std::hypot

 

C++

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Common mathematical functions

Functions
Basic operations
abs(int) labs llabs imaxabs (C++11) abs(float) fabs div ldiv lldiv imaxdiv (C++11) fmod	remainder (C++11) remquo (C++11) fma (C++11) fmax (C++11) fmin (C++11) fdim (C++11) nan nanf nanl (C++11) (C++11) (C++11)
Exponential functions
exp exp2 (C++11) expm1 (C++11)	log log10 log1p (C++11) log2 (C++11)
Power functions
sqrt cbrt (C++11)	hypot (C++11) pow
Trigonometric and hyperbolic functions
sin cos tan asin acos atan atan2	sinh cosh tanh asinh (C++11) acosh (C++11) atanh (C++11)
Error and gamma functions
erf (C++11) erfc (C++11)	lgamma (C++11) tgamma (C++11)
Nearest integer floating point operations
ceil floor round lround llround (C++11) (C++11) (C++11)	trunc (C++11) nearbyint (C++11) rint lrint llrint (C++11) (C++11) (C++11)
Floating point manipulation functions
ldexp scalbn scalbln (C++11) (C++11) ilogb (C++11) logb (C++11)	frexp modf nextafter nexttoward (C++11) (C++11) copysign (C++11)
Classification
fpclassify (C++11) isfinite (C++11) isinf (C++11)	isnan (C++11) isnormal (C++11) signbit (C++11)
Macro constants
HUGE_VALF HUGE_VAL HUGE_VALL (C++11) (C++11) INFINITY (C++11) NAN (C++11) math_errhandling MATH_ERRNO MATH_ERREXCEPT (C++11)	FP_NORMAL FP_SUBNORMAL FP_ZERO FP_INFINITE FP_NAN (C++11) (C++11) (C++11) (C++11) (C++11) FLT_EVAL_METHOD (C++11)

 

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( Arithmetic x, Arithmetic y );	(4)	(since C++11)

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. This 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

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.

Parameters

x	-	floating point value
y	-	floating point value

Return value

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

Exceptions

If the result overflows, a range error may occur and FE_OVERFLOW may be raised.

If the result is subnormal, an underflow error may occur and FE_UNDERFLOW may be raised.

Notes

Typical implementation strategy is to calculate an equivalent of u√1+(

v

u

)2
where u is std::max(x,y) and v is std::min(x,y).

Example

#include <cmath>
#include <utility>
#include <iostream>
 
std::pair<double, double> cartesian_to_polar(double x, double y)
{
    return {std::hypot(x, y), std::atan2(y,x)};
}
 
int main()
{
    std::pair<double, double> polar = cartesian_to_polar(1, 1);
    std::cout << "(1,1) cartesian is (" << polar.first
               << "," << polar.second<< ") polar\n";
}

Output:

(1,1) cartesian is (1.41421,0.785398) polar

See also

sqrt	computes square root (√x) (function)
pow	raises a number to the given power (xy) (function)
abs(std::complex)	returns the magnitude of a complex number (function template)