diff options
Diffstat (limited to 'std/Number.bruijn')
| -rw-r--r-- | std/Number.bruijn | 59 |
1 files changed, 34 insertions, 25 deletions
diff --git a/std/Number.bruijn b/std/Number.bruijn index 812a5c4..f6aba7d 100644 --- a/std/Number.bruijn +++ b/std/Number.bruijn @@ -70,6 +70,12 @@ down [~(0 z a⁻ a⁺ a⁰)] a⁺ [0 [[↑⁺1 : 1]]] a⁰ [0 [[↑⁰1 : 1]]] +# infinity +# WARNING: using this mostly results in undefined behavior! (TODO?) +infty z [[[[[1 (4 1)]]]]] + +∞ infty + # negates a balanced ternary number negate [[[[[4 3 1 2 0]]]]] @@ -152,6 +158,7 @@ zero? [0 true [false] [false] i] :test (=?(+42)) (false) # converts the normal balanced ternary representation into abstract +# infinity can't be abstracted in finite time # → the abstract representation is used in eq?/add/sub/mul abstract! [0 z a⁻ a⁺ a⁰] z (+0) @@ -166,9 +173,11 @@ abstract! [0 z a⁻ a⁺ a⁰] :test (→^(+3)) ([[[[0 [[[[1 [[[[3]]]]]]]]]]]]) # converts the abstracted balanced ternary representation back to normal -# using ω to solve recursion -normal! ω rec - rec [[0 (+0) [↑⁻([3 3 0] 0)] [↑⁺([3 3 0] 0)] [↑⁰([3 3 0] 0)]]] +normal! ω [[0 z a⁻ a⁺ a⁰]] + z (+0) + a⁻ [↑⁻([3 3 0] 0)] + a⁺ [↑⁺([3 3 0] 0)] + a⁰ [↑⁰([3 3 0] 0)] →_‣ normal! @@ -188,7 +197,7 @@ eq? [[abs 1 →^0]] …=?… eq? -…/=?… not! .. eq? +…/=?… not! ∘∘ eq? :test ((-42) =? (-42)) (true) :test ((-1) =? (-1)) (true) @@ -216,7 +225,7 @@ inc [~(0 z a⁻ a⁺ a⁰)] ++‣ inc # adds (+1) to a balanced ternary number and strips leading 0s -ssinc strip . inc +ssinc strip ∘ inc :test ((++(-42)) =? (-41)) (true) :test ((++(-1)) =? (+0)) (true) @@ -234,7 +243,7 @@ dec [~(0 z a⁻ a⁺ a⁰)] --‣ dec # subs (+1) from a balanced ternary number and strips leading 0s -sdec strip . dec +sdec strip ∘ dec :test ((--(-42)) =? (-43)) (true) :test ((--(+0)) =? (-1)) (true) @@ -243,7 +252,7 @@ sdec strip . dec :test ((--(+42)) =? (+41)) (true) # adds two balanced ternary numbers (can introduce leading 0s) -# larger numbers should be second argument (performance) +# second argument gets abstracted (performance) add [[abs 1 →^0]] abs [c (0 z a⁻ a⁺ a⁰)] b⁻ [1 ↑⁺(3 0 t⁻) ↑⁰(3 0 t⁰) ↑⁻(3 0 t⁰)] @@ -260,7 +269,7 @@ add [[abs 1 →^0]] …+… add # adds two balanced ternary numbers and strips leading 0s -sadd strip .. add +sadd strip ∘∘ add :test (((-42) + (-1)) =? (-43)) (true) :test (((-5) + (+6)) =? (+1)) (true) @@ -270,13 +279,13 @@ sadd strip .. add :test (((+42) + (+1)) =? (+43)) (true) # subs two balanced ternary numbers (can introduce leading 0s) -# larger numbers should be second argument (performance) +# second argument gets abstracted (performance) sub [[1 + -0]] …-… sub # subs two balanced ternary numbers and strips leading 0s -ssub strip .. sub +ssub strip ∘∘ sub :test (((-42) - (-1)) =? (-41)) (true) :test (((-5) - (+6)) =? (-11)) (true) @@ -285,6 +294,21 @@ ssub strip .. sub :test (((+1) - (+2)) =? (-1)) (true) :test (((+42) - (+1)) =? (+41)) (true) +# muls two balanced ternary numbers (can introduce leading 0s) +mul [[1 (+0) a⁻ a⁺ a⁰]] + a⁻ [↑⁰0 - 1] + a⁺ [↑⁰0 + 1] + a⁰ [↑⁰0] + +…*… mul + +smul strip ∘∘ mul + +:test (((+42) * (+0)) =? (+0)) (true) +:test (((-1) * (+42)) =? (-42)) (true) +:test (((+3) * (+11)) =? (+33)) (true) +:test (((+42) * (-4)) =? (-168)) (true) + # returns true if number is greater than other number # larger numbers should be second argument (performance) gre? [[>?(1 - 0)]] @@ -330,18 +354,3 @@ max [[(1 ≤? 0) 0 1]] # returns min number of two min [[(1 ≤? 0) 1 0]] - -# muls two balanced ternary numbers (can introduce leading 0s) -mul [[1 (+0) a⁻ a⁺ a⁰]] - a⁻ [↑⁰0 - 1] - a⁺ [↑⁰0 + 1] - a⁰ [↑⁰0] - -…*… mul - -smul strip .. mul - -:test (((+42) * (+0)) =? (+0)) (true) -:test (((-1) * (+42)) =? (-42)) (true) -:test (((+3) * (+11)) =? (+33)) (true) -:test (((+42) * (-4)) =? (-168)) (true) |