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// Copyright (c) 2017, the Dart project authors. Please see the AUTHORS file
// for details. All rights reserved. Use of this source code is governed by a
// BSD-style license that can be found in the LICENSE file.
// Testing Bigints with and without intrinsics.
// VMOptions=
// VMOptions=--no_intrinsify
// VMOptions=--optimization_counter_threshold=10 --no-background_compilation
import "package:expect/expect.dart";
import 'dart:math' show pow;
var smallNumber = new BigInt.from(1234567890); // is 31-bit integer.
var mediumNumber = new BigInt.from(1234567890123456); // is 53-bit integer
var bigNumber = BigInt.parse("590295810358705600000"); // > 64-bit integer
testModPow() {
void test(BigInt x, BigInt e, BigInt m, BigInt expectedResult) {
// Check that expected result is correct, using an unoptimized version.
assert(() {
slowModPow(BigInt x, BigInt e, BigInt m) {
var r = BigInt.one;
while (e > BigInt.zero) {
if (e.isOdd) r = (r * x) % m;
e >>= 1;
x = (x * x) % m;
}
return r;
}
return slowModPow(x, e, m) == expectedResult;
}());
var result = x.modPow(e, m);
Expect.equals(expectedResult, result, "$x.modPow($e, $m)");
}
test(new BigInt.from(10), new BigInt.from(20), BigInt.one, BigInt.zero);
test(new BigInt.from(1234567890), new BigInt.from(1000000001),
new BigInt.from(19), new BigInt.from(11));
test(new BigInt.from(1234567890), new BigInt.from(19),
new BigInt.from(1000000001), new BigInt.from(122998977));
test(new BigInt.from(19), new BigInt.from(1234567890),
new BigInt.from(1000000001), new BigInt.from(619059596));
test(new BigInt.from(19), new BigInt.from(1000000001),
new BigInt.from(1234567890), new BigInt.from(84910879));
test(new BigInt.from(1000000001), new BigInt.from(19),
new BigInt.from(1234567890), new BigInt.from(872984351));
test(new BigInt.from(1000000001), new BigInt.from(1234567890),
new BigInt.from(19), BigInt.zero);
test(BigInt.parse("12345678901234567890"),
BigInt.parse("10000000000000000001"), new BigInt.from(19), BigInt.two);
test(
BigInt.parse("12345678901234567890"),
new BigInt.from(19),
BigInt.parse("10000000000000000001"),
BigInt.parse("3239137215315834625"));
test(
new BigInt.from(19),
BigInt.parse("12345678901234567890"),
BigInt.parse("10000000000000000001"),
BigInt.parse("4544207837373941034"));
test(
new BigInt.from(19),
BigInt.parse("10000000000000000001"),
BigInt.parse("12345678901234567890"),
BigInt.parse("11135411705397624859"));
test(
BigInt.parse("10000000000000000001"),
new BigInt.from(19),
BigInt.parse("12345678901234567890"),
BigInt.parse("2034013733189773841"));
test(BigInt.parse("10000000000000000001"),
BigInt.parse("12345678901234567890"), new BigInt.from(19), BigInt.one);
test(
BigInt.parse("12345678901234567890"),
new BigInt.from(19),
BigInt.parse("10000000000000000001"),
BigInt.parse("3239137215315834625"));
test(BigInt.parse("12345678901234567890"),
BigInt.parse("10000000000000000001"), new BigInt.from(19), BigInt.two);
test(
BigInt.parse("123456789012345678901234567890"),
BigInt.parse("123456789012345678901234567891"),
BigInt.parse("123456789012345678901234567899"),
BigInt.parse("116401406051033429924651549616"));
test(
BigInt.parse("123456789012345678901234567890"),
BigInt.parse("123456789012345678901234567899"),
BigInt.parse("123456789012345678901234567891"),
BigInt.parse("123456789012345678901234567890"));
test(
BigInt.parse("123456789012345678901234567899"),
BigInt.parse("123456789012345678901234567890"),
BigInt.parse("123456789012345678901234567891"),
BigInt.parse("35088523091000351053091545070"));
test(
BigInt.parse("123456789012345678901234567899"),
BigInt.parse("123456789012345678901234567891"),
BigInt.parse("123456789012345678901234567890"),
BigInt.parse("18310047270234132455316941949"));
test(
BigInt.parse("123456789012345678901234567891"),
BigInt.parse("123456789012345678901234567899"),
BigInt.parse("123456789012345678901234567890"),
BigInt.one);
test(
BigInt.parse("123456789012345678901234567891"),
BigInt.parse("123456789012345678901234567890"),
BigInt.parse("123456789012345678901234567899"),
BigInt.parse("40128068573873018143207285483"));
}
testModInverse() {
void test(BigInt x, BigInt m, BigInt expectedResult) {
//print("$x op $m == $expectedResult");
// Check that expectedResult is an inverse.
assert(expectedResult < m);
// The 1 % m handles the m = 1 special case.
assert((((x % m) * expectedResult) - BigInt.one) % m == BigInt.zero);
var result = x.modInverse(m);
Expect.equals(expectedResult, result, "$x modinv $m");
if (x > m) {
x = x % m;
var result = x.modInverse(m);
Expect.equals(expectedResult, result, "$x modinv $m");
}
}
void testThrows(BigInt x, BigInt m) {
// Throws if not co-prime, which is a symmetric property.
