/*============================================================================*\
*
* 模拟实现 math.h 库中的函数
*
*
*
\*============================================================================*/
#include <iostream>
#include <iomanip>
#include <string>
#include <cstdlib>
#include <cstdio>
using namespace std;
typedef int MODE; // 计算sin(x)时采用弧度还是角度
const int BY_RADIDAN = 0; // 弧度
const int BY_ANGLE = 1; // 角度
const double RATIO = 0.01745329251994; // 角度转弧度的转换率
long Factorial( long x ); // 阶乘
double Pow( double x, double y = 2 ); // 求x^y
double Square( double x ); // 求平方
double Cube( double x ); // 求立方
double Sin( double x, MODE mode = BY_RADIDAN ); // 计算sin(x)
double Cos( double x , MODE mode = BY_RADIDAN ); // 计算cos(x)
double Tan( double x , MODE mode = BY_RADIDAN ); // 计算tan(x)
int Int(double x); // 取整, 不进行四舍五入
double Fabs( double x ); // 求绝对值
double Arctanh(double x); // 求achtanh()
double Ln(double x); // 求自然对数
double Exp( double x ); // 求e的x次幂
double Sinh( double x ); // 求双曲正弦 sinh()
double Cosh( double x ); // 求双曲余弦 cosh()
double Tanh(double x); // 求双曲正切 tanh()
double PI(); // 求圆周率
double gen(double x, double y); // 求根
// 计算阶乘
long Factorial( long x )
{
if( 0 == x || 1 == x )
{
return 1;
}
long ans = 1;
for( int i = 2; i <= x; i++ )
{
ans *= i;
}
return ans;
}
// 计算求幂, 默认是平方
// x^y=e^(ln(x)*y)
double Pow(double x, double y)
{
return Exp( (Ln(x)*y) );
}
// 求根
double gen(double x, double y)
{
return Pow(x,1/y);
}
// 计算绝对值
double Fabs( double x )
{
if( x < -1e-9)
return -x;
return x;
}
int Int(double x)
{
return static_cast<int>(Fabs( x ));
}
// 利用泰勒级数算 sin(x) , 默认传入弧度
// sinx ≈x-(x^3)/3!+(x^5)/5!-(x^7)/7!-(x^9)/9!...
// 计算精度为7位
double Sin( double x, MODE mode )
{
// 如果是角度则转换成弧度计算
if( BY_ANGLE == mode )
{
x *= RATIO;
}
x = x - Int( (x/( 2 * PI() ) ) ) * 2 * PI();
if( 0 == x )
return 0;
double sum = 0, fs = x, fm = 1, t, t1 = 1; //求和、分子、分母、精度、t1表示符号位
int n=1; //项数
t = fs / fm; //精度赋值
while( Fabs(t) >= 1e-8) //循环条件
{
sum = sum + t; //求和
n++; //基数增加
fs = fs * x * x; //新分子
fm = fm * ( 2*n - 2) * ( 2*n - 1 ); //新分母
t1= -t1; //符号位 一正一负
t = t1 * ( fs / fm ); //精度
}
return sum;
}
// cos(x) = 1 - (x^2)/2! + (x^4)/4!......
// 结果精度为7位
double Cos( double x , MODE mode)
{
double term,sum;
int n = 2;
sum = 1.0;
term = 1.0;
while(Fabs(term) > 1e-7)
{
term = term * x * x / (n * (n-1)) * (-1.0);
sum = sum + term;
n += 2;
}
return sum;
}
// tanθ = sinθ / cosθ
// 结果精度为7位
double Tan( double x , MODE mode)
{
return ( Sin(x) / Cos(x) );
}
// 计算 x^2
double Square( double x )
{
return ( x*x );
}
// 计算 x^3
double Cube( double x )
{
return ( x*x*x );
}
// arctanh(x)= x + x^3/3 + x^5/5 + ... (x≤1)
// 求sinh(y) 会用到
// 精度为7位
double Arctanh(double x)
{
int n = 1;
double sum = 0, term = x, numer = x, denom = 1;
while(Fabs(term) > 1e-8)
{
sum += term; // 求和
numer = numer * x * x; // 分子
denom = n+2; // 分母
term = numer/denom; // 精度
n += 2; // 计数
}
return sum;
}
// ln(x) = 2 arctanh((x-1)/(x+1))
// 调用了Arctanh(double) 方法
double Ln(double x)
{
return 2 * Arctanh((x-1)/(x+1));
}
// 求e^x 用于Pow( double, double )调用
// e^x = 1+x+(x^2)/2!+(x^3)/3!+...
// 精度为7位
double Exp( double x )
{
double ret = 1, term = x, numer = x, denom = 1;;
int n = 1;
while(Fabs(term) > 1e-8)
{
ret += term; // 求和
numer *= x; // 分子
denom = denom * (n+1); // 分母
n++; // 累加
term = numer/denom; // 精度
}
return ret;
}
// sinh(x)=(exp(x) - exp(-x)) / 2.0
// 精度为7位
double Sinh(double x)
{
return ( ( Exp(x) - Exp(-x) ) / 2.0 );
}
// cosh(x)=(exp(x) + exp(-x)) / 2.0;
// 精度为7位
double Cosh(double x)
{
return ( ( Exp(x) + Exp(-x) ) / 2.0 );
}
// tanh(x) = sinh(x) / cosh(x);
// 精度为7位
double Tanh(double x)
{
return ( Sinh(x) / Cosh(x) );
}
// 求PI: pi/4 = 1 - 1/3 + 1/5 - 1/7...
