2373 lines
55 KiB
C#
2373 lines
55 KiB
C#
//
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// BigInteger.cs - Big Integer implementation
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//
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// Authors:
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// Ben Maurer
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// Chew Keong TAN
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// Sebastien Pouliot <sebastien@ximian.com>
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// Pieter Philippaerts <Pieter@mentalis.org>
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//
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// Copyright (c) 2003 Ben Maurer
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// All rights reserved
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//
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// Copyright (c) 2002 Chew Keong TAN
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// All rights reserved.
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//
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// Copyright (C) 2004, 2007 Novell, Inc (http://www.novell.com)
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//
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// Permission is hereby granted, free of charge, to any person obtaining
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// a copy of this software and associated documentation files (the
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// "Software"), to deal in the Software without restriction, including
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// without limitation the rights to use, copy, modify, merge, publish,
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// distribute, sublicense, and/or sell copies of the Software, and to
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// permit persons to whom the Software is furnished to do so, subject to
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// the following conditions:
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//
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// The above copyright notice and this permission notice shall be
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// included in all copies or substantial portions of the Software.
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//
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// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
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// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
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// MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
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// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE
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// LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION
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// OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION
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// WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
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//
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using System;
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using System.Security.Cryptography;
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using Mono.Math.Prime.Generator;
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using Mono.Math.Prime;
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namespace Mono.Math {
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#if INSIDE_CORLIB
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internal
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#else
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public
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#endif
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class BigInteger {
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#region Data Storage
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/// <summary>
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/// The Length of this BigInteger
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/// </summary>
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uint length = 1;
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/// <summary>
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/// The data for this BigInteger
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/// </summary>
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uint [] data;
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#endregion
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#region Constants
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/// <summary>
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/// Default length of a BigInteger in bytes
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/// </summary>
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const uint DEFAULT_LEN = 20;
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/// <summary>
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/// Table of primes below 2000.
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/// </summary>
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/// <remarks>
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/// <para>
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/// This table was generated using Mathematica 4.1 using the following function:
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/// </para>
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/// <para>
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/// <code>
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/// PrimeTable [x_] := Prime [Range [1, PrimePi [x]]]
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/// PrimeTable [6000]
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/// </code>
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/// </para>
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/// </remarks>
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internal static readonly uint [] smallPrimes = {
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2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71,
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73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151,
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157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233,
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239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317,
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331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419,
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421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503,
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509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607,
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613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701,
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709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811,
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821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911,
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919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997,
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1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087,
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1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171, 1181,
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1187, 1193, 1201, 1213, 1217, 1223, 1229, 1231, 1237, 1249, 1259, 1277, 1279,
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1283, 1289, 1291, 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373,
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1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453, 1459, 1471,
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1481, 1483, 1487, 1489, 1493, 1499, 1511, 1523, 1531, 1543, 1549, 1553, 1559,
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1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637,
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1657, 1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733, 1741, 1747,
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1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, 1823, 1831, 1847, 1861, 1867,
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1871, 1873, 1877, 1879, 1889, 1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973,
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1979, 1987, 1993, 1997, 1999,
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2003, 2011, 2017, 2027, 2029, 2039, 2053, 2063, 2069, 2081, 2083, 2087, 2089,
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2099, 2111, 2113, 2129, 2131, 2137, 2141, 2143, 2153, 2161, 2179, 2203, 2207,
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2213, 2221, 2237, 2239, 2243, 2251, 2267, 2269, 2273, 2281, 2287, 2293, 2297,
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2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357, 2371, 2377, 2381, 2383, 2389,
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2393, 2399, 2411, 2417, 2423, 2437, 2441, 2447, 2459, 2467, 2473, 2477, 2503,
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2521, 2531, 2539, 2543, 2549, 2551, 2557, 2579, 2591, 2593, 2609, 2617, 2621,
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2633, 2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687, 2689, 2693, 2699, 2707,
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2711, 2713, 2719, 2729, 2731, 2741, 2749, 2753, 2767, 2777, 2789, 2791, 2797,
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2801, 2803, 2819, 2833, 2837, 2843, 2851, 2857, 2861, 2879, 2887, 2897, 2903,
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2909, 2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999,
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3001, 3011, 3019, 3023, 3037, 3041, 3049, 3061, 3067, 3079, 3083, 3089, 3109,
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3119, 3121, 3137, 3163, 3167, 3169, 3181, 3187, 3191, 3203, 3209, 3217, 3221,
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3229, 3251, 3253, 3257, 3259, 3271, 3299, 3301, 3307, 3313, 3319, 3323, 3329,
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3331, 3343, 3347, 3359, 3361, 3371, 3373, 3389, 3391, 3407, 3413, 3433, 3449,
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3457, 3461, 3463, 3467, 3469, 3491, 3499, 3511, 3517, 3527, 3529, 3533, 3539,
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3541, 3547, 3557, 3559, 3571, 3581, 3583, 3593, 3607, 3613, 3617, 3623, 3631,
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3637, 3643, 3659, 3671, 3673, 3677, 3691, 3697, 3701, 3709, 3719, 3727, 3733,
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3739, 3761, 3767, 3769, 3779, 3793, 3797, 3803, 3821, 3823, 3833, 3847, 3851,
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3853, 3863, 3877, 3881, 3889, 3907, 3911, 3917, 3919, 3923, 3929, 3931, 3943,
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3947, 3967, 3989,
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4001, 4003, 4007, 4013, 4019, 4021, 4027, 4049, 4051, 4057, 4073, 4079, 4091,
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4093, 4099, 4111, 4127, 4129, 4133, 4139, 4153, 4157, 4159, 4177, 4201, 4211,
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4217, 4219, 4229, 4231, 4241, 4243, 4253, 4259, 4261, 4271, 4273, 4283, 4289,
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4297, 4327, 4337, 4339, 4349, 4357, 4363, 4373, 4391, 4397, 4409, 4421, 4423,
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4441, 4447, 4451, 4457, 4463, 4481, 4483, 4493, 4507, 4513, 4517, 4519, 4523,
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4547, 4549, 4561, 4567, 4583, 4591, 4597, 4603, 4621, 4637, 4639, 4643, 4649,
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4651, 4657, 4663, 4673, 4679, 4691, 4703, 4721, 4723, 4729, 4733, 4751, 4759,
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4783, 4787, 4789, 4793, 4799, 4801, 4813, 4817, 4831, 4861, 4871, 4877, 4889,
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4903, 4909, 4919, 4931, 4933, 4937, 4943, 4951, 4957, 4967, 4969, 4973, 4987,
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4993, 4999,
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5003, 5009, 5011, 5021, 5023, 5039, 5051, 5059, 5077, 5081, 5087, 5099, 5101,
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5107, 5113, 5119, 5147, 5153, 5167, 5171, 5179, 5189, 5197, 5209, 5227, 5231,
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5233, 5237, 5261, 5273, 5279, 5281, 5297, 5303, 5309, 5323, 5333, 5347, 5351,
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5381, 5387, 5393, 5399, 5407, 5413, 5417, 5419, 5431, 5437, 5441, 5443, 5449,
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5471, 5477, 5479, 5483, 5501, 5503, 5507, 5519, 5521, 5527, 5531, 5557, 5563,
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5569, 5573, 5581, 5591, 5623, 5639, 5641, 5647, 5651, 5653, 5657, 5659, 5669,
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5683, 5689, 5693, 5701, 5711, 5717, 5737, 5741, 5743, 5749, 5779, 5783, 5791,
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5801, 5807, 5813, 5821, 5827, 5839, 5843, 5849, 5851, 5857, 5861, 5867, 5869,
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5879, 5881, 5897, 5903, 5923, 5927, 5939, 5953, 5981, 5987
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};
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public enum Sign : int {
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Negative = -1,
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Zero = 0,
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Positive = 1
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};
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#region Exception Messages
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const string WouldReturnNegVal = "Operation would return a negative value";
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#endregion
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#endregion
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#region Constructors
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public BigInteger ()
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{
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data = new uint [DEFAULT_LEN];
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this.length = DEFAULT_LEN;
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}
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#if !INSIDE_CORLIB
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[CLSCompliant (false)]
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#endif
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public BigInteger (Sign sign, uint len)
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{
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this.data = new uint [len];
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this.length = len;
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}
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public BigInteger (BigInteger bi)
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{
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this.data = (uint [])bi.data.Clone ();
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this.length = bi.length;
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}
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#if !INSIDE_CORLIB
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[CLSCompliant (false)]
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#endif
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public BigInteger (BigInteger bi, uint len)
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{
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this.data = new uint [len];
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for (uint i = 0; i < bi.length; i++)
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this.data [i] = bi.data [i];
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this.length = bi.length;
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}
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#endregion
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#region Conversions
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public BigInteger (byte [] inData)
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{
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if (inData.Length == 0)
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inData = new byte [1];
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length = (uint)inData.Length >> 2;
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int leftOver = inData.Length & 0x3;
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// length not multiples of 4
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if (leftOver != 0) length++;
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data = new uint [length];
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for (int i = inData.Length - 1, j = 0; i >= 3; i -= 4, j++) {
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data [j] = (uint)(
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(inData [i-3] << (3*8)) |
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(inData [i-2] << (2*8)) |
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(inData [i-1] << (1*8)) |
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(inData [i])
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);
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}
