Inital draft for stringify.

Author: make-github-pseudonymous-again

src/decimals.js

@@ -0,0 +1,39 @@
+// 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 , 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 ;
+
+		}
+
+		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/stringify.js

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+import { _decimals } from './_decimals' ;
+import { _transient } from './_transient' ;
+
+export function _stringify ( { b , bfactors , jz , gt1 , eq , muln , divmodn , divmod , egcd } ) {
+
+	const tr = _transient( { bfactors , jz , gt1 , divmodn } ) ;
+	const dec = _decimals( { b , eq , muln , divmod } ) ;
+
+	return function ( x , d ) {
+
+		const [ left , r ] = divmod(x, d) ;
+
+		const { u , v } = egcd(d, r) ;
+
+		const [ transient_length , has_repetend ] = tr( v ) ;
+
+		const right = [ ...dec(v, transient_length, u) ] ;
+
+		return [ left , right ] ;
+
+	}
+
+}

src/transient.js

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+// 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 ;
+
+				++mm ;
+				d = q ;
+
+			}
+
+			n = Math.max(n, m) ;
+
+		}
+
+		return [ n , gt1(d) ] ;
+
+	} ;
+
+}