std::hypot

float       hypot( float x, float y );

double      hypot( double x, double y );

long double hypot( long double x, long double y );

Promoted    hypot( Arithmetic1 x, Arithmetic2 y );

The value computed by this function is the length of the hypotenuse of a right-angled triangle with sides of length x and y, or the distance of the point (x,y) from the origin (0,0), or the magnitude of a complex number x+iy.

Parameters

Return value

If no errors occur, the hypotenuse of a right-angled triangle, √x2
+y2
, is returned.

If a range error due to overflow occurs, +HUGE_VAL, +HUGE_VALF, or +HUGE_VALL is returned.

If a range error due to underflow occurs, 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),

• hypot(x, y), hypot(y, x), and hypot(x, -y) are equivalent
• if one of the arguments is ±0, hypot is equivalent to fabs called with the non-zero argument
• if one of the arguments is ±∞, hypot returns +∞ even if the other argument is NaN
• otherwise, if any of the arguments is NaN, NaN is returned

Notes

Implementations usually guarantee precision of less than 1 ulp (units in the last place): GNU, BSD, Open64.

std::hypot(x, y) is equivalent to std::abs(std::complex<double>(x,y)).

POSIX specifies that underflow may only occur when both arguments are subnormal and the correct result is also subnormal (this forbids naive implementations).

Example

#include <iostream>
#include <cmath>
#include <cerrno>
#include <cfenv>
#include <cfloat>
#include <cstring>
 
#pragma STDC FENV_ACCESS ON
int main()
{
    // typical usage
    std::cout << "(1,1) cartesian is (" << std::hypot(1,1)
              << ',' << std::atan2(1,1) << ") polar\n";
    // special values
    std::cout << "hypot(NAN,INFINITY) = " << std::hypot(NAN,INFINITY) << '\n';
    // error handling 
    errno = 0; std::feclearexcept(FE_ALL_EXCEPT);
    std::cout << "hypot(DBL_MAX,DBL_MAX) = " << std::hypot(DBL_MAX,DBL_MAX) << '\n';
    if(errno == ERANGE)
        std::cout << "    errno = ERANGE " << std::strerror(errno) << '\n';
    if(fetestexcept(FE_OVERFLOW))
        std::cout << "    FE_OVERFLOW raised\n";
}

(1,1) cartesian is (1.41421,0.785398) polar
hypot(NAN,INFINITY) = inf
hypot(DBL_MAX,DBL_MAX) = inf
    errno = ERANGE Numerical result out of range
    FE_OVERFLOW raised

See also