lib/libm/src/e_acosh.c

   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  * $NetBSD: e_acosh.c,v 1.12 2002/05/26 22:01:48 wiz Exp $
  13  * $DragonFly: src/lib/libm/src/e_acosh.c,v 1.1 2005/07/26 21:15:20 joerg Exp $
  14  */
  15
  16
  17 /* acosh(x)
  18  * Method :
  19  *      Based on
  20  *              acosh(x) = log [ x + sqrt(x*x-1) ]
  21  *      we have
  22  *              acosh(x) := log(x)+ln2, if x is large; else
  23  *              acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else
  24  *              acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1.
  25  *
  26  * Special cases:
  27  *      acosh(x) is NaN with signal if x<1.
  28  *      acosh(NaN) is NaN without signal.
  29  */
  30
  31 #include <math.h>
  32 #include "math_private.h"
  33
  34 static const double
  35 one     = 1.0,
  36 ln2     = 6.93147180559945286227e-01;  /* 0x3FE62E42, 0xFEFA39EF */
  37
  38 double
  39 acosh(double x)
  40 {
  41         double t;
  42         int32_t hx;
  43         u_int32_t lx;
  44         EXTRACT_WORDS(hx,lx,x);
  45         if(hx<0x3ff00000) {             /* x < 1 */
  46             return (x-x)/(x-x);
  47         } else if(hx >=0x41b00000) {    /* x > 2**28 */
  48             if(hx >=0x7ff00000) {       /* x is inf of NaN */
  49                 return x+x;
  50             } else
  51                 return log(x)+ln2;      /* acosh(huge)=log(2x) */
  52         } else if(((hx-0x3ff00000)|lx)==0) {
  53             return 0.0;                 /* acosh(1) = 0 */
  54         } else if (hx > 0x40000000) {   /* 2**28 > x > 2 */
  55             t=x*x;
  56             return log(2.0*x-one/(x+sqrt(t-one)));
  57         } else {                        /* 1<x<2 */
  58             t = x-one;
  59             return log1p(t+sqrt(2.0*t+t*t));
  60         }
  61 }