abs number → absolute-value

number — a number.

absolute-value — a non-negative real.

abs returns the absolute value of number.

If number is a real, the result is of the same type as number.

If number is a complex, the result is a positive real with the same magnitude as number. The result can be a float even if number’s components are rationals and an exact rational result would have been possible. Thus the result of (abs #c(3 4)) can be either 5 or 5.0, depending on the implementation.

(abs 0) → 0 
(abs 12/13) → 12/13 
(abs -1.09) → 1.09 
(abs #c(5.0 -5.0)) → 7.071068 
(abs #c(5 5)) → 7.071068 
(abs #c(3/5 4/5)) → 1 or approximately 1.0 
(eql (abs -0.0) -0.0) → true

Section 12.1.3.3 (Rule of Float Substitutability)

If number is a complex, the result is equivalent to the following:

(sqrt (+ (expt (realpart number) 2) (expt (imagpart number) 2)))

An implementation should not use this formula directly for all complexes but should handle very large or very small components specially to avoid intermediate overflow or underflow.