将大型十六进制字符串转换为十进制字符串

Question

我需要将一个很大的（比内置数据类型还要大）十六进制字符串转换为其十进制表示的字符串。例如：

std::string sHex = "07AA17C660F3DD1D2A1B48F1B746C148";
std::string sDec; // should end up with: "10187768649047767717933300899576725832"

我目前正在使用C++ BigInt类，它提供了一种非常简单的方法来实现这一点（但仅限GPL）：

BigInt::Vin vbiTemp(sHex, 16);
sDec = vbiTemp.toStrDec();

有没有简单的方法可以在不使用第三方算术库的情况下完成这种转换？或者你能推荐一个免费（非GPL）的替代品，具有类似的简单性（效率无关紧要）吗？

- Flavio

Answer 1

好的，这是一个通用的进制转换器类。我最初在C#中编写了原始实现，并将其转换为了C++。它仍然具有.NET的特点。随意使用它。

您可以像这样使用它：

const BaseConverter& hex2dec = BaseConverter::HexToDecimalConverter();
std::cout << hex2dec.Convert("07AA17C660F3DD1D2A1B48F1B746C148");

输出将会是：

10187768649047767717933300899576725832

该类不仅局限于十六进制数字，而是可以使用任何进制和任何基本数字编码之间进行转换。

API

• BaseConverter::BaseConverter(const std::string& sourceBaseSet, const std::string& targetBaseSet);

  构造一个新的 BaseConverter 实例。该类可实现在源数字系统和目标数字系统之间的数字转换。

  构造函数有两个参数，均为 string 类型，用于指定源和目标数字系统的符号。字符串中第一个字符的值为 0，第二个字符的值为 1，以此类推。例如，八进制数字系统的符号通常为 "01234567"，十六进制数字系统的符号为 "0123456789ABCDEF"。您可以使用任何可打印的 ASCII 字符作为符号，因此您可以将 "OI"（而不是 "01"）用于二进制系统。

  注意：基础符号是区分大小写的，因此符号"0123456789abcdef"不能解码使用大写字母表示的十六进制数。

• std::string BaseConverter::Convert(std::string value) const;
std::string BaseConverter::Convert(const std::string& value, size_t minDigits) const;

  将源数字系统中的数字value转换为目标数字系统中的数字并返回结果。第二个重载接受额外的参数minDigits，用于指定结果中数字的最小位数。返回值将通过在目标数字系统中前置零或多个值为0的符号进行填充。

• std::string BaseConverter::FromDecimal(unsigned int value) const;
std::string BaseConverter::FromDecimal(unsigned int value, size_t minDigits) const;
  

  将unsigned int类型的十进制数字转换为目标数字系统中的数字。

• unsigned int BaseConverter::ToDecimal(std::string value) const;

  将源数字系统中的数字转换为十进制的unsigned int类型。 注意：如果源数字系统中的数字的十进制值超过UINT_MAX，则结果将不正确。

static const BaseConverter& BaseConverter::DecimalToBinaryConverter();
static const BaseConverter& BaseConverter::BinaryToDecimalConverter();
static const BaseConverter& BaseConverter::DecimalToHexConverter();
static const BaseConverter& BaseConverter::HexToDecimalConverter();

这些函数是方便的函数，返回适合于在常见数字进制之间进行转换的BaseConverter实例。注意：十六进制数使用大写字母A到F。

BaseConverter.h:

// Arbitrary precision base conversion by Daniel Gehriger <[e-mail]>   

#include <string>

class BaseConverter
{
public:
    std::string GetSourceBaseSet() const { return sourceBaseSet_; }
    std::string GetTargetBaseSet() const { return targetBaseSet_; }
    unsigned int GetSourceBase() const { return (unsigned int)sourceBaseSet_.length(); }
    unsigned int GetTargetBase() const { return (unsigned int)targetBaseSet_.length(); }

    /// <summary>
    /// Constructor
    /// </summary>
    /// <param name="sourceBaseSet">Characters used for source base</param>
    /// <param name="targetBaseSet">Characters used for target base</param>
    BaseConverter(const std::string& sourceBaseSet, const std::string& targetBaseSet);

    /// <summary>
    /// Get a base converter for decimal to binary numbers
    /// </summary>
    static const BaseConverter& DecimalToBinaryConverter();

