std::hypot, std::hypotf, std::hypotl

The value computed by the two-argument version of 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.

The value computed by the three-argument version of this function is the distance of the point (x,y,z) from the origin (0,0,0).

[edit] Parameters

[edit] Return value

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.

[edit] Error handling

Errors are reported as specified in math_errhandling.

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

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

[edit] Notes

Implementations usually guarantee precision of less than 1 ulp (Unit in the Last Place — Unit of Least Precision): GNU, BSD.

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).

The additional overloads are not required to be provided exactly as (A,B). They only need to be sufficient to ensure that for their first argument num1, second argument num2 and the optional third argument num3:

[edit] Example

#include <cerrno>
#include <cfenv>
#include <cfloat>
#include <cmath>
#include <cstring>
#include <iostream>
 
// #pragma STDC FENV_ACCESS ON
 
struct Point3D { float x, y, z; };
 
int main()
{
    // typical usage
    std::cout << "(1,1) cartesian is (" << std::hypot(1, 1)
              << ',' << std::atan2(1,1) << ") polar\n";
 
    Point3D a{3.14, 2.71, 9.87}, b{1.14, 5.71, 3.87};
    // C++17 has 3-argument hypot overload:
    std::cout << "distance(a,b) = "
              << std::hypot(a.x - b.x, a.y - b.y, a.z - b.z) << '\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 (std::fetestexcept(FE_OVERFLOW))
        std::cout << "    FE_OVERFLOW raised\n";
}

(1,1) cartesian is (1.41421,0.785398) polar
distance(a,b) = 7
hypot(NAN,INFINITY) = inf
hypot(DBL_MAX,DBL_MAX) = inf
    errno = ERANGE Numerical result out of range
    FE_OVERFLOW raised

[edit] See also