1 /* @(#)e_acosh.c 5.1 93/09/24 */ 2 /* 3 * ==================================================== 4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 5 * 6 * Developed at SunPro, a Sun Microsystems, Inc. business. 7 * Permission to use, copy, modify, and distribute this 8 * software is freely granted, provided that this notice 9 * is preserved. 10 * ==================================================== 11 */ 12 13 #ifndef lint 14 static char rcsid[] = "$Id: e_acosh.c,v 1.4 1994/03/03 17:04:05 jtc Exp $"; 15 #endif 16 17 /* __ieee754_acosh(x) 18 * Method : 19 * Based on 20 * acosh(x) = log [ x + sqrt(x*x-1) ] 21 * we have 22 * acosh(x) := log(x)+ln2, if x is large; else 23 * acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else 24 * acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1. 25 * 26 * Special cases: 27 * acosh(x) is NaN with signal if x<1. 28 * acosh(NaN) is NaN without signal. 29 */ 30 31 #include <math.h> 32 #include <machine/endian.h> 33 34 #if BYTE_ORDER == LITTLE_ENDIAN 35 #define n0 1 36 #else 37 #define n0 0 38 #endif 39 40 #ifdef __STDC__ 41 static const double 42 #else 43 static double 44 #endif 45 one = 1.0, 46 ln2 = 6.93147180559945286227e-01; /* 0x3FE62E42, 0xFEFA39EF */ 47 48 #ifdef __STDC__ 49 double __ieee754_acosh(double x) 50 #else 51 double __ieee754_acosh(x) 52 double x; 53 #endif 54 { 55 double t; 56 int hx; 57 58 hx = *(n0+(int*)&x); 59 if(hx<0x3ff00000) { /* x < 1 */ 60 return (x-x)/(x-x); 61 } else if(hx >=0x41b00000) { /* x > 2**28 */ 62 if(hx >=0x7ff00000) { /* x is inf of NaN */ 63 return x+x; 64 } else 65 return __ieee754_log(x)+ln2; /* acosh(huge)=log(2x) */ 66 } else if(((hx-0x3ff00000)|*(1-n0+(int*)&x))==0) { 67 return 0.0; /* acosh(1) = 0 */ 68 } else if (hx > 0x40000000) { /* 2**28 > x > 2 */ 69 t=x*x; 70 return __ieee754_log(2.0*x-one/(x+sqrt(t-one))); 71 } else { /* 1<x<2 */ 72 t = x-one; 73 return log1p(t+sqrt(2.0*t+t*t)); 74 } 75 } 76