bt{⎕IO ⎕ML←0 1                         ⍝ Balanced Ternary Arithmetic.

    monadic{                           ⍝ ⍺⍺ ⍵, where ⍺⍺ ∊ +-×|
        fn←⍺⍺{aa←⍺⍺ ⋄ ⊃⎕CR'aa'}⍵        ⍝ char rep of operand function.
        '+'≡fn:⍵                        ⍝ identity.
        '-'≡fn:-⍵                       ⍝ negative.
        '×'≡fn:1↑⍵                      ⍝ signum.
        '|'≡fn:⍵×⊃⍵                     ⍝ abs value.
        '⊤'≡fn:encode ⍵                 ⍝ encode BT from int.
        '⊥'≡fn:3⊥⍵                      ⍝ decode int from BT.
        err'Can''t do: ',fn             ⍝ :-(
    }                                   ⍝ :: ∇ bt → bt

    dyadic{                            ⍝ ⍺ ⍺⍺ ⍵, where ⍺⍺ ∊ +-×÷|* ...
        fn←⍺⍺{aa←⍺⍺ ⋄ ⊃⎕CR'aa'}⍵        ⍝ char rep of operand function.
        '+'≡fn:⍺ add ⍵                  ⍝ sum.
        '-'≡fn:⍺ add-⍵                  ⍝ difference.
        '×'≡fn:⍺ mul ⍵                  ⍝ product.
        '÷'≡fn:norm 0⊃⍺ div ⍵           ⍝ quotient.
        '|'≡fn:⍺ res ⍵                  ⍝ residue.
        '*'≡fn:⍺ pow ⍵                  ⍝ power.
        '<≤=≥>≠'∊⍨fn:⍺ ⍺⍺ cmp ⍵         ⍝ relational.
        '⌊'≡fn:(1+⊃⍺ add-⍵)⊃⍺ ⍺ ⍵       ⍝ min.
        '⌈'≡fn:(1+⊃⍺ add-⍵)⊃⍵ ⍺ ⍺       ⍝ max.
        '∨'≡fn:⍺ gcd ⍵                  ⍝ greatest common divisor.
        '∧'≡fn:⍺ lcm ⍵                  ⍝ least common multiple.
        err'Can''t do: ',fn             ⍝ :-(
    }                                   ⍝ :: bt ∇ bt → bt

    div←{                               ⍝ quotient ⍺÷⍵.
        ⍺≡⍵:1 0                         ⍝ ⍵÷⍵ → 1r0 (includes 0÷0 → 1r0).
        ⍵ is 0:err'Divide by zero'      ⍝ ÷0 error.
        q←⍵                             ⍝ named divisor (invariant).
        part(⍴⍺)⌊⍴⍵                    ⍝ dividend partition size.
        0{                              ⍝ result.
            p s←⍵                       ⍝ partitioned dividend.
            m←×/⊃¨p q                   ⍝ multiple: ¯1, 0 or 1.
            i←{(0≤⊃⍺)∧⍺<cmp ⍵}/p q×⊃q   ⍝ p in interval 0≤p<q?
            ~i:(add m)(p add-m×q)s   ⍝ no: r+←m ⋄ p-←m×q
            ⍬≡s:⍺ p                     ⍝ s exhausted: quotient and remainder.
            (⍺,0)(tlz p,1↑s)(1↓s)      ⍝  r×←3 ⋄ p,← next digit.
        }(part↑⍺)(part↓⍺)               ⍝ partitioned dividend.
    }                                   ⍝ :: bt ∇ bt → bt bt

    res←{                               ⍝ residue.
        ⍺ is 0:⍵                        ⍝ 0|⍵ → ⍵
        norm 1⊃⍵ div ⍺                  ⍝ otherwise: remainder from ⍺÷⍵.
    }                                   ⍝ :: bt ∇ bt → bt

    pow←{                               ⍝ power: ⍺*⍵.
        ¯1=⊃⍵:err'Negative power'       ⍝ no negative powers.
        ⍵ is 0:,1                       ⍝ ⍺*0 → 1
        ⍵ is 1:⍺                        ⍝ ⍺*1 → ⍺
        ⍵ is 1 ¯1:⍺ mul ⍺               ⍝ ⍺*2 → ⍺×⍺
        p←⍵ add ¯1                      ⍝ predecessor.
        q r←⍺∘∇¨(¯1↓p)(1 add ¯1↑p)      ⍝ 0 3⊤⍵ → quotient, remainder.
        r mul q mul q mul q             ⍝ ⍺*⍵ → (⍺*3|⍵)×{⍵×⍵×⍵}⍺*⌊⍵÷3
    }                                   ⍝ :: bt ∇ bt → bt

    gcd←{                               ⍝ greatest common divisor (Euclid).
        ⍵ is 0:⍺×⊃⍺                     ⍝ ⍺∨0 → |⍺
        ⍵ ∇ norm 1⊃⍺ div ⍵              ⍝ ⍵∨⍵|⍺
    }                                   ⍝ :: bt ∇ bt → bt

    encode←{                            ⍝ balanced ternary from integer.
        digs←1+⌈3⍟1⌈|⍵                  ⍝ number of ternary digits.
        tlz ¯1+(digs⍴3)⊤⍵+3⊥digs⍴1      ⍝ vector of bt digits.
    }                                   ⍝ :: ∇ num → bt

    norm←{                              ⍝ digit-overflow normalisation.
        2∧.>|⍵:tlz ⍵                    ⍝ normal: done.
        ∇ ¯1++⌿1 0⌽0 3⊤1+0,⍵            ⍝ carry overflow and try again.
    }                                   ⍝ :: ∇ bt → bt

    add←{norm+⌿⍺ mat ⍵}                 ⍝ sum.
    mul←{norm+⌿(⌽⍳⍴⍺)⌽⍺∘.×(0×1↓⍺),⍵}    ⍝ product.
    lcm←{⍺ mul norm 0⊃⍵ divgcd ⍵}    ⍝ least common multiple.
    cmp{⍺⍺{⍺⍺/,(<\∨\≠⌿⍵)/⍵}mat}    ⍝ relational functions.
    mat←{⌽↑⌽¨⍺ ⍵}                       ⍝ right-aligned matrix.
    tlz←{(-1⌈+/∨\0≠⍵)↑⍵}                ⍝ without superfluous leading zeros.
    is←{∧/=⌿⍺ mat ⍵}                    ⍝ comparison.
    err←⎕SIGNAL∘11                      ⍝ stop with error msg ⍵.

    0=⎕NC'⍺':⍺⍺ monadic ⍵               ⍝ monadic:
    ⍺ ⍺⍺ dyadic ⍵                       ⍝ dyadic:
}
code_colours

test script

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