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  /* asinh(x)
      14   * Method :
      15   *	Based on
      16   *		asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]
      17   *	we have
      18   *	asinh(x) := x  if  1+x*x=1,
      19   *		 := sign(x)*(log(x)+ln2)) for large |x|, else
      20   *		 := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else
      21   *		 := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2)))
      22   */
      23  
      24  #include <float.h>
      25  #include <math.h>
      26  #include <math_private.h>
      27  #include <math-underflow.h>
      28  #include <libm-alias-double.h>
      29  
      30  static const double
      31    one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
      32    ln2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
      33    huge = 1.00000000000000000000e+300;
      34  
      35  double
      36  __asinh (double x)
      37  {
      38    double w;
      39    int32_t hx, ix;
      40    GET_HIGH_WORD (hx, x);
      41    ix = hx & 0x7fffffff;
      42    if (__glibc_unlikely (ix < 0x3e300000))                  /* |x|<2**-28 */
      43      {
      44        math_check_force_underflow (x);
      45        if (huge + x > one)
      46  	return x;                       /* return x inexact except 0 */
      47      }
      48    if (__glibc_unlikely (ix > 0x41b00000))                  /* |x| > 2**28 */
      49      {
      50        if (ix >= 0x7ff00000)
      51  	return x + x;                           /* x is inf or NaN */
      52        w = __ieee754_log (fabs (x)) + ln2;
      53      }
      54    else
      55      {
      56        double xa = fabs (x);
      57        if (ix > 0x40000000)              /* 2**28 > |x| > 2.0 */
      58  	{
      59  	  w = __ieee754_log (2.0 * xa + one / (sqrt (xa * xa + one) +
      60                xa));
      61  	}
      62        else                      /* 2.0 > |x| > 2**-28 */
      63  	{
      64  	  double t = xa * xa;
      65  	  w = __log1p (xa + t / (one + sqrt (one + t)));
      66  	}
      67      }
      68    return copysign (w, x);
      69  }
      70  libm_alias_double (__asinh, asinh)