大数科学计算器 C++ - ToB企服应用市场:ToB评测及商务社交产业平台

std::deque<int> digits;
int power;
int sign;

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// 里面定义的各种符号优先级如下:
-1: 左括号(
0: 各种逻辑判断符 >= < != 等 //对你没有看错还能求逻辑运算式
1: 加减+-
2: 乘除*/
3: 乘方^
4: 各种函数运算比如对数log 开根sqrt 三角函数sincos等
5: 百分号% //这个符号很迷其实因为一般百分号是取模但这里放优先级5是只让他求"百分之"的功能没有取模的功能所以这里比较随意不严谨之后可以优化一下

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// 定义的各种错误类型顺序如下
0: 出现除以0
1: 出现0的0次幂
2: 出现负数的分数次幂 //因为负数分数次幂就可能导致虚数我干脆全给禁了
3: 计算表达式非法 //有可能是括号配对错了有可能是数字多了总之表达式算不出来结果
4: log函数出现非正底数 //就是ln(x)里面x必须大于0

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string calstr
std::deque<MyNum> rpn
int type //0 计算式 1 逻辑条件式
MyNum ans //计算结果

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//构造函数
MyNum(const std::deque<int>& d=ZERODEQUE,int p=0,int s=0)
:digits(d),power(p),sign(s){}
MyNum(int i);
MyNum(long long i);
MyNum(double d);
MyNum(std::string str);
//拷贝构造拷贝赋值
MyNum(const MyNum& other)
:digits(other.digits), power(other.power),sign(other.sign) {}
MyNum& operator= (const MyNum& other) {
this->digits = other.digits;
this->power = other.power;
this->sign = other.sign;
return *this;
}

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MyNum::MyNum(std::string str) {
if (str.size() && (str[0] < '0' || str[0]>'9')) { //string不是数字是个计算符号
if (!((str[0] == '-' || str[0] == '+') && str.size() > 1 && str[1] >= '0' && str[1] <= '9')) {
this->sign = 2;
if (str[0] >= 'a' && str[0] <= 'z' || str[0] >= 'A' && str[0] <= 'Z') //函数类型计算优先级4
power = 4;
else {
if (str[0] == '(') power = -2;
if (str[0] == '=' || str[0] == '<' || str[0] == '>') power = 0;
if (str[0] == '+' || str[0] == '-') power = 1;
if (str[0] == '*' || str[0] == '/') power = 2;
if (str[0] == '^') power = 3;
if (str[0] == '%') power = 5;
if (str[0] == ',') power = -1; //根据不同的符号确定各自的优先级
}
for (int i = 0; i < str.size(); i++) {
this->digits.push_back(int(str[i])); //将名字存进digits里面
}
return;
}
}
//下面就是str表示的是数字情况
this->sign = 1;
int i = 0;
while (str[i] == ' ') i++;
if (str[i] == '-') {
this->sign = -1; i++;
}
if (str[i] == '+') i++;
int retpower = 0;
bool startdigits = false; //开始有效数字
int powerchange = 1; //1表示每往后一格power++ -1就是小数情况
int ifdecimal = false;
bool ifmeetpoint = false; //有无遇见小数点
while (i < str.size()) {
if (startdigits && str[i]>='0' && str[i]<='9') {
this->digits.push_back(str[i] - '0');
if (!ifmeetpoint)
retpower++;
}
else {
if (str[i] >= '1' && str[i] <= '9') {
startdigits = true;
this->digits.push_back(str[i] - '0');
if (!ifmeetpoint)
retpower++;
if (ifdecimal) {
this->power = retpower;
}
}
if (str[i] == '0' && ifdecimal) {
retpower--;
}
if (str[i] == '.') {
ifmeetpoint = true;
if (!startdigits) { //小数
ifdecimal = true;
}
else {
this->power = retpower;
}
}
}
i++;
}
while (!this->digits.empty() && this->digits.back() == 0) //去除末尾的0 保证digits里是纯纯的有效数字
this->digits.pop_back();
if (digits.empty()) { //如果去掉0之后发现没东西了那么说明这个数字就是0 返回ZERO零常量
*this = ZERO;
}
this->power = retpower;
this->setPrecision(); //规定小数位数精度毕竟无限小数不能有无限大的digits给你用
}

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//数学函数
static MyNum getPI(); //求π
//单目数学函数
MyNum My_sqrt() const;
MyNum My_sin() const; MyNum My_cos() const; MyNum My_tan() const;
MyNum My_exp() const;
MyNum My_fabs() const;
MyNum My_neg() const;
MyNum My_log() const;
//多目数学函数
friend MyNum My_gcd(const MyNum& a, const MyNum& b);
friend MyNum My_lcm(const MyNum& a, const MyNum& b);

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MyNum MyNum::getPI() { //危!!! 会超时
MyNum ret;
MyNum add(1);
for (int i = 1; add.sign != 0; i+=2) {
add = ONE / MyNum(i);
if ((i / 2) % 2)
ret -= add;
else
ret += add;
}
return ret*MyNum(4);
}

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MyNum MyNum::My_exp() const {
if (this->sign == 0) return ONE; //e^0=1
if(*this>MyNum(TAYLOR_LIMIT))
return MyNum(exp(this->to_double())); //如果x太大那么就直接用内置函数了不然迭代计算量太大
MyNum ret;
MyNum add(1);
for (int i = 1; add.sign != 0; i++) { //注意这里的跳出条件如果add太小了变成0了说明我们迭代到我们要的精度了这个时候就可以跳出
ret += add;
add *= (*this) / MyNum(i); //迭代
}
return ret;
}