Expect.throws(() => x.modInverse(m), null, "$x modinv $m");
Expect.throws(() => m.modInverse(x), null, "$m modinv $x");
}
test(BigInt.one, BigInt.one, BigInt.zero);
testThrows(BigInt.zero, new BigInt.from(1000000001));
testThrows(BigInt.two, new BigInt.from(4));
testThrows(new BigInt.from(99), new BigInt.from(9));
testThrows(new BigInt.from(19), new BigInt.from(1000000001));
testThrows(BigInt.parse("123456789012345678901234567890"),
BigInt.parse("123456789012345678901234567899"));
// Co-prime numbers
test(new BigInt.from(1234567890), new BigInt.from(19), new BigInt.from(11));
test(new BigInt.from(1234567890), new BigInt.from(1000000001),
new BigInt.from(189108911));
test(new BigInt.from(19), new BigInt.from(1234567890),
new BigInt.from(519818059));
test(new BigInt.from(1000000001), new BigInt.from(1234567890),
new BigInt.from(1001100101));
test(new BigInt.from(12345), new BigInt.from(12346), new BigInt.from(12345));
test(new BigInt.from(12345), new BigInt.from(12346), new BigInt.from(12345));
test(smallNumber, new BigInt.from(137), new BigInt.from(42));
test(new BigInt.from(137), smallNumber, new BigInt.from(856087223));
test(mediumNumber, new BigInt.from(137), new BigInt.from(77));
test(new BigInt.from(137), mediumNumber, new BigInt.from(540686667207353));
test(bigNumber, new BigInt.from(137), new BigInt.from(128));
}
testGcd() {
// Call testFunc with all combinations and orders of plus/minus
// value and other.
void callCombos(
BigInt value, BigInt other, void testFunc(BigInt a, BigInt b)) {
testFunc(value, other);
testFunc(value, -other);
testFunc(-value, other);
testFunc(-value, -other);
if (value == other) return;
testFunc(other, value);
testFunc(other, -value);
testFunc(-other, value);
testFunc(-other, -value);
}
// Test that gcd of value and other (non-negative) is expectedResult.
// Tests all combinations of positive and negative values and order of
// operands, so use positive values and order is not important.
void test(BigInt value, BigInt other, BigInt expectedResult) {
// Check for bug in test.
assert(
expectedResult == BigInt.zero || value % expectedResult == BigInt.zero);
assert(
expectedResult == BigInt.zero || other % expectedResult == BigInt.zero);
callCombos(value, other, (BigInt a, BigInt b) {
var result = a.gcd(b);
/// Check that the result is a divisor.
Expect.equals(
BigInt.zero, result == BigInt.zero ? a : a % result, "$result | $a");
Expect.equals(
BigInt.zero, result == BigInt.zero ? b : b % result, "$result | $b");
// Check for bug in test. If assert fails, the expected value is too low,
// and the gcd call has found a greater common divisor.
assert(result >= expectedResult);
Expect.equals(expectedResult, result, "$a.gcd($b)");
});
}
// Test that gcd of value and other (non-negative) throws.
testThrows(value, other) {
callCombos(value, other, (a, b) {
Expect.throws(() => a.gcd(b), null, "$a.gcd($b)");
});
}
// Format:
// test(value1, value2, expectedResult);
test(BigInt.one, BigInt.one, BigInt.one); // both are 1
test(BigInt.one, BigInt.two, BigInt.one); // one is 1
test(new BigInt.from(3), new BigInt.from(5), BigInt.one); // coprime.
test(new BigInt.from(37), new BigInt.from(37),
new BigInt.from(37)); // Same larger prime.
test(new BigInt.from(9999), new BigInt.from(7272),
new BigInt.from(909)); // Larger numbers
test(BigInt.zero, new BigInt.from(1000),
new BigInt.from(1000)); // One operand is zero.
test(BigInt.zero, BigInt.zero, BigInt.zero); // Both operands are zero.
// Multiplying both operands by a number multiplies result by same number.
test(new BigInt.from(693), new BigInt.from(609), new BigInt.from(21));
test(new BigInt.from(693) << 5, new BigInt.from(609) << 5,
new BigInt.from(21) << 5);
test(
new BigInt.from(693) * new BigInt.from(937),
new BigInt.from(609) * new BigInt.from(937),
new BigInt.from(21) * new BigInt.from(937));
test(
new BigInt.from(693) * new BigInt.from(pow(2, 32)),
new BigInt.from(609) * new BigInt.from(pow(2, 32)),
new BigInt.from(21) * new BigInt.from(pow(2, 32)));
test(
new BigInt.from(693) * BigInt.two.pow(52),
new BigInt.from(609) * BigInt.two.pow(52),
new BigInt.from(21) * BigInt.two.pow(52));
test(
new BigInt.from(693) * BigInt.two.pow(53),
new BigInt.from(609) * BigInt.two.pow(53),
new BigInt.from(21) * BigInt.two.pow(53)); // Regression.
