For real numbers, R is the largest integer value less than or equal to Y within the comparison tolerance ⎕CT.
Examples
⌊¯2.3 0.1 100 3.3 ¯3 0 100 3 ⌊0.5 + 0.4 0.5 0.6 0 1 1
For complex numbers, R depends on the relationship between the real and imaginary parts of the numbers in Y.
⌊1j3.2 3.3j2.5 ¯3.3j¯2.5 1J3 3J2 ¯3J¯3
Complex Floor
The following (deliberately) simple function illustrates one way to express the rules for evaluating complex Floor.
∇ fl←CpxFloor cpxs;a;b [1] ⍝ Complex floor of scalar complex number (a+ib) [2] a b←9 11○cpxs [3] :If 1>(a-⌊a)+b-⌊b [4] fl←(⌊a)+0J1×⌊b [5] :Else [6] :If (a-⌊a)<b-⌊b [7] fl←(⌊a)+0J1×1+⌊b [8] :Else [9] fl←(1+⌊a)+0J1×⌊b [10] :EndIf [11] :EndIf ∇ CpxFloor¨1j3.2 3.3j2.5 ¯3.3j¯2.5 1J3 3J2 ¯3J¯3
⎕CT and ⎕DCT are implicit arguments of Floor.