diff options
Diffstat (limited to 'std/Number/Ternary.bruijn')
| -rw-r--r-- | std/Number/Ternary.bruijn | 273 |
1 files changed, 82 insertions, 191 deletions
diff --git a/std/Number/Ternary.bruijn b/std/Number/Ternary.bruijn index 03af0e9..27da643 100644 --- a/std/Number/Ternary.bruijn +++ b/std/Number/Ternary.bruijn @@ -79,61 +79,19 @@ t⁰? [0 false false true] ⧗ Trit → Boolean # rshifts a zero trit into a balanced ternary number (pad) →⁰‣ [[[[[4 (0 3) 2 1 0]]]]] ⧗ Number → Number -# infinity -# WARNING: using this mostly results in undefined behavior! (TODO?) -infty z [[[[[1 (4 1)]]]]] ⧗ Number - -# negates a balanced ternary number -negate [[[[[4 3 1 2 0]]]]] ⧗ Number → Number - --‣ negate - -:test (-(+0)) ((+0)) -:test (-(-1)) ((+1)) -:test (-(+42)) ((-42)) - -# converts a balanced ternary number to a list of trits -number→trits [0 z a⁻ a⁺ a⁰] ⧗ Number → (List Trit) - z [[0]] - a⁻ pair t⁻ - a⁺ pair t⁺ - a⁰ pair t⁰ - -:test (number→trits (+0)) ([[0]]) -:test (number→trits (+5)) (t⁻ : (t⁻ : (t⁺ : [[0]]))) - -# strips leading 0s from a balanced ternary number -strip [^(0 z a⁻ a⁺ a⁰)] ⧗ Number → Number - z (+0) : true - a⁻ &[[↑⁻1 : false]] - a⁺ &[[↑⁺1 : false]] - a⁰ &[[(0 (+0) ↑⁰1) : 0]] - -%‣ strip - -:test (%[[[[0 3]]]]) ((+0)) -:test (%[[[[2 (0 (0 (0 (0 3))))]]]]) ((-1)) -:test (%(+42)) ((+42)) - -# returns true if balanced ternary number is zero -zero? [0 true [false] [false] i] ⧗ Number → Boolean - -=?‣ zero? - -:test (=?(+0)) (true) -:test (=?(-1)) (false) -:test (=?(+1)) (false) -:test (=?(+42)) (false) - -# returns true if balanced ternary number is not zero -not-zero? [0 false [true] [true] i] ⧗ Number → Boolean +# rshifts least significant trit of a balanced ternary number +# WARNING: Not necessarily equivalent to (/ (+3)): e.g. /³(+5) == (+2)! +div³ [~(0 z a⁻ a⁺ a⁰)] ⧗ Number → Number + z (+0) : (+0) + a⁻ &[[↑⁻1 : 1]] + a⁺ &[[↑⁺1 : 1]] + a⁰ &[[↑⁰1 : 1]] -≠?‣ not-zero? +/³‣ div³ -:test (≠?(+0)) (false) -:test (≠?(-1)) (true) -:test (≠?(+1)) (true) -:test (≠?(+42)) (true) +:test (/³(+6)) ((+2)) +:test (/³(-6)) ((-2)) +:test (/³(+5)) ((+2)) # extracts least significant trit from a balanced ternary number lst [0 t⁰ [t⁻] [t⁺] [t⁰]] ⧗ Number → Trit @@ -169,25 +127,29 @@ mst [B.get t⁰ (0 z a⁻ a⁺ a⁰)] ⧗ Number → Trit :test (mst (+1)) (t⁺) :test (mst (+42)) (t⁺) -# returns true if balanced ternary number is negative -negative? t⁻? ∘ mst ⧗ Number → Boolean +# returns true if balanced ternary number is zero +zero? [0 true [false] [false] i] ⧗ Number → Boolean -<?‣ negative? +=?‣ zero? -:test (<?(+0)) (false) -:test (<?(-1)) (true) -:test (<?(+1)) (false) -:test (<?(+42)) (false) +:test (=?(+0)) (true) +:test (=?(-1)) (false) +:test (=?(+1)) (false) +:test (=?(+42)) (false) -# returns true if balanced ternary number is positive -positive? t⁺? ∘ mst ⧗ Number → Boolean +# returns true if the number is even (remainder mod 2 == 0) +# TODO: faster solution (using tupling?) +even? z [[rec]] ⧗ Number → Boolean + rec =?0 case-end case-rec + case-rec t⁰? (lst 0) (1 /³0) ¬(1 /³0) + case-end true ->?‣ positive? +=²?‣ even? -:test (>?(+0)) (false) -:test (>?(-1)) (false) -:test (>?(+1)) (true) -:test (>?(+42)) (true) +:test (=²?(+0)) (true) +:test (=²?(+1)) (false) +:test (=²?(+41)) (false) +:test (=²?(+42)) (true) # converts the normal balanced ternary representation into abstract # infinity can't be abstracted in finite time @@ -228,25 +190,6 @@ eq? [[abs 1 →^0]] ⧗ Number → Number → Boolean …=?