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Difference between revisions of "cpp/numeric/math/lgamma"

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< cpp‎ | numeric‎ | math
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{{cpp/title|lgamma|lgammaf|lgammal}}
 
{{cpp/title|lgamma|lgammaf|lgammal}}
 
{{cpp/numeric/math/navbar}}
 
{{cpp/numeric/math/navbar}}
−
{{dcl begin}}
+
{{cpp/numeric/math/declarations
−
{{dcl header|cmath}}
+
|family=lgamma
−
{{dcl|since=c++11|num=1|
+
|param1=num
−
float      lgamma ( float arg );
+
|constexpr_since=26
−
float      lgammaf( float arg );
+
|desc=Computes the natural logarithm of the absolute value of the {{enwiki|gamma function}} of {{c|num}}.
 
}}
 
}}
−
{{dcl|since=c++11|num=2|
 
−
double      lgamma ( double arg );
 
−
}}
 
−
{{dcl|since=c++11|num=3|
 
−
long double lgamma ( long double arg );
 
−
long double lgammal( long double arg );
 
−
}}
 
−
{{dcl|since=c++11|num=4|
 
−
double      lgamma ( IntegralType arg );
 
−
}}
 
−
{{dcl end}}
 
−
 
−
@1-3@ Computes the natural logarithm of the absolute value of the {{enwiki|gamma function}} of {{tt|arg}}.
 
−
@4@ A set of overloads or a function template accepting an argument of any [[cpp/types/is_integral|integral type]]. Equivalent to {{v|2}} (the argument is cast to {{c/core|double}}).
 
  
 
===Parameters===
 
===Parameters===
 
{{par begin}}
 
{{par begin}}
−
{{par|arg|value of a floating-point or [[cpp/types/is_integral|Integral type]]}}
+
{{par|num|floating-point or integer value}}
 
{{par end}}
 
{{par end}}
  
 
===Return value===
 
===Return value===
−
If no errors occur, the value of the logarithm of the gamma function of {{tt|arg}}, that is {{mathjax-or|1=\(\log_{e}{{!}}{\int_0^\infty t^{arg-1} e^{-t} \mathsf{d}t}{{!}}\)|2=log{{su|b=e}}{{!}}{{minteg|0|∞|''t''{{su|p=arg-1}} {{mexp|-t}} d''t''}}{{!}}}}, is returned.
+
If no errors occur, the value of the logarithm of the gamma function of {{c|num}}, that is {{mathjax-or|1=\(\log_{e}{{!}}{\int_0^\infty t^{num-1} e^{-t} \mathsf{d}t}{{!}}\)|2=log{{su|b=e}}{{!}}{{minteg|0|∞|''t''{{su|p=num-1}} {{mexp|-t}} d''t''}}{{!}}}}, is returned.
  
 
If a pole error occurs, {{lc|HUGE_VAL|+HUGE_VAL}}, {{tt|+HUGE_VALF}}, or {{tt|+HUGE_VALL}} is returned.
 
If a pole error occurs, {{lc|HUGE_VAL|+HUGE_VAL}}, {{tt|+HUGE_VALF}}, or {{tt|+HUGE_VALL}} is returned.
Line 37: Line 23:
 
Errors are reported as specified in {{lc|math_errhandling}}.
 
Errors are reported as specified in {{lc|math_errhandling}}.
  
−
If {{tt|arg}} is zero or is an integer less than zero, a pole error may occur.
+
If {{c|num}} is zero or is an integer less than zero, a pole error may occur.
  
 
If the implementation supports IEEE floating-point arithmetic (IEC 60559),
 
If the implementation supports IEEE floating-point arithmetic (IEC 60559),
Line 48: Line 34:
  
 
===Notes===
 
===Notes===
−
If {{tt|arg}} is a natural number, {{c|std::lgamma(arg)}} is the logarithm of the factorial of {{c|arg - 1}}.
+
If {{c|num}} is a natural number, {{c|std::lgamma(num)}} is the logarithm of the factorial of {{c|num - 1}}.
  
−
The [https://pubs.opengroup.org/onlinepubs/9699919799/functions/lgamma.html POSIX version of {{tt|lgamma}}] is not thread-safe: each execution of the function stores the sign of the gamma function of {{tt|arg}} in the static external variable {{tt|signgam}}. Some implementations provide {{tt|lgamma_r}}, which takes a pointer to user-provided storage for {{tt|singgam}} as the second parameter, and is thread-safe.
+
The [https://pubs.opengroup.org/onlinepubs/9699919799/functions/lgamma.html POSIX version of {{tt|lgamma}}] is not thread-safe: each execution of the function stores the sign of the gamma function of {{c|num}} in the static external variable {{tt|signgam}}. Some implementations provide {{tt|lgamma_r}}, which takes a pointer to user-provided storage for {{tt|singgam}} as the second parameter, and is thread-safe.
  
 
There is a non-standard function named {{tt|gamma}} in various implementations, but its definition is inconsistent. For example, glibc and 4.2BSD version of {{tt|gamma}} executes {{tt|lgamma}}, but 4.4BSD version of {{tt|gamma}} executes {{tt|tgamma}}.
 
