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