Merge remote-tracking branch 'origin/feature-stringify'

* origin/feature-stringify:
  Test with bases other than 10.
  Finish implementation of stringify.
  Update dependency @aureooms/js-integer to v6
  Inital draft for stringify.
  🔍 test: Extract fixtures.

package.json

@@ -27,9 +27,13 @@
   "bugs": {
     "url": "https://github.com/aureooms/js-rational/issues"
   },
-  "dependencies": {},
+  "dependencies": {
+    "@aureooms/js-itertools": "^4.0.0"
+  },
   "devDependencies": {
     "@aureooms/js-integer": "6.0.0",
+    "@aureooms/js-number": "^3.1.0",
+    "@aureooms/js-prime": "^4.0.0",
     "@babel/cli": "7.8.4",
     "@babel/core": "7.9.6",
     "@babel/polyfill": "7.8.7",

src/_stringify_digits.js

@@ -0,0 +1,19 @@
+export function _stringify_digits ( str , base , { sign , left , transient , repetend } ) {
+
+	const toStr = x => str(x, base);
+
+	let repr = '' ;
+
+	if (sign < 0) repr += '-' ;
+
+	repr += toStr(left) ;
+
+	if (transient.length || repetend.length) repr += '.' ;
+	repr += transient.map(toStr).join('') ;
+
+	if (repetend.length) repr += '|' ;
+	repr += repetend.map(toStr).join('') ;
+
+	return repr ;
+
+}

src/decimals.js

@@ -0,0 +1,41 @@
+// TODO instead allocate enough space M < log_2(d) + d
+// for transient + repetend by multiplying x by b**M and do a single division ?
+// That may be too much space in most cases. Though necessary when d is prime.
+
+export function _decimals ( { b , eq , muln , divmod } ) {
+
+	return function* ( d , n , hasrepetend , x ) {
+
+		// Computes the length of the repetend of x/d (1 <= x < d) in base b
+		// with transient part of size n.
+
+		while ( n-- ) {
+
+			x = muln(x, b) ;
+			const [q, r] = divmod(x, d) ;
+			yield q ;
+			x = r ;
+
+		}
+
+		if ( !hasrepetend ) return ;
+
+		const first = x ;
+
+		x = muln(x, b) ;
+		const [q, r] = divmod(x, d) ;
+		yield q ;
+		x = r ;
+
+		while (!eq(first, x)) {
+
+			x = muln(x, b) ;
+			const [q, r] = divmod(x, d) ;
+			yield q ;
+			x = r ;
+
+		}
+
+	} ;
+
+}

src/digits.js

@@ -0,0 +1,28 @@
+import { take } from '@aureooms/js-itertools' ;
+import { _decimals } from './decimals' ;
+import { _transient } from './transient' ;
+
+export function _digits ( { b , bfactors , jz , gt1 , eq , muln , divmodn , divmod , egcd , sgn , abs } ) {
+
+	const tr = _transient( { bfactors , jz , gt1 , divmodn } ) ;
+	const dec = _decimals( { b , eq , muln , divmod } ) ;
+
+	return function ( x , d ) {
+
+		const [ left , r ] = divmod(abs(x), d) ;
+
+		const { u , v } = egcd(d, r) ;
+
+		const [ transient_length , has_repetend ] = tr( v ) ;
+
+		const decimals = dec(v, transient_length, has_repetend , u) ;
+
+		const transient = [ ...take(decimals, transient_length) ] ;
+
+		const repetend = [ ...decimals ] ;
+
+		return { sign: sgn(x) , left , transient , repetend } ;
+
+	}
+
+}

src/index.js

@@ -6,3 +6,5 @@ export * from './pow' ;
 export * from './cmp' ;
 export * from './cmp_no_bounds' ;
 export * from './simplify' ;
+export * from './digits' ;
+export * from './_stringify_digits' ;

