| 1 | # Test vectors for MP functions |
| 2 | |
| 3 | add { |
| 4 | 5 4 9; 5 -4 1; -5 4 -1; -5 -4 -9; |
| 5 | 0xffffffff 1 0x100000000; |
| 6 | } |
| 7 | |
| 8 | sub { |
| 9 | 5 4 1; 5 -4 9; -5 4 -9; -5 -4 -1; |
| 10 | 4 5 -1; 4 -5 9; -4 5 -9; -4 -5 1; |
| 11 | } |
| 12 | |
| 13 | mul { |
| 14 | 5 4 20; -5 4 -20; 5 -4 -20; -5 -4 20; |
| 15 | 0x10000 0x10000 0x100000000; |
| 16 | } |
| 17 | |
| 18 | div { |
| 19 | 9 4 2 1; -9 4 -3 3; 9 -4 -3 -3; -9 -4 2 -1; |
| 20 | -3 6277101735386680763835789423207666416083908700390324961279 |
| 21 | -1 6277101735386680763835789423207666416083908700390324961276; |
| 22 | 3131675836296406071791252329528905062261497366991742517193 |
| 23 | 1110875761630725856340142297645383444629395595869672555585 |
| 24 | 2 909924313034954359110967734238138173002706175252397406023; |
| 25 | 3131675836296406071791252329528905062261497366991742517193 |
| 26 | 53 |
| 27 | 59088223326347284373419855274130284193613157867768726739 26; |
| 28 | 1552518092300708935130918131258481755631334049434514313202351194902966239949102107258669453876591642442910007680288864229150803718918046342632727613031282983744380820890196288509170691316593175367469551763119843371637221007210577919 |
| 29 | 776259046150354467565459065629240877815667024717257156601175597451483119974551053629334726938295821221455003840144432114575401859459023171316363806515641491872190410445098144254585345658296587683734775881559921685818610503605288959 |
| 30 | 2 1; |
| 31 | } |
| 32 | |
| 33 | exp { |
| 34 | 4 0 1; |
| 35 | 4 1 4; |
| 36 | 7 2 49; |
| 37 | 3 564 124849745640593184256214502788000232711984346194239284918599169775251467106591187580476305077269760425019686159071753053924227569816588462643229463821875763427430576080998505780547826368760514503807579784278708008217584939464444237989070811887584423210788916656247499281; |
| 38 | } |
| 39 | |
| 40 | bin2c { |
| 41 | and 5 3 1; |
| 42 | or 5 3 7; |
| 43 | xor 5 3 6; |
| 44 | 1111 0 0 -1; |
| 45 | or 45 -7 -3; |
| 46 | xor 0x343cd5 -0x6a49c -0x32984f; |
| 47 | } |
| 48 | |
| 49 | lsr2c { |
| 50 | -1 5 -1; |
| 51 | 1 5 0; |
| 52 | -6 2 -2; |
| 53 | 5 0 5; |
| 54 | -4 0 -4; |
| 55 | 7 2 1; |
| 56 | -7 2 -2; |
| 57 | -7 20 -1; |
| 58 | } |
| 59 | |
| 60 | lsl2c { |
| 61 | -1 5 -32; |
| 62 | 5 0 5; |
| 63 | -4 0 -4; |
| 64 | 7 2 28; |
| 65 | -7 2 -28; |
| 66 | 0xc0000000 1 0x180000000; |
| 67 | -0xc0000000 1 -0x180000000; |
| 68 | -1 32 -0x100000000; |
| 69 | } |
| 70 | |
| 71 | setbit { |
| 72 | 0 40 0x10000000000; |
| 73 | 0x87348 40 0x10000087348; |
| 74 | 5 1 7; |
| 75 | 7 1 7; |
| 76 | -3 1 -1; |
| 77 | } |
| 78 | |
| 79 | clrbit { |
| 80 | 0x10000000000 40 0; |
| 81 | 0x87348 40 0x87348; |
| 82 | 5 1 5; |
| 83 | 7 1 5; |
| 84 | -1 1 -3; |
| 85 | } |
| 86 | |
| 87 | neg { |
| 88 | 0 0; |
| 89 | 15 -15; |
| 90 | -15 15; |
| 91 | } |
| 92 | |
| 93 | odd { |
| 94 | 1 0 1; |
| 95 | 2 1 1; |
| 96 | 4 2 1; |
| 97 | 12 2 3; |
| 98 | 0x10000000000000 52 1; |
| 99 | 0x10000000400000 22 0x40000001; |
| 100 | } |
| 101 | |
| 102 | sqrt { |
| 103 | 0 0; |
| 104 | 1 1; |
| 105 | 4 2; |
| 106 | 9 3; |
| 107 | 16 4; |
| 108 | 99 9; |
| 109 | 100 10; |
| 110 | 101 10; |
| 111 | 120 10; |
| 112 | 121 11; |
| 113 | |
| 114 | 10106623487257186586 3179091613; |
