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The double and float types both offer the ability to support numbers with a fractional component. For example, you can represent the value 1.5 with either of these types, which you can t do with any of the integer types. The only difference between double and float is the level of precision available: since floating-point numbers have a fixed size, they can offer only a limited amount of precision. This means that they cannot represent any fraction the limited precision means floating-point numbers can only represent most numbers approximately.
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Whenever more than one way of doing something exists in a programming system, a schism inevitably forms, offering the opportunity for long and pointless arguments over which is better.
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If you re wondering why these are called floating-point types, the name is a technical description of how they work internally. These numbers contain a fixed number of binary digits to hold the value, and then another number that says where the . should go. So the point is a binary point, the binary equivalent of a decimal point. It s floating because it can move around.
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A float offers about seven decimal places of precision, whereas a double offers about 17. (Strictly speaking, they offer 23 and 52 binary places of precision, respectively. These are binary formats, so their precision does not correspond to an exact number of decimal places of precision.) So the following code:
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double x = 1234.5678; double y = x + 0.0001; Console.WriteLine(x); Console.WriteLine(y);
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prints out what you d expect:
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1234.5678 1234.5679
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If instead we use the float type:
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float x = 1234.5678f; float y = x + 0.0001f; Console.WriteLine(x); Console.WriteLine(y);
we get this:
1234.568 1234.568
This often surprises new developers, but it s normal, and is by no means unique to C#. If only a limited amount of space is available, you simply cannot represent all possible numbers with complete accuracy. Floating point, approximate as it is, is the standard way to represent noninteger numbers in most programming languages, and you ll see this sort of inaccuracy anywhere.
Notice that when modifying the code to use float instead of double, we added the letter f to the end of the constants 0.0001f instead of just 0.0001, for example. This is because C# treats a number with a decimal point as a value of type double, and if we try to store this in a variable of type float, we risk losing data due to the lower precision. Such code is treated as an error, hence the need to explicitly tell C# that we know we re working with single-precision floating-point values, with the f suffix. If you have a double you really would like to turn into a float, and you are prepared to tolerate the loss of precision, you can tell C# this with a cast operator. For example:
double x = 1234.5678; double y = x + 0.0001; float impreciseSum = (float) (x + y);
The (float) syntax here is a cast, an explicit instruction to the compiler that we want to convert the type. Since we are being explicit, the compiler does not treat this as an error.
For a lot of applications, limited precision is not too big a problem as long as you re aware of it, but there s a slightly subtler problem that afflicts double and float. They are both binary representations, because that s the most efficient way of packing precision into the space available. However, it means that you can get some surprisinglooking results when working in decimal. For example, the number 0.1 cannot be represented accurately as a finite-length binary fraction. (For much the same reason that 1/9 cannot accurately be represented as a finite-length decimal fraction. In either case, you end up with a recurring [i.e., infinitely long] number: 1/9 in decimal is 0.1111 recurring; 1/10 in decimal is 0.1, but in binary it s 0.00011001100110011 recurring.) Take the following example:
float f1 = 0.1f; float f2 = f1 + 0.1f; float f3 = f2 + 0.1f; float f4 = f3 + 0.1f; float f5 = f4 + 0.1f; float f6 = f5 + 0.1f; float f7 = f6 + 0.1f; float f8 = f7 + 0.1f; float f9 = f8 + 0.1f; Console.WriteLine(f1); Console.WriteLine(f2); Console.WriteLine(f3); Console.WriteLine(f4); Console.WriteLine(f5); Console.WriteLine(f6); Console.WriteLine(f7); Console.WriteLine(f8); Console.WriteLine(f9);
(We ll see how to avoid such highly repetitive code when we get to loops later in the chapter, by the way.) This shows the following rather suspect output:
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8000001 0.9000001
The inability to represent 0.1 accurately is not initially obvious, because .NET rounds the numbers when displaying them, masking the problem. However, as we keep adding numbers together, the inaccuracies add up and eventually start to become visible. As you can imagine, accountants don t like this sort of thing if those numbers happened to represent fund transfers measured in billions of dollars, having $0.0000001 billion ($100) suddenly appear out of nowhere every eight transactions would be considered a bad practice. This is why there s a special numeric type just for working in decimal.
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