erfc, erfcf, erfcl

float       erfcf( float arg );

double      erfc( double arg );

long double erfcl( long double arg );

#define erfc( arg )

Parameters

Return value

If no errors occur, value of the complementary error function of arg, that is {{mathjax-or|\(\frac{2}{\sqrt{\pi} }\int_{arg}^{\infty}{e^{-{t^2} }\mathsf{d}t}\)|

∫∞
arge^-t2
dt}} or \({\small 1-\operatorname{erf}(arg)}\)1-erf(arg), is returned.

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

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.

Notes

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

Example

#include <math.h>
#include <stdio.h>

double normalCDF(double x) // Phi(-∞, x) aka N(x)
{
    return erfc(-x / sqrt(2)) / 2;
}

int main(void)
{
    puts("normal cumulative distribution function:");
    for (double n = 0; n < 1; n += 0.1)
        printf("normalCDF(%.2f) %5.2f%%\n", n, 100 * normalCDF(n));

    printf("special values:\n"
           "erfc(-Inf) = %f\n"
           "erfc(Inf) = %f\n",
           erfc(-INFINITY),
           erfc(INFINITY));
}

normal cumulative distribution function:
normalCDF(0.00) 50.00%
normalCDF(0.10) 53.98%
normalCDF(0.20) 57.93%
normalCDF(0.30) 61.79%
normalCDF(0.40) 65.54%
normalCDF(0.50) 69.15%
normalCDF(0.60) 72.57%
normalCDF(0.70) 75.80%
normalCDF(0.80) 78.81%
normalCDF(0.90) 81.59%
normalCDF(1.00) 84.13%
special values:
erfc(-Inf) = 2.000000
erfc(Inf) = 0.000000

References

See also

External links