BigZ, Zet with big integers included

Forth is a very special computer language - a kind of smart macro assembler. Even if the programming is on high level you always program directly upon an addressable part of the memory. The visible stack orientation is the simple way to handle data. Postfix notation makes brackets and operator priorities unnecessary. There is no black box parser limiting what is allowed and possible. The programmer decide virtually everything about the procedures, input, output and memory. And this makes it very easy to extend the system with new data types with postfix algebra.

In BigZ (see the top bar) a system for big integers is included to Zet. It's simple, efficient and rather complete, in spite of my limited programming ability. As for integers, floating point numbers and sets, there are stacks for numbers of dynamical length. And as for sets, there is no other limit of the size than the allocated memory. When needed the memory is reallocated. 

The stack for big numbers is really two stacks in the same area of memory: one growing towards high memory (the numbers) and one growing towards low memory (the addresses to the numbers). Writing

b 702486742867487684278678476028746724601 

and pressing enter, reads the number string and convert it to a multi-decimal number A_0*B^0+...+A_r*B^r where B is 2^b and b is the maximal number of bits of a single cell integer. The single cell numbers A_i are stored in the stack with i growing towards hi memory.

The operators have the usual names but with the prefix b.

b 2000 bfaculty cr b.

fill the screen with a 5736 figure number within some tenth of a second.

The word 

b**mod \ -- | a n m -- b

counts aⁿ(mod m) and 

b 26359783991551070871965201979080333254038743646746158379582192038055842791146833506745978666309678710238746262325665407448047112858614221184120023774728850927701745782077979943165434355776993447809155163506304287949484786229043007193369097865681445643720004387345872800008950502312482268122160708155160328564   ok
b 39327375191467048647521018841730348998598651522372708158670691892420060531890655533991461398550696324722351925617448324344083141484661951392820800479947685042791549748743564268081958080246132723174581232969062661990556972176861792341905425252382562697686127413259201904144867482279552760624394742040590855602   ok
b 16306675630939784626502807161425612212340131109932460322238576590610976549235432503764166590338557086651302692446204937053886057954003032814801648230668894753863150108029570966337696939560565101312815273803547555619029325583815565767168841836143511237512006023630352590540140638620838094344583215840893265550   ok
b**mod cr b.
13589152355661418800480923196880892958242540305591911682228289531245831992616543540153046075650497423341388067834762342417455873016510076223412593080539625696104324076486611754715629613440368922879919737699812253207474005960378943204378352266794545844684513362891786202126506784931492440650088987888029494246  ok

executes in about 0.5 seconds, which might be fast enough for some encryption experiments.

Some of the most important words are:

bdrop, bdup, bover, brot, bnip, btuck, bswap, b+, b-, b*, b/, b=, b<, b>, b0=, bmod, b/mod, bsqrtf, bgcd and b**mod.

with obvious operations. The word .b prints the b-stack. There are also mixed words:

bs* \ n -- | b -- n*b
bs/mod \ n -- r | b -- q, where b=nq+r

which is much faster than the corresponding b* and b/mod.

Ahead I will try so submit adequate prime tests and factoring functions.