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// Extensive test for (BigInt R Int32) comparison operations, testing the output
// is correct and consistent with (Int32 R⁻¹ BigInt).
function gcd(a, b) {
a |= 0;
b |= 0;
while (b !== 0) {
[a, b] = [b, a % b];
}
return Math.abs(a);
}
const ITERATIONS = 150;
function assertAllCombinationsTested(xs, ys, n) {
// If the array lengths are relatively prime and their product is at least
// |n| long, all possible combinations are tested at least once. Make sure
// we test each combination at least three times.
var m = 3;
assertEq(gcd(xs.length, ys.length), 1);
assertEq(m * xs.length * ys.length <= n, true);
}
function LessThan(xs, ys, n = ITERATIONS) {
assertAllCombinationsTested(xs, ys, n);
for (var i = 0; i < n; ++i) {
var x = xs[i % xs.length];
var y = ys[i % ys.length]|0; // Ensure int32 typed
assertEq(x == y, false);
assertEq(y == x, false);
assertEq(x != y, true);
assertEq(y != x, true);
assertEq(x < y, true);
assertEq(y < x, false);
assertEq(x <= y, true);
assertEq(y <= x, false);
assertEq(x > y, false);
assertEq(y > x, true);
assertEq(x >= y, false);
assertEq(y >= x, true);
}
}
function GreaterThan(xs, ys, n = ITERATIONS) {
assertAllCombinationsTested(xs, ys, n);
for (var i = 0; i < n; ++i) {
var x = xs[i % xs.length];
var y = ys[i % ys.length]|0; // Ensure int32 typed
assertEq(x == y, false);
assertEq(y == x, false);
assertEq(x != y, true);
assertEq(y != x, true);
assertEq(x < y, false);
assertEq(y < x, true);
assertEq(x <= y, false);
assertEq(y <= x, true);
assertEq(x > y, true);
assertEq(y > x, false);
assertEq(x >= y, true);
assertEq(y >= x, false);
}
}
function Equal(xs, ys, n = ITERATIONS) {
assertAllCombinationsTested(xs, ys, n);
for (var i = 0; i < n; ++i) {
var x = xs[i % xs.length];
var y = ys[i % ys.length]|0; // Ensure int32 typed
assertEq(x == y, true);
assertEq(y == x, true);
assertEq(x != y, false);
assertEq(y != x, false);
assertEq(x < y, false);
assertEq(y < x, false);
assertEq(x <= y, true);
assertEq(y <= x, true);
assertEq(x > y, false);
assertEq(y > x, false);
assertEq(x >= y, true);
assertEq(y >= x, true);
}
}
function test(fn) {
// Clone the test function to ensure a new function is compiled each time.
return Function(`return ${fn}`)();
}
const negativeInt32 = [-2147483648, -2147483647, -1];
const zeroInt32 = [0];
const positiveInt32 = [1, 2147483646, 2147483647];
const zeroOrPositiveInt32 = [...zeroInt32, ...positiveInt32];
const anyInt32 = [...negativeInt32, ...zeroInt32, ...positiveInt32];
// Test when the BigInt is too large to be representable as a single BigInt digit.
function testLarge() {
var xs = [
2n ** 32n, // exceeds single digit limit on 32-bit
2n ** 64n, // exceeds single digit limit on 64-bit
2n ** 96n, // not a single digit on either platform
];
test(GreaterThan)(xs, anyInt32);
var xs = [
-(2n ** 32n), // exceeds single digit limit on 32-bit
-(2n ** 64n), // exceeds single digit limit on 64-bit
-(2n ** 96n), // not a single digit on either platform
];
test(LessThan)(xs, anyInt32);
}
testLarge();
// Test when the BigInt is 0n.
function testZero() {
var xs = [
0n
];
test(GreaterThan)(xs, negativeInt32);
test(Equal)(xs, zeroInt32);
test(LessThan)(xs, positiveInt32);
}
testZero();
// Test when both numbers are negative.
function testNegative() {
var xs = [
-(2n ** 64n) - 2n,
-(2n ** 64n) - 1n, // Max negative using a single BigInt digit on 64-bit.
-(2n ** 64n),
-(2n ** 32n) - 2n,
-(2n ** 32n) - 1n, // Max negative using a single BigInt digit on 32-bit.
-(2n ** 32n),
-(2n ** 31n) - 1n, // One past max negative for Int32.
];
test(LessThan)(xs, negativeInt32);
var xs = [
-(2n ** 31n), // Max negative for Int32.
];
test(Equal)(xs, [-2147483648]);
test(LessThan)(xs, [-2147483647, -1]);
var xs = [
-(2n ** 31n) + 1n,
];
test(GreaterThan)(xs, [-2147483648]);
test(Equal)(xs, [-2147483647]);
test(LessThan)(xs, [-1]);
var xs = [
-1n,
];
test(GreaterThan)(xs, [-2147483648, -2147483647]);
test(Equal)(xs, [-1]);
}
testNegative();
// Test when both numbers are positive (and BigInt strictly positive).
function testPositive() {
var xs = [
1n,
];
test(GreaterThan)(xs, [0]);
test(Equal)(xs, [1]);
test(LessThan)(xs, [2147483646, 2147483647]);
var xs = [
2n ** 31n - 2n,
];
test(GreaterThan)(xs, [0, 1]);
test(Equal)(xs, [2147483646]);
test(LessThan)(xs, [2147483647]);
var xs = [
2n ** 31n - 1n, // Max positive for Int32.
];
test(GreaterThan)(xs, [0, 1, 2147483646]);
test(Equal)(xs, [2147483647]);
var xs = [
2n ** 31n, // One past max positive for Int32.
2n ** 32n - 2n,
2n ** 32n - 1n, // Max positive using a single BigInt digit on 32-bit.
2n ** 32n,
2n ** 64n - 2n,
2n ** 64n - 1n, // Max positive using a single BigInt digit on 64-bit.
2n ** 64n,
];
test(GreaterThan)(xs, zeroOrPositiveInt32);
}
testPositive();
// Test negative BigInt and positive Int32.
function testNegativePositive() {
var xs = [
-(2n ** 64n) - 2n,
-(2n ** 64n) - 1n, // Max negative using a single BigInt digit on 64-bit.
-(2n ** 64n),
-(2n ** 32n) - 2n,
-(2n ** 32n) - 1n, // Max negative using a single BigInt digit on 32-bit.
-(2n ** 32n),
-(2n ** 31n) - 1n,
-(2n ** 31n), // Max negative for Int32.
-(2n ** 31n) + 1n,
-2n, // Extra entry to ensure assertAllCombinationsTested passes.
-1n,
];
test(LessThan)(xs, zeroOrPositiveInt32);
}
testNegativePositive();
// Test (strictly) positive BigInt and negative Int32.
function testPositiveNegative() {
var xs = [
1n,
2n ** 31n - 2n,
2n ** 31n - 1n, // Max positive for Int32.
2n ** 31n,
2n ** 32n - 2n,
2n ** 32n - 1n, // Max positive using a single BigInt digit on 32-bit.
2n ** 32n,
2n ** 64n - 2n,
2n ** 64n - 1n, // Max positive using a single BigInt digit on 64-bit.
2n ** 64n,
];
test(GreaterThan)(xs, negativeInt32);
}
testPositiveNegative();
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