Cbrt

Defined in header <cmath>.

Description

Computes the cube root of num. The library provides overloads of std::cbrt for all cv-unqualified floating-point types as the type of the parameter num. Additional Overloads are provided for all integer types, which are treated as double.

Declarations

C++23

// 1)
/* floating-point-type */ cbrt( /* floating-point-type */ num );
// 2)
float cbrtf( float num );
// 3)
long double cbrtl( long double num );

Additional Overloads

// 4)
template< class Integer >
double cbrt ( Integer num );

C++11

// 1)
float cbrt ( float num );
// 2)
double cbrt ( double num );
// 3)
long double cbrt ( long double num );
// 4)
float cbrtf( float num );
// 5)
long double cbrtl( long double num );

Additional Overloads

// 6)
template< class Integer >
double cbrt ( Integer num );

Parameters

​num - floating-point or integer value

Return value

If no errors occur, the cube root of num (³√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 or ±∞, it is returned, unchanged if the argument is NaN, NaN is returned

Notes

std::cbrt(num) is not equivalent to std::pow(num, 1.0 / 3) because the rational number ⅓ is typically not equal to 1.0 / 3 and std::pow cannot raise a negative base to a fractional exponent. Moreover, std::cbrt(num) usually gives more accurate results than std::pow(num, 1.0 / 3) (see example).
The additional overloads are not required to be provided exactly as Additional Overloads. They only need to be sufficient to ensure that for their argument num of integer type, std::cbrt(num) has the same effect as std::cbrt(static_cast<double>(num)).

Examples

#include <cmath>
#include <limits>
#include <iomanip>
#include <iostream>
 
int main()
{
    std::cout
        << "Normal use:\n"
        << "cbrt(729)       = " 
        << std::cbrt(729) << '\n'
        << "cbrt(-0.125)    = " 
        << std::cbrt(-0.125) << '\n'
        << "Special values:\n"
        << "cbrt(-0)        = " 
        << std::cbrt(-0.0) << '\n'
        << "cbrt(+inf)      = " 
        << std::cbrt(INFINITY) << '\n'
        << "Accuracy and comparison with `pow`:\n"
        << std::setprecision(std::numeric_limits<double>::max_digits10)
        << "cbrt(343)       = " 
        << std::cbrt(343) << '\n'
        << "pow(343,1.0/3)  = " 
        << std::pow(343, 1.0 / 3) << '\n'
        << "cbrt(-343)      = " 
        << std::cbrt(-343) << '\n'
        << "pow(-343,1.0/3) = " 
        << std::pow(-343, 1.0 / 3) << '\n';
}

Possible Result

Normal use:
cbrt(729)       = 9
cbrt(-0.125)    = -0.5
Special values:
cbrt(-0)        = -0
cbrt(+inf)      = inf
Accuracy and comparison with `pow`:
cbrt(343)       = 7
pow(343,1.0/3)  = 6.9999999999999991
cbrt(-343)      = -7
pow(-343,1.0/3) = -nan