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 #include <sys/cdefs.h> 15 16 #include "namespace.h" 17 #include <float.h> 18 #include <machine/ieee.h> 19 20 #include "math.h" 21 #include "math_private.h" 22 23 __weak_alias(tanhl, _tanhl) 24 25 #ifdef __HAVE_LONG_DOUBLE 26 /* 27 * See s_tanh.c for complete comments. 28 * 29 * Converted to long double by Bruce D. Evans. 30 */ 31 32 #ifdef __i386__ 33 #include <ieeefp.h> 34 #endif 35 36 #if LDBL_MANT_DIG == 64 37 #include "../ld80/k_expl.h" 38 #elif LDBL_MANT_DIG == 113 39 #include "../ld128/k_expl.h" 40 #else 41 #error "Unsupported long double format" 42 #endif 43 44 #if LDBL_MAX_EXP != 0x4000 45 /* We also require the usual expsign encoding. */ 46 #error "Unsupported long double format" 47 #endif 48 49 #define BIAS (LDBL_MAX_EXP - 1) 50 51 static const volatile double tiny = 1.0e-300; 52 static const double one = 1.0; 53 #if LDBL_MANT_DIG == 64 54 /* 55 * Domain [-0.25, 0.25], range ~[-1.6304e-22, 1.6304e-22]: 56 * |tanh(x)/x - t(x)| < 2**-72.3 57 */ 58 static const union ieee_ext_u 59 T3u = LD80C(0xaaaaaaaaaaaaaa9f, -2, -3.33333333333333333017e-1L); 60 #define T3 T3u.extu_ld 61 static const double 62 T5 = 1.3333333333333314e-1, /* 0x1111111111110a.0p-55 */ 63 T7 = -5.3968253968210485e-2, /* -0x1ba1ba1ba1a1a1.0p-57 */ 64 T9 = 2.1869488531393817e-2, /* 0x1664f488172022.0p-58 */ 65 T11 = -8.8632352345964591e-3, /* -0x1226e34bc138d5.0p-59 */ 66 T13 = 3.5921169709993771e-3, /* 0x1d6d371d3e400f.0p-61 */ 67 T15 = -1.4555786415756001e-3, /* -0x17d923aa63814d.0p-62 */ 68 T17 = 5.8645267876296793e-4, /* 0x13378589b85aa7.0p-63 */ 69 T19 = -2.1121033571392224e-4; /* -0x1baf0af80c4090.0p-65 */ 70 #elif LDBL_MANT_DIG == 113 71 /* 72 * Domain [-0.25, 0.25], range ~[-2.4211e-37, 2.4211e-37]: 73 * |tanh(x)/x - t(x)| < 2**121.6 74 */ 75 static const long double 76 T3 = -3.33333333333333333333333333333332980e-1L, /* -0x1555555555555555555555555554e.0p-114L */ 77 T5 = 1.33333333333333333333333333332707260e-1L, /* 0x1111111111111111111111110ab7b.0p-115L */ 78 T7 = -5.39682539682539682539682535723482314e-2L, /* -0x1ba1ba1ba1ba1ba1ba1ba17b5fc98.0p-117L */ 79 T9 = 2.18694885361552028218693591149061717e-2L, /* 0x1664f4882c10f9f32d6b1a12a25e5.0p-118L */ 80 T11 = -8.86323552990219656883762347736381851e-3L, /* -0x1226e355e6c23c8f5a5a0f386cb4d.0p-119L */ 81 T13 = 3.59212803657248101358314398220822722e-3L, /* 0x1d6d3d0e157ddfb403ad3637442c6.0p-121L */ 82 T15 = -1.45583438705131796512568010348874662e-3L; /* -0x17da36452b75e150c44cc34253b34.0p-122L */ 83 static const double 84 T17 = 5.9002744094556621e-4, /* 0x1355824803668e.0p-63 */ 85 T19 = -2.3912911424260516e-4, /* -0x1f57d7734c8dde.0p-65 */ 86 T21 = 9.6915379535512898e-5, /* 0x1967e18ad6a6ca.0p-66 */ 87 T23 = -3.9278322983156353e-5, /* -0x1497d8e6b75729.0p-67 */ 88 T25 = 1.5918887220143869e-5, /* 0x10b1319998cafa.0p-68 */ 89 T27 = -6.4514295231630956e-6, /* -0x1b0f2b71b218eb.0p-70 */ 90 T29 = 2.6120754043964365e-6, /* 0x15e963a3cf3a39.0p-71 */ 91 T31 = -1.0407567231003314e-6, /* -0x1176041e656869.0p-72 */ 92 T33 = 3.4744117554063574e-7; /* 0x1750fe732cab9c.0p-74 */ 93 #endif /* LDBL_MANT_DIG == 64 */ 94 95 static inline long double 96 divl(long double a, long double b, long double c, long double d, 97 long double e, long double f) 98 { 99 long double inv, r; 100 float fr, fw; 101 102 _2sumF(a, c); 103 b = b + c; 104 _2sumF(d, f); 105 e = e + f; 106 107 inv = 1 / (d + e); 108 109 r = (a + b) * inv; 110 fr = r; 111 r = fr; 112 113 fw = d + e; 114 e = d - fw + e; 115 d = fw; 116 117 r = r + (a - d * r + b - e * r) * inv; 118 119 return r; 120 } 121 122 long double 123 tanhl(long double x) 124 { 125 long double hi,lo,s,x2,z; 126 #if LDBL_MANT_DIG == 113 127 double dx2; 128 #endif 129 int16_t jx,ix; 130 131 GET_LDBL_EXPSIGN(jx,x); 132 ix = jx&0x7fff; 133 134 /* x is INF or NaN */ 135 if(ix>=0x7fff) { 136 if (jx>=0) return one/x+one; /* tanh(+-inf)=+-1 */ 137 else return one/x-one; /* tanh(NaN) = NaN */ 138 } 139 140 ENTERI(); 141 142 /* |x| < 40 */ 143 if (ix < 0x4004 || fabsl(x) < 40) { /* |x|<40 */ 144 if (__predict_false(ix<BIAS-(LDBL_MANT_DIG+1)/2)) { /* |x|<TINY */ 145 /* tanh(+-0) = +0; tanh(tiny) = tiny(-+) with inexact: */ 146 return (x == 0 ? x : (0x1p200 * x - x) * 0x1p-200); 147 } 148 if (ix<0x3ffd) { /* |x|<0.25 */ 149 x2 = x*x; 150 #if LDBL_MANT_DIG == 64 151 long double x4 = x2*x2; 152 RETURNI(((T19*x2 + T17)*x4 + (T15*x2 + T13))*(x2*x*x2*x4*x4) + 153 ((T11*x2 + T9)*x4 + (T7*x2 + T5))*(x2*x*x2) + 154 T3*(x2*x) + x); 155 #elif LDBL_MANT_DIG == 113 156 dx2 = x2; 157 #if 0 158 RETURNI(((((((((((((((T33*dx2 + T31)*dx2 + T29)*dx2 + T27)*dx2 + 159 T25)*x2 + T23)*x2 + T21)*x2 + T19)*x2 + T17)*x2 + 160 T15)*x2 + T13)*x2 + T11)*x2 + T9)*x2 + T7)*x2 + T5)* 161 (x2*x*x2) + 162 T3*(x2*x) + x); 163 #else 164 long double q = ((((((((((((((T33*dx2 + T31)*dx2 + T29)*dx2 + T27)*dx2 + 165 T25)*x2 + T23)*x2 + T21)*x2 + T19)*x2 + T17)*x2 + 166 T15)*x2 + T13)*x2 + T11)*x2 + T9)*x2 + T7)*x2 + T5)* 167 (x2*x*x2); 168 RETURNI(q + T3*(x2*x) + x); 169 #endif 170 #endif 171 } 172 k_hexpl(2*fabsl(x), &hi, &lo); 173 if (ix<0x4001 && fabsl(x) < 1.5) /* |x|<1.5 */ 174 z = divl(hi, lo, -0.5, hi, lo, 0.5); 175 else 176 z = one - one/(lo+0.5+hi); 177 /* |x| >= 40, return +-1 */ 178 } else { 179 z = one - tiny; /* raise inexact flag */ 180 } 181 s = 1; 182 if (jx<0) s = -1; 183 RETURNI(s*z); 184 } 185 #else 186 187 long double 188 tanhl(long double x) 189 { 190 return tanh(x); 191 } 192 #endif 193