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 #ifndef lint 14 static char rcsid[] = "$Id: s_asinh.c,v 1.1.1.1 1994/08/19 09:39:45 jkh Exp $"; 15 #endif 16 17 /* asinh(x) 18 * Method : 19 * Based on 20 * asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ] 21 * we have 22 * asinh(x) := x if 1+x*x=1, 23 * := sign(x)*(log(x)+ln2)) for large |x|, else 24 * := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else 25 * := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2))) 26 */ 27 28 #include "math.h" 29 #include "math_private.h" 30 31 #ifdef __STDC__ 32 static const double 33 #else 34 static double 35 #endif 36 one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ 37 ln2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */ 38 huge= 1.00000000000000000000e+300; 39 40 #ifdef __STDC__ 41 double asinh(double x) 42 #else 43 double asinh(x) 44 double x; 45 #endif 46 { 47 double t,w; 48 int32_t hx,ix; 49 GET_HIGH_WORD(hx,x); 50 ix = hx&0x7fffffff; 51 if(ix>=0x7ff00000) return x+x; /* x is inf or NaN */ 52 if(ix< 0x3e300000) { /* |x|<2**-28 */ 53 if(huge+x>one) return x; /* return x inexact except 0 */ 54 } 55 if(ix>0x41b00000) { /* |x| > 2**28 */ 56 w = __ieee754_log(fabs(x))+ln2; 57 } else if (ix>0x40000000) { /* 2**28 > |x| > 2.0 */ 58 t = fabs(x); 59 w = __ieee754_log(2.0*t+one/(sqrt(x*x+one)+t)); 60 } else { /* 2.0 > |x| > 2**-28 */ 61 t = x*x; 62 w =log1p(fabs(x)+t/(one+sqrt(one+t))); 63 } 64 if(hx>0) return w; else return -w; 65 } 66