signum (Function)

Syntax:

Arguments and Values:

number—a number.

signed-prototype—a number.

Description:

signum determines a numerical value that indicates whether number is negative, zero, or positive.

For a rational, signum returns one of -1, 0, or 1 according to whether number is negative, zero, or positive. For a float, the result is a float of the same format whose value is minus one, zero, or one. For a complex number z, (signum z) is a complex number of the same phase but with unit magnitude, unless z is a complex zero, in which case the result is z.

For rational arguments, signum is a rational function, but it may be irrational for complex arguments.

If number is a float, the result is a float. If number is a rational, the result is a rational. If number is a complex float, the result is a complex float. If number is a complex rational, the result is a complex, but it is implementation-dependent whether that result is a complex rational or a complex float.

Examples:

 (signum 0) → 0
 (signum 99) → 1
 (signum 4/5) → 1
 (signum -99/100) → -1
 (signum 0.0) → 0.0
 (signum #c(0 33)) → #C(0.0 1.0)
 (signum #c(7.5 10.0)) → #C(0.6 0.8)
 (signum #c(0.0 -14.7)) → #C(0.0 -1.0)
 (eql (signum -0.0) -0.0) → true

See Also:

Section 12.1.3.3 (Rule of Float Substitutability)

Notes:

 (signum x) ≡ (if (zerop x) x (/ x (abs x)))