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switch (leftOver) {
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case 1: data [length-1] = (uint)inData [0]; break;
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case 2: data [length-1] = (uint)((inData [0] << 8) | inData [1]); break;
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case 3: data [length-1] = (uint)((inData [0] << 16) | (inData [1] << 8) | inData [2]); break;
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}
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this.Normalize ();
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}
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#if !INSIDE_CORLIB
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[CLSCompliant (false)]
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#endif
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public BigInteger (uint [] inData)
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{
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if (inData.Length == 0)
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inData = new uint [1];
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length = (uint)inData.Length;
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data = new uint [length];
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for (int i = (int)length - 1, j = 0; i >= 0; i--, j++)
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data [j] = inData [i];
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this.Normalize ();
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}
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#if !INSIDE_CORLIB
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[CLSCompliant (false)]
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#endif
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public BigInteger (uint ui)
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{
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data = new uint [] {ui};
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}
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#if !INSIDE_CORLIB
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[CLSCompliant (false)]
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#endif
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public BigInteger (ulong ul)
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{
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data = new uint [2] { (uint)ul, (uint)(ul >> 32)};
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length = 2;
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this.Normalize ();
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}
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#if !INSIDE_CORLIB
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[CLSCompliant (false)]
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#endif
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public static implicit operator BigInteger (uint value)
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{
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return (new BigInteger (value));
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}
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public static implicit operator BigInteger (int value)
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{
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if (value < 0) throw new ArgumentOutOfRangeException ("value");
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return (new BigInteger ((uint)value));
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}
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#if !INSIDE_CORLIB
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[CLSCompliant (false)]
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#endif
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public static implicit operator BigInteger (ulong value)
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{
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return (new BigInteger (value));
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}
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/* This is the BigInteger.Parse method I use. This method works
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because BigInteger.ToString returns the input I gave to Parse. */
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public static BigInteger Parse (string number)
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{
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if (number == null)
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throw new ArgumentNullException ("number");
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int i = 0, len = number.Length;
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char c;
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bool digits_seen = false;
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BigInteger val = new BigInteger (0);
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if (number [i] == '+') {
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i++;
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}
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else if (number [i] == '-') {
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throw new FormatException (WouldReturnNegVal);
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}
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for (; i < len; i++) {
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c = number [i];
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if (c == '\0') {
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i = len;
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continue;
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}
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if (c >= '0' && c <= '9') {
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val = val * 10 + (c - '0');
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digits_seen = true;
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}
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else {
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if (Char.IsWhiteSpace (c)) {
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for (i++; i < len; i++) {
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if (!Char.IsWhiteSpace (number [i]))
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throw new FormatException ();
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}
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break;
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}
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else
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throw new FormatException ();
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}
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}
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if (!digits_seen)
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throw new FormatException ();
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return val;
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}
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#endregion
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#region Operators
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public static BigInteger operator + (BigInteger bi1, BigInteger bi2)
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{
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if (bi1 == 0)
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return new BigInteger (bi2);
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else if (bi2 == 0)
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return new BigInteger (bi1);
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else
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return Kernel.AddSameSign (bi1, bi2);
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}
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public static BigInteger operator - (BigInteger bi1, BigInteger bi2)
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{
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if (bi2 == 0)
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return new BigInteger (bi1);
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if (bi1 == 0)
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throw new ArithmeticException (WouldReturnNegVal);
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switch (Kernel.Compare (bi1, bi2)) {
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case Sign.Zero:
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return 0;
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case Sign.Positive:
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return Kernel.Subtract (bi1, bi2);
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case Sign.Negative:
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throw new ArithmeticException (WouldReturnNegVal);
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default:
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throw new Exception ();
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}
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}
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public static int operator % (BigInteger bi, int i)
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{
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if (i > 0)
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return (int)Kernel.DwordMod (bi, (uint)i);
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else
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return -(int)Kernel.DwordMod (bi, (uint)-i);
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}
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#if !INSIDE_CORLIB
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[CLSCompliant (false)]
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#endif
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public static uint operator % (BigInteger bi, uint ui)
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{
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return Kernel.DwordMod (bi, (uint)ui);
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}
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public static BigInteger operator % (BigInteger bi1, BigInteger bi2)
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{
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return Kernel.multiByteDivide (bi1, bi2)[1];
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}
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public static BigInteger operator / (BigInteger bi, int i)
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{
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if (i > 0)
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return Kernel.DwordDiv (bi, (uint)i);
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throw new ArithmeticException (WouldReturnNegVal);
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}
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public static BigInteger operator / (BigInteger bi1, BigInteger bi2)
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{
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return Kernel.multiByteDivide (bi1, bi2)[0];
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}
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public static BigInteger operator * (BigInteger bi1, BigInteger bi2)
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{
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if (bi1 == 0 || bi2 == 0) return 0;
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//
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// Validate pointers
|
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//
|
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if (bi1.data.Length < bi1.length) throw new IndexOutOfRangeException ("bi1 out of range");
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if (bi2.data.Length < bi2.length) throw new IndexOutOfRangeException ("bi2 out of range");
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BigInteger ret = new BigInteger (Sign.Positive, bi1.length + bi2.length);
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Kernel.Multiply (bi1.data, 0, bi1.length, bi2.data, 0, bi2.length, ret.data, 0);
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ret.Normalize ();
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return ret;
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}
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public static BigInteger operator * (BigInteger bi, int i)
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{
|
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if (i < 0) throw new ArithmeticException (WouldReturnNegVal);
|
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if (i == 0) return 0;
|
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if (i == 1) return new BigInteger (bi);
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return Kernel.MultiplyByDword (bi, (uint)i);
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}
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public static BigInteger operator << (BigInteger bi1, int shiftVal)
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{
|
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return Kernel.LeftShift (bi1, shiftVal);
|
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}
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public static BigInteger operator >> (BigInteger bi1, int shiftVal)
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{
|
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return Kernel.RightShift (bi1, shiftVal);
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}
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#endregion
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#region Friendly names for operators
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// with names suggested by FxCop 1.30
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|
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public static BigInteger Add (BigInteger bi1, BigInteger bi2)
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{
|
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return (bi1 + bi2);
|
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}
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public static BigInteger Subtract (BigInteger bi1, BigInteger bi2)
|
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{
|
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return (bi1 - bi2);
|
|
}
|
|
|
|
public static int Modulus (BigInteger bi, int i)
|
|
{
|
|
return (bi % i);
|
|
}
|
|
|
|
#if !INSIDE_CORLIB
|
|
[CLSCompliant (false)]
|
|
#endif
|
|
public static uint Modulus (BigInteger bi, uint ui)
|
|
{
|
|
return (bi % ui);
|
|
}
|
|
|
|
public static BigInteger Modulus (BigInteger bi1, BigInteger bi2)
|
|
{
|
|
return (bi1 % bi2);
|
|
}
|
|
|
|
public static BigInteger Divid (BigInteger bi, int i)
|
|
{
|
|
return (bi / i);
|
|
}
|
|
|
|
public static BigInteger Divid (BigInteger bi1, BigInteger bi2)
|
|
{
|
|
return (bi1 / bi2);
|
|
}
|
|
|
|
public static BigInteger Multiply (BigInteger bi1, BigInteger bi2)
|
|
{
|
|
return (bi1 * bi2);
|
|
}
|
|
|
|
public static BigInteger Multiply (BigInteger bi, int i)
|
|
{
|
|
return (bi * i);
|
|
}
|
|
|
|
#endregion
|
|
|
|
#region Random
|
|
private static RandomNumberGenerator rng;
|
|
private static RandomNumberGenerator Rng {
|
|
get {
|
|
if (rng == null)
|
|
rng = RandomNumberGenerator.Create ();
|
|
return rng;
|
|
}
|
|
}
|
|
|
|
/// <summary>
|
|
/// Generates a new, random BigInteger of the specified length.
|
|
/// </summary>
|
|
/// <param name="bits">The number of bits for the new number.</param>
|
|
/// <param name="rng">A random number generator to use to obtain the bits.</param>
|
|
/// <returns>A random number of the specified length.</returns>
|
|
public static BigInteger GenerateRandom (int bits, RandomNumberGenerator rng)
|
|
{
|
|
int dwords = bits >> 5;
|
|
int remBits = bits & 0x1F;
|
|
|
|
if (remBits != 0)
|
|
dwords++;
|
|
|
|
BigInteger ret = new BigInteger (Sign.Positive, (uint)dwords + 1);
|
|
byte [] random = new byte [dwords << 2];
|
|
|
|
rng.GetBytes (random);
|
|
Buffer.BlockCopy (random, 0, ret.data, 0, (int)dwords << 2);
|
|
|
|
if (remBits != 0) {
|
|
uint mask = (uint)(0x01 << (remBits-1));
|
|
ret.data [dwords-1] |= mask;
|
|
|
|
mask = (uint)(0xFFFFFFFF >> (32 - remBits));
|
|
ret.data [dwords-1] &= mask;
|
|
}
|
|
else
|
|
ret.data [dwords-1] |= 0x80000000;
|
|
|
|
ret.Normalize ();
|
|
return ret;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Generates a new, random BigInteger of the specified length using the default RNG crypto service provider.
|
|
/// </summary>
|
|
/// <param name="bits">The number of bits for the new number.</param>
|
|
/// <returns>A random number of the specified length.</returns>
|
|
public static BigInteger GenerateRandom (int bits)
|
|
{
|
|
return GenerateRandom (bits, Rng);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Randomizes the bits in "this" from the specified RNG.
|
|
/// </summary>
|
|
/// <param name="rng">A RNG.</param>
|
|
public void Randomize (RandomNumberGenerator rng)
|
|
{
|
|
if (this == 0)
|
|
return;
|
|
|
|
int bits = this.BitCount ();
|
|
int dwords = bits >> 5;
|
|
int remBits = bits & 0x1F;
|
|
|
|
if (remBits != 0)
|
|
dwords++;
|
|
|
|
byte [] random = new byte [dwords << 2];
|
|
|
|
rng.GetBytes (random);
|
|
Buffer.BlockCopy (random, 0, data, 0, (int)dwords << 2);
|
|
|
|
if (remBits != 0) {
|
|
uint mask = (uint)(0x01 << (remBits-1));
|
|
data [dwords-1] |= mask;
|
|
|
|
mask = (uint)(0xFFFFFFFF >> (32 - remBits));
|
|
data [dwords-1] &= mask;
|
|
}
|
|
|
|
else
|
|
data [dwords-1] |= 0x80000000;
|
|
|
|
Normalize ();
|
|
}
|
|
|
|
/// <summary>
|
|
/// Randomizes the bits in "this" from the default RNG.
