erfc, erfcf, erfcl

 

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Common mathematical functions

Functions
Basic operations
abslabsllabsimaxabs (C99) fabs divldivlldivimaxdiv (C99) fmod	remainder (C99) remquo (C99) fma (C99) fmax (C99) fmin (C99) fdim (C99) nannanfnanl (C99)(C99)(C99)
Exponential functions
exp exp2 (C99) expm1 (C99)	log log10 log1p (C99) log2 (C99)
Power functions
sqrt cbrt (C99)	hypot (C99) pow
Trigonometric and hyperbolic functions
sin cos tan asin acos atan atan2	sinh cosh tanh asinh (C99) acosh (C99) atanh (C99)
Error and gamma functions
erf (C99) erfc (C99)	lgamma (C99) tgamma (C99)
Nearest integer floating point operations
ceil floor roundlroundllround (C99)(C99)(C99)	trunc (C99) nearbyint (C99) rintlrintllrint (C99)(C99)(C99)
Floating point manipulation functions
ldexp scalbnscalbln (C99)(C99) ilogb (C99) logb (C99)	frexp modf nextafternexttoward (C99)(C99) copysign (C99)
Classification
fpclassify (C99)
isfinite (C99)
isinf (C99)
isnan (C99)
isnormal (C99)
signbit (C99)
Macro constants
HUGE_VALFHUGE_VALHUGE_VALL (C99)(C99)	FP_NORMALFP_SUBNORMALFP_ZEROFP_INFINITEFP_NAN (C99)(C99)(C99)(C99)(C99)

 

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

2

√π

∫∞
arge^-t2
dt or 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

Run this code

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

Output:

normal cumulative distribution function:
normalCDF(0.00) 50.00%
normalCDF(0.10) 57.93%
normalCDF(0.20) 65.54%
normalCDF(0.30) 72.57%
normalCDF(0.40) 78.81%
normalCDF(0.50) 84.13%
normalCDF(0.60) 88.49%
normalCDF(0.70) 91.92%
normalCDF(0.80) 94.52%
normalCDF(0.90) 96.41%
normalCDF(1.00) 97.72%
special values:
erfc(-Inf) = 2.000000
erfc(Inf) = 0.000000

See also

erferfferfl (C99)(C99)(C99)	computes error function (function)
C++ documentation for erfc

External links

Weisstein, Eric W. "Erfc." From MathWorld--A Wolfram Web Resource.