定點小數補碼一位乘（Booth比較法）

程式：

// 定點小數補碼一位乘（Booth比較法）// http://blog.csdn.net/justme0#define _CRT_SECURE_NO_WARNINGS#include <iostream>#include <bitset>#include <string>using namespace std;const int n = 4;// 數值位位元// a,b聯合右移（算術移位）void RightMove(bitset<n + 2> &a, bitset<n + 1> &b, bool &eBit){eBit = b[0];b >>= 1;b[n] = a[0];a >>= 1;a[n + 1] = a[n];// 算術右移}bitset<n + 2> operator+(bitset<n + 2> a, bitset<n + 2> b)// 求a,b的算術和{return a.to_ullong() + b.to_ullong();}bitset<n + 2> operator-(bitset<n + 2> a, bitset<n + 2> b){return a.to_ullong() - b.to_ullong();}bitset<n + 1> GetComplement(bitset<n + 1> a){if (a[n]){a = ~a.to_ullong() + 1;a.set(n);// NOTE}return a;}bitset<2 * n + 1> GetComplement(const bitset<n + 2> high, const bitset<n + 1> low)// low的最低位捨棄，因為它不屬於積，而是原來乘數的符號{bitset<2 * n + 1> ans(high.to_string().substr(1) + low.to_string().substr(0, 4));if (ans[2 * n]){ans = ~ans.to_ullong() + 1;ans.set(2 * n);// NOTE}return ans;}enum Sign{_00, _01, _10, _11};Sign Test(bool a, bool b){if (!a && !b){return _00;}else if (!a && b){return _01;}else if (a && !b){return _10;} else // if (a && b) // 所有路徑都必須傳回值{return _11;}}bitset<2 * n + 1> ComplementOneMul(const bitset<n + 1> X, const bitset<n + 1> Y)//傳進被乘數X和乘數Y（原碼錶示）{bitset<n + 2> A;// A放部分積（最後是積的高位）bitset<n + 2> tmp = GetComplement(X).to_ullong();tmp[n + 1] = tmp[n];// 注意補碼最高位的擴充const bitset<n + 2> B(tmp);// B是X的補碼  //無法利用傳回值的不同而重載，故引入tmpbitset<n + 1> C = GetComplement(Y);// C是Y0.Y1Y2...Yn（Y的補碼）int cd = n + 1;// cd是計數器bool Yn1 = 0;#pragma region 核心演算法while (cd--){switch (Test(C[0], Yn1))// 檢測Y(i+1)-Y(i){case _00: case _11:break;case _10:A = A - B;break;case _01:A = A + B;break;default:break;}if (cd != 0)// 最後一次不移位{RightMove(A, C, Yn1);// A,C聯合右移，C的低位移至Yn1}}#pragma endregion 核心演算法return GetComplement(A, C);}bitset<2 * n + 1> DirectMul(const bitset<n + 1> X, const bitset<n + 1> Y){const bitset<n> x(X.to_ullong());// 用截斷高位的方法取絕對值const bitset<n> y(Y.to_ullong());bitset<2 * n + 1> ans(x.to_ullong() * y.to_ullong());ans[2 * n] = X[n] ^ Y[n];// 最後單獨計算符號位return ans;}int main(int argc, char **argv){//freopen("cin.txt", "r", stdin);string inputStrX;string inputStrY;while (cin >> inputStrX >> inputStrY){const bitset<n + 1> X(inputStrX);// X是被乘數const bitset<n + 1> Y(inputStrY);// Y是乘數cout << "ComplementOneMul:\t" << X << " * " << Y << " = "<< ComplementOneMul(X, Y) << endl;cout << "DirectMul:\t\t" << X << " * " << Y << " = "<< DirectMul(X, Y) << endl << endl;}return 0;}

運行結果：