arith_uint256.h raw
1 // Copyright (c) 2009-2010 Satoshi Nakamoto
2 // Copyright (c) 2009-2022 The Limenka developers
3 // Distributed under the MIT software license, see the accompanying
4 // file COPYING or http://www.opensource.org/licenses/mit-license.php.
5
6 #ifndef LIMENKA_ARITH_UINT256_H
7 #define LIMENKA_ARITH_UINT256_H
8
9 #include <cstdint>
10 #include <cstring>
11 #include <limits>
12 #include <stdexcept>
13 #include <string>
14
15 class uint256;
16
17 class uint_error : public std::runtime_error {
18 public:
19 explicit uint_error(const std::string& str) : std::runtime_error(str) {}
20 };
21
22 /** Template base class for unsigned big integers. */
23 template<unsigned int BITS>
24 class base_uint
25 {
26 protected:
27 static_assert(BITS / 32 > 0 && BITS % 32 == 0, "Template parameter BITS must be a positive multiple of 32.");
28 static constexpr int WIDTH = BITS / 32;
29 /** Big integer represented with 32-bit digits, least-significant first. */
30 uint32_t pn[WIDTH];
31 public:
32
33 base_uint()
34 {
35 for (int i = 0; i < WIDTH; i++)
36 pn[i] = 0;
37 }
38
39 base_uint(const base_uint& b) = default;
40 base_uint& operator=(const base_uint& b) = default;
41
42 base_uint(uint64_t b)
43 {
44 pn[0] = (unsigned int)b;
45 pn[1] = (unsigned int)(b >> 32);
46 for (int i = 2; i < WIDTH; i++)
47 pn[i] = 0;
48 }
49
50 base_uint operator~() const
51 {
52 base_uint ret;
53 for (int i = 0; i < WIDTH; i++)
54 ret.pn[i] = ~pn[i];
55 return ret;
56 }
57
58 base_uint operator-() const
59 {
60 base_uint ret;
61 for (int i = 0; i < WIDTH; i++)
62 ret.pn[i] = ~pn[i];
63 ++ret;
64 return ret;
65 }
66
67 double getdouble() const;
68
69 base_uint& operator=(uint64_t b)
70 {
71 pn[0] = (unsigned int)b;
72 pn[1] = (unsigned int)(b >> 32);
73 for (int i = 2; i < WIDTH; i++)
74 pn[i] = 0;
75 return *this;
76 }
77
78 base_uint& operator^=(const base_uint& b)
79 {
80 for (int i = 0; i < WIDTH; i++)
81 pn[i] ^= b.pn[i];
82 return *this;
83 }
84
85 base_uint& operator&=(const base_uint& b)
86 {
87 for (int i = 0; i < WIDTH; i++)
88 pn[i] &= b.pn[i];
89 return *this;
90 }
91
92 base_uint& operator|=(const base_uint& b)
93 {
94 for (int i = 0; i < WIDTH; i++)
95 pn[i] |= b.pn[i];
96 return *this;
97 }
98
99 base_uint& operator^=(uint64_t b)
100 {
101 pn[0] ^= (unsigned int)b;
102 pn[1] ^= (unsigned int)(b >> 32);
103 return *this;
104 }
105
106 base_uint& operator|=(uint64_t b)
107 {
108 pn[0] |= (unsigned int)b;
109 pn[1] |= (unsigned int)(b >> 32);
110 return *this;
111 }
112
113 base_uint& operator<<=(unsigned int shift);
114 base_uint& operator>>=(unsigned int shift);
115
116 base_uint& operator+=(const base_uint& b)
117 {
118 uint64_t carry = 0;
119 for (int i = 0; i < WIDTH; i++)
120 {
121 uint64_t n = carry + pn[i] + b.pn[i];
122 pn[i] = n & 0xffffffff;
123 carry = n >> 32;
124 }
125 return *this;
126 }
127
128 base_uint& operator-=(const base_uint& b)
129 {
130 *this += -b;
131 return *this;
132 }
133
134 base_uint& operator+=(uint64_t b64)
135 {
136 base_uint b;
137 b = b64;
138 *this += b;
139 return *this;
140 }
141
142 base_uint& operator-=(uint64_t b64)
143 {
144 base_uint b;
145 b = b64;
146 *this += -b;
147 return *this;
148 }
149
150 base_uint& operator*=(uint32_t b32);
151 base_uint& operator*=(const base_uint& b);
152 base_uint& operator/=(const base_uint& b);
153
154 base_uint& operator++()
155 {
156 // prefix operator
157 int i = 0;
158 while (i < WIDTH && ++pn[i] == 0)
159 i++;
160 return *this;
161 }
162
163 base_uint operator++(int)
164 {
165 // postfix operator
166 const base_uint ret = *this;
167 ++(*this);
168 return ret;
169 }
170
171 base_uint& operator--()
172 {
173 // prefix operator
174 int i = 0;
175 while (i < WIDTH && --pn[i] == std::numeric_limits<uint32_t>::max())
176 i++;
177 return *this;
178 }
179
180 base_uint operator--(int)
181 {
182 // postfix operator
183 const base_uint ret = *this;
184 --(*this);
185 return ret;
186 }
187
188 /** Numeric ordering (unlike \ref base_blob::Compare) */
189 int CompareTo(const base_uint& b) const;
190 bool EqualTo(uint64_t b) const;
191
192 friend inline base_uint operator+(const base_uint& a, const base_uint& b) { return base_uint(a) += b; }
