signum number => signed-prototype
number---a number.
signed-prototype---a number.
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.
(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
section Rule of Float Substitutability
(signum x) == (if (zerop x) x (/ x (abs x)))
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