float erfcf( float arg );
(1) (since C99)double erfc( double arg );
(2) (since C99)long double erfcl( long double arg );
(3) (since C99)#define erfc( arg )
(4) (since C99)4) Type-generic macro: If arg has type long double, erfcl is called. Otherwise, if arg has integer type or the type double, erfc is called. Otherwise, erfcf is called.
If no errors occur, value of the complementary error function of
arg, that is
\(\frac{2}{\sqrt{\pi} }\int_{arg}^{\infty}{e^{-{t^2} }\mathsf{d}t}\)∫âor
\({\small 1-\operatorname{erf}(arg)}\)1-erf(arg), is returned.
If a range error occurs due to underflow, the correct result (after rounding) is returned.
[edit] Error handlingErrors are reported as specified in math_errhandling.
If the implementation supports IEEE floating-point arithmetic (IEC 60559),
For the IEEE-compatible type double, underflow is guaranteed if arg > 26.55.
#include <math.h>
#include <stdio.h>
double normalCDF(double x) // Phi(-â, 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));
}
Output:
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[edit] References
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