# FreeBSD Manual Pages

```HYPOT(3)	       FreeBSD Library Functions Manual		      HYPOT(3)

NAME
hypot, hypotf, hypotl, cabs, cabsf, cabsl -- Euclidean distance and com-
plex absolute value functions

LIBRARY
Math Library (libm, -lm)

SYNOPSIS
#include <math.h>

double
hypot(double x, double y);

float
hypotf(float x, float y);

long double
hypotl(long double	x, long	double y);

#include <complex.h>

double
cabs(double complex z);

float
cabsf(float complex z);

long double
cabsl(long	double complex z);

DESCRIPTION
The hypot(), hypotf() and hypotl()	functions compute the sqrt(x*x+y*y) in
such a way	that underflow will not	happen,	and overflow occurs only if
the final result deserves it.  The	cabs(),	cabsf()	and cabsl() functions
compute the complex absolute value	of z.

hypot(infinity, v)	= hypot(v, infinity) = +infinity for all v, including
NaN.

ERROR (due to Roundoff,	etc.)
Below 0.97	ulps.  Consequently hypot(5.0, 12.0) = 13.0 exactly; in	gen-
eral, hypot and cabs return an integer whenever an	integer	might be ex-
pected.

NOTES
As	might be expected, hypot(v, NaN) and hypot(NaN,	v) are NaN for all
finite v.	But programmers	might be surprised at first to discover	that
hypot(+-infinity, NaN) = +infinity.  This is intentional; it happens be-
cause hypot(infinity, v) =	+infinity for all v, finite or infinite.
Hence hypot(infinity, v) is independent of	v.  Unlike the reserved	oper-
and fault on a VAX, the IEEE NaN is designed to disappear when it turns
out to be irrelevant, as it does in hypot(infinity, NaN).

SEE ALSO
carg(3), math(3), sqrt(3)

STANDARDS
The hypot(), hypotf(), hypotl(), cabs(), cabsf(), and cabsl() functions
conform to	ISO/IEC	9899:1999 ("ISO	C99").

HISTORY
Both a hypot() function and a cabs() function appeared in Version 7 AT&T
UNIX.

FreeBSD	13.0			March 30, 2008			  FreeBSD 13.0
```

NAME | LIBRARY | SYNOPSIS | DESCRIPTION | ERROR (due to Roundoff, etc.) | NOTES | SEE ALSO | STANDARDS | HISTORY

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