This is something I've been working on for the past few months. It's in
"Daryle Walker" wrote in message the
Sandbox and I just uploaded it to the new Vault as "big_radix_whole.tar.bz2" under the "Math - Numerics" directory, i.e.
For this an interface should be proposed first, to be accepted by the LWG, see http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2006/n2020.pdf The Revision 2 of this document will be submitted soon.
e=big_radix_whole.tar.bz2&directory=Math%20-%20Numerics&>. The files might choke on some systems, since I used naked min & max and the test file has #pragma marks all over it. (My IDE function-lists all the test modules as "BOOST_AUTO_TEST_CASE()", without anything in the parentheses, so I needed the marks to navigate the huge file.) I'm using Xcode 2.4, with Apple's special GCC, on a Mac OS X 10.4.8 PowerPC system. The only documentation right now is the Doxygen comments.
It's a run-of-the-mill bignum type. It uses the philosophy of the STL containers to use a separate template parameter for the memory allocations. The type is radix-specific, also given as a template parameter. It's of
<http://www.boost-consulting.com/vault/index.php?action=downloadfile&filenam the
simplest bignum type, an arbitrary-length unsigned integer class. (Signed integers, fixed-point, floating-point, rational, etc., variants can all be built off of this kind of bignum.) As such, the renditions of the traditional algorithms are fairly pure. The biggest issue from a mathematical standpoint is that the type can't be a proper ring, since it doesn't support additive inverses (besides zero). Every other arithmetic operation (that doesn't need negative values) can work. The work-around for subtraction is the addition of "subtract-absolutely" member functions, which compute the absolute value of the difference, and return a "bool" indicating what the sign would have been.
The integer data should not be in an STL container, but in a contiguous memory block, so that an assembler module is possible for performance, see http:://www.swox.com/gmp (see also my document referred to above).
Many of the operations are repeated, each with optimized algorithms for
the
different sizes of the parameters. Since the traditional method of multiplication is actually a fused-add/multiply, member functions for such fused actions were added. There are many variants for shifting-up where additions/subtractions start since it's faster than doing a separate shifting operation first. And it saves memory, which was an important goal in all the algorithms, along with the strong exception guarantee. Besides the asserts, there is generally no protection for pre-condition violations (except for exceptions for negative results, divides by zero, and conversions).
There are commented-out plans for functions that do powers and (truncated) roots, especially squaring and square-roots, and pseudo-reciprocals (for an N-digit value, find another M-digit value, with M <= N, closest to giving a product of Radix**2N, useful to implement exact-division by multiply-by-reciprocal, which is cheaper for huge N). What other routines should be added? Any hints on how to do said routines? Should there be Serialization? Could Spirit and/or Regex be used for the I/O routines? Any compiler workarounds to be added?
This is called requirements (see my document referred to above). I'm happy to discuss it here with anyone. Regards, Maarten.
-- Daryle Walker Mac, Internet, and Video Game Junkie darylew AT hotmail DOT com