1  /* s_asinhl.c -- long double version of s_asinh.c.
       2   */
       3  
       4  /*
       5   * ====================================================
       6   * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
       7   *
       8   * Developed at SunPro, a Sun Microsystems, Inc. business.
       9   * Permission to use, copy, modify, and distribute this
      10   * software is freely granted, provided that this notice
      11   * is preserved.
      12   * ====================================================
      13   */
      14  
      15  #if defined(LIBM_SCCS) && !defined(lint)
      16  static char rcsid[] = "$NetBSD: $";
      17  #endif
      18  
      19  /* asinhl(x)
      20   * Method :
      21   *      Based on
      22   *              asinhl(x) = signl(x) * logl [ |x| + sqrtl(x*x+1) ]
      23   *      we have
      24   *      asinhl(x) := x  if  1+x*x=1,
      25   *                := signl(x)*(logl(x)+ln2)) for large |x|, else
      26   *                := signl(x)*logl(2|x|+1/(|x|+sqrtl(x*x+1))) if|x|>2, else
      27   *                := signl(x)*log1pl(|x| + x^2/(1 + sqrtl(1+x^2)))
      28   */
      29  
      30  #include <float.h>
      31  #include <math.h>
      32  #include <math_private.h>
      33  #include <math-underflow.h>
      34  #include <libm-alias-ldouble.h>
      35  
      36  static const _Float128
      37    one = 1,
      38    ln2 = L(6.931471805599453094172321214581765681e-1),
      39    huge = L(1.0e+4900);
      40  
      41  _Float128
      42  __asinhl (_Float128 x)
      43  {
      44    _Float128 t, w;
      45    int32_t ix, sign;
      46    ieee854_long_double_shape_type u;
      47  
      48    u.value = x;
      49    sign = u.parts32.w0;
      50    ix = sign & 0x7fffffff;
      51    if (ix == 0x7fff0000)
      52      return x + x;		/* x is inf or NaN */
      53    if (ix < 0x3fc70000)
      54      {				/* |x| < 2^ -56 */
      55        math_check_force_underflow (x);
      56        if (huge + x > one)
      57  	return x;		/* return x inexact except 0 */
      58      }
      59    u.parts32.w0 = ix;
      60    if (ix > 0x40350000)
      61      {				/* |x| > 2 ^ 54 */
      62        w = __ieee754_logl (u.value) + ln2;
      63      }
      64    else if (ix >0x40000000)
      65      {				/* 2^ 54 > |x| > 2.0 */
      66        t = u.value;
      67        w = __ieee754_logl (2.0 * t + one / (sqrtl (x * x + one) + t));
      68      }
      69    else
      70      {				/* 2.0 > |x| > 2 ^ -56 */
      71        t = x * x;
      72        w = __log1pl (u.value + t / (one + sqrtl (one + t)));
      73      }
      74    if (sign & 0x80000000)
      75      return -w;
      76    else
      77      return w;
      78  }
      79  libm_alias_ldouble (__asinh, asinh)