arith_uint256.h raw
1 // Copyright (c) 2009-2010 Satoshi Nakamoto
2 // Copyright (c) 2009-present The Bitcoin Core 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 BITCOIN_ARITH_UINT256_H
7 #define BITCOIN_ARITH_UINT256_H
8
9 #include <compare>
10 #include <cstdint>
11 #include <cstring>
12 #include <limits>
13 #include <stdexcept>
14 #include <string>
15
16 class uint256;
17
18 class uint_error : public std::runtime_error {
19 public:
20 explicit uint_error(const std::string& str) : std::runtime_error(str) {}
21 };
22
23 /** Template base class for unsigned big integers. */
24 template <unsigned int BITS>
25 class base_uint
26 {
27 protected:
28 static_assert(BITS / 32 > 0 && BITS % 32 == 0, "Template parameter BITS must be a positive multiple of 32.");
29 static constexpr int WIDTH = BITS / 32;
30 /** Big integer represented with 32-bit digits, least-significant first. */
31 uint32_t pn[WIDTH];
32
33 public:
34 constexpr base_uint()
35 {
36 for (int i = 0; i < WIDTH; i++)
37 pn[i] = 0;
38 }
39
40 base_uint(const base_uint& b) = default;
41 base_uint& operator=(const base_uint& b) = default;
42
43 constexpr base_uint(uint64_t b)
44 {
45 pn[0] = (unsigned int)b;
46 pn[1] = (unsigned int)(b >> 32);
47 for (int i = 2; i < WIDTH; i++)
48 pn[i] = 0;
49 }
50
51 base_uint operator~() const
52 {
53 base_uint ret;
54 for (int i = 0; i < WIDTH; i++)
55 ret.pn[i] = ~pn[i];
56 return ret;
57 }
58
59 base_uint operator-() const
60 {
61 base_uint ret;
62 for (int i = 0; i < WIDTH; i++)
63 ret.pn[i] = ~pn[i];
64 ++ret;
65 return ret;
66 }
67
68 double getdouble() const;
69
70 base_uint& operator=(uint64_t b)
71 {
72 pn[0] = (unsigned int)b;
73 pn[1] = (unsigned int)(b >> 32);
74 for (int i = 2; i < WIDTH; i++)
75 pn[i] = 0;
76 return *this;
77 }
78
79 base_uint& operator^=(const base_uint& b)
80 {
81 for (int i = 0; i < WIDTH; i++)
82 pn[i] ^= b.pn[i];
83 return *this;
84 }
85
86 base_uint& operator&=(const base_uint& b)
87 {
88 for (int i = 0; i < WIDTH; i++)
89 pn[i] &= b.pn[i];
90 return *this;
91 }
92
93 base_uint& operator|=(const base_uint& b)
94 {
95 for (int i = 0; i < WIDTH; i++)
96 pn[i] |= b.pn[i];
97 return *this;
98 }
99
100 base_uint& operator^=(uint64_t b)
101 {
102 pn[0] ^= (unsigned int)b;
103 pn[1] ^= (unsigned int)(b >> 32);
104 return *this;
105 }
106
107 base_uint& operator|=(uint64_t b)
108 {
109 pn[0] |= (unsigned int)b;
110 pn[1] |= (unsigned int)(b >> 32);
111 return *this;
112 }
113
114 base_uint& operator<<=(unsigned int shift);
115 base_uint& operator>>=(unsigned int shift);
116
117 base_uint& operator+=(const base_uint& b)
118 {
119 uint64_t carry = 0;
120 for (int i = 0; i < WIDTH; i++)
121 {
122 uint64_t n = carry + pn[i] + b.pn[i];
123 pn[i] = n & 0xffffffff;
124 carry = n >> 32;
125 }
126 return *this;
127 }
128
129 base_uint& operator-=(const base_uint& b)
130 {
131 *this += -b;
132 return *this;
133 }
134
135 base_uint& operator+=(uint64_t b64)
136 {
137 base_uint b;
138 b = b64;
139 *this += b;
140 return *this;
141 }
142
143 base_uint& operator-=(uint64_t b64)
144 {
145 base_uint b;
146 b = b64;
147 *this += -b;
148 return *this;
149 }
150
151 base_uint& operator*=(uint32_t b32);
152 base_uint& operator*=(const base_uint& b);
153 base_uint& operator/=(const base_uint& b);
154
155 base_uint& operator++()
156 {
157 // prefix operator
158 int i = 0;
159 while (i < WIDTH && ++pn[i] == 0)
160 i++;
161 return *this;
162 }
163
164 base_uint operator++(int)
165 {
166 // postfix operator
167 const base_uint ret = *this;
