std::erf, std::erff, std::erfl
From cppreference.com
Defined in header <cmath>
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(1) | ||
float erf ( float num ); double erf ( double num ); |
(until C++23) | |
/* floating-point-type */ erf ( /* floating-point-type */ num ); |
(since C++23) (constexpr since C++26) |
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float erff( float num ); |
(2) | (since C++11) (constexpr since C++26) |
long double erfl( long double num ); |
(3) | (since C++11) (constexpr since C++26) |
Additional overloads (since C++11) |
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Defined in header <cmath>
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template< class Integer > double erf ( Integer num ); |
(A) | (constexpr since C++26) |
1-3) Computes the error function of num. The library provides overloads of
std::erf
for all cv-unqualified floating-point types as the type of the parameter.(since C++23)
A) Additional overloads are provided for all integer types, which are treated as double.
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(since C++11) |
Contents |
[edit] Parameters
num | - | floating-point or integer value |
[edit] Return value
If no errors occur, value of the error function of num, that is2 |
√π |
0e-t2
dt, is returned.
If a range error occurs due to underflow, the correct result (after rounding), that is
2*num |
√π |
[edit] 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.
[edit] Notes
Underflow is guaranteed if |num| < DBL_MIN * (std::sqrt(π) / 2).
erf(x |
σ√2 |
The additional overloads are not required to be provided exactly as (A). They only need to be sufficient to ensure that for their argument num of integer type, std::erf(num) has the same effect as std::erf(static_cast<double>(num)).
[edit] Example
The following example calculates the probability that a normal variate is on the interval (x1, x2):
Run this code
#include <cmath> #include <iomanip> #include <iostream> double phi(double x1, double x2) { return (std::erf(x2 / std::sqrt(2)) - std::erf(x1 / std::sqrt(2))) / 2; } int main() { std::cout << "Normal variate probabilities:\n" << std::fixed << std::setprecision(2); for (int n = -4; n < 4; ++n) std::cout << '[' << std::setw(2) << n << ':' << std::setw(2) << n + 1 << "]: " << std::setw(5) << 100 * phi(n, n + 1) << "%\n"; std::cout << "Special values:\n" << "erf(-0) = " << std::erf(-0.0) << '\n' << "erf(Inf) = " << std::erf(INFINITY) << '\n'; }
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) = -0.00 erf(Inf) = 1.00
[edit] See also
(C++11)(C++11)(C++11) |
complementary error function (function) |
C documentation for erf
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[edit] External links
Weisstein, Eric W. "Erf." From MathWorld — A Wolfram Web Resource. |