|
|
/// </summary>
|
|
public void Randomize ()
|
|
{
|
|
Randomize (Rng);
|
|
}
|
|
|
|
#endregion
|
|
|
|
#region Bitwise
|
|
|
|
public int BitCount ()
|
|
{
|
|
this.Normalize ();
|
|
|
|
uint value = data [length - 1];
|
|
uint mask = 0x80000000;
|
|
uint bits = 32;
|
|
|
|
while (bits > 0 && (value & mask) == 0) {
|
|
bits--;
|
|
mask >>= 1;
|
|
}
|
|
bits += ((length - 1) << 5);
|
|
|
|
return (int)bits;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Tests if the specified bit is 1.
|
|
/// </summary>
|
|
/// <param name="bitNum">The bit to test. The least significant bit is 0.</param>
|
|
/// <returns>True if bitNum is set to 1, else false.</returns>
|
|
#if !INSIDE_CORLIB
|
|
[CLSCompliant (false)]
|
|
#endif
|
|
public bool TestBit (uint bitNum)
|
|
{
|
|
uint bytePos = bitNum >> 5; // divide by 32
|
|
byte bitPos = (byte)(bitNum & 0x1F); // get the lowest 5 bits
|
|
|
|
uint mask = (uint)1 << bitPos;
|
|
return ((this.data [bytePos] & mask) != 0);
|
|
}
|
|
|
|
public bool TestBit (int bitNum)
|
|
{
|
|
if (bitNum < 0) throw new IndexOutOfRangeException ("bitNum out of range");
|
|
|
|
uint bytePos = (uint)bitNum >> 5; // divide by 32
|
|
byte bitPos = (byte)(bitNum & 0x1F); // get the lowest 5 bits
|
|
|
|
uint mask = (uint)1 << bitPos;
|
|
return ((this.data [bytePos] | mask) == this.data [bytePos]);
|
|
}
|
|
|
|
#if !INSIDE_CORLIB
|
|
[CLSCompliant (false)]
|
|
#endif
|
|
public void SetBit (uint bitNum)
|
|
{
|
|
SetBit (bitNum, true);
|
|
}
|
|
|
|
#if !INSIDE_CORLIB
|
|
[CLSCompliant (false)]
|
|
#endif
|
|
public void ClearBit (uint bitNum)
|
|
{
|
|
SetBit (bitNum, false);
|
|
}
|
|
|
|
#if !INSIDE_CORLIB
|
|
[CLSCompliant (false)]
|
|
#endif
|
|
public void SetBit (uint bitNum, bool value)
|
|
{
|
|
uint bytePos = bitNum >> 5; // divide by 32
|
|
|
|
if (bytePos < this.length) {
|
|
uint mask = (uint)1 << (int)(bitNum & 0x1F);
|
|
if (value)
|
|
this.data [bytePos] |= mask;
|
|
else
|
|
this.data [bytePos] &= ~mask;
|
|
}
|
|
}
|
|
|
|
public int LowestSetBit ()
|
|
{
|
|
if (this == 0) return -1;
|
|
int i = 0;
|
|
while (!TestBit (i)) i++;
|
|
return i;
|
|
}
|
|
|
|
public byte[] GetBytes ()
|
|
{
|
|
if (this == 0) return new byte [1];
|
|
|
|
int numBits = BitCount ();
|
|
int numBytes = numBits >> 3;
|
|
if ((numBits & 0x7) != 0)
|
|
numBytes++;
|
|
|
|
byte [] result = new byte [numBytes];
|
|
|
|
int numBytesInWord = numBytes & 0x3;
|
|
if (numBytesInWord == 0) numBytesInWord = 4;
|
|
|
|
int pos = 0;
|
|
for (int i = (int)length - 1; i >= 0; i--) {
|
|
uint val = data [i];
|
|
for (int j = numBytesInWord - 1; j >= 0; j--) {
|
|
result [pos+j] = (byte)(val & 0xFF);
|
|
val >>= 8;
|
|
}
|
|
pos += numBytesInWord;
|
|
numBytesInWord = 4;
|
|
}
|
|
return result;
|
|
}
|
|
|
|
#endregion
|
|
|
|
#region Compare
|
|
|
|
#if !INSIDE_CORLIB
|
|
[CLSCompliant (false)]
|
|
#endif
|
|
public static bool operator == (BigInteger bi1, uint ui)
|
|
{
|
|
if (bi1.length != 1) bi1.Normalize ();
|
|
return bi1.length == 1 && bi1.data [0] == ui;
|
|
}
|
|
|
|
#if !INSIDE_CORLIB
|
|
[CLSCompliant (false)]
|
|
#endif
|
|
public static bool operator != (BigInteger bi1, uint ui)
|
|
{
|
|
if (bi1.length != 1) bi1.Normalize ();
|
|
return !(bi1.length == 1 && bi1.data [0] == ui);
|
|
}
|
|
|
|
public static bool operator == (BigInteger bi1, BigInteger bi2)
|
|
{
|
|
// we need to compare with null
|
|
if ((bi1 as object) == (bi2 as object))
|
|
return true;
|
|
if (null == bi1 || null == bi2)
|
|
return false;
|
|
return Kernel.Compare (bi1, bi2) == 0;
|
|
}
|
|
|
|
public static bool operator != (BigInteger bi1, BigInteger bi2)
|
|
{
|
|
// we need to compare with null
|
|
if ((bi1 as object) == (bi2 as object))
|
|
return false;
|
|
if (null == bi1 || null == bi2)
|
|
return true;
|
|
return Kernel.Compare (bi1, bi2) != 0;
|
|
}
|
|
|
|
public static bool operator > (BigInteger bi1, BigInteger bi2)
|
|
{
|
|
return Kernel.Compare (bi1, bi2) > 0;
|
|
}
|
|
|
|
public static bool operator < (BigInteger bi1, BigInteger bi2)
|
|
{
|
|
return Kernel.Compare (bi1, bi2) < 0;
|
|
}
|
|
|
|
public static bool operator >= (BigInteger bi1, BigInteger bi2)
|
|
{
|
|
return Kernel.Compare (bi1, bi2) >= 0;
|
|
}
|
|
|
|
public static bool operator <= (BigInteger bi1, BigInteger bi2)
|
|
{
|
|
return Kernel.Compare (bi1, bi2) <= 0;
|
|
}
|
|
|
|
public Sign Compare (BigInteger bi)
|
|
{
|
|
return Kernel.Compare (this, bi);
|
|
}
|
|
|
|
#endregion
|
|
|
|
#region Formatting
|
|
|
|
#if !INSIDE_CORLIB
|
|
[CLSCompliant (false)]
|
|
#endif
|
|
public string ToString (uint radix)
|
|
{
|
|
return ToString (radix, "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ");
|
|
}
|
|
|
|
#if !INSIDE_CORLIB
|
|
[CLSCompliant (false)]
|
|
#endif
|
|
public string ToString (uint radix, string characterSet)
|
|
{
|
|
if (characterSet.Length < radix)
|
|
throw new ArgumentException ("charSet length less than radix", "characterSet");
|
|
if (radix == 1)
|
|
throw new ArgumentException ("There is no such thing as radix one notation", "radix");
|
|
|
|
if (this == 0) return "0";
|
|
if (this == 1) return "1";
|
|
|
|
string result = "";
|
|
|
|
BigInteger a = new BigInteger (this);
|
|
|
|
while (a != 0) {
|
|
uint rem = Kernel.SingleByteDivideInPlace (a, radix);
|
|
result = characterSet [(int) rem] + result;
|
|
}
|
|
|
|
return result;
|
|
}
|
|
|
|
#endregion
|
|
|
|
#region Misc
|
|
|
|
/// <summary>
|
|
/// Normalizes this by setting the length to the actual number of
|
|
/// uints used in data and by setting the sign to Sign.Zero if the
|
|
/// value of this is 0.
|
|
/// </summary>
|
|
private void Normalize ()
|
|
{
|
|
// Normalize length
|
|
while (length > 0 && data [length-1] == 0) length--;
|
|
|
|
// Check for zero
|
|
if (length == 0)
|
|
length++;
|
|
}
|
|
|
|
public void Clear ()
|
|
{
|
|
for (int i=0; i < length; i++)
|
|
data [i] = 0x00;
|
|
}
|
|
|
|
#endregion
|
|
|
|
#region Object Impl
|
|
|
|
public override int GetHashCode ()
|
|
{
|
|
uint val = 0;
|
|
|
|
for (uint i = 0; i < this.length; i++)
|
|
val ^= this.data [i];
|
|
|
|
return (int)val;
|
|
}
|
|
|
|
public override string ToString ()
|
|
{
|
|
return ToString (10);
|
|
}
|
|
|
|
public override bool Equals (object o)
|
|
{
|
|
if (o == null)
|
|
return false;
|
|
if (o is int)
|
|
return (int)o >= 0 && this == (uint)o;
|
|
|
|
BigInteger bi = o as BigInteger;
|
|
if (bi == null)
|
|
return false;
|
|
|
|
return Kernel.Compare (this, bi) == 0;
|
|
}
|
|
|
|
#endregion
|
|
|
|
#region Number Theory
|
|
|
|
public BigInteger GCD (BigInteger bi)
|
|
{
|
|
return Kernel.gcd (this, bi);
|
|
}
|
|
|
|
public BigInteger ModInverse (BigInteger modulus)
|
|
{
|
|
return Kernel.modInverse (this, modulus);
|
|
}
|
|
|
|
public BigInteger ModPow (BigInteger exp, BigInteger n)
|
|
{
|
|
ModulusRing mr = new ModulusRing (n);
|
|
return mr.Pow (this, exp);
|
|
}
|
|
|
|
#endregion
|
|
|
|
#region Prime Testing
|
|
|
|
public bool IsProbablePrime ()
|
|
{
|
|
// can we use our small-prime table ?