There is a non-standard function named {{tt|gamma}} in various implementations, but its definition is inconsistent. For example, glibc and 4.2BSD version of {{tt|gamma}} executes {{tt|lgamma}}, but 4.4BSD version of {{tt|gamma}} executes {{tt|tgamma}}.
 +
 +
{{cpp/numeric/math/additional integer overload note|lgamma}}
  
 
===Example===
 
===Example===
−
{{example|code=
+
{{example
 +
|code=
 
#include <cerrno>
 
#include <cerrno>
 
#include <cfenv>
 
#include <cfenv>
Line 61: Line 50:
 
#include <cstring>
 
#include <cstring>
 
#include <iostream>
 
#include <iostream>
 +
 
// #pragma STDC FENV_ACCESS ON
 
// #pragma STDC FENV_ACCESS ON
  
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               << "lgamma(0.5) = " << std::lgamma(0.5)
 
               << "lgamma(0.5) = " << std::lgamma(0.5)
 
               << ", log(sqrt(pi)) = " << std::log(std::sqrt(pi)) << '\n';
 
               << ", log(sqrt(pi)) = " << std::log(std::sqrt(pi)) << '\n';
 +
   
 
     // special values
 
     // special values
 
     std::cout << "lgamma(1) = " << std::lgamma(1) << '\n'
 
     std::cout << "lgamma(1) = " << std::lgamma(1) << '\n'
 
               << "lgamma(+Inf) = " << std::lgamma(INFINITY) << '\n';
 
               << "lgamma(+Inf) = " << std::lgamma(INFINITY) << '\n';
 +
   
 
     // error handling
 
     // error handling
 
     errno = 0;
 
     errno = 0;
 
     std::feclearexcept(FE_ALL_EXCEPT);
 
     std::feclearexcept(FE_ALL_EXCEPT);
 +
   
 
     std::cout << "lgamma(0) = " << std::lgamma(0) << '\n';
 
     std::cout << "lgamma(0) = " << std::lgamma(0) << '\n';
 +
   
 
     if (errno == ERANGE)
 
     if (errno == ERANGE)
 
         std::cout << "    errno == ERANGE: " << std::strerror(errno) << '\n';
 
         std::cout << "    errno == ERANGE: " << std::strerror(errno) << '\n';

Latest revision as of 09:10, 28 June 2023

 
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Defined in header <cmath>
(1)
float       lgamma ( float num );

double      lgamma ( double num );

long double lgamma ( long double num );
 (until C++23)
/* floating-point-type */
            lgamma ( /* floating-point-type */ num );
 (since C++23)
(constexpr since C++26)
float       lgammaf( float num );
 (2) (since C++11)
(constexpr since C++26)
long double lgammal( long double num );
 (3) (since C++11)
(constexpr since C++26)
Additional overloads (since C++11)
Defined in header <cmath>
template< class Integer >
double      lgamma ( Integer num );
 (A) (constexpr since C++26)
1-3) Computes the natural logarithm of the absolute value of the gamma function of num. The library provides overloads of std::lgamma 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)

Contents

[edit] Parameters

num - floating-point or integer value

[edit] Return value

If no errors occur, the value of the logarithm of the gamma function of num, that is loge|∫∞0tnum-1 e-t dt|, 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.

[edit] Error handling

Errors are reported as specified in math_errhandling.

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

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

  • If the argument is 1, +0 is returned.
  • If the argument is 2, +0 is returned.
  • If the argument is ±0, +∞ is returned and FE_DIVBYZERO is raised.
  • If the argument is a negative integer, +∞ is returned and FE_DIVBYZERO is raised.
  • If the argument is ±∞, +∞ is returned.
  • If the argument is NaN, NaN is returned.

[edit] Notes

If num is a natural number, std::lgamma(num) is the logarithm of the factorial of num - 1.

The POSIX version of lgamma is not thread-safe: each execution of the function stores the sign of the gamma function of num in the static external variable signgam. Some implementations provide lgamma_r, which takes a pointer to user-provided storage for singgam as the second parameter, and is thread-safe.

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::lgamma(num) has the same effect as std::lgamma(static_cast<double>(num)).

[edit] Example

Run this code
#include <cerrno>
#include <cfenv>
#include <cmath>
#include <cstring>
#include <iostream>
 
// #pragma STDC FENV_ACCESS ON
 
const double pi = std::acos(-1); // or std::numbers::pi since C++20
 
int main()
{
    std::cout << "lgamma(10) = " << std::lgamma(10)
              << ", log(9!) = " << std::log(std::tgamma(10))
              << ", exp(lgamma(10)) = " << std::exp(std::lgamma(10)) << '\n'
              << "lgamma(0.5) = " << std::lgamma(0.5)
              << ", log(sqrt(pi)) = " << std::log(std::sqrt(pi)) << '\n';
 
    // special values
    std::cout << "lgamma(1) = " << std::lgamma(1) << '\n'
              << "lgamma(+Inf) = " << std::lgamma(INFINITY) << '\n';
 
    // error handling
    errno = 0;
    std::feclearexcept(FE_ALL_EXCEPT);
 
    std::cout << "lgamma(0) = " << std::lgamma(0) << '\n';
 
    if (errno == ERANGE)
        std::cout << "    errno == ERANGE: " << std::strerror(errno) << '\n';
    if (std::fetestexcept(FE_DIVBYZERO))
        std::cout << "    FE_DIVBYZERO raised\n";
}

Output: 

lgamma(10) = 12.8018, log(9!) = 12.8018, exp(lgamma(10)) = 362880
lgamma(0.5) = 0.572365, log(sqrt(pi)) = 0.572365
lgamma(1) = 0
lgamma(+Inf) = inf
lgamma(0) = inf
    errno == ERANGE: Numerical result out of range
    FE_DIVBYZERO raised

[edit] See also

(C++11)(C++11)(C++11)
 gamma function
(function) [edit]
C documentation for lgamma

[edit] External links

Weisstein, Eric W. "Log Gamma Function." From MathWorld — A Wolfram Web Resource.
Retrieved from "https://en.cppreference.com/mwiki/index.php?title=cpp/numeric/math/lgamma&oldid=154203"