# hypot

## 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
           _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 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.
    


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