168 ++(*this);
169 return ret;
170 }
171
172 base_uint& operator--()
173 {
174 // prefix operator
175 int i = 0;
176 while (i < WIDTH && --pn[i] == std::numeric_limits<uint32_t>::max())
177 i++;
178 return *this;
179 }
180
181 base_uint operator--(int)
182 {
183 // postfix operator
184 const base_uint ret = *this;
185 --(*this);
186 return ret;
187 }
188
189 /** Numeric ordering (unlike \ref base_blob::Compare) */
190 int CompareTo(const base_uint& b) const;
191 bool EqualTo(uint64_t b) const;
192
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, const base_uint& b) { return base_uint(a) ^= b; }
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, int shift) { return base_uint(a) <<= shift; }
202 friend inline base_uint operator*(const base_uint& a, uint32_t b) { return base_uint(a) *= b; }
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 std::strong_ordering operator<=>(const base_uint& a, const base_uint& b) { return a.CompareTo(b) <=> 0; }
205 friend inline bool operator==(const base_uint& a, uint64_t b) { return a.EqualTo(b); }
206
207 /** Hex encoding of the number (with the most significant digits first). */
208 std::string GetHex() const;
209 std::string ToString() const;
210
211 unsigned int size() const
212 {
213 return sizeof(pn);
214 }
215
216 /**
217 * Returns the position of the highest bit set plus one, or zero if the
218 * value is zero.
219 */
220 unsigned int bits() const;
221
222 uint64_t GetLow64() const
223 {
224 static_assert(WIDTH >= 2, "Assertion WIDTH >= 2 failed (WIDTH = BITS / 32). BITS is a template parameter.");
225 return pn[0] | (uint64_t)pn[1] << 32;
226 }
227 };
228
229 /** 256-bit unsigned big integer. */
230 class arith_uint256 : public base_uint<256>
231 {
232 public:
233 constexpr arith_uint256() = default;
234 constexpr arith_uint256(const base_uint& b) : base_uint(b) {}
235 constexpr arith_uint256(uint64_t b) : base_uint(b) {}
236
237 /**
238 * The "compact" format is a representation of a whole
239 * number N using an unsigned 32bit number similar to a
240 * floating point format.
241 * The most significant 8 bits are the unsigned exponent of base 256.
242 * This exponent can be thought of as "number of bytes of N".
243 * The lower 23 bits are the mantissa.
244 * Bit number 24 (0x800000) represents the sign of N.
245 * N = (-1^sign) * mantissa * 256^(exponent-3)
246 *
247 * Satoshi's original implementation used BN_bn2mpi() and BN_mpi2bn().
248 * MPI uses the most significant bit of the first byte as sign.
249 * Thus 0x1234560000 is compact (0x05123456)
250 * and 0xc0de000000 is compact (0x0600c0de)
251 *
252 * Bitcoin only uses this "compact" format for encoding difficulty
253 * targets, which are unsigned 256bit quantities. Thus, all the
254 * complexities of the sign bit and using base 256 are probably an
255 * implementation accident.
256 */
257 arith_uint256& SetCompact(uint32_t nCompact, bool *pfNegative = nullptr, bool *pfOverflow = nullptr);
258 uint32_t GetCompact(bool fNegative = false) const;
259
260 friend uint256 ArithToUint256(const arith_uint256 &);
261 friend arith_uint256 UintToArith256(const uint256 &);
262 };
263
264 // Keeping the trivially copyable property is beneficial for performance
265 static_assert(std::is_trivially_copyable_v<arith_uint256>);
266
267 uint256 ArithToUint256(const arith_uint256 &);
268 arith_uint256 UintToArith256(const uint256 &);
269
270 extern template class base_uint<256>;
271
272 #endif // BITCOIN_ARITH_UINT256_H
273