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 #include <sys/cdefs.h> 16 /* 17 * See e_acosh.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 acosh(x) ~= log(2x). */ 33 #if LDBL_MANT_DIG == 64 34 #define EXP_LARGE 34 35 #elif LDBL_MANT_DIG == 113 36 #define EXP_LARGE 58 37 #else 38 #error "Unsupported long double format" 39 #endif 40 41 #if LDBL_MAX_EXP != 0x4000 42 /* We also require the usual expsign encoding. */ 43 #error "Unsupported long double format" 44 #endif 45 46 #define BIAS (LDBL_MAX_EXP - 1) 47 48 static const double 49 one = 1.0; 50 51 #if LDBL_MANT_DIG == 64 52 static const union IEEEl2bits 53 u_ln2 = LD80C(0xb17217f7d1cf79ac, -1, 6.93147180559945309417e-1L); 54 #define ln2 u_ln2.e 55 #elif LDBL_MANT_DIG == 113 56 static const long double 57 ln2 = 6.93147180559945309417232121458176568e-1L; /* 0x162e42fefa39ef35793c7673007e6.0p-113 */ 58 #else 59 #error "Unsupported long double format" 60 #endif 61 62 long double 63 acoshl(long double x) 64 { 65 long double t; 66 int16_t hx; 67 68 ENTERI(); 69 GET_LDBL_EXPSIGN(hx, x); 70 if (hx < 0x3fff) { /* x < 1, or misnormal */ 71 RETURNI((x-x)/(x-x)); 72 } else if (hx >= BIAS + EXP_LARGE) { /* x >= LARGE */ 73 if (hx >= 0x7fff) { /* x is inf, NaN or misnormal */ 74 RETURNI(x+x); 75 } else 76 RETURNI(logl(x)+ln2); /* acosh(huge)=log(2x), or misnormal */ 77 } else if (hx == 0x3fff && x == 1) { 78 RETURNI(0.0); /* acosh(1) = 0 */ 79 } else if (hx >= 0x4000) { /* LARGE > x >= 2, or misnormal */ 80 t=x*x; 81 RETURNI(logl(2.0*x-one/(x+sqrtl(t-one)))); 82 } else { /* 1<x<2 */ 83 t = x-one; 84 RETURNI(log1pl(t+sqrtl(2.0*t+t*t))); 85 } 86 } 87