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.
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(__INTEL_COMPILER) && defined(_M_AMD64)
21 #include <intrin.h> // for _umul128
22 #if !defined(_ARM64EC_)
23 #pragma intrinsic(_umul128)
24 #else
25 #pragma comment(lib,"softintrin")
26 #endif
27 #endif
28 
29 RAPIDJSON_NAMESPACE_BEGIN
30 namespace internal {
31 
32 class BigInteger {
33 public:
34     typedef uint64_t Type;
35 
BigInteger(const BigInteger & rhs)36     BigInteger(const BigInteger& rhs) : count_(rhs.count_) {
37         std::memcpy(digits_, rhs.digits_, count_ * sizeof(Type));
38     }
39 
BigInteger(uint64_t u)40     explicit BigInteger(uint64_t u) : count_(1) {
41         digits_[0] = u;
42     }
43 
44     template<typename Ch>
BigInteger(const Ch * decimals,size_t length)45     BigInteger(const Ch* decimals, size_t length) : count_(1) {
46         RAPIDJSON_ASSERT(length > 0);
47         digits_[0] = 0;
48         size_t i = 0;
49         const size_t kMaxDigitPerIteration = 19;  // 2^64 = 18446744073709551616 > 10^19
50         while (length >= kMaxDigitPerIteration) {
51             AppendDecimal64(decimals + i, decimals + i + kMaxDigitPerIteration);
52             length -= kMaxDigitPerIteration;
53             i += kMaxDigitPerIteration;
54         }
55 
56         if (length > 0)
57             AppendDecimal64(decimals + i, decimals + i + length);
58     }
59 
60     BigInteger& operator=(const BigInteger &rhs)
61     {
62         if (this != &rhs) {
63             count_ = rhs.count_;
64             std::memcpy(digits_, rhs.digits_, count_ * sizeof(Type));
65         }
66         return *this;
67     }
68 
69     BigInteger& operator=(uint64_t u) {
70         digits_[0] = u;
71         count_ = 1;
72         return *this;
73     }
74 
75     BigInteger& operator+=(uint64_t u) {
76         Type backup = digits_[0];
77         digits_[0] += u;
78         for (size_t i = 0; i < count_ - 1; i++) {
79             if (digits_[i] >= backup)
80                 return *this; // no carry
81             backup = digits_[i + 1];
82             digits_[i + 1] += 1;
83         }
84 
85         // Last carry
86         if (digits_[count_ - 1] < backup)
87             PushBack(1);
88 
89         return *this;
90     }
91 
92     BigInteger& operator*=(uint64_t u) {
93         if (u == 0) return *this = 0;
94         if (u == 1) return *this;
95         if (*this == 1) return *this = u;
96 
97         uint64_t k = 0;
98         for (size_t i = 0; i < count_; i++) {
99             uint64_t hi;
100             digits_[i] = MulAdd64(digits_[i], u, k, &hi);
101             k = hi;
102         }
103 
104         if (k > 0)
105             PushBack(k);
106 
107         return *this;
108     }
109 
110     BigInteger& operator*=(uint32_t u) {
111         if (u == 0) return *this = 0;
112         if (u == 1) return *this;
113         if (*this == 1) return *this = u;
114 
115         uint64_t k = 0;
116         for (size_t i = 0; i < count_; i++) {
117             const uint64_t c = digits_[i] >> 32;
118             const uint64_t d = digits_[i] & 0xFFFFFFFF;
119             const uint64_t uc = u * c;
120             const uint64_t ud = u * d;
121             const uint64_t p0 = ud + k;
122             const uint64_t p1 = uc + (p0 >> 32);
123             digits_[i] = (p0 & 0xFFFFFFFF) | (p1 << 32);
124             k = p1 >> 32;
125         }
126 
127         if (k > 0)
128             PushBack(k);
129 
130         return *this;
131     }
132 
133     BigInteger& operator<<=(size_t shift) {
134         if (IsZero() || shift == 0) return *this;
135 
136         size_t offset = shift / kTypeBit;
137         size_t interShift = shift % kTypeBit;
138         RAPIDJSON_ASSERT(count_ + offset <= kCapacity);
139 
140         if (interShift == 0) {
141             std::memmove(digits_ + offset, digits_, count_ * sizeof(Type));
142             count_ += offset;
143         }
144         else {
145             digits_[count_] = 0;
146             for (size_t i = count_; i > 0; i--)
147                 digits_[i + offset] = (digits_[i] << interShift) | (digits_[i - 1] >> (kTypeBit - interShift));
148             digits_[offset] = digits_[0] << interShift;
149             count_ += offset;
150             if (digits_[count_])
151                 count_++;
152         }
153 
154         std::memset(digits_, 0, offset * sizeof(Type));
155 
156         return *this;
157     }
158 
159     bool operator==(const BigInteger& rhs) const {
160         return count_ == rhs.count_ && std::memcmp(digits_, rhs.digits_, count_ * sizeof(Type)) == 0;
161     }
162 
163     bool operator==(const Type rhs) const {
164         return count_ == 1 && digits_[0] == rhs;
165     }
166 
MultiplyPow5(unsigned exp)167     BigInteger& MultiplyPow5(unsigned exp) {
168         static const uint32_t kPow5[12] = {
169             5,
170             5 * 5,
171             5 * 5 * 5,
172             5 * 5 * 5 * 5,
173             5 * 5 * 5 * 5 * 5,
174             5 * 5 * 5 * 5 * 5 * 5,
175             5 * 5 * 5 * 5 * 5 * 5 * 5,
176             5 * 5 * 5 * 5 * 5 * 5 * 5 * 5,
177             5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5,
178             5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5,
179             5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5,
180             5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5
181         };
182         if (exp == 0) return *this;
183         for (; exp >= 27; exp -= 27) *this *= RAPIDJSON_UINT64_C2(0X6765C793, 0XFA10079D); // 5^27
184         for (; exp >= 13; exp -= 13) *this *= static_cast<uint32_t>(1220703125u); // 5^13
185         if (exp > 0)                 *this *= kPow5[exp - 1];
186         return *this;
187     }
188 
189     // Compute absolute difference of this and rhs.
