+ Add∙ Alternant∧ And≈ Approximate∡ Arctangent⎕ Array Input@ At⍥ At Depth⍤ At Rank∘ Atop⤺ Backward∘ Bind! Binomial∵ Bitwiseᑣ Boxed⊕ Cartesian× Case| Case Fold⎊ Catch⍪ Catenate⌈ Ceilingᓗ Cells Leftᓚ Cells Right⍞ Character Input⍨ Commute+ Conjugate⍨ Constant⍫ Contextual Under⋵ Count? Deal⊥ Decodeⵧ Decrement○ Default Bind⍜ Default Reverse Bind∨ Demote⩔ Denominator≡ Depth⊩ Dex~ Difference× Direction÷ Divide↓ Drop⍨ Duplicate¨ Eachᐵ Each Leftᑈ Each Right∊ Element Of∻ Empty Dictionary⍬ Empty Vector⊂ Enclose⊤ Encode∊ Enlist= Equal To⍎ Execute* Exponential! Factorial⬚ Fill⍷ Find⊃ First> First Cell⌊ Floor/ Fold«» Fork⍕ Format⊇ From‥ From Inverted Table‥ From Keys And Values߹ From Pairs⍒ Grade Down⍋ Grade Up> Greater Than≥ Greater Than or Equal To⩔ Greatest Common Divisor⫇ Group⋵ Histogram⫤ Ident≡ Identicalℑ Imaginary Part⧺ Increment⌷ Index⍳ Index Generator⍳ Index Of∙ Inner Product∩ Intersection⍸ Interval Index˝ Inverse⍉ Inverted Table⍪ Join⌸ Key⌸ Key With Vocabulary߹ Key-Value Pair↓ Key-Value Pairs⊃ Keys, Laminate⊇ Last≥ Last Cell⩓ Least Common Multiple⊣ Left⇾ Left Fork⊸ Left Hook< Less Than≤ Less Than or Equal To⫣ Lev⍟ Logarithm⌊ Lowercase| Magnitude↓ Major Cells⋷ Mask⌹ Matrix Divide⌹ Matrix Inverse↾ Maximal⌈ Maximum⇂ Minimal⌊ Minimum⸚ Mirror↑ Mix× Multiply⍦ Multisets⍲ Nand⍟ Natural Logarithm- Negate⊆ Nest⍱ Nor~ Not≠ Not Equal To≢ Not Identical≠ Nub Sieve⩓ Numerator◡ On Cellsᑒ On Contents⍦ On Counts⌺ On Infixes⥽ On Left⌺ On Pairs\ On Prefixes⥼ On Right◠ On Scalars⌓ On Simple Scalars… One Range∨ Or⑴ Origin One○ Over⍮ Pair⊆ Partition⊂ Partitioned Enclose∡ Phase⊃ Pick⊗ Polar* Power⊲ Precedes⊴ Precedes Or Identical∧ Promote⊕ Pure Imaginary⨳ Raise↗ Raises… Rangeϼ Rank, Ravelℜ Real Part÷ Reciprocal/ Reduce| Remainder⍣ Repeat⌿ Replicateϼ Rerank⍴ Reshape⌽ Reverse⍛ Reverse Atop⍛ Reverse Bind⍜ Reverse Over⊢ Right⇽ Right Fork⟜ Right Hook? Roll√ Root⌽ Rotate⸠ Round⸠ Round To Nearest⍴ Shape⍮ Singleton⍒ Sort By Down⍋ Sort By Up⊵ Sort Down⊴ Sort Upⵧ Span↗ Square√ Square Root⍞ Standard Error⎕ Standard Output- Subtract⊳ Succeeds⊵ Succeeds Or Identical§ Symmetric Difference⊞ Table↑ Take≢ Tally⍉ Transpose⍢ Under∪ Union∪ Unique⊗ Unit Polar⍣ Until⌈ Uppercase⁖ Valences⊇ Values⍸ Where⎕_BinFile Binary File⎕Assert Assert⎕CSV CSV⎕ct Comparison Tolerance⎕d Digits⎕Delay Delay⎕DT Date Time⎕Exists Exists⎕ffi FFI Helpers⎕FFI FFI⎕file→Read File⎕file→Write File⎕HTTP HTTP⎕Import Import⎕io Index Origin⎕JSON JSON⎕l Lowercase Alphabet⎕math→Arccos Arccosine⎕math→Arcosh Hyperbolic Arcosine⎕math→Arcsin