While I'm new here, I'm not new to solving problems. On the site for GIMPS,there was mention of verification of multiplication routines. Please consider the following:
for integers x and y, (y-x)^2 mod y = (y^2 - 2xy + x^2) mod y = x^2 mod y if y = 2^z - 1, then conjugate x = y - x = y xor x, an easy calculation that runs at the speed of memory. Since x and conjugate x are entirely different bit patterns that produce the same comparable result, that would validate the multiplication routines via any method. If an arbitrary bit pattern from a good RNG can produce long arbitrary bit patterns that can be referred to by their RNG seed, reproducible results can be obtained by simply emailing the seed instead of the huge bit stream. An optional 128 bit xor checksum can be included for the two results so that the source guru can be sure they are seeing the same error with their equipment. Personally, I use the 4 shift register version of xorwow() that I found on the Wikipedia page for "xorshift". The current posted version is 5 shift registers and I encapsulated the version I use in to an unmanaged VC++ DLL that is callable from any high level language and I can provide it free of charge for anyone to use if you send me an email request for a download with or without source. That's one from me. On the flip side, I could use a DLL that is callable from any high level language (same calling method) that does fast arbitrary bit sized multiplications, divisions and modulos called with the base pointers in memory of the source bit patten, it's padded size in bytes and a base pointer in memory to store the return results. That will be an enormous benefit to anyone who wants to work with big numbers without being a code guru in a language with good GUI access. Note: A while back, I wrote a useful machine code Miller Rabin witness a function that tests 64 bit values at a velocity of 70,000 tests per second (good luck trying to read the code as I spent 40 hours coding it in the assembly language debugger doing line by line verification with int 3). The code includes a source readable prepended fast trial divide (DIV-less, RAM-less method on the last 24 primes in the set) that reduces the input set of off 64-bit integers to 1 in 15 with a velocity of 1.1 million odd 64 bit integers per second on one core of my Core2 Quad Extreme Series (I got it for the 12 MB L2 cache) 2.83 GHZ with 1333 mhz memory, amplifying the MR-a test by 15x. This is useful for doing trial divides of large numbers by 64-bit values by knowing with good or near certainty that your trial divide factors are prime prior to committing to the big trial divides. The source project, including usable windows DLL and VB.net calling source code can be found here for anyone to use http://v-sonline.com/MrPrimer/mrprimer.zip (Posted 12-5-2007) While the MA-a function would require an entire rewrite go go wider, the fast trial divide could be modified with minimal difficulty with two 64-bit inputs instead of one (128-bit test). I originally wrote it for an online programming contest involving 64-bit primes. Sincerely, James J Youlton, Ph.D. p.s. To demonstrate my skills since I'm new here, these are mine from a programming contest in 2010. https://commons.wikimedia.org/wiki/File:MagicSquare_10x10b.png https://commons.wikimedia.org/wiki/File:MagicSquare15.jpg https://commons.wikimedia.org/wiki/File:MagicSquare16.jpg _______________________________________________ gmp-devel mailing list gmp-devel@gmplib.org https://gmplib.org/mailman/listinfo/gmp-devel
