[444] | 1 | |
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| 2 | /* @(#)w_gamma.c 5.1 93/09/24 */ |
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| 3 | /* |
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| 4 | * ==================================================== |
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| 5 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
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| 6 | * |
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| 7 | * Developed at SunPro, a Sun Microsystems, Inc. business. |
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| 8 | * Permission to use, copy, modify, and distribute this |
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| 9 | * software is freely granted, provided that this notice |
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| 10 | * is preserved. |
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| 11 | * ==================================================== |
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| 12 | * |
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| 13 | */ |
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| 14 | |
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| 15 | /* BUG: FIXME? |
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| 16 | According to Linux man pages for tgamma, lgamma, and gamma, the gamma |
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| 17 | function was originally defined in BSD as implemented here--the log of the gamma |
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| 18 | function. BSD 4.3 changed the name to lgamma, apparently removing gamma. BSD |
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| 19 | 4.4 re-introduced the gamma name with the more intuitive, without logarithm, |
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| 20 | plain gamma function. The C99 standard apparently wanted to avoid a problem |
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| 21 | with the poorly-named earlier gamma and used tgamma when adding a plain |
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| 22 | gamma function. |
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| 23 | So the current gamma is matching an old, bad definition, and not |
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| 24 | matching a newer, better definition. */ |
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| 25 | /* |
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| 26 | FUNCTION |
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| 27 | <<gamma>>, <<gammaf>>, <<lgamma>>, <<lgammaf>>, <<gamma_r>>, <<gammaf_r>>, <<lgamma_r>>, <<lgammaf_r>>, <<tgamma>>, and <<tgammaf>>---logarithmic and plain gamma functions |
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| 28 | |
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| 29 | INDEX |
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| 30 | gamma |
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| 31 | INDEX |
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| 32 | gammaf |
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| 33 | INDEX |
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| 34 | lgamma |
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| 35 | INDEX |
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| 36 | lgammaf |
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| 37 | INDEX |
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| 38 | gamma_r |
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| 39 | INDEX |
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| 40 | gammaf_r |
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| 41 | INDEX |
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| 42 | lgamma_r |
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| 43 | INDEX |
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| 44 | lgammaf_r |
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| 45 | INDEX |
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| 46 | tgamma |
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| 47 | INDEX |
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| 48 | tgammaf |
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| 49 | |
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| 50 | SYNOPSIS |
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| 51 | #include <math.h> |
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| 52 | double gamma(double <[x]>); |
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| 53 | float gammaf(float <[x]>); |
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| 54 | double lgamma(double <[x]>); |
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| 55 | float lgammaf(float <[x]>); |
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| 56 | double gamma_r(double <[x]>, int *<[signgamp]>); |
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| 57 | float gammaf_r(float <[x]>, int *<[signgamp]>); |
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| 58 | double lgamma_r(double <[x]>, int *<[signgamp]>); |
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| 59 | float lgammaf_r(float <[x]>, int *<[signgamp]>); |
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| 60 | double tgamma(double <[x]>); |
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| 61 | float tgammaf(float <[x]>); |
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| 62 | |
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| 63 | DESCRIPTION |
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| 64 | <<gamma>> calculates |
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| 65 | @tex |
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| 66 | $\mit ln\bigl(\Gamma(x)\bigr)$, |
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| 67 | @end tex |
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| 68 | the natural logarithm of the gamma function of <[x]>. The gamma function |
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| 69 | (<<exp(gamma(<[x]>))>>) is a generalization of factorial, and retains |
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| 70 | the property that |
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| 71 | @ifnottex |
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| 72 | <<exp(gamma(N))>> is equivalent to <<N*exp(gamma(N-1))>>. |
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| 73 | @end ifnottex |
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| 74 | @tex |
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| 75 | $\mit \Gamma(N)\equiv N\times\Gamma(N-1)$. |
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| 76 | @end tex |
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| 77 | Accordingly, the results of the gamma function itself grow very |
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| 78 | quickly. <<gamma>> is defined as |
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| 79 | @tex |
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| 80 | $\mit ln\bigl(\Gamma(x)\bigr)$ rather than simply $\mit \Gamma(x)$ |
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| 81 | @end tex |
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| 82 | @ifnottex |
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| 83 | the natural log of the gamma function, rather than the gamma function |
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| 84 | itself, |
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| 85 | @end ifnottex |
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| 86 | to extend the useful range of results representable. |
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| 87 | |
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| 88 | The sign of the result is returned in the global variable <<signgam>>, |
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| 89 | which is declared in math.h. |
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| 90 | |
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| 91 | <<gammaf>> performs the same calculation as <<gamma>>, but uses and |
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| 92 | returns <<float>> values. |
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| 93 | |
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| 94 | <<lgamma>> and <<lgammaf>> are alternate names for <<gamma>> and |
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| 95 | <<gammaf>>. The use of <<lgamma>> instead of <<gamma>> is a reminder |
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| 96 | that these functions compute the log of the gamma function, rather |
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| 97 | than the gamma function itself. |
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| 98 | |
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| 99 | The functions <<gamma_r>>, <<gammaf_r>>, <<lgamma_r>>, and |
