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) |
x and y, without undue overflow or underflow at intermediate stages of the computation.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,
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
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 <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 raisedReferences
- 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) |