sysdeps/ieee754/dbl-64/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 /* __ieee754_acosh(x)
  14  * Method :
  15  *      Based on
  16  *              acosh(x) = log [ x + sqrt(x*x-1) ]
  17  *      we have
  18  *              acosh(x) := log(x)+ln2, if x is large; else
  19  *              acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else
  20  *              acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1.
  21  *
  22  * Special cases:
  23  *      acosh(x) is NaN with signal if x<1.
  24  *      acosh(NaN) is NaN without signal.
  25  */
  26
  27 #include <math.h>
  28 #include <math_private.h>
  29
  30 static const double
  31   one = 1.0,
  32   ln2 = 6.93147180559945286227e-01;    /* 0x3FE62E42, 0xFEFA39EF */
  33
  34 double
  35 __ieee754_acosh (double x)
  36 {
  37   double t;
  38   int32_t hx;
  39   u_int32_t lx;
  40   EXTRACT_WORDS (hx, lx, x);
  41   if (hx < 0x3ff00000)                  /* x < 1 */
  42     {
  43       return (x - x) / (x - x);
  44     }
  45   else if (hx >= 0x41b00000)            /* x > 2**28 */
  46     {
  47       if (hx >= 0x7ff00000)             /* x is inf of NaN */
  48         {
  49           return x + x;
  50         }
  51       else
  52         return __ieee754_log (x) + ln2;         /* acosh(huge)=log(2x) */
  53     }
  54   else if (((hx - 0x3ff00000) | lx) == 0)
  55     {
  56       return 0.0;                       /* acosh(1) = 0 */
  57     }
  58   else if (hx > 0x40000000)             /* 2**28 > x > 2 */
  59     {
  60       t = x * x;
  61       return __ieee754_log (2.0 * x - one / (x + __ieee754_sqrt (t - one)));
  62     }
  63   else                                  /* 1<x<2 */
  64     {
  65       t = x - one;
  66       return __log1p (t + __ieee754_sqrt (2.0 * t + t * t));
  67     }
  68 }
  69 strong_alias (__ieee754_acosh, __acosh_finite)