# hypot - Man Page

Euclidean distance function

## Prolog

This manual page is part of the POSIX Programmer's Manual. The Linux implementation of this interface may differ (consult the corresponding Linux manual page for details of Linux behavior), or the interface may not be implemented on Linux.

## Synopsis

#include <math.h> double hypot(doublex, doubley); float hypotf(floatx, floaty); long double hypotl(long doublex, long doubley);

## Description

The functionality described on this reference page is aligned with the ISO C standard. Any conflict between the requirements described here and the ISO C standard is unintentional. This volume of POSIX.1-2017 defers to the ISO C standard.

These functions shall compute the value of the square root of *x*^{2}+*y*^{2} without undue overflow or underflow.

An application wishing to check for error situations should set *errno* to zero and call *feclearexcept*(FE_ALL_EXCEPT) before calling these functions. On return, if *errno* is non-zero or *fetestexcept*(FE_INVALID | FE_DIVBYZERO | FE_OVERFLOW | FE_UNDERFLOW) is non-zero, an error has occurred.

## Return Value

Upon successful completion, these functions shall return the length of the hypotenuse of a right-angled triangle with sides of length *x* and *y*.

If the correct value would cause overflow, a range error shall occur and *hypot*(), *hypotf*(), and *hypotl*() shall return the value of the macro HUGE_VAL, HUGE_VALF, and HUGE_VALL, respectively.

If *x* or *y* is ±Inf, +Inf shall be returned (even if one of *x* or *y* is NaN).

If *x* or *y* is NaN, and the other is not ±Inf, a NaN shall be returned.

If both arguments are subnormal and the correct result is subnormal, a range error may occur and the correct result shall be returned.

## Errors

These functions shall fail if:

- Range Error
The result overflows.

If the integer expression (

*math_errhandling*& MATH_ERRNO) is non-zero, then*errno*shall be set to**[ERANGE]**. If the integer expression (*math_errhandling*& MATH_ERREXCEPT) is non-zero, then the overflow floating-point exception shall be raised.

These functions may fail if:

- Range Error
The result underflows.

If the integer expression (

*math_errhandling*& MATH_ERRNO) is non-zero, then*errno*shall be set to**[ERANGE]**. If the integer expression (*math_errhandling*& MATH_ERREXCEPT) is non-zero, then the underflow floating-point exception shall be raised.

*The following sections are informative.*

## Examples

See the EXAMPLES section in *atan2*().

## Application Usage

*hypot*(*x*,*y*), *hypot*(*y*,*x*), and *hypot*(*x*, -*y*) are equivalent.

*hypot*(*x*, ±0) is equivalent to *fabs*(*x*).

Underflow only happens when both *x* and *y* are subnormal and the (inexact) result is also subnormal.

These functions take precautions against overflow during intermediate steps of the computation.

On error, the expressions (*math_errhandling* & MATH_ERRNO) and (*math_errhandling* & MATH_ERREXCEPT) are independent of each other, but at least one of them must be non-zero.

## Rationale

None.

## Future Directions

None.

## See Also

atan2(), feclearexcept(), fetestexcept(), isnan(), sqrt()

The Base Definitions volume of POSIX.1-2017, *Section 4.20*, *Treatment of Error Conditions for Mathematical Functions*, <math.h>

## Copyright

Portions of this text are reprinted and reproduced in electronic form from IEEE Std 1003.1-2017, Standard for Information Technology -- Portable Operating System Interface (POSIX), The Open Group Base Specifications Issue 7, 2018 Edition, Copyright (C) 2018 by the Institute of Electrical and Electronics Engineers, Inc and The Open Group. In the event of any discrepancy between this version and the original IEEE and The Open Group Standard, the original IEEE and The Open Group Standard is the referee document. The original Standard can be obtained online at http://www.opengroup.org/unix/online.html .

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