I am implementing a BigInt class that must support arbitrary-precision operations on integers.
Quote from "The Algorithm Design Manual" by S.Skiena:
What base should I do [editor's note: arbitrary-precision] arithmetic in? - It is perhaps simplest to implement your own high-precision arithmetic package in decimal, and thus represent each integer as a string of base-10 digits. However, it is far more efficient to use a higher base, ideally equal to the square root of the largest integer supported fully by hardware arithmetic.
How do I find the largest integer supported fully by hardware arithmetic? If I understand correctly, being my machine an x64 based PC, the largest integer supported should be 2^64 (http://en.wikipedia.org/wiki/X86-64 - Architectural features: 64-bit integer capability), so I should use base 2^32, but is there a way in c++ to get this size programmatically so I can typedef my base_type to it?
int (and, by extension, unsigned int) is the "natural" size for the architecture. So a type that has half the bits of an int should work reasonably well. Beyond that, you really need to configure for the particular hardware; the type of the storage unit and the type of the calculation unit should be typedefs in a header and their type selected to match the particular processor. Typically you'd make this selection after running some speed tests.
INT_MAX doesn't help here; it tells you the largest value that can be stored in an int, which may or may not be the largest value that the hardware can support directly. Similarly, INTMAX_MAX is no help, either; it tells you the largest value that can be stored as an integral type, but doesn't tell you whether operations on such a value can be done in hardware or require software emulation.
Back in the olden days, the rule of thumb was that operations on ints were done directly in hardware, and operations on longs were done as multiple integer operations, so operations on longs were much slower than operations on ints. That's no longer a good rule of thumb.