C++请设计一个理论无限精度小数的类并提供operator+operator-operatoroperatoroperator+=operator-=operator=operator=并支持一个double +- 这个类的对象就像：BigFloat a;BigFloat b;int c;double d;诸如a = cd -= b的行为是受支持的

下面是一个简单的实现，可以实现无限精度小数的类：

#include <iostream>
#include <vector>

class BigFloat {
private:
    std::vector<int> digits;
    int decimalPoint;
    bool negative;

public:
    BigFloat() : decimalPoint(0), negative(false) {}

    BigFloat(int num) {
        if (num < 0) {
            negative = true;
            num *= -1;
        } else {
            negative = false;
        }

        decimalPoint = 0;
        while (num > 0) {
            digits.push_back(num % 10);
            num /= 10;
        }
    }

    BigFloat(double num) {
        if (num < 0) {
            negative = true;
            num *= -1;
        } else {
            negative = false;
        }

        decimalPoint = 0;
        while (num > 0) {
            digits.insert(digits.begin(), static_cast<int>(num) % 10);
            num /= 10;
        }
    }

    BigFloat operator+(const BigFloat& other) const {
        BigFloat result;
        result.digits = digits;
        result.decimalPoint = decimalPoint;

        int diff = decimalPoint - other.decimalPoint;
        if (diff > 0) {
            for (int i = 0; i < diff; ++i) {
                result.digits.insert(result.digits.begin(), 0);
            }
        } else if (diff < 0) {
            for (int i = 0; i < -diff; ++i) {
                result.digits.push_back(0);
            }
        }

        int carry = 0;
        for (int i = other.digits.size() - 1; i >= 0; --i) {
            int sum = result.digits[i] + other.digits[i] + carry;
            result.digits[i] = sum % 10;
            carry = sum / 10;
        }
        if (carry > 0) {
            result.digits.insert(result.digits.begin(), carry);
            ++result.decimalPoint;
        }

        return result;
    }

    BigFloat operator-(const BigFloat& other) const {
        BigFloat result;
        result.digits = digits;
        result.decimalPoint = decimalPoint;

        int diff = decimalPoint - other.decimalPoint;
        if (diff > 0) {
            for (int i = 0; i < diff; ++i) {
                result.digits.insert(result.digits.begin(), 0);
            }
        } else if (diff < 0) {
            for (int i = 0; i < -diff; ++i) {
                result.digits.push_back(0);
            }
        }

        int borrow = 0;
        for (int i = other.digits.size() - 1; i >= 0; --i) {
            int diff = result.digits[i] - other.digits[i] - borrow;
            if (diff < 0) {
                diff += 10;
                borrow = 1;
            } else {
                borrow = 0;
            }
            result.digits[i] = diff;
        }

        return result;
    }

    BigFloat operator*(const BigFloat& other) const {
        BigFloat result;
        result.decimalPoint = decimalPoint + other.decimalPoint;
        result.digits.resize(digits.size() + other.digits.size(), 0);

        for (int i = digits.size() - 1; i >= 0; --i) {
            int carry = 0;
            for (int j = other.digits.size() - 1; j >= 0; --j) {
                int product = digits[i] * other.digits[j] + result.digits[i + j + 1] + carry;
                result.digits[i + j + 1] = product % 10;
                carry = product / 10;
            }
            result.digits[i] += carry;
        }

        while (result.digits.size() > 1 && result.digits.front() == 0) {
            result.digits.erase(result.digits.begin());
            --result.decimalPoint;
        }

        return result;
    }

    BigFloat operator/(const BigFloat& other) const {
        BigFloat result;
        result.decimalPoint = decimalPoint - other.decimalPoint;
        result.digits.resize(digits.size(), 0);

        BigFloat remainder = *this;
        while (remainder >= other) {
            int quotient = 0;
            while (remainder >= other * (quotient + 1)) {
                ++quotient;
            }

            remainder -= other * quotient;
            result += BigFloat(quotient);
            result.decimalPoint = decimalPoint - other.decimalPoint;
        }

        return result;
    }

    BigFloat& operator+=(const BigFloat& other) {
        *this = *this + other;
        return *this;
    }

    BigFloat& operator-=(const BigFloat& other) {
        *this = *this - other;
        return *this;
    }

    BigFloat& operator*=(const BigFloat& other) {
        *this = *this * other;
        return *this;
    }

    BigFloat& operator/=(const BigFloat& other) {
        *this = *this / other;
        return *this;
    }

    bool operator<(const BigFloat& other) const {
        if (negative && !other.negative) {
            return true;
        } else if (!negative && other.negative) {
            return false;
        } else if (negative && other.negative) {
            return (-(*this)) > (-other);
        }

        if (decimalPoint > other.decimalPoint) {
            return false;
        } else if (decimalPoint < other.decimalPoint) {
            return true;
        }

        for (int i = 0; i < digits.size(); ++i) {
            if (digits[i] < other.digits[i]) {
                return true;
            } else if (digits[i] > other.digits[i]) {
                return false;
            }
        }

        return false;
    }

    bool operator>(const BigFloat& other) const {
        return other < *this;
    }

    bool operator<=(const BigFloat& other) const {
        return !(*this > other);
    }

    bool operator>=(const BigFloat& other) const {
        return !(*this < other);
    }

    bool operator==(const BigFloat& other) const {
        if (decimalPoint != other.decimalPoint || digits.size() != other.digits.size()) {
            return false;
        }

        for (int i = 0; i < digits.size(); ++i) {
            if (digits[i] != other.digits[i]) {
                return false;
            }
        }

        return true;
    }

    bool operator!=(const BigFloat& other) const {
        return !(*this == other);
    }

    BigFloat operator-() const {
        BigFloat result = *this;
        result.negative = !result.negative;
        return result;
    }

    friend std::ostream& operator<<(std::ostream& os, const BigFloat& num);
};

std::ostream& operator<<(std::ostream& os, const BigFloat& num) {
    if (num.negative) {
        os << "-";
    }

    for (int i = 0; i < num.digits.size(); ++i) {
        if (i == num.decimalPoint) {
            os << ".";
        }
        os << num.digits[i];
    }

    return os;
}

int main() {
    BigFloat a(123456789);
    BigFloat b(987654321);

    BigFloat c = a + b;
    BigFloat d = a - b;
    BigFloat e = a * b;
    BigFloat f = a / b;

    std::cout << "a + b = " << c << std::endl;
    std::cout << "a - b = " << d << std::endl;
    std::cout << "a * b = " << e << std::endl;
    std::cout << "a / b = " << f << std::endl;

    double g = 12.345;
    BigFloat h = a * g;
    std::cout << "a * g = " << h << std::endl;

    return 0;
}

这个实现使用一个vector来存储小数的每一位数字，使用一个int来记录小数点的位置，使用一个bool来表示是否为负数。在各个运算符重载函数中，将两个BigFloat对象的小数点对齐，然后根据运算符的不同进行相应的运算