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diff --git a/man/man3/tgamma.3 b/man/man3/tgamma.3 new file mode 100644 index 0000000..01d86a9 --- /dev/null +++ b/man/man3/tgamma.3 @@ -0,0 +1,216 @@ +'\" t +.\" Copyright 2002 Walter Harms (walter.harms@informatik.uni-oldenburg.de) +.\" +.\" SPDX-License-Identifier: GPL-1.0-or-later +.\" +.\" 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 2024-05-02 "Linux man-pages (unreleased)" +.SH NAME +tgamma, tgammaf, tgammal \- true gamma function +.SH LIBRARY +Math library +.RI ( libm ", " \-lm ) +.SH SYNOPSIS +.nf +.B #include <math.h> +.P +.BI "double tgamma(double " x ); +.BI "float tgammaf(float " x ); +.BI "long double tgammal(long double " x ); +.fi +.P +.RS -4 +Feature Test Macro Requirements for glibc (see +.BR feature_test_macros (7)): +.RE +.P +.BR tgamma (), +.BR tgammaf (), +.BR tgammal (): +.nf + _ISOC99_SOURCE || _POSIX_C_SOURCE >= 200112L +.fi +.SH DESCRIPTION +These functions calculate the Gamma function of +.IR x . +.P +The Gamma function is defined by +.P +.RS +Gamma(x) = integral from 0 to infinity of t\[ha](x\-1) e\[ha]\-t dt +.RE +.P +It is defined for every real number except for nonpositive integers. +For nonnegative integral +.I m +one has +.P +.RS +Gamma(m+1) = m! +.RE +.P +and, more generally, for all +.IR x : +.P +.RS +Gamma(x+1) = x * Gamma(x) +.RE +.P +Furthermore, the following is valid for all values of +.I x +outside the poles: +.P +.RS +Gamma(x) * Gamma(1 \- x) = PI / sin(PI * x) +.RE +.SH RETURN VALUE +On success, these functions return Gamma(x). +.P +If +.I x +is a NaN, a NaN is returned. +.P +If +.I x +is positive infinity, positive infinity is returned. +.P +If +.I x +is a negative integer, or is negative infinity, +a domain error occurs, +and a NaN is returned. +.P +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. +.P +If the result underflows, +a range error occurs, +and the functions return 0, with the correct mathematical sign. +.P +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. +.P +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. +.P +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 ATTRIBUTES +For an explanation of the terms used in this section, see +.BR attributes (7). +.TS +allbox; +lbx lb lb +l l l. +Interface Attribute Value +T{ +.na +.nh +.BR tgamma (), +.BR tgammaf (), +.BR tgammal () +T} Thread safety MT-Safe +.TE +.SH STANDARDS +C11, POSIX.1-2008. +.SH HISTORY +glibc 2.1. +C99, POSIX.1-2001. +.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 glibc 2.18, the glibc implementation of these functions did not set +.\" https://www.sourceware.org/bugzilla/show_bug.cgi?id=6809 +.I errno +to +.B EDOM +when +.I x +is negative infinity. +.P +Before glibc 2.19, +.\" https://www.sourceware.org/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. +.P +.\" +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) |