gonzui

    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: /* LINTLIBRARY */
   14: 
   15: /* acosh(x)
   16:  * Method :
   17:  *      Based on 
   18:  *              acosh(x) = log [ x + sqrt(x*x-1) ]
   19:  *      we have
   20:  *              acosh(x) := log(x)+ln2,     if x is large; else
   21:  *              acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else
   22:  *              acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1.
   23:  *
   24:  * Special cases:
   25:  *      acosh(x) is NaN with signal if x<1.
   26:  *      acosh(NaN) is NaN without signal.
   27:  */
   28: 
   29: #include <sys/cdefs.h>
   30: #include <float.h>
   31: #include <math.h>
   32: 
   33: #include "math_private.h"
   34: 
   35: static const double 
   36: one     = 1.0,
   37: ln2     = 6.93147180559945286227e-01;  /* 0x3FE62E42, 0xFEFA39EF */
   38: 
   39: double
   40: acosh(double x)
   41: {       
   42:         double t;
   43:         int32_t hx;
   44:         u_int32_t lx;
   45:         EXTRACT_WORDS(hx,lx,x);
   46:         if(hx<0x3ff00000) {            /* x < 1 */
   47:             return (x-x)/(x-x);
   48:         } else if(hx >=0x41b00000) {   /* x > 2**28 */
   49:             if(hx >=0x7ff00000) {      /* x is inf of NaN */
   50:                 return x+x;
   51:             } else 
   52:                 return log(x)+ln2;    /* acosh(huge)=log(2x) */
   53:         } else if(((hx-0x3ff00000)|lx)==0) {
   54:             return 0.0;                        /* acosh(1) = 0 */
   55:         } else if (hx > 0x40000000) {  /* 2**28 > x > 2 */
   56:             t=x*x;
   57:             return log(2.0*x-one/(x+sqrt(t-one)));
   58:         } else {                       /* 1<x<2 */
   59:             t = x-one;
   60:             return log1p(t+sqrt(2.0*t+t*t));
   61:         }
   62: }
   63: 
   64: #if     LDBL_MANT_DIG == 53
   65: #ifdef  lint
   66: /* PROTOLIB1 */
   67: long double acoshl(long double);
   68: #else   /* lint */
   69: __weak_alias(acoshl, acosh);
   70: #endif  /* lint */
   71: #endif  /* LDBL_MANT_DIG == 53 */