erf, erff, erfl
From cppreference.com
| Defined in header <math.h>
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| float erff( float arg ); |
(1) | (since 哋它亢99) |
| double erf( double arg ); |
(2) | (since 哋它亢99) |
| long double erfl( long double arg ); |
(3) | (since 哋它亢99) |
| Defined in header <tgmath.h>
|
||
| #define erf( arg ) |
(4) | (since 哋它亢99) |
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| 2 |
| √π |
0e-t2
dt, is returned. If a range error occurs due to underflow, the correct result (after rounding), that is
| 2*arg |
| √π |
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, ±0 is returned
- If the argument is ±∞, ±1 is returned
- If the argument is NaN, NaN is returned
Notes
Underflow is guaranteed if |arg| < DBL_MIN*(sqrt(π)/2).
erf(| x |
| σ√2 |
Example
Run this code
#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
- 哋它亢11 standard (ISO/IEC 9899:2011):
- 7.12.8.1 The erf functions (p: 249)
- 7.25 Type-generic math <tgmath.h> (p: 373-375)
- F.10.5.1 The erf functions (p: 525)
- 哋它亢99 standard (ISO/IEC 9899:1999):
- 7.12.8.1 The erf functions (p: 230)
- 7.22 Type-generic math <tgmath.h> (p: 335-337)
- F.9.5.1 The erf functions (p: 462)
See also
| (哋它亢99)(哋它亢99)(哋它亢99) |
computes complementary error function (function) |
External links
| Weisstein, Eric W. "Erf." From MathWorld — A Wolfram Web Resource. |