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/* @(#)w_gamma.c 5.1 93/09/24 */
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/* @(#)w_gamma.c 5.1 93/09/24 */
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/*
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/*
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* ====================================================
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* ====================================================
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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*
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*
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* Developed at SunPro, a Sun Microsystems, Inc. business.
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* Developed at SunPro, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* software is freely granted, provided that this notice
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* is preserved.
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* is preserved.
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* ====================================================
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* ====================================================
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*
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*
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*/
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*/
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/* BUG: FIXME?
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/* BUG: FIXME?
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According to Linux man pages for tgamma, lgamma, and gamma, the gamma
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According to Linux man pages for tgamma, lgamma, and gamma, the gamma
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function was originally defined in BSD as implemented here--the log of the gamma
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function was originally defined in BSD as implemented here--the log of the gamma
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function. BSD 4.3 changed the name to lgamma, apparently removing gamma. BSD
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function. BSD 4.3 changed the name to lgamma, apparently removing gamma. BSD
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4.4 re-introduced the gamma name with the more intuitive, without logarithm,
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4.4 re-introduced the gamma name with the more intuitive, without logarithm,
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plain gamma function. The C99 standard apparently wanted to avoid a problem
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plain gamma function. The C99 standard apparently wanted to avoid a problem
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with the poorly-named earlier gamma and used tgamma when adding a plain
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with the poorly-named earlier gamma and used tgamma when adding a plain
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gamma function.
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gamma function.
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So the current gamma is matching an old, bad definition, and not
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So the current gamma is matching an old, bad definition, and not
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matching a newer, better definition. */
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matching a newer, better definition. */
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/*
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/*
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FUNCTION
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FUNCTION
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<<gamma>>, <<gammaf>>, <<lgamma>>, <<lgammaf>>, <<gamma_r>>, <<gammaf_r>>, <<lgamma_r>>, <<lgammaf_r>>, <<tgamma>>, and <<tgammaf>>--logarithmic and plain gamma functions
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<<gamma>>, <<gammaf>>, <<lgamma>>, <<lgammaf>>, <<gamma_r>>, <<gammaf_r>>, <<lgamma_r>>, <<lgammaf_r>>, <<tgamma>>, and <<tgammaf>>--logarithmic and plain gamma functions
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INDEX
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INDEX
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gamma
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gamma
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INDEX
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INDEX
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gammaf
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gammaf
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INDEX
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INDEX
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lgamma
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lgamma
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INDEX
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INDEX
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lgammaf
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lgammaf
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INDEX
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INDEX
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gamma_r
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gamma_r
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INDEX
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INDEX
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gammaf_r
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gammaf_r
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INDEX
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INDEX
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lgamma_r
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lgamma_r
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INDEX
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INDEX
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lgammaf_r
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lgammaf_r
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INDEX
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INDEX
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tgamma
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tgamma
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INDEX
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INDEX
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tgammaf
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tgammaf
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ANSI_SYNOPSIS
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ANSI_SYNOPSIS
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#include <math.h>
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#include <math.h>
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double gamma(double <[x]>);
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double gamma(double <[x]>);
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float gammaf(float <[x]>);
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float gammaf(float <[x]>);
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double lgamma(double <[x]>);
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double lgamma(double <[x]>);
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float lgammaf(float <[x]>);
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float lgammaf(float <[x]>);
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double gamma_r(double <[x]>, int *<[signgamp]>);
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double gamma_r(double <[x]>, int *<[signgamp]>);
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float gammaf_r(float <[x]>, int *<[signgamp]>);
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float gammaf_r(float <[x]>, int *<[signgamp]>);
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double lgamma_r(double <[x]>, int *<[signgamp]>);
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double lgamma_r(double <[x]>, int *<[signgamp]>);
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float lgammaf_r(float <[x]>, int *<[signgamp]>);
