/// <summary>
/// 求两个数的最小公倍数。如果其中有个数为0，则返回0
/// </summary>
/// <param name="a"></param>
/// <param name="b"></param>
/// <returns></returns>
public static NaturalNumStr LeastCommonMultiple(NaturalNumStr a, NaturalNumStr b)
{
if (a == null || b == null)
{
throw new ProgramInterruptException(ProgramInterruptExceptionType.IllegalValue);
}
//统一计算空间
if (a.Space != b.Space)
{
if (a.Space == OperationSpace.DefaultSpace)
{
a = (NaturalNumStr)a.ChangeOperationSpace(b.Space);
}
else if (b.Space == OperationSpace.DefaultSpace)
{
b = (NaturalNumStr)b.ChangeOperationSpace(a.Space);
}
else
{
throw new ProgramInterruptException(ProgramInterruptExceptionType.NotSameOperationSpace);
}
}
if (a == 0 || b == 0)
{
return(new NaturalNumStr(0, a.Space));
}
return(a * b / GreatestCommonDivisor(a, b));
}
/// <summary>
/// 取模
/// </summary>
/// <param name="a">被模数</param>
/// <param name="b">模数</param>
/// <returns>包含余数和商的元组</returns>
public static (NaturalNumStr, NaturalNumStr) Mod(NaturalNumStr a, NaturalNumStr b)
{
var ans = a.Mod_unsigned(b, 0);
var new_ans = (new NaturalNumStr(ans.Item1 as NumStr, false), new NaturalNumStr(ans.Item2 as NumStr, false));
new_ans.Item1.PositiveOrNegative = new_ans.Item1.IsEmpty() ? 0 : 1;
new_ans.Item2.PositiveOrNegative = new_ans.Item2.IsEmpty() ? 0 : 1;
return(new_ans);
}
/// <summary>
/// 输出将该数去掉小数点以后的数
/// </summary>
/// <returns></returns>
public NaturalNumStr RemoveDecimalPoint()
{
var n = new NaturalNumStr(0, Space);
if (IsZero)
{
return(n);
}
else
{
n.integerNumList = new LinkedList <uint>();
n.PositiveOrNegative = 1;
}
if (decimalNumList != null)
{
if (integerNumList == null)
{
var i = decimalNumList.GetEnumerator();
//跳过高位0
do
{
i.MoveNext();
}while (i.Current == 0);
do
{
n.integerNumList.AddFirst(i.Current);
}while (i.MoveNext());
return(n);
}
else
{
foreach (var i in decimalNumList)
{
n.integerNumList.AddFirst(i);
}
}
}
if (integerNumList != null)
{
foreach (var i in integerNumList)
{
n.integerNumList.AddLast(i);
}
}
return(n);
}
/// <summary>
/// 求两个数的最大公约数。如果其中一个数为0、另一个不为0，则返回不为0的那个数
/// </summary>
/// <param name="a"></param>
/// <param name="b"></param>
/// <returns></returns>
public static NaturalNumStr GreatestCommonDivisor(NaturalNumStr a, NaturalNumStr b)
{
if (a == null || b == null)
{
throw new ProgramInterruptException(ProgramInterruptExceptionType.IllegalValue);
}
var old_a = a;
var old_b = b;
//统一计算空间
if (a.Space != b.Space)
{
if (a.Space == OperationSpace.DefaultSpace)
{
a = (NaturalNumStr)a.ChangeOperationSpace(b.Space);
}
else if (b.Space == OperationSpace.DefaultSpace)
{
b = (NaturalNumStr)b.ChangeOperationSpace(a.Space);
}
else
{
throw new ProgramInterruptException(ProgramInterruptExceptionType.NotSameOperationSpace);
}
}
if (a == 0)
{
if (b == 0)
{
throw new IllegalOperationException();
}
else
{
if (ReferenceEquals(b, old_b))
{
return(new NaturalNumStr(b));
}
else
{
return(b);
}
}
}
else if (b == 0)
{
if (ReferenceEquals(a, old_a))
{
return(new NaturalNumStr(a));
}
else
{
return(a);
}
}
if (b > a)
{
var t = a;
a = b;
b = t;
}
//辗转相除法
while (!b.IsZero)
{
var t = a;
a = b;
b = t % b;
}
if (ReferenceEquals(a, old_a) || ReferenceEquals(a, old_b))
{
return(new NaturalNumStr(a));
}
else
{
return(a);
}
}
/// <summary>
/// 开平方运算
/// </summary>
/// <param name="maxDecimalPlaces">答案保留小数位数</param>
/// <returns></returns>
protected override Digitable Sqrt(int maxDecimalPlaces)
{
NumStr a = new NumStr(this);
if (a == null)
{
throw new ProgramInterruptException(ProgramInterruptExceptionType.IllegalValue);
}
//特殊情况
if (a.IsNegative)
{
throw new IllegalOperationException();
}
else if (a.IsZero)
{
return(new NumStr(0, a.Space, maxDecimalPlaces));
}
//设进制为k，先将数字多次放大或缩小k^2倍，使其归一化为：1<=a<=k^2
var one = new NaturalNumStr(1, a.Space);
var k2 = new NaturalNumStr(a.Space.NumberBase * a.Space.NumberBase, a.Space);
var shiftTimes = 0;
while (a < one)
{
a.RightShift(2);
shiftTimes++;
}
while (a > k2)
{
a.LeftShift(2);
shiftTimes--;
}
//平方根初值x
var x = new NumStr(0, a.Space);
//x当前的有效数字位数
var nx = 0;
//x^2初值
var x2 = new NumStr(0, a.Space);
//(x+1)^2的值
NumStr x12;
do
{
//用完全平方公式计算(y+1)^2
x12 = x2 + x + x + one;
if (a < x12)
{
//本位枚举完成，开始枚举下一位
x.RightShift(1); //x=x*k
nx++;
x2.RightShift(2); //x2=x2*k^2
a.RightShift(2); //a=a*k^2
}
else
{
//继续枚举
x = x + one;
x2 = x12;
}
} while (nx < maxDecimalPlaces + 1 - shiftTimes && a != x12);
x.LeftShift(x.IntegerPlaces + x.DecimalPlaces - 1 + shiftTimes);
return(x);
}