std::erfc,std::erfcf,std::erfcl

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Numerics library

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)

(C++17)

(C++17)

(C++20)

(C++20)

Generic numeric operations

iota (C++11)
ranges::iota (C++23)
accumulate
inner_product
adjacent_difference
partial_sum

reduce (C++17)
transform_reduce (C++17)
inclusive_scan (C++17)
exclusive_scan (C++17)
transform_inclusive_scan (C++17)
transform_exclusive_scan (C++17)

C-style checked integer arithmetic

ckd_add (C++26)
ckd_sub (C++26)

ckd_mul (C++26)

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Common mathematical functions

Functions

Basic operations

abs(int)labsllabsimaxabs (C++11)
abs(float)fabs
divldivlldivimaxdiv (C++11)

fmod
remainder (C++11)
remquo (C++11)
fma (C++11)
fmax (C++11)
fmin (C++11)
fdim (C++11)
nannanfnanl (C++11)(C++11)(C++11)

Exponential functions

exp
exp2 (C++11)
expm1 (C++11)

log
log10
log1p (C++11)
log2 (C++11)

Power functions

sqrt
cbrt (C++11)

hypot (C++11)
pow

Trigonometric and
hyperbolic functions

sin
cos
tan
asin
acos
atan
atan2

sinh
cosh
tanh
asinh (C++11)
acosh (C++11)
atanh (C++11)

Error and gamma functions

erf (C++11)
erfc (C++11)

lgamma (C++11)
tgamma (C++11)

Nearest integer floating point operations

ceil
floor
roundlroundllround (C++11)(C++11)(C++11)

trunc (C++11)
nearbyint (C++11)
rintlrintllrint (C++11)(C++11)(C++11)

Floating point manipulation functions

ldexp
scalbnscalbln (C++11)(C++11)
ilogb (C++11)
logb (C++11)

frexp
modf
nextafternexttoward (C++11)(C++11)
copysign (C++11)

Classification and comparison

fpclassify (C++11)
isfinite (C++11)
isinf (C++11)
isnan (C++11)
isnormal (C++11)
signbit (C++11)

isgreater (C++11)
isgreaterequal (C++11)
isless (C++11)
islessequal (C++11)
islessgreater (C++11)
isunordered (C++11)

Types

div_t
ldiv_t
lldiv_t (C++11)

imaxdiv_t (C++11)
float_t (C++11)
double_t (C++11)

Macro constants

HUGE_VALFHUGE_VALHUGE_VALL (C++11)(C++11)
math_errhandlingMATH_ERRNOMATH_ERREXCEPT (C++11)
INFINITY (C++11)
NAN (C++11)

Classification
FP_NORMALFP_SUBNORMALFP_ZEROFP_INFINITEFP_NAN (C++11)(C++11)(C++11)(C++11)(C++11)

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Defined in header`<cmath>`
	(1)
float erfc(float num); double erfc(double num); longdouble erfc(longdouble 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> erfc(const V& v_num);		(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)

1-3) Computes thecomplementary error function ofnum, that is1.0-std::erf(num), but without loss of precision for largenum. The library provides overloads ofstd::erfc for all cv-unqualified floating-point types as the type of the parameter.(since C++23)

S) The SIMD overload performs an element-wisestd::erfc onv_num.

(Seemath-floating-point anddeduced-simd-t for their definitions.)

(since C++26)

A) Additional overloads are provided for all integer types, which are treated asdouble.

(since C++11)

[edit]Parameters

num

floating-point or integer value

[edit]Return value

If no errors occur, value of the complementary error function ofnum, that is\(\frac{2}{\sqrt{\pi} }\int_{num}^{\infty}{e^{-{t^2} }\mathsf{d}t}\)

√π

∫∞
nume^-t2dt or\({\small 1-\operatorname{erf}(num)}\)1-erf(num), is returned.

If a range error occurs due to underflow, the correct result (after rounding) is returned.

[edit]Error handling

Errors are reported as specified inmath_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.

[edit]Notes

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)).

[edit]Example

Run this code

#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