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 SunSoft, 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 /* 16 * See e_acosh.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 acosh(x) ~= log(2x). */ 32 #if LDBL_MANT_DIG == 64 33 #define EXP_LARGE 34 34 #elif LDBL_MANT_DIG == 113 35 #define EXP_LARGE 58 36 #else 37 #error "Unsupported long double format" 38 #endif 39 40 #if LDBL_MAX_EXP != 0x4000 41 /* We also require the usual expsign encoding. */ 42 #error "Unsupported long double format" 43 #endif 44 45 #define BIAS (LDBL_MAX_EXP - 1) 46 47 static const double 48 one = 1.0; 49 50 #if LDBL_MANT_DIG == 64 51 static const union IEEEl2bits 52 u_ln2 = LD80C(0xb17217f7d1cf79ac, -1, 6.93147180559945309417e-1L); 53 #define ln2 u_ln2.e 54 #elif LDBL_MANT_DIG == 113 55 static const long double 56 ln2 = 6.93147180559945309417232121458176568e-1L; /* 0x162e42fefa39ef35793c7673007e6.0p-113 */ 57 #else 58 #error "Unsupported long double format" 59 #endif 60 61 long double 62 acoshl(long double x) 63 { 64 long double t; 65 int16_t hx; 66 67 ENTERI(); 68 GET_LDBL_EXPSIGN(hx, x); 69 if (hx < 0x3fff) { /* x < 1, or misnormal */ 70 RETURNI((x-x)/(x-x)); 71 } else if (hx >= BIAS + EXP_LARGE) { /* x >= LARGE */ 72 if (hx >= 0x7fff) { /* x is inf, NaN or misnormal */ 73 RETURNI(x+x); 74 } else 75 RETURNI(logl(x)+ln2); /* acosh(huge)=log(2x), or misnormal */ 76 } else if (hx == 0x3fff && x == 1) { 77 RETURNI(0.0); /* acosh(1) = 0 */ 78 } else if (hx >= 0x4000) { /* LARGE > x >= 2, or misnormal */ 79 t=x*x; 80 RETURNI(logl(2.0*x-one/(x+sqrtl(t-one)))); 81 } else { /* 1<x<2 */ 82 t = x-one; 83 RETURNI(log1pl(t+sqrtl(2.0*t+t*t))); 84 } 85 } 86