/* s_asinhl.c -- long double version of s_asinh.c.
* Conversion to long double by Ulrich Drepper,
* Cygnus Support, [email protected].
*/

/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/

#if defined(LIBM_SCCS) && !defined(lint)
static char rcsid[] = "NetBSD: ";
#endif

/* asinhq(x)
* Method :
*      Based on
*              asinhq(x) = signl(x) * logq [ |x| + sqrtq(x*x+1) ]
*      we have
*      asinhq(x) := x  if  1+x*x=1,
*                := signl(x)*(logq(x)+ln2)) for large |x|, else
*                := signl(x)*logq(2|x|+1/(|x|+sqrtq(x*x+1))) if|x|>2, else
*                := signl(x)*log1pq(|x| + x^2/(1 + sqrtq(1+x^2)))
*/

#include "quadmath-imp.h"

static const __float128
 one = 1,
 ln2 = 6.931471805599453094172321214581765681e-1Q,
 huge = 1.0e+4900Q;

__float128
asinhq (__float128 x)
{
 __float128 t, w;
 int32_t ix, sign;
 ieee854_float128 u;

 u.value = x;
 sign = u.words32.w0;
 ix = sign & 0x7fffffff;
 if (ix == 0x7fff0000)
   return x + x;               /* x is inf or NaN */
 if (ix < 0x3fc70000)
   {                           /* |x| < 2^ -56 */
     math_check_force_underflow (x);
     if (huge + x > one)
       return x;               /* return x inexact except 0 */
   }
 u.words32.w0 = ix;
 if (ix > 0x40350000)
   {                           /* |x| > 2 ^ 54 */
     w = logq (u.value) + ln2;
   }
 else if (ix >0x40000000)
   {                           /* 2^ 54 > |x| > 2.0 */
     t = u.value;
     w = logq (2.0 * t + one / (sqrtq (x * x + one) + t));
   }
 else
   {                           /* 2.0 > |x| > 2 ^ -56 */
     t = x * x;
     w = log1pq (u.value + t / (one + sqrtq (one + t)));
   }
 if (sign & 0x80000000)
   return -w;
 else
   return w;
}