test(
new BigInt.from(693) * BigInt.two.pow(99),
new BigInt.from(609) * BigInt.two.pow(99),
new BigInt.from(21) * BigInt.two.pow(99));
test(new BigInt.from(1234567890), new BigInt.from(19), BigInt.one);
test(new BigInt.from(1234567890), new BigInt.from(1000000001), BigInt.one);
test(new BigInt.from(19), new BigInt.from(1000000001), new BigInt.from(19));
test(new BigInt.from(0x3FFFFFFF), new BigInt.from(0x3FFFFFFF),
new BigInt.from(0x3FFFFFFF));
test(new BigInt.from(0x3FFFFFFF), new BigInt.from(0x40000000), BigInt.one);
test(BigInt.two.pow(54), BigInt.two.pow(53), BigInt.two.pow(53));
test(
(BigInt.two.pow(52) - BigInt.one) * BigInt.two.pow(14),
(BigInt.two.pow(26) - BigInt.one) * BigInt.two.pow(22),
(BigInt.two.pow(26) - BigInt.one) * BigInt.two.pow(14));
}
foo() => BigInt.parse("1234567890123456789");
bar() => BigInt.parse("12345678901234567890");
testSmiOverflow() {
var a = new BigInt.from(1073741823);
var b = new BigInt.from(1073741822);
Expect.equals(new BigInt.from(2147483645), a + b);
a = -new BigInt.from(1000000000);
b = new BigInt.from(1000000001);
Expect.equals(-new BigInt.from(2000000001), a - b);
Expect.equals(-BigInt.parse("1000000001000000000"), a * b);
}
testBigintAdd() {
// Bigint and Smi.
var a = BigInt.parse("12345678901234567890");
var b = BigInt.two;
Expect.equals(BigInt.parse("12345678901234567892"), a + b);
Expect.equals(BigInt.parse("12345678901234567892"), b + a);
// Bigint and Bigint.
a = BigInt.parse("10000000000000000001");
Expect.equals(BigInt.parse("20000000000000000002"), a + a);
}
testBigintSub() {
// Bigint and Smi.
var a = BigInt.parse("12345678901234567890");
var b = BigInt.two;
Expect.equals(BigInt.parse("12345678901234567888"), a - b);
Expect.equals(-BigInt.parse("12345678901234567888"), b - a);
// Bigint and Bigint.
a = BigInt.parse("10000000000000000001");
Expect.equals(BigInt.parse("20000000000000000002"), a + a);
}
testBigintMul() {
// Bigint and Smi.
var a = BigInt.parse("12345678901234567890");
var b = new BigInt.from(10);
Expect.equals(BigInt.parse("123456789012345678900"), a * b);
Expect.equals(BigInt.parse("123456789012345678900"), b * a);
// Bigint and Bigint.
a = BigInt.parse("12345678901234567890");
b = BigInt.parse("10000000000000000");
Expect.equals(BigInt.parse("123456789012345678900000000000000000"), a * b);
}
testBigintTruncDiv() {
var a = BigInt.parse("12345678901234567890");
var b = new BigInt.from(10);
// Bigint and Smi.
Expect.equals(BigInt.parse("1234567890123456789"), a ~/ b);
Expect.equals(BigInt.zero, b ~/ a);
Expect.equals(new BigInt.from(123456789),
BigInt.parse("123456789012345678") ~/ new BigInt.from(1000000000));
// TruncDiv as used in toString().
a = BigInt.parse("4503599627370496"); // 0x10000000000000
b = new BigInt.from(10000);
Expect.equals(new BigInt.from(450359962737), a ~/ b);
b = new BigInt.from(1000000000);
Expect.equals(new BigInt.from(4503599), a ~/ b);
// Bigint and Bigint.
a = BigInt.parse("12345678901234567890");
b = BigInt.parse("10000000000000000");
Expect.equals(new BigInt.from(1234), a ~/ b);
}
testBigintDiv() {
// Bigint and Smi.
Expect.equals(1234567890123456789.1,
BigInt.parse("12345678901234567891") / new BigInt.from(10));
Expect.equals(
0.000000001234, new BigInt.from(1234) / new BigInt.from(1000000000000));
Expect.equals(12345678901234000000.0,
BigInt.parse("123456789012340000000") / new BigInt.from(10));
// Bigint and Bigint.
var a = BigInt.parse("12345670000000000000");
var b = BigInt.parse("10000000000000000");
Expect.equals(1234.567, a / b);
}
testBigintModulo() {
// Bigint and Smi.
var a = new BigInt.from(1000000000005);
var b = new BigInt.from(10);
Expect.equals(new BigInt.from(5), a % b);
Expect.equals(new BigInt.from(10), b % a);
// Modulo as used in toString().
