CoCalc -- arithmetic-test.js

Summer of Sage Days 2015: San Diego (sd64.25), etc.
react / wstein / node_modules / browserify / node_modules / crypto-browserify / node_modules / browserify-sign / node_modules / bn.js / test / arithmetic-test.js
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var assert = require('assert');
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var BN = require('../').BN;
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var fixtures = require('./fixtures');
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describe('BN.js/Arithmetic', function() {
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  describe('.add()', function() {
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    it('should add numbers', function() {
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      assert.equal(new BN(14).add(new BN(26)).toString(16), '28');
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      var k = new BN(0x1234);
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      var r = k;
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      for (var i = 0; i < 257; i++)
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        r = r.add(k);
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      assert.equal(r.toString(16), '125868');
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    });
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    it('should handle carry properly (in-place)', function() {
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      var k = new BN('abcdefabcdefabcdef', 16);
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      var r = new BN('deadbeef', 16);
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      for (var i = 0; i < 257; i++)
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        r.iadd(k);
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      assert.equal(r.toString(16), 'ac79bd9b79be7a277bde');
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    });
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    it('should properly do positive + negative', function() {
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      var a = new BN('abcd', 16);
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      var b = new BN('-abce', 16);
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      assert.equal(a.iadd(b).toString(16), '-1');
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      var a = new BN('abcd', 16);
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      var b = new BN('-abce', 16);
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      assert.equal(a.add(b).toString(16), '-1');
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      assert.equal(b.add(a).toString(16), '-1');
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    });
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  });
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  describe('.iaddn()', function() {
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    it('should allow a sign change', function() {
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      var a = new BN(-100);
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      assert.equal(a.sign, true);
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      a.iaddn(200);
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      assert.equal(a.sign, false);
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      assert.equal(a.toString(), '100');
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    });
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    it('should add negative number', function() {
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      var a = new BN(-100);
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      assert.equal(a.sign, true);
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      a.iaddn(-200);
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      assert.equal(a.toString(), '-300');
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    });
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    it('should allow neg + pos with big number', function() {
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      var a = new BN('-1000000000', 10);
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      assert.equal(a.sign, true);
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      a.iaddn(200);
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      assert.equal(a.toString(), '-999999800');
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    });
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    it('should carry limb', function() {
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      var a = new BN('3ffffff', 16);
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      assert.equal(a.iaddn(1).toString(16), '4000000');
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    });
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  });
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  describe('.sub()', function() {
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    it('should subtract small numbers', function() {
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      assert.equal(new BN(26).sub(new BN(14)).toString(16), 'c');
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      assert.equal(new BN(14).sub(new BN(26)).toString(16), '-c');
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      assert.equal(new BN(26).sub(new BN(26)).toString(16), '0');
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      assert.equal(new BN(-26).sub(new BN(26)).toString(16), '-34');
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    });
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    var a = new BN(
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      '31ff3c61db2db84b9823d320907a573f6ad37c437abe458b1802cda041d6384' +
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          'a7d8daef41395491e2',
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      16);
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    var b = new BN(
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      '6f0e4d9f1d6071c183677f601af9305721c91d31b0bbbae8fb790000',
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      16);
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    var r = new BN(
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      '31ff3c61db2db84b9823d3208989726578fd75276287cd9516533a9acfb9a67' +
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          '76281f34583ddb91e2',
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      16);
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    it('should subtract big numbers', function() {
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      assert.equal(a.sub(b).cmp(r), 0);
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    });
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    it('should subtract numbers in place', function() {
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      assert.equal(b.clone().isub(a).neg().cmp(r), 0);
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    });
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    it('should subtract with carry', function() {
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      // Carry and copy
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      var a = new BN('12345', 16);
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      var b = new BN('1000000000000', 16);
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      assert.equal(a.isub(b).toString(16), '-fffffffedcbb');
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      var a = new BN('12345', 16);
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      var b = new BN('1000000000000', 16);
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      assert.equal(b.isub(a).toString(16), 'fffffffedcbb');
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    });
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  });
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  describe('.isubn()', function() {
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    it('should subtract negative number', function() {
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      var r = new BN(
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        '7fffffffffffffffffffffffffffffff5d576e7357a4501ddfe92f46681b', 16);
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      assert.equal(r.isubn(-1).toString(16),
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        '7fffffffffffffffffffffffffffffff5d576e7357a4501ddfe92f46681c');
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    });
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    it('should work for positive numbers', function() {
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      var a = new BN(-100);
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      assert.equal(a.sign, true);
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      a.isubn(200);
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      assert.equal(a.sign, true);
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      assert.equal(a.toString(), '-300');
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    });
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    it('should not allow a sign change', function() {
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      var a = new BN(-100);
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      assert.equal(a.sign, true);
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      a.isubn(-200);
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      assert.equal(a.sign, false);
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      assert.equal(a.toString(), '100');
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    });
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  });