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float lgammaf_r(float <[x]>, int *<[signgamp]>);
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double tgamma(double <[x]>);
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double tgamma(double <[x]>);
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float tgammaf(float <[x]>);
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float tgammaf(float <[x]>);
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TRAD_SYNOPSIS
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TRAD_SYNOPSIS
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#include <math.h>
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#include <math.h>
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double gamma(<[x]>)
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double gamma(<[x]>)
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double <[x]>;
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double <[x]>;
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float gammaf(<[x]>)
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float gammaf(<[x]>)
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float <[x]>;
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float <[x]>;
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double lgamma(<[x]>)
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double lgamma(<[x]>)
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double <[x]>;
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double <[x]>;
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float lgammaf(<[x]>)
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float lgammaf(<[x]>)
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float <[x]>;
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float <[x]>;
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double gamma_r(<[x]>, <[signgamp]>)
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double gamma_r(<[x]>, <[signgamp]>)
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double <[x]>;
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double <[x]>;
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int <[signgamp]>;
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int <[signgamp]>;
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float gammaf_r(<[x]>, <[signgamp]>)
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float gammaf_r(<[x]>, <[signgamp]>)
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float <[x]>;
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float <[x]>;
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int <[signgamp]>;
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int <[signgamp]>;
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double lgamma_r(<[x]>, <[signgamp]>)
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double lgamma_r(<[x]>, <[signgamp]>)
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double <[x]>;
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double <[x]>;
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int <[signgamp]>;
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int <[signgamp]>;
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float lgammaf_r(<[x]>, <[signgamp]>)
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float lgammaf_r(<[x]>, <[signgamp]>)
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float <[x]>;
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float <[x]>;
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int <[signgamp]>;
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int <[signgamp]>;
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double tgamma(<[x]>)
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double tgamma(<[x]>)
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double <[x]>;
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double <[x]>;
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float tgammaf(<[x]>)
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float tgammaf(<[x]>)
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float <[x]>;
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float <[x]>;
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DESCRIPTION
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DESCRIPTION
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<<gamma>> calculates
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<<gamma>> calculates
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@tex
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@tex
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$\mit ln\bigl(\Gamma(x)\bigr)$,
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$\mit ln\bigl(\Gamma(x)\bigr)$,
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@end tex
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@end tex
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the natural logarithm of the gamma function of <[x]>. The gamma function
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the natural logarithm of the gamma function of <[x]>. The gamma function
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(<<exp(gamma(<[x]>))>>) is a generalization of factorial, and retains
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(<<exp(gamma(<[x]>))>>) is a generalization of factorial, and retains
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the property that
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the property that
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@ifnottex
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@ifnottex
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<<exp(gamma(N))>> is equivalent to <<N*exp(gamma(N-1))>>.
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<<exp(gamma(N))>> is equivalent to <<N*exp(gamma(N-1))>>.
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@end ifnottex
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@end ifnottex
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@tex
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@tex
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$\mit \Gamma(N)\equiv N\times\Gamma(N-1)$.
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$\mit \Gamma(N)\equiv N\times\Gamma(N-1)$.
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@end tex
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@end tex
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Accordingly, the results of the gamma function itself grow very
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Accordingly, the results of the gamma function itself grow very
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quickly. <<gamma>> is defined as
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quickly. <<gamma>> is defined as
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@tex
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@tex
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$\mit ln\bigl(\Gamma(x)\bigr)$ rather than simply $\mit \Gamma(x)$
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$\mit ln\bigl(\Gamma(x)\bigr)$ rather than simply $\mit \Gamma(x)$
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@end tex
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@end tex
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@ifnottex
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@ifnottex
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the natural log of the gamma function, rather than the gamma function
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the natural log of the gamma function, rather than the gamma function
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itself,
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itself,
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@end ifnottex
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@end ifnottex
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to extend the useful range of results representable.
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to extend the useful range of results representable.
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The sign of the result is returned in the global variable <<signgam>>,
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The sign of the result is returned in the global variable <<signgam>>,
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which is declared in math.h.
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which is declared in math.h.
