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 /* asinhq.c -- __float128 version of s_asinh.c. * Conversion to long double by Ulrich Drepper, * Cygnus Support, drepper@cygnus.com. */ /* * ==================================================== * 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. * ==================================================== */ /* asinhl(x) * Method : * Based on * asinhl(x) = signl(x) * logl [ |x| + sqrtl(x*x+1) ] * we have * asinhl(x) := x if 1+x*x=1, * := signl(x)*(logl(x)+ln2)) for large |x|, else * := signl(x)*logl(2|x|+1/(|x|+sqrtl(x*x+1))) if|x|>2, else * := signl(x)*log1pl(|x| + x^2/(1 + sqrtl(1+x^2))) */ #include "quadmath-imp.h" static const __float128 one = 1.0Q, 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; }