biginteger.h Source File

biginteger.h Source File#

Composable Kernel: biginteger.h Source File
// 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
#if !defined(_ARM64EC_)
#pragma intrinsic(_umul128)
#else
#pragma comment(lib, "softintrin")
#endif
#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; }
 
    template <typename Ch>
    BigInteger(const Ch* 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:
    template <typename Ch>
    void AppendDecimal64(const Ch* begin, const Ch* 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;
    }
 
    template <typename Ch>
    static uint64_t ParseUint64(const Ch* begin, const Ch* end)
    {
        uint64_t r = 0;
        for(const Ch* p = begin; p != end; ++p)
        {
            RAPIDJSON_ASSERT(*p >= Ch('0') && *p <= Ch('9'));
            r = r * 10u + static_cast<unsigned>(*p - Ch('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 defined(__GNUC__) && (__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_