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 /* 17 * See s_asinh.c for complete comments. 18 * 19 * Converted to long double by David Schultz <das@FreeBSD.ORG> and 20 * Bruce D. Evans. 21 */ 22 23 #include <float.h> 24 #ifdef __i386__ 25 #include <ieeefp.h> 26 #endif 27 28 #include "fpmath.h" 29 #include "math.h" 30 #include "math_private.h" 31 32 /* EXP_LARGE is the threshold above which we use asinh(x) ~= log(2x). */ 33 /* EXP_TINY is the threshold below which we use asinh(x) ~= x. */ 34 #if LDBL_MANT_DIG == 64 35 #define EXP_LARGE 34 36 #define EXP_TINY -34 37 #elif LDBL_MANT_DIG == 113 38 #define EXP_LARGE 58 39 #define EXP_TINY -58 40 #else 41 #error "Unsupported long double format" 42 #endif 43 44 #if LDBL_MAX_EXP != 0x4000 45 /* We also require the usual expsign encoding. */ 46 #error "Unsupported long double format" 47 #endif 48 49 #define BIAS (LDBL_MAX_EXP - 1) 50 51 static const double 52 one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ 53 huge= 1.00000000000000000000e+300; 54 55 #if LDBL_MANT_DIG == 64 56 static const union IEEEl2bits 57 u_ln2 = LD80C(0xb17217f7d1cf79ac, -1, 6.93147180559945309417e-1L); 58 #define ln2 u_ln2.e 59 #elif LDBL_MANT_DIG == 113 60 static const long double 61 ln2 = 6.93147180559945309417232121458176568e-1L; /* 0x162e42fefa39ef35793c7673007e6.0p-113 */ 62 #else 63 #error "Unsupported long double format" 64 #endif 65 66 long double 67 asinhl(long double x) 68 { 69 long double t, w; 70 uint16_t hx, ix; 71 72 ENTERI(); 73 GET_LDBL_EXPSIGN(hx, x); 74 ix = hx & 0x7fff; 75 if (ix >= 0x7fff) RETURNI(x+x); /* x is inf, NaN or misnormal */ 76 if (ix < BIAS + EXP_TINY) { /* |x| < TINY, or misnormal */ 77 if (huge + x > one) RETURNI(x); /* return x inexact except 0 */ 78 } 79 if (ix >= BIAS + EXP_LARGE) { /* |x| >= LARGE, or misnormal */ 80 w = logl(fabsl(x))+ln2; 81 } else if (ix >= 0x4000) { /* LARGE > |x| >= 2.0, or misnormal */ 82 t = fabsl(x); 83 w = logl(2.0*t+one/(sqrtl(x*x+one)+t)); 84 } else { /* 2.0 > |x| >= TINY, or misnormal */ 85 t = x*x; 86 w =log1pl(fabsl(x)+t/(one+sqrtl(one+t))); 87 } 88 RETURNI((hx & 0x8000) == 0 ? w : -w); 89 } 90