std::hypot

Defined in header <cmath>

1	`float` `hypot(` `float` `x,` `float` `y );`

(1)

(since C++11)

1	`double` `hypot(` `double` `x,` `double` `y );`

(2)

(since C++11)

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

(3)

(since C++11)

1	`Promoted hypot( Arithmetic1 x, Arithmetic2 y );`

(4)

(since C++11)

1-3) Computes the square root of the sum of the squares of x and y, without undue overflow or underflow at intermediate stages of the computation.

4) A set of overloads or a function template for all combinations of arguments of arithmetic type not covered by 1-3). If any argument has integral type, it is cast to double. If any other argument is long double, then the return type is long double, otherwise it is double.

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

x, y

values of floating-point or integral types

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";
}

Output:

(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

pow	raises a number to the given power (x^y) (function)
sqrt	computes square root (√x) (function)
cbrt (C++11)	computes cubic root (3√x) (function)
abs(std::complex)	returns the magnitude of a complex number (function template)
C documentation for `hypot`

std::hypot

Parameters

Return value

Error handling

Notes

Example

See also