hypot, hypotf, hypotl

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Defined in header <math.h>
float       hypotf( float x, float y );
 (1) (since C99)
double      hypot( double x, double y );
 (2) (since C99)
long double hypotl( long double x, long double y );
 (3) (since C99)
Defined in header <tgmath.h>
#define hypot( x, y )
 (4) (since C99)
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) Type-generic macro: If any argument has type long double, the long double version of the function is called. Otherwise, if any argument has integer type or has type double, the double version of the function is called. Otherwise, the float version of the function is called.

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.

Parameters

x - floating-point value
y - floating-point value

Return value

If no errors occur, the hypotenuse of a right-angled triangle, √x2
+y2
, 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 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.

hypot(x, y) is equivalent to cabs(x + I*y).

POSIX specifies that underflow may only occur when both arguments are subnormal and the correct result is also subnormal (this forbids naive implementations).

hypot(INFINITY, NAN) returns +∞, but sqrt(INFINITY * INFINITY + NAN * NAN) returns NaN.

Example

Run this code
#include <errno.h>
#include <fenv.h>
#include <float.h>
#include <math.h>
#include <stdio.h>
// #pragma STDC FENV_ACCESS ON
 
int main(void)
{
    // typical usage
    printf("(1,1) cartesian is (%f,%f) polar\n", hypot(1,1), atan2(1, 1));
 
    // special values
    printf("hypot(NAN,INFINITY) = %f\n", hypot(NAN, INFINITY));
 
    // error handling
    errno = 0;
    feclearexcept(FE_ALL_EXCEPT);
    printf("hypot(DBL_MAX,DBL_MAX) = %f\n", hypot(DBL_MAX, DBL_MAX));
    if (errno == ERANGE)
        perror("    errno == ERANGE");
    if (fetestexcept(FE_OVERFLOW))
        puts("    FE_OVERFLOW raised");
}

Possible output: 

(1,1) cartesian is (1.414214,0.785398) polar
hypot(NAN,INFINITY) = inf
hypot(DBL_MAX,DBL_MAX) = inf
    errno == ERANGE: Numerical result out of range
    FE_OVERFLOW raised

References

  • C23 standard (ISO/IEC 9899:2024):
  • 7.12.7.3 The hypot functions (p: TBD)
  • 7.25 Type-generic math <tgmath.h> (p: TBD)
  • F.10.4.3 The hypot functions (p: TBD)
  • C17 standard (ISO/IEC 9899:2018):
  • 7.12.7.3 The hypot functions (p: 181)
  • 7.25 Type-generic math <tgmath.h> (p: 272-273)
  • F.10.4.3 The hypot functions (p: 382)
  • C11 standard (ISO/IEC 9899:2011):
  • 7.12.7.3 The hypot functions (p: 248)
  • 7.25 Type-generic math <tgmath.h> (p: 373-375)
  • F.10.4.3 The hypot functions (p: 524)
  • C99 standard (ISO/IEC 9899:1999):
  • 7.12.7.3 The hypot functions (p: 229)
  • 7.22 Type-generic math <tgmath.h> (p: 335-337)
  • F.9.4.3 The hypot functions (p: 461)

See also

(C99)(C99)
 computes a number raised to the given power (xy)
(function)
(C99)(C99)
 computes square root (√x)
(function)
(C99)(C99)(C99)
 computes cube root (3√x)
(function)
(C99)(C99)(C99)
 computes the magnitude of a complex number
(function)
C++ documentation for hypot
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