libm/e_acosh.c

   1 /*
   2  * ====================================================
   3  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   4  *
   5  * Developed at SunPro, a Sun Microsystems, Inc. business.
   6  * Permission to use, copy, modify, and distribute this
   7  * software is freely granted, provided that this notice
   8  * is preserved.
   9  * ====================================================
  10  */
  11
  12 /* __ieee754_acosh(x)
  13  * Method :
  14  *      Based on
  15  *              acosh(x) = log [ x + sqrt(x*x-1) ]
  16  *      we have
  17  *              acosh(x) := log(x)+ln2, if x is large; else
  18  *              acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else
  19  *              acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1.
  20  *
  21  * Special cases:
  22  *      acosh(x) is NaN with signal if x<1.
  23  *      acosh(NaN) is NaN without signal.
  24  */
  25
  26 #include "math.h"
  27 #include "math_private.h"
  28
  29 static const double
  30 one     = 1.0,
  31 ln2     = 6.93147180559945286227e-01;  /* 0x3FE62E42, 0xFEFA39EF */
  32
  33 double __ieee754_acosh(double x)
  34 {
  35         double t;
  36         int32_t hx;
  37         u_int32_t lx;
  38         EXTRACT_WORDS(hx,lx,x);
  39         if(hx<0x3ff00000) {             /* x < 1 */
  40             return (x-x)/(x-x);
  41         } else if(hx >=0x41b00000) {    /* x > 2**28 */
  42             if(hx >=0x7ff00000) {       /* x is inf of NaN */
  43                 return x+x;
  44             } else
  45                 return __ieee754_log(x)+ln2;    /* acosh(huge)=log(2x) */
  46         } else if(((hx-0x3ff00000)|lx)==0) {
  47             return 0.0;                 /* acosh(1) = 0 */
  48         } else if (hx > 0x40000000) {   /* 2**28 > x > 2 */
  49             t=x*x;
  50             return __ieee754_log(2.0*x-one/(x+__ieee754_sqrt(t-one)));
  51         } else {                        /* 1<x<2 */
  52             t = x-one;
  53             return log1p(t+__ieee754_sqrt(2.0*t+t*t));
  54         }
  55 }