BigInt for Standard ML/NJ

Question

Is there a Java BigInt equivalent for Standard ML? The normal int type throws an exception when it overflows.

Answer 1

是的，请参阅IntInf结构。

Answer 2

The official SML'97 standard basis library introduces a zoo of structures like Int, IntInf, Int32, Int64, LargeInt etc.

To actually use them in practice to make things work as expected, and make them work efficiently, you need to look closely at the SML implementation at hand.

• One family of implementations imitates the memory layout of C and Java, so Int32 will be really a 32bit machine word (but with overflow checking), and Int64 a 64bit machine word. SML/NJ is a notable example for that, and its small int arithmentic is fast, but its big int arithmentic slow.

• Another family of implementations come from the background of symbolic computation (LISP or Computer Algebra), where Poly/ML is a notable example. Here you have Int = IntInf = LargeInt by default, and the implementation first uses (part of) the native machine word as approximation, until it overflows and then switches to really big integers that are allocated on the heap (as boxed values). Poly/ML uses the GNU MP library for that big part.

Thus Int/IntInf is very efficient as long as your application is about integers, not machine words of a specific size: Int32 in the symbolic model won't fit into a single word on 32bit hardware due to the extra tag bits that are required. So some algorithms that are actually about word arithmetic will degrade, for example SHA1 on 32bit hardware.

On the other hand, the implicit upgrade of shorter-than-wordsize int to heap-allocated big int gives you something better than BigInt in Java, because you won't need the full object overhead for small values: 42 will be just some bit pattern in a register (with additional tag bit), but not a heavy box on the heap.

Answer 3

The BigInt-equivalent is called LargeInt. See these lecture notes to see some functions on how to convert between int (aka Int) and LargeInt.

Answer 4

While this isn't exactly what you were asking, you don't actually want an equivalent to the Java BigInt class. Java's BigInt class implements O(n^2) time for multiplication (essentially multiplying the way it's taught in elementary school), instead of O(n log n), which is possible. This is really important, as a lot of trivial BigInt programming simply doesn't work with the n^2 version.

Answer 5

Well, int puts a nasty limit on stuff like calculating permutations. SML needs a large numeric datatype thats more natural to use.