finished mostly. code at:
https://github.com/Pascal-J/BN-openssl-bindings-for-J New sample functions I added since yesterday are a lcg and blum blum shub RNGs. In J and explicit and tacit BN code the creation parameters for lcg are: PrimeModulus Addition and seed 298617423759287597949893501491962328326117452597400961294601101680264341574651169007633933450439527729433352349130831796973181706060273249989873557896536953533949729466518411328037250569573370887517227493158889591388495032255785041665435956093 1902831092831029812830 85129617461891649734274611646334861564198564772449744004786622524842236224099696226154815067523x those should auto linebreak in mail reader. The parameters for BBS generator are the first and third(last) the key J code for each is: roll =: (] | 'seed' ([ assign a + ]) (p|seed) (p|*) 3 : 'seed')"0 rollb =: (] | 'seedb' assign [: p&|@(*:) 3 : 'seedb')"0 The equivalent BN code. First explicit: rollE =: 3 : 0"0 NB. LCG (M is basically static initial seed) BNmod_mul__C S;S;M;P;CTX__C BNmod_add__C S;S;A;P;CTX__C BNmod_word__C S;y ) rollE =: 3 : 0"0 NB. BBS BNmod_sqr__C S;S;P;CTX__C BNmod_word__C S;y ) timings: ======= More timings, not dumping the file just yet, but showing interface samples. I made a direct pointer locale that still manages memory. Its much faster than managing J objects, but will segfault if you think you are passing a pointer when you are not. The J object version gives an innocent locale error. So there is room for both. Miller Rabin prime test in J MRabin =: 4 : 0 NB. millerrabin test. x is random witnesses < y e =. <. @ -:^:(0=2&|)^:a: y-1 for_a. x do. if. (+./c=y-1) +: 1={:c=. a y&|@^"0 e do. 0 return. end. end. 1 ) In oop BN mode, MRabinBN=: 4 : 0 NB. millerrabin text. x is random witnesses < y Y =. newM y E =. newM e =. <. @ -:^:(0=2&|)^:a: y-1 for_a. 'I' inl newM x do. BNmod_exp"1 EEi ;"0 1 a ;"1 EEi;"0 1 I__Y ; (CTX)[EEi =. 'I' inl EE =. dupM E 'toX a:' inl EE if. (+./ (y-1) = 'toX a:' inl EE) +: 1= BNget_word {: EEi do. out=.0 return. end. end. 1 ) In new raw BN mode (still managed memory) MRabinBN=: 4 : 0 NB. millerrabin text. x is random witnesses < y Y =. newM y E =. newM e =. <. @ -:^:(0=2&|)^:a: y-1 for_a. newM x do. BNmod_exp"1 EEi ;"0 1 a ;"1 EEi;"0 1 Y ; (CTX)[EEi =. dupM E NB.pD toX EEi if. (+./ (y-1) = toX EEi) +: 1= BNget_word {: EEi do. out=.0 return. end. end. 1 ) testing a prime with 3 witnesses C is OOP locale, D is direct locale Pure J, timespacex '123 129830012 12382902983209832098338901x MRabin__C 16513016020288569463710715785129617461891649734274611646334861564198564772449744004786622524842236224099696226154815067523x' 0.22579 3.07098e6 Direct BN: 100+x faster timespacex '123 129830012 12382902983209832098338901x MRabinBN__D 16513016020288569463710715785129617461891649734274611646334861564198564772449744004786622524842236224099696226154815067523x' 0.00196416 18816 Object BN: 40x faster, timespacex '123 129830012 12382902983209832098338901x MRabinBN__C 16513016020288569463710715785129617461891649734274611646334861564198564772449744004786622524842236224099696226154815067523x' 0.00597568 68096 J is faster at pure multiplication (of many smaller numbers) though. But its easy, as in the miller rabin code above to mix and match J operations with BN operations modular exponentiation is the main thing it does fast. ProductW =: 3 : 0 acc =. newM {: y (}: y) 4 : 'y[ BNfree a [ BNmul_word y;a =. newI x' reduce acc ) timespacex 'ProductW__D p: i.300' 0.013215 79488 timespacex '*/ p: i.300x' 0.00380256 109312 There's actually not much gain to erasing things as you go along, instead of all at once when you are done (if you have the memory). This is my new sum code, XC displays the Jxint values and releases the BNs sum =: (][ [: BNadd_ctx_ ] ; ;)/@:newM XC__D sum__D i.10 45 product just needs to add a context (only variable in the manager) product =: (][ [: BNmul_ctx_ ] ;wCTX ;)/@:newM XC__D product__D p: i.10 6469693230 speed gains over J as numbers get larger (timings include memory free) timespacex'( ] * 32 ^ ~ [ ) / p: i. 50x' 0.0053535982868485486 339840 timespacex'''XC (][[:BNmul ];wCTX ];[ [ [:BNexp [;wCTX a ;~[)/@:newM p:i.50 [ a =: newM 32'' inl D' 0.0057142381714437853 63232 timespacex'''XC (][[:BNmul ];wCTX ];[ [ [:BNexp [;wCTX a ;~[)/@:newM p:i.200 [ a =: newM 47'' inl D' 0.0611437 182528 timespacex'( ] * 47 ^ ~ [ ) / p: i. 200x' 0.135313 259840 ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