190     // Assume this != rhs
Difference(const BigInteger & rhs,BigInteger * out)191     bool Difference(const BigInteger& rhs, BigInteger* out) const {
192         int cmp = Compare(rhs);
193         RAPIDJSON_ASSERT(cmp != 0);
194         const BigInteger *a, *b;  // Makes a > b
195         bool ret;
196         if (cmp < 0) { a = &rhs; b = this; ret = true; }
197         else         { a = this; b = &rhs; ret = false; }
198 
199         Type borrow = 0;
200         for (size_t i = 0; i < a->count_; i++) {
201             Type d = a->digits_[i] - borrow;
202             if (i < b->count_)
203                 d -= b->digits_[i];
204             borrow = (d > a->digits_[i]) ? 1 : 0;
205             out->digits_[i] = d;
206             if (d != 0)
207                 out->count_ = i + 1;
208         }
209 
210         return ret;
211     }
212 
Compare(const BigInteger & rhs)213     int Compare(const BigInteger& rhs) const {
214         if (count_ != rhs.count_)
215             return count_ < rhs.count_ ? -1 : 1;
216 
217         for (size_t i = count_; i-- > 0;)
218             if (digits_[i] != rhs.digits_[i])
219                 return digits_[i] < rhs.digits_[i] ? -1 : 1;
220 
221         return 0;
222     }
223 
GetCount()224     size_t GetCount() const { return count_; }
GetDigit(size_t index)225     Type GetDigit(size_t index) const { RAPIDJSON_ASSERT(index < count_); return digits_[index]; }
IsZero()226     bool IsZero() const { return count_ == 1 && digits_[0] == 0; }
227 
228 private:
229     template<typename Ch>
AppendDecimal64(const Ch * begin,const Ch * end)230     void AppendDecimal64(const Ch* begin, const Ch* end) {
231         uint64_t u = ParseUint64(begin, end);
232         if (IsZero())
233             *this = u;
234         else {
235             unsigned exp = static_cast<unsigned>(end - begin);
236             (MultiplyPow5(exp) <<= exp) += u;   // *this = *this * 10^exp + u
237         }
238     }
239 
PushBack(Type digit)240     void PushBack(Type digit) {
241         RAPIDJSON_ASSERT(count_ < kCapacity);
242         digits_[count_++] = digit;
243     }
244 
245     template<typename Ch>
ParseUint64(const Ch * begin,const Ch * end)246     static uint64_t ParseUint64(const Ch* begin, const Ch* end) {
247         uint64_t r = 0;
248         for (const Ch* p = begin; p != end; ++p) {
249             RAPIDJSON_ASSERT(*p >= Ch('0') && *p <= Ch('9'));
250             r = r * 10u + static_cast<unsigned>(*p - Ch('0'));
251         }
252         return r;
253     }
254 
255     // Assume a * b + k < 2^128
MulAdd64(uint64_t a,uint64_t b,uint64_t k,uint64_t * outHigh)256     static uint64_t MulAdd64(uint64_t a, uint64_t b, uint64_t k, uint64_t* outHigh) {
257 #if defined(_MSC_VER) && defined(_M_AMD64)
258         uint64_t low = _umul128(a, b, outHigh) + k;
259         if (low < k)
260             (*outHigh)++;
261         return low;
262 #elif defined(__GNUC__) && (__GNUC__ > 4 || (__GNUC__ == 4 && __GNUC_MINOR__ >= 6)) && defined(__x86_64__)
263         __extension__ typedef unsigned __int128 uint128;
264         uint128 p = static_cast<uint128>(a) * static_cast<uint128>(b);
265         p += k;
266         *outHigh = static_cast<uint64_t>(p >> 64);
267         return static_cast<uint64_t>(p);
268 #else
269         const uint64_t a0 = a & 0xFFFFFFFF, a1 = a >> 32, b0 = b & 0xFFFFFFFF, b1 = b >> 32;
270         uint64_t x0 = a0 * b0, x1 = a0 * b1, x2 = a1 * b0, x3 = a1 * b1;
271         x1 += (x0 >> 32); // can't give carry
272         x1 += x2;
273         if (x1 < x2)
274             x3 += (static_cast<uint64_t>(1) << 32);
275         uint64_t lo = (x1 << 32) + (x0 & 0xFFFFFFFF);
276         uint64_t hi = x3 + (x1 >> 32);
277 
278         lo += k;
279         if (lo < k)
280             hi++;
281         *outHigh = hi;
282         return lo;
283 #endif
284     }
285 
286     static const size_t kBitCount = 3328;  // 64bit * 54 > 10^1000
287     static const size_t kCapacity = kBitCount / sizeof(Type);
288     static const size_t kTypeBit = sizeof(Type) * 8;
289 
290     Type digits_[kCapacity];
291     size_t count_;
292 };
293 
294 } // namespace internal
295 RAPIDJSON_NAMESPACE_END
296 
297 #endif // RAPIDJSON_BIGINTEGER_H_
298