Common mathematical functions | |||||||||||||||||||||||||||||||
Mathematical special functions(C++17) | |||||||||||||||||||||||||||||||
Mathematical constants(C++20) | |||||||||||||||||||||||||||||||
Basic linear algebra algorithms(C++26) | |||||||||||||||||||||||||||||||
Data-parallel types (SIMD)(C++26) | |||||||||||||||||||||||||||||||
Floating-point environment(C++11) | |||||||||||||||||||||||||||||||
Complex numbers | |||||||||||||||||||||||||||||||
Numeric array (valarray ) | |||||||||||||||||||||||||||||||
Pseudo-random number generation | |||||||||||||||||||||||||||||||
Bit manipulation(C++20) | |||||||||||||||||||||||||||||||
Saturation arithmetic(C++26) | |||||||||||||||||||||||||||||||
Factor operations | |||||||||||||||||||||||||||||||
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Interpolations | |||||||||||||||||||||||||||||||
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Generic numeric operations | |||||||||||||||||||||||||||||||
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C-style checked integer arithmetic | |||||||||||||||||||||||||||||||
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Functions | ||||||||||||||||
Basic operations | ||||||||||||||||
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Exponential functions | ||||||||||||||||
Power functions | ||||||||||||||||
Trigonometric and hyperbolic functions | ||||||||||||||||
Error and gamma functions | ||||||||||||||||
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Nearest integer floating point operations | |||||||||||||||||||||||||||||||||||||||||
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Floating point manipulation functions | |||||||||||||||||||||||||||||||||||||||||
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Classification and comparison | |||||||||||||||||||||||||||||||||||||||||
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Types | |||||||||||||||||||||||||||||||||||||||||
Macro constants | |||||||||||||||||||||||||||||||||||||||||
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Defined in header <cmath> | ||
(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) | |
float erff(float num); | (2) | (since C++11) (constexpr since C++26) |
longdouble erfl(longdouble num); | (3) | (since C++11) (constexpr since C++26) |
SIMD overload(since C++26) | ||
Defined in header <simd> | ||
template</*math-floating-point*/ V> constexpr/*deduced-simd-t*/<V> | (S) | (since C++26) |
Additional overloads(since C++11) | ||
Defined in header <cmath> | ||
template<class Integer> double erf( Integer num); | (A) | (constexpr since C++26) |
std::erf
for all cv-unqualified floating-point types as the type of the parameter.(since C++23)S) The SIMD overload performs an element-wise std::erf onv_num.
| (since C++26) |
A) Additional overloads are provided for all integer types, which are treated asdouble. | (since C++11) |
Contents |
num | - | floating-point or integer value |
2 |
√π |
2*num |
√π |
Errors are reported as specified inmath_errhandling.
If the implementation supports IEEE floating-point arithmetic (IEC 60559),
Underflow is guaranteed if|num|<DBL_MIN*(std::sqrt(π)/2).
\(\operatorname{erf}(\frac{x}{\sigma \sqrt{2} })\)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 argumentnum of integer type,std::erf(num) has the same effect asstd::erf(static_cast<double>(num)).
The following example calculates the probability that a normal variate is on the interval (x1, x2):
#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) = -0.00erf(Inf) = 1.00
(C++11)(C++11)(C++11) | complementary error function (function)[edit] |
C documentation forerf |
Weisstein, Eric W. "Erf." From MathWorld — A Wolfram Web Resource. |