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
  13 #include <sys/cdefs.h>
  14 #if defined(LIBM_SCCS) && !defined(lint)
  15 __RCSID("$NetBSD: e_acosh.c,v 1.12 2002/05/26 22:01:48 wiz Exp $");
  16 #endif
  17
  18 /* __ieee754_acosh(x)
  19  * Method :
  20  *      Based on
  21  *              acosh(x) = log [ x + sqrt(x*x-1) ]
  22  *      we have
  23  *              acosh(x) := log(x)+ln2, if x is large; else
  24  *              acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else
  25  *              acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1.
  26  *
  27  * Special cases:
  28  *      acosh(x) is NaN with signal if x<1.
  29  *      acosh(NaN) is NaN without signal.
  30  */
  31
  32 #include "math.h"
  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 __ieee754_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 __ieee754_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 __ieee754_log(2.0*x-one/(x+__ieee754_sqrt(t-one)));
  58         } else {                        /* 1<x<2 */
  59             t = x-one;
  60             return log1p(t+sqrt(2.0*t+t*t));
  61         }
  62 }