2014-09-21 17:33:12 +00:00
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/* asinhq.c -- __float128 version of s_asinh.c.
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2012-03-27 23:13:14 +00:00
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* Conversion to long double by Ulrich Drepper,
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* Cygnus Support, drepper@cygnus.com.
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*/
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/*
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* ====================================================
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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*
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* Developed at SunPro, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* is preserved.
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* ====================================================
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*/
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/* asinhl(x)
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* Method :
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* Based on
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* asinhl(x) = signl(x) * logl [ |x| + sqrtl(x*x+1) ]
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* we have
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* asinhl(x) := x if 1+x*x=1,
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* := signl(x)*(logl(x)+ln2)) for large |x|, else
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* := signl(x)*logl(2|x|+1/(|x|+sqrtl(x*x+1))) if|x|>2, else
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* := signl(x)*log1pl(|x| + x^2/(1 + sqrtl(1+x^2)))
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*/
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#include "quadmath-imp.h"
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static const __float128
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one = 1.0Q,
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ln2 = 6.931471805599453094172321214581765681e-1Q,
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huge = 1.0e+4900Q;
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__float128
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asinhq (__float128 x)
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{
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__float128 t, w;
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int32_t ix, sign;
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ieee854_float128 u;
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u.value = x;
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sign = u.words32.w0;
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ix = sign & 0x7fffffff;
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if (ix == 0x7fff0000)
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return x + x; /* x is inf or NaN */
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if (ix < 0x3fc70000)
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{ /* |x| < 2^ -56 */
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2018-12-28 15:30:48 +00:00
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math_check_force_underflow (x);
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2012-03-27 23:13:14 +00:00
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if (huge + x > one)
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return x; /* return x inexact except 0 */
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}
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u.words32.w0 = ix;
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if (ix > 0x40350000)
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{ /* |x| > 2 ^ 54 */
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w = logq (u.value) + ln2;
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}
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else if (ix >0x40000000)
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{ /* 2^ 54 > |x| > 2.0 */
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t = u.value;
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w = logq (2.0 * t + one / (sqrtq (x * x + one) + t));
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}
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else
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{ /* 2.0 > |x| > 2 ^ -56 */
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t = x * x;
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w = log1pq (u.value + t / (one + sqrtq (one + t)));
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}
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if (sign & 0x80000000)
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return -w;
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else
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return w;
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}
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