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 = 1.0L, 30 ln2 = 6.931471805599453094172321214581765681e-1L, 31 huge = 1.0e+4900L; 32 33 long double 34 asinhl(long double x) 35 { 36 long double t, w; 37 int32_t ix, sign; 38 ieee_quad_shape_type u; 39 40 u.value = x; 41 sign = u.parts32.mswhi; 42 ix = sign & 0x7fffffff; 43 if (ix == 0x7fff0000) 44 return x + x; /* x is inf or NaN */ 45 if (ix < 0x3fc70000) 46 { /* |x| < 2^ -56 */ 47 if (huge + x > one) 48 return x; /* return x inexact except 0 */ 49 } 50 u.parts32.mswhi = ix; 51 if (ix > 0x40350000) 52 { /* |x| > 2 ^ 54 */ 53 w = logl (u.value) + ln2; 54 } 55 else if (ix >0x40000000) 56 { /* 2^ 54 > |x| > 2.0 */ 57 t = u.value; 58 w = logl (2.0 * t + one / (sqrtl (x * x + one) + t)); 59 } 60 else 61 { /* 2.0 > |x| > 2 ^ -56 */ 62 t = x * x; 63 w = log1pl (u.value + t / (one + sqrtl (one + t))); 64 } 65 if (sign & 0x80000000) 66 return -w; 67 else 68 return w; 69 } 70