1260067Skargl/* from: FreeBSD: head/lib/msun/src/e_sinhl.c XXX */ 2260067Skargl 3260067Skargl/* 4260067Skargl * ==================================================== 5260067Skargl * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 6260067Skargl * 7260067Skargl * Developed at SunPro, a Sun Microsystems, Inc. business. 8260067Skargl * Permission to use, copy, modify, and distribute this 9260067Skargl * software is freely granted, provided that this notice 10260067Skargl * is preserved. 11260067Skargl * ==================================================== 12260067Skargl */ 13260067Skargl 14260067Skargl#include <sys/cdefs.h> 15260067Skargl__FBSDID("$FreeBSD: stable/11/lib/msun/src/e_sinhl.c 324006 2017-09-26 09:01:56Z dim $"); 16260067Skargl 17260067Skargl/* 18260067Skargl * See e_sinh.c for complete comments. 19260067Skargl * 20260067Skargl * Converted to long double by Bruce D. Evans. 21260067Skargl */ 22260067Skargl 23260067Skargl#include <float.h> 24260067Skargl#ifdef __i386__ 25260067Skargl#include <ieeefp.h> 26260067Skargl#endif 27260067Skargl 28260067Skargl#include "fpmath.h" 29260067Skargl#include "math.h" 30260067Skargl#include "math_private.h" 31260067Skargl#include "k_expl.h" 32260067Skargl 33260067Skargl#if LDBL_MAX_EXP != 0x4000 34260067Skargl/* We also require the usual expsign encoding. */ 35260067Skargl#error "Unsupported long double format" 36260067Skargl#endif 37260067Skargl 38260067Skargl#define BIAS (LDBL_MAX_EXP - 1) 39260067Skargl 40260067Skarglstatic const long double shuge = 0x1p16383L; 41260067Skargl#if LDBL_MANT_DIG == 64 42260067Skargl/* 43260067Skargl * Domain [-1, 1], range ~[-6.6749e-22, 6.6749e-22]: 44260067Skargl * |sinh(x)/x - s(x)| < 2**-70.3 45260067Skargl */ 46260067Skarglstatic const union IEEEl2bits 47260067SkarglS3u = LD80C(0xaaaaaaaaaaaaaaaa, -3, 1.66666666666666666658e-1L); 48260067Skargl#define S3 S3u.e 49260067Skarglstatic const double 50260067SkarglS5 = 8.3333333333333332e-3, /* 0x11111111111111.0p-59 */ 51260067SkarglS7 = 1.9841269841270074e-4, /* 0x1a01a01a01a070.0p-65 */ 52260067SkarglS9 = 2.7557319223873889e-6, /* 0x171de3a5565fe6.0p-71 */ 53260067SkarglS11 = 2.5052108406704084e-8, /* 0x1ae6456857530f.0p-78 */ 54260067SkarglS13 = 1.6059042748655297e-10, /* 0x161245fa910697.0p-85 */ 55260067SkarglS15 = 7.6470006914396920e-13, /* 0x1ae7ce4eff2792.0p-93 */ 56260067SkarglS17 = 2.8346142308424267e-15; /* 0x19882ce789ffc6.0p-101 */ 57260067Skargl#elif LDBL_MANT_DIG == 113 58260067Skargl/* 59260067Skargl * Domain [-1, 1], range ~[-2.9673e-36, 2.9673e-36]: 60260067Skargl * |sinh(x)/x - s(x)| < 2**-118.0 61260067Skargl */ 62260067Skarglstatic const long double 63260067SkarglS3 = 1.66666666666666666666666666666666033e-1L, /* 0x1555555555555555555555555553b.0p-115L */ 64260067SkarglS5 = 8.33333333333333333333333333337643193e-3L, /* 0x111111111111111111111111180f5.0p-119L */ 65260067SkarglS7 = 1.98412698412698412698412697391263199e-4L, /* 0x1a01a01a01a01a01a01a0176aad11.0p-125L */ 66260067SkarglS9 = 2.75573192239858906525574406205464218e-6L, /* 