public void BasicAdditionMultiplicationTest()
{
var value = new Natural(ulong.MaxValue);
Assert.AreEqual(value + value, value * 2);
Assert.AreEqual(value + value + value, value * 3);
}
public Integer(long value)
{
this.sign = value < 0 ? (sbyte)(-1) : (sbyte)1;
if (value == Int64.MinValue)
this.magnitude = new Natural((ulong)Int64.MaxValue) + 1;
else
this.magnitude = new Natural((ulong)Math.Abs(value));
}
public Natural Factorial()
{
var result = new Natural(1);
for (Natural i = new Natural(1); i <= this; i++) {
result = result * i;
}
return result;
}
public static void Divide(Natural a, Natural b, out Natural quotient, out Natural remainder)
{
// Taken from http://en.wikipedia.org/wiki/Division_algorithm#Integer_division_.28unsigned.29_with_remainder
if (b == 0)
throw new DivideByZeroException();
remainder = 0;
List<bool> q = new List<bool>();
foreach (var bit in a.WalkBits()) {
remainder *= 2;
if (bit)
remainder += 1;
if (remainder >= b) {
remainder = (remainder - b).Magnitude;
q.Add(true);
}
else
q.Add(false);
}
List<uint> uints = new List<uint>();
uint current = 0;
uint currentMask = 0x1;
while (q.Count > 0) {
if (currentMask == 0) {
uints.Add(current);
currentMask = 0x1;
current = 0;
}
if (q[q.Count - 1])
current |= currentMask;
q.RemoveAt(q.Count - 1);
currentMask = currentMask << 1;
}
uints.Add(current);
if (uints.Count == 0)
quotient = 0;
else {
var tail = uints[0];
uints.RemoveAt(0);
uints.Reverse();
while (uints.Count > 0 && uints[0] == 0)
uints.RemoveAt(0);
quotient = new Natural(tail, uints.ToArray());
}
}
public static Natural operator *(Natural a, Natural b)
{
if (a.head.Length < b.head.Length)
return b * a;
List<Natural> partialProducts = new List<Natural>(b.head.Length + 1);
partialProducts.Add(a * b.tail);
for (var i = 0; i < b.head.Length; i++) {
var product = a * b.head[i];
var newHead = new uint[product.head.Length + i + 1];
product.head.CopyTo(newHead, 0);
newHead[product.head.Length] = product.tail;
product = new Natural(0, newHead);
partialProducts.Add(product);
}
return partialProducts.Aggregate((u, v) => u + v);
}
public void BasicComparisonTest()
{
var value = GetRandomUlong();
var v1 = new Natural(value);
var v2 = v1 * GetRandomUlong();
Assert.IsTrue(v2 > v1);
Assert.IsFalse(v1 > v2);
Assert.IsTrue(v1 < v2);
Assert.IsFalse(v2 < v1);
Assert.IsTrue(v2 >= v2);
Assert.IsTrue(v2 >= v1);
Assert.IsFalse(v1 >= v2);
Assert.IsTrue(v1 <= v1);
Assert.IsTrue(v1 <= v2);
Assert.IsFalse(v2 <= v1);
}
public void BasicEquality()
{
var value = GetRandomUlong();
var v1 = new Natural(value);
var v2 = new Natural(value);
Assert.IsTrue(v1.Equals(v2));
Assert.IsTrue(v2.Equals(v1));
Assert.IsTrue(v1 == v2);
Assert.IsTrue(v1 == value);
Assert.IsTrue(v2 == value);
}
public void CastUlongToUintOverflow()
{
var value = UInt64.MaxValue;
var bignum = new Natural(value);
Assert.AreEqual(value, (ulong)bignum);
var uintValue = (uint)bignum; // Should overflow
}
public Integer(int value)
{
this.sign = value < 0 ? (sbyte)(-1) : (sbyte)1;
this.magnitude = new Natural((ulong)Math.Abs((long)value));
}
public Integer(sbyte sign, Natural magnitude)
{
this.sign = sign;
this.magnitude = magnitude;
}
static bool CompareEqualLengthHeads(Natural a, Natural b, Func<uint, uint, bool> op)
{
for (var i = 0; i < a.head.Length; i++) {
if (a.head[i] == b.head[i])
continue;
return op(a.head[i], b.head[i]);
}
return op(a.tail, b.tail);
}
public static bool Equals(Natural a, Natural b)
{
if (a.tail != b.tail)
return false;
if (a.head.Length != b.head.Length)
return false;
for (int i = 0; i < a.head.Length; i++) {
if (a.head[i] != b.head[i])
return false;
}
return true;
}