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加法(Java BigInteger源码)
private static readonly long LONG_MASK = 0xFFFF_FFFFL;
/// <summary>
/// 大数加法,数组第一个int存放最高32位,最后一个int存放最低32位。
/// </summary>
public static uint[] AddNonegative(uint[] left, uint[] right)
{
// If left is shorter, swap the two arrays
if (left.Length < right.Length)
{
var tmp = left;
left = right;
right = tmp;
}
var xIndex = left.Length;
var yIndex = right.Length;
var result = new uint[xIndex];
var sum = 0L;
if (yIndex == 1)
{
sum = (left[--xIndex] & LONG_MASK) + (right[0] & LONG_MASK);
result[xIndex] = (uint)sum;
}
else
{
// Add common parts of both numbers
while (yIndex > 0)
{
sum = (left[--xIndex] & LONG_MASK) +
(right[--yIndex] & LONG_MASK) + (long)((ulong)sum >> 32);
result[xIndex] = (uint)sum;
}
}
// Copy remainder of longer number while carry propagation is required
var carry = ((ulong)sum >> 32) != 0;
while (xIndex > 0 && carry)
carry = ((result[--xIndex] = left[xIndex] + 1) == 0);
// Copy remainder of longer number
while (xIndex > 0)
result[--xIndex] = left[xIndex];
// Grow result if necessary
if (carry)
{
Array.Resize(ref result, result.Length + 1);
for (var i = result.Length - 1; i > 0; --i)
result[i] = result[i - 1];
result[0] = 0x01;
}
return result;
}
测试
[TestMethod]
public void AddNonegativeTest()
{
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 = AddNonegative(ToIntArray(left), ToIntArray(right));
var expected = left + right;
Assert.AreEqual(expected, ValueOf(test));
}
}
Unsigned减法(Java BigInteger源码)
/// <summary>
/// 大数减法,<paramref name="left"/> 大于<paramref name="right"/>。数组第一个int存放最高32位,最后一个int存放最低32位。
/// </summary>
public static uint[] SubtractNonegative(uint[] left, uint[] right)
{
var bigIndex = left.Length;
var result = new uint[bigIndex];
var littleIndex = right.Length;
var difference = 0L;
// Subtract common parts of both numbers
while (littleIndex > 0)
{
difference = (left[--bigIndex] & LONG_MASK) -
(right[--littleIndex] & LONG_MASK) +
(difference >> 32);
result[bigIndex] = (uint)difference;
}
// Subtract remainder of longer number while borrow propagates
var borrow = (difference >> 32) != 0;
while (bigIndex > 0 && borrow)
borrow = ((result[--bigIndex] = left[bigIndex] - 1) == uint.MaxValue);
// Copy remainder of longer number
while (bigIndex > 0)
result[--bigIndex] = left[bigIndex];
return result;
}
测试
[TestMethod]
public void SubtractNonegativeTest()
{
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));
while (right > left) right >>= 1;
var test = SubtractNonegative(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加法
/// <summary>
/// 大数加法,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) Add((uint[], bool) left, (uint[], bool) right)
{
if (IsZero(left))
return right;
if (IsZero(right))
return left;
if (left.Item2 == right.Item2)//正负相同
return (AddNonegative(left.Item1, right.Item1), left.Item2);
var cmp = Compare(left.Item1, right.Item1);
if (cmp < 0)//abs(left) < abs(right)
return (SubtractNonegative(right.Item1, left.Item1), right.Item2);
else
return (SubtractNonegative(left.Item1, right.Item1), left.Item2);
}
private static int Compare(uint[] left, uint[] right)
{
var len1 = left.Length;
var len2 = right.Length;
if (len1 < len2)
return -1;
if (len1 > len2)
return 1;
for (var i = 0; i < len1; i++)
{
var a = left[i];
var b = right[i];
if (a != b)
return ((a & LONG_MASK) < (b & LONG_MASK)) ? -1 : 1;
}
return 0;
}
private static bool IsZero((uint[], bool) value)
=> value.Item1.Length == 1 && value.Item1[0] == 0;
测试
[TestMethod]
public void AddTest()
{
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 = Add(ToTuple(left), ToTuple(right));
var expected = left + right;
Assert.AreEqual(expected, ValueOf(test));
}
}
Signed减法
/// <summary>
/// 大数减法,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) Subtract((uint[], bool) left, (uint[], bool) right)
{
if (IsZero(left))
return (right.Item1, !right.Item2);
if (IsZero(right))
return left;
if (left.Item2 != right.Item2)//正负相异
return (AddNonegative(left.Item1, right.Item1), left.Item2);
var cmp = Compare(left.Item1, right.Item1);
if (cmp == 0)
return (new uint[] { 0 }, true);
else if (cmp < 0)//abs(left) < abs(right)
return (SubtractNonegative(right.Item1, left.Item1), !right.Item2);
else
return (SubtractNonegative(left.Item1, right.Item1), left.Item2);
}
测试
[TestMethod]
public void SubtractTest()
{
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 = Subtract(ToTuple(left), ToTuple(right));
var expected = left - right;
Assert.AreEqual(expected, ValueOf(test));
}
}