From 7fc946443adcef9224a3c672b5929a93489c8c93 Mon Sep 17 00:00:00 2001
From: Marvin Borner <git@marvinborner.de>
Date: Wed, 13 Mar 2024 01:47:46 +0100
Subject: [PATCH] Added much faster division algorithm

---
 std/Number/Ternary.bruijn | 100 +++++++++++++++++++++++++-------------
 1 file changed, 65 insertions(+), 35 deletions(-)

diff --git a/std/Number/Ternary.bruijn b/std/Number/Ternary.bruijn
index 86f4593..8cf891f 100644
--- a/std/Number/Ternary.bruijn
+++ b/std/Number/Ternary.bruijn
@@ -37,36 +37,47 @@ t⁰? [0 false false true] ⧗ Trit → Boolean
 :test (t⁰? t⁺) (false)
 :test (t⁰? t⁰) (true)
 
-# shifts a negative trit into a balanced ternary number
+# lshifts a negative trit into a balanced ternary number
 ↑⁻‣ [[[[[2 (4 3 2 1 0)]]]]] ⧗ Number → Number
 
 :test (↑⁻(+0)) ((-1))
 :test (↑⁻(-1)) ((-4))
 :test (↑⁻(+42)) ((+125))
 
-# shifts a positive trit into a balanced ternary number
+# lshifts a positive trit into a balanced ternary number
 ↑⁺‣ [[[[[1 (4 3 2 1 0)]]]]] ⧗ Number → Number
 
 :test (↑⁺(+0)) ((+1))
 :test (↑⁺(-1)) ((-2))
 :test (↑⁺(+42)) ((+127))
 
-# shifts a zero trit into a balanced ternary number
+# lshifts a zero trit into a balanced ternary number
 ↑⁰‣ [[[[[0 (4 3 2 1 0)]]]]] ⧗ Number → Number
 
 :test (↑⁰(+0)) ([[[[0 3]]]])
 :test (↑⁰(+1)) ((+3))
 :test (↑⁰(+42)) ((+126))
 
-# shifts a specified trit into a balanced ternary number
+# lshifts a specified trit into a balanced ternary number
 …↑… [[[[[[5 2 1 0 (4 3 2 1 0)]]]]]] ⧗ Trit → Number → Number
 
 :test (t⁻ ↑ (+42)) (↑⁻(+42))
 :test (t⁺ ↑ (+42)) (↑⁺(+42))
 :test (t⁰ ↑ (+42)) (↑⁰(+42))
 
-# lshifts a zero trit into a balanced ternary number
-←⁰‣ [[[[[4 (0 3) 2 1 0]]]]]
+# lshifts balanced ternary number without pushing new trit
+# basically removes mst or leading 0
+←‣ [^(0 z a⁻ a⁺ a⁰)] ⧗ Number → Number
+	z (+0) : true
+	a⁻ &[[(0 (+0) ↑⁻1) : false]]
+	a⁺ &[[(0 (+0) ↑⁺1) : false]]
+	a⁰ &[[(0 (+0) ↑⁰1) : false]]
+
+:test (←(+3)) ([[[[0 3]]]])
+:test (←(+5)) ([[[[2 (2 3)]]]])
+
+# 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?)
@@ -82,13 +93,14 @@ negate [[[[[4 3 1 2 0]]]]] ⧗ Number → Number
 :test (-(+42)) ((-42))
 
 # converts a balanced ternary number to a list of trits
-list! [0 z a⁻ a⁺ a⁰] ⧗ Number → List
+number→trits [0 z a⁻ a⁺ a⁰] ⧗ Number → (List Trit)
 	z [[0]]
-	a⁻ [t⁻ : 0]
-	a⁺ [t⁺ : 0]
-	a⁰ [t⁰ : 0]
+	a⁻ pair t⁻
+	a⁺ pair t⁺
+	a⁰ pair t⁰
 
-# TODO: Tests!
+: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
@@ -134,9 +146,9 @@ lst [0 t⁰ [t⁻] [t⁺] [t⁰]] ⧗ Number → Trit
 # extracts most significant trit from a balanced ternary number
 mst* [B.get t⁰ (0 z a⁻ a⁺ a⁰)] ⧗ Number → Trit
 	z B.empty
-	a⁻ [B.store! 0 t⁻]
-	a⁺ [B.store! 0 t⁺]
-	a⁰ [B.store! 0 t⁰]
+	a⁻ \B.store! t⁻
+	a⁺ \B.store! t⁺
+	a⁰ \B.store! t⁰
 
 :test (mst* (-1)) (t⁻)
 :test (mst* (+0)) (t⁰)
@@ -148,8 +160,8 @@ mst* [B.get t⁰ (0 z a⁻ a⁺ a⁰)] ⧗ Number → Trit
 # ignores leading 0s
 mst [B.get t⁰ (0 z a⁻ a⁺ a⁰)] ⧗ Number → Trit
 	z B.empty
-	a⁻ [B.store! 0 t⁻]
-	a⁺ [B.store! 0 t⁺]
+	a⁻ \B.store! t⁻
+	a⁺ \B.store! t⁺
 	a⁰ [0]
 
 :test (mst (-1)) (t⁻)
@@ -463,47 +475,65 @@ ternary-search z [[[[rec]]]] ⧗ (Number → Number) → Number → Number → N
 
