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[u/mdw/catacomb] / math / t / mp

# Test vectors for MP functions

add {
  5 4 9; 5 -4 1; -5 4 -1; -5 -4 -9;
  0xffffffff 1 0x100000000;
}

sub {
  5 4 1; 5 -4 9; -5 4 -9; -5 -4 -1;
  4 5 -1; 4 -5 9; -4 5 -9; -4 -5 1;
}

mul {
  5 4 20; -5 4 -20; 5 -4 -20; -5 -4 20;
  0x10000 0x10000 0x100000000;
}

div {
  9 4 2 1; -9 4 -3 3; 9 -4 -3 -3; -9 -4 2 -1;
  -3 6277101735386680763835789423207666416083908700390324961279
    -1 6277101735386680763835789423207666416083908700390324961276;
  3131675836296406071791252329528905062261497366991742517193
    1110875761630725856340142297645383444629395595869672555585
    2 909924313034954359110967734238138173002706175252397406023;
  3131675836296406071791252329528905062261497366991742517193
    53
    59088223326347284373419855274130284193613157867768726739 26;
  1552518092300708935130918131258481755631334049434514313202351194902966239949102107258669453876591642442910007680288864229150803718918046342632727613031282983744380820890196288509170691316593175367469551763119843371637221007210577919
  776259046150354467565459065629240877815667024717257156601175597451483119974551053629334726938295821221455003840144432114575401859459023171316363806515641491872190410445098144254585345658296587683734775881559921685818610503605288959
  2 1;
}

exp {
  4 0 1;
  4 1 4;
  7 2 49;
  3 564 124849745640593184256214502788000232711984346194239284918599169775251467106591187580476305077269760425019686159071753053924227569816588462643229463821875763427430576080998505780547826368760514503807579784278708008217584939464444237989070811887584423210788916656247499281;
}

bin2c {
  and 5 3 1;
  or 5 3 7;
  xor 5 3 6;
  1111 0 0 -1;
  or 45 -7 -3;
  xor 0x343cd5 -0x6a49c -0x32984f;
}

lsr2c {
  -1 5 -1;
  1 5 0;
  -6 2 -2;
  5 0 5;
  -4 0 -4;
  7 2 1;
 -7 2 -2;
  -7 20 -1;
}

lsl2c {
  -1 5 -32;
  5 0 5;
  -4 0 -4;
  7 2 28;
  -7 2 -28;
  0xc0000000 1 0x180000000;
  -0xc0000000 1 -0x180000000;
  -1 32 -0x100000000;
}

setbit {
  0 40 0x10000000000;
  0x87348 40 0x10000087348;
  5 1 7;
  7 1 7;
  -3 1 -1;
}

clrbit {
  0x10000000000 40 0;
  0x87348 40 0x87348;
  5 1 5;
  7 1 5;
  -1 1 -3;
}

neg {
  0 0;
  15 -15;
  -15 15;
}

odd {
  1 0 1;
  2 1 1;
  4 2 1;
  12 2 3;
  0x10000000000000 52 1;
  0x10000000400000 22 0x40000001;
}

sqrt {
  0 0;
  1 1;
  4 2;
  9 3;
 16 4;
 99 9;
100 10;
101 10;
120 10;
121 11;

10106623487257186586 3179091613;
14565040310136678240 3816417208;
}

gcd {
  # --- Simple tests ---

  16 12 4 -11 15;
  12 16 4 -1 1;
  693 609 21 -7 8;
  4398082908043 90980984098081324 1 -32483863573352089 1570292150447;

  # --- Negative argument tests ---

  16 -12 4 -11 -15;
  -16 12 4 11 15;
  -12 -16 4 1 -1;
  -12 16 4 1 1;
  -693 609 21 7 8;
  693 -609 21 -7 -8;

  # --- Zero argument tests ---

  15 0 15 1 0;
  0 15 15 0 1;
  -5 0 5 -1 0;
  0 -5 5 0 -1;
  0 0 0 0 0;

