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# std::sqrt

From cppreference.com
< cpp‎ | numeric‎ | math

Defined in header `<cmath>` |  |
float sqrt( float arg ); | (1) |
double sqrt( double arg ); | (2) |
long double sqrt( long double arg ); | (3) |
double sqrt( Integral arg ); | (4) | (since C++11)

Computes the square root of `arg`.

4) A set of overloads or a function template accepting an argument of any integral type. Equivalent to 2) (the argument is cast to double).

### [edit] Parameters

arg | - | Value of a floating-point or Integral type

### [edit] Return value

If no errors occur, square root of `arg` (√arg), 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.

### [edit] Error handling

Errors are reported as specified in math_errhandling

Domain error occurs if `arg` 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

### [edit] Notes

`std::sqrt` is required by the IEEE standard to be exact. The only other operations required to be exact are the arithmetic operators and the function std::fma. After rounding to the return type (using default rounding mode), the result of `std::sqrt` is indistinguishable from the infinitely precise result. In other words, the error is less than 0.5 ulp. Other functions, including std::pow, are not so constrained.

### [edit] Example

Run this code

    #include <iostream>
    #include <cmath>
    #include <cerrno>
    #include <cfenv>
    #include <cstring>

    #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 output:

    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

### [edit] See also

pow | raises a number to the given power (xy) (function) [edit]
cbrt (C++11) | computes cubic root (3√x) (function) [edit]
hypot (C++11) | computes square root of the sum of the squares of two given numbers (√x2 +y2 ) (function) [edit]
sqrt(std::complex) | complex square root in the range of the right half-plane (function template) [edit]
sqrt(std::valarray) | applies the function std::sqrt to each element of valarray (function template) [edit]
C documentation for sqrt

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