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 .