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erfc, erfcf, erfcl

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)
-1-3) Computes the complementary error function of arg, that is 1.0 - erf(arg), but without loss of precision for large arg.
-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.

Parameters

- -
arg - floating point value

Return value

If no errors occur, value of the complementary error function of arg, that is \(\frac{2}{\sqrt{\pi} }\int_{arg}^{\infty}{e^{-{t^2} }\mathsf{d}t}\)2/√π∫∞arge-t2dt 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),

-

Notes

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

-

Example

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

References

See also

- -
-
(C99)(C99)(C99)
 computes error function
(function)
C++ documentation for erfc
- -
-Weisstein, Eric W. "Erfc." From MathWorld — A Wolfram Web Resource.
-

- © cppreference.com
Licensed under the Creative Commons Attribution-ShareAlike Unported License v3.0.
- https://en.cppreference.com/w/c/numeric/math/erfc -

-
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