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biginteger.h
1// Tencent is pleased to support the open source community by making RapidJSON available.
2//
3// Copyright (C) 2015 THL A29 Limited, a Tencent company, and Milo Yip. All rights reserved.
4//
5// Licensed under the MIT License (the "License"); you may not use this file except
6// in compliance with the License. You may obtain a copy of the License at
7//
8// http://opensource.org/licenses/MIT
9//
10// Unless required by applicable law or agreed to in writing, software distributed
11// under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR
12// CONDITIONS OF ANY KIND, either express or implied. See the License for the
13// specific language governing permissions and limitations under the License.
14
15#ifndef RAPIDJSON_BIGINTEGER_H_
16#define RAPIDJSON_BIGINTEGER_H_
17
18#include "../rapidjson.h"
19
20#if defined(_MSC_VER) && defined(_M_AMD64)
21#include <intrin.h> // for _umul128
22#pragma intrinsic(_umul128)
23#endif
24
25RAPIDJSON_NAMESPACE_BEGIN
26 namespace internal {
27
28 class BigInteger {
29 public:
30 typedef uint64_t Type;
31
32 BigInteger(const BigInteger& rhs) : count_(rhs.count_) {
33 std::memcpy(digits_, rhs.digits_, count_ * sizeof(Type));
34 }
35
36 explicit BigInteger(uint64_t u) : count_(1) {
37 digits_[0] = u;
38 }
39
40 BigInteger(const char* decimals, size_t length) : count_(1) {
41 RAPIDJSON_ASSERT(length > 0);
42 digits_[0] = 0;
43 size_t i = 0;
44 const size_t kMaxDigitPerIteration = 19; // 2^64 = 18446744073709551616 > 10^19
45 while (length >= kMaxDigitPerIteration) {
46 AppendDecimal64(decimals + i, decimals + i + kMaxDigitPerIteration);
47 length -= kMaxDigitPerIteration;
48 i += kMaxDigitPerIteration;
49 }
50
51 if (length > 0)
52 AppendDecimal64(decimals + i, decimals + i + length);
53 }
54
55 BigInteger& operator=(const BigInteger &rhs)
56 {
57 if (this != &rhs) {
58 count_ = rhs.count_;
59 std::memcpy(digits_, rhs.digits_, count_ * sizeof(Type));
60 }
61 return *this;
62 }
63
64 BigInteger& operator=(uint64_t u) {
65 digits_[0] = u;
66 count_ = 1;
67 return *this;
68 }
69
70 BigInteger& operator+=(uint64_t u) {
71 Type backup = digits_[0];
72 digits_[0] += u;
73 for (size_t i = 0; i < count_ - 1; i++) {
74 if (digits_[i] >= backup)
75 return *this; // no carry
76 backup = digits_[i + 1];
77 digits_[i + 1] += 1;
78 }
79
80 // Last carry
81 if (digits_[count_ - 1] < backup)
82 PushBack(1);
83
84 return *this;
85 }
86
87 BigInteger& operator*=(uint64_t u) {
88 if (u == 0) return *this = 0;
89 if (u == 1) return *this;
90 if (*this == 1) return *this = u;
91
92 uint64_t k = 0;
93 for (size_t i = 0; i < count_; i++) {
94 uint64_t hi;
95 digits_[i] = MulAdd64(digits_[i], u, k, &hi);
96 k = hi;
97 }
98
99 if (k > 0)
100 PushBack(k);
101
102 return *this;
103 }
104
105 BigInteger& operator*=(uint32_t u) {
106 if (u == 0) return *this = 0;
107 if (u == 1) return *this;
108 if (*this == 1) return *this = u;
109
110 uint64_t k = 0;
111 for (size_t i = 0; i < count_; i++) {
112 const uint64_t c = digits_[i] >> 32;
113 const uint64_t d = digits_[i] & 0xFFFFFFFF;
114 const uint64_t uc = u * c;
115 const uint64_t ud = u * d;
116 const uint64_t p0 = ud + k;
117 const uint64_t p1 = uc + (p0 >> 32);
118 digits_[i] = (p0 & 0xFFFFFFFF) | (p1 << 32);
119 k = p1 >> 32;
120 }
121
122 if (k > 0)
123 PushBack(k);
124
125 return *this;
126 }
127
128 BigInteger& operator<<=(size_t shift) {
129 if (IsZero() || shift == 0) return *this;
130
131 size_t offset = shift / kTypeBit;
132 size_t interShift = shift % kTypeBit;
133 RAPIDJSON_ASSERT(count_ + offset <= kCapacity);
134
135 if (interShift == 0) {
136 std::memmove(&digits_[count_ - 1 + offset], &digits_[count_ - 1], count_ * sizeof(Type));
137 count_ += offset;
138 }
139 else {
140 digits_[count_] = 0;
141 for (size_t i = count_; i > 0; i--)
142 digits_[i + offset] = (digits_[i] << interShift) | (digits_[i - 1] >> (kTypeBit - interShift));
143 digits_[offset] = digits_[0] << interShift;
144 count_ += offset;
145 if (digits_[count_])
146 count_++;
147 }
148
149 std::memset(digits_, 0, offset * sizeof(Type));
150
151 return *this;
152 }
153
154 bool operator==(const BigInteger& rhs) const {
155 return count_ == rhs.count_ && std::memcmp(digits_, rhs.digits_, count_ * sizeof(Type)) == 0;
156 }
157
158 bool operator==(const Type rhs) const {
159 return count_ == 1 && digits_[0] == rhs;
160 }
161
162 BigInteger& MultiplyPow5(unsigned exp) {
163 static const uint32_t kPow5[12] = {
164 5,
165 5 * 5,
166 5 * 5 * 5,
167 5 * 5 * 5 * 5,
168 5 * 5 * 5 * 5 * 5,
169 5 * 5 * 5 * 5 * 5 * 5,
170 5 * 5 * 5 * 5 * 5 * 5 * 5,
171 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5,
172 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5,
173 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5,
174 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5,
175 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5
176 };
177 if (exp == 0) return *this;
178 for (; exp >= 27; exp -= 27) *this *= RAPIDJSON_UINT64_C2(0X6765C793, 0XFA10079D); // 5^27
179 for (; exp >= 13; exp -= 13) *this *= static_cast<uint32_t>(1220703125u); // 5^13
180 if (exp > 0) *this *= kPow5[exp - 1];
181 return *this;
182 }
183
184 // Compute absolute difference of this and rhs.
