sysdeps/ieee754/dbl-64/s_asinh.c

   1 /* @(#)s_asinh.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 /* asinh(x)
  14  * Method :
  15  *      Based on
  16  *              asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]
  17  *      we have
  18  *      asinh(x) := x  if  1+x*x=1,
  19  *               := sign(x)*(log(x)+ln2)) for large |x|, else
  20  *               := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else
  21  *               := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2)))
  22  */
  23
  24 #include <float.h>
  25 #include <math.h>
  26 #include <math_private.h>
  27 #include <libm-alias-double.h>
  28
  29 static const double
  30   one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
  31   ln2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
  32   huge = 1.00000000000000000000e+300;
  33
  34 double
  35 __asinh (double x)
  36 {
  37   double w;
  38   int32_t hx, ix;
  39   GET_HIGH_WORD (hx, x);
  40   ix = hx & 0x7fffffff;
  41   if (__glibc_unlikely (ix < 0x3e300000))                  /* |x|<2**-28 */
  42     {
  43       math_check_force_underflow (x);
  44       if (huge + x > one)
  45         return x;                       /* return x inexact except 0 */
  46     }
  47   if (__glibc_unlikely (ix > 0x41b00000))                  /* |x| > 2**28 */
  48     {
  49       if (ix >= 0x7ff00000)
  50         return x + x;                           /* x is inf or NaN */
  51       w = __ieee754_log (fabs (x)) + ln2;
  52     }
  53   else
  54     {
  55       double xa = fabs (x);
  56       if (ix > 0x40000000)              /* 2**28 > |x| > 2.0 */
  57         {
  58           w = __ieee754_log (2.0 * xa + one / (__ieee754_sqrt (xa * xa + one) +
  59               xa));
  60         }
  61       else                      /* 2.0 > |x| > 2**-28 */
  62         {
  63           double t = xa * xa;
  64           w = __log1p (xa + t / (one + __ieee754_sqrt (one + t)));
  65         }
  66     }
  67   return __copysign (w, x);
  68 }
  69 libm_alias_double (__asinh, asinh)