libquadmath/math/asinhq.c

   1 /* s_asinhl.c -- long double 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 #if defined(LIBM_SCCS) && !defined(lint)
  18 static char rcsid[] = "$NetBSD: $";
  19 #endif
  20
  21 /* asinhq(x)
  22  * Method :
  23  *      Based on
  24  *              asinhq(x) = signl(x) * logq [ |x| + sqrtq(x*x+1) ]
  25  *      we have
  26  *      asinhq(x) := x  if  1+x*x=1,
  27  *                := signl(x)*(logq(x)+ln2)) for large |x|, else
  28  *                := signl(x)*logq(2|x|+1/(|x|+sqrtq(x*x+1))) if|x|>2, else
  29  *                := signl(x)*log1pq(|x| + x^2/(1 + sqrtq(1+x^2)))
  30  */
  31
  32 #include "quadmath-imp.h"
  33
  34 static const __float128
  35   one = 1,
  36   ln2 = 6.931471805599453094172321214581765681e-1Q,
  37   huge = 1.0e+4900Q;
  38
  39 __float128
  40 asinhq (__float128 x)
  41 {
  42   __float128 t, w;
  43   int32_t ix, sign;
  44   ieee854_float128 u;
  45
  46   u.value = x;
  47   sign = u.words32.w0;
  48   ix = sign & 0x7fffffff;
  49   if (ix == 0x7fff0000)
  50     return x + x;               /* x is inf or NaN */
  51   if (ix < 0x3fc70000)
  52     {                           /* |x| < 2^ -56 */
  53       math_check_force_underflow (x);
  54       if (huge + x > one)
  55         return x;               /* return x inexact except 0 */
  56     }
  57   u.words32.w0 = ix;
  58   if (ix > 0x40350000)
  59     {                           /* |x| > 2 ^ 54 */
  60       w = logq (u.value) + ln2;
  61     }
  62   else if (ix >0x40000000)
  63     {                           /* 2^ 54 > |x| > 2.0 */
  64       t = u.value;
  65       w = logq (2.0 * t + one / (sqrtq (x * x + one) + t));
  66     }
  67   else
  68     {                           /* 2.0 > |x| > 2 ^ -56 */
  69       t = x * x;
  70       w = log1pq (u.value + t / (one + sqrtq (one + t)));
  71     }
  72   if (sign & 0x80000000)
  73     return -w;
  74   else
  75     return w;
  76 }