| 115 | 14565040310136678240 3816417208; |
| 116 | } |
| 117 | |
| 118 | gcd { |
| 119 | # --- Simple tests --- |
| 120 | |
| 121 | 16 12 4 -11 15; |
| 122 | 12 16 4 -1 1; |
| 123 | 693 609 21 -7 8; |
| 124 | 4398082908043 90980984098081324 1 -32483863573352089 1570292150447; |
| 125 | |
| 126 | # --- Negative argument tests --- |
| 127 | |
| 128 | 16 -12 4 -11 -15; |
| 129 | -16 12 4 11 15; |
| 130 | -12 -16 4 1 -1; |
| 131 | -12 16 4 1 1; |
| 132 | -693 609 21 7 8; |
| 133 | 693 -609 21 -7 -8; |
| 134 | |
| 135 | # --- Zero argument tests --- |
| 136 | |
| 137 | 15 0 15 1 0; |
| 138 | 0 15 15 0 1; |
| 139 | -5 0 5 -1 0; |
| 140 | 0 -5 5 0 -1; |
| 141 | 0 0 0 0 0; |
| 142 | |
| 143 | # --- Random number tests --- |
| 144 | |
| 145 | 829561629303257626084392170900075 32498098450983560651904114638965 |
| 146 | 5 -29340810037249902802634060204608 748967211613630574419802053172497; |
| 147 | |
| 148 | 5509672937670943767152343650729669537671508 |
| 149 | 398326674296699796695672966992514673531 |
| 150 | 17 |
| 151 | -4158709420138833210339208344965073815 |
| 152 | 57523460582278135926717203882531035926727; |
| 153 | |
| 154 | 324098408098290809832490802984098208098324 |
| 155 | 23430980840982340982098409823089098443 |
| 156 | 1 |
| 157 | -4158709420138833210339208344965073815 |
| 158 | 57523460582278135926717203882531035926727; |
| 159 | |
| 160 | # --- RSA test --- |
| 161 | # |
| 162 | # The first number is (p - 1)(q - 1) from `mpmont'. The second is a |
| 163 | # random number (it's actually prime, but that doesn't matter) which I |
| 164 | # can use as an RSA encryption exponent. The last is the partner |
| 165 | # decryption exponent, produced using the extended GCD algorithm. |
| 166 | |
| 167 | 665251164384574309450646977867043764321191240895546832784045453360 |
| 168 | 5945908509680983480596809586040589085680968709809890671 |
| 169 | 1 |
| 170 | -4601007896041464028712478963832994007038251361995647370 |
| 171 | 514778499400157641662814932021958856708417966520837469125919104431; |
| 172 | |
| 173 | # --- Misery --- |
| 174 | # |
| 175 | # Some bugs discovered during RSA testing. |
| 176 | |
| 177 | 100000423751500546004561515884626739136961367515520675987004088469753859696407139054406989735113827981148062449057870561788973142250811838720214530386151198455545176591384352343648452329042764530196327665219224050630680827543991306749402959935685172017409062967157813233001567797128414009962262840951763040181 |
| 178 | 44895767034162990997987303986882660674722497505237491649296190658571471979065889234144353811843706629535512848235473808330181517421970135930320187227697512315919757806204341545022714991717913006031724818461724742069401359454784533576615919680949125073761586043027941204059690093447093117249681641020785611986 |
| 179 | 1 |
| 180 | -44146175664861261172356293340716833133750232401287328189797639296698679436925232375473973898100363205157703913050824405116878299310008848005045714833814493992539429428295945643439440068026313232881493081836812480325977761600303456915493177366981470223898994906470419007730670657168179659899713837827764669213 |
