1c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes/* from: FreeBSD: head/lib/msun/src/e_sinhl.c XXX */ 2c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes 3c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes/* 4c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes * ==================================================== 5c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 6c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes * 7c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes * Developed at SunPro, a Sun Microsystems, Inc. business. 8c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes * Permission to use, copy, modify, and distribute this 9c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes * software is freely granted, provided that this notice 10c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes * is preserved. 11c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes * ==================================================== 12c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes */ 13c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes 14c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes#include <sys/cdefs.h> 15c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes__FBSDID("$FreeBSD$"); 16c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes 17c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes/* 18c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes * See e_sinh.c for complete comments. 19c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes * 20c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes * Converted to long double by Bruce D. Evans. 21c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes */ 22c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes 23c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes#include <float.h> 24c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes#ifdef __i386__ 25c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes#include <ieeefp.h> 26c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes#endif 27c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes 28c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes#include "fpmath.h" 29c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes#include "math.h" 30c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes#include "math_private.h" 31c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes#include "k_expl.h" 32c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes 33c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes#if LDBL_MAX_EXP != 0x4000 34c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes/* We also require the usual expsign encoding. */ 35c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes#error "Unsupported long double format" 36c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes#endif 37c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes 38c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes#define BIAS (LDBL_MAX_EXP - 1) 39c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes 40c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughesstatic const long double shuge = 0x1p16383L; 41c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes#if LDBL_MANT_DIG == 64 42c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes/* 43c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes * Domain [-1, 1], range ~[-6.6749e-22, 6.6749e-22]: 44c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes * |sinh(x)/x - s(x)| < 2**-70.3 45c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes */ 46c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughesstatic const union IEEEl2bits 47c729d4f23771a01226c761423c6b35210dbb6ca7Elliott HughesS3u = LD80C(0xaaaaaaaaaaaaaaaa, -3, 1.66666666666666666658e-1L); 48c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes#define S3 S3u.e 49c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughesstatic const double 50c729d4f23771a01226c761423c6b35210dbb6ca7Elliott HughesS5 = 8.3333333333333332e-3, /* 0x11111111111111.0p-59 */ 51c729d4f23771a01226c761423c6b35210dbb6ca7Elliott HughesS7 = 1.9841269841270074e-4, /* 0x1a01a01a01a070.0p-65 */ 52c729d4f23771a01226c761423c6b35210dbb6ca7Elliott HughesS9 = 2.7557319223873889e-6, /* 0x171de3a5565fe6.0p-71 */ 53c729d4f23771a01226c761423c6b35210dbb6ca7Elliott HughesS11 = 2.5052108406704084e-8, /* 0x1ae6456857530f.0p-78 */ 54c729d4f23771a01226c761423c6b35210dbb6ca7Elliott HughesS13 = 1.6059042748655297e-10, /* 0x161245fa910697.0p-85 */ 55c729d4f23771a01226c761423c6b35210dbb6ca7Elliott HughesS15 = 7.6470006914396920e-13, /* 0x1ae7ce4eff2792.0p-93 */ 56c729d4f23771a01226c761423c6b35210dbb6ca7Elliott HughesS17 = 2.8346142308424267e-15; /* 0x19882ce789ffc6.0p-101 */ 57c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes#elif LDBL_MANT_DIG == 113 58c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes/* 59c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes * Domain [-1, 1], range ~[-2.9673e-36, 2.9673e-36]: 60c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes * |sinh(x)/x - s(x)| < 2**-118.0 61c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes */ 62c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughesstatic const long double 63c729d4f23771a01226c761423c6b35210dbb6ca7Elliott HughesS3 = 1.66666666666666666666666666666666033e-1L, /* 0x1555555555555555555555555553b.0p-115L */ 64c729d4f23771a01226c761423c6b35210dbb6ca7Elliott HughesS5 = 8.33333333333333333333333333337643193e-3L, /* 0x111111111111111111111111180f5.0p-119L */ 65c729d4f23771a01226c761423c6b35210dbb6ca7Elliott HughesS7 = 1.98412698412698412698412697391263199e-4L, /* 0x1a01a01a01a01a01a01a0176aad11.0p-125L */ 66c729d4f23771a01226c761423c6b35210dbb6ca7Elliott HughesS9 = 2.75573192239858906525574406205464218e-6L, /* 