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Diffstat (limited to 'lib/base/devel/bignums.nim')
| -rw-r--r-- | lib/base/devel/bignums.nim | 1712 |
1 files changed, 0 insertions, 1712 deletions
diff --git a/lib/base/devel/bignums.nim b/lib/base/devel/bignums.nim deleted file mode 100644 index 1d2b3685d..000000000 --- a/lib/base/devel/bignums.nim +++ /dev/null @@ -1,1712 +0,0 @@ -# -# -# Nimrod's Runtime Library -# (c) Copyright 2008 Andreas Rumpf -# -# See the file "copying.txt", included in this -# distribution, for details about the copyright. -# - -## This module implements big integers for Nimrod. -## This module is an adaptation of the FGInt module for Pascal by Walied -## Othman: http://triade.studentenweb.org - - -# License, info, etc -# ------------------ -# -# This implementation is made by me, Walied Othman, to contact me -# mail to Walied.Othman@belgacom.net or Triade@ulyssis.org, -# always mention wether it 's about the FGInt for Delphi or for -# FreePascal, or wether it 's about the 6xs, preferably in the subject line. -# 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 software. Encryption, as a tool to ensure privacy -# should be free and accessible for anyone. If you plan to use these -# implementations in a commercial application, contact me before -# doing so, that way you can license the software to use it in commercial -# Software. If any algorithm is patented in your country, you should -# acquire a license before using this software. Modified versions of this -# software must contain an acknowledgement of the original author (=me). -# This implementation is available at -# http://triade.studentenweb.org -# -# copyright 2000, Walied Othman -# This header may not be removed. -# - -type - TBigInt* {.final.} = object ## type that represent an arbitrary long - ## signed integer - s: int # sign: -1 or 1 - n: seq[int] # the number part - -proc len(x: TBigInt): int {.inline.} = return x.n.len - -proc CompareAbs(a, b: TBigInt): int = - result = a.len - b.len - if result == 0: - var i = b.len-1 - while (i > 0) and a.n[i] == b.n[i]: dec(i) - result = a.n[i] - b.n[i] - -const - bitMask = high(int) - bitshift = sizeof(int)*8 - 1 - -proc cutZeros(a: var TBigInt) = - var L = a.len - while a.len > 0 and a[L-1] == 0: dec(L) - setLen(a.n, L) - -proc addAux(a, b: TBigInt, bSign: int): TBigInt - if a.len < b.len: - result = addAux(b, a, bSign) - elif a.s == bSign: - result.s = a.s - result.n = [] - setlen(result.n, a.len+1) - var rest = 0 - for i in 0..b.len-1: - var trest = a.n[i] - trest = trest +% b.n[i] +% rest - result.n[i] = trest and bitMask - rest = trest shr bitshift - for i in b.len .. a.len-1: - var trest = a.n[i] +% rest - result.n[i] = trest and bitMask - rest = trest shr bitshift - result.n[a.len] = rest - cutZeros(result) - elif compareAbs(a, b) > 0: - result = addAux(b, a, bSign) - else: - setlen(result.n, a.len+1) - result.s = a.s - var rest = 0 - for i in 0..b.len-1: - var Trest = low(int) - TRest = Trest +% a.n[i] -% b.n[i] -% rest - result.n[i] = Trest and bitmask - if Trest >% bitMask: rest = 0 else: rest = 1 - for i in b.len .. a.len-1: - var Trest = low(int) - TRest = Trest +% a.n[i] -% rest - result.n[i] = Trest and bitmask - if (Trest >% bitmask): rest = 0 else: rest = 1 - cutZeros(result) - -proc `+` *(a, b: TBigInt): TBigInt = - ## the `+` operator for bigints - result = addAux(a, b, +1) - -proc `-` *(a, b: TBigInt): TBigInt = - ## the `-` operator for bigints - result = addAux(a, b, -1) - -proc mulInPlace(a: var TBigInt, b: int) = - var - size, rest: int32 - Trest: int64 - size = FGInt.Number[0] - setlen(FGInt.Number, size + 2) - rest = 0 - for i in countup(1, size): - Trest = FGInt.Number[i] - TRest = Trest * by - TRest = Trest + rest - FGInt.Number[i] = Trest And 2147483647 - rest = Trest Shr 31 - if rest != 0: - size = size + 1 - FGInt.Number[size] = rest - else: - setlen(FGInt.Number, size + 1) - FGInt.Number[0] = size - - -import - SysUtils, Math - -type - TCompare* = enum - Lt, St, Eq, Er - TSign = enum - negative, positive - TBigInt* {.final.} = object - Sign: TSign - Number: seq[int32] - - -proc zeronetochar8*(g: var char, x: String) -proc zeronetochar6*(g: var int, x: String) -proc initialize8*(trans: var openarray[String]) -proc initialize6*(trans: var openarray[String]) -proc initialize6PGP*(trans: var openarray[String]) -proc ConvertBase256to64*(str256: String, str64: var String) -proc ConvertBase64to256*(str64: String, str256: var String) -proc ConvertBase256to2*(str256: String, str2: var String) -proc ConvertBase64to2*(str64: String, str2: var String) -proc ConvertBase2to256*(str2: String, str256: var String) -proc ConvertBase2to64*(str2: String, str64: var String) -proc ConvertBase256StringToHexString*(Str256: String, HexStr: var String) -proc ConvertHexStringToBase256String*(HexStr: String, Str256: var String) -proc PGPConvertBase256to64*(str256, str64: var String) -proc PGPConvertBase64to256*(str64: String, str256: var String) -proc PGPConvertBase64to2*(str64: String, str2: var String) -proc FGIntToBase2String*(FGInt: TBigInt, S: var String) -proc Base2StringToFGInt*(S: String, FGInt: var TBigInt) -proc FGIntToBase256String*(FGInt: TBigInt, str256: var String) -proc Base256StringToFGInt*(str256: String, FGInt: var TBigInt) -proc PGPMPIToFGInt*(PGPMPI: String, FGInt: var TBigInt) -proc FGIntToPGPMPI*(FGInt: TBigInt, PGPMPI: var String) -proc Base10StringToFGInt*(Base10: String, FGInt: var TBigInt) -proc FGIntToBase10String*(FGInt: TBigInt, Base10: var String) -proc FGIntDestroy*(FGInt: var TBigInt) -proc FGIntCompareAbs*(FGInt1, FGInt2: TBigInt): TCompare -proc FGIntAdd*(FGInt1, FGInt2: TBigInt, Sum: var TBigInt) -proc FGIntChangeSign*(FGInt: