When should I use double instead of decimal?

I think you've summarised the advantages quite well. You are however missing one point. The decimal type is only more accurate at representing base 10 numbers (e.g. those used in currency/financial calculations). In general, the double type is going to offer at least as great precision (someone correct me if I'm wrong) and definitely greater speed for arbitrary real numbers. The simple conclusion is: when considering which to use, always use double unless you need the base 10 accuracy that decimal offers.

Edit:

Regarding your additional question about the decrease in accuracy of floating-point numbers after operations, this is a slightly more subtle issue. Indeed, precision (I use the term interchangeably for accuracy here) will steadily decrease after each operation is performed. This is due to two reasons:

1. the fact that certain numbers (most obviously decimals) can't be truly represented in floating point form
2. rounding errors occur, just as if you were doing the calculation by hand. It depends greatly on the context (how many operations you're performing) whether these errors are significant enough to warrant much thought however.

In all cases, if you want to compare two floating-point numbers that should in theory be equivalent (but were arrived at using different calculations), you need to allow a certain degree of tolerance (how much varies, but is typically very small).

For a more detailed overview of the particular cases where errors in accuracies can be introduced, see the Accuracy section of the Wikipedia article. Finally, if you want a seriously in-depth (and mathematical) discussion of floating-point numbers/operations at machine level, try reading the oft-quoted article What Every Computer Scientist Should Know About Floating-Point Arithmetic.

You seem spot on with the benefits of using a floating point type. I tend to design for decimals in all cases, and rely on a profiler to let me know if operations on decimal is causing bottlenecks or slow-downs. In those cases, I will "down cast" to double or float, but only do it internally, and carefully try to manage precision loss by limiting the number of significant digits in the mathematical operation being performed.

In general, if your value is transient (not reused), you're safe to use a floating point type. The real problem with floating point types is the following three scenarios.

1. You are aggregating floating point values (in which case the precision errors compound)
2. You build values based on the floating point value (for example in a recursive algorithm)
3. You are doing math with a very wide number of significant digits (for example, 123456789.1 * .000000000000000987654321)

EDIT

According to the reference documentation on C# decimals:

The decimal keyword denotes a 128-bit data type. Compared to floating-point types, the decimal type has a greater precision and a smaller range, which makes it suitable for financial and monetary calculations.

So to clarify my above statement:

I tend to design for decimals in all cases, and rely on a profiler to let me know if operations on decimal is causing bottlenecks or slow-downs.

I have only ever worked in industries where decimals are favorable. If you're working on phsyics or graphics engines, it's probably much more beneficial to design for a floating point type (float or double).

Decimal is not infinitely precise (it is impossible to represent infinite precision for non-integral in a primitive data type), but it is far more precise than double:

• decimal = 28-29 significant digits
• double = 15-16 significant digits
• float = 7 significant digits

EDIT 2

In response to Konrad Rudolph's comment, item # 1 (above) is definitely correct. Aggregation of imprecision does indeed compound. See the below code for an example:

private const float THREE_FIFTHS = 3f / 5f;
private const int ONE_MILLION = 1000000;

public static void Main(string[] args)
{
    Console.WriteLine("Three Fifths: {0}", THREE_FIFTHS.ToString("F10"));
    float asSingle = 0f;
    double asDouble = 0d;
    decimal asDecimal = 0M;

    for (int i = 0; i < ONE_MILLION; i++)
    {
        asSingle += THREE_FIFTHS;
        asDouble += THREE_FIFTHS;
        asDecimal += (decimal) THREE_FIFTHS;
    }
    Console.WriteLine("Six Hundred Thousand: {0:F10}", THREE_FIFTHS * ONE_MILLION);
    Console.WriteLine("Single: {0}", asSingle.ToString("F10"));
    Console.WriteLine("Double: {0}", asDouble.ToString("F10"));
    Console.WriteLine("Decimal: {0}", asDecimal.ToString("F10"));
    Console.ReadLine();
}

This outputs the following:

Three Fifths: 0.6000000000
Six Hundred Thousand: 600000.0000000000
Single: 599093.4000000000
Double: 599999.9999886850
Decimal: 600000.0000000000

As you can see, even though we are adding from the same source constant, the results of the double is less precise (although probably will round correctly), and the float is far less precise, to the point where it has been reduced to only two significant digits.

Use decimal for base 10 values, e.g. financial calculations, as others have suggested.

But double is generally more accurate for arbitrary calculated values.

For example if you want to calculate the weight of each line in a portfolio, use double as the result will more nearly add up to 100%.

In the following example, doubleResult is closer to 1 than decimalResult:

// Add one third + one third + one third with decimal
decimal decimalValue = 1M / 3M;
decimal decimalResult = decimalValue + decimalValue + decimalValue;
// Add one third + one third + one third with double
double doubleValue = 1D / 3D;
double doubleResult = doubleValue + doubleValue + doubleValue;

So again taking the example of a portfolio:

• The market value of each line in the portfolio is a monetary value and would probably be best represented as decimal.

• The weight of each line in the portfolio (= Market Value / SUM(Market Value)) is usually better represented as double.