aureooms-js-integer/src/1-new/arithmetic/div/_div.js

integer code bricks for JavaScript

import { _sub } from '../sub' ;
import { _lt } from '../../compare' ;

/**
 * Computes quotient and remainder of two big endian arrays.
 * <p>
 * Computes quotient and remainder of two big endian arrays
 * using long division algorithm (the one teached in
 * european primary schools).
 *
 * /!\ This algorithm modifies its first operand.
 *
 * HYP : q is at least as large as r
 *       b is not zero
 *
 * @param {int} x the radix
 * @param {array} r dividend and remainder
 * @param {int} ri r left
 * @param {int} rj r right
 * @param {array} b divisor
 * @param {int} bi b left
 * @param {int} bj b right
 * @param {array} q quotient, must be 0 initialized
 * @param {int} qi q left
 */

// /!\ There are implicit hypotheses
//     made on the size of the operands.
//     Should clarify.

export function _div ( x , r , ri , rj , b , bi , bj , q , qi ) {

	var k, t = ri + 1;

	do {

		// trim leading zeros
		//     - maybe could try to put this procedure inside the _sub loop
		//     - or assume that the number is trimed at the begining
		//       and put this statement at the end of the main loop
		while (ri < rj && r[ri] === 0) ++ri;

		// search for a remainder block interval
		// greater than the divisor
		//     - maybe could try binary search on the _lt function
		//     for another implementation
		k = ri + 1;
		while (k <= rj && _lt(r, ri, k, b, bi, bj)) ++k;

		// remainder smaller than divisor --> end
		if (k > rj) break;

		// divide current block interval by quotient
		do{

			// increment quotient block corresponding
			// to current ls block of remainder interval
			++q[qi + k - t];

			// subtract divisor from current remainder
			// block interval
			_sub(x, r, ri, k, b, bi, bj, r, ri, k);

		} while(!_lt(r, ri, k, b, bi, bj));


	} while(true);

}