1*37da2899SCharles.Forsyth /* derived from /netlib/fdlibm */ 2*37da2899SCharles.Forsyth 3*37da2899SCharles.Forsyth /* @(#)e_acosh.c 1.3 95/01/18 */ 4*37da2899SCharles.Forsyth /* 5*37da2899SCharles.Forsyth * ==================================================== 6*37da2899SCharles.Forsyth * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 7*37da2899SCharles.Forsyth * 8*37da2899SCharles.Forsyth * Developed at SunSoft, a Sun Microsystems, Inc. business. 9*37da2899SCharles.Forsyth * Permission to use, copy, modify, and distribute this 10*37da2899SCharles.Forsyth * software is freely granted, provided that this notice 11*37da2899SCharles.Forsyth * is preserved. 12*37da2899SCharles.Forsyth * ==================================================== 13*37da2899SCharles.Forsyth * 14*37da2899SCharles.Forsyth */ 15*37da2899SCharles.Forsyth 16*37da2899SCharles.Forsyth /* __ieee754_acosh(x) 17*37da2899SCharles.Forsyth * Method : 18*37da2899SCharles.Forsyth * Based on 19*37da2899SCharles.Forsyth * acosh(x) = log [ x + sqrt(x*x-1) ] 20*37da2899SCharles.Forsyth * we have 21*37da2899SCharles.Forsyth * acosh(x) := log(x)+ln2, if x is large; else 22*37da2899SCharles.Forsyth * acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else 23*37da2899SCharles.Forsyth * acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1. 24*37da2899SCharles.Forsyth * 25*37da2899SCharles.Forsyth * Special cases: 26*37da2899SCharles.Forsyth * acosh(x) is NaN with signal if x<1. 27*37da2899SCharles.Forsyth * acosh(NaN) is NaN without signal. 28*37da2899SCharles.Forsyth */ 29*37da2899SCharles.Forsyth 30*37da2899SCharles.Forsyth #include "fdlibm.h" 31*37da2899SCharles.Forsyth 32*37da2899SCharles.Forsyth static const double 33*37da2899SCharles.Forsyth one = 1.0, 34*37da2899SCharles.Forsyth ln2 = 6.93147180559945286227e-01; /* 0x3FE62E42, 0xFEFA39EF */ 35*37da2899SCharles.Forsyth __ieee754_acosh(double x)36*37da2899SCharles.Forsyth double __ieee754_acosh(double x) 37*37da2899SCharles.Forsyth { 38*37da2899SCharles.Forsyth double t; 39*37da2899SCharles.Forsyth int hx; 40*37da2899SCharles.Forsyth hx = __HI(x); 41*37da2899SCharles.Forsyth if(hx<0x3ff00000) { /* x < 1 */ 42*37da2899SCharles.Forsyth return (x-x)/(x-x); 43*37da2899SCharles.Forsyth } else if(hx >=0x41b00000) { /* x > 2**28 */ 44*37da2899SCharles.Forsyth if(hx >=0x7ff00000) { /* x is inf of NaN */ 45*37da2899SCharles.Forsyth return x+x; 46*37da2899SCharles.Forsyth } else 47*37da2899SCharles.Forsyth return __ieee754_log(x)+ln2; /* acosh(Huge)=log(2x) */ 48*37da2899SCharles.Forsyth } else if(((hx-0x3ff00000)|__LO(x))==0) { 49*37da2899SCharles.Forsyth return 0.0; /* acosh(1) = 0 */ 50*37da2899SCharles.Forsyth } else if (hx > 0x40000000) { /* 2**28 > x > 2 */ 51*37da2899SCharles.Forsyth t=x*x; 52*37da2899SCharles.Forsyth return __ieee754_log(2.0*x-one/(x+sqrt(t-one))); 53*37da2899SCharles.Forsyth } else { /* 1<x<2 */ 54*37da2899SCharles.Forsyth t = x-one; 55*37da2899SCharles.Forsyth return log1p(t+sqrt(2.0*t+t*t)); 56*37da2899SCharles.Forsyth } 57*37da2899SCharles.Forsyth } 58