arithmetic.cpp

可进行大数的加减乘除、阶乘、三角函数、幂指数（指数只支持整数）的运算

\*******************************************************/
Arithmetic operator - (Arithmetic& numa, Arithmetic& numb)
{
	std::string strNuma = numa.GetData(), strNumb = "-" + numb.GetData();
	Arithmetic result = numa.PlusMinus(strNuma, strNumb);
	return result;
}

/*******************************************************\
函数: operator *
功能: 计算大数乘法
输入: Arithmetic对象
输出: 无
返回: 2数之积
备注: 模仿竖式的乘法计算
\*******************************************************/
Arithmetic operator * (Arithmetic& numa, Arithmetic& numb)
{
	int digCount = 0, i;
	std::string strNuma = numa.GetData(), strNumb = numb.GetData();

	int state = 0;
	if(strNuma[0] == '-' && strNumb[0] != '-')
	{
		state = 1;
		strNuma.erase(0, 1);
	}
	if(strNuma[0] != '-' && strNumb[0] == '-')
	{
		state = 1;
		strNumb.erase(0, 1);
	}

	if((i = strNuma.find(".")) < strNuma.length())
	{
		digCount += (strNuma.length() - 1 - i);
		strNuma.erase(i, 1);
	}
	if((i = strNumb.find(".")) < strNumb.length())
	{
		digCount += (strNumb.length() - 1 - i);
		strNumb.erase(i, 1);
	}
	std::string strResult = numa.Multiply(strNuma, strNumb, digCount);
	if(state == 1)
		strResult.insert(0, "-");
	Arithmetic result = strResult;
	return result;
}

/*******************************************************\
函数: operator %
功能: 计算大数取模
输入: Arithmetic对象
输出: 无
返回: 模
备注: 类似大数除法运算
\*******************************************************/
Arithmetic operator % (Arithmetic& numa, Arithmetic& numb)
{
	if(numa < numb)
		return numa;
	Arithmetic iresult = numa - numb, ia = "";
	if(iresult.GetData() == "0")
		return iresult;
	std::string strNuma = numa.GetData(), carry = "0";
	long lb = numb.GetData().length();
	do
	{
		ia = strNuma.substr(0, lb);
		strNuma.erase(0, lb);
		iresult = ia - numb;
		if(iresult.GetData()[0] == '-')
		{
			std::string t = ia.GetData();
			t += strNuma[0];
			ia = t;
			strNuma.erase(0, 1);
		}
		do
		{
			ia = ia - numb;
			if(ia.GetData()[0] == '-')
				break;
			carry = ia.GetData();
		}while(1);
		if(carry != "0")
			strNuma.insert(0, carry);
		ia = strNuma;
	}while(ia >= numb);

	return ia;
}

/*******************************************************\
函数: operator /
功能: 计算大数除法
输入: Arithmetic对象
输出: 无
返回: 2数差
备注: 用户设置小数点后的精确度.
      分段用相减来获得商,从高位开始去减被除数直到差小于被除数,
	  相减的次数就是商
\*******************************************************/
Arithmetic operator / (Arithmetic& numa, Arithmetic& numb)
{
	std::string strNuma = numa.GetData(), strNumb = numb.GetData();

	int signstate = 0;
	if(strNuma[0] == '-' && strNumb[0] != '-')
	{
		signstate = 1;
		strNuma.erase(0, 1);
	}
	if(strNuma[0] != '-' && strNumb[0] == '-')
	{
		signstate = 1;
		strNumb.erase(0, 1);
	}

