NAME¶

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

Synopsis¶

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

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

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

double hypot ( double x, double y, (since C++17)
double z ); (until C++23)

long double hypot ( long double x, long (1)
double y, long double z );
/* floating-point-type */

hypot ( /* floating-point-type
*/ x, (since C++23)
/* floating-point-type (constexpr since
*/ y, C++26)

/* floating-point-type (4)
*/ z );
Additional overloads
Defined in header <cmath>
template< class Arithmetic1, Arithmetic2 >
(since C++11)
/* common-floating-point-type */ (A) (constexpr since
C++26)
hypot ( Arithmetic1 x,
Arithmetic2 y );
template< class Arithmetic1, Arithmetic2,
Arithmetic3 >
(since C++17)
/* common-floating-point-type */ (B) (constexpr since
C++26)
hypot ( Arithmetic1 x,
Arithmetic2 y, Arithmetic3 z );

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).

Parameters¶

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

Return value¶

1-3,A) If no errors occur, the hypotenuse of a right-angled triangle,
\(\scriptsize{\sqrt{x^2+y^2} }\)
√
x2
+y2
, is returned.
4,B) 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),

* 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.

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).

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 (since C++17)
- x1, y2 - y1, z2 - z1).

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:

* If num1, num2 or num3 has type long double, then

* std::hypot(num1, num2) has the same effect as
std::hypot(static_cast<long double>(num1),
static_cast<long double>(num2)), and
* std::hypot(num1, num2, num3) has the same effect as
std::hypot(static_cast<long double>(num1),
static_cast<long double>(num2),
static_cast<long double>(num3)).
* Otherwise, if num1, num2 and/or num3 has type double or an integer
type, then

* std::hypot(num1, num2) has the same effect as
std::hypot(static_cast<double>(num1), (until C++23)
static_cast<double>(num2)), and
* std::hypot(num1, num2, num3) has the same effect as
std::hypot(static_cast<double>(num1),
static_cast<double>(num2),
static_cast<double>(num3)).
* Otherwise, if num1, num2 or num3 has type float, then

* std::hypot(num1, num2) has the same effect as
std::hypot(static_cast<float>(num1),
static_cast<float>(num2)), and
* std::hypot(num1, num2, num3) has the same effect as
std::hypot(static_cast<float>(num1),
static_cast<float>(num2),
static_cast<float>(num3)).
If num1, num2 and num3 have arithmetic types, then

* std::hypot(num1, num2) has the same effect as
std::hypot(static_cast</* common-floating-point-type */>(num1),
static_cast</* common-floating-point-type */>(num2)),
and
* std::hypot(num1, num2, num3) has the same effect as
std::hypot(static_cast</* common-floating-point-type */>(num1),
static_cast</* common-floating-point-type */>(num2),
static_cast</* common-floating-point-type */>(num3)), (since C++23)

where /* common-floating-point-type */ is the floating-point type with
the greatest floating-point conversion rank and greatest
floating-point conversion subrank among the types of num1, num2 and
num3, arguments of integer type are considered to have the same
floating-point conversion rank as double.

If no such floating-point type with the greatest rank and subrank
exists, then overload resolution does not result in a usable candidate
from the overloads provided.

Feature-test macro Value Std Feature
__cpp_lib_hypot 201603L (C++17) 3-argument overload of std::hypot

Example¶

// Run this code

#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";
}

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 cube 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)
C documentation for
hypot