```HYPOT(3P)                 POSIX Programmer's Manual                HYPOT(3P)
```

## PROLOG         top

```       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.
```

## NAME         top

```       hypot, hypotf, hypotl — Euclidean distance function
```

## SYNOPSIS         top

```       #include <math.h>

double hypot(double x, double y);
float hypotf(float x, float y);
long double hypotl(long double x, long double y);
```

## DESCRIPTION         top

```       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.1‐2008 defers to the ISO C standard.

These functions shall compute the value of the square root of x2+y2
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         top

```       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         top

```       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         top

```       See the EXAMPLES section in atan2().
```

## APPLICATION USAGE         top

```       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         top

```       None.
```

## FUTURE DIRECTIONS         top

```       None.
```

```       atan2(3p), feclearexcept(3p), fetestexcept(3p), isnan(3p), sqrt(3p)

The Base Definitions volume of POSIX.1‐2008, Section 4.19, Treatment
of Error Conditions for Mathematical Functions, math.h(0p)
```

```       Portions of this text are reprinted and reproduced in electronic form
from IEEE Std 1003.1, 2013 Edition, Standard for Information
Technology -- Portable Operating System Interface (POSIX), The Open
Group Base Specifications Issue 7, Copyright (C) 2013 by the
Institute of Electrical and Electronics Engineers, Inc and The Open
Group.  (This is POSIX.1-2008 with the 2013 Technical Corrigendum 1
applied.) 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.unix.org/online.html .