src/transient.js

@@ -0,0 +1,38 @@
+// credits https://github.com/aureooms-research/repeating-decimal
+
+export function _transient ( { bfactors , jz , gt1 , divmodn } ) {
+
+	return function ( d ) {
+
+		// Computes the length of the non repeating part in x / d
+		// ( for any 1 <= x < d with x and d co-prime ) decimals in
+		// base b whose prime factors are given. Returns tuple ( n , hasrepetend )
+		// where n is the length of the non repeating part and hasrepetend
+		// determines if 1 / d repeats or not.
+
+		let n = 0 ;
+
+		for ( const f of bfactors ) {
+
+			let m = 0 ;
+
+			while ( true ) {
+
+				const [ q , r ] = divmodn(d, f) ;
+
+				if (!jz(r)) break ;
+
+				++m ;
+				d = q ;
+
+			}
+
+			n = Math.max(n, m) ;
+
+		}
+
+		return [ n , gt1(d) ] ;
+
+	} ;
+
+}

test/src/_fixtures.js

@@ -8,34 +8,47 @@ export const ALU = [
 		add : (a, b) => a.add(b),
 		sub : (a, b) => a.sub(b),
 		mul : (a, b) => a.mul(b),
+		muln : (a, b) => a.mul(b),
 		div : (a, b) => a.div(b),
 		reg : x => int(x),
 		str : x => x.toString(),
 		jz  : x => x.eq(0),
 		lt0 : x => x.lt(0),
+		gt1 : x => x.gt(1),
 		cmp  : (a,b) => a.cmp(b),
+		eq : (a,b) => a.eq(b),
 		neg : x => x.neg(),
 		sgn : x => x.cmp(0),
+		abs : x => x.abs(),
 		divmod : (a,b) => [a.div(b), a.mod(b)],
+		divmodn : (a,b) => [a.div(b), a.mod(b)],
 		pown : (x,n) => x.pow(n),
 	},
 	{
 		name : 'bn.js',
 		add : (a, b) => a.add(b),
 		sub : (a, b) => a.sub(b),
 		mul : (a, b) => a.mul(b),
+		muln : (a, b) => a.muln(b),
 		div : (a, b) => a.div(b),
 		reg : x => new BN(x),
-		str : x => x.toString(),
+		str : (x, base) => x.toString(base),
 		jz  : x => x.eqn(0),
 		lt0 : x => x.ltn(0),
+		gt1 : x => x.gtn(1),
 		cmp  : (a,b) => a.cmp(b),
+		eq : (a,b) => a.eq(b),
 		sgn : x => x.cmpn(0),
+		abs : x => x.abs(),
 		neg : x => x.neg(),
 		divmod : (a,b) => {
 			const { div , mod } = a.divmod(b) ;
 			return [div, mod] ;
 		} ,
+		divmodn : (a,b) => {
+			const { div , mod } = a.divmod(new BN(b)) ;
+			return [div, mod] ;
+		} ,
 		egcd : (a,b) => {
 			const gcd = a.gcd(b) ;
 			return { u: b.div(gcd), v: a.div(gcd) } ;
@@ -47,16 +60,27 @@ export const ALU = [
 		add : (a, b) => a.add(b),
 		sub : (a, b) => a.sub(b),
 		mul : (a, b) => a.mul(b),
+		muln : (a, b) => a.muln(b),
 		div : (a, b) => a.div(b),
 		reg : x => ZZ.from(x),
-		str : x => x.toString(),
+		str : (x, base) => x.toString(base),
 		jz  : x => x.iszero(),
 		lt0 : x => x.sign() < 0,
+		gt1 : x => x.gtn(1),
 		cmp  : (a,b) => a.cmp(b),
+		eq : (a,b) => a.eq(b),
 		sgn : x => x.sign(),
+		abs : x => x.abs(),
 		neg : x => x.opposite(),
 		divmod : (a,b) => a.divmod(b),
-		egcd : (a,b) => a.egcd(b),
+		divmodn : (a,b) => a.divmodn(b),
+		egcd : (a,b) => {
+			const { u , v } = a.egcd(b) ;
+			return {
+				u: u.iabs(),
+				v: v.iabs(),
+			} ;
+		},
 		pown : (x,n) => x.pown(n),
 	}
 ];

