Ciao, Il Lun, 20 Febbraio 2017 9:25 pm, Torbjörn Granlund ha scritto: > "Marco Bodrato" <bodr...@mail.dm.unipi.it> writes: > > They all will represent the numbers (n) in the range 0..20022 with their > equivalent (2^19937-20023+n). The sketched proof follows. > > Is that true also for n < 20022...?
Yes, because, in the powering process, the number grows larger than 20022, and the reduce process will never give a small number again. I mean: the reduction function we wrote (and the current mpz implementation), would leave a number n<20022 untouched. But the square-reduce-multiply-reduce process used to compute seed^1074888996 will for sure end up with a result >= 20023. This is false if the starting seed is 0 or 1, but this case is avoided by the initial seed1 = seed mod (2^19937-20027) + 2 Regards, m -- http://bodrato.it/toom/ _______________________________________________ gmp-devel mailing list gmp-devel@gmplib.org https://gmplib.org/mailman/listinfo/gmp-devel
