1 2 /* @(#)s_asinh.c 1.3 95/01/18 */ 3 /* 4 * ==================================================== 5 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 6 * 7 * Developed at SunSoft, a Sun Microsystems, Inc. business. 8 * Permission to use, copy, modify, and distribute this 9 * software is freely granted, provided that this notice 10 * is preserved. 11 * ==================================================== 12 */ 13 14 /* asinh(x) 15 * Method : 16 * Based on 17 * asinh(x) = sign(x) * log [ |x| + ieee_sqrt(x*x+1) ] 18 * we have 19 * asinh(x) := x if 1+x*x=1, 20 * := sign(x)*(ieee_log(x)+ln2)) for large |x|, else 21 * := sign(x)*ieee_log(2|x|+1/(|x|+ieee_sqrt(x*x+1))) if|x|>2, else 22 * := sign(x)*ieee_log1p(|x| + x^2/(1 + ieee_sqrt(1+x^2))) 23 */ 24 25 #include "fdlibm.h" 26 27 #ifdef __STDC__ 28 static const double 29 #else 30 static double 31 #endif 32 one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ 33 ln2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */ 34 huge= 1.00000000000000000000e+300; 35 36 #ifdef __STDC__ 37 double asinh(double x) 38 #else 39 double asinh(x) 40 double x; 41 #endif 42 { 43 double t,w; 44 int hx,ix; 45 hx = __HI(x); 46 ix = hx&0x7fffffff; 47 if(ix>=0x7ff00000) return x+x; /* x is inf or NaN */ 48 if(ix< 0x3e300000) { /* |x|<2**-28 */ 49 if(huge+x>one) return x; /* return x inexact except 0 */ 50 } 51 if(ix>0x41b00000) { /* |x| > 2**28 */ 52 w = __ieee754_log(ieee_fabs(x))+ln2; 53 } else if (ix>0x40000000) { /* 2**28 > |x| > 2.0 */ 54 t = ieee_fabs(x); 55 w = __ieee754_log(2.0*t+one/(ieee_sqrt(x*x+one)+t)); 56 } else { /* 2.0 > |x| > 2**-28 */ 57 t = x*x; 58 w =ieee_log1p(ieee_fabs(x)+t/(one+ieee_sqrt(one+t))); 59 } 60 if(hx>0) return w; else return -w; 61 } 62
