转换为分数英寸

Question

我需要将双精度值（厘米）转换为分数值，格式为：3 1/64（英寸）。在阅读了很多有关此内容并找到转换为分数的算法之后，我认为它们不适合我的需要，因为我的分数应该采用这些格式：?/2、?/4、?/8、?/16、？/32，？/64。我见过这样的转换 tables：table。我认为我最好的解决方案是创建一个键值列表，其中包含 table 中的所有值，并为每个数字在列表中找到最佳近似值。

例如：3.21 厘米。 = 1.26378 英寸 = 1 英寸 + 0.26378。所以，根据 table 链接，0.26378 = 17/64。最后的结果应该是 1 17/64 英寸。

所以我的问题是：

有一个包含 table 中的值的列表并找到最接近的值以给出分数是个好主意，还是为此创建一个算法更好？
如果可以创建包含值的列表，我如何才能在我的列表中找到给定数字的最接近值？

Answer 1

我建议使用简单的数学而不是 table

private static string ToFraction64(double value) {
  // denominator is fixed
  int denominator = 64;
  // integer part, can be signed: 1, 0, -3,...
  int integer = (int) value;
  // numerator: always unsigned (the sign belongs to the integer part)
  // + 0.5 - rounding, nearest one: 37.9 / 64 -> 38 / 64; 38.01 / 64 -> 38 / 64
  int numerator = (int) ((Math.Abs(value) - Math.Abs(integer)) * denominator + 0.5);

  // some fractions, e.g. 24 / 64 can be simplified:
  // both numerator and denominator can be divided by the same number
  // since 64 = 2 ** 6 we can try 2 powers only 
  // 24/64 -> 12/32 -> 6/16 -> 3/8
  // In general case (arbitrary denominator) use gcd (Greatest Common Divisor):
  //   double factor = gcd(denominator, numerator);
  //   denominator /= factor;
  //   numerator /= factor;
  while ((numerator % 2 == 0) && (denominator % 2 == 0)) {
    numerator /= 2;
    denominator /= 2;
  }

  // The longest part is formatting out

  // if we have an actual, not degenerated fraction (not, say, 4 0/1)
  if (denominator > 1)
    if (integer != 0) // all three: integer + numerator + denominator
      return string.Format("{0} {1}/{2}", integer, numerator, denominator);
    else if (value < 0) // negative numerator/denominator, e.g. -1/4
      return string.Format("-{0}/{1}", numerator, denominator);
    else // positive numerator/denominator, e.g. 3/8
      return string.Format("{0}/{1}", numerator, denominator);
  else 
    return integer.ToString(); // just an integer value, e.g. 0, -3, 12...  
}

测试

const double cmInInch = 2.54;

// 1 17/64
Console.Write(ToFraction64(3.21 / cmInInch));
// -1 17/64
Console.Write(ToFraction64(-1.26378));
// 3 1/4
Console.Write(ToFraction64(3.25001));
// 3 1/4
Console.Write(ToFraction64(3.24997));
// 5
Console.Write(ToFraction64(5.000001));
// -1/8
Console.Write(ToFraction64(-0.129));
// 1/8
Console.Write(ToFraction64(0.129));

Answer 2

采用 Dmitry Bychenko 的代码，我们需要添加 case "else if (denominator == numerator)" if fraction equals to 1 如果值为正则加 1 或如果值为负则删除 1 （例如 denominator/numerator = 64/64)

    private static string ToFraction64(double value)
    {
        // denominator is fixed
        int denominator = 64;
        // integer part, can be signed: 1, 0, -3,...
        int integer = (int)value;
        // numerator: always unsigned (the sign belongs to the integer part)
        // + 0.5 - rounding, nearest one: 37.9 / 64 -> 38 / 64; 38.01 / 64 -> 38 / 64
        int numerator = (int)((Math.Abs(value) - Math.Abs(integer)) * denominator + 0.5);

        // some fractions, e.g. 24 / 64 can be simplified:
        // both numerator and denominator can be divided by the same number
        // since 64 = 2 ** 6 we can try 2 powers only 
        // 24/64 -> 12/32 -> 6/16 -> 3/8
        // In general case (arbitrary denominator) use gcd (Greatest Common Divisor):
        //   double factor = gcd(denominator, numerator);
        //   denominator /= factor;
        //   numerator /= factor;
        while ((numerator % 2 == 0) && (denominator % 2 == 0))
        {
            numerator /= 2;
            denominator /= 2;
        }