a = BigInt.parse("4503599627370496"); // 0x10000000000000
b = new BigInt.from(10000);
Expect.equals(new BigInt.from(496), a % b);
b = new BigInt.from(1000000000);
Expect.equals(new BigInt.from(627370496), a % b);
// Bigint & Bigint
a = BigInt.parse("10000000000000000001");
b = BigInt.parse("10000000000000000000");
Expect.equals(BigInt.one, a % b);
Expect.equals(BigInt.parse("10000000000000000000"), b % a);
}
testBigintModPow() {
var x, e, m;
x = new BigInt.from(1234567890);
e = new BigInt.from(1000000001);
m = new BigInt.from(19);
Expect.equals(new BigInt.from(11), x.modPow(e, m));
x = new BigInt.from(1234567890);
e = new BigInt.from(19);
m = new BigInt.from(1000000001);
Expect.equals(new BigInt.from(122998977), x.modPow(e, m));
x = new BigInt.from(19);
e = new BigInt.from(1234567890);
m = new BigInt.from(1000000001);
Expect.equals(new BigInt.from(619059596), x.modPow(e, m));
x = new BigInt.from(19);
e = new BigInt.from(1000000001);
m = new BigInt.from(1234567890);
Expect.equals(new BigInt.from(84910879), x.modPow(e, m));
x = new BigInt.from(1000000001);
e = new BigInt.from(19);
m = new BigInt.from(1234567890);
Expect.equals(new BigInt.from(872984351), x.modPow(e, m));
x = new BigInt.from(1000000001);
e = new BigInt.from(1234567890);
m = new BigInt.from(19);
Expect.equals(BigInt.zero, x.modPow(e, m));
x = BigInt.parse("12345678901234567890");
e = BigInt.parse("10000000000000000001");
m = new BigInt.from(19);
Expect.equals(BigInt.two, x.modPow(e, m));
x = BigInt.parse("12345678901234567890");
e = new BigInt.from(19);
m = BigInt.parse("10000000000000000001");
Expect.equals(BigInt.parse("3239137215315834625"), x.modPow(e, m));
x = new BigInt.from(19);
e = BigInt.parse("12345678901234567890");
m = BigInt.parse("10000000000000000001");
Expect.equals(BigInt.parse("4544207837373941034"), x.modPow(e, m));
x = new BigInt.from(19);
e = BigInt.parse("10000000000000000001");
m = BigInt.parse("12345678901234567890");
Expect.equals(BigInt.parse("11135411705397624859"), x.modPow(e, m));
x = BigInt.parse("10000000000000000001");
e = new BigInt.from(19);
m = BigInt.parse("12345678901234567890");
Expect.equals(BigInt.parse("2034013733189773841"), x.modPow(e, m));
x = BigInt.parse("10000000000000000001");
e = BigInt.parse("12345678901234567890");
m = new BigInt.from(19);
Expect.equals(BigInt.one, x.modPow(e, m));
x = BigInt.parse("12345678901234567890");
e = new BigInt.from(19);
m = BigInt.parse("10000000000000000001");
Expect.equals(BigInt.parse("3239137215315834625"), x.modPow(e, m));
x = BigInt.parse("12345678901234567890");
e = BigInt.parse("10000000000000000001");
m = new BigInt.from(19);
Expect.equals(BigInt.two, x.modPow(e, m));
x = BigInt.parse("123456789012345678901234567890");
e = BigInt.parse("123456789012345678901234567891");
m = BigInt.parse("123456789012345678901234567899");
Expect.equals(BigInt.parse("116401406051033429924651549616"), x.modPow(e, m));
x = BigInt.parse("123456789012345678901234567890");
e = BigInt.parse("123456789012345678901234567899");
m = BigInt.parse("123456789012345678901234567891");
Expect.equals(BigInt.parse("123456789012345678901234567890"), x.modPow(e, m));
x = BigInt.parse("123456789012345678901234567899");
e = BigInt.parse("123456789012345678901234567890");
m = BigInt.parse("123456789012345678901234567891");
Expect.equals(BigInt.parse("35088523091000351053091545070"), x.modPow(e, m));
x = BigInt.parse("123456789012345678901234567899");
e = BigInt.parse("123456789012345678901234567891");
m = BigInt.parse("123456789012345678901234567890");
Expect.equals(BigInt.parse("18310047270234132455316941949"), x.modPow(e, m));
x = BigInt.parse("123456789012345678901234567891");
e = BigInt.parse("123456789012345678901234567899");
m = BigInt.parse("123456789012345678901234567890");
Expect.equals(BigInt.one, x.modPow(e, m));
x = BigInt.parse("123456789012345678901234567891");
e = BigInt.parse("123456789012345678901234567890");
m = BigInt.parse("123456789012345678901234567899");
Expect.equals(BigInt.parse("40128068573873018143207285483"), x.modPow(e, m));
}
testBigintModInverse() {
var x, m;
x = BigInt.one;
m = BigInt.one;
Expect.equals(BigInt.zero, x.modInverse(m));
x = BigInt.zero;
m = new BigInt.from(1000000001);
Expect.throws(() => x.modInverse(m), (e) => e is Exception); // Not coprime.
