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std::erfc

From cppreference.com
< cpp‎ | numeric‎ | math
 
 
 
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Defined in header <cmath>
float       erfc( float arg );
(1) (since C++11)
double      erfc( double arg );
(2) (since C++11)
long double erfc( long double arg );
(3) (since C++11)
double      erfc( Integral arg );
(4) (since C++11)
1-3) Computes the complementary error function of arg, that is 1.0-erf(arg), but without loss of precision for large 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).

Contents

[edit] Parameters

arg - value of a floating-point or Integral type

[edit] Return value

If no errors occur, value of the complementary error function of arg, that is
2
π

arg
e-t2
dt
or 1-erf(arg), is returned.

If a range error occurs due to underflow, the correct result (after rounding) is returned

[edit] Error handling

Errors are reported as specified in math_errhandling

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

  • If the argument is +∞, +0 is returned
  • If the argument is -∞, 2 is returned
  • If the argument is NaN, NaN is returned

[edit] Notes

For the IEEE-compatible type double, underflow is guaranteed if arg > 26.55.

[edit] Example

#include <iostream>
#include <cmath>
#include <iomanip>
double normalCDF(double x) // Phi(-∞, x) aka N(x)
{
    return std::erfc(-x*std::sqrt(2))/2;
}
int main()
{
    std::cout << "normal cumulative distribution function:\n"
              << std::fixed << std::setprecision(2);
    for(double n=0; n<1; n+=0.1)
        std::cout << "normalCDF(" << n << ") " << 100*normalCDF(n) << "%\n";
 
    std::cout << "special values:\n"
              << "erfc(-Inf) = " << std::erfc(-INFINITY) << '\n'
              << "erfc(Inf) = " << std::erfc(INFINITY) << '\n';
}

Output:

normal cumulative distribution function:
normalCDF(0.00) 50.00%
normalCDF(0.10) 57.93%
normalCDF(0.20) 65.54%
normalCDF(0.30) 72.57%
normalCDF(0.40) 78.81%
normalCDF(0.50) 84.13%
normalCDF(0.60) 88.49%
normalCDF(0.70) 91.92%
normalCDF(0.80) 94.52%
normalCDF(0.90) 96.41%
normalCDF(1.00) 97.72%
special values:
erfc(-Inf) = 2.00
erfc(Inf) = 0.00

[edit] See also

(C++11)
error function
(function) [edit]

[edit] External links

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