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 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 is 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

       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 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

       feclearexcept()  ,  fetestexcept()  ,   isnan()   ,   sqrt()   ,   the   Base   Definitions   volume   of
       IEEE Std 1003.1-2001, Section 4.18, 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, 2003 Edition,
       Standard for Information Technology -- Portable Operating System Interface (POSIX), The Open  Group  Base
       Specifications Issue 6, Copyright (C) 2001-2003 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 .