> Dr := 50: # number of registers in slice
> k := 1:  # slice width
> Bw := 0.05: # bandwidth into each slice (per bit)
> R := 30 : # registers in algorithm
> Wb := 16 : # bits per word
> Z := 10:   # initial loads/saves
> N := 30:  # number of operations in a sequence
> Er := m * k*Dr/Wb; # effective registers per pixel

                                  Er := 25/8 m
> L := Wb/(m*Bw*k); # latency to load a word

                                     320.0000000
                                L := -----------
                                          m
> A := Wb/(m*k);   # time for an ALU operation on a pixel

                                          16
                                    A := ----
                                           m
> f := max(0.0001,1-Er/R);

                           f := max(.0001, 1 - 5/48 m)
> L_eff :=  ((1-f)^L + f*L -1)/f ;

                                            /320.0000000\
                                            |-----------|
                                            \     m     /
      L_eff := ((1 - max(.0001, 1 - 5/48 m))

                         max(.0001, 1 - 5/48 m)
           + 320.0000000 ---------------------- - 1)/max(.0001, 1 - 5/48 m)
                                    m
> Tload := (Z+2*N*f)*L_eff;

      Tload := (10 + 60 max(.0001, 1 - 5/48 m)) (

                                      /320.0000000\
                                      |-----------|
                                      \     m     /
          (1 - max(.0001, 1 - 5/48 m))

                         max(.0001, 1 - 5/48 m)
           + 320.0000000 ---------------------- - 1)/max(.0001, 1 - 5/48 m)
                                    m
> plot(Tload,m=1..16,title=`Tload vs m`);
> plot({L,L_eff},m=1..16,title=`Leff vs m`);
> 
> plot(f,m=1..16,title=`Fmiss vs. m`);
> Tseq := Tload + N*A;

   Tseq := (10 + 60 max(.0001, 1 - 5/48 m)) (

                                   /320.0000000\
                                   |-----------|
                                   \     m     /
       (1 - max(.0001, 1 - 5/48 m))

                      max(.0001, 1 - 5/48 m)                               480
        + 320.0000000 ---------------------- - 1)/max(.0001, 1 - 5/48 m) + ---
                                 m                                          m
> plot(m*Tseq,m=1..16,title=`Performance as function of m`);
> plot({L,L_eff/L},m=1..16,title=`Leff vs m`);
> evalf(subs(m=16,Tseq));

                                   30.19001394
> plot({m*Tload,m*Tseq},m=1..16,title=`Performance as function of m`);
> plot(f,m=1..16,title=`Miss frequency as function of m`);
> plot(L_eff/L,m=1..16,title=`Leff vs m`);
>