www.pudn.com > rsa.zip > GInt.pas
{License, info, etc
------------------
This implementation is made by Walied Othman, to contact me
mail to Walied.Othman@Student.KULeuven.ac.be or
Triade@ace.Ulyssis.Student.KULeuven.ac.be, or ICQ me on 20388046.
If you 're going to use these implementations, at least mention my
name or something and notify me so I may even put a link on my page.
This implementation is freeware and according to the coderpunks'
manifesto it should remain so, so don 't use these implementations
in commercial applications. Encryption, as a tool to ensure privacy
should be free and accessible for anyone.
If any algorithm is patented in your country, you should acquire a
license before using this software. Modified versions of this
software must remain in the public domain and must contain an
acknowledgement of the original author (=me).
This implementaion is available at
http://ace.ulyssis.student.kuleuven.ac.be/~triade/GInt/index.htm
copyright 1999, Walied Othman
This header may not be removed.
Updates:
--------
9/1/99: Division algorithm speeded up, 3 times faster now
22/1/99: Procedure Added to compute the Legendre symbol
26/2/99: The Procedure GIntToBinStr optimized
28/2/99: signtype changed
19/3/99: TrialDiv range expanded
23/3/99: BinStrToGInt optimized, 4 times faster now
GIntMulByInt and GIntMulByIntBis procedures added
}
Unit GInt;
Interface
Uses Windows, SysUtils, Controls;
Type
TCompare = (Lt, St, Eq, Er);
Tsign = (negative, positive);
TGInt = ^cont;
cont = Record
sign : Tsign;
value : longint;
next, prev : TGInt;
End;
Procedure zeronetochar8(Var g : char; x : String);
Procedure zeronetochar6(Var g : integer; x : String);
Procedure initialize8(Var trans : Array Of String);
Procedure initialize6(Var trans : Array Of String);
Procedure Convert8to6bit(str8 : String; Var str6 : String);
Procedure Convert6to8bit(str6 : String; Var str8 : String);
Procedure Convert8to1bit(str8 : String; Var str1 : String);
Procedure Convert6to1bit(str6 : String; Var str1 : String);
Procedure Convert1to8bit(str1 : String; Var str8 : String);
Procedure Convert1to6bit(str1 : String; Var str6 : String);
Procedure decstrtogint(GIntstr : String; Var GInt : TGInt);
Procedure ginttodecstr(Var GIntstr : String; GInt : TGInt);
Procedure InttoGInt(Int : integer; Var GInt : TGInt);
Procedure gintdestroy(Var GInt : TGInt);
Procedure GIntcopy(GInt1 : TGInt; Var GInt2 : TGInt);
Procedure GIntdivbyint(GInt : TGInt; Var res : TGInt; by : longint; Var m : longint);
Procedure GIntmodbyint(GInt : TGInt; by : longint; Var m : longint);
Function GIntCompareAbs(GInt1, GInt2 : TGInt) : TCompare;
Procedure GIntchangesign(Var GInt : TGInt);
Procedure GIntabs(Var GInt : TGInt);
Procedure GIntadd(GInt1, GInt2 : TGInt; Var sum : TGInt);
Procedure GIntsub(GInt1, GInt2 : TGInt; Var dif : TGInt);
Procedure GIntmul(GInt1, GInt2 : TGInt; Var prod : TGInt);
Procedure GIntMulByInt(GInt1 : TGInt; By : Longint; Var prod : TGInt);
Procedure GIntMulByIntBis(Var GInt : TGInt; By : Longint);
Procedure GIntSquare(GInt : TGInt; Var Square : TGInt);
Procedure GInttobinstr(GInt : TGint; Var S : String);
Procedure Binstrtogint(S : String; Var GInt : TGInt);
Procedure GInttostr(GInt : TGInt; Var str : String);
Procedure strtoGInt(str : String; Var GInt : TGInt);
Procedure GIntExp(GInt, exp : TGInt; Var res : TGInt);
Procedure GIntfac(GInt : TGInt; Var res : TGint);
Procedure GIntdivmod(GInt1, GInt2 : TGInt; Var divres, modres : TGInt);
Procedure GIntdiv(GInt1, GInt2 : TGInt; Var divres : TGInt);
Procedure GIntmod(GInt1, GInt2 : TGInt; Var modres : TGInt);
Procedure GIntSquareMod(GInt, Modb : TGInt; Var GIntSM : TGInt);
Procedure GIntAddMod(GInt1, GInt2, base : TGInt; Var GIntres : TGInt);
Procedure GIntMulMod(GInt1, GInt2, base : TGInt; Var GIntres : TGInt);
Procedure GIntmodExp(GInt, exp, modb : TGInt; Var res : TGInt);
Procedure GIntGCD(GInt1, GInt2 : TGint; Var GCD : TGInt);
Procedure GIntLCM(GInt1, GInt2 : TGInt; Var LCM : TGInt);
Procedure GIntTrialdiv9999(GInt : TGInt; Var ok : boolean);
Procedure GIntRandom1(Seed : TGInt; Var RandomGInt : TGInt);
Procedure GIntRabinMiller(GIntp : TGInt; nrtest : integer; Var ok : boolean);
Procedure GIntBezoutBachet(GInt1, GInt2 : TGInt; Var a, b : TGInt);
Procedure GIntModInv(GInt1, base : TGInt; Var Inverse : TGInt);
Procedure GIntPrimetest(GIntp : TGInt; nrRMtests : integer; Var ok : boolean);
Procedure GIntLegendreSymbol(a, p : TGInt; Var L : integer);
Implementation
Var
primes : Array[1..1227] Of integer =
(3, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127,
131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251,
257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389,
397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541,
547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677,
683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839,
853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997, 1009,
1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123,
1129, 1151, 1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223, 1229, 1231, 1237, 1249, 1259, 1277, 1279,
1283, 1289, 1291, 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, 1381, 1399, 1409, 1423, 1427, 1429,
1433, 1439, 1447, 1451, 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, 1523, 1531, 1543, 1549, 1553,
1559, 1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, 1663, 1667, 1669, 1693,
1697, 1699, 1709, 1721, 1723, 1733, 1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, 1823, 1831, 1847,
1861, 1867, 1871, 1873, 1877, 1879, 1889, 1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987, 1993, 1997,
1999, 2003, 2011, 2017, 2027, 2029, 2039, 2053, 2063, 2069, 2081, 2083, 2087, 2089, 2099, 2111, 2113, 2129, 2131,
2137, 2141, 2143, 2153, 2161, 2179, 2203, 2207, 2213, 2221, 2237, 2239, 2243, 2251, 2267, 2269, 2273, 2281, 2287,
2293, 2297, 2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357, 2371, 2377, 2381, 2383, 2389, 2393, 2399, 2411, 2417,
2423, 2437, 2441, 2447, 2459, 2467, 2473, 2477, 2503, 2521, 2531, 2539, 2543, 2549, 2551, 2557, 2579, 2591, 2593,
2609, 2617, 2621, 2633, 2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687, 2689, 2693, 2699, 2707, 2711, 2713, 2719,
2729, 2731, 2741, 2749, 2753, 2767, 2777, 2789, 2791, 2797, 2801, 2803, 2819, 2833, 2837, 2843, 2851, 2857, 2861,
2879, 2887, 2897, 2903, 2909, 2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999, 3001, 3011, 3019, 3023, 3037,
3041, 3049, 3061, 3067, 3079, 3083, 3089, 3109, 3119, 3121, 3137, 3163, 3167, 3169, 3181, 3187, 3191, 3203, 3209,
3217, 3221, 3229, 3251, 3253, 3257, 3259, 3271, 3299, 3301, 3307, 3313, 3319, 3323, 3329, 3331, 3343, 3347, 3359,
3361, 3371, 3373, 3389, 3391, 3407, 3413, 3433, 3449, 3457, 3461, 3463, 3467, 3469, 3491, 3499, 3511, 3517, 3527,
3529, 3533, 3539, 3541, 3547, 3557, 3559, 3571, 3581, 3583, 3593, 3607, 3613, 3617, 3623, 3631, 3637, 3643, 3659,
3671, 3673, 3677, 3691, 3697, 3701, 3709, 3719, 3727, 3733, 3739, 3761, 3767, 3769, 3779, 3793, 3797, 3803, 3821,
