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

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Defined in header <cmath>
(1)
float       hypot ( float x, float y );

double      hypot ( double x, double y );

long double hypot ( long double x, long double y );
 (since C++11)
(until C++23)
/*floating-point-type*/

            hypot ( /*floating-point-type*/ x,

                    /*floating-point-type*/ y );
 (since C++23)
(constexpr since C++26)
float       hypotf( float x, float y );
 (2) (since C++11)
(constexpr since C++26)
long double hypotl( long double x, long double y );
 (3) (since C++11)
(constexpr since C++26)
(4)
float       hypot ( float x, float y, float z );

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

long double hypot ( long double x, long double y, long double z );
 (since C++17)
(until C++23)
/*floating-point-type*/

            hypot ( /*floating-point-type*/ x,
                    /*floating-point-type*/ y,

                    /*floating-point-type*/ z );
 (since C++23)
(constexpr since C++26)
Defined in header <cmath>
template< class Arithmetic1, Arithmetic2 >

/*common-floating-point-type*/

            hypot ( Arithmetic1 x, Arithmetic2 y );
 (A) (since C++11)
(constexpr since C++26)
template< class Arithmetic1, Arithmetic2, Arithmetic3 >

/*common-floating-point-type*/

            hypot ( Arithmetic1 x, Arithmetic2 y, Arithmetic3 z );
 (B) (since C++17)
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.The library provides overloads of std::hypot for all cv-unqualified floating-point types as the type of the parameters x and y.(since C++23)
4) Computes the square root of the sum of the squares of x, y, and z, without undue overflow or underflow at intermediate stages of the computation.The library provides overloads of std::hypot for all cv-unqualified floating-point types as the type of the parameters x, y and z.(since C++23)
A,B) Additional overloads are provided for all other combinations of arithmetic types.

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).

Contents

[edit] Parameters

x, y, z - floating-point or integer values

[edit] Return value

1-3,A) If no errors occur, the hypotenuse of a right-angled triangle, √x2
+y2
, is returned.
4,B) If no errors occur, the distance from origin in 3D space, √x2
+y2
+z2
, 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.

[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