193 friend inline base_uint operator-(const base_uint& a, const base_uint& b) { return base_uint(a) -= b; }
194 friend inline base_uint operator*(const base_uint& a, const base_uint& b) { return base_uint(a) *= b; }
195 friend inline base_uint operator/(const base_uint& a, const base_uint& b) { return base_uint(a) /= b; }
196 friend inline base_uint operator|(const base_uint& a, const base_uint& b) { return base_uint(a) |= b; }
197 friend inline base_uint operator&(const base_uint& a, const base_uint& b) { return base_uint(a) &= b; }
198 friend inline base_uint operator^(const base_uint& a, const base_uint& b) { return base_uint(a) ^= b; }
199 friend inline base_uint operator>>(const base_uint& a, int shift) { return base_uint(a) >>= shift; }
200 friend inline base_uint operator<<(const base_uint& a, int shift) { return base_uint(a) <<= shift; }
201 friend inline base_uint operator*(const base_uint& a, uint32_t b) { return base_uint(a) *= b; }
202 friend inline bool operator==(const base_uint& a, const base_uint& b) { return memcmp(a.pn, b.pn, sizeof(a.pn)) == 0; }
203 friend inline bool operator!=(const base_uint& a, const base_uint& b) { return memcmp(a.pn, b.pn, sizeof(a.pn)) != 0; }
204 friend inline bool operator>(const base_uint& a, const base_uint& b) { return a.CompareTo(b) > 0; }
205 friend inline bool operator<(const base_uint& a, const base_uint& b) { return a.CompareTo(b) < 0; }
206 friend inline bool operator>=(const base_uint& a, const base_uint& b) { return a.CompareTo(b) >= 0; }
207 friend inline bool operator<=(const base_uint& a, const base_uint& b) { return a.CompareTo(b) <= 0; }
208 friend inline bool operator==(const base_uint& a, uint64_t b) { return a.EqualTo(b); }
209 friend inline bool operator!=(const base_uint& a, uint64_t b) { return !a.EqualTo(b); }
210
211 /** Hex encoding of the number (with the most significant digits first). */
212 std::string GetHex() const;
213 std::string ToString() const;
214
215 unsigned int size() const
216 {
217 return sizeof(pn);
218 }
219
220 /**
221 * Returns the position of the highest bit set plus one, or zero if the
222 * value is zero.
223 */
224 unsigned int bits() const;
225
226 uint64_t GetLow64() const
227 {
228 static_assert(WIDTH >= 2, "Assertion WIDTH >= 2 failed (WIDTH = BITS / 32). BITS is a template parameter.");
229 return pn[0] | (uint64_t)pn[1] << 32;
230 }
231 };
232
233 /** 256-bit unsigned big integer. */
234 class arith_uint256 : public base_uint<256> {
235 public:
236 arith_uint256() = default;
237 arith_uint256(const base_uint<256>& b) : base_uint<256>(b) {}
238 arith_uint256(uint64_t b) : base_uint<256>(b) {}
239
240 /**
241 * The "compact" format is a representation of a whole
242 * number N using an unsigned 32bit number similar to a
243 * floating point format.
244 * The most significant 8 bits are the unsigned exponent of base 256.
245 * This exponent can be thought of as "number of bytes of N".
246 * The lower 23 bits are the mantissa.
247 * Bit number 24 (0x800000) represents the sign of N.
248 * N = (-1^sign) * mantissa * 256^(exponent-3)
249 *
250 * Satoshi's original implementation used BN_bn2mpi() and BN_mpi2bn().
251 * MPI uses the most significant bit of the first byte as sign.
252 * Thus 0x1234560000 is compact (0x05123456)
253 * and 0xc0de000000 is compact (0x0600c0de)
254 *
255 * Limenka only uses this "compact" format for encoding difficulty
256 * targets, which are unsigned 256bit quantities. Thus, all the
257 * complexities of the sign bit and using base 256 are probably an
258 * implementation accident.
259 */
260 arith_uint256& SetCompact(uint32_t nCompact, bool *pfNegative = nullptr, bool *pfOverflow = nullptr);
261 uint32_t GetCompact(bool fNegative = false) const;
262
263 friend uint256 ArithToUint256(const arith_uint256 &);
264 friend arith_uint256 UintToArith256(const uint256 &);
265 };
266
267 // Keeping the trivially copyable property is beneficial for performance
268 static_assert(std::is_trivially_copyable_v<arith_uint256>);
269
270 uint256 ArithToUint256(const arith_uint256 &);
271 arith_uint256 UintToArith256(const uint256 &);
272
273 extern template class base_uint<256>;
274
275 #endif // LIMENKA_ARITH_UINT256_H
276