< cpp‎ | numeric‎ | math
Common mathematical functions
Basic operations
Exponential functions
Power functions
Trigonometric and hyperbolic functions
Error and gamma functions
Nearest integer floating point operations
Floating point manipulation functions
Macro constants
Defined in header <cmath>
float       tgamma( float arg );
(1) (since C++11)
double      tgamma( double arg );
(2) (since C++11)
long double tgamma( long double arg );
(3) (since C++11)
double      tgamma( Integral arg );
(4) (since C++11)
1-3) Computes the gamma function of arg.
4) A set of overloads or a function template accepting an argument of any integral type. Equivalent to 2) (the argument is cast to double).


[edit] Parameters

arg - value of a floating-point or Integral type

[edit] Return value

If no errors occur, the value of the gamma function of arg, that is
e-t dt
, 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.

[edit] Error handling

Errors are reported as specified in math_errhandling

If arg 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

[edit] Notes

If arg is a natural number, std::tgamma(arg) is the factorial of arg-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 < x < 1/DBL_MAX or if x > 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.

[edit] Example

#include <iostream>
#include <cmath>
#include <cerrno>
#include <cstring>
#include <cfenv>
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';
        std::cout << "    FE_INVALID raised\n";

Possible output:

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

[edit] See also

natural logarithm of the gamma function
(function) [edit]
C documentation for tgamma

[edit] External links

Weisstein, Eric W. "Gamma Function." From MathWorld--A Wolfram Web Resource.