std::hypot
| Defined in header
<cmath>
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| float hypot( float x, float y );
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(1) | (since C++11) |
| double hypot( double x, double y );
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(2) | (since C++11) |
| long double hypot( long double x, long double y );
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(3) | (since C++11) |
| Promoted hypot( Arithmetic1 x, Arithmetic2 y );
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(4) | (since C++11) |
| float hypot( float x, float y, float z );
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(5) | (since C++17) |
| double hypot( double x, double y, double z );
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(6) | (since C++17) |
| long double hypot( long double x, long double y, long double z );
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(7) | (since C++17) |
| Promoted hypot( Arithmetic1 x, Arithmetic2 y, Arithmetic3 z );
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(8) | (since C++17) |
x and y, without undue overflow or underflow at intermediate stages of the computation.x, y, and z, without undue overflow or underflow at intermediate stages of the computation.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 | - | values of floating-point or integral types |
[edit] Return value
+y2
, is returned.
+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),
- 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
[edit] Notes
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)
[edit] Example
#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[edit] See also
| raises a number to the given power (xy) (function) |
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| computes square root (√x) (function) |
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| (C++11)
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computes cubic root (3√x) (function) |
| returns the magnitude of a complex number (function template) |
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C documentation for hypot
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