… eq? -# returns true if two balanced ternary numbers are not equal -not-eq? not! ∘∘ eq? ⧗ Number → Number → Boolean - -…≠?… not-eq? - -:test ((-42) =? (-42)) (true) -:test ((-1) =? (-1)) (true) -:test ((-1) =? (+0)) (false) -:test ((+0) =? (+0)) (true) -:test ((+1) =? (+0)) (false) -:test ((+1) =? (+1)) (true) -:test ((+42) =? (+42)) (true) -:test ([[[[(1 (0 (0 (0 (0 3)))))]]]] =? (+1)) (true) -:test ((+1) ≠? (+0)) (true) -:test ((-42) ≠? (+42)) (true) - -# prefix for comparing functions -?‣ &eq? - # adds (+1) to a balanced ternary number (can introduce leading 0s) inc [~(0 z a⁻ a⁺ a⁰)] ⧗ Number → Number z (+0) : (+1) @@ -262,7 +205,7 @@ inc [~(0 z a⁻ a⁺ a⁰)] ⧗ Number → Number :test (++(++(++(++(++(+0))))) =? (+5)) (true) :test (++(+42) =? (+43)) (true) -# subs (+1) from a balanced ternary number (can introduce leading 0s) +# subtracts (+1) from a balanced ternary number (can introduce leading 0s) dec [~(0 z a⁻ a⁺ a⁰)] ⧗ Number → Number z (+0) : (-1) a⁻ &[[↑⁻1 : ↑⁺0]] @@ -300,78 +243,81 @@ add [[abs 1 →^0]] ⧗ Number → Number → Number :test ((+1) + (+2) =? (+3)) (true) :test ((+42) + (+1) =? (+43)) (true) -# subs two balanced ternary numbers (can introduce leading 0s) -sub [[1 + -0]] ⧗ Number → Number → Number - -…-… sub +# returns true if balanced ternary number is negative +negative? t⁻? ∘ mst ⧗ Number → Boolean -:test ((-42) - (-1) =? (-41)) (true) -:test ((-5) - (+6) =? (-11)) (true) -:test ((-1) - (+0) =? (-1)) (true) -:test ((+0) - (+0) =? (+0)) (true) -:test ((+1) - (+2) =? (-1)) (true) -:test ((+42) - (+1) =? (+41)) (true) +<?‣ negative? -# returns true if number is greater than other number -gt? positive? ∘∘ sub ⧗ Number → Number → Boolean +:test (<?(+0)) (false) +:test (<?(-1)) (true) +:test (<?(+1)) (false) +:test (<?(+42)) (false) -…>?… gt? +# returns true if balanced ternary number is positive +positive? t⁺? ∘ mst ⧗ Number → Boolean -:test ((+1) >? (+2)) (false) -:test ((+2) >? (+2)) (false) -:test ((+3) >? (+2)) (true) +>?‣ positive? -# returns true if number is less than other number -lt? \gt? ⧗ Number → Number → Boolean +:test (>?(+0)) (false) +:test (>?(-1)) (false) +:test (>?(+1)) (true) +:test (>?(+42)) (true) -…<?… lt? +# negates a balanced ternary number +negate [[[[[4 3 1 2 0]]]]] ⧗ Number → Number -:test ((+1) <? (+2)) (true) -:test ((+2) <? (+2)) (false) -:test ((+3) <? (+2)) (false) +-‣ negate -# returns true if number is less than or equal to other number -le? not! ∘∘ gt? ⧗ Number → Number → Boolean +:test (-(+0)) ((+0)) +:test (-(-1)) ((+1)) +:test (-(+42)) ((-42)) -…≤?… le? +# subtracts two numbers +sub [[1 + -0]] ⧗ Number → Number → Number -:test ((+1) ≤? (+2)) (true) -:test ((+2) ≤? (+2)) (true) -:test ((+3) ≤? (+2)) (false) +…-… sub -# returns true if number is greater than or equal to other number -ge? \le? ⧗ Number → Number → Boolean +# returns true if number is greater than other number +gt? positive? ∘∘ sub ⧗ Number → Number → Boolean -…≥?… ge? +…>?… gt? -:test ((+1) ≥? (+2)) (false) -:test ((+2) ≥? (+2)) (true) -:test ((+3) ≥? (+2)) (true) +:test ((+1) >? (+2)) (false) +:test ((+2) >? (+2)) (false) +:test ((+3) >? (+2)) (true) # returns eq, gt, lt depending on comparison of two numbers compare-case [[[[[go (1 - 0)]]]]] ⧗ a → b → c → Number → Number → d go [=?0 5 (>?0 4 3)] -# returns 1 if a>b, -1 if a<b and 0 if a=b -# also: spaceship operator -compare compare-case (+0) (+1) (-1) ⧗ Number → Number → Number +# ============================================================================ # +# most