    /// <summary>
    /// Get a base converter for binary to decimal numbers
    /// </summary>
    static const BaseConverter& BinaryToDecimalConverter();

    /// <summary>
    /// Get a base converter for decimal to binary numbers
    /// </summary>
    static const BaseConverter& DecimalToHexConverter();

    /// <summary>
    /// Get a base converter for binary to decimal numbers
    /// </summary>
    static const BaseConverter& HexToDecimalConverter();

    /// <summary>
    /// Convert a value in the source number base to the target number base.
    /// </summary>
    /// <param name="value">Value in source number base.</param>
    /// <returns>Value in target number base.</returns>
    std::string  Convert(std::string value) const;


    /// <summary>
    /// Convert a value in the source number base to the target number base.
    /// </summary>
    /// <param name="value">Value in source number base.</param>
    /// <param name="minDigits">Minimum number of digits for returned value.</param>
    /// <returns>Value in target number base.</returns>
    std::string Convert(const std::string& value, size_t minDigits) const;

    /// <summary>
    /// Convert a decimal value to the target base.
    /// </summary>
    /// <param name="value">Decimal value.</param>
    /// <returns>Result in target base.</returns>
    std::string FromDecimal(unsigned int value) const;

    /// <summary>
    /// Convert a decimal value to the target base.
    /// </summary>
    /// <param name="value">Decimal value.</param>
    /// <param name="minDigits">Minimum number of digits for returned value.</param>
    /// <returns>Result in target base.</returns>
    std::string FromDecimal(unsigned int value, size_t minDigits) const;

    /// <summary>
    /// Convert value in source base to decimal.
    /// </summary>
    /// <param name="value">Value in source base.</param>
    /// <returns>Decimal value.</returns>
    unsigned int ToDecimal(std::string value) const;

private:
    /// <summary>
    /// Divides x by y, and returns the quotient and remainder.
    /// </summary>
    /// <param name="baseDigits">Base digits for x and quotient.</param>
    /// <param name="x">Numerator expressed in base digits; contains quotient, expressed in base digits, upon return.</param>
    /// <param name="y">Denominator</param>
    /// <returns>Remainder of x / y.</returns>
    static unsigned int divide(const std::string& baseDigits, 
                               std::string& x, 
                               unsigned int y);

    static unsigned int base2dec(const std::string& baseDigits,
                                 const std::string& value);

    static std::string dec2base(const std::string& baseDigits, unsigned int value);

private:
    static const char*  binarySet_;
    static const char*  decimalSet_;
    static const char*  hexSet_;
    std::string         sourceBaseSet_;
    std::string         targetBaseSet_;
};

BaseConverter.cpp：

// Arbitrary precision base conversion by Daniel Gehriger <[e-mail]>   

#include "BaseConverter.h"
#include <stdexcept>
#include <algorithm>


const char* BaseConverter::binarySet_ = "01";
const char* BaseConverter::decimalSet_ = "0123456789";
const char* BaseConverter::hexSet_ = "0123456789ABCDEF";

BaseConverter::BaseConverter(const std::string& sourceBaseSet, const std::string& targetBaseSet) 
    : sourceBaseSet_(sourceBaseSet)
    , targetBaseSet_(targetBaseSet)
{
    if (sourceBaseSet.empty() || targetBaseSet.empty())
        throw std::invalid_argument("Invalid base character set");
}

const BaseConverter& BaseConverter::DecimalToBinaryConverter()
{
    static const BaseConverter dec2bin(decimalSet_, binarySet_);
    return dec2bin;
}

const BaseConverter& BaseConverter::BinaryToDecimalConverter()
{
    static const BaseConverter bin2dec(binarySet_, decimalSet_);
    return bin2dec;
}

const BaseConverter& BaseConverter::DecimalToHexConverter()
{
    static const BaseConverter dec2hex(decimalSet_, hexSet_);
    return dec2hex;
}

const BaseConverter& BaseConverter::HexToDecimalConverter()
{
    static const BaseConverter hex2dec(hexSet_, decimalSet_);
    return hex2dec;
}

std::string BaseConverter::Convert(std::string value) const
{
    unsigned int numberBase = GetTargetBase();
    std::string result;

    do
    {
        unsigned int remainder = divide(sourceBaseSet_, value, numberBase);
        result.push_back(targetBaseSet_[remainder]);
    }
    while (!value.empty() && !(value.length() == 1 && value[0] == sourceBaseSet_[0]));