        // The longest part is formatting out

        // if we have an actual, not degenerated fraction (not, say, 4 0/1)
        if (denominator > 1)
            if (integer != 0) // all three: integer + numerator + denominator
                return string.Format("{0} {1}/{2}", integer, numerator, denominator);
            else if (value < 0) // negative numerator/denominator, e.g. -1/4
                return string.Format("-{0}/{1}", numerator, denominator);
            else // positive numerator/denominator, e.g. 3/8
                return string.Format("{0}/{1}", numerator, denominator);
        //if fraction equals to 1 we add 1 if the value is positive or remove 1 if the value is negative (ex denominator/numerator = 64/64)
        else if (denominator == numerator)
        {
            if (value < 0) // negative numerator/denominator, e.g. -1/4               
                integer--;
            else // positive numerator/denominator, e.g. 3/8               
                integer++;
            return integer.ToString();
        }
        else
            return integer.ToString(); // just an integer value, e.g. 0, -3, 12...  
    }

Answer 3

我的功能更简单更简单.. 它 return 一个包含十进制值的三个整数 {Inches, Numerator, Denominator} 的数组，fracBase 参数表示精度为16、32、64、128 ....

public static int[] GetImpFractions(decimal value, int fracBase = 32)
{
    int[] result = { 0, 0, 0 };

    result[0] = (int)Math.Truncate(value);
    decimal num = (value - (decimal)result[0]);
    num *= fracBase;
    decimal denom = fracBase;
    if (num > 0)
    {
        while (num % 2 == 0) 
        {
            num /= 2;
            denom /= 2;
        }
        if (num == 1 && denom == 1)
        {
            result[0] += 1;
            num = 0; 
            denom = 0;
        }
        result[1] = (int)Math.Truncate(num);
        result[2] = (int)Math.Truncate(denom);
    }

    return result;
}

Answer 4

增加了脚的显示

public static string ToFraction(this double source, int denominator)
{
    var divider = denominator;
    var inches = (int) Math.Abs(source);
    var numerator = (int) ((Math.Abs(source) - Math.Abs(inches)) * divider + 0.5);

    while (numerator % 2 == 0 && divider % 2 == 0)
    {
        numerator /= 2;
        divider /= 2;
    }

    if (divider == numerator)
    {
        if (source < 0) inches--;
        else inches++;
        numerator = 0;
    }

    var feet = Math.DivRem(inches, 12, out inches);

    var valueBuilder = new StringBuilder();
    if (source + 1d / denominator < 0) valueBuilder.Insert(0, "-");

    if (feet > 0)
    {
        valueBuilder.Append(feet);
        valueBuilder.Append("'");
        valueBuilder.Append("-");
    }

    valueBuilder.Append(inches);

    if (numerator != 0)
    {
        valueBuilder.Append(" ");
        valueBuilder.Append(numerator);
        valueBuilder.Append("/");
        valueBuilder.Append(divider);
    }

    valueBuilder.Append('"');
    return valueBuilder.ToString();
}

所有测试都通过了

    [TestCase]
    public void FractionTest()
    {
        Assert.AreEqual("0\"", 0d.ToFraction());
        Assert.AreEqual("0\"", (-0d).ToFraction());
        Assert.AreEqual("0\"", (-0.00001d).ToFraction());
        Assert.AreEqual("1\"", 1d.ToFraction());
        Assert.AreEqual("-1\"", (-1d).ToFraction());
        Assert.AreEqual("0 1/8\"", 0.129.ToFraction());
        Assert.AreEqual("-0 1/8\"", (-0.129).ToFraction());
        Assert.AreEqual("-1 1/4\"", (-1.26378).ToFraction());
        Assert.AreEqual("5\"", 5.000001.ToFraction());
        Assert.AreEqual("3 1/4\"", 3.24997.ToFraction());
        Assert.AreEqual("3 1/4\"", 3.25001.ToFraction());
        Assert.AreEqual("1'-0\"", 12d.ToFraction());
        Assert.AreEqual("1'-0 3/32\"", 12.1d.ToFraction());
        Assert.AreEqual("1'-1\"", 13d.ToFraction());
        Assert.AreEqual("1'-3 1/8\"", 15.125d.ToFraction());
        Assert.AreEqual("1'-0\"", 12.00001d.ToFraction());
        Assert.AreEqual("-1'-0\"", (-12.00001d).ToFraction());
        Assert.AreEqual("-2'-1 7/32\"", (-25.231d).ToFraction());
    }

转换为分数英寸

Convert to fraction inches

c#

math

fractions