/C

# hypot, hypotf, hypotl

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

Implementations usually guarantee precision of less than 1 ulp (units in the last place): GNU, BSD, Open64.

`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 <stdio.h>
#include <math.h>
#include <errno.h>
#include <fenv.h>
#include <float.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```
• 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)