Tgamma

Defined in header <cmath>.

Description

Computes the gamma function of num.
​The library provides overloads of std::tgamma for all cv-unqualified floating-point types as the type of the parameter num  (od C++23).

​Additional Overloads are provided for all integer types, which are treated as double.

Declarations

C++23

// 1)
/* floating-point-type */ tgamma( /* floating-point-type */ num );
// 2)
float tgammaf( float num );
// 3)
long double tgammal( long double num );

Additional Overloads

// 4)
template< class Integer >
double tgamma ( Integer num );

C++11

// 1)
float tgamma ( float num );
// 2)
double tgamma ( double num );
//3)
long double tgamma ( long double num );
// 4)
float erfcf( float num );
// 5)
long double erfcl( long double num );

Additional Overloads

// 6)
template< class Integer >
double tgamma ( Integer num );

Parameters

​num - floating-point or integer value

Return value

If no errors occur, the value of the gamma function of num, that is, math here , is returned.

If a domain error occurs, an implementation-defined value (NaN where supported) is returned.

If a pole error occurs, ±HUGE_VAL, ±HUGE_VALF, or ±HUGE_VALL is returned.

If a range error due to overflow occurs, ±HUGE_VAL, ±HUGE_VALF, or ±HUGE_VALL is returned.

If a range error due to underflow occurs, the correct value (after rounding) is returned.

Error handling

Errors are reported as specified in math_errhandling.

If num is zero or is an integer less than zero, a pole error or a domain error may occur.

If the implementation supports IEEE floating-point arithmetic (IEC 60559):

If the argument is ±0, ±∞ is returned and FE_DIVBYZERO is raised If the argument is a negative integer, NaN is returned and FE_INVALID is raised If the argument is -∞, NaN is returned and FE_INVALID is raised If the argument is +∞, +∞ is returned If the argument is NaN, NaN is returned

Notes

If num is a natural number, std::tgamma(num) is the factorial of num - 1. Many implementations calculate the exact integer-domain factorial if the argument is a sufficiently small integer.

For IEEE-compatible type double, overflow happens if 0 < num && num < 1 / DBL_MAX or if num > 171.7.

POSIX requires that a pole error occurs if the argument is zero, but a domain error occurs when the argument is a negative integer. It also specifies that in future, domain errors may be replaced by pole errors for negative integer arguments (in which case the return value in those cases would change from NaN to ±∞).

There is a non-standard function named gamma in various implementations, but its definition is inconsistent. For example, glibc and 4.2BSD version of gamma executes lgamma, but 4.4BSD version of gamma executes tgamma.

The additional overloads are not required to be provided exactly as Additional Overloads. They only need to be sufficient to ensure that for their argument num of integer type,
std::tgamma(num) has the same effect as std::tgamma(static_cast<double>(num)).

Examples

#include <cerrno>
#include <cfenv>
#include <cmath>
#include <cstring>
#include <iostream>
 
// #pragma STDC FENV_ACCESS ON
 
int main()
{
    std::cout 
        << "tgamma(10) = " 
        << std::tgamma(10)
        << ", 9! = " 
        << 2 * 3 * 4 * 5 * 6 * 7 * 8 * 9 
        << '\n'
        << "tgamma(0.5) = " 
        << std::tgamma(0.5)
        << ", sqrt(pi) = " 
        << std::sqrt(std::acos(-1)) 
        << '\n';
 
    // special values
    std::cout 
        << "tgamma(1) = " 
        << std::tgamma(1) << '\n'
        << "tgamma(+Inf) = " 
        << std::tgamma(INFINITY) << '\n';
 
    // error handling
    errno = 0;
    std::feclearexcept(FE_ALL_EXCEPT);
 
    std::cout 
        << "tgamma(-1) = "
        << std::tgamma(-1) << '\n';
 
    if (errno == EDOM)
        std::cout 
            << "errno == EDOM: " 
            << std::strerror(errno) << '\n';
    if (std::fetestexcept(FE_INVALID))
        std::cout 
            << "FE_INVALID raised\n";
}

Possible Result

tgamma(10) = 362880, 9! = 362880
tgamma(0.5) = 1.77245, sqrt(pi) = 1.77245
tgamma(1) = 1
tgamma(+Inf) = inf
tgamma(-1) = nan
errno == EDOM: Numerical argument out of domain
FE_INVALID raised