Line data    Source code

       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             : //#include <sys/cdefs.h>
      16             : //__FBSDID("$FreeBSD$");
      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 <float.h>
      33             : 
      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           0 : __ieee754_acosh(double x)
      42             : {
      43             :         double t;
      44             :         int32_t hx;
      45             :         u_int32_t lx;
      46           0 :         EXTRACT_WORDS(hx,lx,x);
      47           0 :         if(hx<0x3ff00000) {          /* x < 1 */
      48           0 :             return (x-x)/(x-x);
      49           0 :         } else if(hx >=0x41b00000) { /* x > 2**28 */
      50           0 :             if(hx >=0x7ff00000) {    /* x is inf of NaN */
      51           0 :                 return x+x;
      52             :             } else 
      53           0 :                 return __ieee754_log(x)+ln2;    /* acosh(huge)=log(2x) */
      54           0 :         } else if(((hx-0x3ff00000)|lx)==0) {
      55           0 :             return 0.0;                 /* acosh(1) = 0 */
      56           0 :         } else if (hx > 0x40000000) {        /* 2**28 > x > 2 */
      57           0 :             t=x*x;
      58           0 :             return __ieee754_log(2.0*x-one/(x+sqrt(t-one)));
      59             :         } else {                        /* 1<x<2 */
      60           0 :             t = x-one;
      61           0 :             return log1p(t+sqrt(2.0*t+t*t));
      62             :         }
      63             : }