|
|
if (this <= smallPrimes[smallPrimes.Length - 1]) {
|
|
for (int p = 0; p < smallPrimes.Length; p++) {
|
|
if (this == smallPrimes[p])
|
|
return true;
|
|
}
|
|
// the list is complete, so it's not a prime
|
|
return false;
|
|
}
|
|
|
|
// otherwise check if we can divide by one of the small primes
|
|
for (int p = 0; p < smallPrimes.Length; p++) {
|
|
if (this % smallPrimes[p] == 0)
|
|
return false;
|
|
}
|
|
// the last step is to confirm the "large" prime with the SPP or Miller-Rabin test
|
|
return PrimalityTests.Test (this, Prime.ConfidenceFactor.Medium);
|
|
}
|
|
|
|
#endregion
|
|
|
|
#region Prime Number Generation
|
|
|
|
/// <summary>
|
|
/// Generates the smallest prime >= bi
|
|
/// </summary>
|
|
/// <param name="bi">A BigInteger</param>
|
|
/// <returns>The smallest prime >= bi. More mathematically, if bi is prime: bi, else Prime [PrimePi [bi] + 1].</returns>
|
|
public static BigInteger NextHighestPrime (BigInteger bi)
|
|
{
|
|
NextPrimeFinder npf = new NextPrimeFinder ();
|
|
return npf.GenerateNewPrime (0, bi);
|
|
}
|
|
|
|
public static BigInteger GeneratePseudoPrime (int bits)
|
|
{
|
|
SequentialSearchPrimeGeneratorBase sspg = new SequentialSearchPrimeGeneratorBase ();
|
|
return sspg.GenerateNewPrime (bits);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Increments this by two
|
|
/// </summary>
|
|
public void Incr2 ()
|
|
{
|
|
int i = 0;
|
|
|
|
data [0] += 2;
|
|
|
|
// If there was no carry, nothing to do
|
|
if (data [0] < 2) {
|
|
|
|
// Account for the first carry
|
|
data [++i]++;
|
|
|
|
// Keep adding until no carry
|
|
while (data [i++] == 0x0)
|
|
data [i]++;
|
|
|
|
// See if we increased the data length
|
|
if (length == (uint)i)
|
|
length++;
|
|
}
|
|
}
|
|
|
|
#endregion
|
|
|
|
#if INSIDE_CORLIB
|
|
internal
|
|
#else
|
|
public
|
|
#endif
|
|
sealed class ModulusRing {
|
|
|
|
BigInteger mod, constant;
|
|
|
|
public ModulusRing (BigInteger modulus)
|
|
{
|
|
this.mod = modulus;
|
|
|
|
// calculate constant = b^ (2k) / m
|
|
uint i = mod.length << 1;
|
|
|
|
constant = new BigInteger (Sign.Positive, i + 1);
|
|
constant.data [i] = 0x00000001;
|
|
|
|
constant = constant / mod;
|
|
}
|
|
|
|
public void BarrettReduction (BigInteger x)
|
|
{
|
|
BigInteger n = mod;
|
|
uint k = n.length,
|
|
kPlusOne = k+1,
|
|
kMinusOne = k-1;
|
|
|
|
// x < mod, so nothing to do.
|
|
if (x.length < k) return;
|
|
|
|
BigInteger q3;
|
|
|
|
//
|
|
// Validate pointers
|
|
//
|
|
if (x.data.Length < x.length) throw new IndexOutOfRangeException ("x out of range");
|
|
|
|
// q1 = x / b^ (k-1)
|
|
// q2 = q1 * constant
|
|
// q3 = q2 / b^ (k+1), Needs to be accessed with an offset of kPlusOne
|
|
|
|
// TODO: We should the method in HAC p 604 to do this (14.45)
|
|
q3 = new BigInteger (Sign.Positive, x.length - kMinusOne + constant.length);
|
|
Kernel.Multiply (x.data, kMinusOne, x.length - kMinusOne, constant.data, 0, constant.length, q3.data, 0);
|
|
|
|
// r1 = x mod b^ (k+1)
|
|
// i.e. keep the lowest (k+1) words
|
|
|
|
uint lengthToCopy = (x.length > kPlusOne) ? kPlusOne : x.length;
|
|
|
|
x.length = lengthToCopy;
|
|
x.Normalize ();
|
|
|
|
// r2 = (q3 * n) mod b^ (k+1)
|
|
// partial multiplication of q3 and n
|
|
|
|
BigInteger r2 = new BigInteger (Sign.Positive, kPlusOne);
|
|
Kernel.MultiplyMod2p32pmod (q3.data, (int)kPlusOne, (int)q3.length - (int)kPlusOne, n.data, 0, (int)n.length, r2.data, 0, (int)kPlusOne);
|
|
|
|
r2.Normalize ();
|
|
|
|
if (r2 <= x) {
|
|
Kernel.MinusEq (x, r2);
|
|
} else {
|
|
BigInteger val = new BigInteger (Sign.Positive, kPlusOne + 1);
|
|
val.data [kPlusOne] = 0x00000001;
|
|
|
|
Kernel.MinusEq (val, r2);
|
|
Kernel.PlusEq (x, val);
|
|
}
|
|
|
|
while (x >= n)
|
|
Kernel.MinusEq (x, n);
|
|
}
|
|
|
|
public BigInteger Multiply (BigInteger a, BigInteger b)
|
|
{
|
|
if (a == 0 || b == 0) return 0;
|
|
|
|
if (a > mod)
|
|
a %= mod;
|
|
|
|
if (b > mod)
|
|
b %= mod;
|
|
|
|
BigInteger ret = a * b;
|
|
BarrettReduction (ret);
|
|
|
|
return ret;
|
|
}
|
|
|
|
public BigInteger Difference (BigInteger a, BigInteger b)
|
|
{
|
|
Sign cmp = Kernel.Compare (a, b);
|
|
BigInteger diff;
|
|
|
|
switch (cmp) {
|
|
case Sign.Zero:
|
|
return 0;
|
|
case Sign.Positive:
|
|
diff = a - b; break;
|
|
case Sign.Negative:
|
|
diff = b - a; break;
|
|
default:
|
|
throw new Exception ();
|
|
}
|
|
|
|
if (diff >= mod) {
|
|
if (diff.length >= mod.length << 1)
|
|
diff %= mod;
|
|
else
|
|
BarrettReduction (diff);
|
|
}
|
|
if (cmp == Sign.Negative)
|
|
diff = mod - diff;
|
|
return diff;
|
|
}
|
|
#if true
|
|
public BigInteger Pow (BigInteger a, BigInteger k)
|
|
{
|
|
BigInteger b = new BigInteger (1);
|
|
if (k == 0)
|
|
return b;
|
|
|
|
BigInteger A = a;
|
|
if (k.TestBit (0))
|
|
b = a;
|
|
|
|
for (int i = 1; i < k.BitCount (); i++) {
|
|
A = Multiply (A, A);
|
|
if (k.TestBit (i))
|
|
b = Multiply (A, b);
|
|
}
|
|
return b;
|
|
}
|
|
#else
|
|
public BigInteger Pow (BigInteger b, BigInteger exp)
|
|
{
|
|
if ((mod.data [0] & 1) == 1) return OddPow (b, exp);
|
|
else return EvenPow (b, exp);
|
|
}
|
|
|
|
public BigInteger EvenPow (BigInteger b, BigInteger exp)
|
|
{
|
|
BigInteger resultNum = new BigInteger ((BigInteger)1, mod.length << 1);
|
|
BigInteger tempNum = new BigInteger (b % mod, mod.length << 1); // ensures (tempNum * tempNum) < b^ (2k)
|
|
|
|
uint totalBits = (uint)exp.BitCount ();
|
|
|
|
uint [] wkspace = new uint [mod.length << 1];
|
|
|
|
// perform squaring and multiply exponentiation
|
|
for (uint pos = 0; pos < totalBits; pos++) {
|
|
if (exp.TestBit (pos)) {
|
|
|
|
Array.Clear (wkspace, 0, wkspace.Length);
|
|
Kernel.Multiply (resultNum.data, 0, resultNum.length, tempNum.data, 0, tempNum.length, wkspace, 0);
|
|
resultNum.length += tempNum.length;
|
|
uint [] t = wkspace;
|
|
wkspace = resultNum.data;
|
|
resultNum.data = t;
|
|
|
|
BarrettReduction (resultNum);
|
|
}
|
|
|
|
Kernel.SquarePositive (tempNum, ref wkspace);
|
|
BarrettReduction (tempNum);
|
|
|
|
if (tempNum == 1) {
|
|
return resultNum;
|
|
}
|
|
}
|
|
|
|
return resultNum;
|
|
}
|
|
|
|
private BigInteger OddPow (BigInteger b, BigInteger exp)
|
|
{
|
|
BigInteger resultNum = new BigInteger (Montgomery.ToMont (1, mod), mod.length << 1);
|
|
BigInteger tempNum = new BigInteger (Montgomery.ToMont (b, mod), mod.length << 1); // ensures (tempNum * tempNum) < b^ (2k)
|
|
uint mPrime = Montgomery.Inverse (mod.data [0]);
|
|
uint totalBits = (uint)exp.BitCount ();
|
|
|
|
uint [] wkspace = new uint [mod.length << 1];
|
|
|
|
// perform squaring and multiply exponentiation
|
|
for (uint pos = 0; pos < totalBits; pos++) {
|
|
if (exp.TestBit (pos)) {
|
|
|
|
Array.Clear (wkspace, 0, wkspace.Length);
|
|
Kernel.Multiply (resultNum.data, 0, resultNum.length, tempNum.data, 0, tempNum.length, wkspace, 0);
|
|
resultNum.length += tempNum.length;
|
|
uint [] t = wkspace;
|
|
wkspace = resultNum.data;
|
|
resultNum.data = t;
|
|
|
|
Montgomery.Reduce (resultNum, mod, mPrime);
|
|
}
|
|
|
|
// the value of tempNum is required in the last loop
|
|
if (pos < totalBits - 1) {
|
|
Kernel.SquarePositive (tempNum, ref wkspace);
|
|
Montgomery.Reduce (tempNum, mod, mPrime);
|
|
}
|
|
}
|
|
|
|
Montgomery.Reduce (resultNum, mod, mPrime);
|
|
return resultNum;
|
|
}
|
|
#endif
|
|
#region Pow Small Base
|
|
|
|
// TODO: Make tests for this, not really needed b/c prime stuff
|
|
// checks it, but still would be nice
|
|
#if !INSIDE_CORLIB
|
|
[CLSCompliant (false)]
|
|
#endif
|
|
#if true
|
|
public BigInteger Pow (uint b, BigInteger exp)
|
|
{
|
|
return Pow (new BigInteger (b), exp);
|
|
}
|
|
#else
|
|
public BigInteger Pow (uint b, BigInteger exp)
|
|
{
|
|
// if (b != 2) {
|
|
if ((mod.data [0] & 1) == 1)
|
|
return OddPow (b, exp);
|
|
else
|
|
return EvenPow (b, exp);
|
|
/* buggy in some cases (like the well tested primes)
|
|
} else {
|
|
if ((mod.data [0] & 1) == 1)
|
|
return OddModTwoPow (exp);
|
|
else
|
|
return EvenModTwoPow (exp);
|
|
}*/
|
|
}
|
|
|
|
private unsafe BigInteger OddPow (uint b, BigInteger exp)
|
|
{
|
|
exp.Normalize ();
|
|
uint [] wkspace = new uint [mod.length << 1 + 1];
|
|
|
|
BigInteger resultNum = Montgomery.ToMont ((BigInteger)b, this.mod);
|
|
resultNum = new BigInteger (resultNum, mod.length << 1 +1);
|
|
|
|
uint mPrime = Montgomery.Inverse (mod.data [0]);
|
|
|
|
int bc = exp.BitCount () - 2;
|
|
uint pos = (bc > 1 ? (uint) bc : 1);
|
|
|
|
//
|
|
// We know that the first itr will make the val b
|
|
//
|
|
|
|
do {
|
|
//
|
|
// r = r ^ 2 % m
|
|
//
|
|
Kernel.SquarePositive (resultNum, ref wkspace);
|
|
resultNum = Montgomery.Reduce (resultNum, mod, mPrime);
|
|
|
|
if (exp.TestBit (pos)) {
|
|
|
|
//
|
|
// r = r * b % m
|
|
//
|
|
|
|
// TODO: Is Unsafe really speeding things up?
