/

(/ number &rest numbers)

Divides the first argument by the rest, left to right; with one argument returns its reciprocal. Integer division is exact: when the result is not a whole number it is returned as a reduced ratio rather than truncated, and an evenly dividing pair yields an integer. If any argument is a float the result is a float. The division runs one pair at a time, so the arguments ahead of the first float divide exactly and only their quotient turns into a float: (/ 1/10 1/3 1.0) is 0.3, as in SBCL. Dividing by an exact zero signals division-by-zero, also ahead of a float ((/ 1 0 2.0)); a pair with a float operand follows IEEE 754 instead, so (/ 1.5 0) and (/ 1 0.0) are infinities and (/ 0.0 0) is NaN.

With a complex argument the division runs one pair at a time and each pair is SBCL's: a complex over a real divides each part by it ((/ #c(1d0 2d0) 3d0) costs one rounding per part, and (/ #c(1d0 2d0) 0d0) is #C(Infinity Infinity), what the real division answers), and a quotient over a complex folds on whichever part of the divisor is larger, so nothing intermediate overflows where the operands themselves are representable: (/ #c(1d200 1d200) #c(1d200 1d200)) is #C(1.0 0.0). An exact operand turns into a float only where it meets one, so exact parts stay exact rationals, an exact step stays exact whatever float follows, and the signed zeros are SBCL's: (/ 1 #c(1.0 0.0)) is #C(1.0 -0.0). An exact zero divisor signals the same division-by-zero error a real one does.