BigInteger与uint[]
用uint[]来表示非负大数,其中数组开头是大数的最高32位,数组结尾是大数最低32位。其与BigInteger的转换方法
/// <summary>
/// <see cref="uint"/>数组转为非负大整数
/// </summary>
private static BigInteger ValueOf(uint[] value)
{
var result = BigInteger.Zero;
foreach (var num in value)
{
result <<= 32;
result |= (num & 0xFFFF_FFFF);
}
return result;
}
/// <summary>
/// 非负大整数转为<see cref="uint"/>数组
/// </summary>
private static uint[] ToIntArray(BigInteger value)
{
var byteCount = value.GetByteCount();
var len = (int)Math.Ceiling(byteCount / 4d);
var result = new uint[len];
for (var i = len - 1; i >= 0; --i)
{
result[i] = (uint)(value & 0xFFFF_FFFF);
value >>= 32;
}
return result;
}
测试
[TestMethod]
public void ConvertTest()
{
var bytes = new byte[32];
Random ran = new Random();
for (var i = 0; i < 100; ++i)
{
ran.NextBytes(bytes);
var value = BigInteger.Abs(new BigInteger(bytes));
var test = ToIntArray(value);
Assert.AreEqual(value, ValueOf(test));
}
}
Unsigned乘法(Java BigInteger源码)
private static readonly long LONG_MASK = 0xFFFF_FFFFL;
/// <summary>
/// 非负大数乘法,数组第一个<see cref="uint"/>存放最高32位,最后一个<see cref="uint"/>存放最低32位。
/// </summary>
public static uint[] MultiplyNonegative(uint[] left, uint[] right)
{
var xstart = left.Length - 1;
var ystart = right.Length - 1;
var result = new uint[left.Length + right.Length];
var carry = 0L;
for (int j = ystart, k = ystart + 1 + xstart; j >= 0; j--, k--)
{
var product = (right[j] & LONG_MASK) *
(left[xstart] & LONG_MASK) + carry;
result[k] = (uint)product;
carry = (long)((ulong)product >> 32);
}
result[xstart] = (uint)carry;
for (var i = xstart - 1; i >= 0; i--)
{
carry = 0;
for (int j = ystart, k = ystart + 1 + i; j >= 0; j--, k--)
{
var product = (right[j] & LONG_MASK) *
(left[i] & LONG_MASK) +
(result[k] & LONG_MASK) + carry;
result[k] = (uint)product;
carry = (long)((ulong)product >> 32);
}
result[i] = (uint)carry;
}
return result;
}
测试
[TestMethod]
public void MultiplyNonegativeTest()
{
var bytes = new byte[32];
Random ran = new Random();
for (var i = 0; i < 100; ++i)
{
ran.NextBytes(bytes);
var left = BigInteger.Abs(new BigInteger(bytes));
ran.NextBytes(bytes);
var right = BigInteger.Abs(new BigInteger(bytes));
var test = MultiplyNonegative(ToIntArray(left), ToIntArray(right));
var expected = left * right;
Assert.AreEqual(expected, ValueOf(test));
}
}
BigInteger与(uint[], bool)
上面的减法有太多限制,加法也不能计算负数,接下来推广到通用加减法。
用(uint[], bool)来表示有符号大数,其中uint[]是大数的绝对值,bool为false时是负数。
其与BigInteger之间转换方法
/// <summary>
/// (<see cref="uint"/>[], <see cref="bool"/>) to <see cref="BigInteger"/>
/// </summary>
private BigInteger ValueOf((uint[], bool) value)
{
var result = BigInteger.Zero;
foreach (var num in value.Item1)
{
result <<= 32;
result |= (num & 0xFFFF_FFFF);
}
return value.Item2 ? result : -result;
}
/// <summary>
/// <see cref="BigInteger"/> to (<see cref="uint"/>[], <see cref="bool"/>)
/// </summary>
private (uint[], bool) ToTuple(BigInteger value)
{
var positive = BigInteger.Abs(value);
var byteCount = positive.GetByteCount();
var len = (int)Math.Ceiling(byteCount / 4d);
var result = new uint[len];
for (var i = len - 1; i >= 0; --i)
{
result[i] = (uint)(positive & 0xFFFF_FFFF);
positive >>= 32;
}
return (result, value >= 0);
}
测试
[TestMethod]
public void ConvertTest()
{
var bytes = new byte[32];
Random ran = new Random();
for (var i = 0; i < 100; ++i)
{
ran.NextBytes(bytes);
var value = new BigInteger(bytes);
var test = ToTuple(value);
Assert.AreEqual(value, ValueOf(test));
}
}
Signed乘法
/// <summary>
/// 大数乘法,数组第一个<see cref="uint"/>存放最高32位,最后一个<see cref="uint"/>存放最低32位。
/// </summary>
public static (uint[], bool) Multiply((uint[], bool) left, (uint[], bool) right)
{
if (IsZero(left))
return left;
if (IsZero(right))
return right;
if (IsAbsOne(left))
return (right.Item1, right.Item2 == left.Item2);
if (IsAbsOne(right))
return (left.Item1, left.Item2 == right.Item2);
return (MultiplyNonegative(left.Item1, right.Item1), left.Item2 == right.Item2);
}
private static bool IsZero((uint[], bool) value)
=> value.Item1.Length == 1 && value.Item1[0] == 0;
private static bool IsAbsOne((uint[], bool) value)
=> value.Item1.Length == 1 && value.Item1[0] == 1;
测试
[TestMethod]
public void MultiplyTest()
{
var bytes = new byte[32];
Random ran = new Random();
for (var i = 0; i < 100; ++i)
{
ran.NextBytes(bytes);
var left = new BigInteger(bytes);
ran.NextBytes(bytes);
var right = new BigInteger(bytes);
var test = Multiply(ToTuple(left), ToTuple(right));
var expected = left * right;
Assert.AreEqual(expected, ValueOf(test));
}
}