	while(strNumb[0] == '0')
		strNumb.erase(0, 1);
	if(strNumb.find(".") < strNumb.length())
	{
		while(strNumb[strNumb.length()-1] == '0')
			strNumb.erase(strNumb.length()-1, 1);
	}
	if(strNumb == "" || strNumb == ".")//0
	{
		Arithmetic result = "Error: " + strNuma + " / " + "0";
		return result;
	}
	while(strNuma[0] == '0')
		strNuma.erase(0, 1);
	if(strNuma.find(".") < strNuma.length())
	{
		while(strNuma[strNuma.length()-1] == '0')
			strNuma.erase(strNuma.length()-1, 1);
	}
	if(strNuma == "" || strNuma == ".")
	{
		Arithmetic result = "0";
		return result;
	}
	long ib = strNumb.find("."), ia = strNuma.find(".");
	int state = 0;
	if(ib < strNumb.length() && ia < strNuma.length())
		state = 1;
	if(ib > strNumb.length() && ia < strNuma.length())
		state = 2;
	if(ib < strNumb.length() && ia > strNuma.length())
		state = 3;
	switch(state)
	{
	case 1:
		{
		if(strNumb.length() - 1 - ib > strNuma.length() - 1 - ia)
		{
			long i = strNumb.length() - 1 - ib - (strNuma.length() - 1 - ia);
			while(i--)
				strNuma += "0";
		}
		else
		{
			long i = strNuma.length() - 1 - ia - (strNumb.length() - 1 - ib);
			while(i--)
				strNumb += "0";
		}
		strNuma.erase(ia, 1);
		strNumb.erase(ib, 1);
		break;
		}
	case 2:
		{
		long i = strNuma.length() - 1 - ia;
		while(i--)
			strNumb += "0";
		strNuma.erase(ia, 1);
		break;
		}
	case 3:
		{
		long i = strNumb.length() - 1 - ib;
		while(i--)
			strNuma += "0";
		strNumb.erase(ib, 1);
		break;
		}
	default:
		break;
	}
	std::string strResult = numa.Dividle(strNuma, strNumb, Arithmetic::m_precision);
	if(signstate == 1)
		strResult.insert(0, "-");
	Arithmetic result = strResult;
	return result;
}

/*******************************************************\
函数: RootInteger
功能: 计算大数乘方(指数为整数)
输入: string
输出: 无
返回: 得数
备注: 无
\*******************************************************/
Arithmetic Arithmetic::RootInteger(std::string strNumber, std::string strRootInt)
{
	Arithmetic number = strNumber, n = strRootInt, result = "1", one = "1";
	for (Arithmetic i = "0";i < n;i = i + one)
		result = result * number;
	std::string strResult = result.GetData();
	Arithmetic t = strResult;
	return t;
}

/*******************************************************\
函数: < > <= >=
功能: 比较大小
输入: Arithmetic
输出: 无
返回: bool
备注: 无
\*******************************************************/
bool operator < (Arithmetic& numa, Arithmetic& numb)
{
	Arithmetic result = numa - numb;
	if(result.GetData()[0] == '-')
		return 1;
	return 0;
}

bool operator > (Arithmetic& numa, Arithmetic& numb)
{
	Arithmetic result = numa - numb;
	if(result.GetData()[0] == '-')
		return 0;
	return 1;
}

bool operator <= (Arithmetic& numa, Arithmetic& numb)
{
	Arithmetic result = numa - numb;
	if(result.GetData()[0] == '-' || result.GetData() == "0")
		return 1;
	return 0;
}

bool operator >= (Arithmetic& numa, Arithmetic& numb)
{
	Arithmetic result = numa - numb;
	if(result.GetData()[0] == '-' || result.GetData() == "0")
		return 0;
	return 1;
}
/*******************************************************\
函数: Factorial
功能: 计算数的阶乘
输入: 无
输出: 无
返回: string
备注: 无
\*******************************************************/
std::string Arithmetic::Factorial()
{
	Arithmetic i = "2", result = "1", one = "1";
	if(m_num.find(".") < m_num.length())
	{
		std::string t = "Error: ";
		t += m_num;
		return t;
	}
	if(m_num == "1" || m_num == "0")
	{
		std::string result = "1";
		return result;
	}
	while(i <= *this)
	{
		result = result * i;
		i = i + one;
	}
	std::string strResult = result.GetData();
	return strResult;
}

