291 lines
8.9 KiB
C++
291 lines
8.9 KiB
C++
// Tencent is pleased to support the open source community by making RapidJSON available.
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//
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// Copyright (C) 2015 THL A29 Limited, a Tencent company, and Milo Yip. All rights reserved.
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//
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// Licensed under the MIT License (the "License"); you may not use this file except
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// in compliance with the License. You may obtain a copy of the License at
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//
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// http://opensource.org/licenses/MIT
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//
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// Unless required by applicable law or agreed to in writing, software distributed
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// under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR
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// CONDITIONS OF ANY KIND, either express or implied. See the License for the
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// specific language governing permissions and limitations under the License.
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#ifndef RAPIDJSON_BIGINTEGER_H_
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#define RAPIDJSON_BIGINTEGER_H_
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#include "../rapidjson.h"
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#if defined(_MSC_VER) && !defined(__INTEL_COMPILER) && defined(_M_AMD64)
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#include <intrin.h> // for _umul128
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#pragma intrinsic(_umul128)
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#endif
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RAPIDJSON_NAMESPACE_BEGIN
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namespace internal {
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class BigInteger {
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public:
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typedef uint64_t Type;
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BigInteger(const BigInteger& rhs) : count_(rhs.count_) {
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std::memcpy(digits_, rhs.digits_, count_ * sizeof(Type));
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}
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explicit BigInteger(uint64_t u) : count_(1) {
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digits_[0] = u;
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}
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BigInteger(const char* decimals, size_t length) : count_(1) {
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RAPIDJSON_ASSERT(length > 0);
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digits_[0] = 0;
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size_t i = 0;
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const size_t kMaxDigitPerIteration = 19; // 2^64 = 18446744073709551616 > 10^19
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while (length >= kMaxDigitPerIteration) {
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AppendDecimal64(decimals + i, decimals + i + kMaxDigitPerIteration);
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length -= kMaxDigitPerIteration;
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i += kMaxDigitPerIteration;
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}
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if (length > 0)
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AppendDecimal64(decimals + i, decimals + i + length);
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}
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BigInteger& operator=(const BigInteger &rhs)
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{
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if (this != &rhs) {
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count_ = rhs.count_;
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std::memcpy(digits_, rhs.digits_, count_ * sizeof(Type));
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}
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return *this;
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}
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BigInteger& operator=(uint64_t u) {
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digits_[0] = u;
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count_ = 1;
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return *this;
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}
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BigInteger& operator+=(uint64_t u) {
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Type backup = digits_[0];
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digits_[0] += u;
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for (size_t i = 0; i < count_ - 1; i++) {
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if (digits_[i] >= backup)
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return *this; // no carry
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backup = digits_[i + 1];
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digits_[i + 1] += 1;
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}
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// Last carry
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if (digits_[count_ - 1] < backup)
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PushBack(1);
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return *this;
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}
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BigInteger& operator*=(uint64_t u) {
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if (u == 0) return *this = 0;
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if (u == 1) return *this;
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if (*this == 1) return *this = u;
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uint64_t k = 0;
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for (size_t i = 0; i < count_; i++) {
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uint64_t hi;
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digits_[i] = MulAdd64(digits_[i], u, k, &hi);
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k = hi;
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}
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if (k > 0)
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PushBack(k);
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return *this;
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}
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BigInteger& operator*=(uint32_t u) {
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if (u == 0) return *this = 0;
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if (u == 1) return *this;
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if (*this == 1) return *this = u;
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uint64_t k = 0;
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for (size_t i = 0; i < count_; i++) {
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const uint64_t c = digits_[i] >> 32;
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const uint64_t d = digits_[i] & 0xFFFFFFFF;
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const uint64_t uc = u * c;
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const uint64_t ud = u * d;
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const uint64_t p0 = ud + k;
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const uint64_t p1 = uc + (p0 >> 32);
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digits_[i] = (p0 & 0xFFFFFFFF) | (p1 << 32);
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k = p1 >> 32;
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}
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if (k > 0)
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PushBack(k);
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return *this;
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}
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BigInteger& operator<<=(size_t shift) {
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if (IsZero() || shift == 0) return *this;
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size_t offset = shift / kTypeBit;
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size_t interShift = shift % kTypeBit;
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RAPIDJSON_ASSERT(count_ + offset <= kCapacity);
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if (interShift == 0) {
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std::memmove(digits_ + offset, digits_, count_ * sizeof(Type));
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count_ += offset;
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}
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else {
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digits_[count_] = 0;
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for (size_t i = count_; i > 0; i--)
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digits_[i + offset] = (digits_[i] << interShift) | (digits_[i - 1] >> (kTypeBit - interShift));
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digits_[offset] = digits_[0] << interShift;
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count_ += offset;
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if (digits_[count_])
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count_++;
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}
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std::memset(digits_, 0, offset * sizeof(Type));
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return *this;
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}
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bool operator==(const BigInteger& rhs) const {
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return count_ == rhs.count_ && std::memcmp(digits_, rhs.digits_, count_ * sizeof(Type)) == 0;
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}
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bool operator==(const Type rhs) const {
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return count_ == 1 && digits_[0] == rhs;
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}
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BigInteger& MultiplyPow5(unsigned exp) {
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static const uint32_t kPow5[12] = {
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5,
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5 * 5,
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5 * 5 * 5,
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5 * 5 * 5 * 5,
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5 * 5 * 5 * 5 * 5,
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5 * 5 * 5 * 5 * 5 * 5,
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5 * 5 * 5 * 5 * 5 * 5 * 5,
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5 * 5 * 5 * 5 * 5 * 5 * 5 * 5,
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5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5,
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5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5,
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5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5,
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5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5
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};
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if (exp == 0) return *this;
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for (; exp >= 27; exp -= 27) *this *= RAPIDJSON_UINT64_C2(0X6765C793, 0XFA10079D); // 5^27
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for (; exp >= 13; exp -= 13) *this *= static_cast<uint32_t>(1220703125u); // 5^13
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if (exp > 0) *this *= kPow5[exp - 1];
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return *this;
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}
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// Compute absolute difference of this and rhs.
