⌊ — Floor / Minimum

Function. Keys: Alt-d. Hanzi: 下. Ranks: 0 monadic, 0 0 dyadic

⌊Y rounds real numbers down. Pervasive; tolerant near integers. Under dynamic kinds, real float results become ordinary machine integers. Under static kinds they remain floats. ⌊ₓY gives ordinary machine integers in both modes. Exact-domain inputs stay exact.

Integer-producing real forms clamp to the selected integer range: positive infinity gives its maximum, negative infinity its minimum, and NaN gives zero. See Static kinds for the integer width.

⌊1.8 ¯1.8         ⍝ [1 ¯2]ₓ
⌊3r2              ⍝ 1ᵣ

Complex floor uses APL’s Gaussian-integer rule.

⌊1.5j0.5          ⍝ 1j1

X⌊Y takes the real minimum, and for characters the one with the lower code point. A number is less than any character, as ⍋ orders them. Pervasive. Beside NaN it gives NaN or the other argument. Which one can vary by platform. A reduction, scan, window or inner product by ⌊, or a write by ⌊← to one position more than once, gives NaN or the least of the items that aren’t NaN, ∞ where there are none, and never another number. Empty reduction identity: ∞.

3⌊1 5             ⍝ 1 3
"abc"⌊"bab"       ⍝ "aab"
3⌊'a'             ⍝ 3