How do I emulate 256-bit integer math ops on a system with only a 32-bit int?

Question

I'd like to write a deadsimple bignum class using a series of (unsigned) integers. I can loosely see how addition and subtraction would work, but division and multiplication is another story. I know 32-bit compilers can emuate 64-bit int's by splitting the int64 in two int32's. I'm looking for an efficient method to do that.

I'd like to have C++ code, not assembly. Speed is no primary concern, but the most efficient solution without assemble is always nice to have.

Loosely speaking: start with long multiplication and long division (which you learned when you were 6 or whatever) in base 2^16. This at least works, then optimize to taste (http://en.wikipedia.org/wiki/Multiplication_algorithm#Fast_multiplication_algorithms_for_large_inputs). — Steve Jessop, Jan 05 '12 at 12:20
All C++ compilers support `long long`, which is at least 64bits. — Puppy, Jan 05 '12 at 12:21
This is a requirement, rather than a question. What is your specific problem? Are you looking for example code? — Fred Foo, Jan 05 '12 at 12:23
@DeadMG: There are a lot of C++ compilers out there, not all are particularly compliant, and `long long` isn't required until C++11. There is probably an 8-bit C++ compiler out there that doesn't bother with 64 bits. Still, I'd be interested to hear from @rubenvb what he's using… — Potatoswatter, Jan 05 '12 at 12:25
I updated the question to more clearly state what I tried to ask. — rubenvb, Jan 05 '12 at 12:42

unwind · Accepted Answer · 2012-01-05T12:33:53.033

Perhaps this can serve as a starting point. It implements up to 2,048-bit unsigned integers, using a base-65,536 representation. This means each digit fits in 16 bits, and we can trivially detect overflow (even when multiplying) by simply using 32 bits for the results.

This is C code however, but should be trivial to port to C++, or just use as an inspiration. It's very much optimized for readability rather than speed since this is not exactly the kind of stuff I'm good at. :)

score 1 · Answer 2 · answered Apr 17 '15 at 12:22

1

Purchase a hardback book called NUMERICAL RECIPES IN C++ and you will find what you are looking for on pages starting on 20.6 page p916 onto to p925

answered Apr 17 '15 at 12:22

user80998

48
2

score 1 · Answer 3 · answered Jan 05 '12 at 12:27

1

You'd best have a look at arbitrary precision arithmetic which will explain the thinking behind the process of emulating higher precision processors than then one that your code is running on.

answered Jan 05 '12 at 12:27

ChrisBD

9,104
3
22
35

score 0 · Answer 4 · answered Jan 05 '12 at 12:27

0

What's wrong with just using long long? That's guaranteed to be at least 64 bits. Otherwise, your Knuth (vol. 2) should provide the basic algorithms.

answered Jan 05 '12 at 12:27

James Kanze

150,581
18
184
329

score 0 · Answer 5 · answered Jan 05 '12 at 12:28

0

Use simple byte array. You can have size of integer whatever you want*. You just have to operate in binary and take endianess into consideration (your bits will be 7-6-5-4-3-2-1-0-15-14-13...)

*RAM is limited

answered Jan 05 '12 at 12:28

friendzis

799
6
17

score 0 · Answer 6 · answered Jan 05 '12 at 12:32

0

for arbitrary sizes, give GMP a spin, it should also work for your 64bit math on 32bit if for some reason you can't rely on the compiler to do it for you.

answered Jan 05 '12 at 12:32

Necrolis

25,836
3
63
101

GMP is a poor performance choice for small Integers (it typically works better on Integers larger than 256 bits). – user2284570 Aug 12 '22 at 14:58
@user2284570 What about the mpn low-level interface? Does it perform well for integers of 192..256 bit? That API seems not to use heap so it should perform well using non-heap data, doesn't it? – Silicomancer Aug 19 '22 at 23:33
@Silicomancer time spent in algorithm selection ? – user2284570 Aug 23 '22 at 00:07
@Silicomancer `mpn_mul_2` is also undocumented. – user2284570 Aug 23 '22 at 02:34

How do I emulate 256-bit integer math ops on a system with only a 32-bit int?

6 Answers6