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