libquadmath/math/asinhq.c

   1 /* asinhq.c -- __float128 version of s_asinh.c.
   2  * Conversion to long double by Ulrich Drepper,
   3  * Cygnus Support, drepper@cygnus.com.
   4  */
   5
   6 /*
   7  * ====================================================
   8  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   9  *
  10  * Developed at SunPro, a Sun Microsystems, Inc. business.
  11  * Permission to use, copy, modify, and distribute this
  12  * software is freely granted, provided that this notice
  13  * is preserved.
  14  * ====================================================
  15  */
  16
  17 /* asinhl(x)
  18  * Method :
  19  *      Based on
  20  *              asinhl(x) = signl(x) * logl [ |x| + sqrtl(x*x+1) ]
  21  *      we have
  22  *      asinhl(x) := x  if  1+x*x=1,
  23  *                := signl(x)*(logl(x)+ln2)) for large |x|, else
  24  *                := signl(x)*logl(2|x|+1/(|x|+sqrtl(x*x+1))) if|x|>2, else
  25  *                := signl(x)*log1pl(|x| + x^2/(1 + sqrtl(1+x^2)))
  26  */
  27
  28 #include "quadmath-imp.h"
  29
  30 static const __float128
  31   one = 1.0Q,
  32   ln2 = 6.931471805599453094172321214581765681e-1Q,
  33   huge = 1.0e+4900Q;
  34
  35 __float128
  36 asinhq (__float128 x)
  37 {
  38   __float128 t, w;
  39   int32_t ix, sign;
  40   ieee854_float128 u;
  41
  42   u.value = x;
  43   sign = u.words32.w0;
  44   ix = sign & 0x7fffffff;
  45   if (ix == 0x7fff0000)
  46     return x + x;               /* x is inf or NaN */
  47   if (ix < 0x3fc70000)
  48     {                           /* |x| < 2^ -56 */
  49       if (huge + x > one)
  50         return x;               /* return x inexact except 0 */
  51     }
  52   u.words32.w0 = ix;
  53   if (ix > 0x40350000)
  54     {                           /* |x| > 2 ^ 54 */
  55       w = logq (u.value) + ln2;
  56     }
  57   else if (ix >0x40000000)
  58     {                           /* 2^ 54 > |x| > 2.0 */
  59       t = u.value;
  60       w = logq (2.0 * t + one / (sqrtq (x * x + one) + t));
  61     }
  62   else
  63     {                           /* 2.0 > |x| > 2 ^ -56 */
  64       t = x * x;
  65       w = log1pq (u.value + t / (one + sqrtq (one + t)));
  66     }
  67   if (sign & 0x80000000)
  68     return -w;
  69   else
  70     return w;
  71 }