hypot, hypotf, hypotl
<math.h>
<tgmath.h>
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.
[edit] Parameters
[edit] 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.
[edit] 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,
hypotis equivalent to fabs called with the non-zero argument - if one of the arguments is ±∞,
hypotreturns +∞ even if the other argument is NaN - otherwise, if any of the arguments is NaN, NaN is returned.
[edit] 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.
[edit] 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"); }
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
[edit] 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)