Sign function

In mathematics and especially in computer science, the sign function is a logical function which extracts the sign of a real number. The sign function is often represented as sgn and can be defined thus:

${\hbox{sgn}}x=1\qquad \qquad {\hbox{if}}x>0,$

${\hbox{sgn}}x=-1\qquad \qquad {\hbox{if}}x<0,$

${\hbox{sgn}}0=0.$

Any real number can be expressed as the product of its absolute value and its sign function:

$x=({\hbox{sgn}}x)|x|$.