float erff( float arg );
(1) (since C99)double erf( double arg );
(2) (since C99)long double erfl( long double arg );
(3) (since C99)#define erf( arg )
(4) (since C99)4) Type-generic macro: If arg has type long double, erfl is called. Otherwise, if arg has integer type or the type double, erf is called. Otherwise, erff is called.
If no errors occur, value of the error function of
arg, that is
\(\frac{2}{\sqrt{\pi} }\int_{0}^{arg}{e^{-{t^2} }\mathsf{d}t}\)∫arg, is returned. If a range error occurs due to underflow, the correct result (after rounding), that is
\(\frac{2\cdot arg}{\sqrt{\pi} }\), is returned.
[edit] Error handlingErrors are reported as specified in math_errhandling.
If the implementation supports IEEE floating-point arithmetic (IEC 60559),
Underflow is guaranteed if |arg| < DBL_MIN*(sqrt(Ï)/2).
\(\operatorname{erf}(\frac{x}{\sigma \sqrt{2} })\)erf()is the probability that a measurement whose errors are subject to a normal distribution with standard deviation
\(\sigma\)σis less than
\(x\)xaway from the mean value.
[edit] Example#include <math.h>
#include <stdio.h>
double phi(double x1, double x2)
{
return (erf(x2 / sqrt(2)) - erf(x1 / sqrt(2))) / 2;
}
int main(void)
{
puts("normal variate probabilities:");
for (int n = -4; n < 4; ++n)
printf("[%2d:%2d]: %5.2f%%\n", n, n + 1, 100 * phi(n, n + 1));
puts("special values:");
printf("erf(-0) = %f\n", erf(-0.0));
printf("erf(Inf) = %f\n", erf(INFINITY));
}
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% special values: erf(-0) = -0.000000 erf(Inf) = 1.000000[edit] References
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