Should I use double data structure to store very large Integer values?

Question

int types have a very low range of number it supports as compared to double. For example I want to use a integer number with a high range. Should I use double for this purpose. Or is there an alternative for this.

Is arithmetic slow in doubles ?

Answer 1

Whether double arithmetic is slow as compared to integer arithmetic depends on the CPU and the bit size of the integer/double.

On modern hardware floating point arithmetic is generally not slow. Even though the general rule may be that integer arithmetic is typically a bit faster than floating point arithmetic, this is not always true. For instance multiplication & division can even be significantly faster for floating point than the integer counterpart (see this answer)

This may be different for embedded systems with no hardware support for floating point. Then double arithmetic will be extremely slow.

Regarding your original problem: You should note that a 64 bit long long int can store more integers exactly (2^63) while double can store integers only up to 2^53 exactly. It can store higher numbers though, but not all integers: they will get rounded.

The nice thing about floating point is that it is much more convenient to work with. You have special symbols for infinity (Inf) and a symbol for undefined (NaN). This makes division by zero for instance possible and not an exception. Also one can use NaN as a return value in case of error or abnormal conditions. With integers one often uses -1 or something to indicate an error. This can propagate in calculations undetected, while NaN will not be undetected as it propagates.

Practical example: The programming language MATLAB has double as the default data type. It is used always even for cases where integers are typically used, e.g. array indexing. Even though MATLAB is an intepreted language and not so fast as a compiled language such as C or C++ is is quite fast and a powerful tool.

Bottom line: Using double instead of integers will not be slow. Perhaps not most efficient, but performance hit is not severe (at least not on modern desktop computer hardware).