0x171de3a556c7338faac243aaa9592.0p-131L */ 67c729d4f23771a01226c761423c6b35210dbb6ca7Elliott HughesS11 = 2.50521083854417187749675637460977997e-8L, /* 0x1ae64567f544e38fe59b3380d7413.0p-138L */ 68c729d4f23771a01226c761423c6b35210dbb6ca7Elliott HughesS13 = 1.60590438368216146368737762431552702e-10L, /* 0x16124613a86d098059c7620850fc2.0p-145L */ 69c729d4f23771a01226c761423c6b35210dbb6ca7Elliott HughesS15 = 7.64716373181980539786802470969096440e-13L, /* 0x1ae7f3e733b814193af09ce723043.0p-153L */ 70c729d4f23771a01226c761423c6b35210dbb6ca7Elliott HughesS17 = 2.81145725434775409870584280722701574e-15L; /* 0x1952c77030c36898c3fd0b6dfc562.0p-161L */ 71c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughesstatic const double 72c729d4f23771a01226c761423c6b35210dbb6ca7Elliott HughesS19= 8.2206352435411005e-18, /* 0x12f49b4662b86d.0p-109 */ 73c729d4f23771a01226c761423c6b35210dbb6ca7Elliott HughesS21= 1.9572943931418891e-20, /* 0x171b8f2fab9628.0p-118 */ 74c729d4f23771a01226c761423c6b35210dbb6ca7Elliott HughesS23 = 3.8679983530666939e-23, /* 0x17617002b73afc.0p-127 */ 75c729d4f23771a01226c761423c6b35210dbb6ca7Elliott HughesS25 = 6.5067867911512749e-26; /* 0x1423352626048a.0p-136 */ 76c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes#else 77c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes#error "Unsupported long double format" 78c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes#endif /* LDBL_MANT_DIG == 64 */ 79c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes 80c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes/* log(2**16385 - 0.5) rounded up: */ 81c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughesstatic const float 82c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hugheso_threshold = 1.13572168e4; /* 0xb174de.0p-10 */ 83c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes 84c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hugheslong double 85c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughessinhl(long double x) 86c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes{ 87c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes long double hi,lo,x2,x4; 88c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes double dx2,s; 89c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes int16_t ix,jx; 90c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes 91c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes GET_LDBL_EXPSIGN(jx,x); 92c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes ix = jx&0x7fff; 93c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes 94c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes /* x is INF or NaN */ 95c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes if(ix>=0x7fff) return x+x; 96c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes 97c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes ENTERI(); 98c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes 99c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes s = 1; 100c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes if (jx<0) s = -1; 101c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes 102c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes /* |x| < 64, return x, s(x), or accurate s*(exp(|x|)/2-1/exp(|x|)/2) */ 103c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes if (ix<0x4005) { /* |x|<64 */ 104c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes if (ix<BIAS-(LDBL_MANT_DIG+1)/2) /* |x|<TINY */ 105c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes if(shuge+x>1) RETURNI(x); /* sinh(tiny) = tiny with inexact */ 106c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes if (ix<0x3fff) { /* |x|<1 */ 107c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes x2 = x*x; 108c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes#if LDBL_MANT_DIG == 64 109c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes x4 = x2*x2; 110c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes RETURNI(((S17*x2 + S15)*x4 + (S13*x2 + S11))*(x2*x*x4*x4) + 111c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes ((S9*x2 + S7)*x2 + S5)*(x2*x*x2) + S3*(x2*x) + x); 112c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes#elif LDBL_MANT_DIG == 113 113c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes dx2 = x2; 114c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes RETURNI(((((((((((S25*dx2 + S23)*dx2 + 115c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes S21)*x2 + S19)*x2 + 116c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes S17)*x2 + S15)*x2 + S13)*x2 + S11)*x2 + S9)*x2 + S7)*x2 + 117c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes S5)* (x2*x*x2) + 118c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes S3*(x2*x) + x); 119c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes#endif 120c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes } 121c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes k_hexpl(fabsl(x), &hi, &lo); 122c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes RETURNI(s*(lo - 0.25/(hi + lo) + hi)); 123c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes } 124c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes 125c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes /* |x| in [64, o_threshold], return correctly-overflowing s*exp(|x|)/2 */ 126c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes if (fabsl(x) <= o_threshold) 127c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes RETURNI(s*hexpl(fabsl(x))); 128c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes 129c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes /* |x| > o_threshold, sinh(x) overflow */ 130c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes return x*shuge; 131c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes} 132