/*******************************************************\
函数: Sin
功能: 计算三角函数
输入: 无
输出: 无
返回: string
备注: 将角度化简到360以内 弧度化简到2pai以内
\*******************************************************/
std::string Arithmetic::Sin()
{
	if(m_num[0] == '-' && m_Tstate == 0)
	{
		Arithmetic pai2 = "360", zero = "0";
		while(1)
		{
			*this = *this + pai2;
			if(*this >= zero)
				break;
		}
	}
	if(m_num[0] == '-' && m_Tstate == 1)
	{
		Arithmetic pai2 = pai, two = "2", zero = "0";
		pai2 = pai2 * two;
		while(1)
		{
			*this = *this + pai2;
			if(*this >= zero)
				break;
		}
	}
	if(m_Tstate == 0)//角度
	{
		std::string dig = "";
		long i;
		if((i = m_num.find(".")) < m_num.length())//取出小数部分,再对整数模360
		{
			dig = m_num.substr(i+1, m_num.length()-1 - i);
			m_num.erase(i, m_num.length());
		}
		Arithmetic pai2 = "360", paihalf = "180", ipai = pai, strNumi = "";
		strNumi = ipai / paihalf;
		*this = *this % pai2;
		std::string t = this->GetData();
		if(dig != "")
		{
			t += ".";
			t += dig;
		}
		double NumResult = atof(t.c_str());
		NumResult = NumResult * atof(strNumi.GetData().c_str());
		NumResult = sin(NumResult);
		char* p = new char[20];
		sprintf(p, "%f", NumResult);
		t = p;
		delete [] p;
		if(t.find(".") < t.length())
		{
			while(t[t.length()-1] == '0')
				t.erase(t.length()-1, 1);
			if(t[t.length()-1] == '.')
				t.erase(t.length()-1, 1);
		}
		return t;
	}
	if(m_Tstate == 1)//弧度
	{
		Arithmetic i = "2", ipai = pai, t = "";
		ipai = ipai * i;
		while(1)
		{
			t = *this - ipai;
			if(t < ipai)
				break;
			*this = t;
		}
		double NumResult = atof(this->GetData().c_str());
		NumResult = sin(NumResult);
		char *p = new char [20];
		sprintf(p, "%f", NumResult);
		std::string result = p;
		if(result.find(".") < result.length())
		{
			while(result[result.length()-1] == '0')
				result.erase(result.length()-1, 1);
			if(result[result.length()-1] == '.')
				result.erase(result.length()-1, 1);
		}
		delete [] p;
		return result;
	}
}
/*******************************************************\
函数: Cos
功能: 计算三角函数
输入: 无
输出: 无
返回: string
备注: 将角度化简到360以内 弧度化简到2pai以内
\*******************************************************/
std::string Arithmetic::Cos()
{
	if(m_num[0] == '-' && m_Tstate == 0)
	{
		Arithmetic pai2 = "360", zero = "0";
		while(1)
		{
			*this = *this + pai2;
			if(*this >= zero)
				break;
		}
	}
	if(m_num[0] == '-' && m_Tstate == 1)
	{
		Arithmetic pai2 = pai, two = "2", zero = "0";
		pai2 = pai2 * two;
		while(1)
		{
			*this = *this + pai2;
			if(*this >= zero)
				break;
		}
	}
	if(m_Tstate == 0)//角度
	{
		std::string dig = "";
		long i;
		if((i = m_num.find(".")) < m_num.length())//取出小数部分,再对整数模360
		{
			dig = m_num.substr(i+1, m_num.length()-1 - i);
			m_num.erase(i, m_num.length());
		}
		Arithmetic pai2 = "360", paihalf = "180", ipai = pai, strNumi = "";
		strNumi = ipai / paihalf;
		*this = *this % pai2;
		std::string t = this->GetData();
		if(dig != "")
		{
			t += ".";
			t += dig;
		}
		double NumResult = atof(t.c_str());
		NumResult = NumResult * atof(strNumi.GetData().c_str());
		NumResult = cos(NumResult);
		char* p = new char[20];
		sprintf(p, "%f", NumResult);
		t = p;
		delete [] p;
		if(t.find(".") < t.length())
		{
			while(t[t.length()-1] == '0')
				t.erase(t.length()-1, 1);
			if(t[t.length()-1] == '.')
				t.erase(t.length()-1, 1);
		}
		return t;
	}
	if(m_Tstate == 1)//弧度
	{
		Arithmetic i = "2", ipai = pai, t = "";
		ipai = ipai * i;
		while(1)
		{
			t = *this - ipai;
			if(t < ipai)
				break;
			*this = t;
		}
		double NumResult = atof(this->GetData().c_str());
		NumResult = cos(NumResult);
		char *p = new char [20];
		sprintf(p, "%f", NumResult);
		std::string result = p;
		if(result.find(".") < result.length())
		{
			while(result[result.length()-1] == '0')
				result.erase(result.length()-1, 1);
			if(result[result.length()-1] == '.')
				result.erase(result.length()-1, 1);
		}
		delete [] p;
		return result;
	}
}

