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 __FBSDID("$FreeBSD$"); 17 18 /* 19 * See s_tanh.c for complete comments. 20 * 21 * Converted to long double by Bruce D. Evans. 22 */ 23 24 #include <float.h> 25 #ifdef __i386__ 26 #include <ieeefp.h> 27 #endif 28 29 #include "math.h" 30 #include "math_private.h" 31 #include "fpmath.h" 32 #include "k_expl.h" 33 34 #if LDBL_MAX_EXP != 0x4000 35 /* We also require the usual expsign encoding. */ 36 #error "Unsupported long double format" 37 #endif 38 39 #define BIAS (LDBL_MAX_EXP - 1) 40 41 static const volatile double tiny = 1.0e-300; 42 static const double one = 1.0; 43 #if LDBL_MANT_DIG == 64 44 /* 45 * Domain [-0.25, 0.25], range ~[-1.6304e-22, 1.6304e-22]: 46 * |tanh(x)/x - t(x)| < 2**-72.3 47 */ 48 static const union IEEEl2bits 49 T3u = LD80C(0xaaaaaaaaaaaaaa9f, -2, -3.33333333333333333017e-1L); 50 #define T3 T3u.e 51 static const double 52 T5 = 1.3333333333333314e-1, /* 0x1111111111110a.0p-55 */ 53 T7 = -5.3968253968210485e-2, /* -0x1ba1ba1ba1a1a1.0p-57 */ 54 T9 = 2.1869488531393817e-2, /* 0x1664f488172022.0p-58 */ 55 T11 = -8.8632352345964591e-3, /* -0x1226e34bc138d5.0p-59 */ 56 T13 = 3.5921169709993771e-3, /* 0x1d6d371d3e400f.0p-61 */ 57 T15 = -1.4555786415756001e-3, /* -0x17d923aa63814d.0p-62 */ 58 T17 = 5.8645267876296793e-4, /* 0x13378589b85aa7.0p-63 */ 59 T19 = -2.1121033571392224e-4; /* -0x1baf0af80c4090.0p-65 */ 60 #elif LDBL_MANT_DIG == 113 61 /* 62 * Domain [-0.25, 0.25], range ~[-2.4211e-37, 2.4211e-37]: 63 * |tanh(x)/x - t(x)| < 2**121.6 64 */ 65 static const long double 66 T3 = -3.33333333333333333333333333333332980e-1L, /* -0x1555555555555555555555555554e.0p-114L */ 67 T5 = 1.33333333333333333333333333332707260e-1L, /* 0x1111111111111111111111110ab7b.0p-115L */ 68 T7 = -5.39682539682539682539682535723482314e-2L, /* -0x1ba1ba1ba1ba1ba1ba1ba17b5fc98.0p-117L */ 69 T9 = 2.18694885361552028218693591149061717e-2L, /* 0x1664f4882c10f9f32d6b1a12a25e5.0p-118L */ 70 T11 = -8.86323552990219656883762347736381851e-3L, /* -0x1226e355e6c23c8f5a5a0f386cb4d.0p-119L */ 71 T13 = 3.59212803657248101358314398220822722e-3L, /* 0x1d6d3d0e157ddfb403ad3637442c6.0p-121L */ 72 T15 = -1.45583438705131796512568010348874662e-3L; /* -0x17da36452b75e150c44cc34253b34.0p-122L */ 73 static const double 74 T17 = 5.9002744094556621e-4, /* 0x1355824803668e.0p-63 */ 75 T19 = -2.3912911424260516e-4, /* -0x1f57d7734c8dde.0p-65 */ 76 T21 = 9.6915379535512898e-5, /* 0x1967e18ad6a6ca.0p-66 */ 77 T23 = -3.9278322983156353e-5, /* -0x1497d8e6b75729.0p-67 */ 78 T25 = 1.5918887220143869e-5, /* 0x10b1319998cafa.0p-68 */ 79 T27 = -6.4514295231630956e-6, /* -0x1b0f2b71b218eb.0p-70 */ 80 T29 = 2.6120754043964365e-6, /* 0x15e963a3cf3a39.0p-71 */ 81 T31 = -1.0407567231003314e-6, /* -0x1176041e656869.0p-72 */ 82 T33 = 3.4744117554063574e-7; /* 0x1750fe732cab9c.0p-74 */ 83 #endif /* LDBL_MANT_DIG == 64 */ 84 85 static inline long double 86 divl(long double a, long double b, long double c, long double d, 87 long double e, long double f) 88 { 89 long double inv, r; 90 float fr, fw; 91 92 _2sumF(a, c); 93 b = b + c; 94 _2sumF(d, f); 95 e = e + f; 96 97 inv = 1 / (d + e); 98 99 r = (a + b) * inv; 100 fr = r; 101 r = fr; 102 103 fw = d + e; 104 e = d - fw + e; 105 d = fw; 106 107 r = r + (a - d * r + b - e * r) * inv; 108 109 return r; 110 } 111 112 long double 113 tanhl(long double x) 114 { 115 long double hi,lo,s,x2,x4,z; 116 double dx2; 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