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MyNum MyNum::My_sin() const {
if (this->sign == 0) return ZERO; //sin(0)=0
MyNum cal(*this);
while (cal < -PIDOUBLE)
cal += PIDOUBLE;
while (cal > PIDOUBLE)
cal -= PIDOUBLE; //PI优化
MyNum ret;
MyNum add(-1);
for (int i = 1; add.sign != 0; i++) { //泰勒展开迭代过程跳出条件还是跟exp一样 add为0说明精度够了
add = add * cal / MyNum(i);
if (i % 2) {
add.sign *= -1;
ret += add;
}
}
return ret;
}
MyNum MyNum::My_cos() const{
if (this->sign == 0) return ZERO; //cos(0)=1
MyNum cal(*this);
while (cal < -PIDOUBLE)
cal += PIDOUBLE;
while (cal > PIDOUBLE)
cal -= PIDOUBLE; //PI优化
MyNum ret(1);
MyNum add(1);
for (int i = 1; add.sign != 0; i++) { //同上泰勒展开部分
add = add * cal / MyNum(i);
if (i % 2 == 0) {
add.sign *= -1;
ret += add;
}
}
return ret;
}
MyNum MyNum::My_tan() const{
return this->My_sin() / this->My_cos(); //tan就别泰勒展开了会寄掉的直接sin/cos
}

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MyNum My_gcd_recursion(MyNum& a, MyNum& b) { //递归辗转相除
while (a > b)
a -= b;
if (a == b) return a;
else return My_gcd_recursion(b, a);
}
MyNum My_gcd(const MyNum& a,const MyNum& b) {
if (a.sign != b.sign) return ERROR;
MyNum aa(a.digits,a.power,1),bb(b.digits,b.power,1);
MyNum ret(My_gcd_recursion(aa, bb));
ret.sign = a.sign;
return ret;
}
MyNum My_lcm(const MyNum& a,const MyNum& b) {
return a * b / My_gcd(a, b); //注意这里lcm有个数学关系: lcm*gcd=a*b
}

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//转换函数
double to_double() const;
int to_int() const;
long long to_longlong() const;
std::string to_string() const;
MyNum decimalpart() const;
MyNum addError(int i)const;

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MyNum MyNum::addError(int i)const {
MyNum ret(ERROR);
ret.digits.clear();
if (this->sign == -2)
ret = *this;
for (int temp = ret.digits.size(); temp <= i; temp++) { //补全digits到i
ret.digits.push_back(0);
}
ret.digits[i] = 1;
return ret;
}

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//运算符重载
bool operator<(const MyNum& other)const;
bool operator>(const MyNum& other)const;
bool operator==(const MyNum& other)const;
bool operator!=(const MyNum& other)const;
bool operator<=(const MyNum& other)const;
bool operator>=(const MyNum& other)const;
MyNum operator+(const MyNum& other)const;
MyNum operator-()const;
MyNum operator-(const MyNum& other)const;
MyNum operator*(const MyNum& other)const;
MyNum operator/(const MyNum& other)const;
MyNum operator^(const MyNum& other)const;
MyNum power_int(int k)const;
MyNum power_decimal(const MyNum& decimal)const;
MyNum& operator+=(const MyNum& other);
MyNum& operator-=(const MyNum& other);
MyNum& operator*=(const MyNum& other);
MyNum& operator/=(const MyNum& other);

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MyNum MyNum::operator+(const MyNum& other)const {
//ERROR
if ((*this).sign == -2 || other.sign == -2) {
if ((*this).sign == -2 && other.sign == -2) {
MyNum reterror(ERROR);
for (int i = 0; i < this->digits.size(); i++) {
if (this->digits[i]) {
reterror = reterror.addError(i);
}
}
for (int i = 0; i < other.digits.size(); i++) {
if (other.digits[i]) {
reterror = reterror.addError(i);
}
}
return reterror;
}
if ((*this).sign == -2) return *this;
if (other.sign == -2) return other;
}
//异号
if (this->sign * other.sign == -1) {
if (this->sign < 0) return other - (-(*this));
else return (*this) - (-other);
}
//0
if (this->sign == 0) return other;
if (other.sign == 0) return *this;
//同号
//找到较大的那个数用它加上较小的数比较省事
MyNum const *bigger,*smaller;
if (this->My_fabs() >= other.My_fabs())
{ bigger = this; smaller = &other; }
else
{ bigger = &other; smaller = this; }
int retpower = bigger->power;
int retsign = bigger->sign;
//对齐小数点后逐位相加
int diff = bigger->power - smaller->power; //小数点偏差
std::deque<int> retdigits = bigger->digits;
int length = 0;
while (length < diff) {
while (length >= retdigits.size())
retdigits.push_back(0);
length++;
}
for (int temp = 0; temp < smaller->digits.size(); temp++) {
while (length >= retdigits.size())
retdigits.push_back(0);
retdigits[length++] += smaller->digits[temp];
}
//从后往前逐位校准
for (int temp = length - 1; temp >= 1; temp--) {
retdigits[temp - 1] += retdigits[temp] / 10;
retdigits[temp] %= 10;
}
if (retdigits[0] >= 10) {
retdigits.push_front(retdigits[0] / 10);
retdigits[1] %= 10;
retpower++;
}
//末尾去0
while (!retdigits.empty() && retdigits.back() == 0)
retdigits.pop_back();
if (retdigits.empty()) return ZERO;
MyNum ans(retdigits, retpower, retsign);
ans.setPrecision();
return ans;
}