  # --- Random number tests ---

  829561629303257626084392170900075 32498098450983560651904114638965
    5 -29340810037249902802634060204608 748967211613630574419802053172497;

  5509672937670943767152343650729669537671508
  398326674296699796695672966992514673531
  17
  -4158709420138833210339208344965073815
  57523460582278135926717203882531035926727;

  324098408098290809832490802984098208098324
  23430980840982340982098409823089098443
  1
  -4158709420138833210339208344965073815
  57523460582278135926717203882531035926727;

  # --- RSA test ---
  #
  # The first number is (p - 1)(q - 1) from `mpmont'.  The second is a
  # random number (it's actually prime, but that doesn't matter) which I
  # can use as an RSA encryption exponent.  The last is the partner
  # decryption exponent, produced using the extended GCD algorithm.

  665251164384574309450646977867043764321191240895546832784045453360
  5945908509680983480596809586040589085680968709809890671
  1
  -4601007896041464028712478963832994007038251361995647370
  514778499400157641662814932021958856708417966520837469125919104431;

  # --- Misery ---
  #
  # Some bugs discovered during RSA testing.

  100000423751500546004561515884626739136961367515520675987004088469753859696407139054406989735113827981148062449057870561788973142250811838720214530386151198455545176591384352343648452329042764530196327665219224050630680827543991306749402959935685172017409062967157813233001567797128414009962262840951763040181
  44895767034162990997987303986882660674722497505237491649296190658571471979065889234144353811843706629535512848235473808330181517421970135930320187227697512315919757806204341545022714991717913006031724818461724742069401359454784533576615919680949125073761586043027941204059690093447093117249681641020785611986
  1
  -44146175664861261172356293340716833133750232401287328189797639296698679436925232375473973898100363205157703913050824405116878299310008848005045714833814493992539429428295945643439440068026313232881493081836812480325977761600303456915493177366981470223898994906470419007730670657168179659899713837827764669213
  98330790743257232930640417364963717704786040860302439189781385170246412183980882564239377268174203679366339563908361674571088519452885615348465535190260914996055274486493192655677181637142116473172979503236297658204730543049175626205461452256333155750566288282331419748434569978343545573401114593095927172889;

  44895767034162990997987303986882660674722497505237491649296190658571471979065889234144353811843706629535512848235473808330181517421970135930320187227697512315919757806204341545022714991717913006031724818461724742069401359454784533576615919680949125073761586043027941204059690093447093117249681641020785611986
  100000423751500546004561515884626739136961367515520675987004088469753859696407139054406989735113827981148062449057870561788973142250811838720214530386151198455545176591384352343648452329042764530196327665219224050630680827543991306749402959935685172017409062967157813233001567797128414009962262840951763040181
  1
  -1669633008243313073921098519663021432175326655218236797222703299507447512426256490167612466939624301781722885149508887217884622797926223371748995195890283459489902104891159687971270691900648057023348161982926392425950284494815680543941507679352016266842774684826393484566997818784868436561148247855835867292
  749591369301729825631010646165827540972265103950163459498551361872792542140656858670379913743343424377808935184649403213303218111961287925274472393883018323380328377908395901583274923691599773150231736624912261743423597854481076661122742313967654849862591136557522196329019436278913457349967803193020942773;

  # --- Some other bugs ---

  19504439280113284806725522136967618725661733412699408177537810327183285842670
  1
  1
  0
  1;
}

modinv {
  5 9 2;
  15 64 47;
  564566436 546457643 408896426;
}

jacobi {
  4 5 1;
  6 7 -1;
  15 27 0;
  2132498039840981 98729378979237498798347932749951 1;
  98729378979237498798347932749951 2132498039840981 1;

  # --- Kronecker extension ---

  0 0 0;
  1 0 1;
  -1 0 -1;
  2 0 0;

