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[/] [openrisc/] [trunk/] [gnu-old/] [newlib-1.17.0/] [newlib/] [libm/] [math/] [s_asinh.c] - Rev 816
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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 */