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MyNum MyNum::operator-(const MyNum& other)const {
//ERROR
if ((*this).sign == -2 || other.sign == -2) return *this+other;
//异号
if (this->sign * other.sign == -1) {
if (this->sign < 0) return -(other + (-(*this)));
else return (*this) + (-other);
}
//0
if (this->sign == 0) return -other;
if (other.sign == 0) return -(*this);
//同号
if ((*this) == other) return ZERO;
int retsign;
//找到绝对值较大的那个数用它减去较小的数比较省事
MyNum const *bigger, *smaller;
if (this->My_fabs() > other.My_fabs())
{ bigger = this; smaller = &other; retsign = bigger->sign; }
else
{ bigger = &other; smaller = this; retsign = -bigger->sign; }
int retpower = bigger->power;
//对齐小数点逐位相减
int diff = bigger->power - smaller->power; //小数点偏差
std::deque<int> retdigits = bigger->digits;
int length = 0;
while (length < diff) {
while (length >= retdigits.size())
retdigits.push_back(0);
length++;
}
for (int temp = 0; temp < smaller->digits.size(); temp++) {
while (length >= retdigits.size())
retdigits.push_back(0);
retdigits[length++] -= smaller->digits[temp];
}
//从后往前逐位校准
for (int temp = length - 1; temp >= 1; temp--) {
while (retdigits[temp] < 0) {
retdigits[temp - 1]--;
retdigits[temp] += 10;
}
}
//去头0 去尾0
while (!retdigits.empty() && retdigits.front() == 0) {
retdigits.pop_front();
retpower--;
}
while (!retdigits.empty() && retdigits.back() == 0)
retdigits.pop_back();
if (retdigits.empty()) return ZERO;
MyNum ans(retdigits, retpower, retsign);
ans.setPrecision();
return ans;
}

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MyNum MyNum::operator*(const MyNum& other)const {
//ERROR
if ((*this).sign == -2 || other.sign == -2) return *this + other;
//0
if (this->sign == 0) return ZERO;
if (other.sign == 0) return ZERO;
int retsign = this->sign * other.sign;
int retpower = this->power + other.power;
std::deque<int> retdigits;
for (int i = 0; i < this->digits.size(); i++) {
if (this->digits[i] == 0) continue;
int temp = i;
for (int j = 0; j < other.digits.size(); j++) {
while (temp >= retdigits.size())
retdigits.push_back(0);
retdigits[temp++] += this->digits[i] * other.digits[j];
}
}
for (int temp = retdigits.size() - 1; temp >= 1; temp--) {
retdigits[temp - 1] += retdigits[temp] / 10;
retdigits[temp] %= 10;
}
retpower--;
while (retdigits.front() >= 10) {
retdigits.push_front(retdigits[0] / 10);
retdigits[1] %= 10;
retpower++;
}
MyNum ans(retdigits, retpower, retsign);
ans.setPrecision();
return ans;
}

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MyNum MyNum::operator/(const MyNum& other)const {
//ERROR
if ((*this).sign == -2 || other.sign == -2) return *this + other;
//除0
if (other.sign == 0) {
return ERROR.addError(0);
}
if (this->sign == 0) {
return ZERO;
}
if (other == MyNum(1)) return *this;
if (other == MyNum(-1)) return -*this;
int retsign = this->sign * other.sign;
int retpower = this->power - other.power;
std::deque<int> a = this->digits;
std::deque<int> b = other.digits;
std::deque<int> ans;
for (int temp = 0; temp <= PRECISION + retsign; temp++) { //除法核心部分
int next = 0;
while (cmp_digits(a, b) > 0) {
minus_digits(a, b);
next++;
}
if (cmp_digits(a, b) == 0) {
next++;
ans.push_back(next);
break;
}
ans.push_back(next);
b.push_front(0);
}
while (!ans.empty() && ans.front() == 0) {
ans.pop_front();
retpower--;
}
while (!ans.empty() && ans.back() == 0) {
ans.pop_back();
}
retpower++;
MyNum ret(ans, retpower, retsign);
ret.setPrecision();
return ret;
}

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MyNum MyNum::operator^(const MyNum& other) const{
//ERROR
if ((*this).sign == -2 || other.sign == -2) return *this + other;
MyNum b(other);
if (b.sign == 0) return (this->sign == 0) ? ERROR.addError(1) : ZERO;
if (this->sign == 0) return (b.sign > 0) ? ZERO : ERROR.addError(0);
//仅排除了底数为零的情况不保证幂指数的整数部分和小数部分不为0
if (b.sign > 0)
return power_int(other.to_int()) * (power_decimal(other.decimalpart())); //整数部分快速幂小数部分泰勒展开
else
return MyNum(1) / (power_int(-other.to_int()) * (power_decimal(-other.decimalpart())));
}
MyNum MyNum::power_int(int k)const { //整数部分
if (k == 0) return MyNum(1);
if (k < 0) return MyNum(1) / ((*this) ^ (-k));
if (*this == MyNum(1)) return MyNum(1);
//快速幂部分
MyNum ans(1);
MyNum bottom(*this);
while (k) {
if (k & 1) {
ans *= bottom;
}
bottom *= bottom;
k >>= 1;
}
ans.setPrecision();
return ans;
}
MyNum MyNum::power_decimal(const MyNum& decimal) const{ //小数部分
//ERROR
if ((*this).sign == -2) return *this;
if (decimal.sign == 0) return MyNum(1);
if (this->sign < 0) //底数负数不可进行小数幂
return ERROR.addError(2);
MyNum mult = this->My_log() * decimal; //泰勒展开每一项要乘的东西
MyNum add(1);
MyNum ret;
for (int i = 1; add.sign != 0; i++) {
ret += add;
add = add * mult / MyNum(i);
}
return ret;
}

