d = fw; 104 105 r = r + (a - d * r + b - e * r) * inv; 106 107 return r; 108} 109 110long double 111tanhl(long double x) 112{ 113 long double hi,lo,s,x2,x4,z; 114#if LDBL_MANT_DIG == 113 115 double dx2; 116#endif 117 int16_t jx,ix; 118 119 GET_LDBL_EXPSIGN(jx,x); 120 ix = jx&0x7fff; 121 122 /* x is INF or NaN */ 123 if(ix>=0x7fff) { 124 if (jx>=0) return one/x+one; /* tanh(+-inf)=+-1 */ 125 else return one/x-one; /* tanh(NaN) = NaN */ 126 } 127 128 ENTERI(); 129 130 /* |x| < 40 */ 131 if (ix < 0x4004 || fabsl(x) < 40) { /* |x|<40 */ 132 if (__predict_false(ix<BIAS-(LDBL_MANT_DIG+1)/2)) { /* |x|<TINY */ 133 /* tanh(+-0) = +0; tanh(tiny) = tiny(-+) with inexact: */ 134 return (x == 0 ? x : (0x1p200 * x - x) * 0x1p-200); 135 } 136 if (ix<0x3ffd) { /* |x|<0.25 */ 137 x2 = x*x; 138#if LDBL_MANT_DIG == 64 139 x4 = x2*x2; 140 RETURNI(((T19*x2 + T17)*x4 + (T15*x2 + T13))*(x2*x*x2*x4*x4) + 141 ((T11*x2 + T9)*x4 + (T7*x2 + T5))*(x2*x*x2) + 142 T3*(x2*x) + x); 143#elif LDBL_MANT_DIG == 113 144 dx2 = x2; 145#if 0 146 RETURNI(((((((((((((((T33*dx2 + T31)*dx2 + T29)*dx2 + T27)*dx2 + 147 T25)*x2 + T23)*x2 + T21)*x2 + T19)*x2 + T17)*x2 + 148 T15)*x2 + T13)*x2 + T11)*x2 + T9)*x2 + T7)*x2 + T5)* 149 (x2*x*x2) + 150 T3*(x2*x) + x); 151#else 152 long double q = ((((((((((((((T33*dx2 + T31)*dx2 + T29)*dx2 + T27)*dx2 + 153 T25)*x2 + T23)*x2 + T21)*x2 + T19)*x2 + T17)*x2 + 154 T15)*x2 + T13)*x2 + T11)*x2 + T9)*x2 + T7)*x2 + T5)* 155 (x2*x*x2); 156 RETURNI(q + T3*(x2*x) + x); 157#endif 158#endif 159 } 160 k_hexpl(2*fabsl(x), &hi, &lo); 161 if (ix<0x4001 && fabsl(x) < 1.5) /* |x|<1.5 */ 162 z = divl(hi, lo, -0.5, hi, lo, 0.5); 163 else 164 z = one - one/(lo+0.5+hi); 165 /* |x| >= 40, return +-1 */ 166 } else { 167 z = one - tiny; /* raise inexact flag */ 168 } 169 s = 1; 170 if (jx<0) s = -1; 171 RETURNI(s*z); 172} 173