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