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//显示
void show() const;
void setPrecision(int prec = PRECISION);

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void MyNum::show() const {
if (this->sign==-2) {
printf("ERROR\n");
for (int i = 0; i < digits.size(); i++) {
if (digits[i])
std::cout << errorreason[i] << std::endl;
}
return;
}
if (sign == 2) {
if (digits[0] == ',') return;
for (int i = 0; i < digits.size(); i++)
printf("%c", char(digits[i]));
return;
}
int power = this->power;
int sign = this->sign;
std::deque<int> digits = this->digits;
if (sign == -1) printf("-");
if (sign == 0) { printf("0"); return; }
if (power <= 0) {
printf("0.");
while (power < 0) {
printf("0"); power++;
}
power--;
}
for (int i = 0; i < digits.size(); i++) {
if (power-- == 0) {
printf(".");
}
printf("%d", digits[i]);
}
while (power > 0) {
printf("0");
power--;
}
}

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void Method::changetorpn() { this->rpn.clear(); std::deque& retrpn = this->rpn; std::deque opstack; //符号栈(用deque模拟栈) string nowdigits; string op; for (int i = 0; i < calstr.size(); i++) { if (calstr[i] == ' ') continue; if (calstr[i] == ',') { if (!nowdigits.empty()) { retrpn.push_back(MyNum(nowdigits)); nowdigits.clear(); } while (!opstack.empty() && opstack.back() != MyNum("(")) { retrpn.push_back(opstack.back()); opstack.pop_back(); } //opstack.pop_back(); continue; } if (calstr[i] == '-' ) { if (!(!nowdigits.empty() || i > 0 && calstr[i - 1] == ')')) { //'-'是负号不是减号 if (!op.empty()) { opstackpushback(opstack, MyNum(op)); op.clear(); } opstackpushback(opstack, MyNum("neg")); continue; } } if (calstr[i] >= '0' && calstr[i] 12 && str.substr(0,12) == "setprecision") { int newprecision = 0; for (int i = 13; i < str.size(); i++) { newprecision *= 10; newprecision += str[i] - '0'; } SHOW_PRECISION = newprecision; return 4; } Method m(str); history.push_back(m); return 1;}void Func() { int input = 1; while(true) { input = inputMethod(); if (input == 0) break; if (input == 1) { history.back().show(showType); cout digits = other.digits; this->power = other.power; this->sign = other.sign; return *this; } //析构 ~MyNum() {} //数学函数 static MyNum getPI(); //求π //单目数学函数 MyNum My_sqrt() const; MyNum My_sin() const; MyNum My_cos() const; MyNum My_tan() const; MyNum My_exp() const; MyNum My_fabs() const; MyNum My_neg() const; MyNum My_log() const; //多目数学函数 //见类外定义的非成员函数 friend MyNum My_gcd(const MyNum& a, const MyNum& b); friend MyNum My_lcm(const MyNum& a, const MyNum& b); //转换函数
double to_double() const;
int to_int() const;
long long to_longlong() const;
std::string to_string() const;
MyNum decimalpart() const;
MyNum addError(int i)const; //运算符重载 bool operator(const MyNum& other)const; bool operator==(const MyNum& other)const; bool operator!=(const MyNum& other)const; bool operator=(const MyNum& other)const; MyNum operator+(const MyNum& other)const; MyNum operator-()const; MyNum operator-(const MyNum& other)const; MyNum operator*(const MyNum& other)const; MyNum operator/(const MyNum& other)const; MyNum operator^(const MyNum& other)const; MyNum power_int(int k)const; MyNum power_decimal(const MyNum& decimal)const; MyNum& operator+=(const MyNum& other); MyNum& operator-=(const MyNum& other); MyNum& operator*=(const MyNum& other); MyNum& operator/=(const MyNum& other); MyNum MyNum::operator/(const MyNum& other)const {
//ERROR
if ((*this).sign == -2 || other.sign == -2) return *this + other;
//除0
if (other.sign == 0) {
return ERROR.addError(0);
}
if (this->sign == 0) {
return ZERO;
}
if (other == MyNum(1)) return *this;
if (other == MyNum(-1)) return -*this;
int retsign = this->sign * other.sign;
int retpower = this->power - other.power;
std::deque<int> a = this->digits;
std::deque<int> b = other.digits;
std::deque<int> ans;
for (int temp = 0; temp <= PRECISION + retsign; temp++) { //除法核心部分
int next = 0;
while (cmp_digits(a, b) > 0) {
minus_digits(a, b);
next++;
}
if (cmp_digits(a, b) == 0) {
next++;
ans.push_back(next);
break;
}
ans.push_back(next);
b.push_front(0);
}
while (!ans.empty() && ans.front() == 0) {
ans.pop_front();
retpower--;
}
while (!ans.empty() && ans.back() == 0) {
ans.pop_back();
}
retpower++;
MyNum ret(ans, retpower, retsign);
ret.setPrecision();
return ret;
}private: std::deque digits; int power; int sign; friend class Method;};MyNum My_gcd(const MyNum& a, const MyNum& b);MyNum My_lcm(const MyNum& a, const MyNum& b);#endif

