1 // Tencent is pleased to support the open source community by making RapidJSON available.
3 // Copyright (C) 2015 THL A29 Limited, a Tencent company, and Milo Yip. All rights reserved.
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
8 // http://opensource.org/licenses/MIT
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.
15 #ifndef RAPIDJSON_BIGINTEGER_H_
16 #define RAPIDJSON_BIGINTEGER_H_
18 #include "../rapidjson.h"
20 #if defined(_MSC_VER) && defined(_M_AMD64)
21 #include <intrin.h> // for _umul128
22 #pragma intrinsic(_umul128)
25 RAPIDJSON_NAMESPACE_BEGIN
30 typedef uint64_t Type;
32 BigInteger(const BigInteger& rhs) : count_(rhs.count_) {
33 std::memcpy(digits_, rhs.digits_, count_ * sizeof(Type));
36 explicit BigInteger(uint64_t u) : count_(1) {
40 BigInteger(const char* decimals, size_t length) : count_(1) {
41 RAPIDJSON_ASSERT(length > 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;
52 AppendDecimal64(decimals + i, decimals + i + length);
55 BigInteger& operator=(const BigInteger &rhs)
59 std::memcpy(digits_, rhs.digits_, count_ * sizeof(Type));
64 BigInteger& operator=(uint64_t u) {
70 BigInteger& operator+=(uint64_t u) {
71 Type backup = digits_[0];
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];
81 if (digits_[count_ - 1] < backup)
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;
93 for (size_t i = 0; i < count_; i++) {
95 digits_[i] = MulAdd64(digits_[i], u, k, &hi);
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;
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);
128 BigInteger& operator<<=(size_t shift) {
129 if (IsZero() || shift == 0) return *this;
131 size_t offset = shift / kTypeBit;
132 size_t interShift = shift % kTypeBit;
133 RAPIDJSON_ASSERT(count_ + offset <= kCapacity);
135 if (interShift == 0) {
136 std::memmove(&digits_[count_ - 1 + offset], &digits_[count_ - 1], count_ * sizeof(Type));
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;
149 std::memset(digits_, 0, offset * sizeof(Type));
154 bool operator==(const BigInteger& rhs) const {
155 return count_ == rhs.count_ && std::memcmp(digits_, rhs.digits_, count_ * sizeof(Type)) == 0;
158 bool operator==(const Type rhs) const {
159 return count_ == 1 && digits_[0] == rhs;
162 BigInteger& MultiplyPow5(unsigned exp) {
163 static const uint32_t kPow5[12] = {
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
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];
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
191 if (cmp < 0) { a = &rhs; b = this; ret = true; }
192 else { a = this; b = &rhs; ret = false; }
195 for (size_t i = 0; i < a->count_; i++) {
196 Type d = a->digits_[i] - borrow;
199 borrow = (d > a->digits_[i]) ? 1 : 0;
208 int Compare(const BigInteger& rhs) const {
209 if (count_ != rhs.count_)
210 return count_ < rhs.count_ ? -1 : 1;
212 for (size_t i = count_; i-- > 0;)
213 if (digits_[i] != rhs.digits_[i])
214 return digits_[i] < rhs.digits_[i] ? -1 : 1;
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; }
224 void AppendDecimal64(const char* begin, const char* end) {
225 uint64_t u = ParseUint64(begin, end);
229 unsigned exp = static_cast<unsigned>(end - begin);
230 (MultiplyPow5(exp) <<= exp) += u; // *this = *this * 10^exp + u
234 void PushBack(Type digit) {
235 RAPIDJSON_ASSERT(count_ < kCapacity);
236 digits_[count_++] = digit;
239 static uint64_t ParseUint64(const char* begin, const char* end) {
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');
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;
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);
259 *outHigh = static_cast<uint64_t>(p >> 64);
260 return static_cast<uint64_t>(p);
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
267 x3 += (static_cast<uint64_t>(1) << 32);
268 uint64_t lo = (x1 << 32) + (x0 & 0xFFFFFFFF);
269 uint64_t hi = x3 + (x1 >> 32);
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;
283 Type digits_[kCapacity];
287 } // namespace internal
288 RAPIDJSON_NAMESPACE_END
290 #endif // RAPIDJSON_BIGINTEGER_H_