From cppreference.com
Defined in header
floaterf(floatnum);doubleerf(doublenum);longdoubleerf(longdoublenum); (1)(until C++23)/*floating-point-type*/erf(/*floating-point-type*/num);(since C++23)
(constexpr since C++26)floaterff(floatnum); (2)(since C++11)
(constexpr since C++26)longdoubleerfl(longdoublenum); (3)(since C++11)
(constexpr since C++26)
(since C++26)
Defined in header
template</*math-floating-point*/V>constexpr/*deduced-simd-t*/<V>erf(constV&v_num); (S) (since C++26)
(since C++11)
Defined in header
template<classInteger>doubleerf(Integernum); (A)(constexpr since C++26)1-3) Computes the
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.
(since C++11)Parameters
num - floating-point or integer value Return value
If no errors occur, value of the error function of num, that is {{mathjax-or|\(\frac{2}{\sqrt{\pi} }\int_{0}^{num}{e^{-{t^2} }\mathsf{d}t}\)|
2√π
∫num
0e-t2
dt}}, is returned.
If a range error occurs due to underflow, the correct result (after rounding), that is
2*num√π
is returned.
Error handling
Errors are reported as specified in
.
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 |num|<DBL_MIN*(std::sqrt(π)/2).
erf(xσ√2)
is the probability that a measurement whose errors are subject to a normal distribution with standard deviation σ is less than x away from the mean value.
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)).
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>doublephi(doublex1,doublex2){return(std::erf(x2/std::sqrt(2))-std::erf(x1/std::sqrt(2)))/2;}intmain(){std::cout<<"Normal variate probabilities:\n"<<std::fixed<<std::setprecision(2);for(intn=-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 See also
External links