src/core/arithmetic/div/_idivmod_schoolbook_subroutine_do.js
import assert from 'assert';
import gt from '../../../api/compare/gt.js';
import _validate from '../../array/_validate.js';
import _zeros from '../../array/_zeros.js';
import _cmp_half from '../../compare/_cmp_half.js';
import _mul_limb from '../mul/_mul_limb.js';
import _isub from '../sub/_isub.js';
/**
* Input
* -----
* - Two integers A and B such that 0 <= A < B * β and (β^n)/2 <= B < β^n.
* (Hence B >= 1).
* - |A| = |B| + 1
* - |Q| = |A|
*
* Output
* -----
* The quotient floor( A/B ) and the remainder A mod B.
*
* @param {Number} r The radix.
* @param {Array} a Dividend.
* @param {Number} ai Left of dividend.
* @param {Number} aj Right of dividend.
* @param {Array} b Divisor.
* @param {Number} bi Left of divisor.
* @param {Number} bj Right of divisor.
* @param {Array} q Quotient.
* @param {Number} qi Left of quotient.
*/
export default function _idivmod_schoolbook_subroutine_do(
r,
a,
ai,
aj,
b,
bi,
bj,
q,
qi,
) {
assert(r >= 2);
assert(ai >= 0 && aj <= a.length);
assert(bi >= 0 && bj <= b.length);
assert(qi >= 0);
assert(aj - ai === bj - bi + 1); // |a| = |b| + 1
assert(q.length - qi >= aj - ai); // |q| >= |a|
assert(_cmp_half(r, b, bi, bj) >= 0); // (r^n)/2 <= B < r^n
assert(gt(b, bi, bj, a, ai, aj - 1)); // A < B * β
assert(_validate(r, q, qi, qi + aj - ai));
const m = aj - ai;
// Since A < B*β, then A/B < β
// q <- min [ ( β a_0 + a_1 ) / b_0 , β - 1 ]
let _q = Math.min(r - 1, Math.floor((a[ai] * r + a[ai + 1]) / b[bi]));
// Fix _q
const T = _zeros(m);
_mul_limb(r, _q, b, bi, bj, T, 0, m);
if (gt(T, 0, m, a, ai, aj)) {
--_q;
_isub(r, T, 0, m, b, bi, bj);
if (gt(T, 0, m, a, ai, aj)) {
--_q;
_isub(r, T, 0, m, b, bi, bj);
}
}
q[qi + m - 1] += _q;
_isub(r, a, ai, aj, T, 0, m);
}