From 8e177b02e4eb02070c95c4c7732fbd748a3eb764 Mon Sep 17 00:00:00 2001 From: James Stine Date: Tue, 21 Jun 2022 10:14:53 -0500 Subject: [PATCH] Add MATLAB scripts for PD plot --- pipelined/srt/stine/Makefile | 25 +- pipelined/srt/stine/notes | 17 + pipelined/srt/stine/pd_bad.png | Bin 0 -> 122049 bytes pipelined/srt/stine/pd_cpa.png | Bin 0 -> 125945 bytes pipelined/srt/stine/pd_csa.pdf | Bin 0 -> 76541 bytes pipelined/srt/stine/pd_csa.png | Bin 0 -> 169213 bytes pipelined/srt/stine/srt2div | Bin 0 -> 22480 bytes pipelined/srt/stine/srt2div.c | 114 +++++ pipelined/srt/stine/srt4_pd.m | 508 ++++++++++++++++++++ pipelined/srt/stine/srt4_pd2.m | 333 +++++++++++++ pipelined/srt/stine/srt4_pd3.m | 855 +++++++++++++++++++++++++++++++++ pipelined/srt/stine/srt4div | Bin 26896 -> 26896 bytes pipelined/srt/stine/srt4div.c | 2 +- 13 files changed, 1845 insertions(+), 9 deletions(-) create mode 100644 pipelined/srt/stine/pd_bad.png create mode 100644 pipelined/srt/stine/pd_cpa.png create mode 100644 pipelined/srt/stine/pd_csa.pdf create mode 100644 pipelined/srt/stine/pd_csa.png create mode 100755 pipelined/srt/stine/srt2div create mode 100755 pipelined/srt/stine/srt2div.c create mode 100644 pipelined/srt/stine/srt4_pd.m create mode 100644 pipelined/srt/stine/srt4_pd2.m create mode 100644 pipelined/srt/stine/srt4_pd3.m diff --git a/pipelined/srt/stine/Makefile b/pipelined/srt/stine/Makefile index a019b388..8f745b47 100644 --- a/pipelined/srt/stine/Makefile +++ b/pipelined/srt/stine/Makefile @@ -1,17 +1,26 @@ -CC = gcc -CFLAGS = -lm -LIBS = -OBJS = disp.o srt4div.o +CC = gcc +CFLAGS = -lm +LIBS = +OBJS4 = disp.o srt4div.o +OBJS2 = disp.o srt2div.o -srt4div: $(OBJS) - $(CC) -g -O3 -o srt4div $(OBJS) $(CFLAGS) +all: srt4div srt2div disp.o: disp.h disp.c - $(CC) -g -c -o disp.o disp.c $(CFLAGS) + $(CC) -g -c -o disp.o disp.c srt4div.o: srt4div.c - $(CC) -g -c -o srt4div.o srt4div.c $(CFLAGS) + $(CC) -g -c -o srt4div.o srt4div.c + +srt2div.o: srt2div.c + $(CC) -g -c -o srt2div.o srt2div.c + +srt4div: $(OBJS4) + $(CC) -g -O3 -o srt4div $(OBJS4) $(CFLAGS) + +srt2div: $(OBJS2) + $(CC) -g -O3 -o srt2div $(OBJS2) $(CFLAGS) clean: rm -f *.o *~ diff --git a/pipelined/srt/stine/notes b/pipelined/srt/stine/notes index 32cb772c..83be0f20 100644 --- a/pipelined/srt/stine/notes +++ b/pipelined/srt/stine/notes @@ -11,3 +11,20 @@ Note: Add lg(r) extra iterations due to shifting of computed q ./srt4div 0.68359375 0.76953125 4 10 +r=2 +X = 0.10011111 +D = 0.11000101 + +X = 159 (9F) +D = 197 (C5) + +X = 159/256 = 0.62109375 +D = 197/256 = 0.76953125 + +./srt2div 0.62109375 0.76953125 8 9 + + + + + + diff --git a/pipelined/srt/stine/pd_bad.png b/pipelined/srt/stine/pd_bad.png new file mode 100644 index 0000000000000000000000000000000000000000..39df5cdaaf69ed7e120ebdec1e23e4d217fdbc45 GIT binary patch literal 122049 zcmeEvc|4U}*Z)T4BpDi&%!