test/src/core.js

@@ -1,8 +1,18 @@
 import test from 'ava';
-import { _add , _sub , _mul , _div , _pow , _cmp , _cmp_no_bounds , _simplify } from '../../src';
+import { __factorize__ } from '@aureooms/js-prime' ;
+import { $2, iadd1, eq0, gt1, divmod } from "@aureooms/js-number" ;
+import {
+	_add , _sub , _mul , _div , _pow ,
+	_cmp , _cmp_no_bounds ,
+	_simplify , _digits , _stringify_digits
+} from '../../src';
 
 const GOOGOL = '10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000' ;
 
+const factorize = __factorize__( $2, iadd1, eq0, gt1, divmod ) ;
+
+const ufactors = n => new Set(factorize(n)) ;
+
 import { ALU } from './_fixtures' ;
 
 function binary ( t , alu , [ [ _x , _y , factory ] , a , b , c , d , e ] ) {
@@ -51,14 +61,12 @@ function unary ( t , alu , [ [ _x , _y , factory ] , a , b , e ] ) {
 
 	const apply = factory( alu );
 
-	const repr = x => `${alu.str(x[0])}/${alu.str(x[1])}` ;
-
 	const _a = alu.reg(a);
 	const _b = alu.reg(b);
 
 	const z = apply( _a , _b ) ;
 
-	t.is(e, repr(z));
+	t.is(e, z);
 
 }
 
@@ -72,7 +80,24 @@ const mul = [ 'mul' , '*' , [ _mul ] , binary ] ;
 const div = [ 'div' , '/' , [ _div ] , binary ] ;
 const pow = [ 'pow' , '^' , [ _pow ] , binary_n ] ;
 const cmp = [ 'cmp' , '~' , [ _cmp , _cmp_no_bounds ] , binary ] ;
-const simplify = [ 'simplify' , '=' , [ _simplify ] , unary , alu => alu.egcd ] ;
+const simplify = [ 'simplify' , '=' , [
+	alu => {
+		const repr = x => `${alu.str(x[0])}/${alu.str(x[1])}` ;
+		const simp = _simplify(alu) ;
+		return (a,b) => repr(simp(a,b)) ;
+	}
+] , unary , alu => alu.egcd ] ;
+
+
+const stringify_n = b => alu => {
+	const bfactors = ufactors( b ) ;
+	const digits = _digits({ b , bfactors , ...alu }) ;
+	return ( x , d ) => _stringify_digits( alu.str , b , digits(x, d) ) ;
+} ;
+
+const stringify_10 = [ 'stringify_10' , '=' , [ stringify_n(10) ] , unary , alu => alu.egcd ] ;
+const stringify_2 = [ 'stringify_2' , '=' , [ stringify_n(2) ] , unary , alu => alu.egcd ] ;
+const stringify_19 = [ 'stringify_19' , '=' , [ stringify_n(19) ] , unary , alu => alu.egcd ] ;
 
 const PARAMS = [
 
@@ -166,6 +191,29 @@ const PARAMS = [
 	[ simplify , '-170141183460469231731687303715884105729' , '3' , '-56713727820156410577229101238628035243/1' ] ,
 	[ simplify , '-3' , '170141183460469231731687303715884105729' , '-1/56713727820156410577229101238628035243' ] ,
 