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  describe('.mul()', function() {
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    it('should multiply numbers of different signs', function() {
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      assert.equal(new BN(0x1001).mul(new BN(0x1234)).toString(16),
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                   '1235234');
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      assert.equal(new BN(-0x1001).mul(new BN(0x1234)).toString(16),
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                   '-1235234');
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      assert.equal(new BN(-0x1001).mul(new BN(-0x1234)).toString(16),
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                   '1235234');
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    });
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    it('should multiply with carry', function() {
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      var n = new BN(0x1001);
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      var r = n;
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      for (var i = 0; i < 4; i++)
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        r = r.mul(n);
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      assert.equal(r.toString(16),
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                   '100500a00a005001');
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    });
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    it('should correctly multiply big numbers', function() {
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      var n = new BN(
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        '79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798',
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        16
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      );
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      assert.equal(
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        n.mul(n).toString(16),
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        '39e58a8055b6fb264b75ec8c646509784204ac15a8c24e05babc9729ab9' +
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            'b055c3a9458e4ce3289560a38e08ba8175a9446ce14e608245ab3a9' +
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            '978a8bd8acaa40');
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      assert.equal(
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        n.mul(n).mul(n).toString(16),
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        '1b888e01a06e974017a28a5b4da436169761c9730b7aeedf75fc60f687b' +
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            '46e0cf2cb11667f795d5569482640fe5f628939467a01a612b02350' +
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            '0d0161e9730279a7561043af6197798e41b7432458463e64fa81158' +
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            '907322dc330562697d0d600');
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    });
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    it('should multiply neg number on 0', function() {
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      assert.equal(
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        new BN('-100000000000').mul(new BN('3').div(new BN('4'))).toString(16),
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        '0'
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      );
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    });
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    it('should regress mul big numbers', function() {
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      var q = fixtures.dhGroups.p17.q;
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      var qs = fixtures.dhGroups.p17.qs;
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      var q = new BN(q, 16);
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      assert.equal(q.sqr().toString(16), qs);
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      assert.equal(q.isqr().toString(16), qs);
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    });
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  });
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  describe('.imul()', function() {
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    it('should multiply numbers in-place', function() {
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      var a = new BN('abcdef01234567890abcd', 16);
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      var b = new BN('deadbeefa551edebabba8', 16);
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      var c = a.mul(b);
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      assert.equal(a.imul(b).toString(16), c.toString(16));
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      var a = new BN('abcdef01234567890abcd214a25123f512361e6d236', 16);
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      var b = new BN('deadbeefa551edebabba8121234fd21bac0341324dd', 16);
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      var c = a.mul(b);
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      assert.equal(a.imul(b).toString(16), c.toString(16));
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    });
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    it('should multiply by 0', function() {
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      var a = new BN('abcdef01234567890abcd', 16);
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      var b = new BN('0', 16);
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      var c = a.mul(b);
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      assert.equal(a.imul(b).toString(16), c.toString(16));
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    });
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  });
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  describe('.div()', function() {
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    it('should divide numbers', function() {
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      assert.equal(new BN('10').div(new BN(256)).toString(16),
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                   '0');
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      assert.equal(new BN('69527932928').div(new BN('16974594')).toString(16),
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                   'fff');
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      assert.equal(new BN('-69527932928').div(new BN('16974594')).toString(16),
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                   '-fff');
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      var b = new BN(
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        '39e58a8055b6fb264b75ec8c646509784204ac15a8c24e05babc9729ab9' +
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            'b055c3a9458e4ce3289560a38e08ba8175a9446ce14e608245ab3a9' +
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            '978a8bd8acaa40',
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        16);
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      var n = new BN(
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        '79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798',
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        16
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      );
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      assert.equal(b.div(n).toString(16), n.toString(16));
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      assert.equal(new BN('1').div(new BN('-5')).toString(10), '0');
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    });
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    it('should not fail on regression after moving to _wordDiv', function() {
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      // Regression after moving to word div
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      var p = new BN(
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        'fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f',
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        16);
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      var a = new BN(
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        '79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798',
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        16);
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      var as = a.sqr();
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      assert.equal(
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          as.div(p).toString(16),
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          '39e58a8055b6fb264b75ec8c646509784204ac15a8c24e05babc9729e58090b9');
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      var p = new BN(
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        'ffffffff00000001000000000000000000000000ffffffffffffffffffffffff',
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        16);
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      var a = new BN(
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        'fffffffe00000003fffffffd0000000200000001fffffffe00000002ffffffff' +
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        'ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff',
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        16);
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      assert.equal(
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        a.div(p).toString(16),
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        'ffffffff00000002000000000000000000000001000000000000000000000001');
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    });
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  });
