| /* @(#)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. |
| * ==================================================== |
| */ |
| |
| #if defined(LIBM_SCCS) && !defined(lint) |
| static char rcsid[] = "$NetBSD: s_asinh.c,v 1.9 1995/05/12 04:57:37 jtc Exp $"; |
| #endif |
| |
| /* 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> |
| #include <math_ldbl_opt.h> |
| |
| static const long double |
| one = 1.00000000000000000000e+00L, /* 0x3ff0000000000000, 0 */ |
| ln2 = 0.6931471805599453094172321214581766L, /* 0x3fe62e42fefa39ef, 0x3c7abc9e3b398040 */ |
| huge= 1.00000000000000000000e+300L; |
| |
| long double __asinhl(long double x) |
| { |
| long double t,w; |
| int64_t hx,ix; |
| double xhi; |
| |
| xhi = ldbl_high (x); |
| EXTRACT_WORDS64 (hx, xhi); |
| ix = hx&0x7fffffffffffffffLL; |
| if(ix>=0x7ff0000000000000LL) return x+x; /* x is inf or NaN */ |
| if(ix< 0x3e20000000000000LL) { /* |x|<2**-29 */ |
| if(huge+x>one) return x; /* return x inexact except 0 */ |
| } |
| if(ix>0x41b0000000000000LL) { /* |x| > 2**28 */ |
| w = __ieee754_logl(fabsl(x))+ln2; |
| } else if (ix>0x4000000000000000LL) { /* 2**28 > |x| > 2.0 */ |
| t = fabs(x); |
| w = __ieee754_logl(2.0*t+one/(__ieee754_sqrtl(x*x+one)+t)); |
| } else { /* 2.0 > |x| > 2**-29 */ |
| t = x*x; |
| w =__log1pl(fabsl(x)+t/(one+__ieee754_sqrtl(one+t))); |
| } |
| if(hx>0) return w; else return -w; |
| } |
| long_double_symbol (libm, __asinhl, asinhl); |