x = new BigInt.from(1234567890);
m = new BigInt.from(19);
Expect.equals(new BigInt.from(11), x.modInverse(m));
x = new BigInt.from(1234567890);
m = new BigInt.from(1000000001);
Expect.equals(new BigInt.from(189108911), x.modInverse(m));
x = new BigInt.from(19);
m = new BigInt.from(1000000001);
Expect.throws(() => x.modInverse(m), (e) => e is Exception); // Not coprime.
x = new BigInt.from(19);
m = new BigInt.from(1234567890);
Expect.equals(new BigInt.from(519818059), x.modInverse(m));
x = new BigInt.from(1000000001);
m = new BigInt.from(1234567890);
Expect.equals(new BigInt.from(1001100101), x.modInverse(m));
x = new BigInt.from(1000000001);
m = new BigInt.from(19);
Expect.throws(() => x.modInverse(m), (e) => e is Exception); // Not coprime.
x = BigInt.parse("12345678901234567890");
m = new BigInt.from(19);
Expect.equals(new BigInt.from(3), x.modInverse(m));
x = BigInt.parse("12345678901234567890");
m = BigInt.parse("10000000000000000001");
Expect.equals(BigInt.parse("9736746307686209582"), x.modInverse(m));
x = new BigInt.from(19);
m = BigInt.parse("10000000000000000001");
Expect.equals(BigInt.parse("6315789473684210527"), x.modInverse(m));
x = new BigInt.from(19);
m = BigInt.parse("12345678901234567890");
Expect.equals(BigInt.parse("10396361179987004539"), x.modInverse(m));
x = BigInt.parse("10000000000000000001");
m = BigInt.parse("12345678901234567890");
Expect.equals(BigInt.parse("325004555487045911"), x.modInverse(m));
x = BigInt.parse("10000000000000000001");
m = new BigInt.from(19);
Expect.equals(new BigInt.from(7), x.modInverse(m));
x = BigInt.parse("12345678901234567890");
m = BigInt.parse("10000000000000000001");
Expect.equals(BigInt.parse("9736746307686209582"), x.modInverse(m));
x = BigInt.parse("12345678901234567890");
m = new BigInt.from(19);
Expect.equals(new BigInt.from(3), x.modInverse(m));
x = BigInt.parse("123456789012345678901234567890");
m = BigInt.parse("123456789012345678901234567899");
Expect.throws(() => x.modInverse(m), (e) => e is Exception); // Not coprime.
x = BigInt.parse("123456789012345678901234567890");
m = BigInt.parse("123456789012345678901234567891");
Expect.equals(
BigInt.parse("123456789012345678901234567890"), x.modInverse(m));
x = BigInt.parse("123456789012345678901234567899");
m = BigInt.parse("123456789012345678901234567891");
Expect.equals(BigInt.parse("77160493132716049313271604932"), x.modInverse(m));
x = BigInt.parse("123456789012345678901234567899");
m = BigInt.parse("123456789012345678901234567890");
Expect.throws(() => x.modInverse(m), (e) => e is Exception); // Not coprime.
x = BigInt.parse("123456789012345678901234567891");
m = BigInt.parse("123456789012345678901234567890");
Expect.equals(BigInt.one, x.modInverse(m));
x = BigInt.parse("123456789012345678901234567891");
m = BigInt.parse("123456789012345678901234567899");
Expect.equals(BigInt.parse("46296295879629629587962962962"), x.modInverse(m));
}
testBigintGcd() {
var x, m;
x = BigInt.one;
m = BigInt.one;
Expect.equals(BigInt.one, x.gcd(m));
x = new BigInt.from(693);
m = new BigInt.from(609);
Expect.equals(new BigInt.from(21), x.gcd(m));
x = new BigInt.from(693) << 40;
m = new BigInt.from(609) << 40;
Expect.equals(new BigInt.from(21) << 40, x.gcd(m));
x = new BigInt.from(609) << 40;
m = new BigInt.from(693) << 40;
Expect.equals(new BigInt.from(21) << 40, x.gcd(m));
x = BigInt.zero;
m = new BigInt.from(1000000001);
Expect.equals(m, x.gcd(m));
x = new BigInt.from(1000000001);
m = BigInt.zero;
Expect.equals(x, x.gcd(m));
x = BigInt.zero;
m = -new BigInt.from(1000000001);
Expect.equals(-m, x.gcd(m));
x = -new BigInt.from(1000000001);
m = BigInt.zero;
Expect.equals(-x, x.gcd(m));
x = BigInt.zero;
m = BigInt.zero;
Expect.equals(BigInt.zero, x.gcd(m));
x = BigInt.zero;
m = BigInt.parse("123456789012345678901234567890");
Expect.equals(m, x.gcd(m));
x = BigInt.parse("123456789012345678901234567890");
m = BigInt.zero;
Expect.equals(x, x.gcd(m));
x = BigInt.zero;
m = -BigInt.parse("123456789012345678901234567890");
Expect.equals(-m, x.gcd(m));
x = -BigInt.parse("123456789012345678901234567890");
m = BigInt.zero;
Expect.equals(-x, x.gcd(m));
x = new BigInt.from(1234567890);
m = new BigInt.from(19);
Expect.equals(BigInt.one, x.gcd(m));
x = new BigInt.from(1234567890);
m = new BigInt.from(1000000001);
