NAME¶

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

Synopsis¶

Defined in header <cmath>
float hypot ( float x, float y ); (1) (since C++11)
float hypotf( float x, float y );
double hypot ( double x, double y ); (2) (since C++11)
long double hypot ( long double x, long double y ); (3) (since C++11)
long double hypotl( long double x, long double y );
Promoted hypot ( Arithmetic1 x, Arithmetic2 y ); (4) (since C++11)
float hypot ( float x, float y, float z ); (5) (since C++17)
double hypot ( double x, double y, double z ); (6) (since C++17)
long double hypot ( long double x, long double y, long double z ); (7) (since C++17)
Promoted hypot ( Arithmetic1 x, Arithmetic2 y, Arithmetic3 z ); (8) (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.
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.
5-7) 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.
8) A set of overloads or a function template for all combinations of arguments of
arithmetic type not covered by (5-7). 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 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).

Parameters¶

x, y, z - values of floating-point or integral types

Return value¶

1-4) If no errors occur, the hypotenuse of a right-angled triangle,
\(\scriptsize{\sqrt{x^2+y^2} }\)
√
x2
+y2
, is returned.
5-8) If no errors occur, the distance from origin in 3D space,
\(\scriptsize{\sqrt{x^2+y^2+z^2} }\)
√
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.

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(x,y) is equivalent to fabs called with the
non-zero argument
* if one of the arguments is ±∞, hypot(x,y) 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.

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).

Distance between two points (x1,y1,z1) and (x2,y2,z2) on 3D space can
be calculated using 3-argument overload of std::hypot as
std::hypot(x2-x1, y2-y1, z2-z1). (since C++17)

Feature-test macro: __cpp_lib_hypot

Example¶

// Run this code

#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";
struct Point3D { float x, y, z; } a{3.14,2.71,9.87}, b{1.14,5.71,3.87};
// C++17 has 3-argumnet 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";
}

Output:¶

(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

See also¶

pow
powf raises a number to the given power (\(\small{x^y}\)x^y)
powl (function)
(C++11)
(C++11)
sqrt computes square root (\(\small{\sqrt{x} }\)
sqrtf √
sqrtl x)
(C++11) (function)
(C++11)
cbrt computes cubic root (\(\small{\sqrt[3]{x} }\)
cbrtf 3
cbrtl √
(C++11) x)
(C++11) (function)
(C++11)
abs(std::complex) returns the magnitude of a complex number
(function template)