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<<gammaf>> performs the same calculation as <<gamma>>, but uses and
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<<gammaf>> performs the same calculation as <<gamma>>, but uses and
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returns <<float>> values.
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returns <<float>> values.
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<<lgamma>> and <<lgammaf>> are alternate names for <<gamma>> and
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<<lgamma>> and <<lgammaf>> are alternate names for <<gamma>> and
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<<gammaf>>. The use of <<lgamma>> instead of <<gamma>> is a reminder
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<<gammaf>>. The use of <<lgamma>> instead of <<gamma>> is a reminder
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that these functions compute the log of the gamma function, rather
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that these functions compute the log of the gamma function, rather
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than the gamma function itself.
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than the gamma function itself.
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The functions <<gamma_r>>, <<gammaf_r>>, <<lgamma_r>>, and
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The functions <<gamma_r>>, <<gammaf_r>>, <<lgamma_r>>, and
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<<lgammaf_r>> are just like <<gamma>>, <<gammaf>>, <<lgamma>>, and
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<<lgammaf_r>> are just like <<gamma>>, <<gammaf>>, <<lgamma>>, and
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<<lgammaf>>, respectively, but take an additional argument. This
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<<lgammaf>>, respectively, but take an additional argument. This
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additional argument is a pointer to an integer. This additional
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additional argument is a pointer to an integer. This additional
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argument is used to return the sign of the result, and the global
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argument is used to return the sign of the result, and the global
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variable <<signgam>> is not used. These functions may be used for
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variable <<signgam>> is not used. These functions may be used for
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reentrant calls (but they will still set the global variable <<errno>>
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reentrant calls (but they will still set the global variable <<errno>>
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if an error occurs).
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if an error occurs).
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<<tgamma>> and <<tgammaf>> are the "true gamma" functions, returning
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<<tgamma>> and <<tgammaf>> are the "true gamma" functions, returning
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@tex
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@tex
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$\mit \Gamma(x)$,
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$\mit \Gamma(x)$,
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@end tex
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@end tex
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the gamma function of <[x]>--without a logarithm.
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the gamma function of <[x]>--without a logarithm.
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(They are apparently so named because of the prior existence of the old,
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(They are apparently so named because of the prior existence of the old,
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poorly-named <<gamma>> functions which returned the log of gamma up
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poorly-named <<gamma>> functions which returned the log of gamma up
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through BSD 4.2.)
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through BSD 4.2.)
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RETURNS
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RETURNS
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Normally, the computed result is returned.
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Normally, the computed result is returned.
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When <[x]> is a nonpositive integer, <<gamma>> returns <<HUGE_VAL>>
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When <[x]> is a nonpositive integer, <<gamma>> returns <<HUGE_VAL>>
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and <<errno>> is set to <<EDOM>>. If the result overflows, <<gamma>>
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and <<errno>> is set to <<EDOM>>. If the result overflows, <<gamma>>
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returns <<HUGE_VAL>> and <<errno>> is set to <<ERANGE>>.
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returns <<HUGE_VAL>> and <<errno>> is set to <<ERANGE>>.
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You can modify this error treatment using <<matherr>>.
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You can modify this error treatment using <<matherr>>.
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PORTABILITY
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PORTABILITY
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Neither <<gamma>> nor <<gammaf>> is ANSI C. It is better not to use either
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Neither <<gamma>> nor <<gammaf>> is ANSI C. It is better not to use either
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of these; use <<lgamma>> or <<tgamma>> instead.@*
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of these; use <<lgamma>> or <<tgamma>> instead.@*
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<<lgamma>>, <<lgammaf>>, <<tgamma>>, and <<tgammaf>> are nominally C standard
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<<lgamma>>, <<lgammaf>>, <<tgamma>>, and <<tgammaf>> are nominally C standard
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in terms of the base return values, although the <<matherr>> error-handling
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in terms of the base return values, although the <<matherr>> error-handling
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is not standard, nor is the <[signgam]> global for <<lgamma>>.