3823, 3833, 3847, 3851, 3853, 3863, 3877, 3881, 3889, 3907, 3911, 3917, 3919, 3923, 3929, 3931, 3943, 3947, 3967,
3989, 4001, 4003, 4007, 4013, 4019, 4021, 4027, 4049, 4051, 4057, 4073, 4079, 4091, 4093, 4099, 4111, 4127, 4129,
4133, 4139, 4153, 4157, 4159, 4177, 4201, 4211, 4217, 4219, 4229, 4231, 4241, 4243, 4253, 4259, 4261, 4271, 4273,
4283, 4289, 4297, 4327, 4337, 4339, 4349, 4357, 4363, 4373, 4391, 4397, 4409, 4421, 4423, 4441, 4447, 4451, 4457,
4463, 4481, 4483, 4493, 4507, 4513, 4517, 4519, 4523, 4547, 4549, 4561, 4567, 4583, 4591, 4597, 4603, 4621, 4637,
4639, 4643, 4649, 4651, 4657, 4663, 4673, 4679, 4691, 4703, 4721, 4723, 4729, 4733, 4751, 4759, 4783, 4787, 4789,
4793, 4799, 4801, 4813, 4817, 4831, 4861, 4871, 4877, 4889, 4903, 4909, 4919, 4931, 4933, 4937, 4943, 4951, 4957,
4967, 4969, 4973, 4987, 4993, 4999, 5003, 5009, 5011, 5021, 5023, 5039, 5051, 5059, 5077, 5081, 5087, 5099, 5101,
5107, 5113, 5119, 5147, 5153, 5167, 5171, 5179, 5189, 5197, 5209, 5227, 5231, 5233, 5237, 5261, 5273, 5279, 5281,
5297, 5303, 5309, 5323, 5333, 5347, 5351, 5381, 5387, 5393, 5399, 5407, 5413, 5417, 5419, 5431, 5437, 5441, 5443,
5449, 5471, 5477, 5479, 5483, 5501, 5503, 5507, 5519, 5521, 5527, 5531, 5557, 5563, 5569, 5573, 5581, 5591, 5623,
5639, 5641, 5647, 5651, 5653, 5657, 5659, 5669, 5683, 5689, 5693, 5701, 5711, 5717, 5737, 5741, 5743, 5749, 5779,
5783, 5791, 5801, 5807, 5813, 5821, 5827, 5839, 5843, 5849, 5851, 5857, 5861, 5867, 5869, 5879, 5881, 5897, 5903,
5923, 5927, 5939, 5953, 5981, 5987, 6007, 6011, 6029, 6037, 6043, 6047, 6053, 6067, 6073, 6079, 6089, 6091, 6101,
6113, 6121, 6131, 6133, 6143, 6151, 6163, 6173, 6197, 6199, 6203, 6211, 6217, 6221, 6229, 6247, 6257, 6263, 6269,
6271, 6277, 6287, 6299, 6301, 6311, 6317, 6323, 6329, 6337, 6343, 6353, 6359, 6361, 6367, 6373, 6379, 6389, 6397,
6421, 6427, 6449, 6451, 6469, 6473, 6481, 6491, 6521, 6529, 6547, 6551, 6553, 6563, 6569, 6571, 6577, 6581, 6599,
6607, 6619, 6637, 6653, 6659, 6661, 6673, 6679, 6689, 6691, 6701, 6703, 6709, 6719, 6733, 6737, 6761, 6763, 6779,
6781, 6791, 6793, 6803, 6823, 6827, 6829, 6833, 6841, 6857, 6863, 6869, 6871, 6883, 6899, 6907, 6911, 6917, 6947,
6949, 6959, 6961, 6967, 6971, 6977, 6983, 6991, 6997, 7001, 7013, 7019, 7027, 7039, 7043, 7057, 7069, 7079, 7103,
7109, 7121, 7127, 7129, 7151, 7159, 7177, 7187, 7193, 7207, 7211, 7213, 7219, 7229, 7237, 7243, 7247, 7253, 7283,
7297, 7307, 7309, 7321, 7331, 7333, 7349, 7351, 7369, 7393, 7411, 7417, 7433, 7451, 7457, 7459, 7477, 7481, 7487,
7489, 7499, 7507, 7517, 7523, 7529, 7537, 7541, 7547, 7549, 7559, 7561, 7573, 7577, 7583, 7589, 7591, 7603, 7607,
7621, 7639, 7643, 7649, 7669, 7673, 7681, 7687, 7691, 7699, 7703, 7717, 7723, 7727, 7741, 7753, 7757, 7759, 7789,
7793, 7817, 7823, 7829, 7841, 7853, 7867, 7873, 7877, 7879, 7883, 7901, 7907, 7919, 7927, 7933, 7937, 7949, 7951,
7963, 7993, 8009, 8011, 8017, 8039, 8053, 8059, 8069, 8081, 8087, 8089, 8093, 8101, 8111, 8117, 8123, 8147, 8161,
8167, 8171, 8179, 8191, 8209, 8219, 8221, 8231, 8233, 8237, 8243, 8263, 8269, 8273, 8287, 8291, 8293, 8297, 8311,
8317, 8329, 8353, 8363, 8369, 8377, 8387, 8389, 8419, 8423, 8429, 8431, 8443, 8447, 8461, 8467, 8501, 8513, 8521,
8527, 8537, 8539, 8543, 8563, 8573, 8581, 8597, 8599, 8609, 8623, 8627, 8629, 8641, 8647, 8663, 8669, 8677, 8681,
8689, 8693, 8699, 8707, 8713, 8719, 8731, 8737, 8741, 8747, 8753, 8761, 8779, 8783, 8803, 8807, 8819, 8821, 8831,
8837, 8839, 8849, 8861, 8863, 8867, 8887, 8893, 8923, 8929, 8933, 8941, 8951, 8963, 8969, 8971, 8999, 9001, 9007,
9011, 9013, 9029, 9041, 9043, 9049, 9059, 9067, 9091, 9103, 9109, 9127, 9133, 9137, 9151, 9157, 9161, 9173, 9181,
9187, 9199, 9203, 9209, 9221, 9227, 9239, 9241, 9257, 9277, 9281, 9283, 9293, 9311, 9319, 9323, 9337, 9341, 9343,
9349, 9371, 9377, 9391, 9397, 9403, 9413, 9419, 9421, 9431, 9433, 9437, 9439, 9461, 9463, 9467, 9473, 9479, 9491,
9497, 9511, 9521, 9533, 9539, 9547, 9551, 9587, 9601, 9613, 9619, 9623, 9629, 9631, 9643, 9649, 9661, 9677, 9679,
9689, 9697, 9719, 9721, 9733, 9739, 9743, 9749, 9767, 9769, 9781, 9787, 9791, 9803, 9811, 9817, 9829, 9833, 9839,
9851, 9857, 9859, 9871, 9883, 9887, 9901, 9907, 9923, 9929, 9931, 9941, 9949, 9967, 9973);
chr64 : Array[1..64] Of char = ('a', 'A', 'b', 'B', 'c', 'C', 'd', 'D', 'e', 'E', 'f', 'F',
'g', 'G', 'h', 'H', 'i', 'I', 'j', 'J', 'k', 'K', 'l', 'L', 'm', 'M', 'n', 'N', 'o', 'O', 'p',
'P', 'q', 'Q', 'r', 'R', 's', 'S', 't', 'T', 'u', 'U', 'v', 'V', 'w', 'W', 'x', 'X', 'y', 'Y',
'z', 'Z', '0', '1', '2', '3', '4', '5', '6', '7', '8', '9', '+', '=');
{$H+}
Procedure zeronetochar8(Var g : char; x : String);
Begin
If x[1] = '0' Then
Begin
If x[2] = '0' Then
Begin
If x[3] = '0' Then
Begin
If x[4] = '0' Then
Begin
If x[5] = '0' Then
Begin
If x[6] = '0' Then
Begin
If x[7] = '0' Then
Begin
If x[8] = '0' Then g := chr(1) Else g := chr(2);
End
Else
Begin
If x[8] = '0' Then g := chr(4) Else g := chr(3);
End
End
Else
Begin
If x[7] = '0' Then
Begin
If x[8] = '0' Then g := chr(5) Else g := chr(6);
End
Else
Begin
If x[8] = '0' Then g := chr(9) Else g := chr(8);
End
End
End
Else
Begin
If x[6] = '0' Then
Begin
If x[7] = '0' Then
Begin
If x[8] = '0' Then g := chr(7) Else g := chr(10);
End
Else
Begin
If x[8] = '0' Then g := chr(11) Else g := chr(13);
End
End
Else
Begin
If x[7] = '0' Then
Begin
If x[8] = '0' Then g := chr(14) Else g := chr(12);
End
Else
Begin
If x[8] = '0' Then g := chr(15) Else g := chr(16);
End
End
End
End
Else
Begin
If x[5] = '0' Then
Begin
If x[6] = '0' Then
Begin
If x[7] = '0' Then
Begin
If x[8] = '0' Then g := chr(18) Else g := chr(20);
End
Else
Begin
If x[8] = '0' Then g := chr(17) Else g := chr(21);
End
End
Else
Begin
If x[7] = '0' Then
Begin
If x[8] = '0' Then g := chr(19) Else g := chr(25);
End
Else
Begin
If x[8] = '0' Then g := chr(24) Else g := chr(22);
End
End
End
Else
Begin
If x[6] = '0' Then
Begin
If x[7] = '0' Then
Begin
If x[8] = '0' Then g := chr(23) Else g := chr(26);
End
Else
Begin
If x[8] = '0' Then g := chr(28) Else g := chr(31);
End
End
Else
Begin
If x[7] = '0' Then
Begin
If x[8] = '0' Then g := chr(27) Else g := chr(29);
End
Else
Begin
If x[8] = '0' Then g := chr(30) Else g := chr(32);
End
End
End
End
End
Else
Begin
If x[4] = '0' Then
Begin
If x[5] = '0' Then
Begin
If x[6] = '0' Then
Begin
If x[7] = '0' Then
Begin
If x[8] = '0' Then g := chr(0) Else g := chr(33);
End
Else
Begin
If x[8] = '0' Then g := chr(34) Else g := chr(36);
End
End
Else
Begin
If x[7] = '0' Then
Begin
If x[8] = '0' Then g := chr(35) Else g := chr(37);
End
Else
Begin
If x[8] = '0' Then g := chr(38) Else g := chr(40);
End
End
End
Else
Begin
If x[6] = '0' Then
Begin
If x[7] = '0' Then
Begin
If x[8] = '0' Then g := chr(39) Else g := chr(41);
End
Else
Begin
If x[8] = '0' Then g := chr(42) Else g := chr(43);
End
End
Else
Begin
If x[7] = '0' Then
Begin
If x[8] = '0' Then g := chr(44) Else g := chr(45);
End
Else
Begin
If x[8] = '0' Then g := chr(46) Else g := chr(47);
End
End
End
End
Else
Begin
If x[5] = '0' Then
Begin
If x[6] = '0' Then
Begin