+	[ stringify_10 , '1' , '7' , '0.|142857' ] ,
+	[ stringify_10 , '-4' , '8' , '-0.5' ] ,
+	[ stringify_10 , '7' , '14' , '0.5' ] ,
+	[ stringify_10 , '0' , '43' , '0' ] ,
+	[ stringify_10 , '86' , '43' , '2' ] ,
+	[ stringify_10 , '2' , '46' , '0.|0434782608695652173913' ] ,
+	[ stringify_10 , '1' , '46' , '0.0|2173913043478260869565' ] ,
+	[ stringify_10 , '1' , '14' , '0.0|714285'] ,
+	[ stringify_10 , '1' , '45' , '0.0|2' ] ,
+	[ stringify_10 , '733' , '750' , '0.977|3' ] ,
+	[ stringify_10 , '22' , '7' , '3.|142857' ] ,
+	[ stringify_10 , '355' , '113' , '3.|1415929203539823008849557522123893805309734513274336283185840707964601769911504424778761061946902654867256637168' ] ,
+	[ stringify_10 , '7775' , '2260' , '3.44|0265486725663716814159292035398230088495575221238938053097345132743362831858407079646017699115044247787610619469' ] ,
+
+	[ stringify_2 , '-4' , '8' , '-0.1' ] ,
+	[ stringify_2 , '7' , '14' , '0.1' ] ,
+	// printf -- "scale=10;obase=2;1/7\n" | bc --mathlib
+	[ stringify_2 , '1' , '7' , '0.|001' ] ,
+
+	[ stringify_19 , '1' , '2' , '0.|9' ] , // HAHA
+
+	[ stringify_19 , '14' , '13', '1.|18ebd2ha475g'] , // HOHO
+
 ] ;
 
 for (const alu of ALU)

yarn.lock

@@ -2,6 +2,13 @@
 # yarn lockfile v1
 
 
+"@aureooms/js-collections-deque@^4.0.0":
+  version "4.0.0"
+  resolved "https://registry.yarnpkg.com/@aureooms/js-collections-deque/-/js-collections-deque-4.0.0.tgz#cb6ff3070f4413023622db817da261f91e42aef0"
+  integrity sha512-+dI0PSkshl0vKmeyfzWM5Xtfopu4XYIrlqKKq3emjyuCi1DCO9SaPIgKblMDjl9WttmJhTYsunNyPYula5woAw==
+  dependencies:
+    "@aureooms/js-error" "^4.0.0"
+
 "@aureooms/js-error@^4.0.0":
   version "4.0.0"
   resolved "https://registry.yarnpkg.com/@aureooms/js-error/-/js-error-4.0.0.tgz#cea0a145f5290f443911b3d1890d7254a18eeb9b"
@@ -20,6 +27,24 @@
     "@aureooms/js-error" "^4.0.0"
     "@aureooms/js-integer-big-endian" "^8.0.0"
 
+"@aureooms/js-itertools@^4.0.0":
+  version "4.0.0"
+  resolved "https://registry.yarnpkg.com/@aureooms/js-itertools/-/js-itertools-4.0.0.tgz#2f7247b4a89202606bb54a731753590625b4b185"
+  integrity sha512-QhCT+RDUbWPL7h3RA7LcXdC1IQdR3Bfl0Re0ClDxem7DUnRbHuL4Nlwgo3UoqaRBE8OI4RpBw+hXVVqVg14J9Q==
+  dependencies:
+    "@aureooms/js-collections-deque" "^4.0.0"
+    "@aureooms/js-error" "^4.0.0"
+
+"@aureooms/js-number@^3.1.0":
+  version "3.1.0"
+  resolved "https://registry.yarnpkg.com/@aureooms/js-number/-/js-number-3.1.0.tgz#460155de73084d25e648680309d9d1d941e3df89"
+  integrity sha512-Z+Dmml9TjuhnxaOIWu8OZ3iYFPJsLJNynv1qgwYTO7dsZznMPge1ME5VmFeTNNsZSg9DtavXVyfYla+XxWXHRg==
+
+"@aureooms/js-prime@^4.0.0":
+  version "4.0.0"
+  resolved "https://registry.yarnpkg.com/@aureooms/js-prime/-/js-prime-4.0.0.tgz#95ceb59a67ca009afb76b3045daab174b40f24f2"
+  integrity sha512-U5Hji39rqTK+ktMTQZvSx/AhX09wLj3ESQPl7fep/ip/FMskeaHtCK8zAQ6QcneLDBCHOMV0x6C9CckWqiCzag==
+
 "@babel/cli@7.8.4":
   version "7.8.4"
   resolved "https://registry.yarnpkg.com/@babel/cli/-/cli-7.8.4.tgz#505fb053721a98777b2b175323ea4f090b7d3c1c"