shdown / libdeci

Big decimal library for C

libdeci is a big-decimal arithmetics library for C.

Features:

• supports GNU GCC, Clang, ICC, MSVC;

• does not require extra memory for any operation, thus never allocates memory;

• compiles as both C and C++;

• hardware-independent (it even works on WebAssembly);

• simple;

• fast;

• well-tested.

Simplicity, performance and algorithms

In libdeci, only the “basecase” (quadratic) algorithms are implemented for multiplication, division and conversion to/from binary. There are multiple reasons for that:

• In the world of arbitrary-precision arithmetic especially, fancy algorithms are slow when N is small, thus any reasonable implementation that employs them tends to fall back to dumb quadratic algorithms if N is less than some threshold. It is for this reason, combined with the fact that many of the fancy algorithms are divide-and-conquer in nature, the dumb algorithms are also called “basecase” algorithms. So even if you need to use a fancy algorithm to crunch very large decimal numbers, you will still need the “basecase” algorithms.

• If you are crunching very large decimal numbers with fancy algorithms, most likely you are doing something wrong: binary arithmetics is native for computers, so consider using GMP in the first place; or, alternatively, convert “to bits” before doing costly computation, and convert the result back afterwards.

• Fancy algorithms introduce complexity.

• Fancy algorithms allocate extra memory.

But still, what’s your plan?

• For multiplication, we have:

  • libdeci-kara that implements intermediate-fanciness multiplication via Karatsuba algorithm;

  • libdeci-ntt that implements high-fanciness multiplication via the number-theoretic transform (variant of Fourier transform).

• For division, we have libdeci-newt. It implements fancy division via Newton’s method. Note that it requires that a fast (sub-quadratic) multiplication routine be passed as a callback. Use either libdeci-kara or libdeci-ntt for that.

• Divide-and-conquer algorithms for decimal-to-binary and binary-to-decimal radix conversion. Note that in order to use those to convert to binary, you need to be able to multiply big binary numbers; and in order to convert from binary, you need to be able to divide big binary numbers. We recommend using GMP for that (more specifically, the low-level functions operating directly on mp_limb_t spans).