185 // Assume this != rhs
186 bool Difference(const BigInteger& rhs, BigInteger* out) const {
187 int cmp = Compare(rhs);
188 RAPIDJSON_ASSERT(cmp != 0);
189 const BigInteger *a, *b; // Makes a > b
190 bool ret;
191 if (cmp < 0) { a = &rhs; b = this; ret = true; }
192 else { a = this; b = &rhs; ret = false; }
193
194 Type borrow = 0;
195 for (size_t i = 0; i < a->count_; i++) {
196 Type d = a->digits_[i] - borrow;
197 if (i < b->count_)
198 d -= b->digits_[i];
199 borrow = (d > a->digits_[i]) ? 1 : 0;
200 out->digits_[i] = d;
201 if (d != 0)
202 out->count_ = i + 1;
203 }
204
205 return ret;
206 }
207
208 int Compare(const BigInteger& rhs) const {
209 if (count_ != rhs.count_)
210 return count_ < rhs.count_ ? -1 : 1;
211
212 for (size_t i = count_; i-- > 0;)
213 if (digits_[i] != rhs.digits_[i])
214 return digits_[i] < rhs.digits_[i] ? -1 : 1;
215
216 return 0;
217 }
218
219 size_t GetCount() const { return count_; }
220 Type GetDigit(size_t index) const { RAPIDJSON_ASSERT(index < count_); return digits_[index]; }
221 bool IsZero() const { return count_ == 1 && digits_[0] == 0; }
222
223 private:
224 void AppendDecimal64(const char* begin, const char* end) {
225 uint64_t u = ParseUint64(begin, end);
226 if (IsZero())
227 *this = u;
228 else {
229 unsigned exp = static_cast<unsigned>(end - begin);
230 (MultiplyPow5(exp) <<= exp) += u; // *this = *this * 10^exp + u
231 }
232 }
233
234 void PushBack(Type digit) {
235 RAPIDJSON_ASSERT(count_ < kCapacity);
236 digits_[count_++] = digit;
237 }
238
239 static uint64_t ParseUint64(const char* begin, const char* end) {
240 uint64_t r = 0;
241 for (const char* p = begin; p != end; ++p) {
242 RAPIDJSON_ASSERT(*p >= '0' && *p <= '9');
243 r = r * 10u + static_cast<unsigned>(*p - '0');
244 }
245 return r;
246 }
247
248 // Assume a * b + k < 2^128
249 static uint64_t MulAdd64(uint64_t a, uint64_t b, uint64_t k, uint64_t* outHigh) {
250#if defined(_MSC_VER) && defined(_M_AMD64)
251 uint64_t low = _umul128(a, b, outHigh) + k;
252 if (low < k)
253 (*outHigh)++;
254 return low;
255#elif (__GNUC__ > 4 || (__GNUC__ == 4 && __GNUC_MINOR__ >= 6)) && defined(__x86_64__)
256 __extension__ typedef unsigned __int128 uint128;
257 uint128 p = static_cast<uint128>(a) * static_cast<uint128>(b);
258 p += k;
259 *outHigh = static_cast<uint64_t>(p >> 64);
260 return static_cast<uint64_t>(p);
261#else
262 const uint64_t a0 = a & 0xFFFFFFFF, a1 = a >> 32, b0 = b & 0xFFFFFFFF, b1 = b >> 32;
263 uint64_t x0 = a0 * b0, x1 = a0 * b1, x2 = a1 * b0, x3 = a1 * b1;
264 x1 += (x0 >> 32); // can't give carry
265 x1 += x2;
266 if (x1 < x2)
267 x3 += (static_cast<uint64_t>(1) << 32);
268 uint64_t lo = (x1 << 32) + (x0 & 0xFFFFFFFF);
269 uint64_t hi = x3 + (x1 >> 32);
270
271 lo += k;
272 if (lo < k)
273 hi++;
274 *outHigh = hi;
275 return lo;
276#endif
277 }
278
279 static const size_t kBitCount = 3328; // 64bit * 54 > 10^1000
280 static const size_t kCapacity = kBitCount / sizeof(Type);
281 static const size_t kTypeBit = sizeof(Type) * 8;
282
283 Type digits_[kCapacity];
284 size_t count_;
285};
286
287} // namespace internal
288RAPIDJSON_NAMESPACE_END
289
290#endif // RAPIDJSON_BIGINTEGER_H_
RAPIDJSON_ASSERT
#define RAPIDJSON_ASSERT(x)
Assertion.
Definition rapidjson.h:402
rapidjson::Type
Type
Type of JSON value.
Definition rapidjson.h:603
rapidjson.h
common definitions and configuration
RAPIDJSON_UINT64_C2
#define RAPIDJSON_UINT64_C2(high32, low32)
Construct a 64-bit literal by a pair of 32-bit integer.
Definition rapidjson.h:289