If x[7] = '0' Then
Begin
If x[8] = '0' Then g := chr(48) Else g := chr(49);
End
Else
Begin
If x[8] = '0' Then g := chr(50) Else g := chr(51);
End
End
Else
Begin
If x[7] = '0' Then
Begin
If x[8] = '0' Then g := chr(52) Else g := chr(53);
End
Else
Begin
If x[8] = '0' Then g := chr(54) Else g := chr(55);
End
End
End
Else
Begin
If x[6] = '0' Then
Begin
If x[7] = '0' Then
Begin
If x[8] = '0' Then g := chr(56) Else g := chr(57);
End
Else
Begin
If x[8] = '0' Then g := chr(58) Else g := chr(59);
End
End
Else
Begin
If x[7] = '0' Then
Begin
If x[8] = '0' Then g := chr(60) Else g := chr(90);
End
Else
Begin
If x[8] = '0' Then g := chr(89) Else g := chr(88);
End
End
End
End
End
End
Else
Begin
If x[3] = '0' Then
Begin
If x[4] = '0' Then
Begin
If x[5] = '0' Then
Begin
If x[6] = '0' Then
Begin
If x[7] = '0' Then
Begin
If x[8] = '0' Then g := chr(87) Else g := chr(86);
End
Else
Begin
If x[8] = '0' Then g := chr(85) Else g := chr(84);
End
End
Else
Begin
If x[7] = '0' Then
Begin
If x[8] = '0' Then g := chr(83) Else g := chr(82);
End
Else
Begin
If x[8] = '0' Then g := chr(81) Else g := chr(80);
End
End
End
Else
Begin
If x[6] = '0' Then
Begin
If x[7] = '0' Then
Begin
If x[8] = '0' Then g := chr(79) Else g := chr(78);
End
Else
Begin
If x[8] = '0' Then g := chr(77) Else g := chr(76);
End
End
Else
Begin
If x[7] = '0' Then
Begin
If x[8] = '0' Then g := chr(75) Else g := chr(74);
End
Else
Begin
If x[8] = '0' Then g := chr(73) Else g := chr(72);
End
End
End
End
Else
Begin
If x[5] = '0' Then
Begin
If x[6] = '0' Then
Begin
If x[7] = '0' Then
Begin
If x[8] = '0' Then g := chr(71) Else g := chr(70);
End
Else
Begin
If x[8] = '0' Then g := chr(69) Else g := chr(68);
End
End
Else
Begin
If x[7] = '0' Then
Begin
If x[8] = '0' Then g := chr(67) Else g := chr(66);
End
Else
Begin
If x[8] = '0' Then g := chr(65) Else g := chr(64);
End
End
End
Else
Begin
If x[6] = '0' Then
Begin
If x[7] = '0' Then
Begin
If x[8] = '0' Then g := chr(63) Else g := chr(62);
End
Else
Begin
If x[8] = '0' Then g := chr(61) Else g := chr(95);
End
End
Else
Begin
If x[7] = '0' Then
Begin
If x[8] = '0' Then g := chr(94) Else g := chr(93);
End
Else
Begin
If x[8] = '0' Then g := chr(91) Else g := chr(92);
End
End
End
End
End
Else
Begin
If x[4] = '0' Then
Begin
If x[5] = '0' Then
Begin
If x[6] = '0' Then
Begin
If x[7] = '0' Then
Begin
If x[8] = '0' Then g := chr(96) Else g := chr(97);
End
Else
Begin
If x[8] = '0' Then g := chr(98) Else g := chr(99);
End
End
Else
Begin
If x[7] = '0' Then
Begin
If x[8] = '0' Then g := chr(100) Else g := chr(101);
End
Else
Begin
If x[8] = '0' Then g := chr(102) Else g := chr(105);
End
End
End
Else
Begin
If x[6] = '0' Then
Begin
If x[7] = '0' Then
Begin
If x[8] = '0' Then g := chr(103) Else g := chr(104);
End
Else
Begin
If x[8] = '0' Then g := chr(106) Else g := chr(107);
End
End
Else
Begin
If x[7] = '0' Then
Begin
If x[8] = '0' Then g := chr(108) Else g := chr(109);
End
Else
Begin
If x[8] = '0' Then g := chr(110) Else g := chr(111);
End
End
End
End
Else
Begin
If x[5] = '0' Then
Begin
If x[6] = '0' Then
Begin
If x[7] = '0' Then
Begin
If x[8] = '0' Then g := chr(112) Else g := chr(113);
End
Else
Begin
If x[8] = '0' Then g := chr(114) Else g := chr(115);
End
End
Else
Begin
If x[7] = '0' Then
Begin
If x[8] = '0' Then g := chr(116) Else g := chr(117);
End
Else
Begin
If x[8] = '0' Then g := chr(118) Else g := chr(119);
End
End
End
Else
Begin
If x[6] = '0' Then
Begin
If x[7] = '0' Then
Begin
If x[8] = '0' Then g := chr(120) Else g := chr(121);
End
Else
Begin
If x[8] = '0' Then g := chr(125) Else g := chr(124);
End
End
Else
Begin
If x[7] = '0' Then
Begin
If x[8] = '0' Then g := chr(123) Else g := chr(126);
End
Else
Begin
If x[8] = '0' Then g := chr(122) Else g := chr(127);
End
End
End
End
End
End
End
Else
Begin
If x[2] = '0' Then
Begin
If x[3] = '0' Then
Begin
If x[4] = '0' Then
Begin
If x[5] = '0' Then
Begin
If x[6] = '0' Then
Begin
If x[7] = '0' Then
Begin
If x[8] = '0' Then g := chr(128) Else g := chr(130);
End
Else
Begin
If x[8] = '0' Then g := chr(129) Else g := chr(131);
End
End
Else
Begin
If x[7] = '0' Then
Begin
If x[8] = '0' Then g := chr(132) Else g := chr(133);
End
Else
Begin
If x[8] = '0' Then g := chr(134) Else g := chr(135);
End
End
End
Else
Begin
If x[6] = '0' Then
Begin
If x[7] = '0' Then
Begin
If x[8] = '0' Then g := chr(136) Else g := chr(137);
End
Else
Begin
If x[8] = '0' Then g := chr(138) Else g := chr(139);
End
End
Else
Begin
If x[7] = '0' Then
Begin
If x[8] = '0' Then g := chr(140) Else g := chr(141);
End
Else
Begin
If x[8] = '0' Then g := chr(142) Else g := chr(143);
End
End
End
End
Else
Begin
If x[5] = '0' Then
Begin
If x[6] = '0' Then
Begin
If x[7] = '0' Then
Begin
If x[8] = '0' Then g := chr(144) Else g := chr(145);
End
Else
Begin
If x[8] = '0' Then g := chr(150) Else g := chr(149);
End
End
Else
Begin
If x[7] = '0' Then
Begin
If x[8] = '0' Then g := chr(148) Else g := chr(147);
End
Else
Begin
If x[8] = '0' Then g := chr(146) Else g := chr(151);
End
End
End
Else
Begin
If x[6] = '0' Then
Begin
If x[7] = '0' Then
Begin
If x[8] = '0' Then g := chr(152) Else g := chr(154);
End
Else
Begin
If x[8] = '0' Then g := chr(153) Else g := chr(155);
End
End
Else
Begin
If x[7] = '0' Then
Begin
If x[8] = '0' Then g := chr(156) Else g := chr(157);
End
Else
Begin
If x[8] = '0' Then g := chr(158) Else g := chr(159);
End
End
End
End
End
Else
Begin
If x[4] = '0' Then
Begin
If x[5] = '0' Then
Begin
If x[6] = '0' Then
Begin
If x[7] = '0' Then
Begin
If x[8] = '0' Then g := chr(160) Else g := chr(161);
End
Else
Begin
If x[8] = '0' Then g := chr(162) Else g := chr(170);
End
End
Else
Begin
If x[7] = '0' Then
Begin
If x[8] = '0' Then g := chr(165) Else g := chr(166);
End
Else
Begin
If x[8] = '0' Then g := chr(167) Else g := chr(168);
End
End
End
Else
Begin
If x[6] = '0' Then
Begin
If x[7] = '0' Then
Begin
If x[8] = '0' Then g := chr(169) Else g := chr(163);
End
Else
Begin
If x[8] = '0' Then g := chr(164) Else g := chr(171);
End
End
Else
Begin
If x[7] = '0' Then
Begin
If x[8] = '0' Then g := chr(172) Else g := chr(173);
End
Else
Begin
If x[8] = '0' Then g := chr(174) Else g := chr(175);
End
End
End
End
Else
Begin
If x[5] = '0' Then
Begin
If x[6] = '0' Then
Begin
If x[7] = '0' Then
Begin
If x[8] = '0' Then g := chr(176) Else g := chr(177);
End
Else
Begin
If x[8] = '0' Then g := chr(178) Else g := chr(179);
End
End
Else
Begin
If x[7] = '0' Then
Begin
If x[8] = '0' Then g := chr(180) Else g := chr(181);
End
Else
Begin
If x[8] = '0' Then g := chr(200) Else g := chr(199);
End
End
End
Else
Begin
If x[6] = '0' Then
Begin
If x[7] = '0' Then
Begin
If x[8] = '0' Then g := chr(198) Else g := chr(197);
End
Else
Begin
If x[8] = '0' Then g := chr(196) Else g := chr(195);
End
End
Else
Begin
If x[7] = '0' Then
Begin
If x[8] = '0' Then g := chr(194) Else g := chr(193);
End
Else
Begin
If x[8] = '0' Then g := chr(192) Else g := chr(191);
End
End
End
End
End
End
Else
Begin
If x[3] = '0' Then
Begin
If x[4] = '0' Then
Begin
If x[5] = '0' Then
Begin
If x[6] = '0' Then
Begin
If x[7] = '0' Then
Begin
If x[8] = '0' Then g := chr(190) Else g := chr(189);