    std::reverse(result.begin(), result.end());
    return result;
}

std::string BaseConverter::Convert(const std::string& value, size_t minDigits) const
{
    std::string result = Convert(value);
    if (result.length() < minDigits)
        return std::string(minDigits - result.length(), targetBaseSet_[0]) + result;
    else
        return result;
}

std::string BaseConverter::FromDecimal(unsigned int value) const
{
    return dec2base(targetBaseSet_, value);
}

std::string BaseConverter::FromDecimal(unsigned int value, size_t minDigits) const
{
    std::string result = FromDecimal(value);
    if (result.length() < minDigits)
        return std::string(minDigits - result.length(), targetBaseSet_[0]) + result;
    else
        return result;
}

unsigned int BaseConverter::ToDecimal(std::string value) const
{
    return base2dec(sourceBaseSet_, value);
}

unsigned int BaseConverter::divide(const std::string& baseDigits, std::string& x, unsigned int y)
{
    std::string quotient;

    size_t lenght = x.length();
    for (size_t i = 0; i < lenght; ++i)
    {
        size_t j = i + 1 + x.length() - lenght;
        if (x.length() < j)
            break;

        unsigned int value = base2dec(baseDigits, x.substr(0, j));

        quotient.push_back(baseDigits[value / y]);
        x = dec2base(baseDigits, value % y) + x.substr(j);
    }

    // calculate remainder
    unsigned int remainder = base2dec(baseDigits, x);

    // remove leading "zeros" from quotient and store in 'x'
    size_t n = quotient.find_first_not_of(baseDigits[0]);
    if (n != std::string::npos)
    {
        x = quotient.substr(n);
    }
    else
    {
        x.clear();
    }

    return remainder;
}

std::string BaseConverter::dec2base(const std::string& baseDigits, unsigned int value)
{
    unsigned int numberBase = (unsigned int)baseDigits.length();
    std::string result;
    do 
    {
        result.push_back(baseDigits[value % numberBase]);
        value /= numberBase;
    } 
    while (value > 0);

    std::reverse(result.begin(), result.end());
    return result;
}

unsigned int BaseConverter::base2dec(const std::string& baseDigits, const std::string& value)
{
    unsigned int numberBase = (unsigned int)baseDigits.length();
    unsigned int result = 0;
    for (size_t i = 0; i < value.length(); ++i)
    {
        result *= numberBase;
        int c = baseDigits.find(value[i]);
        if (c == std::string::npos)
            throw std::runtime_error("Invalid character");

        result += (unsigned int)c;
    }

    return result;
}

- Daniel Gehriger

---

这太棒了！谢谢！ - Uy Trieu Vi Tran

Answer 2

您可以使用此函数将十六进制字符转换为十进制字符：

void Hex2Char(const char* szHex, unsigned char& rch)
{
    rch = 0;
    for(int i=0; i<2; i++)
    {
        if(*(szHex + i) >='0' && *(szHex + i) <= '9')
            rch = (rch << 4) + (*(szHex + i) - '0');
        else if(*(szHex + i) >='A' && *(szHex + i) <= 'F')
            rch = (rch << 4) + (*(szHex + i) - 'A' + 10);
        else
            break;
    }
}    

然后您可以使用它来转换字符串：

void HexStrToCharStr(const char* hexStr, unsigned char* decStr, int n)
{
    unsigned char d_ch;
    for(int i=0; i<n; i++)
    {
        Hex2Char(hexStr+2*i, d_ch);
        decStr[i] = d_ch;
    }
}

- steg

---

这只会给我一个包含十六进制字符串中每个字符的十进制值的数组，但我需要将整个字符串转换为一个数字。将所有的值相加是不可能的，因为最终结果会超过普通整数的范围。 - Flavio

Answer 3

std::istringstream (sHex ) >> std::hex >> sDec;

- Ash

---

不幸的是，这似乎不起作用，sDec被设置为与sHex相同的值。 - Flavio

你测试了问题中提供的示例输入和输出吗？ - Ben Voigt

是的，较短的十六进制字符串（“std :: istringstream（”2A“）>> std :: hex >> sDec”）会产生相同的行为。 - Flavio

@Flavio：我在问Ashirius。 - Ben Voigt