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NAME

hypot, hypotf, hypotl - Euclidean distance function

SYNOPSIS

#include <math.h> double hypot(doublex, doubley); float hypotf(floatx, floaty); long double hypotl(long doublex, long doubley);

DESCRIPTION

^[CX] The functionality described on this reference page is aligned with the ISO C standard. Any conflict between therequirements described here and the ISO C standard is unintentional. This volume of POSIX.1-2017 defers to the ISO Cstandard.
These functions shall compute the value of the square root ofx²+y² without undue overflow or underflow.
An application wishing to check for error situations should seterrno to zero and callfeclearexcept(FE_ALL_EXCEPT) before calling these functions. On return, iferrno is non-zero orfetestexcept(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 oflengthx andy.
If the correct value would cause overflow, a range error shall occur andhypot(),hypotf(), andhypotl()shall return the value of the macro HUGE_VAL, HUGE_VALF, and HUGE_VALL, respectively.
^[MX] Ifx ory is ±Inf, +Inf shall be returned (even if one ofx ory is NaN).
Ifx ory is NaN, and the other is not ±Inf, a NaN shall be returned.
^[MXX]If both arguments are subnormal and the correct result is subnormal, a range error may occur and the correct result shall bereturned.

ERRORS

These functions shall fail if:
Range Error
The result overflows.
If the integer expression (math_errhandling & MATH_ERRNO) is non-zero, thenerrno shall be set to [ERANGE]. Ifthe integer expression (math_errhandling & MATH_ERREXCEPT) is non-zero, then the overflow floating-point exception shallbe raised.
These functions may fail if:
Range Error
^[MX]The result underflows.
If the integer expression (math_errhandling & MATH_ERRNO) is non-zero, thenerrno shall be set to [ERANGE]. Ifthe integer expression (math_errhandling & MATH_ERREXCEPT) is non-zero, then the underflow floating-point exceptionshall be raised.

The following sections are informative.

EXAMPLES

See the EXAMPLES section inatan2().

APPLICATION USAGE

hypot(x,y),hypot(y,x), andhypot(x, -y) are equivalent.
hypot(x, ±0) is equivalent tofabs(x).
Underflow only happens when bothx andy 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) areindependent of each other, but at least one of them must be non-zero.

RATIONALE

None.

FUTURE DIRECTIONS

None.

CHANGE HISTORY

First released in Issue 1. Derived from Issue 1 of the SVID.

Issue 5

The DESCRIPTION is updated to indicate how an application should check for an error. This text was previously published in theAPPLICATION USAGE section.

Issue 6

Thehypot() function is no longer marked as an extension.
Thehypotf() andhypotl() functions are added for alignment with the ISO/IEC 9899:1999 standard.
The DESCRIPTION, RETURN VALUE, ERRORS, and APPLICATION USAGE sections are revised to align with the ISO/IEC 9899:1999standard.
IEC 60559:1989 standard floating-point extensions over the ISO/IEC 9899:1999 standard are marked.
IEEE Std 1003.1-2001/Cor 2-2004, item XSH/TC2/D6/49 is applied, updating the EXAMPLES section.