|
|
fixed (uint* u = resultNum.data) {
|
|
|
|
uint i = 0;
|
|
ulong mc = 0;
|
|
|
|
do {
|
|
mc += (ulong)u [i] * (ulong)b;
|
|
u [i] = (uint)mc;
|
|
mc >>= 32;
|
|
} while (++i < resultNum.length);
|
|
|
|
if (resultNum.length < mod.length) {
|
|
if (mc != 0) {
|
|
u [i] = (uint)mc;
|
|
resultNum.length++;
|
|
while (resultNum >= mod)
|
|
Kernel.MinusEq (resultNum, mod);
|
|
}
|
|
} else if (mc != 0) {
|
|
|
|
//
|
|
// First, we estimate the quotient by dividing
|
|
// the first part of each of the numbers. Then
|
|
// we correct this, if necessary, with a subtraction.
|
|
//
|
|
|
|
uint cc = (uint)mc;
|
|
|
|
// We would rather have this estimate overshoot,
|
|
// so we add one to the divisor
|
|
uint divEstimate;
|
|
if (mod.data [mod.length - 1] < UInt32.MaxValue) {
|
|
divEstimate = (uint) ((((ulong)cc << 32) | (ulong) u [i -1]) /
|
|
(mod.data [mod.length-1] + 1));
|
|
}
|
|
else {
|
|
// guess but don't divide by 0
|
|
divEstimate = (uint) ((((ulong)cc << 32) | (ulong) u [i -1]) /
|
|
(mod.data [mod.length-1]));
|
|
}
|
|
|
|
uint t;
|
|
|
|
i = 0;
|
|
mc = 0;
|
|
do {
|
|
mc += (ulong)mod.data [i] * (ulong)divEstimate;
|
|
t = u [i];
|
|
u [i] -= (uint)mc;
|
|
mc >>= 32;
|
|
if (u [i] > t) mc++;
|
|
i++;
|
|
} while (i < resultNum.length);
|
|
cc -= (uint)mc;
|
|
|
|
if (cc != 0) {
|
|
|
|
uint sc = 0, j = 0;
|
|
uint [] s = mod.data;
|
|
do {
|
|
uint a = s [j];
|
|
if (((a += sc) < sc) | ((u [j] -= a) > ~a)) sc = 1;
|
|
else sc = 0;
|
|
j++;
|
|
} while (j < resultNum.length);
|
|
cc -= sc;
|
|
}
|
|
while (resultNum >= mod)
|
|
Kernel.MinusEq (resultNum, mod);
|
|
} else {
|
|
while (resultNum >= mod)
|
|
Kernel.MinusEq (resultNum, mod);
|
|
}
|
|
}
|
|
}
|
|
} while (pos-- > 0);
|
|
|
|
resultNum = Montgomery.Reduce (resultNum, mod, mPrime);
|
|
return resultNum;
|
|
|
|
}
|
|
|
|
private unsafe BigInteger EvenPow (uint b, BigInteger exp)
|
|
{
|
|
exp.Normalize ();
|
|
uint [] wkspace = new uint [mod.length << 1 + 1];
|
|
BigInteger resultNum = new BigInteger ((BigInteger)b, mod.length << 1 + 1);
|
|
|
|
uint pos = (uint)exp.BitCount () - 2;
|
|
|
|
//
|
|
// We know that the first itr will make the val b
|
|
//
|
|
|
|
do {
|
|
//
|
|
// r = r ^ 2 % m
|
|
//
|
|
Kernel.SquarePositive (resultNum, ref wkspace);
|
|
if (!(resultNum.length < mod.length))
|
|
BarrettReduction (resultNum);
|
|
|
|
if (exp.TestBit (pos)) {
|
|
|
|
//
|
|
// r = r * b % m
|
|
//
|
|
|
|
// TODO: Is Unsafe really speeding things up?
|
|
fixed (uint* u = resultNum.data) {
|
|
|
|
uint i = 0;
|
|
ulong mc = 0;
|
|
|
|
do {
|
|
mc += (ulong)u [i] * (ulong)b;
|
|
u [i] = (uint)mc;
|
|
mc >>= 32;
|
|
} while (++i < resultNum.length);
|
|
|
|
if (resultNum.length < mod.length) {
|
|
if (mc != 0) {
|
|
u [i] = (uint)mc;
|
|
resultNum.length++;
|
|
while (resultNum >= mod)
|
|
Kernel.MinusEq (resultNum, mod);
|
|
}
|
|
} else if (mc != 0) {
|
|
|
|
//
|
|
// First, we estimate the quotient by dividing
|
|
// the first part of each of the numbers. Then
|
|
// we correct this, if necessary, with a subtraction.