0x171de3a556c7338faac243aaa9592.0p-131L */ 67260067SkarglS11 = 2.50521083854417187749675637460977997e-8L, /* 0x1ae64567f544e38fe59b3380d7413.0p-138L */ 68260067SkarglS13 = 1.60590438368216146368737762431552702e-10L, /* 0x16124613a86d098059c7620850fc2.0p-145L */ 69260067SkarglS15 = 7.64716373181980539786802470969096440e-13L, /* 0x1ae7f3e733b814193af09ce723043.0p-153L */ 70260067SkarglS17 = 2.81145725434775409870584280722701574e-15L; /* 0x1952c77030c36898c3fd0b6dfc562.0p-161L */ 71260067Skarglstatic const double 72260067SkarglS19= 8.2206352435411005e-18, /* 0x12f49b4662b86d.0p-109 */ 73260067SkarglS21= 1.9572943931418891e-20, /* 0x171b8f2fab9628.0p-118 */ 74260067SkarglS23 = 3.8679983530666939e-23, /* 0x17617002b73afc.0p-127 */ 75260067SkarglS25 = 6.5067867911512749e-26; /* 0x1423352626048a.0p-136 */ 76260067Skargl#else 77260067Skargl#error "Unsupported long double format" 78260067Skargl#endif /* LDBL_MANT_DIG == 64 */ 79260067Skargl 80260145Skargl/* log(2**16385 - 0.5) rounded up: */ 81260067Skarglstatic const float 82260067Skarglo_threshold = 1.13572168e4; /* 0xb174de.0p-10 */ 83260067Skargl 84260067Skargllong double 85260067Skarglsinhl(long double x) 86260067Skargl{ 87260067Skargl long double hi,lo,x2,x4; 88324006Sdim#if LDBL_MANT_DIG == 113 89324006Sdim double dx2; 90324006Sdim#endif 91324006Sdim double s; 92260067Skargl int16_t ix,jx; 93260067Skargl 94260067Skargl GET_LDBL_EXPSIGN(jx,x); 95260067Skargl ix = jx&0x7fff; 96260067Skargl 97260067Skargl /* x is INF or NaN */ 98260067Skargl if(ix>=0x7fff) return x+x; 99260067Skargl 100260067Skargl ENTERI(); 101260067Skargl 102260067Skargl s = 1; 103260067Skargl if (jx<0) s = -1; 104260067Skargl 105260067Skargl /* |x| < 64, return x, s(x), or accurate s*(exp(|x|)/2-1/exp(|x|)/2) */ 106260067Skargl if (ix<0x4005) { /* |x|<64 */ 107260067Skargl if (ix<BIAS-(LDBL_MANT_DIG+1)/2) /* |x|<TINY */ 108260067Skargl if(shuge+x>1) RETURNI(x); /* sinh(tiny) = tiny with inexact */ 109260067Skargl if (ix<0x3fff) { /* |x|<1 */ 110260067Skargl x2 = x*x; 111260067Skargl#if LDBL_MANT_DIG == 64 112260067Skargl x4 = x2*x2; 113260067Skargl RETURNI(((S17*x2 + S15)*x4 + (S13*x2 + S11))*(x2*x*x4*x4) + 114260067Skargl ((S9*x2 + S7)*x2 + S5)*(x2*x*x2) + S3*(x2*x) + x); 115260067Skargl#elif LDBL_MANT_DIG == 113 116260067Skargl dx2 = x2; 117260067Skargl RETURNI(((((((((((S25*dx2 + S23)*dx2 + 118260067Skargl S21)*x2 + S19)*x2 + 119260067Skargl S17)*x2 + S15)*x2 + S13)*x2 + S11)*x2 + S9)*x2 + S7)*x2 + 120260067Skargl S5)* (x2*x*x2) + 121260067Skargl S3*(x2*x) + x); 122260067Skargl#endif 123260067Skargl } 124260067Skargl k_hexpl(fabsl(x), &hi, &lo); 125260067Skargl RETURNI(s*(lo - 0.25/(hi + lo) + hi)); 126260067Skargl } 127260067Skargl 128260067Skargl /* |x| in [64, o_threshold], return correctly-overflowing s*exp(|x|)/2 */ 129260067Skargl if (fabsl(x) <= o_threshold) 130260067Skargl RETURNI(s*hexpl(fabsl(x))); 131260067Skargl 132260067Skargl /* |x| > o_threshold, sinh(x) overflow */ 133260067Skargl return x*shuge; 134260067Skargl} 135