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[] = "$FreeBSD$"; 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 "math_private.h" 33 34 #ifdef __STDC__ 35 static const double 36 #else 37 static double 38 #endif 39 one = 1.0, 40 ln2 = 6.93147180559945286227e-01; /* 0x3FE62E42, 0xFEFA39EF */ 41 42 #ifdef __STDC__ 43 double __ieee754_acosh(double x) 44 #else 45 double __ieee754_acosh(x) 46 double x; 47 #endif 48 { 49 double t; 50 int32_t hx; 51 u_int32_t lx; 52 EXTRACT_WORDS(hx,lx,x); 53 if(hx<0x3ff00000) { /* x < 1 */ 54 return (x-x)/(x-x); 55 } else if(hx >=0x41b00000) { /* x > 2**28 */ 56 if(hx >=0x7ff00000) { /* x is inf of NaN */ 57 return x+x; 58 } else 59 return __ieee754_log(x)+ln2; /* acosh(huge)=log(2x) */ 60 } else if(((hx-0x3ff00000)|lx)==0) { 61 return 0.0; /* acosh(1) = 0 */ 62 } else if (hx > 0x40000000) { /* 2**28 > x > 2 */ 63 t=x*x; 64 return __ieee754_log(2.0*x-one/(x+__ieee754_sqrt(t-one))); 65 } else { /* 1<x<2 */ 66 t = x-one; 67 return log1p(t+__ieee754_sqrt(2.0*t+t*t)); 68 } 69 } 70