biginteger.h

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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
#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=(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 * 10 + (*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_