1260067Skargl/* from: FreeBSD: head/lib/msun/src/s_tanhl.c XXX */ 2260067Skargl 3260067Skargl/* @(#)s_tanh.c 5.1 93/09/24 */ 4260067Skargl/* 5260067Skargl * ==================================================== 6260067Skargl * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 7260067Skargl * 8260067Skargl * Developed at SunPro, a Sun Microsystems, Inc. business. 9260067Skargl * Permission to use, copy, modify, and distribute this 10260067Skargl * software is freely granted, provided that this notice 11260067Skargl * is preserved. 12260067Skargl * ==================================================== 13260067Skargl */ 14260067Skargl 15260067Skargl#include <sys/cdefs.h> 16260067Skargl__FBSDID("$FreeBSD: stable/11/lib/msun/src/s_tanhl.c 324006 2017-09-26 09:01:56Z dim $"); 17260067Skargl 18260067Skargl/* 19260067Skargl * See s_tanh.c for complete comments. 20260067Skargl * 21260067Skargl * Converted to long double by Bruce D. Evans. 22260067Skargl */ 23260067Skargl 24260067Skargl#include <float.h> 25260067Skargl#ifdef __i386__ 26260067Skargl#include <ieeefp.h> 27260067Skargl#endif 28260067Skargl 29260067Skargl#include "math.h" 30260067Skargl#include "math_private.h" 31260067Skargl#include "fpmath.h" 32260067Skargl#include "k_expl.h" 33260067Skargl 34260067Skargl#if LDBL_MAX_EXP != 0x4000 35260067Skargl/* We also require the usual expsign encoding. */ 36260067Skargl#error "Unsupported long double format" 37260067Skargl#endif 38260067Skargl 39260067Skargl#define BIAS (LDBL_MAX_EXP - 1) 40260067Skargl 41260067Skarglstatic const volatile double tiny = 1.0e-300; 42260067Skarglstatic const double one = 1.0; 43260067Skargl#if LDBL_MANT_DIG == 64 44260067Skargl/* 45260067Skargl * Domain [-0.25, 0.25], range ~[-1.6304e-22, 1.6304e-22]: 46260067Skargl * |tanh(x)/x - t(x)| < 2**-72.3 47260067Skargl */ 48260067Skarglstatic const union IEEEl2bits 49260067SkarglT3u = LD80C(0xaaaaaaaaaaaaaa9f, -2, -3.33333333333333333017e-1L); 50260067Skargl#define T3 T3u.e 51260067Skarglstatic const double 52260067SkarglT5 = 1.3333333333333314e-1, /* 0x1111111111110a.0p-55 */ 53260067SkarglT7 = -5.3968253968210485e-2, /* -0x1ba1ba1ba1a1a1.0p-57 */ 54260067SkarglT9 = 2.1869488531393817e-2, /* 0x1664f488172022.0p-58 */ 55260067SkarglT11 = -8.8632352345964591e-3, /* -0x1226e34bc138d5.0p-59 */ 56260067SkarglT13 = 3.5921169709993771e-3, /* 0x1d6d371d3e400f.0p-61 */ 57260067SkarglT15 = -1.4555786415756001e-3, /* -0x17d923aa63814d.0p-62 */ 58260067SkarglT17 = 5.8645267876296793e-4, /* 0x13378589b85aa7.0p-63 */ 59260067SkarglT19 = -2.1121033571392224e-4; /* -0x1baf0af80c4090.0p-65 */ 60260067Skargl#elif LDBL_MANT_DIG == 113 61260067Skargl/* 62260067Skargl * Domain [-0.25, 0.25], range ~[-2.4211e-37, 2.4211e-37]: 63260067Skargl * |tanh(x)/x - t(x)| < 2**121.6 64260067Skargl */ 65260067Skarglstatic const long double 66260067SkarglT3 = -3.33333333333333333333333333333332980e-1L, /* -0x1555555555555555555555555554e.0p-114L */ 67260067SkarglT5 = 1.33333333333333333333333333332707260e-1L, /* 0x1111111111111111111111110ab7b.0p-115L */ 68260067SkarglT7 = -5.39682539682539682539682535723482314e-2L, /* -0x1ba1ba1ba1ba1ba1ba1ba17b5fc98.0p-117L */ 69260067SkarglT9 = 2.18694885361552028218693591149061717e-2L, /* 0x1664f4882c10f9f32d6b1a12a25e5.0p-118L */ 70260067SkarglT11 = -8.86323552990219656883762347736381851e-3L, /* -0x1226e355e6c23c8f5a5a0f386cb4d.0p-119L */ 71260067SkarglT13 = 3.59212803657248101358314398220822722e-3L, /* 0x1d6d3d0e157ddfb403ad3637442c6.0p-121L */ 72260067SkarglT15 = -1.45583438705131796512568010348874662e-3L; /* -0x17da36452b75e150c44cc34253b34.0p-122L */ 73260067Skarglstatic const double 74260067SkarglT17 = 5.9002744094556621e-4, /* 0x1355824803668e.0p-63 */ 75260067SkarglT19 = -2.3912911424260516e-4, /* -0x1f57d7734c8dde.0p-65 */ 76260067SkarglT21 = 