
HYPOT(P) POSIX Programmer's Manual HYPOT(P)
NAME
hypot, hypotf, hypotl  Euclidean distance function
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);
DESCRIPTION
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 nonzero,
an error has occurred.
RETURN VALUE
Upon successful completion, these functions shall return the length of the hypotenuse of a
rightangled 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 is returned.
ERRORS
These functions shall fail if:
Range Error
The result overflows.
If the integer expression (math_errhandling & MATH_ERRNO) is nonzero, then errno shall be
set to [ERANGE]. If the integer expression (math_errhandling & MATH_ERREXCEPT) is non
zero, then the overflow floatingpoint exception shall be raised.
These functions may fail if:
Range Error
The result underflows.
If the integer expression (math_errhandling & MATH_ERRNO) is nonzero, then errno shall be
set to [ERANGE]. If the integer expression (math_errhandling & MATH_ERREXCEPT) is non
zero, then the underflow floatingpoint exception shall be raised.
The following sections are informative.
EXAMPLES
None.
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 compu
tation.
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 nonzero.
RATIONALE
None.
FUTURE DIRECTIONS
None.
SEE ALSO
feclearexcept() , fetestexcept() , isnan() , sqrt() , the Base Definitions volume of
IEEE Std 1003.12001, Section 4.18, Treatment of Error Conditions for Mathematical Func
tions, <math.h>
COPYRIGHT
Portions of this text are reprinted and reproduced in electronic form from IEEE Std
1003.1, 2003 Edition, Standard for Information Technology  Portable Operating System
Interface (POSIX), The Open Group Base Specifications Issue 6, Copyright (C) 20012003 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 orig
inal Standard can be obtained online at http://www.opengroup.org/unix/online.html .
IEEE/The Open Group 2003 HYPOT(P) 
