1 /* derived from /netlib/fdlibm */ 2 3 /* @(#)e_acosh.c 1.3 95/01/18 */ 4 /* 5 * ==================================================== 6 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 7 * 8 * Developed at SunSoft, a Sun Microsystems, Inc. business. 9 * Permission to use, copy, modify, and distribute this 10 * software is freely granted, provided that this notice 11 * is preserved. 12 * ==================================================== 13 * 14 */ 15 16 /* __ieee754_acosh(x) 17 * Method : 18 * Based on 19 * acosh(x) = log [ x + sqrt(x*x-1) ] 20 * we have 21 * acosh(x) := log(x)+ln2, if x is large; else 22 * acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else 23 * acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1. 24 * 25 * Special cases: 26 * acosh(x) is NaN with signal if x<1. 27 * acosh(NaN) is NaN without signal. 28 */ 29 30 #include "fdlibm.h" 31 32 static const double 33 one = 1.0, 34 ln2 = 6.93147180559945286227e-01; /* 0x3FE62E42, 0xFEFA39EF */ 35 __ieee754_acosh(double x)36 double __ieee754_acosh(double x) 37 { 38 double t; 39 int hx; 40 hx = __HI(x); 41 if(hx<0x3ff00000) { /* x < 1 */ 42 return (x-x)/(x-x); 43 } else if(hx >=0x41b00000) { /* x > 2**28 */ 44 if(hx >=0x7ff00000) { /* x is inf of NaN */ 45 return x+x; 46 } else 47 return __ieee754_log(x)+ln2; /* acosh(Huge)=log(2x) */ 48 } else if(((hx-0x3ff00000)|__LO(x))==0) { 49 return 0.0; /* acosh(1) = 0 */ 50 } else if (hx > 0x40000000) { /* 2**28 > x > 2 */ 51 t=x*x; 52 return __ieee754_log(2.0*x-one/(x+sqrt(t-one))); 53 } else { /* 1<x<2 */ 54 t = x-one; 55 return log1p(t+sqrt(2.0*t+t*t)); 56 } 57 } 58