RTAI API: base/math/e_acosh.c Source File

00001 /* @(#)e_acosh.c 5.1 93/09/24 */
00002 /*
00003  * ====================================================
00004  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
00005  *
00006  * Developed at SunPro, a Sun Microsystems, Inc. business.
00007  * Permission to use, copy, modify, and distribute this
00008  * software is freely granted, provided that this notice 
00009  * is preserved.
00010  * ====================================================
00011  */
00012 
00013 #if defined(LIBM_SCCS) && !defined(lint)
00014 static char rcsid[] = "$NetBSD: e_acosh.c,v 1.9 1995/05/12 04:57:18 jtc Exp $";
00015 #endif
00016 
00017 /* __ieee754_acosh(x)
00018  * Method :
00019  *  Based on 
00020  *      acosh(x) = log [ x + sqrt(x*x-1) ]
00021  *  we have
00022  *      acosh(x) := log(x)+ln2, if x is large; else
00023  *      acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else
00024  *      acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1.
00025  *
00026  * Special cases:
00027  *  acosh(x) is NaN with signal if x<1.
00028  *  acosh(NaN) is NaN without signal.
00029  */
00030 
00031 #include "math.h"
00032 #include "mathP.h"
00033 
00034 #ifdef __STDC__
00035 static const double 
00036 #else
00037 static double 
00038 #endif
00039 one = 1.0,
00040 ln2 = 6.93147180559945286227e-01;  /* 0x3FE62E42, 0xFEFA39EF */
00041 
00042 #ifdef __STDC__
00043     double __ieee754_acosh(double x)
00044 #else
00045     double __ieee754_acosh(x)
00046     double x;
00047 #endif
00048 {   
00049     double t;
00050     int32_t hx;
00051     u_int32_t lx;
00052     EXTRACT_WORDS(hx,lx,x);
00053     if(hx<0x3ff00000) {     /* x < 1 */
00054         return (x-x)/(x-x);
00055     } else if(hx >=0x41b00000) {    /* x > 2**28 */
00056         if(hx >=0x7ff00000) {   /* x is inf of NaN */
00057             return x+x;
00058         } else 
00059         return __ieee754_log(x)+ln2;    /* acosh(huge)=log(2x) */
00060     } else if(((hx-0x3ff00000)|lx)==0) {
00061         return 0.0;         /* acosh(1) = 0 */
00062     } else if (hx > 0x40000000) {   /* 2**28 > x > 2 */
00063         t=x*x;
00064         return __ieee754_log(2.0*x-one/(x+__ieee754_sqrt(t-one)));
00065     } else {            /* 1<x<2 */
00066         t = x-one;
00067         return log1p(t+sqrt(2.0*t+t*t));
00068     }
00069 }