Defined in header
floattgamma(floatnum);doubletgamma(doublenum);longdoubletgamma(longdoublenum); (1)(until C++23)/*floating-point-type*/tgamma(/*floating-point-type*/num);(since C++23)
(constexpr since C++26)floattgammaf(floatnum); (2)(since C++11)
(constexpr since C++26)longdoubletgammal(longdoublenum); (3)(since C++11)
(constexpr since C++26)
(since C++26)
Defined in header
template</*math-floating-point*/V>constexpr/*deduced-simd-t*/<V>tgamma(constV&v_num); (S) (since C++26)
(since C++11)
Defined in header
template<classInteger>doubletgamma(Integernum); (A)(constexpr since C++26)1-3) Computes the
of num. The library provides overloads of std::tgamma for all cv-unqualified floating-point types as the type of the parameter.(since C++23)
A) Additional overloads are provided for all integer types, which are treated as double.
(since C++11)Parameters
num - floating-point or integer value Return value
If no errors occur, the value of the gamma function of num, that is ∫∞
0tnum-1
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_VALF, or ±HUGE_VALL is returned.
If a range error due to overflow occurs,
, ±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
.
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
is raised.
If the argument is a negative integer, NaN is returned and
is raised.
If the argument is -∞, NaN is returned and
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.
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 (A). 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)).
Example
Run this code
#include<cerrno>#include<cfenv>#include<cmath>#include<cstring>#include<iostream>// #pragma STDC FENV_ACCESS ONintmain(){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 valuesstd::cout<<"tgamma(1) = "<<std::tgamma(1)<<'\n'<<"tgamma(+Inf) = "<<std::tgamma(INFINITY)<<'\n';// error handlingerrno=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 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 See also
External links