End
Else
Begin
If x[8] = '0' Then g := chr(188) Else g := chr(182);
End
End
Else
Begin
If x[7] = '0' Then
Begin
If x[8] = '0' Then g := chr(183) Else g := chr(184);
End
Else
Begin
If x[8] = '0' Then g := chr(185) Else g := chr(186);
End
End
End
Else
Begin
If x[6] = '0' Then
Begin
If x[7] = '0' Then
Begin
If x[8] = '0' Then g := chr(187) Else g := chr(201);
End
Else
Begin
If x[8] = '0' Then g := chr(202) Else g := chr(203);
End
End
Else
Begin
If x[7] = '0' Then
Begin
If x[8] = '0' Then g := chr(204) Else g := chr(205);
End
Else
Begin
If x[8] = '0' Then g := chr(206) Else g := chr(207);
End
End
End
End
Else
Begin
If x[5] = '0' Then
Begin
If x[6] = '0' Then
Begin
If x[7] = '0' Then
Begin
If x[8] = '0' Then g := chr(208) Else g := chr(209);
End
Else
Begin
If x[8] = '0' Then g := chr(210) Else g := chr(220);
End
End
Else
Begin
If x[7] = '0' Then
Begin
If x[8] = '0' Then g := chr(211) Else g := chr(219);
End
Else
Begin
If x[8] = '0' Then g := chr(212) Else g := chr(218);
End
End
End
Else
Begin
If x[6] = '0' Then
Begin
If x[7] = '0' Then
Begin
If x[8] = '0' Then g := chr(213) Else g := chr(217);
End
Else
Begin
If x[8] = '0' Then g := chr(214) Else g := chr(216);
End
End
Else
Begin
If x[7] = '0' Then
Begin
If x[8] = '0' Then g := chr(215) Else g := chr(221);
End
Else
Begin
If x[8] = '0' Then g := chr(222) Else g := chr(223);
End
End
End
End
End
Else
Begin
If x[4] = '0' Then
Begin
If x[5] = '0' Then
Begin
If x[6] = '0' Then
Begin
If x[7] = '0' Then
Begin
If x[8] = '0' Then g := chr(224) Else g := chr(225);
End
Else
Begin
If x[8] = '0' Then g := chr(226) Else g := chr(227);
End
End
Else
Begin
If x[7] = '0' Then
Begin
If x[8] = '0' Then g := chr(228) Else g := chr(229);
End
Else
Begin
If x[8] = '0' Then g := chr(230) Else g := chr(231);
End
End
End
Else
Begin
If x[6] = '0' Then
Begin
If x[7] = '0' Then
Begin
If x[8] = '0' Then g := chr(232) Else g := chr(233);
End
Else
Begin
If x[8] = '0' Then g := chr(234) Else g := chr(235);
End
End
Else
Begin
If x[7] = '0' Then
Begin
If x[8] = '0' Then g := chr(236) Else g := chr(237);
End
Else
Begin
If x[8] = '0' Then g := chr(238) Else g := chr(240);
End
End
End
End
Else
Begin
If x[5] = '0' Then
Begin
If x[6] = '0' Then
Begin
If x[7] = '0' Then
Begin
If x[8] = '0' Then g := chr(239) Else g := chr(241);
End
Else
Begin
If x[8] = '0' Then g := chr(242) Else g := chr(243);
End
End
Else
Begin
If x[7] = '0' Then
Begin
If x[8] = '0' Then g := chr(244) Else g := chr(245);
End
Else
Begin
If x[8] = '0' Then g := chr(255) Else g := chr(254);
End
End
End
Else
Begin
If x[6] = '0' Then
Begin
If x[7] = '0' Then
Begin
If x[8] = '0' Then g := chr(246) Else g := chr(253);
End
Else
Begin
If x[8] = '0' Then g := chr(247) Else g := chr(252);
End
End
Else
Begin
If x[7] = '0' Then
Begin
If x[8] = '0' Then g := chr(248) Else g := chr(251);
End
Else
Begin
If x[8] = '0' Then g := chr(249) Else g := chr(250);
End
End
End
End
End
End
End
End;
Procedure zeronetochar6(Var g : integer; x : String);
Begin
If x[1] = '0' Then
Begin
If x[2] = '0' Then
Begin
If x[3] = '0' Then
Begin
If x[4] = '0' Then
Begin
If x[5] = '0' Then
Begin
If x[6] = '0' Then g := 1 Else g := 2;
End
Else
Begin
If x[6] = '0' Then g := 3 Else g := 4;
End
End
Else
Begin
If x[5] = '0' Then
Begin
If x[6] = '0' Then g := 5 Else g := 6;
End
Else
Begin
If x[6] = '0' Then g := 7 Else g := 8;
End
End
End
Else
Begin
If x[4] = '0' Then
Begin
If x[5] = '0' Then
Begin
If x[6] = '0' Then g := 9 Else g := 10;
End
Else
Begin
If x[6] = '0' Then g := 11 Else g := 12;
End
End
Else
Begin
If x[5] = '0' Then
Begin
If x[6] = '0' Then g := 13 Else g := 14;
End
Else
Begin
If x[6] = '0' Then g := 15 Else g := 16;
End
End
End
End
Else
Begin
If x[3] = '0' Then
Begin
If x[4] = '0' Then
Begin
If x[5] = '0' Then
Begin
If x[6] = '0' Then g := 17 Else g := 18;
End
Else
Begin
If x[6] = '0' Then g := 19 Else g := 20;
End
End
Else
Begin
If x[5] = '0' Then
Begin
If x[6] = '0' Then g := 21 Else g := 22;
End
Else
Begin
If x[6] = '0' Then g := 23 Else g := 24;
End
End
End
Else
Begin
If x[4] = '0' Then
Begin
If x[5] = '0' Then
Begin
If x[6] = '0' Then g := 25 Else g := 26;
End
Else
Begin
If x[6] = '0' Then g := 27 Else g := 28;
End
End
Else
Begin
If x[5] = '0' Then
Begin
If x[6] = '0' Then g := 29 Else g := 30;
End
Else
Begin
If x[6] = '0' Then g := 31 Else g := 32;
End
End
End
End
End
Else
Begin
If x[2] = '0' Then
Begin
If x[3] = '0' Then
Begin
If x[4] = '0' Then
Begin
If x[5] = '0' Then
Begin
If x[6] = '0' Then g := 33 Else g := 34;
End
Else
Begin
If x[6] = '0' Then g := 35 Else g := 36;
End
End
Else
Begin
If x[5] = '0' Then
Begin
If x[6] = '0' Then g := 37 Else g := 38;
End
Else
Begin
If x[6] = '0' Then g := 39 Else g := 40;
End
End
End
Else
Begin
If x[4] = '0' Then
Begin
If x[5] = '0' Then
Begin
If x[6] = '0' Then g := 41 Else g := 42;
End
Else
Begin
If x[6] = '0' Then g := 43 Else g := 44;
End
End
Else
Begin
If x[5] = '0' Then
Begin
If x[6] = '0' Then g := 45 Else g := 46;
End
Else
Begin
If x[6] = '0' Then g := 47 Else g := 48;
End
End
End
End
Else
Begin
If x[3] = '0' Then
Begin
If x[4] = '0' Then
Begin
If x[5] = '0' Then
Begin
If x[6] = '0' Then g := 49 Else g := 50;
End
Else
Begin
If x[6] = '0' Then g := 51 Else g := 52;
End
End
Else
Begin
If x[5] = '0' Then
Begin
If x[6] = '0' Then g := 53 Else g := 54;
End
Else
Begin
If x[6] = '0' Then g := 55 Else g := 56;
End
End
End
Else
Begin
If x[4] = '0' Then
Begin
If x[5] = '0' Then
Begin
If x[6] = '0' Then g := 57 Else g := 58;
End
Else
Begin
If x[6] = '0' Then g := 59 Else g := 60;
End
End
Else
Begin
If x[5] = '0' Then
Begin
If x[6] = '0' Then g := 61 Else g := 62;
End
Else
Begin
If x[6] = '0' Then g := 63 Else g := 64;
End
End
End
End
End
End;
Procedure initialize8(Var trans : Array Of String);
Var
c1, c2, c3, c4, c5, c6, c7, c8 : integer;
x : String;
g : char;
Begin
For c1 := 0 To 1 Do
For c2 := 0 To 1 Do
For c3 := 0 To 1 Do
For c4 := 0 To 1 Do
For c5 := 0 To 1 Do
For c6 := 0 To 1 Do
For c7 := 0 To 1 Do
For c8 := 0 To 1 Do
Begin
x := '';
x := inttostr(c1) + inttostr(c2) + inttostr(c3) + inttostr(c4) + inttostr(c5) + inttostr(c6) + inttostr(c7) + inttostr(c8);
zeronetochar8(g, x);
trans[ord(g)] := x;
End;
End;
Procedure initialize6(Var trans : Array Of String);
Var
c1, c2, c3, c4, c5, c6 : integer;
x : String;
g : integer;
Begin
For c1 := 0 To 1 Do
For c2 := 0 To 1 Do
For c3 := 0 To 1 Do
For c4 := 0 To 1 Do
For c5 := 0 To 1 Do
For c6 := 0 To 1 Do
Begin
x := '';
x := inttostr(c1) + inttostr(c2) + inttostr(c3) + inttostr(c4) + inttostr(c5) + inttostr(c6);
zeronetochar6(g, x);
trans[ord(chr64[g])] := x;
End;
End;
// Convert 8 bit strings to 6 bit strings and visa versa
Procedure Convert8to6bit(str8 : String; Var str6 : String);
Var
temp : String;
trans : Array[0..255] Of String;
i, len6 : longint;
g : integer;
Begin
initialize8(trans);
temp := '';
For i := 1 To length(str8) Do temp := temp + trans[ord(str8[i])];
While (length(temp) Mod 6) <> 0 Do temp := temp + '0';
len6 := length(temp) Div 6;
str6 := '';
For i := 1 To len6 Do
Begin
zeronetochar6(g, copy(temp, 1, 6));