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#define _CRT_SECURE_NO_WARNINGS#include "MyNum.h"#include #include #define ZERO_LIMIT 1e-6 //小于这个数字的浮点数就判定为0#define TAYLOR_LIMIT 50 //数学函数里面使用泰勒展开的数据最大值因为数据过大泰勒展开将会耗时过久extern const MyNum ZERO({ 0 }, 0, 0);extern const MyNum ERROR({}, 0, -2);extern const MyNum ONE(1);//const MyNum PI(MyNum::getPI());extern MyNum PI("3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446"); //运用getPI函数将会超时... 因此直接读入pi会更好extern MyNum PIDOUBLE("6.2831853071795864769252867665590057683943387987502116419498891846156328125724179972560696506842341359642961730265646132941876892");//工具函数int getmin(int a, int b) { return a < b ? a : b; }int getmax(int a, int b) { return a > b ? a : b; }int inttodeque(std::deque& digits, int i) { if (i == 0) { digits.push_back(0); return 0; } int retpower = 0; i = i > 0 ? i : -i; while (i) { digits.push_front(i % 10); i /= 10; retpower++; } return retpower;}int cmp_digits(std::deque& a, std::deque& b) { for (int i = 0; i < getmin(a.size(), b.size());i++) { if (a[i] > b[i]) return 1; if (a[i] < b[i]) return -1; } if (a.size() > b.size()) return 1; if (a.size() < b.size()) return -1; return 0;}int minus_digits(std::deque& a, std::deque& b) { //前提确保了a>b for (int i = 0; i < b.size(); i++) { if (i == a.size()) a.push_back(0); a[i] -= b[i]; } for (int i = a.size() - 1; i >= 1; i--) { while (a[i] < 0) { a[i - 1] --; a[i] += 10; } } int ret = 0; //返回借位 while (a[0] < 0) { ret++; a[0]+=10; } return ret;}string digittostring(std::deque& digits) { string ans; for (int i = 0; i < digits.size(); i++) { ans.push_back(char(digits[i])); } return ans;}//构造函数MyNum::MyNum(int i) { *this = MyNum((long long)i);}MyNum::MyNum(long long i) { if (i == 0ll) { *this = ZERO; return; } int power = 0; std::deque digits; int sign = 1; if (i < 0) sign = -1; i *= sign; while (i) { digits.push_front(i % 10); i /= 10; power++; } while (digits.back() == 0) digits.pop_back(); this->digits = digits; this->power = power; this->sign = sign;}MyNum::MyNum(double d) { if (d < ZERO_LIMIT && d>-ZERO_LIMIT) { *this = ZERO; return; } this->sign = (d > 0) ? 1 : -1; d *= sign; int retpower = 0; if(int(d)!=0) retpower = inttodeque(this->digits, int(d)); bool ifFindDemicalPoint = retpower >= 0; //是否找到小数点 d -= int(d); //只保留小数部分 while (d > ZERO_LIMIT || d < -ZERO_LIMIT) { d *= 10; int integer = int(d); d -= integer; if (ifFindDemicalPoint) this->digits.push_back(integer); else { if (integer == 0) retpower--; else ifFindDemicalPoint = true; } } this->power = retpower; while (this->digits.back() == 0) this->digits.pop_back(); this->setPrecision(); /*char str[1000]; sprintf(str, "%lf", d); *this = MyNum(std::string(str));*/ //sprintf转换成字符串只有6位小数的精度}MyNum::MyNum(std::string str) { if (str.size() && (str[0] < '0' || str[0]>'9')) { if (!((str[0] == '-' || str[0] == '+') && str.size() > 1 && str[1] >= '0' && str[1] sign = 2; if (str[0] >= 'a' && str[0] = 'A' && str[0] digits.push_back(int(str[i])); } return; } } this->sign = 1; int i = 0; while (str[i] == ' ') i++; if (str[i] == '-') { this->sign = -1; i++; } if (str[i] == '+') i++; int retpower = 0; bool startdigits = false; //开始有效数字 int powerchange = 1; //1表示每往后一格power++ -1就是小数情况 int ifdecimal = false; bool ifmeetpoint = false; //有无遇见小数点 while (i < str.size()) { if (startdigits && str[i]>='0' && str[i]digits.push_back(str[i] - '0'); if (!ifmeetpoint) retpower++; } else { if (str[i] >= '1' && str[i] digits.push_back(str[i] - '0'); if (!ifmeetpoint) retpower++; if (ifdecimal) { this->power = retpower; } } if (str[i] == '0' && ifdecimal) { retpower--; } if (str[i] == '.') { ifmeetpoint = true; if (!startdigits) { //小数 ifdecimal = true; } else { this->power = retpower; } } } i++; } while (!this->digits.empty() && this->digits.back() == 0) this->digits.pop_back(); if (digits.empty()) { *this = ZERO; } this->power = retpower; this->setPrecision();}//数学函数MyNum MyNum::getPI() { MyNum ret; MyNum add(1); for (int i = 1; add.sign != 0; i+=2) { add = ONE / MyNum(i); if ((i / 2) % 2) ret -= add; else ret += add; } return ret*MyNum(4);}//单目数学函数MyNum MyNum::My_sqrt() const { //return *this^MyNum(0.5); return MyNum(sqrt(this->to_double()));}MyNum MyNum::My_sin() const { if (this->sign == 0) return ZERO; MyNum cal(*this); while (cal < -PIDOUBLE) cal += PIDOUBLE; while (cal > PIDOUBLE) cal -= PIDOUBLE; //PI优化 MyNum ret; MyNum add(-1); for (int i = 1; add.sign != 0; i++) { add = add * cal / MyNum(i); if (i % 2) { add.sign *= -1; ret += add; } } return ret;}MyNum MyNum::My_cos() const{ if (this->sign == 0) return MyNum(1); MyNum cal(*this); while (cal < -PIDOUBLE) cal += PIDOUBLE; while (cal > PIDOUBLE) cal -= PIDOUBLE; //PI优化 MyNum ret(1); MyNum add(1); for (int i = 1; add.sign != 0; i++) { add = add * cal / MyNum(i); if (i % 2 == 0) { add.sign *= -1; ret += add; } } return ret;}MyNum MyNum::My_tan() const{ return this->My_sin() / this->My_cos();}MyNum MyNum::My_exp() const { if (this->sign == 0) return ONE; if(*this>MyNum(TAYLOR_LIMIT)) return MyNum(exp(this->to_double())); MyNum ret; MyNum add(1); for (int i = 1; add.sign != 0; i++) { ret += add; add *= (*this) / MyNum(i); } return ret;}MyNum MyNum::My_fabs() const { return MyNum(this->digits, this->power, (this->signsign addError(4); } return MyNum(log(this->to_double()));}//多目数学函数MyNum My_gcd_recursion(MyNum& a, MyNum& b) { //递归辗转相除 while (a > b) { a -= b; } if (a == b) return a; else return My_gcd_recursion(b, a);}MyNum My_gcd(const MyNum& a,const MyNum& b) { if (a.sign != b.sign) return ERROR; MyNum aa(a.digits,a.power,1),bb(b.digits,b.power,1); MyNum ret(My_gcd_recursion(aa, bb)); ret.sign = a.sign; return ret;}MyNum My_lcm(const MyNum& a,const MyNum& b) { return a * b / My_gcd(a, b);}//转换函数double MyNum::to_double() const { double ret = 0; const