std::erfc, std::erfcf, std::erfcl
Defined in header <cmath>
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| (1) | ||
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float erfc (
float num )
;
double erfc ( double num ); |
(until C++23) | |
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/*floating-point-type*/
erfc ( /*floating-point-type*/ num ) ; |
(since C++23) (constexpr since C++26) |
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float erfcf( float num );
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(2) | (since C++11) (constexpr since C++26) |
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long
double erfcl(
long
double num )
;
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(3) | (since C++11) (constexpr since C++26) |
SIMD overload (since C++26) |
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Defined in header <simd>
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template
<
/*math-floating-point*/ V >
constexpr /*deduced-simd-t*/<V> |
(S) | (since C++26) |
Additional overloads (since C++11) |
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Defined in header <cmath>
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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)
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S) The SIMD overload performs an element-wise
std::erfc on v_num.
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(since C++26) |
A) Additional overloads are provided for all integer types, which are treated as double.
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(since C++11) |
Parameters
| num | - | floating-point or integer value |
Return value
If no errors occur, value of the complementary error function of num, that is| 2 |
| √π |
num e -t2
dt or 1-erf(num), is returned.
If a range error occurs due to underflow, the correct result (after rounding) is returned.
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 is returned.
- If the argument is -∞, 2 is returned.
- If the argument is NaN, NaN is returned.
Notes
For the IEEE-compatible type double, underflow is guaranteed if num > 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 argument num of integer type, std::erfc(num) has the same effect as std:: erfc ( static_cast < double > (num) )
Example
#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) = 2.00 erfc(Inf) = 0.00
See also
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(C++11)(C++11)(C++11)
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error function (function) |
C documentation for erfc
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External links
| Weisstein, Eric W. "Erfc." From MathWorld — A Wolfram Web Resource. |