str6 := str6 + chr64[g];
delete(temp, 1, 6);
End;
End;
Procedure Convert6to8bit(str6 : String; Var str8 : String);
Var
temp : String;
trans : Array[0..255] Of String;
i, len8 : longint;
g : char;
Begin
initialize6(trans);
temp := '';
For i := 1 To length(str6) Do temp := temp + trans[ord(str6[i])];
str8 := '';
len8 := length(temp) Div 8;
For i := 1 To len8 Do
Begin
zeronetochar8(g, copy(temp, 1, 8));
str8 := str8 + g;
delete(temp, 1, 8);
End;
End;
// Convert 8 & 6 bit strings to 1 bit strings and visa versa
Procedure Convert8to1bit(str8 : String; Var str1 : String);
Var
trans : Array[0..255] Of String;
i : longint;
Begin
str1 := '';
initialize8(trans);
For i := 1 To length(str8) Do str1 := str1 + trans[ord(str8[i])];
End;
Procedure Convert6to1bit(str6 : String; Var str1 : String);
Var
trans : Array[0..255] Of String;
i : longint;
Begin
str1 := '';
initialize6(trans);
For i := 1 To length(str6) Do str1 := str1 + trans[ord(str6[i])];
End;
Procedure Convert1to8bit(str1 : String; Var str8 : String);
Var
i, len8 : longint;
g : char;
Begin
str8 := '';
While (length(str1) Mod 8) <> 0 Do str1 := '0' + str1;
len8 := length(str1) Div 8;
For i := 1 To len8 Do
Begin
zeronetochar8(g, copy(str1, 1, 8));
str8 := str8 + g;
delete(str1, 1, 8);
End;
End;
Procedure Convert1to6bit(str1 : String; Var str6 : String);
Var
i, len6 : longint;
g : integer;
Begin
str6 := '';
While (length(str1) Mod 6) <> 0 Do str1 := '0' + str1;
len6 := length(str1) Div 6;
For i := 1 To len6 Do
Begin
zeronetochar6(g, copy(str1, 1, 6));
str6 := str6 + chr64[g];
delete(str1, 1, 6);
End;
End;
// convert a base 10 string to a GInt and visa versa
Procedure DecStrToGInt(GIntstr : String; Var GInt : TGInt);
Var
temp1, temp2 : TGInt;
p : Tsign;
Begin
While Not (GIntstr[1] In ['-', '0'..'9']) Do delete(GIntstr, 1, 1);
If GIntstr[1] = '-' Then
Begin
delete(GIntstr, 1, 1);
p := negative;
End
Else p := positive;
While (GIntstr[1] = '0') And (length(GIntstr) > 1) Do delete(GIntstr, 1, 1);
new(temp2);
temp2^.next := Nil;
If (length(GIntstr) Mod 4) = 0 Then
Begin
temp2^.value := strtoint(copy(GIntstr, 1, 4));
delete(GIntstr, 1, 4);
End
Else
Begin
temp2^.value := strtoint(copy(GIntstr, 1, (length(GIntstr) Mod 4)));
delete(GIntstr, 1, (length(GIntstr) Mod 4));
End;
While length(GIntstr) > 0 Do
Begin
new(temp1);
temp1^.next := temp2;
temp2^.prev := temp1;
temp1^.value := strtoint(copy(GIntstr, 1, 4));
delete(GIntstr, 1, 4);
temp2 := temp1;
End;
temp2^.prev := Nil;
temp2^.sign := p;
GInt := temp2;
End;
Procedure GIntToDecStr(Var GIntstr : String; GInt : TGInt);
Var
s : String;
p : TSign;
Begin
GIntstr := '';
p := GInt^.sign;
s := inttostr(GInt^.value);
While length(s) < 4 Do s := '0' + s;
GIntstr := s + GIntstr;
While GInt^.next <> Nil Do
Begin
GInt := GInt^.next;
s := inttostr(abs(GInt^.value));
While length(s) < 4 Do s := '0' + s;
GIntstr := s + GIntstr;
End;
While (GIntstr[1] = '0') And (length(GIntstr) > 1) Do delete(GIntstr, 1, 1);
If p = negative Then GIntstr := '-' + GIntstr;
End;
// Convert an integer to a GInt
Procedure IntToGInt(Int : integer; Var GInt : TGInt);
Begin
DecstrtoGInt(inttostr(Int), GInt);
End;
// Destroy a GInt, in order to free memory
Procedure GIntDestroy(Var GInt : TGInt);
Begin
While GInt^.next <> Nil Do GInt := GInt^.next;
While GInt^.prev <> Nil Do
Begin
GInt := GInt^.prev;
dispose(GInt^.next);
End;
dispose(GInt);
End;
// Make a copy of a GInt
Procedure GIntCopy(GInt1 : TGInt; Var GInt2 : TGInt);
Var
temp1, temp2 : TGInt;
Begin
new(GInt2);
GInt2^.sign := GInt1^.sign;
GInt2^.prev := Nil;
GInt2^.value := GInt1^.value;
temp1 := GInt2;
While GInt1^.next <> Nil Do
Begin
GInt1 := GInt1^.next;
new(temp2);
temp2^.value := GInt1^.value;
temp2^.prev := temp1;
temp1^.next := temp2;
temp1 := temp2;
End;
temp1^.next := Nil;
End;
// Divide a GInt by an integer, GInt = res * by + m
Procedure GIntDivByInt(GInt : TGInt; Var res : TGInt; by : longint; Var m : longint);
Var
S, S1 : String;
Begin
If (by Div 10000) = 0 Then
Begin
S := '';
While GInt^.next <> Nil Do GInt := GInt^.next;
S := inttostr(GInt^.value Div by);
m := (GInt^.value Mod by);
While GInt^.prev <> Nil Do
Begin
m := m * 10000;
GInt := GInt^.prev;
S1 := inttostr((GInt^.value + m) Div by);
While length(S1) < 4 Do S1 := '0' + S1;
S := S + S1;
m := ((GInt^.value + m) Mod by);
End;
decstrtogint(S, res);
End;
End;
// GInt modulo an integer, GInt mod by = m
Procedure GIntModByInt(GInt : TGInt; by : longint; Var m : longint);
Begin
If (by Div 10000) = 0 Then
Begin
While GInt^.next <> Nil Do GInt := GInt^.next;
m := (GInt^.value Mod by);
While GInt^.prev <> Nil Do
Begin
m := m * 10000;
GInt := GInt^.prev;
m := ((GInt^.value + m) Mod by);
End;
End;
End;
// Compare two GInts in absolute value, GInt1 < : St, > : Lt, = : Eq, Error : Er GInt2
Function GIntCompareAbs(GInt1, GInt2 : TGInt) : TCompare;
Begin
GIntCompareAbs := Er;
While (GInt1^.next <> Nil) And (GInt2^.next <> Nil) Do
Begin
GInt1 := GInt1^.next;
GInt2 := GInt2^.next;
End;
If (GInt1^.next = Nil) And (GInt2^.next <> Nil) Then GIntCompareAbs := St;
If (GInt2^.next = Nil) And (GInt1^.next <> Nil) Then GIntCompareAbs := Lt;
If (GInt1^.next = Nil) And (GInt2^.next = Nil) Then
Begin
While (GInt1^.value = GInt2^.value) And (GInt1^.prev <> Nil) Do
Begin
GInt1 := GInt1^.prev;
GInt2 := GInt2^.prev;
End;
If (GInt1^.value > GInt2^.value) Then GIntCompareAbs := Lt
Else If (GInt1^.value < GInt2^.value) Then GIntCompareAbs := St Else GIntCompareAbs := Eq;
End
End;
// Change the sign of a GInt
Procedure GIntChangeSign(Var GInt : TGInt);
Begin
If GInt^.sign = negative Then GInt^.sign := positive Else GInt^.sign := negative;
End;
// Returns the GInt in its absolute value
Procedure GIntAbs(Var GInt : TGInt);
Begin
GInt^.sign := positive;
End;
// Add 2 GInts, GInt1 + GInt2 = sum
Procedure GIntAdd(GInt1, GInt2 : TGInt; Var sum : TGInt);
Var
temp1, temp2 : TGInt;
rest : integer;
Tres : Longint;
Begin
If (GInt1^.sign = GInt2^.sign) Then
Begin
new(temp2);
temp2^.prev := Nil;
Tres := GInt1^.value + GInt2^.value;
temp2^.value := Tres Mod 10000;
temp2^.sign := GInt1^.sign;
If Tres >= 10000 Then rest := 1 Else rest := 0;
While (GInt1^.next <> Nil) And (GInt2^.next <> Nil) Do
Begin
GInt1 := GInt1^.next;
GInt2 := GInt2^.next;
new(temp1);
Tres := GInt1^.value + GInt2^.value + rest;
temp1^.value := Tres Mod 10000;
If Tres >= 10000 Then rest := 1 Else rest := 0;
temp1^.prev := temp2;
temp2^.next := temp1;
temp2 := temp1;
End;
While (GInt1^.next) <> Nil Do
Begin
GInt1 := GInt1^.next;
new(temp1);
Tres := GInt1^.value + rest;
temp1^.value := Tres Mod 10000;
If Tres >= 10000 Then rest := 1 Else rest := 0;
temp1^.prev := temp2;
temp2^.next := temp1;
temp2 := temp1;
End;
While (GInt2^.next) <> Nil Do
Begin
GInt2 := GInt2^.next;
new(temp1);
Tres := GInt2^.value + rest;
temp1^.value := Tres Mod 10000;
If Tres >= 10000 Then rest := 1 Else rest := 0;
temp1^.prev := temp2;
temp2^.next := temp1;
temp2 := temp1;
End;
If rest <> 0 Then
Begin
new(temp1);
temp1^.value := (rest) Mod 10000;
temp1^.prev := temp2;
temp2^.next := temp1;
temp2 := temp1;