Expect.equals(BigInt.one, x.gcd(m));
x = new BigInt.from(19);
m = new BigInt.from(1000000001);
Expect.equals(new BigInt.from(19), x.gcd(m));
x = new BigInt.from(19);
m = new BigInt.from(1234567890);
Expect.equals(BigInt.one, x.gcd(m));
x = new BigInt.from(1000000001);
m = new BigInt.from(1234567890);
Expect.equals(BigInt.one, x.gcd(m));
x = new BigInt.from(1000000001);
m = new BigInt.from(19);
Expect.equals(new BigInt.from(19), x.gcd(m));
x = BigInt.parse("12345678901234567890");
m = new BigInt.from(19);
Expect.equals(BigInt.one, x.gcd(m));
x = BigInt.parse("12345678901234567890");
m = BigInt.parse("10000000000000000001");
Expect.equals(BigInt.one, x.gcd(m));
x = new BigInt.from(19);
m = BigInt.parse("10000000000000000001");
Expect.equals(BigInt.one, x.gcd(m));
x = new BigInt.from(19);
m = BigInt.parse("12345678901234567890");
Expect.equals(BigInt.one, x.gcd(m));
x = BigInt.parse("10000000000000000001");
m = BigInt.parse("12345678901234567890");
Expect.equals(BigInt.one, x.gcd(m));
x = BigInt.parse("10000000000000000001");
m = new BigInt.from(19);
Expect.equals(BigInt.one, x.gcd(m));
x = BigInt.parse("12345678901234567890");
m = BigInt.parse("10000000000000000001");
Expect.equals(BigInt.one, x.gcd(m));
x = BigInt.parse("12345678901234567890");
m = new BigInt.from(19);
Expect.equals(BigInt.one, x.gcd(m));
x = BigInt.parse("123456789012345678901234567890");
m = BigInt.parse("123456789012345678901234567899");
Expect.equals(new BigInt.from(9), x.gcd(m));
x = BigInt.parse("123456789012345678901234567890");
m = BigInt.parse("123456789012345678901234567891");
Expect.equals(BigInt.one, x.gcd(m));
x = BigInt.parse("123456789012345678901234567899");
m = BigInt.parse("123456789012345678901234567891");
Expect.equals(BigInt.one, x.gcd(m));
x = BigInt.parse("123456789012345678901234567899");
m = BigInt.parse("123456789012345678901234567890");
Expect.equals(new BigInt.from(9), x.gcd(m));
x = BigInt.parse("123456789012345678901234567891");
m = BigInt.parse("123456789012345678901234567890");
Expect.equals(BigInt.one, x.gcd(m));
x = BigInt.parse("123456789012345678901234567891");
m = BigInt.parse("123456789012345678901234567899");
Expect.equals(BigInt.one, x.gcd(m));
}
testBigintNegate() {
var a = BigInt.parse("0xF000000000000000F");
var b = ~a; // negate.
Expect.equals(BigInt.parse("-0xF0000000000000010"), b);
Expect.equals(BigInt.zero, a & b);
Expect.equals(-BigInt.one, a | b);
}
testShiftAmount() {
Expect.equals(BigInt.zero, new BigInt.from(12) >> 0x7FFFFFFFFFFFFFFF);
Expect.equals(-BigInt.one, -new BigInt.from(12) >> 0x7FFFFFFFFFFFFFFF);
bool exceptionCaught = false;
try {
var a = BigInt.one << 0x7FFFFFFFFFFFFFFF;
} on OutOfMemoryError catch (e) {
exceptionCaught = true;
} catch (e) {
// In JavaScript the allocation of the internal array throws different
// kind of errors. Just assume it's the right one.
exceptionCaught = true;
}
Expect.equals(true, exceptionCaught);
}
void testPow() {
Expect.throws(() => BigInt.zero.pow(-1), (e) => e is ArgumentError);
Expect.throws(() => BigInt.one.pow(-1), (e) => e is ArgumentError);
Expect.equals(BigInt.one, BigInt.zero.pow(0));
Expect.equals(BigInt.one, BigInt.one.pow(0));
Expect.equals(BigInt.one, BigInt.two.pow(0));
Expect.equals(
BigInt.parse("6208695403009031808124000434786599466508260573005"
"3508480680160632742505079094163654310415168343540278191693"
"5380629274547924077088101599462083663373536705603680787010"
"0454231036999140164473780469056908670815701571304455697970"
"9971709527651446612272365411298758026041094781651768636427"
"4780767345075500515905845436036697865291662016364446907149"
"5652136304764312997430969058854587555188117728022873502683"
"6327099687782677885098446991121805146733387058565662606025"
"2854981418159051193843689364388302820905062090182919338371"
"8783490348348213313279505263650976040646393394551465619437"
"7126646818740571207346633109049097273375955956480091920939"
"5595130499375022416542475049562151695680373438890512164488"
"6567991220660935537691145761690539808578087290707813875567"
"9145826183642842261374804672283964244725240865733938342036"
"1216219271232461693264437901347421563392441043817990067322"
"88"),
BigInt.parse("90218646930912603144382974164422").pow(27));
;
}
void testToRadixString() {
// Test that we accept radix 2 to 36 and that we use lower-case
// letters.
