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