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Defined in header <cmath> | ||
| (1) | ||
float tgamma(float num); double tgamma(double num); | (until C++23) | |
/*floating-point-type*/ tgamma(/*floating-point-type*/ num); | (since C++23) (constexpr since C++26) | |
float tgammaf(float num); | (2) | (since C++11) (constexpr since C++26) |
longdouble tgammal(longdouble num); | (3) | (since C++11) (constexpr since C++26) |
SIMD overload(since C++26) | ||
Defined in header <simd> | ||
template</*math-floating-point*/ V> constexpr/*deduced-simd-t*/<V> | (S) | (since C++26) |
Additional overloads(since C++11) | ||
Defined in header <cmath> | ||
template<class Integer> double tgamma( Integer num); | (A) | (constexpr since C++26) |
std::tgamma for all cv-unqualified floating-point types as the type of the parameter.(since C++23)S) The SIMD overload performs an element-wise std::tgamma onv_num.
| (since C++26) |
A) Additional overloads are provided for all integer types, which are treated asdouble. | (since C++11) |
Contents |
| num | - | floating-point or integer value |
If no errors occur, the value of the gamma function ofnum, that is\(\Gamma(\mathtt{num}) = \displaystyle\int_0^\infty\!\! t^{\mathtt{num}-1} e^{-t}\, dt\)∫∞
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_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.
Errors are reported as specified inmath_errhandling.
Ifnum 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),
Ifnum is a natural number,std::tgamma(num) is the factorial ofnum-1. Many implementations calculate the exact integer-domain factorial if the argument is a sufficiently small integer.
For IEEE-compatible typedouble, overflow happens if0< num&& num<1/DBL_MAX or ifnum>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 namedgamma in various implementations, but its definition is inconsistent. For example, glibc and 4.2BSD version ofgamma executeslgamma, but 4.4BSD version ofgamma executestgamma.
The additional overloads are not required to be provided exactly as(A). They only need to be sufficient to ensure that for their argumentnum of integer type,std::tgamma(num) has the same effect asstd::tgamma(static_cast<double>(num)).
#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 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! = 362880tgamma(0.5) = 1.77245, sqrt(pi) = 1.77245tgamma(1) = 1tgamma(+Inf) = inftgamma(-1) = nan errno == EDOM: Numerical argument out of domain FE_INVALID raised
(C++11)(C++11)(C++11) | natural logarithm of the gamma function (function)[edit] |
(C++17)(C++17)(C++17) | beta function (function)[edit] |
C documentation fortgamma | |
| Weisstein, Eric W. "Gamma Function." From MathWorld — A Wolfram Web Resource. |
