1*1e651e1eSRoland Levillain 2*1e651e1eSRoland Levillain /* @(#)e_acosh.c 1.3 95/01/18 */ 3*1e651e1eSRoland Levillain /* 4*1e651e1eSRoland Levillain * ==================================================== 5*1e651e1eSRoland Levillain * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 6*1e651e1eSRoland Levillain * 7*1e651e1eSRoland Levillain * Developed at SunSoft, a Sun Microsystems, Inc. business. 8*1e651e1eSRoland Levillain * Permission to use, copy, modify, and distribute this 9*1e651e1eSRoland Levillain * software is freely granted, provided that this notice 10*1e651e1eSRoland Levillain * is preserved. 11*1e651e1eSRoland Levillain * ==================================================== 12*1e651e1eSRoland Levillain * 13*1e651e1eSRoland Levillain */ 14*1e651e1eSRoland Levillain 15*1e651e1eSRoland Levillain /* __ieee754_acosh(x) 16*1e651e1eSRoland Levillain * Method : 17*1e651e1eSRoland Levillain * Based on 18*1e651e1eSRoland Levillain * acosh(x) = log [ x + ieee_sqrt(x*x-1) ] 19*1e651e1eSRoland Levillain * we have 20*1e651e1eSRoland Levillain * acosh(x) := ieee_log(x)+ln2, if x is large; else 21*1e651e1eSRoland Levillain * acosh(x) := ieee_log(2x-1/(ieee_sqrt(x*x-1)+x)) if x>2; else 22*1e651e1eSRoland Levillain * acosh(x) := ieee_log1p(t+ieee_sqrt(2.0*t+t*t)); where t=x-1. 23*1e651e1eSRoland Levillain * 24*1e651e1eSRoland Levillain * Special cases: 25*1e651e1eSRoland Levillain * acosh(x) is NaN with signal if x<1. 26*1e651e1eSRoland Levillain * acosh(NaN) is NaN without signal. 27*1e651e1eSRoland Levillain */ 28*1e651e1eSRoland Levillain 29*1e651e1eSRoland Levillain #include "fdlibm.h" 30*1e651e1eSRoland Levillain 31*1e651e1eSRoland Levillain #ifdef __STDC__ 32*1e651e1eSRoland Levillain static const double 33*1e651e1eSRoland Levillain #else 34*1e651e1eSRoland Levillain static double 35*1e651e1eSRoland Levillain #endif 36*1e651e1eSRoland Levillain one = 1.0, 37*1e651e1eSRoland Levillain ln2 = 6.93147180559945286227e-01; /* 0x3FE62E42, 0xFEFA39EF */ 38*1e651e1eSRoland Levillain 39*1e651e1eSRoland Levillain #ifdef __STDC__ __ieee754_acosh(double x)40*1e651e1eSRoland Levillain double __ieee754_acosh(double x) 41*1e651e1eSRoland Levillain #else 42*1e651e1eSRoland Levillain double __ieee754_acosh(x) 43*1e651e1eSRoland Levillain double x; 44*1e651e1eSRoland Levillain #endif 45*1e651e1eSRoland Levillain { 46*1e651e1eSRoland Levillain double t; 47*1e651e1eSRoland Levillain int hx; 48*1e651e1eSRoland Levillain hx = __HI(x); 49*1e651e1eSRoland Levillain if(hx<0x3ff00000) { /* x < 1 */ 50*1e651e1eSRoland Levillain return (x-x)/(x-x); 51*1e651e1eSRoland Levillain } else if(hx >=0x41b00000) { /* x > 2**28 */ 52*1e651e1eSRoland Levillain if(hx >=0x7ff00000) { /* x is inf of NaN */ 53*1e651e1eSRoland Levillain return x+x; 54*1e651e1eSRoland Levillain } else 55*1e651e1eSRoland Levillain return __ieee754_log(x)+ln2; /* acosh(huge)=ieee_log(2x) */ 56*1e651e1eSRoland Levillain } else if(((hx-0x3ff00000)|__LO(x))==0) { 57*1e651e1eSRoland Levillain return 0.0; /* acosh(1) = 0 */ 58*1e651e1eSRoland Levillain } else if (hx > 0x40000000) { /* 2**28 > x > 2 */ 59*1e651e1eSRoland Levillain t=x*x; 60*1e651e1eSRoland Levillain return __ieee754_log(2.0*x-one/(x+ieee_sqrt(t-one))); 61*1e651e1eSRoland Levillain } else { /* 1<x<2 */ 62*1e651e1eSRoland Levillain t = x-one; 63*1e651e1eSRoland Levillain return ieee_log1p(t+ieee_sqrt(2.0*t+t*t)); 64*1e651e1eSRoland Levillain } 65*1e651e1eSRoland Levillain } 66