compiler/stdc/math/ld128/s_asinhl.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 /* asinhl(x)
  14  * Method :
  15  *      Based on
  16  *              asinhl(x) = signl(x) * logl [ |x| + sqrtl(x*x+1) ]
  17  *      we have
  18  *      asinhl(x) := x  if  1+x*x=1,
  19  *                := signl(x)*(logl(x)+ln2)) for large |x|, else
  20  *                := signl(x)*logl(2|x|+1/(|x|+sqrtl(x*x+1))) if|x|>2, else
  21  *                := signl(x)*log1pl(|x| + x^2/(1 + sqrtl(1+x^2)))
  22  */
  23
  24 #include "math.h"
  25
  26 #include "math_private.h"
  27
  28 static const long double
  29   one = 1.0L,
  30   ln2 = 6.931471805599453094172321214581765681e-1L,
  31   huge = 1.0e+4900L;
  32
  33 long double
  34 asinhl(long double x)
  35 {
  36   long double t, w;
  37   int32_t ix, sign;
  38   ieee_quad_shape_type u;
  39
  40   u.value = x;
  41   sign = u.parts32.mswhi;
  42   ix = sign & 0x7fffffff;
  43   if (ix == 0x7fff0000)
  44     return x + x;               /* x is inf or NaN */
  45   if (ix < 0x3fc70000)
  46     {                           /* |x| < 2^ -56 */
  47       if (huge + x > one)
  48         return x;               /* return x inexact except 0 */
  49     }
  50   u.parts32.mswhi = ix;
  51   if (ix > 0x40350000)
  52     {                           /* |x| > 2 ^ 54 */
  53       w = logl (u.value) + ln2;
  54     }
  55   else if (ix >0x40000000)
  56     {                           /* 2^ 54 > |x| > 2.0 */
  57       t = u.value;
  58       w = logl (2.0 * t + one / (sqrtl (x * x + one) + t));
  59     }
  60   else
  61     {                           /* 2.0 > |x| > 2 ^ -56 */
  62       t = x * x;
  63       w = log1pl (u.value + t / (one + sqrtl (one + t)));
  64     }
  65   if (sign & 0x80000000)
  66     return -w;
  67   else
  68     return w;
  69 }