RTAI API: base/math/s_asinh.c Source File

00001 /* @(#)s_asinh.c 5.1 93/09/24 */ 00002 /* 00003 * ==================================================== 00004 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 00005 * 00006 * Developed at SunPro, a Sun Microsystems, Inc. business. 00007 * Permission to use, copy, modify, and distribute this 00008 * software is freely granted, provided that this notice 00009 * is preserved. 00010 * ==================================================== 00011 */ 00012 00013 #if defined(LIBM_SCCS) && !defined(lint) 00014 static char rcsid[] = "$NetBSD: s_asinh.c,v 1.9 1995/05/12 04:57:37 jtc Exp $"; 00015 #endif 00016 00017 /* asinh(x) 00018 * Method : 00019 * Based on 00020 * asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ] 00021 * we have 00022 * asinh(x) := x if 1+x*x=1, 00023 * := sign(x)*(log(x)+ln2)) for large |x|, else 00024 * := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else 00025 * := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2))) 00026 */ 00027 00028 #include "math.h" 00029 #include "mathP.h" 00030 00031 #ifdef __STDC__ 00032 static const double 00033 #else 00034 static double 00035 #endif 00036 one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ 00037 ln2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */ 00038 huge= 1.00000000000000000000e+300; 00039 00040 #ifdef __STDC__ 00041 double asinh(double x) 00042 #else 00043 double asinh(x) 00044 double x; 00045 #endif 00046 { 00047 double t,w; 00048 int32_t hx,ix; 00049 GET_HIGH_WORD(hx,x); 00050 ix = hx&0x7fffffff; 00051 if(ix>=0x7ff00000) return x+x; /* x is inf or NaN */ 00052 if(ix< 0x3e300000) { /* |x|<2**-28 */ 00053 if(huge+x>one) return x; /* return x inexact except 0 */ 00054 } 00055 if(ix>0x41b00000) { /* |x| > 2**28 */ 00056 w = __ieee754_log(fabs(x))+ln2; 00057 } else if (ix>0x40000000) { /* 2**28 > |x| > 2.0 */ 00058 t = fabs(x); 00059 w = __ieee754_log(2.0*t+one/(__ieee754_sqrt(x*x+one)+t)); 00060 } else { /* 2.0 > |x| > 2**-28 */ 00061 t = x*x; 00062 w =log1p(fabs(x)+t/(one+__ieee754_sqrt(one+t))); 00063 } 00064 if(hx>0) return w; else return -w; 00065 }