var TBigInt) -proc FGIntSub*(FGInt1, FGInt2, dif: var TBigInt) -proc FGIntMulByInt*(FGInt: TBigInt, res: var TBigInt, by: int32) -proc FGIntMulByIntbis*(FGInt: var TBigInt, by: int32) -proc FGIntDivByInt*(FGInt: TBigInt, res: var TBigInt, by: int32, modres: var int32) -proc FGIntDivByIntBis*(FGInt: var TBigInt, by: int32, modres: var int32) -proc FGIntModByInt*(FGInt: TBigInt, by: int32, modres: var int32) -proc FGIntAbs*(FGInt: var TBigInt) -proc FGIntCopy*(FGInt1: TBigInt, FGInt2: var TBigInt) -proc FGIntShiftLeft*(FGInt: var TBigInt) -proc FGIntShiftRight*(FGInt: var TBigInt) -proc FGIntShiftRightBy31*(FGInt: var TBigInt) -proc FGIntAddBis*(FGInt1: var TBigInt, FGInt2: TBigInt) -proc FGIntSubBis*(FGInt1: var TBigInt, FGInt2: TBigInt) -proc FGIntMul*(FGInt1, FGInt2: TBigInt, Prod: var TBigInt) -proc FGIntSquare*(FGInt: TBigInt, Square: var TBigInt) -proc FGIntExp*(FGInt, exp: TBigInt, res: var TBigInt) -proc FGIntFac*(FGInt: TBigInt, res: var TBigInt) -proc FGIntShiftLeftBy31*(FGInt: var TBigInt) -proc FGIntDivMod*(FGInt1, FGInt2, QFGInt, MFGInt: var TBigInt) -proc FGIntDiv*(FGInt1, FGInt2, QFGInt: var TBigInt) -proc FGIntMod*(FGInt1, FGInt2, MFGInt: var TBigInt) -proc FGIntSquareMod*(FGInt, Modb, FGIntSM: var TBigInt) -proc FGIntAddMod*(FGInt1, FGInt2, base, FGIntres: var TBigInt) -proc FGIntMulMod*(FGInt1, FGInt2, base, FGIntres: var TBigInt) -proc FGIntModExp*(FGInt, exp, modb, res: var TBigInt) -proc FGIntModBis*(FGInt: TBigInt, FGIntOut: var TBigInt, b, head: int32) -proc FGIntMulModBis*(FGInt1, FGInt2: TBigInt, Prod: var TBigInt, b, head: int32) -proc FGIntMontgomeryMod*(GInt, base, baseInv: TBigInt, MGInt: var TBigInt, - b: int32, head: int32) -proc FGIntMontgomeryModExp*(FGInt, exp, modb, res: var TBigInt) -proc FGIntGCD*(FGInt1, FGInt2: TBigInt, GCD: var TBigInt) -proc FGIntLCM*(FGInt1, FGInt2: TBigInt, LCM: var TBigInt) -proc FGIntTrialDiv9999*(FGInt: TBigInt, ok: var bool) -proc FGIntRandom1*(Seed, RandomFGInt: var TBigInt) -proc FGIntRabinMiller*(FGIntp: var TBigInt, nrtest: int32, ok: var bool) -proc FGIntBezoutBachet*(FGInt1, FGInt2, a, b: var TBigInt) -proc FGIntModInv*(FGInt1, base: TBigInt, Inverse: var TBigInt) -proc FGIntPrimetest*(FGIntp: var TBigInt, nrRMtests: int, ok: var bool) -proc FGIntLegendreSymbol*(a, p: var TBigInt, L: var int) -proc FGIntSquareRootModP*(Square, Prime: TBigInt, SquareRoot: var TBigInt) -# implementation - -var - primes: array[1..1228, int] = [3, 5, 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, 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', '+', '='] - PGPchr64: array[1..64, char] = ['A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I', - 'J', 'K', 'L', 'M', 'N', 'O', 'P', 'Q', 'R', - 'S', 'T', 'U', 'V', 'W', 'X', 'Y', 'Z', 'a', - 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j', - 'k', 'l', 'm', 'n', 'o', 'p', 'q', 'r', 's', - 't', 'u', 'v', 'w', 'x', 'y', 'z', '0', '1', - '2', '3', '4', '5', '6', '7', '8', '9', '+', - '/'] - -proc zeronetochar8(g: var char, x: String) = - var b: int8 - b = 0 - for i in countup(1, 8): - if copy(x, i, 1) == '1': b = b Or (1 Shl (8 - I)) - g = chr(b) - -proc zeronetochar6(g: var int, x: String) = - G = 0 - for I in countup(1, len(X)): - if I > 6: break - if X[I] != '0': G = G Or (1 Shl (6 - I)) - Inc(G) - -proc initialize8(trans: var openarray[String]) = - var - x: String - g: char - for c1 in countup(0, 1): - for c2 in countup(0, 1): - for c3 in countup(0, 1): - for c4 in countup(0, 1): - for c5 in countup(0, 1): - for c6 in countup(0, 1): - for c7 in countup(0, 1): - for c8 in countup(0, 1): - x = chr(48 + c1) + chr(48 + c2) + chr(48 + c3) + chr(48 + c4) + - chr(48 + c5) + chr(48 + c6) + chr(48 + c7) + chr(48 + c8) - zeronetochar8(g, x) - trans[ord(g)] = x - -proc initialize6(trans: var openarray[String]) = - var - x: String - g: int - for c1 in countup(0, 1): - for c2 in countup(0, 1): - for c3 in countup(0, 1): - for c4 in countup(0, 1): - for c5 in countup(0, 1): - for c6 in countup(0, 1): - x = chr(48 + c1) + chr(48 + c2) + chr(48 + c3) + chr(48 + c4) + - chr(48 + c5) + chr(48 + c6) - zeronetochar6(g, x) - trans[ord(chr64[g])] = x - -proc initialize6PGP(trans: var openarray[String]) = - var - x: String - g: int - for c1 in countup(0, 1): - for c2 in countup(0, 1): - for c3 in countup(0, 1): - for c4 in countup(0, 1): - for c5 in countup(0, 1): - for c6 in countup(0, 1): - x = chr(48 + c1) + chr(48 + c2) + chr(48 + c3) + chr(48 + c4) + - chr(48 + c5) + chr(48 + c6) - zeronetochar6(g, x) - trans[ord(PGPchr64[g])] = x - -proc ConvertBase256to64(str256: String, str64: var String) = - var - temp: String - trans: array[0..255, String] - len6: int32 - g: int - initialize8(trans) - temp = "" - for i in countup(1, len(str256)): temp = temp + trans[ord(str256[i])] - while (len(temp) Mod 6) != 0: temp = temp & '0' - len6 = len(temp) Div 6 - str64 = "" - for i in countup(1, len6): - zeronetochar6(g, copy(temp, 1, 6)) - str64 = str64 + chr64[g] - delete(temp, 1, 6) - -proc ConvertBase64to256(str64: String, str256: var String) = - var - temp: String - trans: array[0..255, String] - len8: int32 - g: char - initialize6(trans) - temp = "" - for i in countup(1, len(str64)): temp = temp + trans[ord(str64[i])] - str256 = "" - len8 = len(temp) Div 8 - for i in countup(1, len8): - zeronetochar8(g, copy(temp, 1, 8)) - str256 = str256 + g - delete(temp, 1, 8) - -proc ConvertBase256to2(str256: String, str2: var String) = - var trans: array[0..255, String] - str2 = "" - initialize8(trans) - for i in countup(1, len(str256)): str2 = str2 + trans[ord(str256[i])] - -proc ConvertBase64to2(str64: String, str2: var String) = - var trans: array[0..255, String] - str2 = "" - initialize6(trans) - for i in