sysdeps/ieee754/ldbl-128/s_asinhl.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 /* asinhl(x)
  22  * Method :
  23  *      Based on
  24  *              asinhl(x) = signl(x) * logl [ |x| + sqrtl(x*x+1) ]
  25  *      we have
  26  *      asinhl(x) := x  if  1+x*x=1,
  27  *                := signl(x)*(logl(x)+ln2)) for large |x|, else
  28  *                := signl(x)*logl(2|x|+1/(|x|+sqrtl(x*x+1))) if|x|>2, else
  29  *                := signl(x)*log1pl(|x| + x^2/(1 + sqrtl(1+x^2)))
  30  */
  31
  32 #include "math.h"
  33 #include "math_private.h"
  34
  35 #ifdef __STDC__
  36 static const long double
  37 #else
  38 static long double
  39 #endif
  40   one = 1.0L,
  41   ln2 = 6.931471805599453094172321214581765681e-1L,
  42   huge = 1.0e+4900L;
  43
  44 #ifdef __STDC__
  45 long double
  46 __asinhl (long double x)
  47 #else
  48 long double
  49 __asinhl (x)
  50      long double x;
  51 #endif
  52 {
  53   long double t, w;
  54   int32_t ix, sign;
  55   ieee854_long_double_shape_type u;
  56
  57   u.value = x;
  58   sign = u.parts32.w0;
  59   ix = sign & 0x7fffffff;
  60   if (ix == 0x7fff0000)
  61     return x + x;               /* x is inf or NaN */
  62   if (ix < 0x3fc70000)
  63     {                           /* |x| < 2^ -56 */
  64       if (huge + x > one)
  65         return x;               /* return x inexact except 0 */
  66     }
  67   u.parts32.w0 = ix;
  68   if (ix > 0x40350000)
  69     {                           /* |x| > 2 ^ 54 */
  70       w = __ieee754_logl (u.value) + ln2;
  71     }
  72   else if (ix >0x40000000)
  73     {                           /* 2^ 54 > |x| > 2.0 */
  74       t = u.value;
  75       w = __ieee754_logl (2.0 * t + one / (__ieee754_sqrtl (x * x + one) + t));
  76     }
  77   else
  78     {                           /* 2.0 > |x| > 2 ^ -56 */
  79       t = x * x;
  80       w = __log1pl (u.value + t / (one + __ieee754_sqrtl (one + t)));
  81     }
  82   if (sign & 0x80000000)
  83     return -w;
  84   else
  85     return w;
  86 }
  87 weak_alias (__asinhl, asinhl)