C <del>924</del> <del>882</del> 622 chars
=

    #define A sbrk(8);signal(11,S);
    #define U *t++
    #define P t>s?*--t:0
    #define W(x)write(1,&x,1);
    #define B(x,y)break;case 48+x:b=48+x;W(b)w=P;y;U=w;
    *s,*t,w,a,c,d;char b;S(x){A}main(){t=s=A
    U=0;while(read(0,&b,1))switch(b){B(0,w+=a*pow(10,ceil(log10(w))))B(1,++w)B(2,--w)B(3,w*=P)
    B(4,w=P/w)B(5,w+=P)B(6,w=P-w)B(7,w=pow(P,w))B(8,w=P%w)B(9,*t=w;w=*s;memmove(s,s+1,4*(t-s)))
    B(17,memmove(s+1,s,4*(t++-s));*s=w;w=P)B(18,U=w)B(19,a=P;U=a;U=w;U=a)B(20,a=P;U=w;w=a)
    B(21,a=P;c=P;d=P;U=a;U=w;U=c;w=d)B(22,w=P)}
    for(W(*"[")t>s;){w=P;if(w<0){W(*"-")w=-w;}
    for(c=w>0?log10(w):0;c>=0;c--){b=48+(w/(int)pow(10,c))%10;W(b)}b=44,W(b)}W(*"]")}

This implements the "underflow pushes zero" interpretation from Jan Dvorak's comment.

Ungolfed:

    #include<math.h>
    #include<signal.h>
    void S(int x){signal(SIGSEGV,S);sbrk(8*8*8);}
    int*s,*t,*i,w,a,c,d;    //stack top index working accumulator count data
    u(x){*t++=x;}           //push()
    o(){return t>s?*--t:0;} //pop()
    p(x){                   //print()
        char b[1];
        if(x<0){ write(1,"-",1); x=-x; }    //handle negative
        c=floor(log10(x));                  //how many digits?
        for(c=c>=0?c:0;c>=0;c--){
            *b=48+(x/(int)pow(10.0,c))%10;  //isolate digit, convert to ascii
            write(1,b,1);
        }
    }
    main(){
        char b[1];
        signal(SIGSEGV,S);  //auto-allocate memory for stack
        t=s=sbrk(8*8*8);  //get start of memory and allocate
        while(read(0,b,1)){
            write(1,b,1);
            switch(*b){
                case '0': w=o(); a=o(); for(c=ceil(log10(w));c>0;c--) a*=10; u(a+w); break;
                case '1': u(o()+1); break;
                case '2': u(o()-1); break;
                case '3': w=o(); u(o()*w); break;
                case '4': w=o(); u(o()/w); break;
                case '5': u(o()+o()); break;
                case '6': w=o(); u(o()-w); break;
                case '7': c=o();a=1; for(w=o();c>0;c--) a*=w; u(a); break;
                case '8': w=o(); u(o()%w); break;
                case '9': w=*s; memmove(s,s+1,4*(t-s-1)); t[-1]=w; break;
                case 'A': w=t[-1]; memmove(s+1,s,4*(t-s-1)); *s=w; break;
                case 'B': w=o(); u(w); u(w); break;
                case 'C': w=o(); a=o(); u(a); u(w); u(a); u(w); break;
                case 'D': w=o(); a=o(); u(w); u(a); break;
                case 'E': w=o(); a=o(); c=o(); d=o(); u(a); u(w); u(d); u(c); break;
                case 'F': o(); break;
            }
        }
        write(1,"\n[",2);   //dump the stack
        i=t;
        do {
            p(*--i);
        } while(i>s && write(1,",",1));
        write(1,"]\n",2);
    }