std::hypot

C++

Language

Headers

Freestanding and hosted implementations

Named requirements

Language support library

Concepts library (C++20)

Diagnostics library

Utilities library

Strings library

Containers library

Algorithms library

Iterators library

Numerics library

Input/output library

Localizations library

Regular expressions library (C++11)

Atomic operations library (C++11)

Thread support library (C++11)

Filesystem library (C++17)

Technical Specifications

Numerics library

Common mathematical functions

Special mathematical functions

Floating-point environment (C++11)

Complex numbers

Numeric arrays

Pseudo-random number generation

Compile-time rational arithmetic (C++11)

Numeric algorithms

gcd (C++17)

lcm (C++17)

Generic numeric operations

iota (C++11)

accumulate

inner_product

adjacent_difference

partial_sum

reduce (C++17)

transform_reduce (C++17)

inclusive_scan (C++17)

exclusive_scan (C++17)

transform_inclusive_scan (C++17)

transform_exclusive_scan (C++17)

Bit operations

bit_cast (C++20)

ispow2 (C++20)

ceil2 (C++20)

floor2 (C++20)

log2p1 (C++20)

Common mathematical functions

Functions
Basic operations
abs(int)labsllabsimaxabs (C++11) abs(float)fabs divldivlldivimaxdiv (C++11) fmod	remainder (C++11) remquo (C++11) fma (C++11) fmax (C++11) fmin (C++11) fdim (C++11) nannanfnanl (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 roundlroundllround (C++11)(C++11)(C++11)	trunc (C++11) nearbyint (C++11) rintlrintllrint (C++11)(C++11)(C++11)
Floating point manipulation functions
ldexp scalbnscalbln (C++11)(C++11) ilogb (C++11) logb (C++11)	frexp modf nextafternexttoward (C++11)(C++11) copysign (C++11)
Classification/Comparison
fpclassify (C++11) isfinite (C++11) isinf (C++11) isnan (C++11) isnormal (C++11) signbit (C++11)	isgreater (C++11) isgreaterequal (C++11) isless (C++11) islessequal (C++11) islessgreater (C++11) isunordered (C++11)
Macro constants
HUGE_VALFHUGE_VALHUGE_VALL (C++11)(C++11) INFINITY (C++11) NAN (C++11) math_errhandlingMATH_ERRNOMATH_ERREXCEPT (C++11)	FP_NORMALFP_SUBNORMALFP_ZEROFP_INFINITEFP_NAN (C++11)(C++11)(C++11)(C++11)(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( 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)

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) A set of overloads or a function template for all combinations of arguments of arithmetic type not covered by (1-3). 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.

5-7) 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.

8) A set of overloads or a function template for all combinations of arguments of arithmetic type not covered by (5-7). 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 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

-

values of floating-point or integral types

Return value

1-4) If no errors occur, the hypotenuse of a right-angled triangle, x2
+y2
, is returned.

5-8) If no errors occur, the distance from origin in 3D space, 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),

• 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

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)

Example

Run this code

#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

pow	raises a number to the given power (xy) (function)
sqrt	computes square root (x) (function)
cbrt (C++11)	computes cubic root (3x) (function)
abs(std::complex)	returns the magnitude of a complex number (function template)