 :test ((ternary-search [-((0 - (+3)) ⋅ (0 - (+3)))] (+0) (+5)) =? (+3)) (true)
 
-# finds quotient and remainder using binary search
-# TODO: fix for numbers <=1 (case analysis, q,r<0)
-quot-rem [[go --(binary-search [0 ⋅ 1 >? 2] (+0) 1)]] ⧗ Number → Number → (Pair Number Number)
-	go [0 : (2 - (1 ⋅ 0))]
-
 # pads a ternary number with 0s until it's as long a another ternary number
-pad y [[[(log3* 0) <? (log3* 1) (2 1 ←⁰0) 0]]] ⧗ Number → Number → Number
+pad y [[[(log3* 0) <? (log3* 1) (2 1 →⁰0) 0]]] ⧗ Number → Number → Number
 
 # forces number to be exactly n trits long (either pad/trim)
 force [[[0 <? 2 pad trim] (log3* 0)]] ⧗ Number → Number
-	pad y [[[=?1 0 (2 --1 ←⁰0)]]] (2 - 0) 1
-	trim y [[[=?1 0 (2 --1 /³0)]]] (0 - 2) 1
+	pad z [[[=?1 0 (2 --1 →⁰0)]]] (2 - 0) 1
+	trim z [[[=?1 0 (2 --1 ←0)]]] (0 - 2) 1
+
+# lshifts after concat, given trit count
+# TODO: reduce force
+double-shift [[[[[left : right]] (force 2 1) (force 2 0)]]]
+	left force 4 ((mst* 0) ↑ (+0) + (↑⁰1))
+	right force 4 ↑⁰0
 
+# efficient quotient/remainder implementation for balanced ternary
 # technique by Douglas W. Jones
-# TODO: fix
-quot-rem* [[[[z [[[[rec]]]] 1 (+0) 3]] ((max (log3 1) (log3 0)) ⋅ (+2)) 0]]
-	rec =?2 (0 : 1) ([[compare-case eq lt gt 1 (+0)]] rem' quo')
-		rem' force 5 ((mst* (force 5 0)) ↑ (+0) + ↑⁰1)
-		quo' force 5 ↑⁰0
+# algorithm originally intended for fixed-width numbers (=> ugly hacks with force+log3)
+# TODO: remove the final `huh` correction step (probably some off-by-one bug?)
+quot-rem [[[[[z [[[[rec]]]] 1 (+0) 4]]] <?0 (max (log3 1) (log3 0)) 0]] ⧗ Number → Number → (Pair Number Number)
+	rec =?2 huh (double-shift 5 1 0 [[compare-case eq gt lt 1 (+0)]])
+		huh (>?1 ⋀? 6) ⋁? (<?1 ⋀? \6) (--0 : (1 + 7)) (0 : 1)
 		eq 5 --4 1 0
-		lt [(-0 >? 2) ⋁? ((-0 =? 2) ⋀? <?1) fix (6 --5 2 1)] (force 7 (1 + 6))
-			fix 6 --5 0 --1
-		gt [(-0 <? 2) ⋁? ((-0 =? 2) ⋀? >?1) fix (6 --5 2 1)] (force 7 (1 - 6))
-			fix 6 --5 0 ++1
+		gt [-0 <? 2 ⋁? (-0 =? 2 ⋀? >?1) fix (6 --5 2 1)] (8 add sub 1 6)
+			fix 6 --5 0 (9 dec inc 1)
+		lt [-0 >? 2 ⋁? (-0 =? 2 ⋀? <?1) fix (6 --5 2 1)] (8 sub add 1 6)
+			fix 6 --5 0 (9 inc dec 1)
+
+# finds quotient and remainder using binary search
+# TODO: fix for numbers <=1 (case analysis, q,r<0)
+quot-rem* [[go --(binary-search [0 ⋅ 1 >? 2] (+0) 1)]] ⧗ Number → Number → (Pair Number Number)
+	go [0 : (2 - (1 ⋅ 0))]
 
 # divs two balanced ternary numbers
-div ^‣ ∘∘ quot-rem ⧗ Number → Number
+div ^‣ ∘∘ quot-rem ⧗ Number → Number → Number
 
 …/… div
 
 :test ((+42) / (+4) =? (+10)) (true)
 :test ((+5) / (+3) =? (+1)) (true)
+:test ((-5) / (-3) =? (+1)) (true)
+:test ((-5) / (+3) =? (-2)) (true)
+:test ((+5) / (-3) =? (-2)) (true)
+
+# bad mod implementation using repeated subtraction
+mod* z [[[rec]]] ⧗ Number → Number → Number
+	rec [=?0 0 (<?0 2 (3 0 1))] (1 - 0)
 
 # returns remainder of integer division
-mod ~‣ ∘∘ quot-rem ⧗ Number → Number
+mod ~‣ ∘∘ quot-rem ⧗ Number → Number → Number
 
 …%… mod
 
 :test ((+42) % (+4) =? (+2)) (true)
 :test ((+7) % (+3) =? (+1)) (true)
 :test ((+8) % (+2) =? (+0)) (true)
+:test ((+5) % (+3) =? (+2)) (true)
+: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?)