var expected = [
'0', '1', '2', '3', '4', '5', '6', '7', '8', '9', 'a', 'b', 'c', 'd', //
'e', 'f', 'g', 'h', 'i', 'j', 'k', 'l', 'm', 'n', 'o', 'p', 'q', 'r', //
's', 't', 'u', 'v', 'w', 'x', 'y', 'z' //
];
for (var radix = 2; radix <= 36; radix++) {
for (var i = 0; i < radix; i++) {
Expect.equals(expected[i], new BigInt.from(i).toRadixString(radix));
}
}
var illegalRadices = [-1, 0, 1, 37];
for (var radix in illegalRadices) {
try {
new BigInt.from(42).toRadixString(radix);
Expect.fail("Exception expected");
} on ArgumentError catch (e) {
// Nothing to do.
}
}
// Try large numbers (regression test for issue 15316).
var bignums = [
BigInt.parse("0x80000000"),
BigInt.parse("0x100000000"),
BigInt.parse("0x10000000000000"),
BigInt.parse("0x10000000000001"), // 53 significant bits.
BigInt.parse("0x20000000000000"),
BigInt.parse("0x20000000000002"),
BigInt.parse("0x1000000000000000"),
BigInt.parse("0x1000000000000100"),
BigInt.parse("0x2000000000000000"),
BigInt.parse("0x2000000000000200"),
BigInt.parse("0x8000000000000000"),
BigInt.parse("0x8000000000000800"),
BigInt.parse("0x10000000000000000"),
BigInt.parse("0x10000000000001000"),
BigInt.parse("0x100000000000010000"),
BigInt.parse("0x1000000000000100000"),
BigInt.parse("0x10000000000001000000"),
BigInt.parse("0x100000000000010000000"),
BigInt.parse("0x1000000000000100000000"),
BigInt.parse("0x10000000000001000000000"),
];
for (var bignum in bignums) {
for (int radix = 2; radix <= 36; radix++) {
String digits = bignum.toRadixString(radix);
BigInt result = BigInt.parse(digits, radix: radix);
Expect.equals(
bignum, result, "${bignum.toRadixString(16)} -> $digits/$radix");
}
}
}
testToString() {
/// Test that converting [value] to a string gives [expect].
/// Also test that `-value` gives `"-"+expect`.
test(BigInt value, String expect) {
Expect.equals(expect, value.toString());
Expect.equals(expect, "$value");
Expect.equals(expect, (new StringBuffer()..write(value)).toString());
if (value == BigInt.zero) return;
expect = "-$expect";
value = -value;
Expect.equals(expect, value.toString());
Expect.equals(expect, "$value");
Expect.equals(expect, (new StringBuffer()..write(value)).toString());
}
// Very simple tests.
test(BigInt.zero, "0");
test(BigInt.one, "1");
test(BigInt.two, "2");
test(new BigInt.from(5), "5");
// Binary special cases.
// ~2^30.
test(BigInt.parse("0x3fffffff"), "1073741823");
test(BigInt.parse("0x40000000"), "1073741824");
test(BigInt.parse("0x40000001"), "1073741825");
// ~2^31.
test(BigInt.parse("0x7fffffff"), "2147483647");
test(BigInt.parse("0x80000000"), "2147483648");
test(BigInt.parse("0x80000001"), "2147483649");
// ~2^32.
test(BigInt.parse("0xffffffff"), "4294967295");
test(BigInt.parse("0x100000000"), "4294967296");
test(BigInt.parse("0x100000001"), "4294967297");
// ~2^51.
test(BigInt.parse("0x7ffffffffffff"), "2251799813685247");
test(BigInt.parse("0x8000000000000"), "2251799813685248");
test(BigInt.parse("0x8000000000001"), "2251799813685249");
// ~2^52.
test(BigInt.parse("0xfffffffffffff"), "4503599627370495");
test(BigInt.parse("0x10000000000000"), "4503599627370496");
test(BigInt.parse("0x10000000000001"), "4503599627370497");
// ~2^53.
test(BigInt.parse("0x1fffffffffffff"), "9007199254740991");
test(BigInt.parse("0x20000000000000"), "9007199254740992");
test(BigInt.parse("0x20000000000001"), "9007199254740993");
// ~2^62.
test(BigInt.parse("0x3fffffffffffffff"), "4611686018427387903");
test(BigInt.parse("0x4000000000000000"), "4611686018427387904");
test(BigInt.parse("0x4000000000000001"), "4611686018427387905");
// ~2^63.
test(BigInt.parse("0x7fffffffffffffff"), "9223372036854775807");
test(BigInt.parse("0x8000000000000000"), "9223372036854775808");
test(BigInt.parse("0x8000000000000001"), "9223372036854775809");
// ~2^64.
test(BigInt.parse("0xffffffffffffffff"), "18446744073709551615");
test(BigInt.parse("0x10000000000000000"), "18446744073709551616");
test(BigInt.parse("0x10000000000000001"), "18446744073709551617");
// Big bignum.
test(BigInt.parse("123456789012345678901234567890"),
"123456789012345678901234567890");
// Decimal special cases.
