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 #include <sys/cdefs.h> 15 /* 16 * See s_asinh.c for complete comments. 17 * 18 * Converted to long double by David Schultz <das@FreeBSD.ORG> and 19 * Bruce D. Evans. 20 */ 21 22 #include <float.h> 23 #ifdef __i386__ 24 #include <ieeefp.h> 25 #endif 26 27 #include "fpmath.h" 28 #include "math.h" 29 #include "math_private.h" 30 31 /* EXP_LARGE is the threshold above which we use asinh(x) ~= log(2x). */ 32 /* EXP_TINY is the threshold below which we use asinh(x) ~= x. */ 33 #if LDBL_MANT_DIG == 64 34 #define EXP_LARGE 34 35 #define EXP_TINY -34 36 #elif LDBL_MANT_DIG == 113 37 #define EXP_LARGE 58 38 #define EXP_TINY -58 39 #else 40 #error "Unsupported long double format" 41 #endif 42 43 #if LDBL_MAX_EXP != 0x4000 44 /* We also require the usual expsign encoding. */ 45 #error "Unsupported long double format" 46 #endif 47 48 #define BIAS (LDBL_MAX_EXP - 1) 49 50 static const double 51 one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ 52 huge= 1.00000000000000000000e+300; 53 54 #if LDBL_MANT_DIG == 64 55 static const union IEEEl2bits 56 u_ln2 = LD80C(0xb17217f7d1cf79ac, -1, 6.93147180559945309417e-1L); 57 #define ln2 u_ln2.e 58 #elif LDBL_MANT_DIG == 113 59 static const long double 60 ln2 = 6.93147180559945309417232121458176568e-1L; /* 0x162e42fefa39ef35793c7673007e6.0p-113 */ 61 #else 62 #error "Unsupported long double format" 63 #endif 64 65 long double 66 asinhl(long double x) 67 { 68 long double t, w; 69 uint16_t hx, ix; 70 71 ENTERI(); 72 GET_LDBL_EXPSIGN(hx, x); 73 ix = hx & 0x7fff; 74 if (ix >= 0x7fff) RETURNI(x+x); /* x is inf, NaN or misnormal */ 75 if (ix < BIAS + EXP_TINY) { /* |x| < TINY, or misnormal */ 76 if (huge + x > one) RETURNI(x); /* return x inexact except 0 */ 77 } 78 if (ix >= BIAS + EXP_LARGE) { /* |x| >= LARGE, or misnormal */ 79 w = logl(fabsl(x))+ln2; 80 } else if (ix >= 0x4000) { /* LARGE > |x| >= 2.0, or misnormal */ 81 t = fabsl(x); 82 w = logl(2.0*t+one/(sqrtl(x*x+one)+t)); 83 } else { /* 2.0 > |x| >= TINY, or misnormal */ 84 t = x*x; 85 w =log1pl(fabsl(x)+t/(one+sqrtl(one+t))); 86 } 87 RETURNI((hx & 0x8000) == 0 ? w : -w); 88 } 89