Namespaces
Variants
Views
Actions

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

From cppreference.com
< cpp‎ | numeric‎ | math
m (fmt)
(Applied P1467R9.)
Line 3: Line 3:
 
{{dcl begin}}
 
{{dcl begin}}
 
{{dcl header|cmath}}
 
{{dcl header|cmath}}
−
{{dcl|since=c++11|num=1|
+
{{dcl rev multi|num=1|since=c++11|dcl1=
−
float      lgamma ( float arg );
+
float      lgamma ( float num );
−
float      lgammaf( float arg );
+
double      lgamma ( double num );
 +
long double lgamma ( long double num );
 +
|since2=c++23|dcl2=
 +
/* floating-point-type */ lgamma( /* floating-point-type */ num );
 
}}
 
}}
−
{{dcl|since=c++11|num=2|
+
{{dcl|num=2|since=c++11|
−
double      lgamma ( double arg );
+
float      lgammaf( float num );
 
}}
 
}}
−
{{dcl|since=c++11|num=3|
+
{{dcl|num=3|since=c++11|
−
long double lgamma ( long double arg );
+
long double lgammal( long double num );
−
long double lgammal( long double arg );
+
 
}}
 
}}
−
{{dcl|since=c++11|num=4|
+
{{dcl h|[[#Notes|Additional overloads]]}}
−
double      lgamma ( IntegralType arg );
+
{{dcl header|cmath}}
 +
{{dcl|num=A|since=c++11|
 +
template< class Integer >
 +
double      lgamma ( Integer num );
 
}}
 
}}
 
{{dcl end}}
 
{{dcl end}}
  
−
@1-3@ Computes the natural logarithm of the absolute value of the {{enwiki|gamma function}} of {{tt|arg}}.
+
@1-3@ Computes the natural logarithm of the absolute value of the {{enwiki|gamma function}} of {{c|num}}.{{rev inl|since=c++23| The library provides overloads of {{tt|std::lgamma}} for all cv-unqualified floating-point types as the type of the parameter {{c|num}}.}}
−
@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}}).
+
@A@ Additional overloads are provided for all integer types, which are treated as {{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 42:
 
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 53:
  
 
===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 69:
 
#include <cstring>
 
#include <cstring>
 
#include <iostream>
 
#include <iostream>
 +
 
// #pragma STDC FENV_ACCESS ON
 
// #pragma STDC FENV_ACCESS ON
  
Line 72: Line 81:
 
               << "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';

Revision as of 19:08, 16 March 2023

 
C++
 
Numerics library
Common mathematical functions
Mathematical special functions (C++17)
Mathematical constants (C++20)
Basic linear algebra algorithms (C++26)
Floating-point environment (C++11)
Complex numbers
Numeric array (valarray)
Pseudo-random number generation
Factor operations
(C++17)
(C++17)
Interpolations
(C++20)
(C++20)
Saturation arithmetic
(C++26)
(C++26)
(C++26)
(C++26)
(C++26)

Generic numeric operations
Bit operations
(C++20)    
(C++20)
(C++20)
(C++20)
(C++20)
(C++20)
(C++20)
(C++20)
(C++20)
(C++20)
(C++20)
(C++20)
(C++23)
(C++20)
 
Common mathematical functions
Functions
Basic operations
(C++11)  
(C++11)
(C++11)
(C++11)
(C++11)
(C++11)
(C++11)(C++11)(C++11)
Exponential functions
(C++11)
(C++11)

(C++11)
(C++11)
Power functions
(C++11)
(C++11)
Trigonometric and
hyperbolic functions
(C++11)
(C++11)
(C++11)

Error and gamma functions
(C++11)
(C++11)
lgamma
(C++11)
(C++11)
Nearest integer floating point operations
(C++11)(C++11)(C++11)
(C++11)
(C++11)
(C++11)(C++11)(C++11)
Floating point manipulation functions
(C++11)(C++11)
(C++11)
(C++11)
(C++11)(C++11)
(C++11)
Classification and comparison
(C++11)
(C++11)
(C++11)
(C++11)
(C++11)
(C++11)
(C++11)
(C++11)
(C++11)
(C++11)
(C++11)
(C++11)
Types
(C++11)
(C++11)
(C++11)
Macro constants
 
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)
float       lgammaf( float num );
 (2) (since C++11)
long double lgammal( long double num );
 (3) (since C++11)
Defined in header <cmath>
template< class Integer >
double      lgamma ( Integer num );
 (A) (since C++11)
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 num.(since C++23)
A) Additional overloads are provided for all integer types, which are treated as double.

Contents

Parameters

num - floating-point or integer value

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.

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.

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)).

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

See also

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

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=149196"