BigInt number = new BigInt.from(10);
// Numbers 99..99, 100...00, and 100..01 up to 23 digits.
for (int i = 1; i < 22; i++) {
test(number - BigInt.one, "9" * i);
test(number, "1" + "0" * i);
test(number + BigInt.one, "1" + "0" * (i - 1) + "1");
number *= new BigInt.from(10);
}
}
void testFromToInt() {
void test(int x) {
var bigFrom = new BigInt.from(x);
var bigStr = bigFrom.toString();
Expect.equals(x, bigFrom.toInt());
Expect.equals(x, int.parse(bigStr));
}
for (int i = 0; i < 20; i++) {
test(i);
// Dart2js doesn't know that -0 should stay 0.
if (i != 0) test(-i);
}
// For now just test "easy" integers since there is no check yet that clamps
// the returned integer.
for (int i = 0; i < 2000000; i += 10000) {
test(i);
// Dart2js doesn't know that -0 should stay 0.
if (i != 0) test(-i);
}
const minInt64 = -0x80000000 * 0x100000000;
test(minInt64);
}
void testFromToDouble() {
Expect.equals(-1.0, (-BigInt.one).toDouble());
Expect.throws(() => new BigInt.from(double.nan));
Expect.throws(() => new BigInt.from(double.infinity));
Expect.throws(() => new BigInt.from(-double.infinity));
const double maxDouble = 1.7976931348623157e+308;
const String maxDoubleHexStr = "0xfffffffffffff8000000000000000"
"00000000000000000000000000000000000000000000000000000000000000"
"00000000000000000000000000000000000000000000000000000000000000"
"00000000000000000000000000000000000000000000000000000000000000"
"00000000000000000000000000000000000000000";
// The following value lies directly on the boundary between max double and
// infinity. It rounds to infinity. Any value below rounds to a finite double
// value.
const String maxDoubleBoundaryStr = "0xfffffffffffffc0000000000"
"00000000000000000000000000000000000000000000000000000000000000"
"00000000000000000000000000000000000000000000000000000000000000"
"00000000000000000000000000000000000000000000000000000000000000"
"0000000000000000000000000000000000000000000000";
var bigMax = BigInt.parse(maxDoubleHexStr);
var bigBoundary = BigInt.parse(maxDoubleBoundaryStr);
Expect.equals(maxDouble, bigMax.toDouble());
Expect.equals(bigMax, new BigInt.from(maxDouble));
Expect.equals(double.infinity, bigBoundary.toDouble());
Expect.equals(maxDouble, (bigBoundary - BigInt.one).toDouble());
Expect.equals(-maxDouble, (-bigMax).toDouble());
Expect.equals(-bigMax, new BigInt.from(-maxDouble));
Expect.equals(-double.infinity, (-bigBoundary).toDouble());
Expect.equals(-maxDouble, (-(bigBoundary - BigInt.one)).toDouble());
void test(int x) {
var str = x.toString();
var big = BigInt.parse(str);
Expect.equals(x, big.toDouble());
}
for (int i = 0; i < 20; i++) {
test(i);
// Dart2js doesn't know that -0 should stay 0.
if (i != 0) test(-i);
}
for (int i = 0; i < 2000000; i += 10000) {
test(i);
// Dart2js doesn't know that -0 should stay 0.
if (i != 0) test(-i);
}
for (int i = 1000; i < 100000; i += 1000) {
var d = 1 / i;
Expect.equals(BigInt.zero, new BigInt.from(d));
}
// Non-integer values are truncated.
Expect.equals(BigInt.one, new BigInt.from(1.5));
Expect.equals(-BigInt.one, new BigInt.from(-1.5));
Expect.equals(BigInt.zero, new BigInt.from(0.9999999999999999));
Expect.equals(BigInt.zero, new BigInt.from(-0.9999999999999999));
}
main() {
for (int i = 0; i < 10; i++) {
Expect.equals(BigInt.parse("1234567890123456789"), foo());
Expect.equals(BigInt.parse("12345678901234567890"), bar());
testModPow();
testModInverse();
testGcd();
testSmiOverflow();
testBigintAdd();
testBigintSub();
testBigintMul();
testBigintTruncDiv();
testBigintDiv();
testBigintModulo();
testBigintModPow();
testBigintModInverse();
testBigintGcd();
testBigintNegate();
testShiftAmount();
testPow();
testToRadixString();
testToString();
testFromToInt();
testFromToDouble();
Expect.equals(BigInt.parse("12345678901234567890"),
BigInt.parse("12345678901234567890").abs());
Expect.equals(BigInt.parse("12345678901234567890"),
BigInt.parse("-12345678901234567890").abs());
var a = BigInt.parse("10000000000000000000");
var b = BigInt.parse("10000000000000000001");
Expect.equals(false, a.hashCode == b.hashCode);
Expect.equals(true, a.hashCode == (b - BigInt.one).hashCode);
}
}