std::erf

 

C++

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Common mathematical functions

Functions
Basic operations
abs(int) labs llabs imaxabs (C++11) abs(float) fabs div ldiv lldiv imaxdiv (C++11) fmod	remainder (C++11) remquo (C++11) fma (C++11) fmax (C++11) fmin (C++11) fdim (C++11) nan nanf nanl (C++11) (C++11) (C++11)
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sqrt cbrt (C++11)	hypot (C++11) pow
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sin cos tan asin acos atan atan2	sinh cosh tanh asinh (C++11) acosh (C++11) atanh (C++11)
Error and gamma functions
erf (C++11) erfc (C++11)	lgamma (C++11) tgamma (C++11)
Nearest integer floating point operations
ceil floor round lround llround (C++11) (C++11) (C++11)	trunc (C++11) nearbyint (C++11) rint lrint llrint (C++11) (C++11) (C++11)
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ldexp scalbn scalbln (C++11) (C++11) ilogb (C++11) logb (C++11)	frexp modf nextafter nexttoward (C++11) (C++11) copysign (C++11)
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fpclassify (C++11) isfinite (C++11) isinf (C++11)	isnan (C++11) isnormal (C++11) signbit (C++11)
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HUGE_VALF HUGE_VAL HUGE_VALL (C++11) (C++11) INFINITY (C++11) NAN (C++11) math_errhandling MATH_ERRNO MATH_ERREXCEPT (C++11)	FP_NORMAL FP_SUBNORMAL FP_ZERO FP_INFINITE FP_NAN (C++11) (C++11) (C++11) (C++11) (C++11) FLT_EVAL_METHOD (C++11)

 

Defined in header <cmath>
float       erf( float arg );		(since C++11)
double      erf( double arg );		(since C++11)
long double erf( long double arg );		(since C++11)
double      erf( Integral arg );		(since C++11)

Computes the error function of arg.

Parameters

arg

-

floating point value

Return value

The value of the error function of arg, that is

2

√π

∫arg
0e^-t2
dt.

Example

The following example calculates the probability that a normal variate is on the interval (x1, x2)

#include <iostream>
#include <cmath>
#include <iomanip>
double phi(double x1, double x2)
{
    return (std::erf(x2/std::sqrt(2)) - std::erf(x1/std::sqrt(2)))/2;
}
int main()
{
    std::cout << "normal variate probabilities:\n";
    for(int n=-4; n<4; ++n)
        std::cout << "[" << std::setw(2) << n << ":" << std::setw(2) << n+1 << "]: "
                  << std::setw(5) << std::fixed << std::setprecision(2)
                  << 100*phi(n, n+1) << "%\n";
}

Output:

normal variate probabilities:
[-4:-3]:  0.13%
[-3:-2]:  2.14%
[-2:-1]: 13.59%
[-1: 0]: 34.13%
[ 0: 1]: 34.13%
[ 1: 2]: 13.59%
[ 2: 3]:  2.14%
[ 3: 4]:  0.13%

See also

erfc (C++11)	complementary error function (function)

External links

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