std::deque& digits=this->digits; for (int i = digits.size() - 1; i >= 0; i--) { //化为类科学计数法 0.xxx ret += digits[i]; ret /= 10; } if(this->power>0) for (int i = 0; i < this->power; i++) ret *= 10; else { for (int i = 0; i < -this->power; i++) { ret /= 10; } } return ret;}int MyNum::to_int() const { if (power digits[i]; } return ret * this->sign;}long long MyNum::to_longlong() const { if (power digits[i]); } return ret * this->sign;}std::string MyNum::to_string() const { if (sign == -2) return "ERROR"; if (sign == 0) return "0"; string ans; if (sign == -1) ans.push_back('-'); int power = this->power; const std::deque& digits = this->digits; if (power = digits.size()) ans.push_back('0'); else ans.push_back('0' + digits[i]); } if (i < digits.size()) { ans.push_back('.'); for (; i < digits.size(); i++) { ans.push_back(digits[i]); } } } return ans;}MyNum MyNum::decimalpart() const { if (this->power sign == -2) ret = *this; for (int temp = ret.digits.size(); temp sign > other.sign) return false; //下面同号情况 if (this->power < other.power) return sign == 1; //绝对值小判断是否正数 if (this->power > other.power) return sign == -1; //绝对值小判断是否正数 //同号指数相同比较有效数字 int i; for (i = 0; i < getmin(this->digits.size(), other.digits.size()); i++) { if (this->digits[i] < other.digits[i]) return sign == 1; if (this->digits[i] > other.digits[i]) return sign == -1; } //有效数字重叠判断哪个短 if (this->digits.size() < other.digits.size()) return sign == 1; if (this->digits.size() > other.digits.size()) return sign == -1; return false;}bool MyNum::operator>(const MyNum& other)const { if (this->sign > other.sign) return true; if (this->sign < other.sign) return false; //下面同号情况 if (this->power > other.power) return sign == 1; //绝对值大判断是否正数 if (this->power < other.power) return sign == -1; //同号指数相同比较有效数字 int i; for (i = 0; i < getmin(this->digits.size(), other.digits.size()); i++) { if (this->digits[i] > other.digits[i]) return sign == 1; if (this->digits[i] < other.digits[i]) return sign == -1; } //有效数字重叠判断哪个长 if (this->digits.size() > other.digits.size()) return sign == 1; if (this->digits.size() < other.digits.size()) return sign == -1; return false;}bool MyNum::operator==(const MyNum& other)const { return (this->digits == other.digits && this->sign == other.sign && this->power == other.power);}bool MyNum::operator!=(const MyNum& other)const { return !(this->operator==(other));}bool MyNum::operator=(const MyNum& other)const { return (*this) > other || (*this) == other;}MyNum MyNum::operator+(const MyNum& other)const { //ERROR if ((*this).sign == -2 || other.sign == -2) { if ((*this).sign == -2 && other.sign == -2) { MyNum reterror(ERROR); for (int i = 0; i < this->digits.size(); i++) { if (this->digits[i]) { reterror = reterror.addError(i); } } for (int i = 0; i < other.digits.size(); i++) { if (other.digits[i]) { reterror = reterror.addError(i); } } return reterror; } if ((*this).sign == -2) return *this; if (other.sign == -2) return other; } //异号 if (this->sign * other.sign == -1) { if (this->sign < 0) return other - (-(*this)); else return (*this) - (-other); } //0 if (this->sign == 0) return other; if (other.sign == 0) return *this; //同号 //找到较大的那个数用它加上较小的数比较省事 MyNum const *bigger,*smaller; if (this->My_fabs() >= other.My_fabs()) { bigger = this; smaller = &other; } else { bigger = &other; smaller = this; } int retpower = bigger->power; int retsign = bigger->sign; //对齐小数点后逐位相加 int diff = bigger->power - smaller->power; //小数点偏差 std::deque retdigits = bigger->digits; int length = 0; while (length < diff) { while (length >= retdigits.size()) retdigits.push_back(0); length++; } for (int temp = 0; temp < smaller->digits.size(); temp++) { while (length >= retdigits.size()) retdigits.push_back(0); retdigits[length++] += smaller->digits[temp]; } //从后往前逐位校准 for (int temp = length - 1; temp >= 1; temp--) { retdigits[temp - 1] += retdigits[temp] / 10; retdigits[temp] %= 10; } if (retdigits[0] >= 10) { retdigits.push_front(retdigits[0] / 10); retdigits[1] %= 10; retpower++; } //末尾去0 while (!retdigits.empty() && retdigits.back() == 0) retdigits.pop_back(); if (retdigits.empty()) return ZERO; MyNum ans(retdigits, retpower, retsign); ans.setPrecision(); return ans;}MyNum MyNum::operator-()const { return MyNum(this->digits, this->power, -(this->sign));}//运算符重载
bool operator<(const MyNum& other)const;
bool operator>(const MyNum& other)const;
bool operator==(const MyNum& other)const;
bool operator!=(const MyNum& other)const;
bool operator<=(const MyNum& other)const;
bool operator>=(const MyNum& other)const;
MyNum operator+(const MyNum& other)const;
MyNum operator-()const;
MyNum operator-(const MyNum& other)const;
MyNum operator*(const MyNum& other)const;
MyNum operator/(const MyNum& other)const;
MyNum operator^(const MyNum& other)const;
MyNum power_int(int k)const;
MyNum power_decimal(const MyNum& decimal)const;
MyNum& operator+=(const MyNum& other);
MyNum& operator-=(const MyNum& other);
MyNum& operator*=(const MyNum& other);
MyNum& operator/=(const MyNum& other);MyNum MyNum::operator+(const MyNum& other)const {
//ERROR
if ((*this).sign == -2 || other.sign == -2) {
if ((*this).sign == -2 && other.sign == -2) {
MyNum reterror(ERROR);
for (int i = 0; i < this->digits.size(); i++) {
if (this->digits[i]) {
reterror = reterror.addError(i);
}
}
for (int i = 0; i < other.digits.size(); i++) {
if (other.digits[i]) {
reterror = reterror.addError(i);
}
}
return reterror;
}
if ((*this).sign == -2) return *this;
if (other.sign == -2) return other;
}
//异号
if (this->sign * other.sign == -1) {
if (this->sign < 0) return other - (-(*this));
else return (*this) - (-other);
}
//0
if (this->sign == 0) return other;
if (other.sign == 0) return *this;
//同号
//找到较大的那个数用它加上较小的数比较省事
MyNum const *bigger,*smaller;
