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erf, erff, erfl

Defined in header <math.h> 
float       erff( float arg );
-		 (1) (since C99) 
double      erf( double arg );
-		 (2) (since C99) 
long double erfl( long double arg );
-		 (3) (since C99)
Defined in header <tgmath.h> 
#define erf( arg )
-		 (4) (since C99)
-1-3) Computes the error function of arg.
-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.

Parameters

- -
arg - floating point value

Return value

If no errors occur, value of the error function of arg, that is \(\frac{2}{\sqrt{\pi} }\int_{0}^{arg}{e^{-{t^2} }\mathsf{d}t}\)2/√π∫arg0e-t2dt, is returned. If a range error occurs due to underflow, the correct result (after rounding), that is \(\frac{2\cdot arg}{\sqrt{\pi} }\)2*arg/√π, is returned.

Error handling

Errors are reported as specified in math_errhandling.

-

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

-

Notes

Underflow is guaranteed if |arg| < DBL_MIN*(sqrt(π)/2). \(\operatorname{erf}(\frac{x}{\sigma \sqrt{2} })\)erf(

-x/σ√2) is the probability that a measurement whose errors are subject to a normal distribution with standard deviation \(\sigma\)σ is less than \(x\)x away from the mean value.

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

References

See also

- -
-
(C99)(C99)(C99)
 computes complementary error function
(function)
C++ documentation for erf
- -
-Weisstein, Eric W. "Erf." 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/erf -

-
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