1 2 /* @(#)e_acosh.c 1.3 95/01/18 */ 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 "cdefs-compat.h" 16 //__FBSDID("$FreeBSD: src/lib/msun/src/e_acosh.c,v 1.9 2008/02/22 02:30:34 das Exp $"); 17 18 /* __ieee754_acosh(x) 19 * Method : 20 * Based on 21 * acosh(x) = log [ x + sqrt(x*x-1) ] 22 * we have 23 * acosh(x) := log(x)+ln2, if x is large; else 24 * acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else 25 * acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1. 26 * 27 * Special cases: 28 * acosh(x) is NaN with signal if x<1. 29 * acosh(NaN) is NaN without signal. 30 */ 31 32 #include <openlibm.h> 33 34 #include "math_private.h" 35 36 static const double 37 one = 1.0, 38 ln2 = 6.93147180559945286227e-01; /* 0x3FE62E42, 0xFEFA39EF */ 39 40 DLLEXPORT double 41 __ieee754_acosh(double x) 42 { 43 double t; 44 int32_t hx; 45 u_int32_t lx; 46 EXTRACT_WORDS(hx,lx,x); 47 if(hx<0x3ff00000) { /* x < 1 */ 48 return (x-x)/(x-x); 49 } else if(hx >=0x41b00000) { /* x > 2**28 */ 50 if(hx >=0x7ff00000) { /* x is inf of NaN */ 51 return x+x; 52 } else 53 return __ieee754_log(x)+ln2; /* acosh(huge)=log(2x) */ 54 } else if(((hx-0x3ff00000)|lx)==0) { 55 return 0.0; /* acosh(1) = 0 */ 56 } else if (hx > 0x40000000) { /* 2**28 > x > 2 */ 57 t=x*x; 58 return __ieee754_log(2.0*x-one/(x+sqrt(t-one))); 59 } else { /* 1<x<2 */ 60 t = x-one; 61 return log1p(t+sqrt(2.0*t+t*t)); 62 } 63 } 64