| 181 | 98330790743257232930640417364963717704786040860302439189781385170246412183980882564239377268174203679366339563908361674571088519452885615348465535190260914996055274486493192655677181637142116473172979503236297658204730543049175626205461452256333155750566288282331419748434569978343545573401114593095927172889; |
| 182 | |
| 183 | 44895767034162990997987303986882660674722497505237491649296190658571471979065889234144353811843706629535512848235473808330181517421970135930320187227697512315919757806204341545022714991717913006031724818461724742069401359454784533576615919680949125073761586043027941204059690093447093117249681641020785611986 |
| 184 | 100000423751500546004561515884626739136961367515520675987004088469753859696407139054406989735113827981148062449057870561788973142250811838720214530386151198455545176591384352343648452329042764530196327665219224050630680827543991306749402959935685172017409062967157813233001567797128414009962262840951763040181 |
| 185 | 1 |
| 186 | -1669633008243313073921098519663021432175326655218236797222703299507447512426256490167612466939624301781722885149508887217884622797926223371748995195890283459489902104891159687971270691900648057023348161982926392425950284494815680543941507679352016266842774684826393484566997818784868436561148247855835867292 |
| 187 | 749591369301729825631010646165827540972265103950163459498551361872792542140656858670379913743343424377808935184649403213303218111961287925274472393883018323380328377908395901583274923691599773150231736624912261743423597854481076661122742313967654849862591136557522196329019436278913457349967803193020942773; |
| 188 | |
| 189 | # --- Some other bugs --- |
| 190 | |
| 191 | 19504439280113284806725522136967618725661733412699408177537810327183285842670 |
| 192 | 1 |
| 193 | 1 |
| 194 | 0 |
| 195 | 1; |
| 196 | } |
| 197 | |
| 198 | modinv { |
| 199 | 5 9 2; |
| 200 | 15 64 47; |
| 201 | 564566436 546457643 408896426; |
| 202 | -1 257 -1; |
| 203 | } |
| 204 | |
| 205 | jacobi { |
| 206 | 4 5 1; |
| 207 | 6 7 -1; |
| 208 | 15 27 0; |
| 209 | 2132498039840981 98729378979237498798347932749951 1; |
| 210 | 98729378979237498798347932749951 2132498039840981 1; |
| 211 | |
| 212 | # --- Kronecker extension --- |
| 213 | |
| 214 | 0 0 0; |
| 215 | 1 0 1; |
| 216 | -1 0 -1; |
| 217 | 2 0 0; |
| 218 | |
| 219 | 2132498039840981 197458757958474997596695865499902 -1; |
| 220 | 98729378979237498798347932749951 4264996079681962 1; |
| 221 | 98729378979237498798347932749951 -4264996079681962 1; |
| 222 | -98729378979237498798347932749951 -4264996079681962 -1; |
| 223 | |
| 224 | # --- Random tests made by PARI/gp --- |
| 225 | |
| 226 | 22 -19 -1; |
| 227 | 48 -37 1; |
| 228 | -13 29 1; |
| 229 | -19 2 -1; |
| 230 | -43 31 1; |
| 231 | -12 -7 -1; |
| 232 | -14 -34 0; |
| 233 | -30 -29 -1; |
| 234 | 25 26 1; |
| 235 | -27 20 -1; |
| 236 | -5 -45 0; |
| 237 | 9 -42 0; |
| 238 | -51 -3 0; |
| 239 | -39 35 -1; |
| 240 | 37 30 1; |
| 241 | 13 18 -1; |
| 242 | -28 6 0; |
| 243 | -49 -15 1; |
| 244 | -1 1 1; |
| 245 | -9 13 1; |
| 246 | -47 44 -1; |
| 247 | -14 -30 0; |
| 248 | 37 -36 1; |
| 249 | 45 9 0; |
| 250 | -29 30 -1; |
| 251 | 49 49 0; |
| 252 | -27 -10 -1; |
| 253 | -35 -25 0; |
| 254 | 17 14 -1; |
| 255 | -35 29 1; |
| 256 | -1 33 1; |
| 257 | 38 -11 1; |
| 258 | 3 -24 0; |
| 259 | 5 -25 0; |
| 260 | -31 22 -1; |
| 261 | 40 30 0; |
| 262 | -43 26 -1; |
