tgamma(3)

✨ tgamma, tgammaf, tgammal — the TRUE gamma function 💖

okay bestie so this is page tgamma(3) from the library functions manual, and it's the math-library baddie that computes the actual, no-impostor Gamma function. Two cousins ride along: tgammaf and tgammal. Let's get into it 🫶

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📚 LIBRARY

Math library, a.k.a. libm, and you link it with -lm. Yes queen, you actually have to link it. 🙈

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🌸 SYNOPSIS

#include <math.h>

double tgamma(double x);
float tgammaf(float x);
long double tgammal(long double x);

🎀 Feature Test Macro Requirements for glibc (see feature_test_macros(7))

• tgamma(), tgammaf(), tgammal() — _ISOC99_SOURCE || _POSIX_C_SOURCE >= 200112L

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💅 DESCRIPTION

So these functions calculate the Gamma function of x. That's the whole job. Iconic. 🌈

The Gamma function is defined by

Gamma(x) = integral from 0 to infinity of t^(x-1) e^-t dt

It is defined for every real number except for nonpositive integers. Those are the poles, bestie, and we do NOT go there. 🚫

For nonnegative integral m one has

Gamma(m+1) = m!

and, more generally, for all x:

Gamma(x+1) = x * Gamma(x)

Furthermore, the following is valid for all values of x outside the poles:

Gamma(x) * Gamma(1 - x) = PI / sin(PI * x)

the way this function just has a reflection formula? obsessed. periodt. ✨

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🔥 RETURN VALUE

• On success, these functions return Gamma(x).
• If x is a NaN, a NaN is returned.
• If x is positive infinity, positive infinity is returned.
• If x is a negative integer, or is negative infinity, a domain error occurs, and a NaN is returned.
• If the result overflows, a range error occurs, and the functions return HUGE_VAL, HUGE_VALF, or HUGE_VALL, respectively, with the correct mathematical sign.
• If the result underflows, a range error occurs, and the functions return 0, with the correct mathematical sign.
• If x is -0 or +0, a pole error occurs, and the functions return HUGE_VAL, HUGE_VALF, or HUGE_VALL, respectively, with the same sign as the 0.

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😭 ERRORS

See math_error(7) for info on how to figure out whether an error actually happened when you called these functions. Basically the receipts. 🧾

The following errors can occur:

• Domain error: x is a negative integer, or negative infinity — errno is set to EDOM. An invalid floating-point exception (FE_INVALID) is raised (but see BUGS).
• Pole error: x is +0 or -0 — errno is set to ERANGE. A divide-by-zero floating-point exception (FE_DIVBYZERO) is raised.
• Range error: result overflow — errno is set to ERANGE. An overflow floating-point exception (FE_OVERFLOW) is raised.

glibc also gives the following error which is not specified in C99 or POSIX.1-2001.

• Range error: result underflow — An underflow floating-point exception (FE_UNDERFLOW) is raised, and errno is set to ERANGE.

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👑 ATTRIBUTES

For an explanation of the terms used in this section, see attributes(7).

• tgamma(), tgammaf(), tgammal() — Thread safety: MT-Safe 💜

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⭐ STANDARDS

C11, POSIX.1-2008.

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🦋 HISTORY

glibc 2.1. C99, POSIX.1-2001.

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🌸 NOTES

This function had to be called the "true gamma function" since there is already a function gamma(3) that returns something else (see gamma(3) for details). so yeah, it's giving name collision, and this one is the real one fr fr 🎀

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💀 BUGS

• Before glibc 2.18, the glibc implementation of these functions did not set errno to EDOM when x is negative infinity.
• Before glibc 2.19, the glibc implementation of these functions did not set errno to ERANGE on an underflow range error.
• In glibc versions 2.3.3 and earlier, an argument of +0 or -0 incorrectly produced a domain error (errno set to EDOM and an FE_INVALID exception raised), rather than a pole error. ancient history bestie, but now you know 🌈

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🫶 SEE ALSO

• gamma(3)
• lgamma(3)

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ok that's the whole page, no cap. go forth and call your true gamma function, it's literally the main character of special functions 💅✨

and that's a wrap from the Linux man-pages, version 6.20, dated 2026-02-08 — love u, bye bestie 🎀💖