countup(1, len(str64)): str2 = str2 + trans[ord(str64[i])] - -proc ConvertBase2to256(str2: String, str256: var String) = - var - len8: int32 - g: char - str256 = "" - while (len(str2) Mod 8) != 0: str2 = '0' & str2 - len8 = len(str2) Div 8 - for i in countup(1, len8): - zeronetochar8(g, copy(str2, 1, 8)) - str256 = str256 + g - delete(str2, 1, 8) - -proc ConvertBase2to64(str2: String, str64: var String) = - var - len6: int32 - g: int - str64 = "" - while (len(str2) Mod 6) != 0: str2 = '0' & str2 - len6 = len(str2) Div 6 - for i in countup(1, len6): - zeronetochar6(g, copy(str2, 1, 6)) - str64 = str64 + chr64[g] - delete(str2, 1, 6) - -proc ConvertBase256StringToHexString(Str256: String, HexStr: var String) = - var b: int8 - HexStr = "" - for i in countup(1, len(str256)): - b = ord(str256[i]) - if (b Shr 4) < 10: HexStr = HexStr + chr(48 + (b Shr 4)) - else: HexStr = HexStr + chr(55 + (b Shr 4)) - if (b And 15) < 10: HexStr = HexStr + chr(48 + (b And 15)) - else: HexStr = HexStr + chr(55 + (b And 15)) - -proc ConvertHexStringToBase256String(HexStr: String, Str256: var String) = - var - b, h1, h2: int8 - temp: string - Str256 = "" - if (len(Hexstr) mod 2) == 1: temp = '0' & HexStr - else: temp = HexStr - for i in countup(1, (len(temp) Div 2)): - h2 = ord(temp[2 * i]) - h1 = ord(temp[2 * i - 1]) - if h1 < 58: b = ((h1 - 48) Shl 4) - else: b = ((h1 - 55) Shl 4) - if h2 < 58: b = (b Or (h2 - 48)) - else: b = (b Or ((h2 - 55) and 15)) - Str256 = Str256 + chr(b) - -proc PGPConvertBase256to64(str256, str64: var String) = - var - temp, x, a: String - len6: int32 - g: int - trans: array[0..255, String] - initialize8(trans) - temp = "" - for i in countup(1, len(str256)): temp = temp + trans[ord(str256[i])] - if (len(temp) Mod 6) == 0: - a = "" - elif (len(temp) Mod 6) == 4: - temp = temp & "00" - a = '=' - else: - temp = temp & "0000" - a = "==" - str64 = "" - len6 = len(temp) Div 6 - for i in countup(1, len6): - x = copy(temp, 1, 6) - zeronetochar6(g, x) - str64 = str64 + PGPchr64[g] - delete(temp, 1, 6) - str64 = str64 + a - -proc PGPConvertBase64to256(str64: String, str256: var String) = - var - temp, x: String - j, len8: int32 - g: char - trans: array[0..255, String] - initialize6PGP(trans) - temp = "" - str256 = "" - if str64[len(str64) - 1] == '=': j = 2 - elif str64[len(str64)] == '=': j = 1 - else: j = 0 - for i in countup(1, (len(str64) - j)): temp = temp + trans[ord(str64[i])] - if j != 0: delete(temp, len(temp) - 2 * j + 1, 2 * j) - len8 = len(temp) Div 8 - for i in countup(1, len8): - x = copy(temp, 1, 8) - zeronetochar8(g, x) - str256 = str256 + g - delete(temp, 1, 8) - -proc PGPConvertBase64to2(str64: String, str2: var String) = - var - j: int32 - trans: array[0..255, String] - str2 = "" - initialize6(trans) - if str64[len(str64) - 1] == '=': j = 2 - elif str64[len(str64)] == '=': j = 1 - else: j = 0 - for i in countup(1, (len(str64) - j)): str2 = str2 + trans[ord(str64[i])] - delete(str2, len(str2) - 2 * j + 1, 2 * j) - -proc FGIntToBase2String(FGInt: TBigInt, S: var String) = - S = "" - for i in countup(1, FGInt.Number[0]): - for j in countup(0, 30): - if (1 And (FGInt.Number[i] Shr j)) == 1: S = '1' & S - else: S = '0' & S - while (len(S) > 1) And (S[1] == '0'): delete(S, 1, 1) - if S == "": S = '0' - -proc Base2StringToFGInt(S: String, FGInt: var TBigInt) = - var i, j, size: int32 - while (S[1] == '0') And (len(S) > 1): delete(S, 1, 1) - size = len(S) Div 31 - if (len(S) Mod 31) != 0: size = size + 1 - setlen(FGInt.Number, (size + 1)) - FGInt.Number[0] = size - j = 1 - FGInt.Number[j] = 0 - i = 0 - while len(S) > 0: - if S[len(S)] == '1': FGInt.Number[j] = FGInt.Number[j] Or (1 Shl i) - i = i + 1 - if i == 31: - i = 0 - j = j + 1 - if j <= size: FGInt.Number[j] = 0 - delete(S, len(S), 1) - FGInt.Sign = positive - -proc FGIntToBase256String(FGInt: TBigInt, str256: var String) = - var - temp1: String - len8: int32 - g: char - FGIntToBase2String(FGInt, temp1) - while (len(temp1) Mod 8) != 0: temp1 = '0' & temp1 - len8 = len(temp1) Div 8 - str256 = "" - for i in countup(1, len8): - zeronetochar8(g, copy(temp1, 1, 8)) - str256 = str256 + g - delete(temp1, 1, 8) - -proc Base256StringToFGInt(str256: String, FGInt: var TBigInt) = - var - temp1: String - trans: array[0..255, String] - temp1 = "" - initialize8(trans) - for i in countup(1, len(str256)): temp1 = temp1 + trans[ord(str256[i])] - while (temp1[1] == '0') And (temp1 != '0'): delete(temp1, 1, 1) - Base2StringToFGInt(temp1, FGInt) - -proc PGPMPIToFGInt(PGPMPI: String, FGInt: var TBigInt) = - var temp: String - temp = PGPMPI - delete(temp, 1, 2) - Base256StringToFGInt(temp, FGInt) - -proc FGIntToPGPMPI(FGInt: TBigInt, PGPMPI: var String) = - var - length: int16 - c: char - b: int8 - FGIntToBase256String(FGInt, PGPMPI) - length = len(PGPMPI) * 8 - c = PGPMPI[1] - for i in countdown(7, 0): - if (ord(c) Shr i) == 0: length = length - 1 - else: break - b = length Mod 256 - PGPMPI = chr(b) + PGPMPI - b = length Div 256 - PGPMPI = chr(b) + PGPMPI - -proc GIntDivByIntBis1(GInt: var TBigInt, by: int32, modres: var int16) = - var size, rest, temp: int32 - size = GInt.Number[0] - temp = 0 - for i in countdown(size, 1): - temp = temp * 10000 - rest = temp + GInt.Number[i] - GInt.Number[i] = rest Div by - temp = rest Mod by - modres = temp - while (GInt.Number[size] == 0) And (size > 1): size = size - 1 - if size != GInt.Number[0]: - setlen(GInt.Number, size + 1) - GInt.Number[0] = size - -proc Base10StringToFGInt(Base10: String, FGInt: var TBigInt) = - var - size: int32 - j: int16 - S, x: String - sign: TSign - while (Not (Base10[1] In {'-', '0'..'9'})) And (len(Base10) > 1): - delete(Base10, 1, 1) - if copy(Base10, 1, 1) == '-': - Sign = negative - delete(Base10, 1, 1) - else: - Sign = positive - while (len(Base10) > 1) And (copy(Base10, 1, 1) == '0'): delete(Base10, 1, 1) - size = len(Base10) Div 4 - if (len(Base10) Mod 4) != 0: size = size + 1 - setlen(FGInt.Number, size + 1) - FGInt.Number[0] = size - for i in countup(1, (size - 1)): - x = copy(Base10, len(Base10) - 3, 4) - FGInt.Number[i] = StrToInt(x) - delete(Base10, len(Base10) - 3, 4) - FGInt.Number[size] = StrToInt(Base10) - S = "" - while (FGInt.Number[0] != 1) Or (FGInt.Number[1] != 0): - GIntDivByIntBis1(FGInt, 2, j) - S = inttostr(j) + S - if S == "": S = '0' - FGIntDestroy(FGInt) - Base2StringToFGInt(S, FGInt) - FGInt.Sign = sign - -proc FGIntToBase10String(FGInt: TBigInt, Base10: var String) = - var - S: String - j: int32 - temp: TBigInt - FGIntCopy(FGInt, temp) - Base10 = "" - while (temp.Number[0] > 1) Or (temp.Number[1] > 0): - FGIntDivByIntBis(temp, 10000, j) - S = IntToStr(j) - while len(S) < 4: S = '0' & S - Base10 = S + Base10 - Base10 = '0' & Base10 - while (len(Base10) > 1) And (Base10[1] == '0'): delete(Base10, 1, 1) - if FGInt.Sign == negative: Base10 = '-' & Base10 - -proc FGIntDestroy(FGInt: var TBigInt) = - FGInt.Number = nil - -proc FGIntCompareAbs(FGInt1, FGInt2: TBigInt): TCompare = - var size1, size2, i: int32 - FGIntCompareAbs = Er - size1 = FGInt1.Number[0] - size2 = FGInt2.Number[0] - if size1 > size2: - FGIntCompareAbs = Lt - elif size1 < size2: - FGIntCompareAbs = St - else: - i = size2 - while (FGInt1.Number[i] == FGInt2.Number[i]) And (i > 1): i = i - 1 - if FGInt1.Number[i] == FGInt2.Number[i]: FGIntCompareAbs = Eq - elif FGInt1.Number[i] < FGInt2.Number[i]: FGIntCompareAbs = St - elif FGInt1.Number[i] > FGInt2.Number[i]: FGIntCompareAbs = Lt - -proc FGIntAdd(FGInt1, FGInt2: TBigInt, Sum: var TBigInt) = - var size1, size2, size, rest, Trest: int32 - size1 = FGInt1.Number[0] - size2 = FGInt2.Number[0] - if size1 < size2: - FGIntAdd(FGInt2, FGInt1, Sum) - else: - if FGInt1.Sign == FGInt2.Sign: - Sum.Sign = FGInt1.Sign - setlen(Sum.Number, (size1 + 2)) - rest = 0 - for i in countup(1, size2): - Trest = FGInt1.Number[i] - Trest = Trest + FGInt2.Number[i] - Trest = Trest + rest - Sum.Number[i] = Trest And 2147483647 - rest = Trest Shr 31 - for i in countup((size2 + 1), size1): - Trest = FGInt1.Number[i] + rest - Sum.Number[i] = Trest And 2147483647 - rest = Trest Shr 31 - size = size1 + 1 - Sum.Number[0] = size - Sum.Number[size] = rest - while (Sum.Number[size] == 0) And (size > 1): size = size - 1 - if Sum.Number[0] != size: setlen(Sum.Number, size + 1) - Sum.Number[0] = size - else: - if FGIntCompareAbs(FGInt2, FGInt1) == Lt: - FGIntAdd(FGInt2, FGInt1, Sum) - else: - setlen(Sum.Number, (size1 + 1)) - rest = 0 - for i in countup(1, size2): - Trest = 0x80000000 # 2147483648; - TRest = Trest + FGInt1.Number[i] - TRest = Trest - FGInt2.Number[i] - TRest = Trest - rest - Sum.Number[i] = Trest And 2147483647 - if (Trest > 2147483647): rest = 0 - else: rest = 1 - for i in countup((size2 + 1), size1): - Trest = 0x80000000 - TRest = Trest + FGInt1.Number[i] - TRest = Trest - rest - Sum.Number[i] = Trest And 2147483647 - if (Trest > 2147483647): rest = 0 - else: rest = 1 - size = size1 - while (Sum.Number[size] == 0) And (size > 1): size = size - 1 - if size != size1: setlen(Sum.Number, size + 1) - Sum.Number[0] = size - Sum.Sign = FGInt1.Sign - -proc FGIntChangeSign(FGInt: var TBigInt) = - if FGInt.Sign == negative: FGInt.Sign = positive - else: FGInt.Sign = negative - -proc FGIntSub(FGInt1, FGInt2, dif: var TBigInt) = - FGIntChangeSign(FGInt2) - FGIntAdd(FGInt1, FGInt2, dif) - FGIntChangeSign(FGInt2) - -proc FGIntMulByInt(FGInt: TBigInt, res: var TBigInt, by: int32) = - var - size, rest: int32 - Trest: int64 - size = FGInt.Number[0] - setlen(res.Number, (size + 2)) - rest = 0 - for i in countup(1, size): - Trest = FGInt.Number[i] - TRest = Trest * by - TRest = Trest + rest - res.Number[i] = Trest And 2147483647 - rest = Trest Shr 31 - if rest != 0: - size = size + 1 - Res.Number[size] = rest - else: - setlen(Res.Number, size + 1) - Res.Number[0] = size - Res.Sign = FGInt.Sign - -proc FGIntMulByIntbis(FGInt: var TBigInt, by: int32) = - var - size, rest: int32 - Trest: int64 - size = FGInt.Number[0] - setlen(FGInt.Number, size + 2) - rest = 0 - for i in countup(1, size): - Trest = FGInt.Number[i] - TRest = Trest * by - TRest = Trest + rest - FGInt.Number[i] = Trest And 2147483647 - rest = Trest Shr 31 - if rest != 0: - size = size + 1 - FGInt.Number[size] = rest - else: - setlen(FGInt.Number, size + 1) - FGInt.Number[0] = size - -proc FGIntDivByInt(FGInt: TBigInt, res: var TBigInt, by: int32, modres: var int32) = - var - size: int32 - rest: int64 - size = FGInt.Number[0] - setlen(res.Number, (size + 1)) - modres = 0 - for i in countdown(size, 1): - rest = modres - rest = rest Shl 31 - rest = rest Or FGInt.Number[i] - res.Number[i] = rest Div by - modres = rest Mod by - while (res.Number[size] == 0) And (size > 1): size = size - 1 - if size != FGInt.Number[0]: setlen(res.Number, size + 1) - res.Number[0] = size - Res.Sign = FGInt.Sign - if FGInt.sign == negative: modres = by - modres - -proc FGIntDivByIntBis(FGInt: var TBigInt, by: int32, modres: var int32) = - var - size: int32 - temp, rest: int64 - size = FGInt.Number[0] - temp = 0 - for i in countdown(size, 1): - temp = temp Shl 31 - rest = temp Or FGInt.Number[i] - FGInt.Number[i] = rest Div by - temp = rest Mod by - modres = temp - while (FGInt.Number[size] == 0) And (size > 1): size = size - 1 - if size != FGInt.Number[0]: - setlen(FGInt.Number, size + 1) - FGInt.Number[0] = size - -proc FGIntModByInt(FGInt: TBigInt, by: int32, modres: var int32) = - var - size: int32 - temp, rest: int64 - size = FGInt.Number[0] - temp = 0 - for i in countdown(size, 1): - temp = temp Shl 31 - rest = temp Or FGInt.Number[i] - temp = rest Mod by - modres = temp - if FGInt.sign == negative: modres = by - modres - -proc FGIntAbs(FGInt: var TBigInt) = - FGInt.Sign = positive - -proc FGIntCopy(FGInt1: TBigInt, FGInt2: var TBigInt) = - FGInt2.Sign = FGInt1.Sign - FGInt2.Number = nil - FGInt2.Number = Copy(FGInt1.Number, 0, FGInt1.Number[0] + 1) - -proc FGIntShiftLeft(FGInt: var TBigInt) = - var l, m, size: int32 - size = FGInt.Number[0] - l = 0 - for i in countup(1, Size): - m = FGInt.Number[i] Shr 30 - FGInt.Number[i] = ((FGInt.Number[i] Shl 1) Or l) And 2147483647 - l = m - if l != 0: - setlen(FGInt.Number, size + 2) - FGInt.Number[size + 1] = l - FGInt.Number[0] = size + 1 - -proc FGIntShiftRight(FGInt: var TBigInt) = - var l, m, size: int32 - size = FGInt.Number[0] - l = 0 - for i in countdown(size, 1): - m = FGInt.Number[i] And 1 - FGInt.Number[i] = (FGInt.Number[i] Shr 1) Or l - l = m Shl 30 - if (FGInt.Number[size] == 0) And (size > 1): - setlen(FGInt.Number, size) - FGInt.Number[0] = size - 1 - -proc FGIntShiftRightBy31(FGInt: var TBigInt) = - var size: int32 - size = FGInt.Number[0] - if size > 1: - for i in countup(1, size - 1): - FGInt.Number[i] = FGInt.Number[i + 1] - setlen(FGInt.Number, Size) - FGInt.Number[0] = size - 1 - else: - FGInt.Number[1] = 0 - -proc FGIntAddBis(FGInt1: var TBigInt, FGInt2: TBigInt) = - var size1, size2, Trest, rest: int32 - size1 = FGInt1.Number[0] - size2 = FGInt2.Number[0] - rest = 0 - for i in countup(1, size2): - Trest = FGInt1.Number[i] + FGInt2.Number[i] + rest - rest = Trest Shr 31 - FGInt1.Number[i] = Trest And 2147483647 - for i in countup(size2 + 1, size1): - Trest = FGInt1.Number[i] + rest - rest = Trest Shr 31 - FGInt1.Number[i] = Trest And 2147483647 - if rest != 0: - setlen(FGInt1.Number, size1 + 2) - FGInt1.Number[0] = size1 + 1 - FGInt1.Number[size1 + 1] = rest - -proc FGIntSubBis(FGInt1: var TBigInt, FGInt2: TBigInt) = - var size1, size2, rest, Trest: int32 - size1 = FGInt1.Number[0] - size2 = FGInt2.Number[0] - rest = 0 - for i in countup(1, size2): - Trest = (0x80000000 Or FGInt1.Number[i]) - FGInt2.Number[i] - rest - if (Trest > 2147483647): rest = 0 - else: rest = 1 - FGInt1.Number[i] = Trest And 2147483647 - for i in countup(size2 + 1, size1): - Trest = (0x80000000 Or FGInt1.Number[i]) - rest - if (Trest > 2147483647): rest = 0 - else: rest = 1 - FGInt1.Number[i] = Trest And 2147483647 - i = size1 - while (FGInt1.Number[i] == 0) And (i > 1): i = i - 1 - if i != size1: - setlen(FGInt1.Number, i + 1) - FGInt1.Number[0] = i - -proc FGIntMul(FGInt1, FGInt2: TBigInt, Prod: var TBigInt) = - var - size, size1, size2, rest: int32 - Trest: int64 - size1 = FGInt1.Number[0] - size2 = FGInt2.Number[0] - size = size1 + size2 - setlen(Prod.Number, (size + 1)) - for i in countup(1, size): Prod.Number[i] = 0 - for i in countup(1, size2): - rest = 0 - for j in countup(1, size1): - Trest = FGInt1.Number[j] - Trest = Trest * FGInt2.Number[i] - Trest = Trest + Prod.Number[j + i - 1] - Trest = Trest + rest - Prod.Number[j + i - 1] = Trest And 2147483647 - rest = Trest Shr 31 - Prod.Number[i + size1] = rest - Prod.Number[0] = size - while (Prod.Number[size] == 0) And (size > 1): size = size - 1 - if size != Prod.Number[0]: - setlen(Prod.Number, size + 1) - Prod.Number[0] = size - if FGInt1.Sign == FGInt2.Sign: Prod.Sign = Positive - else: prod.Sign = negative - -proc FGIntSquare(FGInt: TBigInt, Square: var TBigInt) = - var - size, size1, rest: int32 - Trest: int64 - size1 = FGInt.Number[0] - size = 2 * size1 - setlen(Square.Number, (size + 1)) - Square.Number[0] = size - for i in countup(1, size): Square.Number[i] = 0 - for i in countup(1, size1): - Trest = FGInt.Number[i] - Trest = Trest * FGInt.Number[i] - Trest = Trest + Square.Number[2 * i - 1] - Square.Number[2 * i - 1] = Trest And 2147483647 - rest = Trest Shr 31 - for j in countup(i + 1, size1): - Trest = FGInt.Number[i] Shl 1 - Trest = Trest * FGInt.Number[j] - Trest = Trest + Square.Number[i + j - 1] - Trest = Trest + rest - Square.Number[i + j - 1] = Trest And 2147483647 - rest = Trest Shr 31 - Square.Number[i + size1] = rest - Square.Sign = positive - while (Square.Number[size] == 0) And (size > 1): size = size - 1 - if size != (2 * size1): - setlen(Square.Number, size + 1) - Square.Number[0] = size - -proc FGIntExp(FGInt, exp: TBigInt, res: var TBigInt) = - var - temp2, temp3: TBigInt - S: String - FGIntToBase2String(exp, S) - if S[len(S)] == '0': Base10StringToFGInt('1', res) - else: FGIntCopy(FGInt, res) - FGIntCopy(FGInt, temp2) - if len(S) > 1: - for i in countdown((len(S) - 1), 1): - FGIntSquare(temp2, temp3) - FGIntCopy(temp3, temp2) - if S[i] == '1': - FGIntMul(res, temp2, temp3) - FGIntCopy(temp3, res) - -proc FGIntFac(FGInt: TBigInt, res: var TBigInt) = - var one, temp, temp1: TBigInt - FGIntCopy(FGInt, temp) - Base10StringToFGInt('1', res) - Base10StringToFGInt('1', one) - while Not (FGIntCompareAbs(temp, one) == Eq): - FGIntMul(temp, res, temp1) - FGIntCopy(temp1, res) - FGIntSubBis(temp, one) - FGIntDestroy(one) - FGIntDestroy(temp) - -proc FGIntShiftLeftBy31(FGInt: var TBigInt) = - var - f1, f2: int32 - size: int32 - size = FGInt.Number[0] - setlen(FGInt.Number, size + 2) - f1 = 0 - for i in countup(1, (size + 1)): - f2 = FGInt.Number[i] - FGInt.Number[i] = f1 - f1 = f2 - FGInt.Number[0] = size + 1 - -proc FGIntDivMod(FGInt1, FGInt2, QFGInt, MFGInt: var TBigInt) = - var - one, zero, temp1, temp2: TBigInt - s1, s2: TSign - j, s: int32 - i: int64 - s1 = FGInt1.Sign - s2 = FGInt2.Sign - FGIntAbs(FGInt1) - FGIntAbs(FGInt2) - FGIntCopy(FGInt1, MFGInt) - FGIntCopy(FGInt2, temp1) - if FGIntCompareAbs(FGInt1, FGInt2) != St: - s = FGInt1.Number[0] - FGInt2.Number[0] - setlen(QFGInt.Number, (s + 2)) - QFGInt.Number[0] = s + 1 - for t in countup(1, s): - FGIntShiftLeftBy31(temp1) - QFGInt.Number[t] = 0 - j = s + 1 - QFGInt.Number[j] = 0 - while FGIntCompareAbs(MFGInt, FGInt2) != St: - while FGIntCompareAbs(MFGInt, temp1) != St: - if MFGInt.Number[0] > temp1.Number[0]: - i = MFGInt.Number[MFGInt.Number[0]] - i = i Shl 31 - i = i + MFGInt.Number[MFGInt.Number[0] - 1] - i = i Div (temp1.Number[temp1.Number[0]] + 1) - else: - i = MFGInt.Number[MFGInt.Number[0]] Div - (temp1.Number[temp1.Number[0]] + 1) - if (i != 0): - FGIntCopy(temp1, temp2) - FGIntMulByIntBis(temp2, i) - FGIntSubBis(MFGInt, temp2) - QFGInt.Number[j] = QFGInt.Number[j] + i - if FGIntCompareAbs(MFGInt, temp2) != St: - QFGInt.Number[j] = QFGInt.Number[j] + i - FGIntSubBis(MFGInt, temp2) - FGIntDestroy(temp2) - else: - QFGInt.Number[j] = QFGInt.Number[j] + 1 - FGIntSubBis(MFGInt, temp1) - if MFGInt.Number[0] <= temp1.Number[0]: - if FGIntCompareAbs(temp1, FGInt2) != Eq: - FGIntShiftRightBy31(temp1) - j = j - 1 - else: - Base10StringToFGInt('0', QFGInt) - s = QFGInt.Number[0] - while (s > 1) And (QFGInt.Number[s] == 0): s = s - 1 - if s < QFGInt.Number[0]: - setlen(QFGInt.Number, s + 1) - QFGInt.Number[0] = s - QFGInt.Sign = positive - FGIntDestroy(temp1) - Base10StringToFGInt('0', zero) - Base10StringToFGInt('1', one) - if s1 == negative: - if FGIntCompareAbs(MFGInt, zero) != Eq: - FGIntadd(QFGInt, one, temp1) - FGIntDestroy(QFGInt) - FGIntCopy(temp1, QFGInt) - FGIntDestroy(temp1) - FGIntsub(FGInt2, MFGInt, temp1) - FGIntDestroy(MFGInt) - FGIntCopy(temp1, MFGInt) - FGIntDestroy(temp1) - if s2 == positive: QFGInt.Sign = negative - else: - QFGInt.Sign = s2 - FGIntDestroy(one) - FGIntDestroy(zero) - FGInt1.Sign = s1 - FGInt2.Sign = s2 - -proc FGIntDiv(FGInt1, FGInt2, QFGInt: var TBigInt) = - var - one, zero, temp1, temp2, MFGInt: TBigInt - s1, s2: TSign - j, s: int32 - i: int64 - s1 = FGInt1.Sign - s2 = FGInt2.Sign - FGIntAbs(FGInt1) - FGIntAbs(FGInt2) - FGIntCopy(FGInt1, MFGInt) - FGIntCopy(FGInt2, temp1) - if FGIntCompareAbs(FGInt1, FGInt2) != St: - s = FGInt1.Number[0] - FGInt2.Number[0] - setlen(QFGInt.Number, (s + 2)) - QFGInt.Number[0] = s + 1 - for t in countup(1, s): - FGIntShiftLeftBy31(temp1) - QFGInt.Number[t] = 0 - j = s + 1 - QFGInt.Number[j] = 0 - while FGIntCompareAbs(MFGInt, FGInt2) != St: - while FGIntCompareAbs(MFGInt, temp1) != St: - if MFGInt.Number[0] > temp1.Number[0]: - i = MFGInt.Number[MFGInt.Number[0]] - i = i Shl 31 - i = i + MFGInt.Number[MFGInt.Number[0] - 1] - i = i Div (temp1.Number[temp1.Number[0]] + 1) - else: - i = MFGInt.Number[MFGInt.Number[0]] Div - (temp1.Number[temp1.Number[0]] + 1) - if (i != 0): - FGIntCopy(temp1, temp2) - FGIntMulByIntBis(temp2, i) - FGIntSubBis(MFGInt, temp2) - QFGInt.Number[j] = QFGInt.Number[j] + i - if FGIntCompareAbs(MFGInt, temp2) != St: - QFGInt.Number[j] = QFGInt.Number[j] + i - FGIntSubBis(MFGInt, temp2) - FGIntDestroy(temp2) - else: - QFGInt.Number[j] = QFGInt.Number[j] + 1 - FGIntSubBis(MFGInt, temp1) - if MFGInt.Number[0] <= temp1.Number[0]: - if FGIntCompareAbs(temp1, FGInt2) != Eq: - FGIntShiftRightBy31(temp1) - j = j - 1 - else: - Base10StringToFGInt('0', QFGInt) - s = QFGInt.Number[0] - while (s > 1) And (QFGInt.Number[s] == 0): s = s - 1 - if s < QFGInt.Number[0]: - setlen(QFGInt.Number, s + 1) - QFGInt.Number[0] = s - QFGInt.Sign = positive - FGIntDestroy(temp1) - Base10StringToFGInt('0', zero) - Base10StringToFGInt('1', one) - if s1 == negative: - if FGIntCompareAbs(MFGInt, zero) != Eq: - FGIntadd(QFGInt, one, temp1) - FGIntDestroy(QFGInt) - FGIntCopy(temp1, QFGInt) - FGIntDestroy(temp1) - FGIntsub(FGInt2, MFGInt, temp1) - FGIntDestroy(MFGInt) - FGIntCopy(temp1, MFGInt) - FGIntDestroy(temp1) - if s2 == positive: QFGInt.Sign = negative - else: - QFGInt.Sign = s2 - FGIntDestroy(one) - FGIntDestroy(zero) - FGIntDestroy(MFGInt) - FGInt1.Sign = s1 - FGInt2.Sign = s2 - -proc FGIntMod(FGInt1, FGInt2, MFGInt: var TBigInt) = - var - one, zero, temp1, temp2: TBigInt - s1, s2: TSign - s: int32 - i: int64 - s1 = FGInt1.Sign - s2 = FGInt2.Sign - FGIntAbs(FGInt1) - FGIntAbs(FGInt2) - FGIntCopy(FGInt1, MFGInt) - FGIntCopy(FGInt2, temp1) - if FGIntCompareAbs(FGInt1, FGInt2) != St: - s = FGInt1.Number[0] - FGInt2.Number[0] - for t in countup(1, s): FGIntShiftLeftBy31(temp1) - while FGIntCompareAbs(MFGInt, FGInt2) != St: - while FGIntCompareAbs(MFGInt, temp1) != St: - if MFGInt.Number[0] > temp1.Number[0]: - i = MFGInt.Number[MFGInt.Number[0]] - i = i Shl 31 - i = i + MFGInt.Number[MFGInt.Number[0] - 1] - i = i Div (temp1.Number[temp1.Number[0]] + 1) - else: - i = MFGInt.Number[MFGInt.Number[0]] Div - (temp1.Number[temp1.Number[0]] + 1) - if (i != 0): - FGIntCopy(temp1, temp2) - FGIntMulByIntBis(temp2, i) - FGIntSubBis(MFGInt, temp2) - if FGIntCompareAbs(MFGInt, temp2) != St: FGIntSubBis(MFGInt, temp2) - FGIntDestroy(temp2) - else: - FGIntSubBis(MFGInt, temp1) # If FGIntCompareAbs(MFGInt, temp1) <> St Then FGIntSubBis(MFGInt,temp1); - if MFGInt.Number[0] <= temp1.Number[0]: - if FGIntCompareAbs(temp1, FGInt2) != Eq: FGIntShiftRightBy31(temp1) - FGIntDestroy(temp1) - Base10StringToFGInt('0', zero) - Base10StringToFGInt('1', one) - if s1 == negative: - if FGIntCompareAbs(MFGInt, zero) != Eq: - FGIntSub(FGInt2, MFGInt, temp1) - FGIntDestroy(MFGInt) - FGIntCopy(temp1, MFGInt) - FGIntDestroy(temp1) - FGIntDestroy(one) - FGIntDestroy(zero) - FGInt1.Sign = s1 - FGInt2.Sign = s2 - -proc FGIntSquareMod(FGInt, Modb, FGIntSM: var TBigInt) = - var temp: TBigInt - FGIntSquare(FGInt, temp) - FGIntMod(temp, Modb, FGIntSM) - FGIntDestroy(temp) - -proc FGIntAddMod(FGInt1, FGInt2, base, FGIntres: var