diff options
Diffstat (limited to 'newlib/libm/math/w_gamma.c')
| -rw-r--r-- | newlib/libm/math/w_gamma.c | 53 |
1 files changed, 43 insertions, 10 deletions
diff --git a/newlib/libm/math/w_gamma.c b/newlib/libm/math/w_gamma.c index fad40496d..3717f53e5 100644 --- a/newlib/libm/math/w_gamma.c +++ b/newlib/libm/math/w_gamma.c @@ -12,11 +12,20 @@ * */ +/* BUG: FIXME? + According to Linux man pages for tgamma, lgamma, and gamma, the gamma +function was originally defined in BSD as implemented here--the log of the gamma +function. BSD 4.3 changed the name to lgamma, apparently removing gamma. BSD +4.4 re-introduced the gamma name with the more intuitive, without logarithm, +plain gamma function. The C99 standard apparently wanted to avoid a problem +with the poorly-named earlier gamma and used tgamma when adding a plain +gamma function. + So the current gamma is matching an old, bad definition, and not +matching a newer, better definition. */ /* FUNCTION - <<gamma>>, <<gammaf>>, <<lgamma>>, <<lgammaf>>, <<gamma_r>>, - <<gammaf_r>>, <<lgamma_r>>, <<lgammaf_r>>---logarithmic gamma - function + <<gamma>>, <<gammaf>>, <<lgamma>>, <<lgammaf>>, <<gamma_r>>, <<gammaf_r>>, <<lgamma_r>>, <<lgammaf_r>>, <<tgamma>>, and <<tgammaf>>--logarithmic and plain gamma functions + INDEX gamma INDEX @@ -33,6 +42,10 @@ INDEX lgamma_r INDEX lgammaf_r +INDEX +tgamma +INDEX +tgammaf ANSI_SYNOPSIS #include <math.h> @@ -44,6 +57,8 @@ double gamma_r(double <[x]>, int *<[signgamp]>); float gammaf_r(float <[x]>, int *<[signgamp]>); double lgamma_r(double <[x]>, int *<[signgamp]>); float lgammaf_r(float <[x]>, int *<[signgamp]>); +double tgamma(double <[x]>); +float tgammaf(float <[x]>); TRAD_SYNOPSIS #include <math.h> @@ -67,15 +82,19 @@ int <[signgamp]>; float lgammaf_r(<[x]>, <[signgamp]>) float <[x]>; int <[signgamp]>; +double tgamma(<[x]>) +double <[x]>; +float tgammaf(<[x]>) +float <[x]>; DESCRIPTION -<<gamma>> calculates +<<gamma>> calculates @tex -$\mit ln\bigl(\Gamma(x)\bigr)$, +$\mit ln\bigl(\Gamma(x)\bigr)$, @end tex the natural logarithm of the gamma function of <[x]>. The gamma function (<<exp(gamma(<[x]>))>>) is a generalization of factorial, and retains -the property that +the property that @ifnottex <<exp(gamma(N))>> is equivalent to <<N*exp(gamma(N-1))>>. @end ifnottex @@ -83,13 +102,13 @@ the property that $\mit \Gamma(N)\equiv N\times\Gamma(N-1)$. @end tex Accordingly, the results of the gamma function itself grow very -quickly. <<gamma>> is defined as +quickly. <<gamma>> is defined as @tex $\mit ln\bigl(\Gamma(x)\bigr)$ rather than simply $\mit \Gamma(x)$ @end tex @ifnottex the natural log of the gamma function, rather than the gamma function -itself, +itself, @end ifnottex to extend the useful range of results representable. @@ -113,8 +132,17 @@ variable <<signgam>> is not used. These functions may be used for reentrant calls (but they will still set the global variable <<errno>> if an error occurs). +<<tgamma>> and <<tgammaf>> are the "true gamma" functions, returning +@tex +$\mit \Gamma(x)$, +@end tex +the gamma function of <[x]>--without a logarithm. +(They are apparently so named because of the prior existence of the old, +poorly-named <<gamma>> functions which returned the log of gamma up +through BSD 4.2.) + RETURNS -Normally, the computed result is returned. +Normally, the computed result is returned. When <[x]> is a nonpositive integer, <<gamma>> returns <<HUGE_VAL>> and <<errno>> is set to <<EDOM>>. If the result overflows, <<gamma>> @@ -123,7 +151,12 @@ returns <<HUGE_VAL>> and <<errno>> is set to <<ERANGE>>. You can modify this error treatment using <<matherr>>. PORTABILITY -Neither <<gamma>> nor <<gammaf>> is ANSI C. */ +Neither <<gamma>> nor <<gammaf>> is ANSI C. It is better not to use either +of these; use <<lgamma>> or <<tgamma>> instead.@* +<<lgamma>>, <<lgammaf>>, <<tgamma>>, and <<tgammaf>> are nominally C standard +in terms of the base return values, although the <<matherr>> error-handling +is not standard, nor is the <[signgam]> global for <<lgamma>>. +*/ /* double gamma(double x) * Return the logarithm of the Gamma function of x. |