  2132498039840981 197458757958474997596695865499902 -1;
  98729378979237498798347932749951 4264996079681962 1;
  98729378979237498798347932749951 -4264996079681962 1;
  -98729378979237498798347932749951 -4264996079681962 -1;

  # --- Random tests made by PARI/gp ---

  22 -19 -1;
  48 -37 1;
  -13 29 1;
  -19 2 -1;
  -43 31 1;
  -12 -7 -1;
  -14 -34 0;
  -30 -29 -1;
  25 26 1;
  -27 20 -1;
  -5 -45 0;
  9 -42 0;
  -51 -3 0;
  -39 35 -1;
  37 30 1;
  13 18 -1;
  -28 6 0;
  -49 -15 1;
  -1 1 1;
  -9 13 1;
  -47 44 -1;
  -14 -30 0;
  37 -36 1;
  45 9 0;
  -29 30 -1;
  49 49 0;
  -27 -10 -1;
  -35 -25 0;
  17 14 -1;
  -35 29 1;
  -1 33 1;
  38 -11 1;
  3 -24 0;
  5 -25 0;
  -31 22 -1;
  40 30 0;
  -43 26 -1;
  -22 10 0;
  11 -29 -1;
  40 -18 0;
}

modsqrt {
  1 3 1;
  4 5 2;
  9775592058107450692 13391974640168007623 3264570455655810730;
  8155671698868891620 10189552848261357803 2073812183305821596;
  3248339460720824413 8976233780911635437 1220523478429582717;
  3447751741648956439 10155704720805654949 2812971608818169892;
  1453601744816463433 3095659104519735473 1260511572497628526;
  3366261317119810224 3756232416311497601 610261287187759737;
  3869491397135339653 5762828162167967567 2788500156455085147;
  660864223630638896 1729533840094059799 671335997718840076;
}

modexp {

  # --- Montgomery exponentiation ---

  435365332435654643667 8745435676786567758678547
    4325987397987458979875737589783
    2439674515119108242643169132064;
  0xfffffffdfffffffffffffffffffffffe 0 0xfffffffdffffffffffffffffffffffff 1;
  1804289383 -8939035539979879765 8939489893434234331 6139425926295484741;

  # --- Barrett exponentiation ---

  435365332435654643667 8745435676786567758678547
    4325987397987458979875737589782
    2425191520487853884024972777945;
}

factorial {
  0 1;
  1 1;
  2 2;
  3 6;
  4 24;
  5 120;
  30 265252859812191058636308480000000;
  100 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000;
  500
   1220136825991110068701238785423046926253574342803192842192413588385845373153881997605496447502203281863013616477148203584163378722078177200480785205159329285477907571939330603772960859086270429174547882424912726344305670173270769461062802310452644218878789465754777149863494367781037644274033827365397471386477878495438489595537537990423241061271326984327745715546309977202781014561081188373709531016356324432987029563896628911658974769572087926928871281780070265174507768410719624390394322536422605234945850129918571501248706961568141625359056693423813008856249246891564126775654481886506593847951775360894005745238940335798476363944905313062323749066445048824665075946735862074637925184200459369692981022263971952597190945217823331756934581508552332820762820023402626907898342451712006207714640979456116127629145951237229913340169552363850942885592018727433795173014586357570828355780158735432768888680120399882384702151467605445407663535984174430480128938313896881639487469658817504506926365338175055478128640000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000;
}

fibonacci {
  -20 -6765;
  -19 4181;
  -10 -55;
  -9 34;
  -2 -1;
  -1 1;
  0 0;
  1 1;
  2 1;
  5 5;
  10 55;
  19 4181;
  20 6765;
  100 354224848179261915075;
  1000 43466557686937456435688527675040625802564660517371780402481729089536555417949051890403879840079255169295922593080322634775209689623239873322471161642996440906533187938298969649928516003704476137795166849228875;
}