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// Assume this != rhs
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bool Difference(const BigInteger& rhs, BigInteger* out) const {
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int cmp = Compare(rhs);
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RAPIDJSON_ASSERT(cmp != 0);
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const BigInteger *a, *b; // Makes a > b
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bool ret;
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if (cmp < 0) { a = &rhs; b = this; ret = true; }
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else { a = this; b = &rhs; ret = false; }
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Type borrow = 0;
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for (size_t i = 0; i < a->count_; i++) {
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Type d = a->digits_[i] - borrow;
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if (i < b->count_)
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d -= b->digits_[i];
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borrow = (d > a->digits_[i]) ? 1 : 0;
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out->digits_[i] = d;
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if (d != 0)
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out->count_ = i + 1;
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}
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return ret;
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}
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int Compare(const BigInteger& rhs) const {
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if (count_ != rhs.count_)
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return count_ < rhs.count_ ? -1 : 1;
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for (size_t i = count_; i-- > 0;)
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if (digits_[i] != rhs.digits_[i])
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return digits_[i] < rhs.digits_[i] ? -1 : 1;
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return 0;
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}
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size_t GetCount() const { return count_; }
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Type GetDigit(size_t index) const { RAPIDJSON_ASSERT(index < count_); return digits_[index]; }
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bool IsZero() const { return count_ == 1 && digits_[0] == 0; }
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private:
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void AppendDecimal64(const char* begin, const char* end) {
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uint64_t u = ParseUint64(begin, end);
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if (IsZero())
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*this = u;
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else {
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unsigned exp = static_cast<unsigned>(end - begin);
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(MultiplyPow5(exp) <<= exp) += u; // *this = *this * 10^exp + u
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}
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}
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void PushBack(Type digit) {
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RAPIDJSON_ASSERT(count_ < kCapacity);
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digits_[count_++] = digit;
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}
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static uint64_t ParseUint64(const char* begin, const char* end) {
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uint64_t r = 0;
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for (const char* p = begin; p != end; ++p) {
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RAPIDJSON_ASSERT(*p >= '0' && *p <= '9');
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r = r * 10u + static_cast<unsigned>(*p - '0');
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}
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return r;
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}
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// Assume a * b + k < 2^128
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static uint64_t MulAdd64(uint64_t a, uint64_t b, uint64_t k, uint64_t* outHigh) {
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#if defined(_MSC_VER) && defined(_M_AMD64)
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uint64_t low = _umul128(a, b, outHigh) + k;
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if (low < k)
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(*outHigh)++;
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return low;
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#elif (__GNUC__ > 4 || (__GNUC__ == 4 && __GNUC_MINOR__ >= 6)) && defined(__x86_64__)
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__extension__ typedef unsigned __int128 uint128;
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uint128 p = static_cast<uint128>(a) * static_cast<uint128>(b);
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p += k;
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*outHigh = static_cast<uint64_t>(p >> 64);
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return static_cast<uint64_t>(p);
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#else
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const uint64_t a0 = a & 0xFFFFFFFF, a1 = a >> 32, b0 = b & 0xFFFFFFFF, b1 = b >> 32;
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uint64_t x0 = a0 * b0, x1 = a0 * b1, x2 = a1 * b0, x3 = a1 * b1;
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x1 += (x0 >> 32); // can't give carry
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x1 += x2;
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if (x1 < x2)
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x3 += (static_cast<uint64_t>(1) << 32);
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uint64_t lo = (x1 << 32) + (x0 & 0xFFFFFFFF);
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uint64_t hi = x3 + (x1 >> 32);
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lo += k;
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if (lo < k)
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hi++;
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*outHigh = hi;
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return lo;
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#endif
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}
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static const size_t kBitCount = 3328; // 64bit * 54 > 10^1000
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static const size_t kCapacity = kBitCount / sizeof(Type);
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static const size_t kTypeBit = sizeof(Type) * 8;
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Type digits_[kCapacity];
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size_t count_;
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};
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} // namespace internal
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RAPIDJSON_NAMESPACE_END
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#endif // RAPIDJSON_BIGINTEGER_H_
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