|
|
//
|
|
|
|
uint cc = (uint)mc;
|
|
|
|
// We would rather have this estimate overshoot,
|
|
// so we add one to the divisor
|
|
uint divEstimate = (uint) ((((ulong)cc << 32) | (ulong) u [i -1]) /
|
|
(mod.data [mod.length-1] + 1));
|
|
|
|
uint t;
|
|
|
|
i = 0;
|
|
mc = 0;
|
|
do {
|
|
mc += (ulong)mod.data [i] * (ulong)divEstimate;
|
|
t = u [i];
|
|
u [i] -= (uint)mc;
|
|
mc >>= 32;
|
|
if (u [i] > t) mc++;
|
|
i++;
|
|
} while (i < resultNum.length);
|
|
cc -= (uint)mc;
|
|
|
|
if (cc != 0) {
|
|
|
|
uint sc = 0, j = 0;
|
|
uint [] s = mod.data;
|
|
do {
|
|
uint a = s [j];
|
|
if (((a += sc) < sc) | ((u [j] -= a) > ~a)) sc = 1;
|
|
else sc = 0;
|
|
j++;
|
|
} while (j < resultNum.length);
|
|
cc -= sc;
|
|
}
|
|
while (resultNum >= mod)
|
|
Kernel.MinusEq (resultNum, mod);
|
|
} else {
|
|
while (resultNum >= mod)
|
|
Kernel.MinusEq (resultNum, mod);
|
|
}
|
|
}
|
|
}
|
|
} while (pos-- > 0);
|
|
|
|
return resultNum;
|
|
}
|
|
#endif
|
|
/* known to be buggy in some cases */
|
|
#if false
|
|
private unsafe BigInteger EvenModTwoPow (BigInteger exp)
|
|
{
|
|
exp.Normalize ();
|
|
uint [] wkspace = new uint [mod.length << 1 + 1];
|
|
|
|
BigInteger resultNum = new BigInteger (2, mod.length << 1 +1);
|
|
|
|
uint value = exp.data [exp.length - 1];
|
|
uint mask = 0x80000000;
|
|
|
|
// Find the first bit of the exponent
|
|
while ((value & mask) == 0)
|
|
mask >>= 1;
|
|
|
|
//
|
|
// We know that the first itr will make the val 2,
|
|
// so eat one bit of the exponent
|
|
//
|
|
mask >>= 1;
|
|
|
|
uint wPos = exp.length - 1;
|
|
|
|
do {
|
|
value = exp.data [wPos];
|
|
do {
|
|
Kernel.SquarePositive (resultNum, ref wkspace);
|
|
if (resultNum.length >= mod.length)
|
|
BarrettReduction (resultNum);
|
|
|
|
if ((value & mask) != 0) {
|
|
//
|
|
// resultNum = (resultNum * 2) % mod
|
|
//
|
|
|
|
fixed (uint* u = resultNum.data) {
|
|
//
|
|
// Double
|
|
//
|
|
uint* uu = u;
|
|
uint* uuE = u + resultNum.length;
|
|
uint x, carry = 0;
|
|
while (uu < uuE) {
|
|
x = *uu;
|
|
*uu = (x << 1) | carry;
|
|
carry = x >> (32 - 1);
|
|
uu++;
|
|
}
|
|
|
|
// subtraction inlined because we know it is square
|
|
if (carry != 0 || resultNum >= mod) {
|
|
uu = u;
|
|
uint c = 0;
|
|
uint [] s = mod.data;
|
|
uint i = 0;
|
|
do {
|
|
uint a = s [i];
|
|
if (((a += c) < c) | ((* (uu++) -= a) > ~a))
|
|
c = 1;
|
|
else
|
|
c = 0;
|
|
i++;
|
|
} while (uu < uuE);
|
|
}
|
|
}
|
|
}
|
|
} while ((mask >>= 1) > 0);
|
|
mask = 0x80000000;
|
|
} while (wPos-- > 0);
|
|
|
|
return resultNum;
|
|
}
|
|
|
|
private unsafe BigInteger OddModTwoPow (BigInteger exp)
|
|
{
|
|
|
|
uint [] wkspace = new uint [mod.length << 1 + 1];
|
|
|
|
BigInteger resultNum = Montgomery.ToMont ((BigInteger)2, this.mod);
|
|
resultNum = new BigInteger (resultNum, mod.length << 1 +1);
|
|
|
|
uint mPrime = Montgomery.Inverse (mod.data [0]);
|
|
|
|
//
|
|
// TODO: eat small bits, the ones we can do with no modular reduction
|
|
//
|
|
uint pos = (uint)exp.BitCount () - 2;
|
|
|
|
do {
|
|
Kernel.SquarePositive (resultNum, ref wkspace);
|
|
resultNum = Montgomery.Reduce (resultNum, mod, mPrime);
|
|
|
|
if (exp.TestBit (pos)) {
|
|
//
|
|
// resultNum = (resultNum * 2) % mod
|
|
//
|
|
|
|
fixed (uint* u = resultNum.data) {
|
|
//
|
|
// Double
|
|
//
|
|
uint* uu = u;
|
|
uint* uuE = u + resultNum.length;
|
|
uint x, carry = 0;
|
|
while (uu < uuE) {
|
|
x = *uu;
|
|
*uu = (x << 1) | carry;
|
|
carry = x >> (32 - 1);
|
|
uu++;
|
|
}
|
|
|
|
// subtraction inlined because we know it is square
|
|
if (carry != 0 || resultNum >= mod) {
|
|
fixed (uint* s = mod.data) {
|
|
uu = u;
|
|
uint c = 0;
|
|
uint* ss = s;
|
|
do {
|
|
uint a = *ss++;
|
|
if (((a += c) < c) | ((* (uu++) -= a) > ~a))
|
|
c = 1;
|
|
else
|
|
c = 0;
|
|
} while (uu < uuE);
|
|
}
|
|
}
|
|
}
|
|
}
|
|
} while (pos-- > 0);
|
|
|
|
resultNum = Montgomery.Reduce (resultNum, mod, mPrime);
|
|
return resultNum;
|
|
}
|
|
#endif
|
|
#endregion
|
|
}
|
|
|
|
/// <summary>
|
|
/// Low level functions for the BigInteger
|
|
/// </summary>
|
|
private sealed class Kernel {
|
|
|
|
#region Addition/Subtraction
|
|
|
|
/// <summary>
|
|
/// Adds two numbers with the same sign.
|
|
/// </summary>
|
|
/// <param name="bi1">A BigInteger</param>
|
|
/// <param name="bi2">A BigInteger</param>
|
|
/// <returns>bi1 + bi2</returns>
|
|
public static BigInteger AddSameSign (BigInteger bi1, BigInteger bi2)
|
|
{
|
|
uint [] x, y;
|
|
uint yMax, xMax, i = 0;
|
|
|
|
// x should be bigger
|
|
if (bi1.length < bi2.length) {
|
|
x = bi2.data;
|
|
xMax = bi2.length;
|
|
y = bi1.data;
|
|
yMax = bi1.length;
|
|
} else {
|
|
x = bi1.data;
|
|
xMax = bi1.length;
|
|
y = bi2.data;
|
|
yMax = bi2.length;
|
|
}
|
|
|
|
BigInteger result = new BigInteger (Sign.Positive, xMax + 1);
|
|
|
|
uint [] r = result.data;
|
|
|
|
ulong sum = 0;
|
|
|
|
// Add common parts of both numbers
|
|
do {
|
|
sum = ((ulong)x [i]) + ((ulong)y [i]) + sum;
|
|
r [i] = (uint)sum;
|
|
sum >>= 32;
|
|
} while (++i < yMax);
|
|
|
|
// Copy remainder of longer number while carry propagation is required
|
|
bool carry = (sum != 0);
|
|
|
|
if (carry) {
|
|
|
|
if (i < xMax) {
|
|
do
|
|
carry = ((r [i] = x [i] + 1) == 0);
|
|
while (++i < xMax && carry);
|
|
}
|
|
|
|
if (carry) {
|
|
r [i] = 1;
|
|
result.length = ++i;
|
|
return result;
|
|
}
|
|
}
|
|
|
|
// Copy the rest
|
|
if (i < xMax) {
|
|
do
|
|
r [i] = x [i];
|
|
while (++i < xMax);
|
|
}
|
|
|
|
result.Normalize ();
|
|
return result;
|
|
}
|
|
|
|
public static BigInteger Subtract (BigInteger big, BigInteger small)
|
|
{
|
|
BigInteger result = new BigInteger (Sign.Positive, big.length);
|
|
|
|
uint [] r = result.data, b = big.data, s = small.data;
|
|
uint i = 0, c = 0;
|
|
|
|
do {
|
|
|
|
uint x = s [i];
|
|
if (((x += c) < c) | ((r [i] = b [i] - x) > ~x))
|
|
c = 1;
|
|
else
|
|
c = 0;
|
|
|
|
} while (++i < small.length);
|
|
|
|
if (i == big.length) goto fixup;
|
|
|
|
if (c == 1) {
|
|
do
|
|
r [i] = b [i] - 1;
|
|
while (b [i++] == 0 && i < big.length);
|
|
|
|
if (i == big.length) goto fixup;
|
|
}
|
|
|
|
do
|
|
r [i] = b [i];
|
|
while (++i < big.length);
|
|
|
|
fixup:
|
|
|
|
result.Normalize ();
|
|
return result;
|
|
}
|
|
|
|
public static void MinusEq (BigInteger big, BigInteger small)
|
|
{
|
|
uint [] b = big.data, s = small.data;
|
|
uint i = 0, c = 0;
|
|
|
|
do {
|
|
uint x = s [i];
|
|
if (((x += c) < c) | ((b [i] -= x) > ~x))
|
|
c = 1;
|
|
else
|
|
c = 0;
|
|
} while (++i < small.length);
|
|
|
|
if (i == big.length) goto fixup;
|
|
|
|
if (c == 1) {
|
|
do
|
|
b [i]--;
|
|
while (b [i++] == 0 && i < big.length);
|
|
}
|
|
|
|
fixup:
|
|
|
|
// Normalize length
|
|
while (big.length > 0 && big.data [big.length-1] == 0) big.length--;
|
|
|
|
// Check for zero
|
|
if (big.length == 0)
|
|
big.length++;
|
|
|
|
}
|
|
|
|
public static void PlusEq (BigInteger bi1, BigInteger bi2)
|
|
{
|
|
uint [] x, y;
|
|
uint yMax, xMax, i = 0;
|
|
bool flag = false;
|
|
|
|
// x should be bigger
|
|
if (bi1.length < bi2.length){
|
|
flag = true;
|
|
x = bi2.data;
|
|
xMax = bi2.length;
|
|
y = bi1.data;
|
|
yMax = bi1.length;
|
|
} else {
|
|
x = bi1.data;
|
|
xMax = bi1.length;
|
|
y = bi2.data;
|
|
yMax = bi2.length;
|
|
}
|
|
|
|
uint [] r = bi1.data;
|
|
|
|
ulong sum = 0;
|
|
|
|
// Add common parts of both numbers
|
|
do {
|
|
sum += ((ulong)x [i]) + ((ulong)y [i]);
|
|
r [i] = (uint)sum;
|
|
sum >>= 32;
|
|
} while (++i < yMax);
|
|
|
|
// Copy remainder of longer number while carry propagation is required
|
|
bool carry = (sum != 0);
|
|
|
|
if (carry){
|
|
|
|
if (i < xMax) {
|
|
do
|
|
carry = ((r [i] = x [i] + 1) == 0);
|
|
while (++i < xMax && carry);
|
|
}
|
|
|
|
if (carry) {
|
|
r [i] = 1;
|
|
bi1.length = ++i;
|
|
return;
|
|
}
|
|
}
|
|
|
|
// Copy the rest
|
|
if (flag && i < xMax - 1) {
|
|
do
|
|
r [i] = x [i];
|
|
while (++i < xMax);
|
|
}
|
|
|
|
bi1.length = xMax + 1;
|
|
bi1.Normalize ();
|
|
}
|
|
|
|
#endregion
|
|
|
|
#region Compare
|
|
|
|
/// <summary>
|
|
/// Compares two BigInteger
|
|
/// </summary>
|
|
/// <param name="bi1">A BigInteger</param>
|
|
/// <param name="bi2">A BigInteger</param>
|
|
/// <returns>The sign of bi1 - bi2</returns>
|
|
public static Sign Compare (BigInteger bi1, BigInteger bi2)
|
|
{
|
|
//
|
|
// Step 1. Compare the lengths
|
|
//
|
|
uint l1 = bi1.length, l2 = bi2.length;
|
|
|
|
while (l1 > 0 && bi1.data [l1-1] == 0) l1--;
|
|
while (l2 > 0 && bi2.data [l2-1] == 0) l2--;
|
|
|
|
if (l1 == 0 && l2 == 0) return Sign.Zero;
|
|
|
|
// bi1 len < bi2 len
|
|
if (l1 < l2) return Sign.Negative;
|
|
// bi1 len > bi2 len
|
|
else if (l1 > l2) return Sign.Positive;
|
|
|
|
//
|
|
// Step 2. Compare the bits
|
|
//
|
|
|
|
uint pos = l1 - 1;
|
|
|
|
while (pos != 0 && bi1.data [pos] == bi2.data [pos]) pos--;
|
|
|
|
if (bi1.data [pos] < bi2.data [pos])
|
|
return Sign.Negative;
|
|
else if (bi1.data [pos] > bi2.data [pos])
|
|
return Sign.Positive;
|
|
else
|
|
return Sign.Zero;
|
|
}
|
|
|
|
#endregion
|
|
|
|
#region Division
|
|
|
|
#region Dword
|
|
|
|
/// <summary>
|
|
/// Performs n / d and n % d in one operation.