End;
temp2^.next := Nil;
sum := temp2;
While sum^.prev <> Nil Do sum := sum^.prev;
End
Else
Begin
If (GIntCompareAbs(GInt1, GInt2) = Lt) Or (GIntCompareAbs(GInt1, GInt2) = Eq) Then
Begin
new(temp2);
temp2^.prev := Nil;
temp2^.sign := GInt1^.sign;
Tres := 10000 + GInt1^.value - GInt2^.value;
temp2^.value := Tres Mod 10000;
If (GInt1^.value - GInt2^.value) < 0 Then rest := -1 Else rest := 0;
While (GInt1^.next <> Nil) And (GInt2^.next <> Nil) Do
Begin
GInt1 := GInt1^.next;
GInt2 := GInt2^.next;
new(temp1);
Tres := GInt1^.value - GInt2^.value + rest;
temp1^.value := (10000 + Tres) Mod 10000;
If Tres < 0 Then rest := -1 Else rest := 0;
temp1^.prev := temp2;
temp2^.next := temp1;
temp2 := temp1;
End;
While (GInt1^.next) <> Nil Do
Begin
GInt1 := GInt1^.next;
new(temp1);
Tres := GInt1^.value + rest;
temp1^.value := (10000 + Tres) Mod 10000;
If Tres < 0 Then rest := -1 Else rest := 0;
temp1^.prev := temp2;
temp2^.next := temp1;
temp2 := temp1;
End;
If rest <> 0 Then
Begin
new(temp1);
temp1^.value := (10000 + rest) Mod 10000;
temp1^.prev := temp2;
temp2^.next := temp1;
temp2 := temp1;
End;
While (temp2^.value = 0) And (temp2^.prev <> Nil) Do
Begin
temp2 := temp2^.prev;
dispose(temp2^.next);
temp2^.next := Nil;
End;
temp2^.next := Nil;
sum := temp2;
While sum^.prev <> Nil Do sum := sum^.prev;
End
Else
GIntadd(GInt2, GInt1, sum);
End
End;
// Subtract 2 GInts, GInt1 - GInt2 = dif
Procedure GIntSub(GInt1, GInt2 : TGInt; Var dif : TGInt);
Begin
GIntchangesign(GInt2);
GIntadd(GInt1, GInt2, dif);
GIntchangesign(GInt2);
End;
// Multiply 2 GInts, GInt1 * GInt2 = prod
Procedure GIntMul(GInt1, GInt2 : TGInt; Var prod : TGInt);
Var
zero, temp1, temp2, temp : TGInt;
sign : Tsign;
rest, Trest : longint;
Begin
decstrtogint('0', zero);
If Not ((GIntcompareabs(zero, GInt1) = Eq) Or (GIntcompareabs(zero, GInt2) = Eq)) Then
Begin
If GInt1^.sign = GInt2^.sign Then sign := positive Else sign := negative;
temp1 := GInt1;
new(temp2);
temp2^.sign := sign;
temp2^.prev := Nil;
temp2^.value := (GInt2^.value * temp1^.value) Mod 10000;
rest := (GInt2^.value * temp1^.value) Div 10000;
temp2^.next := Nil;
prod := temp2;
While temp1^.next <> Nil Do
Begin
temp1 := temp1^.next;
new(temp);
temp^.value := (GInt2^.value * temp1^.value + rest) Mod 10000;
rest := (GInt2^.value * temp1^.value + rest) Div 10000;
temp^.next := Nil;
temp2^.next := temp;
temp^.prev := temp2;
temp2 := temp2^.next;
End;
If rest <> 0 Then
Begin
new(temp);
temp^.value := rest;
temp^.next := Nil;
temp^.prev := temp2;
temp2^.next := temp;
End;
While GInt2^.next <> Nil Do
Begin
If prod^.next = Nil Then
Begin
new(temp2);
temp2^.value := 0;
temp2^.prev := prod;
prod^.next := temp2;
temp2^.next := Nil;
End;
prod := prod^.next;
GInt2 := GInt2^.next;
temp1 := GInt1;
temp2 := prod;
rest := (GInt2^.value * temp1^.value + temp2^.value) Div 10000;
temp2^.value := (GInt2^.value * temp1^.value + temp2^.value) Mod 10000;
While temp1^.next <> Nil Do
Begin
temp1 := temp1^.next;
If temp2^.next = Nil Then
Begin
new(temp);
temp^.value := 0;
temp^.next := Nil;
End
Else temp := temp2^.next;
trest := (GInt2^.value * temp1^.value + rest + temp^.value) Div 10000;
temp^.value := (GInt2^.value * temp1^.value + rest + temp^.value) Mod 10000;
rest := trest;
temp2^.next := temp;
temp^.prev := temp2;
temp2 := temp2^.next;
End;
If rest <> 0 Then
Begin
If temp2^.next = Nil Then
Begin
new(temp);
temp^.value := 0;
temp^.next := Nil;
End
Else temp := temp2^.next;
temp^.value := temp^.value + rest;
temp^.next := Nil;
temp^.prev := temp2;
temp2^.next := temp;
End;
End;
While prod^.prev <> Nil Do prod := prod^.prev;
End
Else decstrtogint('0', prod);
GIntdestroy(zero);
End;
// Prod = GInt1 * By, By < 10000
Procedure GIntMulByInt(GInt1 : TGInt; By : Longint; Var prod : TGInt);
Var
temp2, temp : TGInt;
sign : Tsign;
rest : longint;
Begin
If By < 0 Then sign := negative Else sign := positive;
If GInt1^.sign = sign Then sign := positive Else sign := negative;
by := abs(by);
new(temp2);
temp2^.sign := sign;
temp2^.prev := Nil;
temp2^.value := (GInt1^.value * by) Mod 10000;
rest := (GInt1^.value * by) Div 10000;
temp2^.next := Nil;
prod := temp2;
While GInt1^.next <> Nil Do
Begin
GInt1 := GInt1^.next;
new(temp);
temp^.value := (GInt1^.value * By + rest) Mod 10000;
rest := (GInt1^.value * By + rest) Div 10000;
temp^.next := Nil;
temp2^.next := temp;
temp^.prev := temp2;
temp2 := temp2^.next;
End;
If rest <> 0 Then
Begin
new(temp);
temp^.value := rest;
temp^.next := Nil;
temp^.prev := temp2;
temp2^.next := temp;
End;
While prod^.prev <> Nil Do prod := prod^.prev;
End;
// GInt = GInt * By, By < 10000
Procedure GIntMulByIntBis(Var GInt : TGInt; By : Longint);
Var
temp1, temp : TGInt;
sign : Tsign;
rest, TRest : longint;
Begin
If By < 0 Then sign := negative Else sign := positive;
If GInt^.sign = sign Then sign := positive Else sign := negative;
by := abs(by);
GInt^.sign := sign;
Trest := GInt^.value * By;
GInt^.value := Trest Mod 10000;
rest := Trest Div 10000;
temp1 := GInt;
While GInt^.next <> Nil Do
Begin
GInt := GInt^.next;
Trest := GInt^.value * By + rest;
GInt^.value := Trest Mod 10000;
rest := Trest Div 10000;
End;
If rest <> 0 Then
Begin
new(temp);
temp^.value := rest;
temp^.next := Nil;
temp^.prev := GInt;
GInt^.next := temp;
End;
GInt := temp1;
End;
// Square a GInt, GInt^2 = Square
Procedure GIntSquare(GInt : TGInt; Var Square : TGInt);
Begin
GIntMul(GInt, GInt, square);
End;
// Convert a GInt to a binary string (base 2) & visa versa
Procedure GIntToBinStr(GInt : TGint; Var S : String);
Var
zero, temp, temp1 : TGInt;
i : integer;
Begin
DecStrToGInt('0', zero);
GIntCopy(GInt, temp);
S := '';
While GIntCompareAbs(zero, temp) <> Eq Do
Begin
GIntDivByInt(temp, temp1, 2, i);
S := inttostr(i) + S;
GIntDestroy(temp);
temp := temp1;
End;
If S = '' Then S := '0';
GIntDestroy(temp);
GIntDestroy(zero);
End;
Procedure BinStrToGInt(S : String; Var GInt : TGInt);
Var
temp, temp2 : TGInt;
i : longint;
Begin
While copy(S, 1, 1) = '0' Do delete(S, 1, 1);
decstrtogint('0', GInt);
decstrtogint('1', temp);
For i := length(S) Downto 1 Do
Begin
If S[i] = '1' Then
Begin
GIntadd(GInt, temp, temp2);
GIntdestroy(GInt);
GInt := temp2;
End;
GIntmulByIntBis(temp, 2);
End;
GIntdestroy(temp);
End;
// Convert a GInt to an 8 bit string & visa versa
Procedure GIntToStr(GInt : TGInt; Var str : String);
Var
temp1 : String;
i, len8 : longint;
g : char;
Begin
GInttobinstr(GInt, temp1);
While (length(temp1) Mod 8) <> 0 Do temp1 := '0' + temp1;
len8 := length(temp1) Div 8;
str := '';
For i := 1 To len8 Do
Begin
zeronetochar8(g, copy(temp1, 1, 8));
str := str + g;
delete(temp1, 1, 8);
End;
End;
Procedure StrToGInt(str : String; Var GInt : TGInt);
Var
temp1 : String;
i : longint;
trans : Array[0..255] Of String;
Begin
temp1 := '';
initialize8(trans);
For i := 1 To length(str) Do temp1 := temp1 + trans[ord(str[i])];
While temp1[1] = '0' Do delete(temp1, 1, 1);
binstrtoGInt(temp1, GInt);
End;
// Exponentiate a GInt, GInt^exp = res
Procedure GIntExp(GInt, exp : TGInt; Var res : TGInt);
Var
temp2, temp3 : TGInt;
S : String;
