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| /* @(#)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. |
| * ==================================================== |
| */ |
| |
| /* |
| FUNCTION |
| <<asinh>>, <<asinhf>>---inverse hyperbolic sine |
| |
| INDEX |
| asinh |
| INDEX |
| asinhf |
| |
| ANSI_SYNOPSIS |
| #include <math.h> |
| double asinh(double <[x]>); |
| float asinhf(float <[x]>); |
| |
| TRAD_SYNOPSIS |
| #include <math.h> |
| double asinh(<[x]>) |
| double <[x]>; |
| |
| float asinhf(<[x]>) |
| float <[x]>; |
| |
| DESCRIPTION |
| <<asinh>> calculates the inverse hyperbolic sine of <[x]>. |
| <<asinh>> is defined as |
| @ifnottex |
| . sgn(<[x]>) * log(abs(<[x]>) + sqrt(1+<[x]>*<[x]>)) |
| @end ifnottex |
| @tex |
| $$sign(x) \times ln\Bigl(|x| + \sqrt{1+x^2}\Bigr)$$ |
| @end tex |
| |
| <<asinhf>> is identical, other than taking and returning floats. |
| |
| RETURNS |
| <<asinh>> and <<asinhf>> return the calculated value. |
| |
| PORTABILITY |
| Neither <<asinh>> nor <<asinhf>> are ANSI C. |
| |
| */ |
| |
| /* 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 "fdlibm.h" |
| |
| #ifndef _DOUBLE_IS_32BITS |
| |
| #ifdef __STDC__ |
| static const double |
| #else |
| static double |
| #endif |
| one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ |
| ln2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */ |
| huge= 1.00000000000000000000e+300; |
| |
| #ifdef __STDC__ |
| double asinh(double x) |
| #else |
| double asinh(x) |
| double x; |
| #endif |
| { |
| 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; |
| } |
| |
| #endif /* _DOUBLE_IS_32BITS */ |