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
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8 // http://opensource.org/licenses/MIT
9 //
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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 
25 RAPIDJSON_NAMESPACE_BEGIN
26 namespace internal {
27 
28 class BigInteger {
29 public:
30     typedef uint64_t Type;
31 
BigInteger(const BigInteger & rhs)32     BigInteger(const BigInteger& rhs) : count_(rhs.count_) {
33         std::memcpy(digits_, rhs.digits_, count_ * sizeof(Type));
34     }
35 
BigInteger(uint64_t u)36     explicit BigInteger(uint64_t u) : count_(1) {
37         digits_[0] = u;
38     }
39 
BigInteger(const char * decimals,size_t length)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 
MultiplyPow5(unsigned exp)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
Difference(const BigInteger & rhs,BigInteger * out)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 
Compare(const BigInteger & rhs)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 
GetCount()219     size_t GetCount() const { return count_; }
GetDigit(size_t index)220     Type GetDigit(size_t index) const { RAPIDJSON_ASSERT(index < count_); return digits_[index]; }
IsZero()221     bool IsZero() const { return count_ == 1 && digits_[0] == 0; }
222 
223 private:
AppendDecimal64(const char * begin,const char * end)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 
PushBack(Type digit)234     void PushBack(Type digit) {
235         RAPIDJSON_ASSERT(count_ < kCapacity);
236         digits_[count_++] = digit;
237     }
238 
ParseUint64(const char * begin,const char * end)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 + (unsigned)(*p - '0');
244         }
245         return r;
246     }
247 
248     // Assume a * b + k < 2^128
MulAdd64(uint64_t a,uint64_t b,uint64_t k,uint64_t * outHigh)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
288 RAPIDJSON_NAMESPACE_END
289 
290 #endif // RAPIDJSON_BIGINTEGER_H_
291