Arcsine⎕math→Arctan Arctangent⎕math→Arsinh Hyperbolic Arsine⎕math→Artanh Hyperbolic Artangent⎕math→Complementary Complementary⎕math→Cos Cosine⎕math→Cosh Hyperbolic Cosine⎕math→pi Pi⎕math→Sin Sine⎕math→Sinh Hyperbolic Sine⎕math→Tan Tangent⎕math→Tanh Hyperbolic Tangent⎕Repr Representation⎕seed Seed⎕systemInfo System Information⎕this This⎕ts Timestamp⎕Type Type⎕u Uppercase Alphabet⎕Unicode Unicode⎕unix Unix Timestamp@ At\ Backslashℑ Black Iℜ Black R○ Circle⍉ Circle Backslash⊗ Circle Cross⍥ Circle Dots⊕ Circle Plus⍟ Circle Star⌽ Circle Stile⎊ Circle Triangle⍜ Circle Underbar߹ Colon Overbar∻ Colon Tilde, Comma⍪ Comma Bar× Cross- Dash⸚ Dash Dots⸠ Dash Stile⍢ Del Dots⍒ Del Stile⍫ Del Tilde¨ Dots⬚ Dotted Square˝ Double Acute⨳ Double Cross⩔ Double Down Wedge⫤ Double Left Tack« Double Left Wedgeⵧ Double Minus⧺ Double Plus» Double Right Wedge⩓ Double Up Wedge↓ Down Arrow◡ Down Circle∪ Down Shoe⍦ Down Shoe Stile⌊ Down Stile⊤ Down Tack⍕ Down Tack Jot∨ Down Wedge⍱ Down Wedge Tilde… Ellipsis∊ Epsilon⋵ Epsilon Dot⋷ Epsilon Overbar⍷ Epsilon Underbar= Equal≠ Equal Slash≡ Equal Underbar≢ Equal Underbar Slash! Exclamation Mark⌓ Half Circle⇂ Half Down Arrow↾ Half Up Arrow⍳ Iota⍸ Iota Underbar∘ Jot⍤ Jot Dots⍛ Jot Underbarᓚ Left Circle⥼ Left Fish Tail⟜ Left Jot⊂ Left Shoeᑣ Left Shoe Dots⫇ Left Shoe Tilde⊆ Left Shoe Underbar⊣ Left Tack⫣ Left Tack Stile⊲ Left Triangle⊴ Left Triangle Underbar< Left Wedgeᑈ Left Wedge Dots≤ Left Wedge Underbar∡ Marked Angle∙ Middle Dot÷ Obelus⑴ One Parens+ Plus⎕ Quad⌺ Quad Diamond⌸ Quad Equal⌹ Quad Obelus⍞ Quad Quote? Question Mark⍴ Rhoϼ Rho Underbarᓗ Right Circle⥽ Right Fish Tail⊸ Right Jot⊃ Right Shoeᑒ Right Shoe Dots⊇ Right Shoe Underbar⊢ Right Tack⊩ Right Tack Stile⊳ Right Triangle⊵ Right Triangle Underbar> Right Wedgeᐵ Right Wedge Dots≥ Right Wedge Underbar√ Root§ Section⍮ Semicolon Underbar/ Slash⌿ Slash Bar⌷ Squad⊞ Square Plus* Star⍣ Star Dots| Stile⍋ Stile Delta∵ Three Dots Down⁖ Three Dots Left~ Tilde⍨ Tilde Dots‥ Two Dots≈ Two Tildes↑ Up Arrow◠ Up Circle⤺ Up Circle Anticlockwise↗ Up Right Arrow∩ Up Shoe⌈ Up Stile⊥ Up Tack⍎ Up Tack Jot∧ Up Wedge⍲ Up Wedge Tilde⇽ White Left Arrow⇾ White Right Arrow⍬ Zero Tilde⌊ Floor r←⌊yr is the result of the scalar application of the floor function, ⌊y⌋.
The complex floor is defined by McDonnell as such:
a and b be the real and imaginary parts of yx be 1|a and y be 1|bp be a⊕○⌊b, where the floor is the usual real floorx + y is less than 1, r is px is greater than or equal to y, r is p+1r is p+0ᴊ1