public void TestIsPerfectSquare64()
{
// Test all known suares
for (int i = 0; i < 32; i++)
{
long t = ((long)1) << i;
Assert.IsTrue(IntegerTheory.IsPerfectSquare(t * t), t + "^2 (+)");
}
// Test 1-offset from all known squares
for (int i = 1; i < 32; i++)
{
long t = ((long)1) << i;
Assert.IsFalse(IntegerTheory.IsPerfectSquare((t * t) - 1), t + "^2-1 (-)");
Assert.IsFalse(IntegerTheory.IsPerfectSquare((t * t) + 1), t + "^2+1 (-)");
}
// Selected Cases
Assert.IsTrue(IntegerTheory.IsPerfectSquare((long)1000000000000000000), "1000000000000000000 (+)");
Assert.IsFalse(IntegerTheory.IsPerfectSquare((long)1000000000000000001), "1000000000000000001 (-)");
Assert.IsFalse(IntegerTheory.IsPerfectSquare((long)999999999999999999), "999999999999999999 (-)");
Assert.IsFalse(IntegerTheory.IsPerfectSquare((long)999999999999999993), "999999999999999993 (-)");
Assert.IsFalse(IntegerTheory.IsPerfectSquare((long)-4), "-4 (-)");
Assert.IsFalse(IntegerTheory.IsPerfectSquare(Int64.MinValue), "Int32.MinValue (-)");
Assert.IsFalse(IntegerTheory.IsPerfectSquare(Int64.MaxValue), "Int32.MaxValue (-)");
Assert.IsTrue(IntegerTheory.IsPerfectSquare((long)1), "1 (+)");
Assert.IsTrue(IntegerTheory.IsPerfectSquare((long)0), "0 (+)");
Assert.IsFalse(IntegerTheory.IsPerfectSquare((long)-1), "-1 (-)");
}
public void TestIsPerfectSquare32()
{
// Test all known suares
int lastRadix = (int)Math.Floor(Math.Sqrt(Int32.MaxValue));
for (int i = 0; i <= lastRadix; i++)
{
Assert.IsTrue(IntegerTheory.IsPerfectSquare(i * i), i + "^2 (+)");
}
// Test 1-offset from all known squares
for (int i = 2; i <= lastRadix; i++)
{
Assert.IsFalse(IntegerTheory.IsPerfectSquare((i * i) - 1), i + "^2-1 (-)");
Assert.IsFalse(IntegerTheory.IsPerfectSquare((i * i) + 1), i + "^2+1 (-)");
}
// Selected Cases
Assert.IsTrue(IntegerTheory.IsPerfectSquare(100000000), "100000000 (+)");
Assert.IsFalse(IntegerTheory.IsPerfectSquare(100000001), "100000001 (-)");
Assert.IsFalse(IntegerTheory.IsPerfectSquare(99999999), "99999999 (-)");
Assert.IsFalse(IntegerTheory.IsPerfectSquare(-4), "-4 (-)");
Assert.IsFalse(IntegerTheory.IsPerfectSquare(Int32.MinValue), "Int32.MinValue (-)");
Assert.IsFalse(IntegerTheory.IsPerfectSquare(Int32.MaxValue), "Int32.MaxValue (-)");
Assert.IsTrue(IntegerTheory.IsPerfectSquare(1), "1 (+)");
Assert.IsTrue(IntegerTheory.IsPerfectSquare(0), "0 (+)");
Assert.IsFalse(IntegerTheory.IsPerfectSquare(-1), "-1 (-)");
}
/// <summary>
/// Run example
/// </summary>
public void Run()
{
// 1. Find out whether the provided number is an even number
Console.WriteLine(@"1. Find out whether the provided number is an even number");
Console.WriteLine(@"{0} is even = {1}. {2} is even = {3}", 1, IntegerTheory.IsEven(1), 2, 2.IsEven());
Console.WriteLine();
// 2. Find out whether the provided number is an odd number
Console.WriteLine(@"2. Find out whether the provided number is an odd number");
Console.WriteLine(@"{0} is odd = {1}. {2} is odd = {3}", 1, 1.IsOdd(), 2, IntegerTheory.IsOdd(2));
Console.WriteLine();
// 3. Find out whether the provided number is a perfect power of two
Console.WriteLine(@"2. Find out whether the provided number is a perfect power of two");
Console.WriteLine(@"{0} is power of two = {1}. {2} is power of two = {3}", 5, 5.IsPowerOfTwo(), 16, IntegerTheory.IsPowerOfTwo(16));
Console.WriteLine();
// 4. Find the closest perfect power of two that is larger or equal to 97
Console.WriteLine(@"4. Find the closest perfect power of two that is larger or equal to 97");
Console.WriteLine(97.CeilingToPowerOfTwo());
Console.WriteLine();
// 5. Raise 2 to the 16
Console.WriteLine(@"5. Raise 2 to the 16");
Console.WriteLine(16.PowerOfTwo());
Console.WriteLine();
// 6. Find out whether the number is a perfect square
Console.WriteLine(@"6. Find out whether the number is a perfect square");
Console.WriteLine(@"{0} is perfect square = {1}. {2} is perfect square = {3}", 37, 37.IsPerfectSquare(), 81, IntegerTheory.IsPerfectSquare(81));
Console.WriteLine();
// 7. Compute the greatest common divisor of 32 and 36
Console.WriteLine(@"7. Returns the greatest common divisor of 32 and 36");
Console.WriteLine(IntegerTheory.GreatestCommonDivisor(32, 36));
Console.WriteLine();
// 8. Compute the greatest common divisor of 492, -984, 123, 246
Console.WriteLine(@"8. Returns the greatest common divisor of 492, -984, 123, 246");
Console.WriteLine(IntegerTheory.GreatestCommonDivisor(492, -984, 123, 246));
Console.WriteLine();
// 9. Compute the extended greatest common divisor "z", such that 45*x + 18*y = z
Console.WriteLine(@"9. Compute the extended greatest common divisor Z, such that 45*x + 18*y = Z");
long x, y;
var z = IntegerTheory.ExtendedGreatestCommonDivisor(45, 18, out x, out y);
Console.WriteLine(@"z = {0}, x = {1}, y = {2}. 45*{1} + 18*{2} = {0}", z, x, y);
Console.WriteLine();
// 10. Compute the least common multiple of 16 and 12
Console.WriteLine(@"10. Compute the least common multiple of 16 and 12");
Console.WriteLine(IntegerTheory.LeastCommonMultiple(16, 12));
Console.WriteLine();
}