When Should I Use Double Instead of Decimal

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.

decimal vs double! - Which one should I use and when?

For money, always decimal. It's why it was created.

If numbers must add up correctly or balance, use decimal. This includes any financial storage or calculations, scores, or other numbers that people might do by hand.

If the exact value of numbers is not important, use double for speed. This includes graphics, physics or other physical sciences computations where there is already a "number of significant digits".

Difference between decimal, float and double in .NET?

float and double are floating binary point types (float is 32-bit; double is 64-bit). In other words, they represent a number like this:

10001.10010110011

The binary number and the location of the binary point are both encoded within the value.

decimal is a floating decimal point type. In other words, they represent a number like this:

12345.65789

Again, the number and the location of the decimal point are both encoded within the value – that's what makes decimal still a floating point type instead of a fixed point type.

The important thing to note is that humans are used to representing non-integers in a decimal form, and expect exact results in decimal representations; not all decimal numbers are exactly representable in binary floating point – 0.1, for example – so if you use a binary floating point value you'll actually get an approximation to 0.1. You'll still get approximations when using a floating decimal point as well – the result of dividing 1 by 3 can't be exactly represented, for example.

As for what to use when:

• For values which are "naturally exact decimals" it's good to use decimal. This is usually suitable for any concepts invented by humans: financial values are the most obvious example, but there are others too. Consider the score given to divers or ice skaters, for example.

• For values which are more artefacts of nature which can't really be measured exactly anyway, float/double are more appropriate. For example, scientific data would usually be represented in this form. Here, the original values won't be "decimally accurate" to start with, so it's not important for the expected results to maintain the "decimal accuracy". Floating binary point types are much faster to work with than decimals.

Why is decimal more precise than double if it has a shorter range? C#

what I'm understanding here is that decimal takes more space but provides a shorter range?

Correct. It provides higher precision and smaller range. Plainly if you have a limited number of bits, you can increase precision only by decreasing range!

everyone agrees that decimal should be use when precision is required

Since that statement is false -- in particular, I do not agree with it -- any conclusion you draw from it is not sound.

The purpose of using decimal is not higher precision. It is smaller representation error. Higher precision is one way to achieve smaller representation error, but decimal does not achieve its smaller representation error by being higher precision. It achieves its smaller representation error by exactly representing decimal fractions.

Decimal is for those scenarios where the representation error of a decimal fraction must be zero, such as a financial computation.

Also when doing a calculation like = (1/3)*3, the desire result is 1, but only float and double give me 1

You got lucky. There are lots of fractions where the representation error of that computation is non-zero for both floats and doubles.

Let's do a quick check to see how many there are. We'll just make a million rationals and see:

    var q = from x in Enumerable.Range(1, 1000)
            from y in Enumerable.Range(1, 1000)
            where ((double)x)/y*y != x
            select x + " " + y;
    Console.WriteLine(q.Count()); // 101791

Over 10% of all small-number rationals are represented as doubles with sufficiently large representation error that they do not turn back into whole numbers when multiplied by their denominator!

If your desire is to do exact arithmetic on arbitrary rationals then neither double nor decimal are the appropriate type to use. Use a big-rational library if you need to exactly represent rationals.

why is decimal more precise?

Decimal is more precise than double because it has more bits of precision.

But again, precision is not actually that relevant. What is relevant is that decimal has smaller representation error than double for many common fractions.

It has smaller representation error than double for representing fractions with a small power of ten in the denominator because it was designed specifically to have zero representation error for all fractions with a small power of ten in the denominator.

That's why it is called "decimal", because it represents fractions with powers of ten. It represents the decimal system, which is the system we commonly use for arithmetic.

Double, in contrast, was explicitly not designed to have small representation error. Double was designed to have the range, precision, representation error and performance that is appropriate for physics computations.

There is no bias towards exact decimal quantities in physics. There is such a bias in finance. Use decimals for finance. Use doubles for physics.

Double vs. BigDecimal?

A BigDecimal is an exact way of representing numbers. A Double has a certain precision. Working with doubles of various magnitudes (say d1=1000.0 and d2=0.001) could result in the 0.001 being dropped alltogether when summing as the difference in magnitude is so large. With BigDecimal this would not happen.

The disadvantage of BigDecimal is that it's slower, and it's a bit more difficult to program algorithms that way (due to + - * and / not being overloaded).

If you are dealing with money, or precision is a must, use BigDecimal. Otherwise Doubles tend to be good enough.

I do recommend reading the javadoc of BigDecimal as they do explain things better than I do here :)

Should I define all values as Double or mixed Double and Float when those values will be calculated frequently?

from
THE SWIFT PROGRAMMING LANGUAGE

"NOTE

Double has a precision of at least 15 decimal digits, whereas the precision of Float can be as little as 6 decimal digits. The appropriate floating-point type to use depends on the nature and range of values you need to work with in your code. In situations where either type would be appropriate, Double is preferred."

Should I use decimal, float or double for this simple math result?

What you need is the DECIMAL datatype:

declare @val decimal(10,2)
select @val = 10.155
select @val

When you input values, you can either rely on the built in rounding, or explicitly decide which rounding you want:

select val = round(10.155, 2, 0) -- rounded
select val = round(10.155, 2, 1) -- truncated

Decimal (10,2) means that ten digits can be used, and that two of them are to be taken as being after the decimal point. i.e. The highest number that decimal(4,2) can contain is 99.99. Trying to set it to 100 will result in arithmetic overflow.

Storing statistical data, do I need DECIMAL, FLOAT or DOUBLE?

This link does a good job of explaining what you are looking for. Here is what is says:

All these three Types, can be specified by the following Parameters (size, d). Where size is the total size of the String, and d represents precision. E.g To store a Number like 1234.567, you will set the Datatype to DOUBLE(7, 3) where 7 is the total number of digits and 3 is the number of digits to follow the decimal point.

FLOAT and DOUBLE, both represent floating point numbers. A FLOAT is for single-precision, while a DOUBLE is for double-precision numbers. A precision from 0 to 23 results in a 4-byte single-precision FLOAT column. A precision from 24 to 53 results in an 8-byte double-precision DOUBLE column. FLOAT is accurate to approximately 7 decimal places, and DOUBLE upto 14.

Decimal’s declaration and functioning is similar to Double. But there is one big difference between floating point values and decimal (numeric) values. We use DECIMAL data type to store exact numeric values, where we do not want precision but exact and accurate values. A Decimal type can store a Maximum of 65 Digits, with 30 digits after decimal point.

So, for the most accurate and precise value, Decimal would be the best option.

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