1 /* s_asinhl.c -- long double 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 #if defined(LIBM_SCCS) && !defined(lint) 18 static char rcsid[] = "NetBSD: "; 19 #endif 20 21 /* asinhq(x) 22 * Method : 23 * Based on 24 * asinhq(x) = signl(x) * logq [ |x| + sqrtq(x*x+1) ] 25 * we have 26 * asinhq(x) := x if 1+x*x=1, 27 * := signl(x)*(logq(x)+ln2)) for large |x|, else 28 * := signl(x)*logq(2|x|+1/(|x|+sqrtq(x*x+1))) if|x|>2, else 29 * := signl(x)*log1pq(|x| + x^2/(1 + sqrtq(1+x^2))) 30 */ 31 32 #include "quadmath-imp.h" 33 34 static const __float128 35 one = 1, 36 ln2 = 6.931471805599453094172321214581765681e-1Q, 37 huge = 1.0e+4900Q; 38 39 __float128 40 asinhq (__float128 x) 41 { 42 __float128 t, w; 43 int32_t ix, sign; 44 ieee854_float128 u; 45 46 u.value = x; 47 sign = u.words32.w0; 48 ix = sign & 0x7fffffff; 49 if (ix == 0x7fff0000) 50 return x + x; /* x is inf or NaN */ 51 if (ix < 0x3fc70000) 52 { /* |x| < 2^ -56 */ 53 math_check_force_underflow (x); 54 if (huge + x > one) 55 return x; /* return x inexact except 0 */ 56 } 57 u.words32.w0 = ix; 58 if (ix > 0x40350000) 59 { /* |x| > 2 ^ 54 */ 60 w = logq (u.value) + ln2; 61 } 62 else if (ix >0x40000000) 63 { /* 2^ 54 > |x| > 2.0 */ 64 t = u.value; 65 w = logq (2.0 * t + one / (sqrtq (x * x + one) + t)); 66 } 67 else 68 { /* 2.0 > |x| > 2 ^ -56 */ 69 t = x * x; 70 w = log1pq (u.value + t / (one + sqrtq (one + t))); 71 } 72 if (sign & 0x80000000) 73 return -w; 74 else 75 return w; 76 } 77