double PI()
{
int a = 3, b = 1;
double m = 1.0, sum = 1.0;
while( Fabs(m) > 1e-7 )
{
b = -b;
m = double(b) / a;
sum = sum + m;
a = a + 2;
}
return 4 * sum;
}
//==============================================================================
void drow_line(int i = 39,string s = "━", bool newline = false)
{
if(newline) cout << endl;
while(i--)
cout << s;
cout << endl;
}
void cls()
{
system("cls");
}
void pause()
{
system("pause");
//getchar();
}
// 菜单选项
void menu_option(int& menu_op,
int max = 14,
int min = 0,
string s = " 请选择相应的菜单选项>>> ",
string error = " ERROR:请选择正确的菜单选项! >>> ")
{
cout << s;
cin >> menu_op;
while(cin.fail() || menu_op < min || menu_op > max)
{
cout << error;
cin.clear();
fflush(stdin);
cin >> menu_op;
}
}
// 选择逻辑处理
bool choos()
{
string contin;
while(true)
{
getline(cin, contin);
if(contin == "Y" || contin == "y" || contin == "是")
{
return true;
}
else if(contin == "N" || contin == "n" || contin == "否")
{
return false;
}
else
{
cout << " 提示：请输入(Y/N)！>>> ";
}
}
}
bool check_input(int& x,
string str = " 请输入数据x：",
string err = " 输入数据格式有误！")
{
cout << str;
cin >> x;
if(cin.good())
return true;
cout << err << endl;
return false;
}
bool check_input(double& x,
string str = " 请输入数据 x：",
string err = " 输入数据格式有误！")
{
cout << str;
cin >> x;
if(cin.good())
return true;
cout << err << endl;
return false;
}
void print_result(double ans, string str )
{
cout << str << " = " << ans << endl;
pause();
}
//==============================================================================
/**
*
* 主菜单
*/
void menu_main()
{
cls();
cout << endl << endl << endl;
cout << "\t";
drow_line(35);
cout << "\t\t\t\t*** 主菜单选项 ***" << endl;
cout << "\t";
drow_line(35);
cout << left;
cout << "\t " << setw(25) << "1. 取整 Int( x )";
cout << setw(25) << "2. 计算 sinh( x )" << endl;
cout << "\t " << setw(25) << "3. 计算 sin( x )";
cout << setw(25) << "4. 计算 n^2 " << endl;
cout << "\t " << setw(25) << "5. 计算 n!";
cout << setw(25) << "6. 计算 cosh( x ) " << endl;
cout << "\t " << setw(25) << "7. 计算 cos( x )";
cout << setw(25) << "8. 计算 x^y" << endl;
cout << "\t " << setw(25) << "9. 计算 y√x ";
cout << setw(25) << "10. 计算 tanh( x ) " << endl;
cout << "\t " << setw(25) << "11. 计算 Π";
cout << setw(25) << "12. 计算 tan( x )" << endl;
cout << "\t " << setw(25) << "13. 计算 x^3";
cout << setw(25) << "14. 计算 3√x" << endl;
cout << "\t " << setw(25) << "0. 退出系统" << endl;
cout << "\t";
drow_line(35);
cout << endl << endl;
drow_line(39,"><");
cout << endl;
}
int main()
{
int ansInt;
double ans;
int xi;
double x,y;
while(true)
{
cls();
menu_main();
int option;
menu_option(option); // 选择功能
switch(option)
{
case 0 :
cout << "是否退出？(Y/N)";
if(choos())
exit(0);
break;
case 1:
check_input(x);
ansInt = Int(x);
drow_line(39,"**");
cout << "Int(" << x << ") = " << ansInt << endl;
pause();
break;
case 2:
check_input(x);
ans = Sinh(x);
drow_line(39,"**");
cout << "sinh(" << x << ") = " << ans << endl;
pause();
break;
case 3:
check_input(x);
ans = Sin(x);
drow_line(39,"**");
cout << "sin(" << x << ") = " << ans << endl;
pause();
break;
case 4:
check_input(x);
ans = Square(x);
drow_line(39,"**");
cout << x << "^2 = " << ans << endl;
pause();
break;
case 5:
check_input(xi, " 请输入整数n: ");
ansInt = Factorial(xi);
drow_line(39,"**");
cout << xi << "! = " << ansInt << endl;
pause();
break;
case 6:
check_input(x);
ans = Cosh(x);
drow_line(39,"**");
cout << "cosh(" << x << ") = " << ans << endl;
pause();
break;
case 7:
check_input(x);
ans = Cos(x);
drow_line(39,"**");
cout << "cos(" << x << ") = " << ans << endl;
pause();
break;
case 8:
check_input(x, " 请输入数据 x y : ");
check_input(y, "");
ans = Pow(x,y);
drow_line(39,"**");
cout << x << "^" << y << " = " << ans << endl;
pause();
break;
case 9:
check_input(x, " 请输入数据 x y : ");
check_input(y, "");
ans = gen(x,y);
drow_line(39,"**");
cout << y << "√" << x << " = " << ans << endl;
pause();
break;
case 10:
check_input(x);
ans = Tanh(x);
drow_line(39,"**");
cout << "tanh(" << x << ") = " << ans << endl;
pause();
break;
case 11:
ans = PI();
drow_line(39,"**");
cout << "π = " << ans << endl;
pause();
break;
case 12:
check_input(x);
ans = Tan(x);
drow_line(39,"**");
cout << "tan(" << x << ") = " << ans << endl;
pause();
break;
case 13:
check_input(x);
ans = Cube(x);
drow_line(39,"**");
cout << x << "^3 = " << ans << endl;
pause();
break;
case 14:
check_input(x);
ans = gen(x,3);
drow_line(39,"**");
cout << "3√" << x << " = " << ans << endl;
pause();
break;
default:
break;
}
}
return 0;
}
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