/*******************************************************\
函数: Tan
功能: 计算三角函数
输入: 无
输出: 无
返回: string
备注: 将角度化简到180以内 弧度化简到pai以内
\*******************************************************/
std::string Arithmetic::Tan()
{
	if(m_num[0] == '-' && m_Tstate == 0)
	{
		Arithmetic pai1 = "180", zero = "0";
		while(1)
		{
			*this = *this + pai1;
			if(*this >= zero)
				break;
		}
	}
	if(m_num[0] == '-' && m_Tstate == 1)
	{
		Arithmetic pai1 = pai, zero = "0";
		while(1)
		{
			*this = *this + pai1;
			if(*this >= zero)
				break;
		}
	}
	if(m_Tstate == 0)//角度
	{
		std::string dig = "";
		long i;
		if((i = m_num.find(".")) < m_num.length())//取出小数部分,再对整数模360
		{
			dig = m_num.substr(i+1, m_num.length()-1 - i);
			m_num.erase(i, m_num.length());
		}
		Arithmetic pai1 = "360", paihalf = "180", ipai = pai, strNumi = "";
		strNumi = ipai / paihalf;
		*this = *this % pai1;
		if(this->GetData() == "90")
		{
			std::string t = "None";
			return t;
		}
		std::string t = this->GetData();
		if(dig != "")
		{
			t += ".";
			t += dig;
		}
		double NumResult = atof(t.c_str());
		NumResult = NumResult * atof(strNumi.GetData().c_str());
		NumResult = tan(NumResult);
		char* p = new char[20];
		sprintf(p, "%f", NumResult);
		t = p;
		delete [] p;
		if(t.find(".") < t.length())
		{
			while(t[t.length()-1] == '0')
				t.erase(t.length()-1, 1);
			if(t[t.length()-1] == '.')
				t.erase(t.length()-1, 1);
		}
		return t;
	}
	if(m_Tstate == 1)//弧度
	{
		Arithmetic i = "", ipai = pai, t = "", two = "2";
		while(1)
		{
			t = *this - ipai;
			if(t < ipai)
				break;
			*this = t;
		}
		t = ipai / two;
		if(t.GetData() == this->GetData())
		{
			std::string t = "None";
			return t;
		}
		double NumResult = atof(this->GetData().c_str());
		NumResult = tan(NumResult);
		char *p = new char [20];
		sprintf(p, "%f", NumResult);
		std::string result = p;
		if(result.find(".") < result.length())
		{
			while(result[result.length()-1] == '0')
				result.erase(result.length()-1, 1);
			if(result[result.length()-1] == '.')
				result.erase(result.length()-1, 1);
		}
		delete [] p;
		return result;
	}
}

/*******************************************************\
函数: Abs
功能: 取绝对值
输入: 无
输出: 无
返回: 绝对值
备注: 无
\*******************************************************/
Arithmetic Arithmetic::Abs()
{
	if(m_num[0] == '-')
	{
		Arithmetic result = m_num.substr(1, m_num.length());
		return result;
	}
	return *this;
}