sysdeps/ieee754/dbl-64/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 #include <libm-alias-finite.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   int64_t hx;
  38   EXTRACT_WORDS64 (hx, x);
  39
  40   if (hx > INT64_C (0x4000000000000000))
  41     {
  42       if (__glibc_unlikely (hx >= INT64_C (0x41b0000000000000)))
  43         {
  44           /* x > 2**28 */
  45           if (hx >= INT64_C (0x7ff0000000000000))
  46             /* x is inf of NaN */
  47             return x + x;
  48           else
  49             return __ieee754_log (x) + ln2;/* acosh(huge)=log(2x) */
  50         }
  51
  52       /* 2**28 > x > 2 */
  53       double t = x * x;
  54       return __ieee754_log (2.0 * x - one / (x + sqrt (t - one)));
  55     }
  56   else if (__glibc_likely (hx > INT64_C (0x3ff0000000000000)))
  57     {
  58       /* 1<x<2 */
  59       double t = x - one;
  60       return __log1p (t + sqrt (2.0 * t + t * t));
  61     }
  62   else if (__glibc_likely (hx == INT64_C (0x3ff0000000000000)))
  63     return 0.0;                         /* acosh(1) = 0 */
  64   else                                  /* x < 1 */
  65     return (x - x) / (x - x);
  66 }
  67 libm_alias_finite (__ieee754_acosh, __acosh)