hypot, hypotf, hypotl

float       hypotf( float x, float y );

double      hypot( double x, double y );

long double hypotl( long double x, long double y );

#define hypot( x, y )

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

Return value

If no errors occur, the hypotenuse of a right-angled triangle, \(\scriptsize{\sqrt{x^2+y^2} }\)√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

#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");
}

(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