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is not standard, nor is the <[signgam]> global for <<lgamma>>.
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*/
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*/
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/* double gamma(double x)
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/* double gamma(double x)
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* Return the logarithm of the Gamma function of x.
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* Return the logarithm of the Gamma function of x.
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*
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*
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* Method: call gamma_r
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* Method: call gamma_r
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*/
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*/
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#include "fdlibm.h"
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#include "fdlibm.h"
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#include <reent.h>
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#include <reent.h>
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#include <errno.h>
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#include <errno.h>
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#ifndef _DOUBLE_IS_32BITS
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#ifndef _DOUBLE_IS_32BITS
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#ifdef __STDC__
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#ifdef __STDC__
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double gamma(double x)
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double gamma(double x)
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#else
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#else
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double gamma(x)
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double gamma(x)
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double x;
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double x;
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#endif
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#endif
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{
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{
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#ifdef _IEEE_LIBM
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#ifdef _IEEE_LIBM
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return __ieee754_gamma_r(x,&(_REENT_SIGNGAM(_REENT)));
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return __ieee754_gamma_r(x,&(_REENT_SIGNGAM(_REENT)));
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#else
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#else
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double y;
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double y;
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struct exception exc;
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struct exception exc;
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y = __ieee754_gamma_r(x,&(_REENT_SIGNGAM(_REENT)));
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y = __ieee754_gamma_r(x,&(_REENT_SIGNGAM(_REENT)));
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if(_LIB_VERSION == _IEEE_) return y;
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if(_LIB_VERSION == _IEEE_) return y;
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if(!finite(y)&&finite(x)) {
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if(!finite(y)&&finite(x)) {
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#ifndef HUGE_VAL
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#ifndef HUGE_VAL
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#define HUGE_VAL inf
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#define HUGE_VAL inf
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double inf = 0.0;
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double inf = 0.0;
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SET_HIGH_WORD(inf,0x7ff00000); /* set inf to infinite */
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SET_HIGH_WORD(inf,0x7ff00000); /* set inf to infinite */
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#endif
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#endif
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exc.name = "gamma";
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exc.name = "gamma";
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exc.err = 0;
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exc.err = 0;
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exc.arg1 = exc.arg2 = x;
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exc.arg1 = exc.arg2 = x;
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if (_LIB_VERSION == _SVID_)
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if (_LIB_VERSION == _SVID_)
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exc.retval = HUGE;
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exc.retval = HUGE;
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else
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else
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exc.retval = HUGE_VAL;
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exc.retval = HUGE_VAL;
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if(floor(x)==x&&x<=0.0) {
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if(floor(x)==x&&x<=0.0) {
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/* gamma(-integer) or gamma(0) */
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/* gamma(-integer) or gamma(0) */
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exc.type = SING;
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exc.type = SING;
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if (_LIB_VERSION == _POSIX_)
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if (_LIB_VERSION == _POSIX_)
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errno = EDOM;
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errno = EDOM;
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else if (!matherr(&exc)) {
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else if (!matherr(&exc)) {
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errno = EDOM;
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errno = EDOM;
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}
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}
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} else {
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} else {
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/* gamma(finite) overflow */
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/* gamma(finite) overflow */
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exc.type = OVERFLOW;
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exc.type = OVERFLOW;
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if (_LIB_VERSION == _POSIX_)
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if (_LIB_VERSION == _POSIX_)
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errno = ERANGE;
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errno = ERANGE;
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else if (!matherr(&exc)) {
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else if (!matherr(&exc)) {
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errno = ERANGE;
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errno = ERANGE;
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}
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}
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}
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}
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if (exc.err != 0)
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if (exc.err != 0)
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errno = exc.err;
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errno = exc.err;
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return exc.retval;
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return exc.retval;
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} else
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} else
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return y;
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return y;
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#endif
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#endif
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}
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}
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#endif /* defined(_DOUBLE_IS_32BITS) */
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#endif /* defined(_DOUBLE_IS_32BITS) */
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