PROLOG

       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

       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

       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.1‐2017 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

       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

       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

       See the EXAMPLES section in atan2().

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

       atan2(), feclearexcept(), fetestexcept(), isnan(), sqrt()

       The Base Definitions volume of POSIX.1‐2017, Section 4.20, Treatment of  Error  Conditions
       for Mathematical Functions, <math.h>

COPYRIGHT

       Portions  of  this  text  are  reprinted  and  reproduced in electronic form from IEEE Std
       1003.1-2017, Standard for Information Technology -- Portable  Operating  System  Interface
       (POSIX),  The  Open Group Base Specifications Issue 7, 2018 Edition, Copyright (C) 2018 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 .

       Any  typographical  or  formatting errors that appear in this page are most likely to have
       been introduced during the conversion of the source files to man page  format.  To  report
       such errors, see https://www.kernel.org/doc/man-pages/reporting_bugs.html .