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[/] [openrisc/] [trunk/] [gnu-src/] [newlib-1.17.0/] [newlib/] [libm/] [mathfp/] [e_atanh.c] - Rev 527
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/* @(#)e_atanh.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 <<atanh>>, <<atanhf>>---inverse hyperbolic tangent INDEX atanh INDEX atanhf ANSI_SYNOPSIS #include <math.h> double atanh(double <[x]>); float atanhf(float <[x]>); TRAD_SYNOPSIS #include <math.h> double atanh(<[x]>) double <[x]>; float atanhf(<[x]>) float <[x]>; DESCRIPTION <<atanh>> calculates the inverse hyperbolic tangent of <[x]>. <<atanhf>> is identical, other than taking and returning <<float>> values. RETURNS <<atanh>> and <<atanhf>> return the calculated value. If @ifnottex |<[x]>| @end ifnottex @tex $|x|$ @end tex is greater than 1, the global <<errno>> is set to <<EDOM>> and the result is a NaN. A <<DOMAIN error>> is reported. If @ifnottex |<[x]>| @end ifnottex @tex $|x|$ @end tex is 1, the global <<errno>> is set to <<EDOM>>; and the result is infinity with the same sign as <<x>>. A <<SING error>> is reported. You can modify the error handling for these routines using <<matherr>>. PORTABILITY Neither <<atanh>> nor <<atanhf>> are ANSI C. QUICKREF atanh - pure atanhf - pure */ /* atanh(x) * Method : * 1.Reduced x to positive by atanh(-x) = -atanh(x) * 2.For x>=0.5 * 1 2x x * atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------) * 2 1 - x 1 - x * * For x<0.5 * atanh(x) = 0.5*log1p(2x+2x*x/(1-x)) * * Special cases: * atanh(x) is NaN if |x| > 1 with signal; * atanh(NaN) is that NaN with no signal; * atanh(+-1) is +-INF with signal. * */ #include "fdlibm.h" #ifndef _DOUBLE_IS_32BITS #ifdef __STDC__ static const double one = 1.0, huge = 1e300; #else static double one = 1.0, huge = 1e300; #endif #ifdef __STDC__ static const double zero = 0.0; #else static double zero = 0.0; #endif #ifdef __STDC__ double atanh(double x) #else double atanh(x) double x; #endif { double t; __int32_t hx,ix; __uint32_t lx; EXTRACT_WORDS(hx,lx,x); ix = hx&0x7fffffff; if ((ix|((lx|(-lx))>>31))>0x3ff00000) /* |x|>1 */ return (x-x)/(x-x); if(ix==0x3ff00000) return x/zero; if(ix<0x3e300000&&(huge+x)>zero) return x; /* x<2**-28 */ SET_HIGH_WORD(x,ix); if(ix<0x3fe00000) { /* x < 0.5 */ t = x+x; t = 0.5*log1p(t+t*x/(one-x)); } else t = 0.5*log1p((x+x)/(one-x)); if(hx>=0) return t; else return -t; } #endif /* defined(_DOUBLE_IS_32BITS) */
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