TBigInt) = - var temp: TBigInt - FGIntadd(FGInt1, FGInt2, temp) - FGIntMod(temp, base, FGIntres) - FGIntDestroy(temp) - -proc FGIntMulMod(FGInt1, FGInt2, base, FGIntres: var TBigInt) = - var temp: TBigInt - FGIntMul(FGInt1, FGInt2, temp) - FGIntMod(temp, base, FGIntres) - FGIntDestroy(temp) - -proc FGIntModExp(FGInt, exp, modb, res: var TBigInt) = - var - temp2, temp3: TBigInt - S: String - if (Modb.Number[1] Mod 2) == 1: - FGIntMontgomeryModExp(FGInt, exp, modb, res) - return - FGIntToBase2String(exp, S) - Base10StringToFGInt('1', res) - FGIntcopy(FGInt, temp2) - for i in countdown(len(S), 1): - if S[i] == '1': - FGIntmulMod(res, temp2, modb, temp3) - FGIntCopy(temp3, res) - FGIntSquareMod(temp2, Modb, temp3) - FGIntCopy(temp3, temp2) - FGIntDestroy(temp2) - -proc FGIntModBis(FGInt: TBigInt, FGIntOut: var TBigInt, b, head: int32) = - if b <= FGInt.Number[0]: - setlen(FGIntOut.Number, (b + 1)) - for i in countup(0, b): FGIntOut.Number[i] = FGInt.Number[i] - FGIntOut.Number[b] = FGIntOut.Number[b] And head - i = b - while (FGIntOut.Number[i] == 0) And (i > 1): i = i - 1 - if i < b: setlen(FGIntOut.Number, i + 1) - FGIntOut.Number[0] = i - FGIntOut.Sign = positive - else: - FGIntCopy(FGInt, FGIntOut) - -proc FGIntMulModBis(FGInt1, FGInt2: TBigInt, Prod: var TBigInt, b, head: int32) = - var - size, size1, size2, t, rest: int32 - Trest: int64 - size1 = FGInt1.Number[0] - size2 = FGInt2.Number[0] - size = min(b, size1 + size2) - setlen(Prod.Number, (size + 1)) - for i in countup(1, size): Prod.Number[i] = 0 - for i in countup(1, size2): - rest = 0 - t = min(size1, b - i + 1) - for j in countup(1, t): - Trest = FGInt1.Number[j] - Trest = Trest * FGInt2.Number[i] - Trest = Trest + Prod.Number[j + i - 1] - Trest = Trest + rest - Prod.Number[j + i - 1] = Trest And 2147483647 - rest = Trest Shr 31 - if (i + size1) <= b: Prod.Number[i + size1] = rest - Prod.Number[0] = size - if size == b: Prod.Number[b] = Prod.Number[b] And head - while (Prod.Number[size] == 0) And (size > 1): size = size - 1 - if size < Prod.Number[0]: - setlen(Prod.Number, size + 1) - Prod.Number[0] = size - if FGInt1.Sign == FGInt2.Sign: Prod.Sign = Positive - else: prod.Sign = negative - -proc FGIntMontgomeryMod(GInt, base, baseInv: TBigInt, MGInt: var TBigInt, - b: int32, head: int32) = - var - m, temp, temp1: TBigInt - r: int32 - FGIntModBis(GInt, temp, b, head) - FGIntMulModBis(temp, baseInv, m, b, head) - FGIntMul(m, base, temp1) - FGIntDestroy(temp) - FGIntAdd(temp1, GInt, temp) - FGIntDestroy(temp1) - MGInt.Number = copy(temp.Number, b - 1, temp.Number[0] - b + 2) - MGInt.Sign = positive - MGInt.Number[0] = temp.Number[0] - b + 1 - FGIntDestroy(temp) - if (head Shr 30) == 0: FGIntDivByIntBis(MGInt, head + 1, r) - else: FGIntShiftRightBy31(MGInt) - if FGIntCompareAbs(MGInt, base) != St: FGIntSubBis(MGInt, base) - FGIntDestroy(temp) - FGIntDestroy(m) - -proc FGIntMontgomeryModExp(FGInt, exp, modb, res: var TBigInt) = - var - temp2, temp3, baseInv, r, zero: TBigInt - t, b, head: int32 - S: String - Base2StringToFGInt('0', zero) - FGIntMod(FGInt, modb, res) - if FGIntCompareAbs(res, zero) == Eq: - FGIntDestroy(zero) - return - else: - FGIntDestroy(res) - FGIntDestroy(zero) - FGIntToBase2String(exp, S) - t = modb.Number[0] - b = t - if (modb.Number[t] Shr 30) == 1: t = t + 1 - setlen(r.Number, (t + 1)) - r.Number[0] = t - r.Sign = positive - for i in countup(1, t): r.Number[i] = 0 - if t == modb.Number[0]: - head = 2147483647 - for j in countdown(29, 0): - head = head Shr 1 - if (modb.Number[t] Shr j) == 1: - r.Number[t] = 1 Shl (j + 1) - break - else: - r.Number[t] = 1 - head = 2147483647 - FGIntModInv(modb, r, temp2) - if temp2.Sign == negative: - FGIntCopy(temp2, BaseInv) - else: - FGIntCopy(r, BaseInv) - FGIntSubBis(BaseInv, temp2) - FGIntAbs(BaseInv) - FGIntDestroy(temp2) - FGIntMod(r, modb, res) - FGIntMulMod(FGInt, res, modb, temp2) - FGIntDestroy(r) - for i in countdown(len(S), 1): - if S[i] == '1': - FGIntmul(res, temp2, temp3) - FGIntDestroy(res) - FGIntMontgomeryMod(temp3, modb, baseinv, res, b, head) - FGIntDestroy(temp3) - FGIntSquare(temp2, temp3) - FGIntDestroy(temp2) - FGIntMontgomeryMod(temp3, modb, baseinv, temp2, b, head) - FGIntDestroy(temp3) - FGIntDestroy(temp2) - FGIntMontgomeryMod(res, modb, baseinv, temp3, b, head) - FGIntCopy(temp3, res) - FGIntDestroy(temp3) - FGIntDestroy(baseinv) - -proc FGIntGCD(FGInt1, FGInt2: TBigInt, GCD: var TBigInt) = - var - k: TCompare - zero, temp1, temp2, temp3: TBigInt - k = FGIntCompareAbs(FGInt1, FGInt2) - if (k == Eq): - FGIntCopy(FGInt1, GCD) - elif (k == St): - FGIntGCD(FGInt2, FGInt1, GCD) - else: - Base10StringToFGInt('0', zero) - FGIntCopy(FGInt1, temp1) - FGIntCopy(FGInt2, temp2) - while (temp2.Number[0] != 1) Or (temp2.Number[1] != 0): - FGIntMod(temp1, temp2, temp3) - FGIntCopy(temp2, temp1) - FGIntCopy(temp3, temp2) - FGIntDestroy(temp3) - FGIntCopy(temp1, GCD) - FGIntDestroy(temp2) - FGIntDestroy(zero) - -proc FGIntLCM(FGInt1, FGInt2: TBigInt, LCM: var TBigInt) = - var temp1, temp2: TBigInt - FGIntGCD(FGInt1, FGInt2, temp1) - FGIntmul(FGInt1, FGInt2, temp2) - FGIntdiv(temp2, temp1, LCM) - FGIntDestroy(temp1) - FGIntDestroy(temp2) - -proc FGIntTrialDiv9999(FGInt: TBigInt, ok: var bool) = - var - j: int32 - i: int - if ((FGInt.Number[1] Mod 2) == 0): - ok = false - else: - i = 0 - ok = true - while ok And (i < 1228): - i = i + 1 - FGIntmodbyint(FGInt, primes[i], j) - if j == 0: ok = false - -proc FGIntRandom1(Seed, RandomFGInt: var TBigInt) = - var temp, base: TBigInt - Base10StringToFGInt("281474976710656", base) - Base10StringToFGInt("44485709377909", temp) - FGIntMulMod(seed, temp, base, RandomFGInt) - FGIntDestroy(temp) - FGIntDestroy(base) - -proc FGIntRabinMiller(FGIntp: var TBigInt, nrtest: int32, ok: var bool) = - var - j, b, i: int32 - m, z, temp1, temp2, temp3, zero, one, two, pmin1: TBigInt - ok1, ok2: bool - randomize - j = 0 - Base10StringToFGInt('0', zero) - Base10StringToFGInt('1', one) - Base10StringToFGInt('2', two) - FGIntsub(FGIntp, one, temp1) - FGIntsub(FGIntp, one, pmin1) - b = 0 - while (temp1.Number[1] Mod 2) == 0: - b = b + 1 - FGIntShiftRight(temp1) - m = temp1 - i = 0 - ok = true - Randomize - while (i < nrtest) And ok: - i = i + 1 - Base10StringToFGInt(inttostr(Primes[Random(1227) + 1]), temp2) - FGIntMontGomeryModExp(temp2, m, FGIntp, z) - FGIntDestroy(temp2) - ok1 = (FGIntCompareAbs(z, one) == Eq) - ok2 = (FGIntCompareAbs(z, pmin1) == Eq) - if Not (ok1 Or ok2): - while (ok And (j < b)): - if (j > 0) And ok1: - ok = false - else: - j = j + 1 - if (j < b) And (Not ok2): - FGIntSquaremod(z, FGIntp, temp3) - FGIntCopy(temp3, z) - ok1 = (FGIntCompareAbs(z, one) == Eq) - ok2 = (FGIntCompareAbs(z, pmin1) == Eq) - if ok2: j = b - elif (Not ok2) And (j >= b): - ok = false - FGIntDestroy(zero) - FGIntDestroy(one) - FGIntDestroy(two) - FGIntDestroy(m) - FGIntDestroy(z) - FGIntDestroy(pmin1) - -proc FGIntBezoutBachet(FGInt1, FGInt2, a, b: var TBigInt) = - var zero, r1, r2, r3, ta, gcd, temp, temp1, temp2: TBigInt - if FGIntCompareAbs(FGInt1, FGInt2) != St: - FGIntcopy(FGInt1, r1) - FGIntcopy(FGInt2, r2) - Base10StringToFGInt('0', zero) - Base10StringToFGInt('1', a) - Base10StringToFGInt('0', ta) - while true: - FGIntdivmod(r1, r2, temp, r3) - FGIntDestroy(r1) - r1 = r2 - r2 = r3 - FGIntmul(ta, temp, temp1) - FGIntsub(a, temp1, temp2) - FGIntCopy(ta, a) - FGIntCopy(temp2, ta) - FGIntDestroy(temp1) - FGIntDestroy(temp) - if FGIntCompareAbs(r3, zero) == Eq: break - FGIntGCD(FGInt1, FGInt2, gcd) - FGIntmul(a, FGInt1, temp1) - FGIntsub(gcd, temp1, temp2) - FGIntDestroy(temp1) - FGIntdiv(temp2, FGInt2, b) - FGIntDestroy(temp2) - FGIntDestroy(ta) - FGIntDestroy(r1) - FGIntDestroy(r2) - FGIntDestroy(gcd) - else: - FGIntBezoutBachet(FGInt2, FGInt1, b, a) - -proc FGIntModInv(FGInt1, base: TBigInt, Inverse: var TBigInt) = - var zero, one, r1, r2, r3, tb, gcd, temp, temp1, temp2: TBigInt - Base10StringToFGInt('1', one) - FGIntGCD(FGInt1, base, gcd) - if FGIntCompareAbs(one, gcd) == Eq: - FGIntcopy(base, r1) - FGIntcopy(FGInt1, r2) - Base10StringToFGInt('0', zero) - Base10StringToFGInt('0', inverse) - Base10StringToFGInt('1', tb) - while true: - FGIntDestroy(r3) - FGIntdivmod(r1, r2, temp, r3) - FGIntCopy(r2, r1) - FGIntCopy(r3, r2) - FGIntmul(tb, temp, temp1) - FGIntsub(inverse, temp1, temp2) - FGIntDestroy(inverse) - FGIntDestroy(temp1) - FGIntCopy(tb, inverse) - FGIntCopy(temp2, tb) - FGIntDestroy(temp) - if FGIntCompareAbs(r3, zero) == Eq: break - if inverse.Sign == negative: - FGIntadd(base, inverse, temp) - FGIntCopy(temp, inverse) - FGIntDestroy(tb) - FGIntDestroy(r1) - FGIntDestroy(r2) - FGIntDestroy(gcd) - FGIntDestroy(one) - -proc FGIntPrimetest(FGIntp: var TBigInt, nrRMtests: int, ok: var bool) = - FGIntTrialdiv9999(FGIntp, ok) - if ok: FGIntRabinMiller(FGIntp, nrRMtests, ok) - -proc FGIntLegendreSymbol(a, p: var TBigInt, L: var int) = - var - temp1, temp2, temp3, temp4, temp5, zero, one: TBigInt - i: int32 - ok1, ok2: bool - Base10StringToFGInt('0', zero) - Base10StringToFGInt('1', one) - FGIntMod(a, p, temp1) - if FGIntCompareAbs(zero, temp1) == Eq: - FGIntDestroy(temp1) - L = 0 - else: - FGIntDestroy(temp1) - FGIntCopy(p, temp1) - FGIntCopy(a, temp2) - L = 1 - while FGIntCompareAbs(temp2, one) != Eq: - if (temp2.Number[1] Mod 2) == 0: - FGIntSquare(temp1, temp3) - FGIntSub(temp3, one, temp4) - FGIntDestroy(temp3) - FGIntDivByInt(temp4, temp3, 8, i) - if (temp3.Number[1] Mod 2) == 0: ok1 = false - else: ok1 = true - FGIntDestroy(temp3) - FGIntDestroy(temp4) - if ok1 == true: L = L * (- 1) - FGIntDivByIntBis(temp2, 2, i) - else: - FGIntSub(temp1, one, temp3) - FGIntSub(temp2, one, temp4) - FGIntMul(temp3, temp4, temp5) - FGIntDestroy(temp3) - FGIntDestroy(temp4) - FGIntDivByInt(temp5, temp3, 4, i) - if (temp3.Number[1] Mod 2) == 0: ok2 = false - else: ok2 = true - FGIntDestroy(temp5) - FGIntDestroy(temp3) - if ok2 == true: L = L * (- 1) - FGIntMod(temp1, temp2, temp3) - FGIntCopy(temp2, temp1) - FGIntCopy(temp3, temp2) - FGIntDestroy(temp1) - FGIntDestroy(temp2) - FGIntDestroy(zero) - FGIntDestroy(one) - -proc FGIntSquareRootModP(Square, Prime: TBigInt, SquareRoot: var TBigInt) = - var - one, n, b, s, r, temp, temp1, temp2, temp3: TBigInt - a: int32 - L: int - Base2StringToFGInt('1', one) - Base2StringToFGInt("10", n) - a = 0 - FGIntLegendreSymbol(n, Prime, L) - while L != - 1: - FGIntAddBis(n, one) - FGIntLegendreSymbol(n, Prime, L) - FGIntCopy(Prime, s) - s.Number[1] = s.Number[1] - 1 - while (s.Number[1] Mod 2) == 0: - FGIntShiftRight(s) - a = a + 1 - FGIntMontgomeryModExp(n, s, Prime, b) - FGIntAdd(s, one, temp) - FGIntShiftRight(temp) - FGIntMontgomeryModExp(Square, temp, Prime, r) - FGIntDestroy(temp) - FGIntModInv(Square, Prime, temp1) - for i in countup(0, (a - 2)): - FGIntSquareMod(r, Prime, temp2) - FGIntMulMod(temp1, temp2, Prime, temp) - FGIntDestroy(temp2) - for j in countup(1, (a - i - 2)): - FGIntSquareMod(temp, Prime, temp2) - FGIntDestroy(temp) - FGIntCopy(temp2, temp) - FGIntDestroy(temp2) - if FGIntCompareAbs(temp, one) != Eq: - FGIntMulMod(r, b, Prime, temp3) - FGIntDestroy(r) - FGIntCopy(temp3, r) - FGIntDestroy(temp3) - FGIntDestroy(temp) - FGIntDestroy(temp2) - if i == (a - 2): break - FGIntSquareMod(b, Prime, temp3) - FGIntDestroy(b) - FGIntCopy(temp3, b) - FGIntDestroy(temp3) - FGIntCopy(r, SquareRoot) - FGIntDestroy(r) - FGIntDestroy(s) - FGIntDestroy(b) - FGIntDestroy(temp1) - FGIntDestroy(one) - FGIntDestroy(n) |