1 /* @(#)s_asinh.c 5.1 93/09/24 */ 2 /* 3 * ==================================================== 4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 5 * 6 * Developed at SunPro, a Sun Microsystems, Inc. business. 7 * Permission to use, copy, modify, and distribute this 8 * software is freely granted, provided that this notice 9 * is preserved. 10 * ==================================================== 11 */ 12 13 /* asinhl(x) 14 * Method : 15 * Based on 16 * asinhl(x) = signl(x) * logl [ |x| + sqrtl(x*x+1) ] 17 * we have 18 * asinhl(x) := x if 1+x*x=1, 19 * := signl(x)*(logl(x)+ln2)) for large |x|, else 20 * := signl(x)*logl(2|x|+1/(|x|+sqrtl(x*x+1))) if|x|>2, else 21 * := signl(x)*log1pl(|x| + x^2/(1 + sqrtl(1+x^2))) 22 */ 23 24 #include <math.h> 25 26 #include "math_private.h" 27 28 static const long double 29 one = 1.000000000000000000000e+00L, /* 0x3FFF, 0x00000000, 0x00000000 */ 30 ln2 = 6.931471805599453094287e-01L, /* 0x3FFE, 0xB17217F7, 0xD1CF79AC */ 31 huge= 1.000000000000000000e+4900L; 32 33 long double 34 asinhl(long double x) 35 { 36 long double t,w; 37 int32_t hx,ix; 38 GET_LDOUBLE_EXP(hx,x); 39 ix = hx&0x7fff; 40 if(ix==0x7fff) return x+x; /* x is inf or NaN */ 41 if(ix< 0x3fde) { /* |x|<2**-34 */ 42 if(huge+x>one) return x; /* return x inexact except 0 */ 43 } 44 if(ix>0x4020) { /* |x| > 2**34 */ 45 w = logl(fabsl(x))+ln2; 46 } else if (ix>0x4000) { /* 2**34 > |x| > 2.0 */ 47 t = fabsl(x); 48 w = logl(2.0*t+one/(sqrtl(x*x+one)+t)); 49 } else { /* 2.0 > |x| > 2**-28 */ 50 t = x*x; 51 w =log1pl(fabsl(x)+t/(one+sqrtl(one+t))); 52 } 53 if(hx&0x8000) return -w; else return w; 54 } 55