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Generic numeric operations | |||||||||||||||||||||||||||||||
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Functions | ||||||||||||||||
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Floating point manipulation functions | |||||||||||||||||||||||||||||||||||||||||
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Defined in header <cmath> | ||
(1) | ||
float erfc(float num); double erfc(double num); | (until C++23) | |
/*floating-point-type*/ erfc(/*floating-point-type*/ num); | (since C++23) (constexpr since C++26) | |
float erfcf(float num); | (2) | (since C++11) (constexpr since C++26) |
longdouble erfcl(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 erfc( Integer num); | (A) | (constexpr since C++26) |
std::erfc
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::erfc 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 |
If a range error occurs due to underflow, the correct result (after rounding) is returned.
Errors are reported as specified inmath_errhandling.
If the implementation supports IEEE floating-point arithmetic (IEC 60559),
For the IEEE-compatible typedouble, underflow is guaranteed ifnum>26.55.
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::erfc(num) has the same effect asstd::erfc(static_cast<double>(num)).
#include <cmath>#include <iomanip>#include <iostream> double normalCDF(double x)// Phi(-∞, x) aka N(x){return std::erfc(-x/std::sqrt(2))/2;} int main(){std::cout<<"normal cumulative distribution function:\n"<<std::fixed<<std::setprecision(2);for(double n=0; n<1; n+=0.1)std::cout<<"normalCDF("<< n<<") = "<<100* normalCDF(n)<<"%\n"; std::cout<<"special values:\n"<<"erfc(-Inf) = "<< std::erfc(-INFINITY)<<'\n'<<"erfc(Inf) = "<< std::erfc(INFINITY)<<'\n';}
Output:
normal cumulative distribution function:normalCDF(0.00) = 50.00%normalCDF(0.10) = 53.98%normalCDF(0.20) = 57.93%normalCDF(0.30) = 61.79%normalCDF(0.40) = 65.54%normalCDF(0.50) = 69.15%normalCDF(0.60) = 72.57%normalCDF(0.70) = 75.80%normalCDF(0.80) = 78.81%normalCDF(0.90) = 81.59%normalCDF(1.00) = 84.13%special values:erfc(-Inf) = 2.00erfc(Inf) = 0.00
(C++11)(C++11)(C++11) | error function (function)[edit] |
C documentation forerfc |
Weisstein, Eric W. "Erfc." From MathWorld — A Wolfram Web Resource. |