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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.
//
// 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(__INTEL_COMPILER) && 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_ + offset, digits_, 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_