| .\" Copyright 2002 Walter Harms (walter.harms@informatik.uni-oldenburg.de) |
| .\" |
| .\" %%%LICENSE_START(GPL_NOVERSION_ONELINE) |
| .\" Distributed under GPL |
| .\" %%%LICENSE_END |
| .\" |
| .\" Based on glibc infopages |
| .\" and Copyright 2008, Linux Foundation, written by Michael Kerrisk |
| .\" <mtk.manpages@gmail.com> |
| .\" Modified 2004-11-15, fixed error noted by Fabian Kreutz |
| .\" <kreutz@dbs.uni-hannover.de> |
| .\" |
| .TH TGAMMA 3 2017-09-15 "GNU" "Linux Programmer's Manual" |
| .SH NAME |
| tgamma, tgammaf, tgammal \- true gamma function |
| .SH SYNOPSIS |
| .B #include <math.h> |
| .PP |
| .BI "double tgamma(double " x ); |
| .br |
| .BI "float tgammaf(float " x ); |
| .br |
| .BI "long double tgammal(long double " x ); |
| .PP |
| Link with \fI\-lm\fP. |
| .PP |
| .in -4n |
| Feature Test Macro Requirements for glibc (see |
| .BR feature_test_macros (7)): |
| .in |
| .PP |
| .ad l |
| .BR tgamma (), |
| .BR tgammaf (), |
| .BR tgammal (): |
| .RS 4 |
| _ISOC99_SOURCE || |
| _POSIX_C_SOURCE\ >=\ 200112L |
| .RE |
| .ad |
| .SH DESCRIPTION |
| These functions calculate the Gamma function of |
| .IR x . |
| .PP |
| The Gamma function is defined by |
| .PP |
| .RS |
| Gamma(x) = integral from 0 to infinity of t^(x\-1) e^\-t dt |
| .RE |
| .PP |
| It is defined for every real number except for nonpositive integers. |
| For nonnegative integral |
| .I m |
| one has |
| .PP |
| .RS |
| Gamma(m+1) = m! |
| .RE |
| .PP |
| and, more generally, for all |
| .IR x : |
| .PP |
| .RS |
| Gamma(x+1) = x * Gamma(x) |
| .RE |
| .PP |
| Furthermore, the following is valid for all values of |
| .I x |
| outside the poles: |
| .PP |
| .RS |
| Gamma(x) * Gamma(1 \- x) = PI / sin(PI * x) |
| .RE |
| .SH RETURN VALUE |
| On success, these functions return Gamma(x). |
| .PP |
| If |
| .I x |
| is a NaN, a NaN is returned. |
| .PP |
| If |
| .I x |
| is positive infinity, positive infinity is returned. |
| .PP |
| If |
| .I x |
| is a negative integer, or is negative infinity, |
| a domain error occurs, |
| and a NaN is returned. |
| .PP |
| If the result overflows, |
| a range error occurs, |
| and the functions return |
| .BR HUGE_VAL , |
| .BR HUGE_VALF , |
| or |
| .BR HUGE_VALL , |
| respectively, with the correct mathematical sign. |
| .PP |
| If the result underflows, |
| a range error occurs, |
| and the functions return 0, with the correct mathematical sign. |
| .PP |
| If |
| .I x |
| is \-0 or +0, |
| a pole error occurs, |
| and the functions return |
| .BR HUGE_VAL , |
| .BR HUGE_VALF , |
| or |
| .BR HUGE_VALL , |
| respectively, with the same sign as the 0. |
| .SH ERRORS |
| See |
| .BR math_error (7) |
| for information on how to determine whether an error has occurred |
| when calling these functions. |
| .PP |
| The following errors can occur: |
| .TP |
| Domain error: \fIx\fP is a negative integer, or negative infinity |
| .I errno |
| is set to |
| .BR EDOM . |
| An invalid floating-point exception |
| .RB ( FE_INVALID ) |
| is raised (but see BUGS). |
| .TP |
| Pole error: \fIx\fP is +0 or \-0 |
| .I errno |
| is set to |
| .BR ERANGE . |
| A divide-by-zero floating-point exception |
| .RB ( FE_DIVBYZERO ) |
| is raised. |
| .TP |
| Range error: result overflow |
| .I errno |
| is set to |
| .BR ERANGE . |
| An overflow floating-point exception |
| .RB ( FE_OVERFLOW ) |
| is raised. |
| .PP |
| glibc also gives the following error which is not specified |
| in C99 or POSIX.1-2001. |
| .TP |
| Range error: result underflow |
| .\" e.g., tgamma(-172.5) on glibc 2.8/x86-32 |
| .\" .I errno |
| .\" is set to |
| .\" .BR ERANGE . |
| An underflow floating-point exception |
| .RB ( FE_UNDERFLOW ) |
| is raised, and |
| .I errno |
| is set to |
| .BR ERANGE . |
| .\" glibc (as at 2.8) also supports an inexact |
| .\" exception for various cases. |
| .SH VERSIONS |
| These functions first appeared in glibc in version 2.1. |
| .SH ATTRIBUTES |
| For an explanation of the terms used in this section, see |
| .BR attributes (7). |
| .TS |
| allbox; |
| lbw30 lb lb |
| l l l. |
| Interface Attribute Value |
| T{ |
| .BR tgamma (), |
| .BR tgammaf (), |
| .BR tgammal () |
| T} Thread safety MT-Safe |
| .TE |
| .SH CONFORMING TO |
| C99, POSIX.1-2001, POSIX.1-2008. |
| .SH NOTES |
| This function had to be called "true gamma function" |
| since there is already a function |
| .BR gamma (3) |
| that returns something else (see |
| .BR gamma (3) |
| for details). |
| .SH BUGS |
| Before version 2.18, the glibc implementation of these functions did not set |
| .\" http://sources.redhat.com/bugzilla/show_bug.cgi?id=6809 |
| .I errno |
| to |
| .B EDOM |
| when |
| .I x |
| is negative infinity. |
| .PP |
| Before glibc 2.19, |
| .\" http://sources.redhat.com/bugzilla/show_bug.cgi?id=6810 |
| the glibc implementation of these functions did not set |
| .I errno |
| to |
| .B ERANGE |
| on an underflow range error. |
| .I x |
| .PP |
| .\" |
| In glibc versions 2.3.3 and earlier, |
| an argument of +0 or \-0 incorrectly produced a domain error |
| .RI ( errno |
| set to |
| .B EDOM |
| and an |
| .B FE_INVALID |
| exception raised), rather than a pole error. |
| .SH SEE ALSO |
| .BR gamma (3), |
| .BR lgamma (3) |