relevant functions are defined - we can now derive from Generic/Number! # +# ============================================================================ # -…<=>… compare +:input std/Generic/Number -<=>‣ &compare +# converts a balanced ternary number to a list of trits +number→trits [0 z a⁻ a⁺ a⁰] ⧗ Number → (List Trit) + z [[0]] + a⁻ pair t⁻ + a⁺ pair t⁺ + a⁰ pair t⁰ -:test (compare (+2) (+2)) ((+0)) -:test (compare (+2) (+1)) ((+1)) -:test (compare (+1) (+2)) ((-1)) +:test (number→trits (+0)) ([[0]]) +:test (number→trits (+5)) (t⁻ : (t⁻ : (t⁺ : [[0]]))) -# returns true if comparison result is equal (EQ) -c-eq? eq? (+0) ⧗ Number → Number +# strips leading 0s from a balanced ternary number +strip [^(0 z a⁻ a⁺ a⁰)] ⧗ Number → Number + z (+0) : true + a⁻ &[[↑⁻1 : false]] + a⁺ &[[↑⁺1 : false]] + a⁰ &[[(0 (+0) ↑⁰1) : 0]] -# returns true if comparison result is less than (LT) -c-lt? eq? (-1) ⧗ Number → Number +%‣ strip -# returns true if comparison result is greater than (GT) -c-gt? eq? (+1) ⧗ Number → Number +:test (%[[[[0 3]]]]) ((+0)) +:test (%[[[[2 (0 (0 (0 (0 3))))]]]]) ((-1)) +:test (%(+42)) ((+42)) # negates a balanced ternary number if <0 abs [<?0 -0 0] ⧗ Number → Number @@ -382,23 +328,6 @@ abs [<?0 -0 0] ⧗ Number → Number :test (|(-1)) ((+1)) :test (|(+42)) ((+42)) -# returns max number of two -max [[(1 ≤? 0) 0 1]] ⧗ Number → Number → Number - -:test (max (+5) (+2)) ((+5)) - -# returns min number of two -min [[(1 ≤? 0) 1 0]] ⧗ Number → Number → Number - -:test (min (+5) (+2)) ((+2)) - -# clamps a number between two numbers -clamp [[[min 1 (max 0 2)]]] ⧗ Number → Number → Number - -:test (clamp (+0) (+5) (+3)) ((+3)) -:test (clamp (+0) (+5) (-2)) ((+0)) -:test (clamp (+0) (+5) (+7)) ((+5)) - # apply a function n times to a value # ~> substitute church numbers apply z [[[rec]]] ⧗ Number → (a → a) → a → a @@ -408,7 +337,7 @@ apply z [[[rec]]] ⧗ Number → (a → a) → a → a :test (apply (+5) ++‣ (+3)) ((+8)) -# muls two balanced ternary numbers (can introduce leading 0s) +# multplies two balanced ternary numbers (can introduce leading 0s) mul [[1 z a⁻ a⁺ a⁰]] ⧗ Number → Number → Number z (+0) a⁻ [↑⁰0 - 1] @@ -422,20 +351,6 @@ mul [[1 z a⁻ a⁺ a⁰]] ⧗ Number → Number → Number :test ((+3) ⋅ (+11) =? (+33)) (true) :test ((+42) ⋅ (-4) =? (-168)) (true) -# rshifts least significant trit of a balanced ternary number -# WARNING: Not necessarily equivalent to (/ (+3)): e.g. /³(+5) == (+2)! -div³ [~(0 z a⁻ a⁺ a⁰)] ⧗ Number → Number - z (+0) : (+0) - a⁻ &[[↑⁻1 : 1]] - a⁺ &[[↑⁺1 : 1]] - a⁰ &[[↑⁰1 : 1]] - -/³‣ div³ - -:test (/³(+6)) ((+2)) -:test (/³(-6)) ((-2)) -:test (/³(+5)) ((+2)) - # divs a balanced ternary number by two (binary >>1) div² [z [[[[rec]]]] (+0) 0 0] ⧗ Number → Number rec =?1 case-end case-div @@ -546,27 +461,3 @@ mod ~‣ ∘∘ quot-rem ⧗ Number → Number → Number :test ((-5) % (-3) =? (-2)) (true) :test ((-5) % (+3) =? (+1)) (true) :test ((+5) % (-3) =? (-1)) (true) - -# returns true if the number is even (remainder mod 2 == 0) -# TODO: faster solution (using tupling?) -even? z [[rec]] ⧗ Number → Boolean - rec =?0 case-end case-rec - case-rec t⁰? (lst 0) (1 /³0) ¬(1 /³0) - case-end true - -=²?‣ even? - -:test (=²?(+0)) (true) -:test (=²?(+1)) (false) -:test (=²?(+41)) (false) -:test (=²?(+42)) (true) - -# returns true if the number is odd (remainder mod 2 == 1) -odd? ¬‣ ∘ even? ⧗ Number → Boolean - -≠²?‣ odd? - -:test (≠²?(+0)) (false) -:test (≠²?(+1)) (true) -:test (≠²?(+41)) (true) -:test (≠²?(+42)) (false) |