hypot, hypotf, hypotl

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+ i y .

Parameters

Return value

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

See also