std::hypot, std::hypotf, std::hypotl

 

C++

Compiler support

Freestanding and hosted

Language

Standard library

Standard library headers

Named requirements

Feature test macros (C++20)

Language support library

Concepts library (C++20)

Metaprogramming library (C++11)

Diagnostics library

General utilities library

Strings library

Containers library

Iterators library

Ranges library (C++20)

Algorithms library

Numerics library

Localizations library

Input/output library

Filesystem library (C++17)

Regular expressions library (C++11)

Concurrency support library (C++11)

Technical specifications

Symbols index

External libraries

 

Numerics library

Common mathematical functions

Mathematical special functions (C++17)

Mathematical constants (C++20)

Floating-point environment (C++11)

Complex numbers

Numeric arrays

Pseudo-random number generation

Factor operations

gcd (C++17)

lcm (C++17)

Interpolations

midpoint (C++20)

lerp (C++20)

Generic numeric operations

iota (C++11)

ranges::iota (C++23)

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)

byteswap (C++23)

has_single_bit (C++20)

bit_ceil (C++20)

bit_floor (C++20)

bit_width (C++20)

rotl (C++20)

rotr (C++20)

countl_zero (C++20)

countl_one (C++20)

countr_zero (C++20)

countr_one (C++20)

popcount (C++20)

endian (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>
	(1)
float       hypot ( float x, float y ); double      hypot ( double x, double y ); long double hypot ( long double x, long double y );			(since C++11) (until C++23)
/* floating-point-type */             hypot ( /* floating-point-type */ x,                     /* floating-point-type */ y );			(since C++23) (constexpr since C++26)
float       hypotf( float x, float y );		(2)	(since C++11) (constexpr since C++26)
long double hypotl( long double x, long double y );		(3)	(since C++11) (constexpr since C++26)
		(4)
float       hypot ( float x, float y, float z ); double      hypot ( double x, double y, double z ); long double hypot ( long double x, long double y, long double z );				(since C++17) (until C++23)
/* floating-point-type */             hypot ( /* floating-point-type */ x,                     /* floating-point-type */ y,                     /* floating-point-type */ z );				(since C++23) (constexpr since C++26)
Additional overloads
Defined in header <cmath>
template< class Arithmetic1, Arithmetic2 > /* common-floating-point-type */             hypot ( Arithmetic1 x, Arithmetic2 y );			(A)	(since C++11) (constexpr since C++26)
template< class Arithmetic1, Arithmetic2, Arithmetic3 > /* common-floating-point-type */             hypot ( Arithmetic1 x, Arithmetic2 y, Arithmetic3 z );			(B)	(since C++17) (constexpr since C++26)

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. The library provides overloads of std::hypot for all cv-unqualified floating-point types as the type of the parameters x and y. (since C++23)

4) 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. The library provides overloads of std::hypot for all cv-unqualified floating-point types as the type of the parameters x, y and z. (since C++23)

A,B) Additional overloads are provided for all other combinations of arithmetic types.

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

-

floating-point or integer values

Return value

1-3,A) If no errors occur, the hypotenuse of a right-angled triangle, \(\scriptsize{\sqrt{x^2+y^2} }\)√x2
+y2
, is returned.

4,B) If no errors occur, the distance from origin in 3D space, \(\scriptsize{\sqrt{x^2+y^2+z^2} }\)√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),

• std::hypot(x, y), std::hypot(y, x), and std::hypot(x, -y) are equivalent
• if one of the arguments is ±0, std::hypot(x, y) is equivalent to std::fabs called with the non-zero argument
• if one of the arguments is ±∞, std::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 (Unit in the Last Place — Unit of Least Precision): GNU, BSD.

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 using 3-argument overload of std::hypot as std::hypot(x2 - x1, y2 - y1, z2 - z1).

(since C++17)

The additional overloads are not required to be provided exactly as (A,B). They only need to be sufficient to ensure that for their first argument num1, second argument num2 and the optional third argument num3:

If num1, num2 or num3 has type long double, then std::hypot(num1, num2) has the same effect as std::hypot(static_cast<long double>(num1),            static_cast<long double>(num2)), and std::hypot(num1, num2, num3) has the same effect as std::hypot(static_cast<long double>(num1),            static_cast<long double>(num2),            static_cast<long double>(num3)). Otherwise, if num1, num2 and/or num3 has type double or an integer type, then std::hypot(num1, num2) has the same effect as std::hypot(static_cast<double>(num1),            static_cast<double>(num2)), and std::hypot(num1, num2, num3) has the same effect as std::hypot(static_cast<double>(num1),            static_cast<double>(num2),            static_cast<double>(num3)). Otherwise, if num1, num2 or num3 has type float, then std::hypot(num1, num2) has the same effect as std::hypot(static_cast<float>(num1),            static_cast<float>(num2)), and std::hypot(num1, num2, num3) has the same effect as std::hypot(static_cast<float>(num1),            static_cast<float>(num2),            static_cast<float>(num3)).

(until C++23)

If num1, num2 and num3 have arithmetic types, then std::hypot(num1, num2) has the same effect as std::hypot(static_cast</* common-floating-point-type */>(num1),            static_cast</* common-floating-point-type */>(num2)), and std::hypot(num1, num2, num3) has the same effect as std::hypot(static_cast</* common-floating-point-type */>(num1),            static_cast</* common-floating-point-type */>(num2),            static_cast</* common-floating-point-type */>(num3)), where /* common-floating-point-type */ is the floating-point type with the greatest floating-point conversion rank and greatest floating-point conversion subrank among the types of num1, num2 and num3, arguments of integer type are considered to have the same floating-point conversion rank as double. If no such floating-point type with the greatest rank and subrank exists, then overload resolution does not result in a usable candidate from the overloads provided.

(since C++23)

Feature-test macro	Value	Std	Comment
__cpp_lib_hypot	201603L	(C++17)	3-argument overload of std::hypot

Example

Run this code

#include <cerrno>
#include <cfenv>
#include <cfloat>
#include <cmath>
#include <cstring>
#include <iostream>
 
// #pragma STDC FENV_ACCESS ON
 
struct Point3D { float x, y, z; };
 
int main()
{
    // typical usage
    std::cout << "(1,1) cartesian is (" << std::hypot(1,1)
              << ',' << std::atan2(1,1) << ") polar\n";
 
    Point3D a{3.14, 2.71, 9.87}, b{1.14, 5.71, 3.87};
    // C++17 has 3-argument hypot overload:
    std::cout << "distance(a,b) = "
              << std::hypot(a.x - b.x, a.y - b.y, a.z - b.z) << '\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 (std::fetestexcept(FE_OVERFLOW))
        std::cout << "    FE_OVERFLOW raised\n";
}

Output:

(1,1) cartesian is (1.41421,0.785398) polar
distance(a,b) = 7
hypot(NAN,INFINITY) = inf
hypot(DBL_MAX,DBL_MAX) = inf
    errno = ERANGE Numerical result out of range
    FE_OVERFLOW raised

See also

powpowfpowl (C++11)(C++11)	raises a number to the given power (\(\small{x^y}\)xy) (function)
sqrtsqrtfsqrtl (C++11)(C++11)	computes square root (\(\small{\sqrt{x} }\)√x) (function)
cbrtcbrtfcbrtl (C++11)(C++11)(C++11)	computes cube root (\(\small{\sqrt[3]{x} }\)3√x) (function)
abs(std::complex)	returns the magnitude of a complex number (function template)