if (this->My_fabs() >= other.My_fabs())
{ bigger = this; smaller = &other; }
else
{ bigger = &other; smaller = this; }
int retpower = bigger->power;
int retsign = bigger->sign;
//对齐小数点后逐位相加
int diff = bigger->power - smaller->power; //小数点偏差
std::deque<int> retdigits = bigger->digits;
int length = 0;
while (length < diff) {
while (length >= retdigits.size())
retdigits.push_back(0);
length++;
}
for (int temp = 0; temp < smaller->digits.size(); temp++) {
while (length >= retdigits.size())
retdigits.push_back(0);
retdigits[length++] += smaller->digits[temp];
}
//从后往前逐位校准
for (int temp = length - 1; temp >= 1; temp--) {
retdigits[temp - 1] += retdigits[temp] / 10;
retdigits[temp] %= 10;
}
if (retdigits[0] >= 10) {
retdigits.push_front(retdigits[0] / 10);
retdigits[1] %= 10;
retpower++;
}
//末尾去0
while (!retdigits.empty() && retdigits.back() == 0)
retdigits.pop_back();
if (retdigits.empty()) return ZERO;
MyNum ans(retdigits, retpower, retsign);
ans.setPrecision();
return ans;
}MyNum MyNum::operator-(const MyNum& other)const {
//ERROR
if ((*this).sign == -2 || other.sign == -2) return *this+other;
//异号
if (this->sign * other.sign == -1) {
if (this->sign < 0) return -(other + (-(*this)));
else return (*this) + (-other);
}
//0
if (this->sign == 0) return -other;
if (other.sign == 0) return -(*this);
//同号
if ((*this) == other) return ZERO;
int retsign;
//找到绝对值较大的那个数用它减去较小的数比较省事
MyNum const *bigger, *smaller;
if (this->My_fabs() > other.My_fabs())
{ bigger = this; smaller = &other; retsign = bigger->sign; }
else
{ bigger = &other; smaller = this; retsign = -bigger->sign; }
int retpower = bigger->power;
//对齐小数点逐位相减
int diff = bigger->power - smaller->power; //小数点偏差
std::deque<int> retdigits = bigger->digits;
int length = 0;
while (length < diff) {
while (length >= retdigits.size())
retdigits.push_back(0);
length++;
}
for (int temp = 0; temp < smaller->digits.size(); temp++) {
while (length >= retdigits.size())
retdigits.push_back(0);
retdigits[length++] -= smaller->digits[temp];
}
//从后往前逐位校准
for (int temp = length - 1; temp >= 1; temp--) {
while (retdigits[temp] < 0) {
retdigits[temp - 1]--;
retdigits[temp] += 10;
}
}
//去头0 去尾0
while (!retdigits.empty() && retdigits.front() == 0) {
retdigits.pop_front();
retpower--;
}
while (!retdigits.empty() && retdigits.back() == 0)
retdigits.pop_back();
if (retdigits.empty()) return ZERO;
MyNum ans(retdigits, retpower, retsign);
ans.setPrecision();
return ans;
}MyNum MyNum::operator^(const MyNum& other) const{ //ERROR if ((*this).sign == -2 || other.sign == -2) return *this + other; MyNum b(other); if (b.sign == 0) return (this->sign == 0) ? ERROR.addError(1) : ZERO; if (this->sign == 0) return (b.sign > 0) ? ZERO : ERROR.addError(0); //仅排除了底数为零的情况不保证幂指数的整数部分和小数部分不为0 if (b.sign > 0) return power_int(other.to_int()) * (power_decimal(other.decimalpart())); //整数部分快速幂小数部分泰勒展开 else return MyNum(1) / (power_int(-other.to_int()) * (power_decimal(-other.decimalpart())));}MyNum MyNum::power_int(int k)const { if (k == 0) return MyNum(1); if (k < 0) return MyNum(1) / ((*this) ^ (-k)); if (*this == MyNum(1)) return MyNum(1); //快速幂部分 MyNum ans(1); MyNum bottom(*this); while (k) { if (k & 1) { ans *= bottom; } bottom *= bottom; k >>= 1; } ans.setPrecision(); return ans;}MyNum MyNum::power_decimal(const MyNum& decimal) const{ //ERROR if ((*this).sign == -2) return *this; if (decimal.sign == 0) return MyNum(1); if (this->sign < 0) //底数负数不可进行小数幂 return ERROR.addError(2); MyNum mult = this->My_log() * decimal; //泰勒展开每一项要乘的东西 MyNum add(1); MyNum ret; for (int i = 1; add.sign != 0; i++) { ret += add; add = add * mult / MyNum(i); } return ret;}MyNum& MyNum::operator+=(const MyNum& other) { *this = *this + other; return *this;}MyNum& MyNum::operator-=(const MyNum& other) { *this = *this - other; return *this;}MyNum& MyNum::operator*=(const MyNum& other) { *this = *this * other; return *this;}MyNum& MyNum::operator/=(const MyNum& other) { *this = *this / other; return *this;}//显示MyNum MyNum::operator^(const MyNum& other) const{
//ERROR
if ((*this).sign == -2 || other.sign == -2) return *this + other;
MyNum b(other);
if (b.sign == 0) return (this->sign == 0) ? ERROR.addError(1) : ZERO;
if (this->sign == 0) return (b.sign > 0) ? ZERO : ERROR.addError(0);
//仅排除了底数为零的情况不保证幂指数的整数部分和小数部分不为0
if (b.sign > 0)
return power_int(other.to_int()) * (power_decimal(other.decimalpart())); //整数部分快速幂小数部分泰勒展开
else
return MyNum(1) / (power_int(-other.to_int()) * (power_decimal(-other.decimalpart())));
}
MyNum MyNum::power_int(int k)const { //整数部分
if (k == 0) return MyNum(1);
if (k < 0) return MyNum(1) / ((*this) ^ (-k));
if (*this == MyNum(1)) return MyNum(1);
//快速幂部分
MyNum ans(1);
MyNum bottom(*this);
while (k) {
if (k & 1) {
ans *= bottom;
}
bottom *= bottom;
k >>= 1;
}
ans.setPrecision();
return ans;
}
MyNum MyNum::power_decimal(const MyNum& decimal) const{ //小数部分
//ERROR
if ((*this).sign == -2) return *this;
if (decimal.sign == 0) return MyNum(1);
if (this->sign < 0) //底数负数不可进行小数幂
return ERROR.addError(2);
MyNum mult = this->My_log() * decimal; //泰勒展开每一项要乘的东西
MyNum add(1);
MyNum ret;
for (int i = 1; add.sign != 0; i++) {
ret += add;
add = add * mult / MyNum(i);
}
return ret;
}void MyNum::setPrecision(int prec) { int decimalpart = this->digits.size() - this->power; //小数部分长度 if (decimalpart digits.empty()) this->digits.pop_back(); int diff = 0; //四舍五入的偏差值 if (!this->digits.empty()) { if (this->digits.back() >= 5) { diff = 1; //进1 } this->digits.pop_back(); } if (this->digits.empty()) { *this = ZERO; } else { int i = this->digits.size() - 1; while (diff) { if (i == -1) break; this->digits[i] += diff; diff = this->digits[i] / 10; this->digits[i] %= 10; i--; } if (i == -1 && diff) { this->power++; this->digits.front() %= 10; this->digits.push_front(1); } }}

