Defined in header <cmath> | ||
---|---|---|
float hypot ( float x, float y ); float hypotf( float x, float y ); | (1) | (since C++11) |
double hypot ( double x, double y ); | (2) | (since C++11) |
long double hypot ( long double x, long double y ); long double hypotl( long double x, long double y ); | (3) | (since C++11) |
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) |
x
and y
, without undue overflow or underflow at intermediate stages of the computation.double
. If any other argument is long double
, then the return type is long double
, otherwise it is double
.x
, y
, and z
, without undue overflow or underflow at intermediate stages of the computation.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)
.
x, y, z | - | values of floating-point or integral types |
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.
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 hypot(x,y)
is equivalent to fabs
called with the non-zero argument hypot(x,y)
returns +∞ even if the other argument is NaN 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).
Distance between two points (x1,y1,z1)
and (x2,y2,z2)
on 3D space can be calculated as std::hypot(x2-x1, y2-y1, z2-z1)
.
#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
(C++11)(C++11) | raises a number to the given power (x^{y}) (function) |
(C++11)(C++11) | computes square root (√x) (function) |
(C++11)(C++11)(C++11) | computes cubic root (3√x) (function) |
returns the magnitude of a complex number (function template) |
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