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 1.4 1994/03/03 17:04:26 jtc 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 <machine/endian.h> 30 31 #if BYTE_ORDER == LITTLE_ENDIAN 32 #define n0 1 33 #else 34 #define n0 0 35 #endif 36 37 #ifdef __STDC__ 38 static const double 39 #else 40 static double 41 #endif 42 one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ 43 ln2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */ 44 huge= 1.00000000000000000000e+300; 45 46 #ifdef __STDC__ 47 double asinh(double x) 48 #else 49 double asinh(x) 50 double x; 51 #endif 52 { 53 double t,w; 54 int hx,ix; 55 hx = *(n0+(int*)&x); 56 ix = hx&0x7fffffff; 57 if(ix>=0x7ff00000) return x+x; /* x is inf or NaN */ 58 if(ix< 0x3e300000) { /* |x|<2**-28 */ 59 if(huge+x>one) return x; /* return x inexact except 0 */ 60 } 61 if(ix>0x41b00000) { /* |x| > 2**28 */ 62 w = __ieee754_log(fabs(x))+ln2; 63 } else if (ix>0x40000000) { /* 2**28 > |x| > 2.0 */ 64 t = fabs(x); 65 w = __ieee754_log(2.0*t+one/(sqrt(x*x+one)+t)); 66 } else { /* 2.0 > |x| > 2**-28 */ 67 t = x*x; 68 w =log1p(fabs(x)+t/(one+sqrt(one+t))); 69 } 70 if(hx>0) return w; else return -w; 71 } 72