erfc, erfcf, erfcl - cppreference.com (original) (raw)

Defined in header <math.h>
float erfcf( float arg ); (1) (since C99)
double erfc( double arg ); (2) (since C99)
long double erfcl( long double arg ); (3) (since C99)
Defined in header <tgmath.h>
#define erfc( arg ) (4) (since C99)
  1. 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.

Contents

[edit] Parameters

arg - floating-point value

[edit] Return value

If no errors occur, value of the complementary error function of arg, that is \(\frac{2}{\sqrt{\pi} }\int_{arg}^{\infty}{e^{-{t^2} }\mathsf{d}t}\)∫∞
arg_e_-t2
d_t_ 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.

[edit] Error handling

Errors are reported as specified in math_errhandling.

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

[edit] Notes

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

[edit] 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)); }

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

[edit] See also