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  describe('.idivn()', function() {
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    it('should divide numbers in-place', function() {
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      assert.equal(new BN('10', 16).idivn(3).toString(16), '5');
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      assert.equal(new BN('12', 16).idivn(3).toString(16), '6');
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      assert.equal(new BN('10000000000000000').idivn(3).toString(10),
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                   '3333333333333333');
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      assert.equal(
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          new BN('100000000000000000000000000000').idivn(3).toString(10),
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          '33333333333333333333333333333');
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      var t = new BN(3);
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      assert.equal(
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          new BN('12345678901234567890123456', 16).idivn(3).toString(16),
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          new BN('12345678901234567890123456', 16).div(t).toString(16));
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    });
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  });
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  describe('.divRound()', function() {
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    it('should divide numbers with rounding', function() {
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      assert.equal(new BN(9).divRound(new BN(20)).toString(10),
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                   '0');
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      assert.equal(new BN(10).divRound(new BN(20)).toString(10),
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                   '1');
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      assert.equal(new BN(150).divRound(new BN(20)).toString(10),
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                   '8');
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      assert.equal(new BN(149).divRound(new BN(20)).toString(10),
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                   '7');
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      assert.equal(new BN(149).divRound(new BN(17)).toString(10),
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                   '9');
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      assert.equal(new BN(144).divRound(new BN(17)).toString(10),
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                   '8');
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      assert.equal(new BN(-144).divRound(new BN(17)).toString(10),
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                   '-8');
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    });
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    it('should return 1 on exact division', function() {
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      assert.equal(new BN(144).divRound(new BN(144)).toString(10), '1');
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    });
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  });
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  describe('.mod()', function() {
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    it('should mod numbers', function() {
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      assert.equal(new BN('10').mod(new BN(256)).toString(16),
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                   'a');
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      assert.equal(new BN('69527932928').mod(new BN('16974594')).toString(16),
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                   '102f302');
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      assert.equal(new BN('-69527932928').mod(new BN('16974594')).toString(16),
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                   '1000');
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      var p = new BN(
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        'ffffffff00000001000000000000000000000000ffffffffffffffffffffffff',
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        16);
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      var a = new BN(
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        'fffffffe00000003fffffffd0000000200000001fffffffe00000002ffffffff' +
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        'ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff',
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        16);
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      assert.equal(
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        a.mod(p).toString(16),
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        '0');
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    });
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    it('should properly carry the sign inside division', function() {
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      var a = new BN('945304eb96065b2a98b57a48a06ae28d285a71b5', 'hex');
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      var b = new BN(
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        'fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe',
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        'hex');
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      assert.equal(a.mul(b).mod(a).cmpn(0), 0);
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    });
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  });
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  describe('.modn()', function() {
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    it('should act like .mod() on small numbers', function() {
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      assert.equal(new BN('10', 16).modn(256).toString(16), '10');
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      assert.equal(new BN('100', 16).modn(256).toString(16), '0');
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      assert.equal(new BN('1001', 16).modn(256).toString(16), '1');
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      assert.equal(new BN('100000000001', 16).modn(256).toString(16), '1');
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      assert.equal(new BN('100000000001', 16).modn(257).toString(16),
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                   new BN('100000000001', 16).mod(new BN(257)).toString(16));
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      assert.equal(new BN('123456789012', 16).modn(3).toString(16),
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                   new BN('123456789012', 16).mod(new BN(3)).toString(16));
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    });
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  });
351

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  describe('.abs()', function() {
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    it('should return absolute value', function() {
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      assert.equal(new BN(0x1001).abs().toString(), '4097');
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      assert.equal(new BN(-0x1001).abs().toString(), '4097');
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      assert.equal(new BN('ffffffff', 16).abs().toString(), '4294967295');
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    })
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  });
359

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  describe('.invm()', function() {
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    it('should invert relatively-prime numbers', function() {
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      var p = new BN(257);
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      var a = new BN(3);
364
      var b = a.invm(p);
365
      assert.equal(a.mul(b).mod(p).toString(16), '1');
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367
      var p192 = new BN(
368
          'fffffffffffffffffffffffffffffffeffffffffffffffff',
369
          16);
370
      var a = new BN('deadbeef', 16);
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      var b = a.invm(p192);
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      assert.equal(a.mul(b).mod(p192).toString(16), '1');
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      // Even base
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      var phi = new BN('872d9b030ba368706b68932cf07a0e0c', 16);
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      var e = new BN(65537);
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      var d = e.invm(phi);
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      assert.equal(e.mul(d).mod(phi).toString(16), '1');
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380
      // Even base (take #2)
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      var a = new BN('5');
382
      var b = new BN('6');
383
      var r = a.invm(b);
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      assert.equal(r.mul(a).mod(b).toString(16), '1');
385
    });
386
  });
387

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  describe('.gcd()', function() {
389
    it('should return GCD', function() {
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      assert.equal(new BN(3).gcd(new BN(2)).toString(16), '1');
391
      assert.equal(new BN(18).gcd(new BN(12)).toString(16), '6');
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      assert.equal(new BN(-18).gcd(new BN(12)).toString(16), '6');
393
    });
394
  });
395
});
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