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#ifndef _METHOD_H_#define _METHOD_H_/* Method类存放计算式的原式后缀表达式以及计算答案 string calstr //计算的原式 std::deque rpn //ReversePolishNotation 逆波兰表示法/后缀表达式 int type //0 计算式 1 逻辑条件式 MyNum ans //计算结果*/#include #include #include #include "MyNum.h"using std::string;extern int SHOW_PRECISION;class Method{public: //显示
void show() const;
void setPrecision(int prec = PRECISION); void MyNum::show() const {
if (this->sign==-2) {
printf("ERROR\n");
for (int i = 0; i < digits.size(); i++) {
if (digits[i])
std::cout << errorreason[i] << std::endl;
}
return;
}
if (sign == 2) {
if (digits[0] == ',') return;
for (int i = 0; i < digits.size(); i++)
printf("%c", char(digits[i]));
return;
}
int power = this->power;
int sign = this->sign;
std::deque<int> digits = this->digits;
if (sign == -1) printf("-");
if (sign == 0) { printf("0"); return; }
if (power <= 0) {
printf("0.");
while (power < 0) {
printf("0"); power++;
}
power--;
}
for (int i = 0; i < digits.size(); i++) {
if (power-- == 0) {
printf(".");
}
printf("%d", digits[i]);
}
while (power > 0) {
printf("0");
power--;
}
} //显示 void showCalstr(); void showRPN(); void showAns(int showprecision=SHOW_PRECISION); void show(int type = 0);private: string calstr; std::deque rpn; int type; MyNum ans;};#endif

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