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| 100 | <<lgammaf_r>> are just like <<gamma>>, <<gammaf>>, <<lgamma>>, and |
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| 101 | <<lgammaf>>, respectively, but take an additional argument. This |
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| 102 | additional argument is a pointer to an integer. This additional |
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| 103 | argument is used to return the sign of the result, and the global |
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| 104 | variable <<signgam>> is not used. These functions may be used for |
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| 105 | reentrant calls (but they will still set the global variable <<errno>> |
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| 106 | if an error occurs). |
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| 107 | |
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| 108 | <<tgamma>> and <<tgammaf>> are the "true gamma" functions, returning |
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| 109 | @tex |
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| 110 | $\mit \Gamma(x)$, |
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| 111 | @end tex |
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| 112 | the gamma function of <[x]>--without a logarithm. |
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| 113 | (They are apparently so named because of the prior existence of the old, |
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| 114 | poorly-named <<gamma>> functions which returned the log of gamma up |
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| 115 | through BSD 4.2.) |
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| 116 | |
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| 117 | RETURNS |
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| 118 | Normally, the computed result is returned. |
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| 119 | |
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| 120 | When <[x]> is a nonpositive integer, <<gamma>> returns <<HUGE_VAL>> |
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| 121 | and <<errno>> is set to <<EDOM>>. If the result overflows, <<gamma>> |
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| 122 | returns <<HUGE_VAL>> and <<errno>> is set to <<ERANGE>>. |
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| 123 | |
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| 124 | You can modify this error treatment using <<matherr>>. |
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| 125 | |
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| 126 | PORTABILITY |
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| 127 | Neither <<gamma>> nor <<gammaf>> is ANSI C. It is better not to use either |
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| 128 | of these; use <<lgamma>> or <<tgamma>> instead.@* |
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| 129 | <<lgamma>>, <<lgammaf>>, <<tgamma>>, and <<tgammaf>> are nominally C standard |
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| 130 | in terms of the base return values, although the <<matherr>> error-handling |
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| 131 | is not standard, nor is the <[signgam]> global for <<lgamma>>. |
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| 132 | */ |
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| 133 | |
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| 134 | /* double gamma(double x) |
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| 135 | * Return the logarithm of the Gamma function of x. |
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| 136 | * |
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| 137 | * Method: call gamma_r |
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| 138 | */ |
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| 139 | |
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| 140 | #include "fdlibm.h" |
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| 141 | #include <reent.h> |
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| 142 | #include <errno.h> |
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| 143 | |
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| 144 | #ifndef _DOUBLE_IS_32BITS |
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| 145 | |
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| 146 | #ifdef __STDC__ |
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| 147 | double gamma(double x) |
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| 148 | #else |
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| 149 | double gamma(x) |
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| 150 | double x; |
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| 151 | #endif |
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| 152 | { |
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| 153 | #ifdef _IEEE_LIBM |
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| 154 | return __ieee754_gamma_r(x,&(_REENT_SIGNGAM(_REENT))); |
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| 155 | #else |
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| 156 | double y; |
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| 157 | struct exception exc; |
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| 158 | y = __ieee754_gamma_r(x,&(_REENT_SIGNGAM(_REENT))); |
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| 159 | if(_LIB_VERSION == _IEEE_) return y; |
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| 160 | if(!finite(y)&&finite(x)) { |
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| 161 | #ifndef HUGE_VAL |
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| 162 | #define HUGE_VAL inf |
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| 163 | double inf = 0.0; |
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| 164 | |
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| 165 | SET_HIGH_WORD(inf,0x7ff00000); /* set inf to infinite */ |
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| 166 | #endif |
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| 167 | exc.name = "gamma"; |
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| 168 | exc.err = 0; |
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| 169 | exc.arg1 = exc.arg2 = x; |
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| 170 | if (_LIB_VERSION == _SVID_) |
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| 171 | exc.retval = HUGE; |
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| 172 | else |
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| 173 | exc.retval = HUGE_VAL; |
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| 174 | if(floor(x)==x&&x<=0.0) { |
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| 175 | /* gamma(-integer) or gamma(0) */ |
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| 176 | exc.type = SING; |
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| 177 | if (_LIB_VERSION == _POSIX_) |
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| 178 | errno = EDOM; |
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| 179 | else if (!matherr(&exc)) { |
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| 180 | errno = EDOM; |
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| 181 | } |
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| 182 | } else { |
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| 183 | /* gamma(finite) overflow */ |
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| 184 | exc.type = OVERFLOW; |
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| 185 | if (_LIB_VERSION == _POSIX_) |
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| 186 | errno = ERANGE; |
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| 187 | else if (!matherr(&exc)) { |
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| 188 | errno = ERANGE; |
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| 189 | } |
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| 190 | } |
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| 191 | if (exc.err != 0) |
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| 192 | errno = exc.err; |
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| 193 | return exc.retval; |
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| 194 | } else |
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| 195 | return y; |
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| 196 | #endif |
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| 197 | } |
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| 198 | |
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| 199 | #endif /* defined(_DOUBLE_IS_32BITS) */ |
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