*WKk_aa%Lj$RV$`D0LhD7Gm?TC^{hDtapQz{aXGNg$# z7)ug~WXP0x{;hpo=g|GU?=!rA{Qi5c&*%Q+oO50K+I#J_*ZQvST6^E;^>%5_=32~! 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mode 100755 index 00000000..9b404d94 --- /dev/null +++ b/pipelined/srt/stine/srt2div.c @@ -0,0 +1,114 @@ +#include "disp.h" + +// QSLC is for division by recuerrence for +// r=2 using a CPA - See 5.109 EL +int qst (double D, double prem) { + + int q; + + // For Debugging + printf("rw --> %lg\n", prem); + + if (prem >= 0.5) { + q = 1; + } else if (prem >= -0.5) { + q = 0; + } else { + q = -1; + } + return q; + +} + +/* + This routine performs a radix-2 SRT division + algorithm. The user inputs the numerator, the denominator, + and the number of iterations. It assumes that 0.5 <= D < 1. + +*/ + +int main(int argc, char* argv[]) { + + double P, N, D, Q, RQ, RD, RREM, scale; + int q; + int num_iter, i; + int prec; + int radix = 2; + + if (argc < 5) { + fprintf(stderr, + "Usage: %s numerator denominator num_iterations prec\n", + argv[0]); + exit(1); + } + sscanf(argv[1],"%lg", &N); + sscanf(argv[2],"%lg", &D); + sscanf(argv[3],"%d", &num_iter); + sscanf(argv[4],"%d", &prec); + // Round to precision + N = rne(N, prec); + D = rne(D, prec); + printf("N = "); + disp_bin(N, 3, prec, stdout); + printf("\n"); + printf("D = "); + disp_bin(D, 3, prec, stdout); + printf("\n"); + + Q = 0; + P = N * pow(2.0, -log2(radix)); + printf("N = %lg, D = %lg, N/D = %lg, num_iter = %d \n\n", + N, D, N/D, num_iter); + for (scale = 1, i = 0; i < num_iter; i++) { + scale = scale * pow(2.0, -log2(radix)); + q = qst(flr(2*D, 1), 2*P); + printf("2*W[n] = "); + disp_bin(radix*P, 3, prec, stdout); + printf("\n"); + printf("q*D = "); + disp_bin(q*D, 3, prec, stdout); + printf("\n"); + printf("W[n+1] = "); + disp_bin(P ,3, prec, stdout); + printf("\n"); + // Recurrence + P = radix * P - q * D; + Q = Q + q*scale; + printf("i = %d, q = %d, Q = %1.18lf, W = %1.18lf\n", i, q, Q, P); + printf("i = %d, q = %d", i, q); + printf(", Q = "); + disp_bin(Q, 3, prec, stdout); + printf(", W = "); + disp_bin(P, 3, prec, stdout); + printf("\n\n"); + } + if (P < 0) { + Q = Q - scale; + P = P + D; + printf("\nCorrecting Negative Remainder\n"); + printf("Q = %1.18lf, W = %1.18lf\n", Q, P); + printf("Q = "); + disp_bin(Q, 3, prec, stdout); + printf(", W = "); + disp_bin(P, 3, prec, stdout); + printf("\n"); + } + + // Output Results + RQ = N/D; + // Since q_{computed} = q / radix, multiply by radix + RD = Q * radix; + printf("true = %1.18lf, computed = %1.18lf, \n", RQ, RD); + printf("true = "); + disp_bin(RQ, 3, prec, stdout); + printf(", computed = "); + disp_bin(RD, 3, prec, stdout); + printf("\n\n"); + printf("REM = %1.18lf \n", P); + printf("REM = "); + disp_bin(P, 3, prec, stdout); + printf("\n\n"); + + return 0; + +} diff --git a/pipelined/srt/stine/srt4_pd.m b/pipelined/srt/stine/srt4_pd.m new file mode 100644 index 00000000..815c84c7 --- /dev/null +++ b/pipelined/srt/stine/srt4_pd.m @@ -0,0 +1,508 @@ +% +% PD Region for Np = 3; Nd = 4; +% w/CPA +% +% Clear all variables and screen +clear +clf +% Define the number of bits (input Dividend) +n = 4; +% +% Define Divisor Range +% Normalized Floating Point [Dmin,Dmax] = [1,2] +% Normalized Fixed Point [Dmin, Dmax] =[1/2,1] +% +Dminimum = 1.0/2; +Dmaximum = 2.0/2; +% Define an ulp +ulp = 2^(-n); +% radix = beta +beta = 4; +% rho = redundancy factor -> SHOULD ALWAYS BE >= THAN 1/2 +% +% SD representations have alpha < beta - 1 +% +% alpha = ceil(beta/2) minimially redundant +% alpha = beta -1 maximally redundant (rho = 1) +% alpha = (beta-1)/2 nonredundant +% alpha > beta - 1 over-redundant +% +rho = 2/3; +% Calculation of max digit set +alpha = rho*(beta-1); +% Da contains digit set +q = []; +for i = -alpha:alpha + q = [q; i]; +end +% 4r(i-1)/D values +hold on +% figure(1) +grid off +for i = 1:length(q) + x = -rho+q(i):ulp:rho+q(i); + % Plot redundancy (overlap) Positive + z = [rho+q(i),rho+q(i)]; + y = [x(length(x))-q(i),0]; + % Plot redundancy (overlap) Negative + if (i ~= length(q)) + w = [-rho+q(i+1)-q(i+1),0]; + u = [-rho+q(i+1),-rho+q(i+1)]; + % plot(u,w,'b') + end + % plot(x,x-q(i)) + % plot(z,y,'r') + +end +% title('Robertson Diagram for Radix-4 SRT Divison') + +Np = 3; +Nd = 4; +Dmin = Dminimum; +Dmax = Dmaximum; +ulpd = 2^(-Nd); +ulpp = 2^(-Np); + +% +% Plot Atkins P-D plot +% Normalized Floating Point [Dmin,Dmax] = [1,2] +% Normalized Fixed Point [Dmin, Dmax] =[1/2,1] +% +Dmin = Dminimum; +Dmax = Dmaximum; +for i = 1:length(q) + D = Dmin:ulp:Dmax; + P1 = (rho+q(i))*D; + P2 = (-rho+q(i))*D; + hold on + p1 = plot(D,P1); + p1.Color = '#0000ff'; + p2 = plot(D,P2); + p2.Color = '#ff0000'; + axis([Dmin Dmax -beta*rho*Dmaximum beta*rho*Dmaximum]) + xticks(D) + p1.LineWidth = 2.0; + p2.LineWidth = 2.0; +end + +% Let's make x/y axis binary +j = []; +for i=1:length(D) + j = [j disp_bin(D(i), 1, 4)]; +end +yk = []; +yk2 = []; +for i=-2.5:0.5:2.5; + yk = [yk disp_bin(i, 3, 3)]; + yk2 = [yk2 i]; +end +xtickangle(90) +xticklabels(j) +yticklabels(yk) + +% Let's draw allow points on PD plot +% Positive Portions +index = 1; +i = 0:ulpp:rho*beta*Dmaximum; +for j = Dmin:ulpd:Dmax + plot(j*ones(1,length(i)),i,'k') +end + +j = Dmin:ulpd:Dmax; +for i = 0:ulpp:rho*beta*Dmaximum + plot(j,i*ones(length(j)),'k') +end + +% Negative Portions +index = 1; +i = 0:-ulpp:rho*-beta*Dmaximum; +for j = Dmin:ulpd:Dmax + plot(j*ones(1,length(i)),i,'k') +end + +j = Dmin:ulpd:Dmax; +for i = 0:-ulpp:-rho*beta*Dmaximum + plot(j,i*ones(length(j)),'k') +end + +% Labels and Printing +xlh = xlabel(['Divisor (d)']); +%xlh.FontSize = 18; +xlh.Position(2) = xlh.Position(2) - 0.1; +ylh = ylabel(['P = 4 \cdot w_i']); +ylh.Position(1) = ylh.Position(1)-0.02; +%ylh.FontSize = 18; + +% Containment Values (placed manually although not bad) +m2 = [3/4 7/8 1.0 1.0 5/4 5/4 5/4 3/2 3/2]; +m1 = [1/4 1/4 1/4 1/4 1/2 1/2 1/2 1/2 1/2]; +m0 = [-1/4 -1/4 -1/4 -1/4 -1/2 -1/2 -1/2 -1/2 -1/2]; +m1b = [-3/4 -7/8 -1 -1 -5/4 -5/4 -5/4 -3/2 -3/2]; +x2 = Dmin:ulpd:Dmax; +s2 = stairs(x2, m2); +s2.Color = '#8f08d1'; +s2.LineWidth = 3.0; +%s2.LineStyle = '--'; +s1 = stairs(x2, m1); +s1.Color = '#8f08d1'; +s1.LineWidth = 3.0; +s0 = stairs(x2, m0); +s0.Color = '#8f08d1'; +s0.LineWidth = 3.0; +s1b = stairs(x2, m1b); +s1b.Color = '#8f08d1'; +s1b.LineWidth = 3.0; + +% Place manually Quotient (ugh) +j = Dmin+ulpd/2:ulpd:Dmax; +i = rho*beta*Dmaximum-ulpp*3/4:-ulpp:-rho*beta*Dmaximum; +text(j(1), i(1), '2') +text(j(1), i(2), '2') +text(j(1), i(3), '2') +text(j(1), i(4), '2') +text(j(1), i(5), '2') +text(j(1), i(6), '2') +text(j(1), i(7), '2') +text(j(1), i(8), '2') +text(j(1), i(9), '2') +text(j(1), i(10), '2') +text(j(1), i(11), '2') +text(j(1), i(12), '2') +text(j(1), i(13), '2') +text(j(1), i(14), '2') +text(j(1), i(15), '2') +text(j(1), i(16), '1') +text(j(1), i(17), '1') +text(j(1), i(18), '1') +text(j(1), i(19), '1') +text(j(1), i(20), '0') +text(j(1), i(21), '0') +text(j(1), i(22), '0') +text(j(1), i(23), '0') +text(j(1), i(24), '-1') +text(j(1), i(25), '-1') +text(j(1), i(26), '-1') +text(j(1), i(27), '-1') +text(j(1), i(28), '-2') +text(j(1), i(29), '-2') +text(j(1), i(30), '-2') +text(j(1), i(31), '-2') +text(j(1), i(32), '-2') +text(j(1), i(33), '-2') +text(j(1), i(34), '-2') +text(j(1), i(35), '-2') +text(j(1), i(36), '-2') +text(j(1), i(37), '-2') +text(j(1), i(38), '-2') +text(j(1), i(39), '-2') +text(j(1), i(40), '-2') +text(j(1), i(41), '-2') +text(j(1), i(42), '-2') + +text(j(2), i(1), '2') +text(j(2), i(2), '2') +text(j(2), i(3), '2') +text(j(2), i(4), '2') +text(j(2), i(5), '2') +text(j(2), i(6), '2') +text(j(2), i(7), '2') +text(j(2), i(8), '2') +text(j(2), i(9), '2') +text(j(2), i(10), '2') +text(j(2), i(11), '2') +text(j(2), i(12), '2') +text(j(2), i(13), '2') +text(j(2), i(14), '2') +text(j(2), i(15), '1') +text(j(2), i(16), '1') +text(j(2), i(17), '1') +text(j(2), i(18), '1') +text(j(2), i(19), '1') +text(j(2), i(20), '0') +text(j(2), i(21), '0') +text(j(2), i(22), '0') +text(j(2), i(23), '0') +text(j(2), i(24), '-1') +text(j(2), i(25), '-1') +text(j(2), i(26), '-1') +text(j(2), i(27), '-1') +text(j(2), i(28), '-1') +text(j(2), i(29), '-2') +text(j(2), i(30), '-2') +text(j(2), i(31), '-2') +text(j(2), i(32), '-2') +text(j(2), i(33), '-2') +text(j(2), i(34), '-2') +text(j(2), i(35), '-2') +text(j(2), i(36), '-2') +text(j(2), i(37), '-2') +text(j(2), i(38), '-2') +text(j(2), i(39), '-2') +text(j(2), i(40), '-2') +text(j(2), i(41), '-2') +text(j(2), i(42), '-2') + +text(j(3), i(1), '2') +text(j(3), i(2), '2') +text(j(3), i(3), '2') +text(j(3), i(4), '2') +text(j(3), i(5), '2') +text(j(3), i(6), '2') +text(j(3), i(7), '2') +text(j(3), i(8), '2') +text(j(3), i(9), '2') +text(j(3), i(10), '2') +text(j(3), i(11), '2') +text(j(3), i(12), '2') +text(j(3), i(13), '2') +text(j(3), i(14), '1') +text(j(3), i(15), '1') +text(j(3), i(16), '1') +text(j(3), i(17), '1') +text(j(3), i(18), '1') +text(j(3), i(19), '1') +text(j(3), i(20), '0') +text(j(3), i(21), '0') +text(j(3), i(22), '0') +text(j(3), i(23), '0') +text(j(3), i(24), '-1') +text(j(3), i(25), '-1') +text(j(3), i(26), '-1') +text(j(3), i(27), '-1') +text(j(3), i(28), '-1') +text(j(3), i(29), '-1') +text(j(3), i(30), '-2') +text(j(3), i(31), '-2') +text(j(3), i(32), '-2') +text(j(3), i(33), '-2') +text(j(3), i(34), '-2') +text(j(3), i(35), '-2') +text(j(3), i(36), '-2') +text(j(3), i(37), '-2') +text(j(3), i(38), '-2') +text(j(3), i(39), '-2') +text(j(3), i(40), '-2') +text(j(3), i(41), '-2') +text(j(3), i(42), '-2') + +text(j(4), i(1), '2') +text(j(4), i(2), '2') +text(j(4), i(3), '2') +text(j(4), i(4), '2') +text(j(4), i(5), '2') +text(j(4), i(6), '2') +text(j(4), i(7), '2') +text(j(4), i(8), '2') +text(j(4), i(9), '2') +text(j(4), i(10), '2') +text(j(4), i(11), '2') +text(j(4), i(12), '2') +text(j(4), i(13), '2') +text(j(4), i(14), '1') +text(j(4), i(15), '1') +text(j(4), i(16), '1') +text(j(4), i(17), '1') +text(j(4), i(18), '1') +text(j(4), i(19), '1') +text(j(4), i(20), '0') +text(j(4), i(21), '0') +text(j(4), i(22), '0') +text(j(4), i(23), '0') +text(j(4), i(24), '-1') +text(j(4), i(25), '-1') +text(j(4), i(26), '-1') +text(j(4), i(27), '-1') +text(j(4), i(28), '-1') +text(j(4), i(29), '-1') +text(j(4), i(30), '-2') +text(j(4), i(31), '-2') +text(j(4), i(32), '-2') +text(j(4), i(33), '-2') +text(j(4), i(34), '-2') +text(j(4), i(35), '-2') +text(j(4), i(36), '-2') +text(j(4), i(37), '-2') +text(j(4), i(38), '-2') +text(j(4), i(39), '-2') +text(j(4), i(40), '-2') +text(j(4), i(41), '-2') +text(j(4), i(42), '-2') + +text(j(5), i(1), '2') +text(j(5), i(2), '2') +text(j(5), i(3), '2') +text(j(5), i(4), '2') +text(j(5), i(5), '2') +text(j(5), i(6), '2') +text(j(5), i(7), '2') +text(j(5), i(8), '2') +text(j(5), i(9), '2') +text(j(5), i(10), '2') +text(j(5), i(11), '2') +text(j(5), i(12), '1') +text(j(5), i(13), '1') +text(j(5), i(14), '