9.6915379535512898e-5, /* 0x1967e18ad6a6ca.0p-66 */ 77260067SkarglT23 = -3.9278322983156353e-5, /* -0x1497d8e6b75729.0p-67 */ 78260067SkarglT25 = 1.5918887220143869e-5, /* 0x10b1319998cafa.0p-68 */ 79260067SkarglT27 = -6.4514295231630956e-6, /* -0x1b0f2b71b218eb.0p-70 */ 80260067SkarglT29 = 2.6120754043964365e-6, /* 0x15e963a3cf3a39.0p-71 */ 81260067SkarglT31 = -1.0407567231003314e-6, /* -0x1176041e656869.0p-72 */ 82260067SkarglT33 = 3.4744117554063574e-7; /* 0x1750fe732cab9c.0p-74 */ 83260067Skargl#endif /* LDBL_MANT_DIG == 64 */ 84260067Skargl 85260067Skarglstatic inline long double 86260067Skargldivl(long double a, long double b, long double c, long double d, 87260067Skargl long double e, long double f) 88260067Skargl{ 89260145Skargl long double inv, r; 90260067Skargl float fr, fw; 91260067Skargl 92260067Skargl _2sumF(a, c); 93260067Skargl b = b + c; 94260067Skargl _2sumF(d, f); 95260067Skargl e = e + f; 96260067Skargl 97260067Skargl inv = 1 / (d + e); 98260067Skargl 99260067Skargl r = (a + b) * inv; 100260067Skargl fr = r; 101260067Skargl r = fr; 102260067Skargl 103260067Skargl fw = d + e; 104260067Skargl e = d - fw + e; 105260067Skargl d = fw; 106260067Skargl 107260067Skargl r = r + (a - d * r + b - e * r) * inv; 108260067Skargl 109260067Skargl return r; 110260067Skargl} 111260067Skargl 112260067Skargllong double 113260067Skargltanhl(long double x) 114260067Skargl{ 115260067Skargl long double hi,lo,s,x2,x4,z; 116324006Sdim#if LDBL_MANT_DIG == 113 117260067Skargl double dx2; 118324006Sdim#endif 119260067Skargl int16_t jx,ix; 120260067Skargl 121260067Skargl GET_LDBL_EXPSIGN(jx,x); 122260067Skargl ix = jx&0x7fff; 123260067Skargl 124260067Skargl /* x is INF or NaN */ 125260067Skargl if(ix>=0x7fff) { 126260067Skargl if (jx>=0) return one/x+one; /* tanh(+-inf)=+-1 */ 127260067Skargl else return one/x-one; /* tanh(NaN) = NaN */ 128260067Skargl } 129260067Skargl 130260067Skargl ENTERI(); 131260067Skargl 132260145Skargl /* |x| < 40 */ 133260145Skargl if (ix < 0x4004 || fabsl(x) < 40) { /* |x|<40 */ 134260067Skargl if (__predict_false(ix<BIAS-(LDBL_MANT_DIG+1)/2)) { /* |x|<TINY */ 135260067Skargl /* tanh(+-0) = +0; tanh(tiny) = tiny(-+) with inexact: */ 136260067Skargl return (x == 0 ? x : (0x1p200 * x - x) * 0x1p-200); 137260067Skargl } 138260145Skargl if (ix<0x3ffd) { /* |x|<0.25 */ 139260067Skargl x2 = x*x; 140260067Skargl#if LDBL_MANT_DIG == 64 141260067Skargl x4 = x2*x2; 142260067Skargl RETURNI(((T19*x2 + T17)*x4 + (T15*x2 + T13))*(x2*x*x2*x4*x4) + 143260067Skargl ((T11*x2 + T9)*x4 + (T7*x2 + T5))*(x2*x*x2) + 144260067Skargl T3*(x2*x) + x); 145260067Skargl#elif LDBL_MANT_DIG == 113 146260067Skargl dx2 = x2; 147260145Skargl#if 0 148260067Skargl RETURNI(((((((((((((((T33*dx2 + T31)*dx2 + T29)*dx2 + T27)*dx2 + 149260067Skargl T25)*x2 + T23)*x2 + T21)*x2 + T19)*x2 + T17)*x2 + 150260067Skargl T15)*x2 + T13)*x2 + T11)*x2 + T9)*x2 + T7)*x2 + T5)* 151260067Skargl (x2*x*x2) + 152260067Skargl T3*(x2*x) + x); 153260145Skargl#else 154260145Skargl long double q = ((((((((((((((T33*dx2 + T31)*dx2 + T29)*dx2 + T27)*dx2 + 155260145Skargl T25)*x2 + T23)*x2 + T21)*x2 + T19)*x2 + T17)*x2 + 156260145Skargl T15)*x2 + T13)*x2 + T11)*x2 + T9)*x2 + T7)*x2 + T5)* 157260145Skargl (x2*x*x2); 158260145Skargl RETURNI(q + T3*(x2*x) + x); 159260067Skargl#endif 160260145Skargl#endif 161260067Skargl } 162260067Skargl k_hexpl(2*fabsl(x), &hi, &lo); 163260145Skargl if (ix<0x4001 && fabsl(x) < 1.5) /* |x|<1.5 */ 164260067Skargl z = divl(hi, lo, -0.5, hi, lo, 0.5); 165260067Skargl else 166260067Skargl z = one - one/(lo+0.5+hi); 167260067Skargl /* |x| >= 40, return +-1 */ 168260067Skargl } else { 169260067Skargl z = one - tiny; /* raise inexact flag */ 170260067Skargl } 171260067Skargl s = 1; 172260067Skargl if (jx<0) s = -1; 173260067Skargl RETURNI(s*z); 174260067Skargl} 175