i : longint;
Begin
GInttobinstr(exp, S);
If S[length(S)] = '0' Then decstrtogint('1', res) Else GIntcopy(GInt, res);
GIntcopy(GInt, temp2);
If length(S) > 1 Then
For i := (length(S) - 1) Downto 1 Do
Begin
GIntSquare(temp2, temp3);
GIntdestroy(temp2);
temp2 := temp3;
If S[i] = '1' Then
Begin
GIntmul(res, temp2, temp3);
GIntdestroy(res);
res := temp3;
End;
End;
End;
// Compute GInt! = GInt * (GInt - 1) * (GInt - 2) * ... * 3 * 2 * 1
Procedure GIntFac(GInt : TGInt; Var res : TGint);
Var
one, temp, temp1 : TGInt;
Begin
GIntcopy(GInt, temp);
decstrtogint('1', res);
decstrtogint('1', one);
While Not ((temp^.next = Nil) And (temp^.value = 1)) Do
Begin
GIntmul(temp, res, temp1);
GIntdestroy(res);
res := temp1;
GIntsub(temp, one, temp1);
GIntdestroy(temp);
temp := temp1;
End;
GIntdestroy(one);
GIntdestroy(temp);
End;
// Divide 2 GInts, GInt1 = GInt2 * divres + modres, modres is always positive
Procedure GIntDivMod(GInt1, GInt2 : TGInt; Var divres, modres : TGInt);
Var
s1, s2 : TSign;
Tempstr1, tempstr2, tempstr, QStr : String;
lend, k, i : longint;
temp1, temp2, one, zero, temp : TGInt;
QCnt : integer;
Begin
s1 := GInt1^.sign;
s2 := GInt2^.sign;
GIntabs(GInt1);
GIntabs(GInt2);
GInttodecstr(tempstr1, GInt1);
GInttodecstr(tempstr2, GInt2);
lend := length(tempstr2);
QStr := '0';
decstrtogint('0', zero);
If Not ((GInt1^.value = 0) And (GInt1^.next = Nil)) Then
Begin
GIntcopy(GInt1, temp);
tempstr := tempstr1;
k := lend;
While (GIntcompareabs(temp, GInt2) <> St) Do
Begin
GIntDestroy(temp);
tempstr := copy(tempstr1, 1, k);
delete(tempstr1, 1, k);
While (length(tempstr) < lend) And (length(tempstr1) > 0) Do
Begin
tempstr := tempstr + copy(tempstr1, 1, 1);
delete(tempstr1, 1, 1);
QStr := QStr + '0';
End;
decstrtoGInt(tempstr, temp1);
QCnt := 0;
While GIntcompareabs(temp1, GInt2) <> St Do
Begin
GIntSub(temp1, GInt2, temp2);
GIntdestroy(temp1);
temp1 := temp2;
QCnt := QCnt + 1;
End;
QStr := QStr + inttostr(QCnt);
GInttodecstr(tempstr, temp1);
k := length(tempstr) + 1;
tempstr1 := tempstr + tempstr1;
GIntdestroy(temp1);
DecStrToGInt(tempstr1, temp);
End;
If (GIntcompareabs(temp, GInt2) = St) And ((k - 1) <> length(tempstr1)) Then
For i := 1 To (length(tempstr1) - k + 1) Do QStr := QStr + '0';
GIntDestroy(temp);
DecstrtoGInt(tempstr1, modres);
DecstrtoGInt(QStr, divres);
decstrtogint('1', one);
If s1 = negative Then
Begin
If GIntcompareabs(modres, zero) <> Eq Then
Begin
GIntadd(divres, one, temp1);
GIntdestroy(divres);
divres := temp1;
GIntAbs(GInt2);
GIntsub(GInt2, modres, temp1);
GIntdestroy(modres);
GInt2^.sign := s2;
modres := temp1;
End;
If s2 = positive Then divres^.sign := negative;
End
Else divres^.sign := s2;
GIntdestroy(one);
End
Else
Begin
GIntcopy(zero, divres);
GIntcopy(zero, modres);
End;
GIntdestroy(zero);
GInt1^.sign := s1;
GInt2^.sign := s2;
End;
// Same as above but doesn't compute modres
Procedure GIntDiv(GInt1, GInt2 : TGInt; Var divres : TGInt);
Var
s1, s2 : TSign;
Tempstr1, tempstr2, tempstr, QStr : String;
lend, k, i : longint;
temp1, temp2, one, zero, temp, modres : TGInt;
QCnt : integer;
Begin
s1 := GInt1^.sign;
s2 := GInt2^.sign;
GIntabs(GInt1);
GIntabs(GInt2);
GInttodecstr(tempstr1, GInt1);
GInttodecstr(tempstr2, GInt2);
lend := length(tempstr2);
QStr := '0';
decstrtogint('0', zero);
If Not ((GInt1^.value = 0) And (GInt1^.next = Nil)) Then
Begin
GIntcopy(GInt1, temp);
tempstr := tempstr1;
k := lend;
While (GIntcompareabs(temp, GInt2) <> St) Do
Begin
GIntDestroy(temp);
tempstr := copy(tempstr1, 1, k);
delete(tempstr1, 1, k);
While (length(tempstr) < lend) And (length(tempstr1) > 0) Do
Begin
tempstr := tempstr + copy(tempstr1, 1, 1);
delete(tempstr1, 1, 1);
QStr := QStr + '0';
End;
decstrtoGInt(tempstr, temp1);
QCnt := 0;
While GIntcompareabs(temp1, GInt2) <> St Do
Begin
GIntSub(temp1, GInt2, temp2);
GIntdestroy(temp1);
temp1 := temp2;
QCnt := QCnt + 1;
End;
QStr := QStr + inttostr(QCnt);
GInttodecstr(tempstr, temp1);
k := length(tempstr) + 1;
tempstr1 := tempstr + tempstr1;
GIntdestroy(temp1);
DecStrToGInt(tempstr1, temp);
End;
If (GIntcompareabs(temp, GInt2) = St) And ((k - 1) <> length(tempstr1)) Then
For i := 1 To (length(tempstr1) - k + 1) Do QStr := QStr + '0';
GIntDestroy(temp);
DecstrtoGInt(tempstr1, modres);
DecstrtoGInt(QStr, divres);
decstrtogint('1', one);
If s1 = negative Then
Begin
If GIntcompareabs(modres, zero) <> Eq Then
Begin
GIntadd(divres, one, temp1);
GIntdestroy(divres);
divres := temp1;
GIntAbs(GInt2);
GIntsub(GInt2, modres, temp1);
GIntdestroy(modres);
GInt2^.sign := s2;
modres := temp1;
End;
If s2 = positive Then divres^.sign := negative;
End
Else divres^.sign := s2;
GIntdestroy(one);
End
Else
Begin
GIntcopy(zero, divres);
GIntcopy(zero, modres);
End;
GIntdestroy(zero);
GInt1^.sign := s1;
GInt2^.sign := s2;
GIntDestroy(modres);
End;
// Same as above but computes modres and not divres
Procedure GIntMod(GInt1, GInt2 : TGInt; Var modres : TGInt);
Var
s1, s2 : TSign;
Tempstr1, tempstr2, tempstr, QStr : String;
lend, k : longint;
temp1, temp2, zero, temp : TGInt;
Begin
s1 := GInt1^.sign;
s2 := GInt2^.sign;
GIntabs(GInt1);
GIntabs(GInt2);
GInttodecstr(tempstr1, GInt1);
GInttodecstr(tempstr2, GInt2);
lend := length(tempstr2);
QStr := '0';
decstrtogint('0', zero);
If Not ((GInt1^.value = 0) And (GInt1^.next = Nil)) Then
Begin
GIntcopy(GInt1, temp);
tempstr := tempstr1;
k := lend;
While (GIntcompareabs(temp, GInt2) <> St) Do
Begin
GIntDestroy(temp);
tempstr := copy(tempstr1, 1, k);
delete(tempstr1, 1, k);
While (length(tempstr) < lend) And (length(tempstr1) > 0) Do
Begin
tempstr := tempstr + copy(tempstr1, 1, 1);
delete(tempstr1, 1, 1);
End;
decstrtoGInt(tempstr, temp1);
While GIntcompareabs(temp1, GInt2) <> St Do
Begin
GIntSub(temp1, GInt2, temp2);
GIntdestroy(temp1);
temp1 := temp2;
End;
GInttodecstr(tempstr, temp1);
k := length(tempstr) + 1;
tempstr1 := tempstr + tempstr1;
GIntdestroy(temp1);
DecStrToGInt(tempstr1, temp);
End;
GIntDestroy(temp);
DecstrtoGInt(tempstr1, modres);
If s1 = negative Then
Begin
If GIntcompareabs(modres, zero) <> Eq Then
Begin
GIntAbs(GInt2);
GIntsub(GInt2, modres, temp1);
GIntdestroy(modres);
GInt2^.sign := s2;
modres := temp1;
End;
End;
End
Else
Begin
GIntcopy(zero, modres);
End;
GIntdestroy(zero);
GInt1^.sign := s1;
GInt2^.sign := s2;
End;
// Square a GInt modulo Modb, GInt^2 mod Modb = GIntSM
Procedure GIntSquareMod(GInt, Modb : TGInt; Var GIntSM : TGInt);
Var
temp : TGInt;
Begin
GIntSquare(GInt, temp);
GIntMod(temp, Modb, GIntSM);
GIntDestroy(temp);
End;
// Add 2 GInts modulo base, (GInt1 + GInt2) mod base = GIntres
Procedure GIntAddMod(GInt1, GInt2, base : TGInt; Var GIntres : TGInt);
Var
temp : TGInt;
Begin
GIntadd(GInt1, GInt2, temp);
GIntMod(temp, base, GIntres);
GIntdestroy(temp);
End;
// Multiply 2 GInts modulo base, (GInt1 * GInt2) mod base = GIntres
Procedure GIntMulMod(GInt1, GInt2, base : TGInt; Var GIntres : TGInt);
Var
temp : TGInt;
Begin
GIntMul(GInt1, GInt2, temp);
GIntMod(temp, base, GIntres);
GIntdestroy(temp);
End;
// Exponentiate 2 GInts modulo base, (GInt1 ^ GInt2) mod modb = res
