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std::hypot

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< cpp‎ | numeric‎ | math
Revision as of 09:22, 11 May 2014 by Cubbi (Talk | contribs)

 
 
 
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Defined in header <cmath>
float       hypot( 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 );
(3) (since C++11)
Promoted    hypot( Arithmetic1 x, Arithmetic2 y );
(4) (since C++11)
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) 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 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

Contents

Parameters

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

Return value

The hypotenuse of a right-angled triangle, x2
+y2
.

Exceptions

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 is equivalent to fabs called with the non-zero argument
  • if one of the arguments is ±∞, hypot 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, Open64

std::hypot(x, y) is equivalent to std::abs(std::complex<double>(x,y))

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

See also

computes square root (x)
(function) [edit]
raises a number to the given power (xy)
(function) [edit]
returns the magnitude of a complex number
(function template) [edit]
C documentation for hypot