1 /* from: FreeBSD: head/lib/msun/src/e_acosh.c 176451 2008-02-22 02:30:36Z das */ 2 3 /* @(#)e_acosh.c 1.3 95/01/18 */ 4 /* 5 * ==================================================== 6 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 7 * 8 * Developed at SunSoft, 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 16 #include <sys/cdefs.h> 17 __FBSDID("$FreeBSD$"); 18 19 /* 20 * See e_acosh.c for complete comments. 21 * 22 * Converted to long double by David Schultz <das@FreeBSD.ORG> and 23 * Bruce D. Evans. 24 */ 25 26 #include <float.h> 27 #ifdef __i386__ 28 #include <ieeefp.h> 29 #endif 30 31 #include "fpmath.h" 32 #include "math.h" 33 #include "math_private.h" 34 35 /* EXP_LARGE is the threshold above which we use acosh(x) ~= log(2x). */ 36 #if LDBL_MANT_DIG == 64 37 #define EXP_LARGE 34 38 #elif LDBL_MANT_DIG == 113 39 #define EXP_LARGE 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 = 1.0; 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 acoshl(long double x) 67 { 68 long double t; 69 int16_t hx; 70 71 ENTERI(); 72 GET_LDBL_EXPSIGN(hx, x); 73 if (hx < 0x3fff) { /* x < 1, or misnormal */ 74 RETURNI((x-x)/(x-x)); 75 } else if (hx >= BIAS + EXP_LARGE) { /* x >= LARGE */ 76 if (hx >= 0x7fff) { /* x is inf, NaN or misnormal */ 77 RETURNI(x+x); 78 } else 79 RETURNI(logl(x)+ln2); /* acosh(huge)=log(2x), or misnormal */ 80 } else if (hx == 0x3fff && x == 1) { 81 RETURNI(0.0); /* acosh(1) = 0 */ 82 } else if (hx >= 0x4000) { /* LARGE > x >= 2, or misnormal */ 83 t=x*x; 84 RETURNI(logl(2.0*x-one/(x+sqrtl(t-one)))); 85 } else { /* 1<x<2 */ 86 t = x-one; 87 RETURNI(log1pl(t+sqrtl(2.0*t+t*t))); 88 } 89 } 90