Procedure GIntModExp(GInt, exp, modb : TGInt; Var res : TGInt);
Var
temp2, temp3 : TGInt;
S : String;
i : longint;
Begin
GInttobinstr(exp, S);
If S[length(S)] = '0' Then decstrtogint('1', res) Else GIntcopy(GInt, res);
GIntcopy(GInt, temp2);
If length(S) > 1 Then
For i := (length(S) - 1) Downto 1 Do
Begin
GIntSquareMod(temp2, Modb, temp3);
GIntdestroy(temp2);
temp2 := temp3;
If S[i] = '1' Then
Begin
GIntmulMod(res, temp2, modb, temp3);
GIntdestroy(res);
res := temp3;
End;
End;
End;
// Compute the Greatest Common Divisor of 2 GInts
Procedure GIntGCD(GInt1, GInt2 : TGint; Var GCD : TGInt);
Var
k : TCompare;
zero, temp1, temp2, temp3 : TGInt;
Begin
k := GIntcompareabs(GInt1, GInt2);
If (k = Eq) Then GIntCopy(GInt1, GCD) Else
If (k = St) Then GIntGCD(GInt2, GInt1, GCD) Else
Begin
decstrtogint('0', zero);
GIntCopy(GInt1, temp1);
GIntCopy(GInt2, temp2);
While GIntcompareabs(temp2, zero) <> Eq Do
Begin
GIntmod(temp1, temp2, temp3);
GIntdestroy(temp1);
temp1 := temp2;
temp2 := temp3;
End;
GCD := temp1;
GIntdestroy(temp2);
GIntdestroy(zero);
End;
End;
// Compute the Least Common Multiple of 2 GInts
Procedure GIntLCM(GInt1, GInt2 : TGInt; Var LCM : TGInt);
Var
temp1, temp2 : TGInt;
Begin
GIntGCD(GInt1, GInt2, temp1);
GIntmul(GInt1, GInt2, temp2);
GIntdiv(temp2, temp1, LCM);
GIntDestroy(temp1);
GIntDestroy(temp2);
End;
// Trialdivision of a GInt upto 8192 and stopping when a divisor is found, returning ok=false
Procedure GIntTrialDiv9999(GInt : TGInt; Var ok : boolean);
Var
i, j : integer;
Begin
If ((GInt^.value Mod 2) = 0) Or ((GInt^.value Mod 5) = 0) Then ok := false
Else
Begin
i := 0;
ok := true;
While ok And (i < 1227) Do
Begin
i := i + 1;
GIntmodbyint(GInt, primes[i], j);
If j = 0 Then ok := false;
End;
End;
End;
// A prng
Procedure GIntRandom1(Seed : TGInt; Var RandomGInt : TGInt);
Var
temp, base : TGInt;
Begin
decstrtoGInt('281474976710656', base);
decstrtoGInt('44485709377909', temp);
GIntMulMod(seed, temp, base, RandomGInt);
GIntdestroy(temp);
GIntdestroy(base);
End;
// Perform a Rabin Miller Primality Test nrtest times on GIntp, returns ok=true when GIntp passes the test
Procedure GIntRabinMiller(GIntp : TGInt; nrtest : integer; Var ok : boolean);
Var
j, b, i : longint;
m, z, temp1, temp2, temp3, zero, one, two, pmin1 : TGInt;
ok1, ok2 : boolean;
Begin
randomize;
j := 0;
b := 0;
decstrtogint('0', zero);
decstrtogint('1', one);
decstrtogint('2', two);
GIntsub(GIntp, one, temp1);
GIntsub(GIntp, one, pmin1);
While (temp1^.value Mod 2) = 0 Do
Begin
b := b + 1;
GIntdivbyint(temp1, temp2, 2, i);
GIntdestroy(temp1);
temp1 := temp2;
End;
m := temp1;
i := 0;
ok := true;
Randomize;
While (i < nrtest) And ok Do
Begin
i := i + 1;
DecStrToGInt(inttostr(Primes[Random(1227) + 1]), temp2);
GIntmodexp(temp2, m, GIntp, z);
GIntdestroy(temp2);
ok1 := (GIntcompareabs(z, one) = Eq);
ok2 := (GIntcompareabs(z, pmin1) = Eq);
If Not (ok1 Or ok2) Then
Begin
While (ok And (j < b)) Do
Begin
If (j > 0) And ok1 Then ok := false
Else
Begin
j := j + 1;
If (j < b) And (Not ok2) Then
Begin
GIntSquaremod(z, GIntp, temp3);
GIntdestroy(z);
z := temp3;
ok1 := (GIntcompareabs(z, one) = Eq);
ok2 := (GIntcompareabs(z, pmin1) = Eq);
If ok2 Then j := b;
End
Else If (Not ok2) And (j >= b) Then ok := false;
End;
End;
End
End;
GIntdestroy(zero);
GIntdestroy(one);
GIntdestroy(two);
GIntdestroy(m);
GIntdestroy(z);
GIntdestroy(pmin1);
End;
// Compute the coefficients from the Bezout Bachet theorem, GInt1 * a + GInt2 * b = GCD(GInt1, GInt2)
Procedure GIntBezoutBachet(GInt1, GInt2 : TGInt; Var a, b : TGInt);
Var
zero, r1, r2, r3, ta, gcd, temp, temp1, temp2 : TGInt;
Begin
If GIntcompareabs(GInt1, GInt2) <> St Then
Begin
GIntcopy(GInt1, r1);
GIntcopy(GInt2, r2);
decstrtogint('0', zero);
decstrtogint('1', a);
decstrtogint('0', ta);
Repeat
GIntdivmod(r1, r2, temp, r3);
GIntdestroy(r1);
r1 := r2;
r2 := r3;
GIntmul(ta, temp, temp1);
GIntsub(a, temp1, temp2);
GIntdestroy(a);
GIntdestroy(temp1);
a := ta;
ta := temp2;
GIntdestroy(temp);
Until GIntcompareabs(r3, zero) = Eq;
GIntGCD(GInt1, GInt2, gcd);
GIntmul(a, GInt1, temp1);
GIntsub(gcd, temp1, temp2);
GIntDestroy(temp1);
GIntdiv(temp2, GInt2, b);
GIntDestroy(temp2);
GIntdestroy(ta);
GIntdestroy(r1);
GIntdestroy(r2);
GIntdestroy(gcd);
End
Else GIntBezoutBachet(GInt2, GInt1, b, a);
End;
// Find the (multiplicative) Modular inverse of a GInt in a finite ring of additive order base
Procedure GIntModInv(GInt1, base : TGInt; Var Inverse : TGInt);
Var
zero, one, r1, r2, r3, tb, gcd, temp, temp1, temp2 : TGInt;
Begin
decstrtogint('1', one);
GIntGCD(GInt1, base, gcd);
If GIntcompareabs(one, gcd) = Eq Then
Begin
GIntcopy(base, r1);
GIntcopy(GInt1, r2);
decstrtogint('0', zero);
decstrtogint('0', inverse);
decstrtogint('1', tb);
Repeat
GIntdivmod(r1, r2, temp, r3);
GIntdestroy(r1);
r1 := r2;
r2 := r3;
GIntmul(tb, temp, temp1);
GIntsub(inverse, temp1, temp2);
GIntdestroy(inverse);
GIntdestroy(temp1);
inverse := tb;
tb := temp2;
GIntdestroy(temp);
Until GIntcompareabs(r3, zero) = Eq;
If inverse^.sign = negative Then
Begin
GIntadd(base, inverse, temp);
GIntdestroy(inverse);
inverse := temp;
End;
GIntdestroy(tb);
GIntdestroy(r1);
GIntdestroy(r2);
End;
GIntdestroy(gcd);
GIntdestroy(one);
End;
// Perform a (combined) primality test on GIntp consisting of a trialdivision upto 8192,
// if the GInt passes perform nrRMtests Rabin Miller primality tests, returns ok when a
// GInt is probably prime
Procedure GIntPrimetest(GIntp : TGInt; nrRMtests : integer; Var ok : boolean);
Begin
GIntTrialdiv9999(GIntp, ok);
If ok Then GIntRabinMiller(GIntp, nrRMtests, ok);
End;
// Computes the Legendre symbol for a any number and
// p a prime, returns 0 if p divides a, 1 if a is a
// quadratic residu mod p, -1 if a is a quadratic
// nonresidu mod p
Procedure GIntLegendreSymbol(a, p : TGInt; Var L : integer);
Var
temp1, temp2, temp3, temp4, temp5, zero, one : TGInt;
i : integer;
ok1, ok2 : boolean;
Begin
DecStrToGInt('0', zero);
DecStrToGInt('1', one);
GIntMod(a, p, temp1);
If GIntCompareabs(zero, temp1) = Eq Then
Begin
GIntDestroy(temp1);
L := 0;
End
Else
Begin
GIntDestroy(temp1);
GIntCopy(p, temp1);
GIntCopy(a, temp2);
L := 1;
While GIntCompareAbs(temp2, one) <> Eq Do
Begin
If (temp2^.value Mod 2) = 0 Then
Begin
GIntSquare(temp1, temp3);
GIntSub(temp3, one, temp4);
GIntDestroy(temp3);
GIntDivByInt(temp4, temp3, 8, i);
If (temp3^.value Mod 2) = 0 Then ok1 := false Else ok1 := true;
GIntDestroy(temp3);
GIntDestroy(temp4);
If ok1 = true Then L := L * (-1);
GIntDivByInt(temp2, temp3, 2, i);
GIntDestroy(temp2);
temp2 := temp3;
End
Else
Begin
GIntSub(temp1, one, temp3);
GIntSub(temp2, one, temp4);
GIntMul(temp3, temp4, temp5);
GIntDestroy(temp3);
GIntDestroy(temp4);
GIntDivByInt(temp5, temp3, 4, i);
If (temp3^.value Mod 2) = 0 Then ok2 := false Else ok2 := true;
GIntDestroy(temp5);
GIntDestroy(temp3);
If ok2 = true Then L := L * (-1);
GIntMod(temp1, temp2, temp3);
GIntDestroy(temp1);
temp1 := temp2;
temp2 := temp3;
End;
End;
GIntDestroy(temp1);
GIntDestroy(temp2);
End;
GIntDestroy(zero);
GIntDestroy(one);
End;
End.