| 263 | -22 10 0; |
| 264 | 11 -29 -1; |
| 265 | 40 -18 0; |
| 266 | } |
| 267 | |
| 268 | modsqrt { |
| 269 | 0 5 0; |
| 270 | 1 3 1; |
| 271 | 4 5 2; |
| 272 | 9775592058107450692 13391974640168007623 3264570455655810730; |
| 273 | 8155671698868891620 10189552848261357803 2073812183305821596; |
| 274 | 3248339460720824413 8976233780911635437 1220523478429582717; |
| 275 | 3447751741648956439 10155704720805654949 2812971608818169892; |
| 276 | 1453601744816463433 3095659104519735473 1260511572497628526; |
| 277 | 3366261317119810224 3756232416311497601 610261287187759737; |
| 278 | 3869491397135339653 5762828162167967567 2788500156455085147; |
| 279 | 660864223630638896 1729533840094059799 671335997718840076; |
| 280 | } |
| 281 | |
| 282 | modexp { |
| 283 | |
| 284 | # --- Montgomery exponentiation --- |
| 285 | |
| 286 | 435365332435654643667 8745435676786567758678547 |
| 287 | 4325987397987458979875737589783 |
| 288 | 2439674515119108242643169132064; |
| 289 | 0xfffffffdfffffffffffffffffffffffe 0 0xfffffffdffffffffffffffffffffffff 1; |
| 290 | 1804289383 -8939035539979879765 8939489893434234331 6139425926295484741; |
| 291 | |
| 292 | # --- Barrett exponentiation --- |
| 293 | |
| 294 | 435365332435654643667 8745435676786567758678547 |
| 295 | 4325987397987458979875737589782 |
| 296 | 2425191520487853884024972777945; |
| 297 | } |
| 298 | |
| 299 | factorial { |
| 300 | 0 1; |
| 301 | 1 1; |
| 302 | 2 2; |
| 303 | 3 6; |
| 304 | 4 24; |
| 305 | 5 120; |
| 306 | 30 265252859812191058636308480000000; |
| 307 | 100 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000; |
| 308 | 500 |
| 309 | 1220136825991110068701238785423046926253574342803192842192413588385845373153881997605496447502203281863013616477148203584163378722078177200480785205159329285477907571939330603772960859086270429174547882424912726344305670173270769461062802310452644218878789465754777149863494367781037644274033827365397471386477878495438489595537537990423241061271326984327745715546309977202781014561081188373709531016356324432987029563896628911658974769572087926928871281780070265174507768410719624390394322536422605234945850129918571501248706961568141625359056693423813008856249246891564126775654481886506593847951775360894005745238940335798476363944905313062323749066445048824665075946735862074637925184200459369692981022263971952597190945217823331756934581508552332820762820023402626907898342451712006207714640979456116127629145951237229913340169552363850942885592018727433795173014586357570828355780158735432768888680120399882384702151467605445407663535984174430480128938313896881639487469658817504506926365338175055478128640000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000; |
| 310 | } |
| 311 | |
| 312 | fibonacci { |
| 313 | -20 -6765; |
| 314 | -19 4181; |
| 315 | -10 -55; |
| 316 | -9 34; |
| 317 | -2 -1; |
| 318 | -1 1; |
| 319 | 0 0; |
| 320 | 1 1; |
| 321 | 2 1; |
| 322 | 5 5; |
| 323 | 10 55; |
| 324 | 19 4181; |
| 325 | 20 6765; |
| 326 | 100 354224848179261915075; |
| 327 | 1000 43466557686937456435688527675040625802564660517371780402481729089536555417949051890403879840079255169295922593080322634775209689623239873322471161642996440906533187938298969649928516003704476137795166849228875; |
| 328 | } |