compiler/mlib/e_acosh.c

   1
   2 /* @(#)e_acosh.c 1.3 95/01/18 */
   3 /*
   4  * ====================================================
   5  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   6  *
   7  * Developed at SunSoft, a Sun Microsystems, Inc. business.
   8  * Permission to use, copy, modify, and distribute this
   9  * software is freely granted, provided that this notice
  10  * is preserved.
  11  * ====================================================
  12  *
  13  */
  14
  15 #ifndef lint
  16 static char rcsid[] = "$FreeBSD: src/lib/msun/src/e_acosh.c,v 1.8 2005/02/04 18:26:05 das Exp $";
  17 #endif
  18
  19 /* __ieee754_acosh(x)
  20  * Method :
  21  *      Based on
  22  *              acosh(x) = log [ x + sqrt(x*x-1) ]
  23  *      we have
  24  *              acosh(x) := log(x)+ln2, if x is large; else
  25  *              acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else
  26  *              acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1.
  27  *
  28  * Special cases:
  29  *      acosh(x) is NaN with signal if x<1.
  30  *      acosh(NaN) is NaN without signal.
  31  */
  32
  33 #include "math.h"
  34 #include "math_private.h"
  35
  36 static const double
  37 one     = 1.0,
  38 ln2     = 6.93147180559945286227e-01;  /* 0x3FE62E42, 0xFEFA39EF */
  39
  40 double
  41 __ieee754_acosh(double x)
  42 {
  43         double t;
  44         int32_t hx;
  45         uint32_t lx;
  46         EXTRACT_WORDS(hx,lx,x);
  47         if(hx<0x3ff00000) {             /* x < 1 */
  48             return (x-x)/(x-x);
  49         } else if(hx >=0x41b00000) {    /* x > 2**28 */
  50             if(hx >=0x7ff00000) {       /* x is inf of NaN */
  51                 return x+x;
  52             } else
  53                 return __ieee754_log(x)+ln2;    /* acosh(huge)=log(2x) */
  54         } else if(((hx-0x3ff00000)|lx)==0) {
  55             return 0.0;                 /* acosh(1) = 0 */
  56         } else if (hx > 0x40000000) {   /* 2**28 > x > 2 */
  57             t=x*x;
  58             return __ieee754_log(2.0*x-one/(x+sqrt(t-one)));
  59         } else {                        /* 1<x<2 */
  60             t = x-one;
  61             return log1p(t+sqrt(2.0*t+t*t));
  62         }
  63 }