1/* asinhq.c -- __float128 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/* asinhl(x)
18 * Method :
19 *      Based on
20 *              asinhl(x) = signl(x) * logl [ |x| + sqrtl(x*x+1) ]
21 *      we have
22 *      asinhl(x) := x  if  1+x*x=1,
23 *                := signl(x)*(logl(x)+ln2)) for large |x|, else
24 *                := signl(x)*logl(2|x|+1/(|x|+sqrtl(x*x+1))) if|x|>2, else
25 *                := signl(x)*log1pl(|x| + x^2/(1 + sqrtl(1+x^2)))
26 */
27
28#include "quadmath-imp.h"
29
30static const __float128
31  one = 1.0Q,
32  ln2 = 6.931471805599453094172321214581765681e-1Q,
33  huge = 1.0e+4900Q;
34
35__float128
36asinhq (__float128 x)
37{
38  __float128 t, w;
39  int32_t ix, sign;
40  ieee854_float128 u;
41
42  u.value = x;
43  sign = u.words32.w0;
44  ix = sign & 0x7fffffff;
45  if (ix == 0x7fff0000)
46    return x + x;		/* x is inf or NaN */
47  if (ix < 0x3fc70000)
48    {				/* |x| < 2^ -56 */
49      if (huge + x > one)
50	return x;		/* return x inexact except 0 */
51    }
52  u.words32.w0 = ix;
53  if (ix > 0x40350000)
54    {				/* |x| > 2 ^ 54 */
55      w = logq (u.value) + ln2;
56    }
57  else if (ix >0x40000000)
58    {				/* 2^ 54 > |x| > 2.0 */
59      t = u.value;
60      w = logq (2.0 * t + one / (sqrtq (x * x + one) + t));
61    }
62  else
63    {				/* 2.0 > |x| > 2 ^ -56 */
64      t = x * x;
65      w = log1pq (u.value + t / (one + sqrtq (one + t)));
66    }
67  if (sign & 0x80000000)
68    return -w;
69  else
70    return w;
71}
72