1 /* from: FreeBSD: head/lib/msun/src/e_sinhl.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 e_sinh.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 "fpmath.h" 26 #include "math.h" 27 #include "math_private.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 long double shuge = 0x1p16383L; 38 #if LDBL_MANT_DIG == 64 39 /* 40 * Domain [-1, 1], range ~[-6.6749e-22, 6.6749e-22]: 41 * |sinh(x)/x - s(x)| < 2**-70.3 42 */ 43 static const union IEEEl2bits 44 S3u = LD80C(0xaaaaaaaaaaaaaaaa, -3, 1.66666666666666666658e-1L); 45 #define S3 S3u.e 46 static const double 47 S5 = 8.3333333333333332e-3, /* 0x11111111111111.0p-59 */ 48 S7 = 1.9841269841270074e-4, /* 0x1a01a01a01a070.0p-65 */ 49 S9 = 2.7557319223873889e-6, /* 0x171de3a5565fe6.0p-71 */ 50 S11 = 2.5052108406704084e-8, /* 0x1ae6456857530f.0p-78 */ 51 S13 = 1.6059042748655297e-10, /* 0x161245fa910697.0p-85 */ 52 S15 = 7.6470006914396920e-13, /* 0x1ae7ce4eff2792.0p-93 */ 53 S17 = 2.8346142308424267e-15; /* 0x19882ce789ffc6.0p-101 */ 54 #elif LDBL_MANT_DIG == 113 55 /* 56 * Domain [-1, 1], range ~[-2.9673e-36, 2.9673e-36]: 57 * |sinh(x)/x - s(x)| < 2**-118.0 58 */ 59 static const long double 60 S3 = 1.66666666666666666666666666666666033e-1L, /* 0x1555555555555555555555555553b.0p-115L */ 61 S5 = 8.33333333333333333333333333337643193e-3L, /* 0x111111111111111111111111180f5.0p-119L */ 62 S7 = 1.98412698412698412698412697391263199e-4L, /* 0x1a01a01a01a01a01a01a0176aad11.0p-125L */ 63 S9 = 2.75573192239858906525574406205464218e-6L, /* 0x171de3a556c7338faac243aaa9592.0p-131L */ 64 S11 = 2.50521083854417187749675637460977997e-8L, /* 0x1ae64567f544e38fe59b3380d7413.0p-138L */ 65 S13 = 1.60590438368216146368737762431552702e-10L, /* 0x16124613a86d098059c7620850fc2.0p-145L */ 66 S15 = 7.64716373181980539786802470969096440e-13L, /* 0x1ae7f3e733b814193af09ce723043.0p-153L */ 67 S17 = 2.81145725434775409870584280722701574e-15L; /* 0x1952c77030c36898c3fd0b6dfc562.0p-161L */ 68 static const double 69 S19= 8.2206352435411005e-18, /* 0x12f49b4662b86d.0p-109 */ 70 S21= 1.9572943931418891e-20, /* 0x171b8f2fab9628.0p-118 */ 71 S23 = 3.8679983530666939e-23, /* 0x17617002b73afc.0p-127 */ 72 S25 = 6.5067867911512749e-26; /* 0x1423352626048a.0p-136 */ 73 #else 74 #error "Unsupported long double format" 75 #endif /* LDBL_MANT_DIG == 64 */ 76 77 /* log(2**16385 - 0.5) rounded up: */ 78 static const float 79 o_threshold = 1.13572168e4; /* 0xb174de.0p-10 */ 80 81 long double 82 sinhl(long double x) 83 { 84 long double hi,lo,x2,x4; 85 #if LDBL_MANT_DIG == 113 86 double dx2; 87 #endif 88 double s; 89 int16_t ix,jx; 90 91 GET_LDBL_EXPSIGN(jx,x); 92 ix = jx&0x7fff; 93 94 /* x is INF or NaN */ 95 if(ix>=0x7fff) return x+x; 96 97 ENTERI(); 98 99 s = 1; 100 if (jx<0) s = -1; 101 102 /* |x| < 64, return x, s(x), or accurate s*(exp(|x|)/2-1/exp(|x|)/2) */ 103 if (ix<0x4005) { /* |x|<64 */ 104 if (ix<BIAS-(LDBL_MANT_DIG+1)/2) /* |x|<TINY */ 105 if(shuge+x>1) RETURNI(x); /* sinh(tiny) = tiny with inexact */ 106 if (ix<0x3fff) { /* |x|<1 */ 107 x2 = x*x; 108 #if LDBL_MANT_DIG == 64 109 x4 = x2*x2; 110 RETURNI(((S17*x2 + S15)*x4 + (S13*x2 + S11))*(x2*x*x4*x4) + 111 ((S9*x2 + S7)*x2 + S5)*(x2*x*x2) + S3*(x2*x) + x); 112 #elif LDBL_MANT_DIG == 113 113 dx2 = x2; 114 RETURNI(((((((((((S25*dx2 + S23)*dx2 + 115 S21)*x2 + S19)*x2 + 116 S17)*x2 + S15)*x2 + S13)*x2 + S11)*x2 + S9)*x2 + S7)*x2 + 117 S5)* (x2*x*x2) + 118 S3*(x2*x) + x); 119 #endif 120 } 121 k_hexpl(fabsl(x), &hi, &lo); 122 RETURNI(s*(lo - 0.25/(hi + lo) + hi)); 123 } 124 125 /* |x| in [64, o_threshold], return correctly-overflowing s*exp(|x|)/2 */ 126 if (fabsl(x) <= o_threshold) 127 RETURNI(s*hexpl(fabsl(x))); 128 129 /* |x| > o_threshold, sinh(x) overflow */ 130 return x*shuge; 131 } 132