c# - 如何进行定点除法？

Question

我有一个使用 long 的 8 字节定点数，其恒定分母为 (1 << 24)。如何对两个 Fixed8 值进行除法？由于我使用的是 C#，因此我不能简单地转换为更大的整数。还是我在语言上想太多了？

谢谢。

public struct Fixed8
{
    private long _numerator;
    public const long DENOMINATOR = 1 << 24;
}

Answer 1

这是一种将所有计算保存在longs 中的方法。不过，它可能不会更快。我没有量过。

public struct Fixed8
{
    public Fixed8(double value)
    {
        _numerator = (long)(value * DENOMINATOR);
    }

    private long _numerator;
    public const long DENOMINATOR = 1 << 24;

    public static Fixed8 operator /(Fixed8 a, Fixed8 b)
    {
        long remainder;
        long quotient = Math.DivRem(a._numerator, b._numerator, out remainder) * DENOMINATOR;

        long morePrecision = remainder * DENOMINATOR / b._numerator;

        return new Fixed8 { _numerator = quotient + morePrecision };
    }
}

Answer 2

您可以使用BigInteger 结构来执行计算：

public static Fixed8 operator /(Fixed8 a, Fixed8 b)
{
    Fixed8 result;
    result._numerator = (long)( new BigInteger(a._numerator) *
                                new BigInteger(DENOMINATOR)  /
                                new BigInteger(b._numerator) );
    return result;
}

完整代码：

public const long DENOMINATOR = 1 << 24;

private long _numerator;

public Fixed8(double value)
{
    _numerator = (long)(value * DENOMINATOR);
}

public static Fixed8 operator /(Fixed8 a, Fixed8 b)
{
    Fixed8 result;
    result._numerator = (long)( new BigInteger(a._numerator) * 
                                new BigInteger(DENOMINATOR)  / 
                                new BigInteger(b._numerator) );
    return result;
}

public static explicit operator double(Fixed8 a)
{
    return (double)a._numerator / (double)DENOMINATOR;
}

public override string ToString()
{
    return ((double)this).ToString();
}

例子：

var a = new Fixed8(7);
var b = new Fixed8(1.7);

Console.WriteLine(a);
Console.WriteLine(b);
Console.WriteLine(a / b);

输出：

7
1.69999998807907
4.11764705181122

Answer 3

public long Division()
{
    long result = _numerator / DENOMINATOR;
    return result;
}

Answer 4

使用 aSystem.Numerics.BigInteger很好。但是在这种特定情况下， aSystem.Decimal实际上具有足够的精度。所以这是我的建议：

 public static Fixed8 operator /(Fixed8 a, Fixed8 b)
 {
   decimal resultNumerator = (decimal)a._numerator * DENOMINATOR / b._numerator;
   return new Fixed8 { _numerator = Convert.ToInt64(resultNumerator) };
 }