1/* from: FreeBSD: head/lib/msun/src/e_acosh.c 176451 2008-02-22 02:30:36Z das */ 2 3/* @(#)s_asinh.c 5.1 93/09/24 */ 4/* 5 * ==================================================== 6 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 7 * 8 * Developed at SunPro, a Sun Microsystems, Inc. business. 9 * Permission to use, copy, modify, and distribute this 10 * software is freely granted, provided that this notice 11 * is preserved. 12 * ==================================================== 13 */ 14 15#include <sys/cdefs.h> 16__FBSDID("$FreeBSD$"); 17 18/* 19 * See s_asinh.c for complete comments. 20 * 21 * Converted to long double by David Schultz <das@FreeBSD.ORG> and 22 * Bruce D. Evans. 23 */ 24 25#include <float.h> 26#ifdef __i386__ 27#include <ieeefp.h> 28#endif 29 30#include "fpmath.h" 31#include "math.h" 32#include "math_private.h" 33 34/* EXP_LARGE is the threshold above which we use asinh(x) ~= log(2x). */ 35/* EXP_TINY is the threshold below which we use asinh(x) ~= x. */ 36#if LDBL_MANT_DIG == 64 37#define EXP_LARGE 34 38#define EXP_TINY -34 39#elif LDBL_MANT_DIG == 113 40#define EXP_LARGE 58 41#define EXP_TINY -58 42#else 43#error "Unsupported long double format" 44#endif 45 46#if LDBL_MAX_EXP != 0x4000 47/* We also require the usual expsign encoding. */ 48#error "Unsupported long double format" 49#endif 50 51#define BIAS (LDBL_MAX_EXP - 1) 52 53static const double 54one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ 55huge= 1.00000000000000000000e+300; 56 57#if LDBL_MANT_DIG == 64 58static const union IEEEl2bits 59u_ln2 = LD80C(0xb17217f7d1cf79ac, -1, 6.93147180559945309417e-1L); 60#define ln2 u_ln2.e 61#elif LDBL_MANT_DIG == 113 62static const long double 63ln2 = 6.93147180559945309417232121458176568e-1L; /* 0x162e42fefa39ef35793c7673007e6.0p-113 */ 64#else 65#error "Unsupported long double format" 66#endif 67 68long double 69asinhl(long double x) 70{ 71 long double t, w; 72 uint16_t hx, ix; 73 74 ENTERI(); 75 GET_LDBL_EXPSIGN(hx, x); 76 ix = hx & 0x7fff; 77 if (ix >= 0x7fff) RETURNI(x+x); /* x is inf, NaN or misnormal */ 78 if (ix < BIAS + EXP_TINY) { /* |x| < TINY, or misnormal */ 79 if (huge + x > one) RETURNI(x); /* return x inexact except 0 */ 80 } 81 if (ix >= BIAS + EXP_LARGE) { /* |x| >= LARGE, or misnormal */ 82 w = logl(fabsl(x))+ln2; 83 } else if (ix >= 0x4000) { /* LARGE > |x| >= 2.0, or misnormal */ 84 t = fabsl(x); 85 w = logl(2.0*t+one/(sqrtl(x*x+one)+t)); 86 } else { /* 2.0 > |x| >= TINY, or misnormal */ 87 t = x*x; 88 w =log1pl(fabsl(x)+t/(one+sqrtl(one+t))); 89 } 90 RETURNI((hx & 0x8000) == 0 ? w : -w); 91} 92