| /* @(#)s_asinh.c 5.1 93/09/24 */ |
| /* |
| * ==================================================== |
| * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
| * |
| * Developed at SunPro, a Sun Microsystems, Inc. business. |
| * Permission to use, copy, modify, and distribute this |
| * software is freely granted, provided that this notice |
| * is preserved. |
| * ==================================================== |
| */ |
| |
| #include <sys/cdefs.h> |
| __FBSDID("$FreeBSD$"); |
| |
| /* asinh(x) |
| * Method : |
| * Based on |
| * asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ] |
| * we have |
| * asinh(x) := x if 1+x*x=1, |
| * := sign(x)*(log(x)+ln2)) for large |x|, else |
| * := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else |
| * := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2))) |
| */ |
| |
| #include "math.h" |
| #include "math_private.h" |
| |
| static const double |
| one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ |
| ln2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */ |
| huge= 1.00000000000000000000e+300; |
| |
| double |
| asinh(double x) |
| { |
| double t,w; |
| int32_t hx,ix; |
| GET_HIGH_WORD(hx,x); |
| ix = hx&0x7fffffff; |
| if(ix>=0x7ff00000) return x+x; /* x is inf or NaN */ |
| if(ix< 0x3e300000) { /* |x|<2**-28 */ |
| if(huge+x>one) return x; /* return x inexact except 0 */ |
| } |
| if(ix>0x41b00000) { /* |x| > 2**28 */ |
| w = __ieee754_log(fabs(x))+ln2; |
| } else if (ix>0x40000000) { /* 2**28 > |x| > 2.0 */ |
| t = fabs(x); |
| w = __ieee754_log(2.0*t+one/(__ieee754_sqrt(x*x+one)+t)); |
| } else { /* 2.0 > |x| > 2**-28 */ |
| t = x*x; |
| w =log1p(fabs(x)+t/(one+__ieee754_sqrt(one+t))); |
| } |
| if(hx>0) return w; else return -w; |
| } |