|
|
/// </summary>
|
|
/// <param name="n">A BigInteger, upon exit this will hold n / d</param>
|
|
/// <param name="d">The divisor</param>
|
|
/// <returns>n % d</returns>
|
|
public static uint SingleByteDivideInPlace (BigInteger n, uint d)
|
|
{
|
|
ulong r = 0;
|
|
uint i = n.length;
|
|
|
|
while (i-- > 0) {
|
|
r <<= 32;
|
|
r |= n.data [i];
|
|
n.data [i] = (uint)(r / d);
|
|
r %= d;
|
|
}
|
|
n.Normalize ();
|
|
|
|
return (uint)r;
|
|
}
|
|
|
|
public static uint DwordMod (BigInteger n, uint d)
|
|
{
|
|
ulong r = 0;
|
|
uint i = n.length;
|
|
|
|
while (i-- > 0) {
|
|
r <<= 32;
|
|
r |= n.data [i];
|
|
r %= d;
|
|
}
|
|
|
|
return (uint)r;
|
|
}
|
|
|
|
public static BigInteger DwordDiv (BigInteger n, uint d)
|
|
{
|
|
BigInteger ret = new BigInteger (Sign.Positive, n.length);
|
|
|
|
ulong r = 0;
|
|
uint i = n.length;
|
|
|
|
while (i-- > 0) {
|
|
r <<= 32;
|
|
r |= n.data [i];
|
|
ret.data [i] = (uint)(r / d);
|
|
r %= d;
|
|
}
|
|
ret.Normalize ();
|
|
|
|
return ret;
|
|
}
|
|
|
|
public static BigInteger [] DwordDivMod (BigInteger n, uint d)
|
|
{
|
|
BigInteger ret = new BigInteger (Sign.Positive , n.length);
|
|
|
|
ulong r = 0;
|
|
uint i = n.length;
|
|
|
|
while (i-- > 0) {
|
|
r <<= 32;
|
|
r |= n.data [i];
|
|
ret.data [i] = (uint)(r / d);
|
|
r %= d;
|
|
}
|
|
ret.Normalize ();
|
|
|
|
BigInteger rem = (uint)r;
|
|
|
|
return new BigInteger [] {ret, rem};
|
|
}
|
|
|
|
#endregion
|
|
|
|
#region BigNum
|
|
|
|
public static BigInteger [] multiByteDivide (BigInteger bi1, BigInteger bi2)
|
|
{
|
|
if (Kernel.Compare (bi1, bi2) == Sign.Negative)
|
|
return new BigInteger [2] { 0, new BigInteger (bi1) };
|
|
|
|
bi1.Normalize (); bi2.Normalize ();
|
|
|
|
if (bi2.length == 1)
|
|
return DwordDivMod (bi1, bi2.data [0]);
|
|
|
|
uint remainderLen = bi1.length + 1;
|
|
int divisorLen = (int)bi2.length + 1;
|
|
|
|
uint mask = 0x80000000;
|
|
uint val = bi2.data [bi2.length - 1];
|
|
int shift = 0;
|
|
int resultPos = (int)bi1.length - (int)bi2.length;
|
|
|
|
while (mask != 0 && (val & mask) == 0) {
|
|
shift++; mask >>= 1;
|
|
}
|
|
|
|
BigInteger quot = new BigInteger (Sign.Positive, bi1.length - bi2.length + 1);
|
|
BigInteger rem = (bi1 << shift);
|
|
|
|
uint [] remainder = rem.data;
|
|
|
|
bi2 = bi2 << shift;
|
|
|
|
int j = (int)(remainderLen - bi2.length);
|
|
int pos = (int)remainderLen - 1;
|
|
|
|
uint firstDivisorByte = bi2.data [bi2.length-1];
|
|
ulong secondDivisorByte = bi2.data [bi2.length-2];
|
|
|
|
while (j > 0) {
|
|
ulong dividend = ((ulong)remainder [pos] << 32) + (ulong)remainder [pos-1];
|
|
|
|
ulong q_hat = dividend / (ulong)firstDivisorByte;
|
|
ulong r_hat = dividend % (ulong)firstDivisorByte;
|
|
|
|
do {
|
|
|
|
if (q_hat == 0x100000000 ||
|
|
(q_hat * secondDivisorByte) > ((r_hat << 32) + remainder [pos-2])) {
|
|
q_hat--;
|
|
r_hat += (ulong)firstDivisorByte;
|
|
|
|
if (r_hat < 0x100000000)
|
|
continue;
|
|
}
|
|
break;
|
|
} while (true);
|
|
|
|
//
|
|
// At this point, q_hat is either exact, or one too large
|
|
// (more likely to be exact) so, we attempt to multiply the
|
|
// divisor by q_hat, if we get a borrow, we just subtract
|
|
// one from q_hat and add the divisor back.
|
|
//
|
|
|
|
uint t;
|
|
uint dPos = 0;
|
|
int nPos = pos - divisorLen + 1;
|
|
ulong mc = 0;
|
|
uint uint_q_hat = (uint)q_hat;
|
|
do {
|
|
mc += (ulong)bi2.data [dPos] * (ulong)uint_q_hat;
|
|
t = remainder [nPos];
|
|
remainder [nPos] -= (uint)mc;
|
|
mc >>= 32;
|
|
if (remainder [nPos] > t) mc++;
|
|
dPos++; nPos++;
|
|
} while (dPos < divisorLen);
|
|
|
|
nPos = pos - divisorLen + 1;
|
|
dPos = 0;
|
|
|
|
// Overestimate
|
|
if (mc != 0) {
|
|
uint_q_hat--;
|
|
ulong sum = 0;
|
|
|
|
do {
|
|
sum = ((ulong)remainder [nPos]) + ((ulong)bi2.data [dPos]) + sum;
|
|
remainder [nPos] = (uint)sum;
|
|
sum >>= 32;
|
|
dPos++; nPos++;
|
|
} while (dPos < divisorLen);
|
|
|
|
}
|
|
|
|
quot.data [resultPos--] = (uint)uint_q_hat;
|
|
|
|
pos--;
|
|
j--;
|
|
}
|
|
|
|
quot.Normalize ();
|
|
rem.Normalize ();
|
|
BigInteger [] ret = new BigInteger [2] { quot, rem };
|
|
|
|
if (shift != 0)
|
|
ret [1] >>= shift;
|
|
|
|
return ret;
|
|
}
|
|
|
|
#endregion
|
|
|
|
#endregion
|
|
|
|
#region Shift
|
|
public static BigInteger LeftShift (BigInteger bi, int n)
|
|
{
|
|
if (n == 0) return new BigInteger (bi, bi.length + 1);
|
|
|
|
int w = n >> 5;
|
|
n &= ((1 << 5) - 1);
|
|
|
|
BigInteger ret = new BigInteger (Sign.Positive, bi.length + 1 + (uint)w);
|
|
|
|
uint i = 0, l = bi.length;
|
|
if (n != 0) {
|
|
uint x, carry = 0;
|
|
while (i < l) {
|
|
x = bi.data [i];
|
|
ret.data [i + w] = (x << n) | carry;
|
|
carry = x >> (32 - n);
|
|
i++;
|
|
}
|
|
ret.data [i + w] = carry;
|
|
} else {
|
|
while (i < l) {
|
|
ret.data [i + w] = bi.data [i];
|
|
i++;
|
|
}
|
|
}
|
|
|
|
ret.Normalize ();
|
|
return ret;
|
|
}
|
|
|
|
public static BigInteger RightShift (BigInteger bi, int n)
|
|
{
|
|
if (n == 0) return new BigInteger (bi);
|
|
|
|
int w = n >> 5;
|
|
int s = n & ((1 << 5) - 1);
|
|
|
|
BigInteger ret = new BigInteger (Sign.Positive, bi.length - (uint)w + 1);
|
|
uint l = (uint)ret.data.Length - 1;
|
|
|
|
if (s != 0) {
|
|
|
|
uint x, carry = 0;
|
|
|
|
while (l-- > 0) {
|
|
x = bi.data [l + w];
|
|
ret.data [l] = (x >> n) | carry;
|
|
carry = x << (32 - n);
|
|
}
|
|
} else {
|
|
while (l-- > 0)
|
|
ret.data [l] = bi.data [l + w];
|
|
|
|
}
|
|
ret.Normalize ();
|
|
return ret;
|
|
}
|
|
|
|
#endregion
|
|
|
|
#region Multiply
|
|
|
|
public static BigInteger MultiplyByDword (BigInteger n, uint f)
|
|
{
|
|
BigInteger ret = new BigInteger (Sign.Positive, n.length + 1);
|
|
|
|
uint i = 0;
|
|
ulong c = 0;
|
|
|
|
do {
|
|
c += (ulong)n.data [i] * (ulong)f;
|
|
ret.data [i] = (uint)c;
|
|
c >>= 32;
|
|
} while (++i < n.length);
|
|
ret.data [i] = (uint)c;
|
|
ret.Normalize ();
|
|
return ret;
|
|
|
|
}
|
|
|
|
/// <summary>
|
|
/// Multiplies the data in x [xOffset:xOffset+xLen] by
|
|
/// y [yOffset:yOffset+yLen] and puts it into
|
|
/// d [dOffset:dOffset+xLen+yLen].
