What is the purpose of long, double, byte, char in Java?

With the possible exception of "short", which arguably is a bit of a waste of space-- sometimes literally, they're all horses for courses:

• Use an int when you don't need fractional numbers and you've no reason to use anything else; on most processors/OS configurations, this is the size of number that the machine can deal with most efficiently;
• Use a double when you need fractional numbers and you've no reason to use anything else;
• Use a char when you want to represent a character (or possibly rare cases where you need two-byte unsigned arithmetic);
• Use a byte if either you specifically need to manipulate a signed byte (rare!), or when you need to move around a block of bytes;
• Use a boolean when you need a simple "yes/no" flag;
• Use a long for those occasions where you need a whole number, but where the magnitude could exceed 2 billion (file sizes, time measurements in milliseconds/nanoseconds, in advanced uses for compacting several pieces of data into a single number);
• Use a float for those rare cases where you either (a) are storing a huge number of them and the memory saving is worthwhile, or (b) are performing a massive number of calculations, and can afford the loss in accuracy. For most applications, "float" offers very poor precision, but operations can be twice as fast -- it's worth testing this on your processor, though, to find that it's actually the case! [*]
• Use a short if you really need 2-byte signed arithmetic. There aren't so many cases...

[*] For example, in Hotspot on Pentium architectures, float and double operations generally take exactly the same time, except for division.

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