Sqrt

Defined in header <cmath>.

Description

Computes the square root of num. The library provides overloads of std::sqrt for all cv-unqualified floating-point types as the type of the parameter num.  (since C++23)
Additional Overloads are provided for all integer types, which are treated as double.  (since C++11)

Declarations

C++23

// 1)
/* floating-point-type */ sqrt( /* floating-point-type */ num );
// 2)
float sqrtf( float num );
// 3)
long double sqrtl( long double num );

Additional Overloads

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

C++11

// 1)
float sqrt ( float num );
// 2)
double sqrt ( double num );
// 3)
long double sqrt ( long double num );
// 4)
float sqrtf( float num );
// 5)
long double sqrtl( long double num );

Additional Overloads

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

Parameters

​num - floating-point or integer value

Return value

If no errors occur, square root of num (√num), is returned.

If a domain error occurs, an implementation-defined value is returned (NaN where supported).

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.

Domain error occurs if num is less than zero.

If the implementation supports IEEE floating-point arithmetic (IEC 60559):

If the argument is less than -0, FE_INVALID is raised and NaN is returned
If the argument is +∞ or ±0, it is returned, unmodified
If the argument is NaN, NaN is returned

Notes

std::sqrt is required by the IEEE standard to be correctly rounded from the infinitely precise result. In particular, the exact result is produced if it can be represented in the floating-point type. The only other operations which require this are the arithmetic operators and the function std::fma. Other functions, including std::pow, are not so constrained.

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::sqrt(num) has the same effect as std::sqrt(static_cast<double>(num)).

Examples

#include <cerrno>
#include <cfenv>
#include <cmath>
#include <cstring>
#include <iostream>
 
#pragma STDC FENV_ACCESS ON
 
int main()
{
    // normal use
    std::cout 
        << "sqrt(100) = " 
        << std::sqrt(100) << '\n'
        << "sqrt(2) = " 
        << std::sqrt(2) << '\n'
        << "golden ratio = " 
        << (1 + std::sqrt(5)) / 2 << '\n';
 
    // special values
    std::cout 
        << "sqrt(-0) = " 
        << std::sqrt(-0.0) << '\n';
 
    // error handling
    errno = 0;
    std::feclearexcept(FE_ALL_EXCEPT);
 
    std::cout 
        << "sqrt(-1.0) = " 
        << std::sqrt(-1) << '\n';
    if (errno == EDOM)
        std::cout 
            << "errno = EDOM "
            << std::strerror(errno) << '\n';
    if (std::fetestexcept(FE_INVALID))
        std::cout 
            << "FE_INVALID raised\n";
}

Possible Result

sqrt(100) = 10
sqrt(2) = 1.41421
golden ratio = 1.61803
sqrt(-0) = -0
sqrt(-1.0) = -nan
errno = EDOM Numerical argument out of domain
FE_INVALID raised