整数运算_atom_整数运算_

#include<stdio.h> #include<stdlib.h> #include<string.h> #include<iostream> #include<string> #include<algorithm> #define HALFINT 0x8000 using namespace std; typedef unsigned int word; typedef unsigned char byte; typedef unsigned dwrd; word atom(char* s){//字符串转换成对应的二进制原码 word u=0; int i; i=(s[0]=='-')?1:0; for(;s[i]!=0;i++){ u=(u*10)+(s[i]-'0'); } u=(s[0]=='-')?(HALFINT|u):u; return u; } word add(word x,word y){//原码加法，返回的是运算结果的原码 word tempx=x&0x7FFF,tempy=y&0x7FFF,result; if((!(x&HALFINT))&&(y&HALFINT)){ result=tempx-tempy; } else if((x&HALFINT)&&(!(y&HALFINT))){ result=tempy-tempx; } else if((x&HALFINT)&&(y&HALFINT)){ result=-tempx-tempy; } else if((!(x&HALFINT))&&(!(y&HALFINT))) result=tempx+tempy; if(result&HALFINT){ result=~result+1; result=result&0x7FFF; result=result|HALFINT; } return result; } word sub(word x,word y){//原码减法，返回的是运算结果的原码 if(!(y&HALFINT)){ y=y|HALFINT; } else{ y=y&0x7FFF; } return(add(x,y)); } word mul(word x,word y){//本程序通过1位booth算法实现乘法运算，先将原码转化成补码，再将1位booth算法的运算结果转化成原码返回 可接受的参数范围为[-127,127] word mm=0; if(x==0||y==0) return 0; if(x&HALFINT){ x=x&0x7FFF; x=-x; } if(y&HALFINT){ y=y&0x7FFF; y=-y; } mm=(y<<1)&0xFFFF; word addx=x<<16; word subx=-addx,cnt=0; while(cnt<15){ if((mm&3)==1){ mm+=addx; } else if((mm&3)==2){ mm+=subx; } mm>>=1; cnt++; } mm>>=1; mm=mm&0xFFFF; if(mm&HALFINT){ mm=~mm+1; mm=mm&0xFFFF; mm=mm|HALFINT; } return mm; } word div(word x,word y){//本程序通过加减交替算法实现除法运算，先计算|x|/|y|，再判断运算结果的符号 if(x==0) return 0; word div,addy,quo=0,mod,sign,cnt=0; sign=(x&HALFINT)^(y&HALFINT)?-1:1; if(x&HALFINT){ div=x&0x7FFF; } else{ div=x; } if(y&HALFINT){ addy=y&0x7FFF; } else{ addy=y; } mod=div; addy=addy<<16; while(cnt<17){ mod-=addy; quo=quo<<1; if(mod&0x80000000){ mod+=addy; } else{ quo=quo|0x0001; } addy=addy>>1; cnt++; } if(sign==-1){ quo=quo|HALFINT; } return quo; } word mmod(word x,word y){//余数通过公式 被除数=除数*商+余数 运算而来 word quo=div(x,y); word pro=mul(quo,y); word mod=sub(x,pro); return mod; } word expend(word x){//位扩展运算，用于将16位二进制数扩展成32位二进制数 if(x&HALFINT){ x=x&0x7FFF; x=x|0x80000000; } else{ x=x|0x00000000; } return x; } word compare(word x,word y){//大小比较通过两数之间的减法运算结果是否为0以及符号判断来实现 word result; if((sub(x,y)&0x7FFF)==0){ result=0; } else result=(sub(x,y)&HALFINT)?-1:1; return result; } string mtoa(word u){//二进制转换成字符串 string s; word i=0,j,sign=0; if(u&HALFINT){ sign=1; } u=u&0x7FFF; word mod,ten=10; do{ mod=mmod(u,ten); s+=mod+'0'; u=div(u,ten); }while(u); if(sign){ s+='-'; } reverse(s.begin(),s.end()); return s; } int main(){ char s[80]; word x,y,z; scanf("%s",s); x=atom(s); scanf("%s",s); y=atom(s); if(((x&0x7FFF)&0xFFFF8000)||((y&0x7FFF)&0xFFFF8000)){ printf("输入发生了溢出！\n"); return 0; } printf("x=%x,y=%x\n",x,y); z=expend(x); printf("x扩展成32位后的结果是：%x\n",z); z=expend(y); printf("y扩展成32位后的结果是：%x\n",z); word tempx=x&0x7FFF; word tempy=y&0x7FFF; word tempz=add(tempx,tempy); if(tempz&HALFINT){ printf("加减法运算发生了溢出！\n"); return 0; } z=add(x,y); cout<<mtoa(x); printf("(%x)+",x); cout<<mtoa(y); printf("(%x)=",y); cout<<mtoa(z); printf("(%x)\n",z); z=sub(x,y); word cmp=compare(z,0); if(cmp){ if(cmp==1){ printf("x>y\n"); } else if(cmp==-1){ printf("x<y\n"); } } else{ printf("x==y\n"); } cout<<mtoa(x); printf("(%x)-",x); cout<<mtoa(y); printf("(%x)=",y); cout<<mtoa(z); printf("(%x)\n",z); tempz=mul(tempx,tempy); if((tempx!=0)&&(tempy!=0)){ if(tempz&0x8000){ printf("乘法运算发生了溢出！\n"); return 0; } tempz=mul(tempx|0x8000,tempy); if(!(tempz&0x8000)){ printf("乘法运算发生了溢出！\n"); return 0; } tempz=mul(tempx,tempy|0x8000); if(!(tempz&0x8000)){ printf("乘法运算发生了溢出！\n"); return 0; } tempz=mul(tempx|0x8000,tempy|0x8000); if(tempz&0x8000){ printf("乘法运算发生了溢出！\n"); return 0; } } z=mul(x,y); cout<<mtoa(x); printf("(%x)*",x); cout<<mtoa(y); printf("(%x)=",y); cout<<mtoa(z); printf("(%x)\n",z); if(y==0){ printf("除数为0！\n"); return 0; } z=div(x,y); cout<<mtoa(x); printf("(%x)/",x); cout<<mtoa(y); printf("(%x)=",y); cout<<mtoa(z); printf("(%x)\n",z); z=mmod(x,y); cout<<mtoa(x); printf("(%x)mod",x); cout<<mtoa(y); printf("(%x)=",y); cout<<mtoa(z); printf("(%x)\n",z); return 0; }