|
|
/// </summary>
|
|
/// <remarks>
|
|
/// This code is unsafe! It is the caller's responsibility to make
|
|
/// sure that it is safe to access x [xOffset:xOffset+xLen],
|
|
/// y [yOffset:yOffset+yLen], and d [dOffset:dOffset+xLen+yLen].
|
|
/// </remarks>
|
|
public static unsafe void Multiply (uint [] x, uint xOffset, uint xLen, uint [] y, uint yOffset, uint yLen, uint [] d, uint dOffset)
|
|
{
|
|
fixed (uint* xx = x, yy = y, dd = d) {
|
|
uint* xP = xx + xOffset,
|
|
xE = xP + xLen,
|
|
yB = yy + yOffset,
|
|
yE = yB + yLen,
|
|
dB = dd + dOffset;
|
|
|
|
for (; xP < xE; xP++, dB++) {
|
|
|
|
if (*xP == 0) continue;
|
|
|
|
ulong mcarry = 0;
|
|
|
|
uint* dP = dB;
|
|
for (uint* yP = yB; yP < yE; yP++, dP++) {
|
|
mcarry += ((ulong)*xP * (ulong)*yP) + (ulong)*dP;
|
|
|
|
*dP = (uint)mcarry;
|
|
mcarry >>= 32;
|
|
}
|
|
|
|
if (mcarry != 0)
|
|
*dP = (uint)mcarry;
|
|
}
|
|
}
|
|
}
|
|
|
|
/// <summary>
|
|
/// Multiplies the data in x [xOffset:xOffset+xLen] by
|
|
/// y [yOffset:yOffset+yLen] and puts the low mod words into
|
|
/// d [dOffset:dOffset+mod].
|
|
/// </summary>
|
|
/// <remarks>
|
|
/// This code is unsafe! It is the caller's responsibility to make
|
|
/// sure that it is safe to access x [xOffset:xOffset+xLen],
|
|
/// y [yOffset:yOffset+yLen], and d [dOffset:dOffset+mod].
|
|
/// </remarks>
|
|
public static unsafe void MultiplyMod2p32pmod (uint [] x, int xOffset, int xLen, uint [] y, int yOffest, int yLen, uint [] d, int dOffset, int mod)
|
|
{
|
|
fixed (uint* xx = x, yy = y, dd = d) {
|
|
uint* xP = xx + xOffset,
|
|
xE = xP + xLen,
|
|
yB = yy + yOffest,
|
|
yE = yB + yLen,
|
|
dB = dd + dOffset,
|
|
dE = dB + mod;
|
|
|
|
for (; xP < xE; xP++, dB++) {
|
|
|
|
if (*xP == 0) continue;
|
|
|
|
ulong mcarry = 0;
|
|
uint* dP = dB;
|
|
for (uint* yP = yB; yP < yE && dP < dE; yP++, dP++) {
|
|
mcarry += ((ulong)*xP * (ulong)*yP) + (ulong)*dP;
|
|
|
|
*dP = (uint)mcarry;
|
|
mcarry >>= 32;
|
|
}
|
|
|
|
if (mcarry != 0 && dP < dE)
|
|
*dP = (uint)mcarry;
|
|
}
|
|
}
|
|
}
|
|
|
|
public static unsafe void SquarePositive (BigInteger bi, ref uint [] wkSpace)
|
|
{
|
|
uint [] t = wkSpace;
|
|
wkSpace = bi.data;
|
|
uint [] d = bi.data;
|
|
uint dl = bi.length;
|
|
bi.data = t;
|
|
|
|
fixed (uint* dd = d, tt = t) {
|
|
|
|
uint* ttE = tt + t.Length;
|
|
// Clear the dest
|
|
for (uint* ttt = tt; ttt < ttE; ttt++)
|
|
*ttt = 0;
|
|
|
|
uint* dP = dd, tP = tt;
|
|
|
|
for (uint i = 0; i < dl; i++, dP++) {
|
|
if (*dP == 0)
|
|
continue;
|
|
|
|
ulong mcarry = 0;
|
|
uint bi1val = *dP;
|
|
|
|
uint* dP2 = dP + 1, tP2 = tP + 2*i + 1;
|
|
|
|
for (uint j = i + 1; j < dl; j++, tP2++, dP2++) {
|
|
// k = i + j
|
|
mcarry += ((ulong)bi1val * (ulong)*dP2) + *tP2;
|
|
|
|
*tP2 = (uint)mcarry;
|
|
mcarry >>= 32;
|
|
}
|
|
|
|
if (mcarry != 0)
|
|
*tP2 = (uint)mcarry;
|
|
}
|
|
|
|
// Double t. Inlined for speed.
|
|
|
|
tP = tt;
|
|
|
|
uint x, carry = 0;
|
|
while (tP < ttE) {
|
|
x = *tP;
|
|
*tP = (x << 1) | carry;
|
|
carry = x >> (32 - 1);
|
|
tP++;
|
|
}
|
|
if (carry != 0) *tP = carry;
|
|
|
|
// Add in the diagnals
|
|
|
|
dP = dd;
|
|
tP = tt;
|
|
for (uint* dE = dP + dl; (dP < dE); dP++, tP++) {
|
|
ulong val = (ulong)*dP * (ulong)*dP + *tP;
|
|
*tP = (uint)val;
|
|
val >>= 32;
|
|
*(++tP) += (uint)val;
|
|
if (*tP < (uint)val) {
|
|
uint* tP3 = tP;
|
|
// Account for the first carry
|
|
(*++tP3)++;
|
|
|
|
// Keep adding until no carry
|
|
while ((*tP3++) == 0)
|
|
(*tP3)++;
|
|
}
|
|
|
|
}
|
|
|
|
bi.length <<= 1;
|
|
|
|
// Normalize length
|
|
while (tt [bi.length-1] == 0 && bi.length > 1) bi.length--;
|
|
|
|
}
|
|
}
|
|
|
|
/*
|
|
* Never called in BigInteger (and part of a private class)
|
|
* public static bool Double (uint [] u, int l)
|
|
{
|
|
uint x, carry = 0;
|
|
uint i = 0;
|
|
while (i < l) {
|
|
x = u [i];
|
|
u [i] = (x << 1) | carry;
|
|
carry = x >> (32 - 1);
|
|
i++;
|
|
}
|
|
if (carry != 0) u [l] = carry;
|
|
return carry != 0;
|
|
}*/
|
|
|
|
#endregion
|
|
|
|
#region Number Theory
|
|
|
|
public static BigInteger gcd (BigInteger a, BigInteger b)
|
|
{
|
|
BigInteger x = a;
|
|
BigInteger y = b;
|
|
|
|
BigInteger g = y;
|
|
|
|
while (x.length > 1) {
|
|
g = x;
|
|
x = y % x;
|
|
y = g;
|
|
|
|
}
|
|
if (x == 0) return g;
|
|
|
|
// TODO: should we have something here if we can convert to long?
|
|
|
|
//
|
|
// Now we can just do it with single precision. I am using the binary gcd method,
|
|
// as it should be faster.
|
|
//
|
|
|
|
uint yy = x.data [0];
|
|
uint xx = y % yy;
|
|
|
|
int t = 0;
|
|
|
|
while (((xx | yy) & 1) == 0) {
|
|
xx >>= 1; yy >>= 1; t++;
|
|
}
|
|
while (xx != 0) {
|
|
while ((xx & 1) == 0) xx >>= 1;
|
|
while ((yy & 1) == 0) yy >>= 1;
|
|
if (xx >= yy)
|
|
xx = (xx - yy) >> 1;
|
|
else
|
|
yy = (yy - xx) >> 1;
|
|
}
|
|
|
|
return yy << t;
|
|
}
|
|
|
|
public static uint modInverse (BigInteger bi, uint modulus)
|
|
{
|
|
uint a = modulus, b = bi % modulus;
|
|
uint p0 = 0, p1 = 1;
|
|
|
|
while (b != 0) {
|
|
if (b == 1)
|
|
return p1;
|
|
p0 += (a / b) * p1;
|
|
a %= b;
|
|
|
|
if (a == 0)
|
|
break;
|
|
if (a == 1)
|
|
return modulus-p0;
|
|
|
|
p1 += (b / a) * p0;
|
|
b %= a;
|
|
|
|
}
|
|
return 0;
|
|
}
|
|
|
|
public static BigInteger modInverse (BigInteger bi, BigInteger modulus)
|
|
{
|
|
if (modulus.length == 1) return modInverse (bi, modulus.data [0]);
|
|
|
|
BigInteger [] p = { 0, 1 };
|
|
BigInteger [] q = new BigInteger [2]; // quotients
|
|
BigInteger [] r = { 0, 0 }; // remainders
|
|
|
|
int step = 0;
|
|
|
|
BigInteger a = modulus;
|
|
BigInteger b = bi;
|
|
|
|
ModulusRing mr = new ModulusRing (modulus);
|
|
|
|
while (b != 0) {
|
|
|
|
if (step > 1) {
|
|
|
|
BigInteger pval = mr.Difference (p [0], p [1] * q [0]);
|
|
p [0] = p [1]; p [1] = pval;
|
|
}
|
|
|
|
BigInteger [] divret = multiByteDivide (a, b);
|
|
|
|
q [0] = q [1]; q [1] = divret [0];
|
|
r [0] = r [1]; r [1] = divret [1];
|
|
a = b;
|
|
b = divret [1];
|
|
|
|
step++;
|
|
}
|
|
|
|
if (r [0] != 1)
|
|
throw (new ArithmeticException ("No inverse!"));
|
|
|
|
return mr.Difference (p [0], p [1] * q [0]);
|
|
|
|
}
|
|
#endregion
|
|
}
|
|
}
|
|
}
|