1') +text(j(5), i(15), '1') +text(j(5), i(16), '1') +text(j(5), i(17), '1') +text(j(5), i(18), '0') +text(j(5), i(19), '0') +text(j(5), i(20), '0') +text(j(5), i(21), '0') +text(j(5), i(22), '0') +text(j(5), i(23), '0') +text(j(5), i(24), '0') +text(j(5), i(25), '0') +text(j(5), i(26), '-1') +text(j(5), i(27), '-1') +text(j(5), i(28), '-1') +text(j(5), i(29), '-1') +text(j(5), i(30), '-1') +text(j(5), i(31), '-1') +text(j(5), i(32), '-2') +text(j(5), i(33), '-2') +text(j(5), i(34), '-2') +text(j(5), i(35), '-2') +text(j(5), i(36), '-2') +text(j(5), i(37), '-2') +text(j(5), i(38), '-2') +text(j(5), i(39), '-2') +text(j(5), i(40), '-2') +text(j(5), i(41), '-2') +text(j(5), i(42), '-2') + +text(j(6), i(1), '2') +text(j(6), i(2), '2') +text(j(6), i(3), '2') +text(j(6), i(4), '2') +text(j(6), i(5), '2') +text(j(6), i(6), '2') +text(j(6), i(7), '2') +text(j(6), i(8), '2') +text(j(6), i(9), '2') +text(j(6), i(10), '2') +text(j(6), i(11), '2') +text(j(6), i(12), '1') +text(j(6), i(13), '1') +text(j(6), i(14), '1') +text(j(6), i(15), '1') +text(j(6), i(16), '1') +text(j(6), i(17), '1') +text(j(6), i(18), '0') +text(j(6), i(19), '0') +text(j(6), i(20), '0') +text(j(6), i(21), '0') +text(j(6), i(22), '0') +text(j(6), i(23), '0') +text(j(6), i(24), '0') +text(j(6), i(25), '0') +text(j(6), i(26), '-1') +text(j(6), i(27), '-1') +text(j(6), i(28), '-1') +text(j(6), i(29), '-1') +text(j(6), i(30), '-1') +text(j(6), i(31), '-1') +text(j(6), i(32), '-2') +text(j(6), i(33), '-2') +text(j(6), i(34), '-2') +text(j(6), i(35), '-2') +text(j(6), i(36), '-2') +text(j(6), i(37), '-2') +text(j(6), i(38), '-2') +text(j(6), i(39), '-2') +text(j(6), i(40), '-2') +text(j(6), i(41), '-2') +text(j(6), i(42), '-2') + +text(j(7), i(1), '2') +text(j(7), i(2), '2') +text(j(7), i(3), '2') +text(j(7), i(4), '2') +text(j(7), i(5), '2') +text(j(7), i(6), '2') +text(j(7), i(7), '2') +text(j(7), i(8), '2') 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+text(j(8), i(8), '2') +text(j(8), i(9), '2') +text(j(8), i(10), '1') +text(j(8), i(11), '1') +text(j(8), i(12), '1') +text(j(8), i(13), '1') +text(j(8), i(14), '1') +text(j(8), i(15), '1') +text(j(8), i(16), '1') +text(j(8), i(17), '1') +text(j(8), i(18), '0') +text(j(8), i(19), '0') +text(j(8), i(20), '0') +text(j(8), i(21), '0') +text(j(8), i(22), '0') +text(j(8), i(23), '0') +text(j(8), i(24), '0') +text(j(8), i(25), '0') +text(j(8), i(26), '-1') +text(j(8), i(27), '-1') +text(j(8), i(28), '-1') +text(j(8), i(29), '-1') +text(j(8), i(30), '-2') +text(j(8), i(31), '-2') +text(j(8), i(32), '-2') +text(j(8), i(33), '-2') +text(j(8), i(34), '-2') +text(j(8), i(35), '-2') +text(j(8), i(36), '-2') +text(j(8), i(37), '-2') +text(j(8), i(38), '-2') +text(j(8), i(39), '-2') +text(j(8), i(40), '-2') +text(j(8), i(41), '-2') +text(j(8), i(42), '-2') + +print -dpng pd_cpa.png + + + + + diff --git a/pipelined/srt/stine/srt4_pd2.m b/pipelined/srt/stine/srt4_pd2.m new file mode 100644 index 00000000..9c60923a --- /dev/null +++ b/pipelined/srt/stine/srt4_pd2.m @@ -0,0 +1,333 @@ +% +% Clear all variables and screen +clear +clf +% Define the number of bits (input Dividend) +n = 4; +% +% Define Divisor Range +% Normalized Floating Point [Dmin,Dmax] = [1,2] +% Normalized Fixed Point [Dmin, Dmax] =[1/2,1] +% +Dminimum = 1.0/2; +Dmaximum = 2.0/2; +% Define an ulp +ulp = 2^(-n); +% radix = beta +beta = 4; +% rho = redundancy factor -> SHOULD ALWAYS BE >= THAN 1/2 +% +% SD representations have alpha < beta - 1 +% +% alpha = ceil(beta/2) minimially redundant +% alpha = beta -1 maximally redundant (rho = 1) +% alpha = (beta-1)/2 nonredundant +% alpha > beta - 1 over-redundant +% +rho = 2/3; +% Calculation of max digit set +alpha = rho*(beta-1); +% Da contains digit set +q = []; +for i = -alpha:alpha + q = [q; i]; +end +% 4r(i-1)/D values +hold on +% figure(1) +grid off +for i = 1:length(q) + x = -rho+q(i):ulp:rho+q(i); + % Plot redundancy (overlap) Positive + z = [rho+q(i),rho+q(i)]; + y = [x(length(x))-q(i),0]; + % Plot redundancy (overlap) Negative + if (i ~= length(q)) + w = [-rho+q(i+1)-q(i+1),0]; + u = [-rho+q(i+1),-rho+q(i+1)]; + % plot(u,w,'b') + end + % plot(x,x-q(i)) + % plot(z,y,'r') + +end +% title('Robertson Diagram for Radix-4 SRT Divison') + +Np = 3; +Nd = 3; +Dmin = Dminimum; +Dmax = Dmaximum; +ulpd = 2^(-Nd); +ulpp = 2^(-Np); + +% +% Plot Atkins P-D plot +% Normalized Floating Point [Dmin,Dmax] = [1,2] +% Normalized Fixed Point [Dmin, Dmax] =[1/2,1] +% +Dmin = Dminimum; +Dmax = Dmaximum; +for i = 1:length(q) + D = Dmin:ulpd:Dmax; + P1 = (rho+q(i))*D; + P2 = (-rho+q(i))*D; + hold on + p1 = plot(D,P1,'b'); + p2 = plot(D,P2,'r'); + axis([Dmin Dmax -beta*rho*Dmaximum beta*rho*Dmaximum]) + xticks(D) + p1.LineWidth = 2.0; + p2.LineWidth = 2.0; +end + +% Let's make x axis binary +D = Dmin:ulpd:Dmax; +j = []; +for i=1:length(D) + j = [j disp_bin(D(i), 1, 3)]; +end +yk = []; +yk2 = []; +for i=-2.5:0.5:2.5; + yk = [yk disp_bin(i, 3, 3)]; + yk2 = [yk2 i]; +end +xtickangle(90) +xticklabels(j) +yticklabels(yk) + +% Let's draw allow points on PD plot +% Positive Portions +index = 1; +i = 0:ulpp:rho*beta*Dmaximum; +for j = Dmin:ulpd:Dmax + plot(j*ones(1,length(i)),i,'k'); +end + +j = Dmin:ulpd:Dmax; +for i = 0:ulpp:rho*beta*Dmaximum + plot(j,i*ones(length(j)),'k'); +end + +% Negative Portions +index = 1; +i = 0:-ulpp:rho*-beta*Dmaximum; +for j = Dmin:ulpd:Dmax + plot(j*ones(1,length(i)),i,'k'); +end + +j = Dmin:ulpd:Dmax; +for i = 0:-ulpp:-rho*beta*Dmaximum + plot(j,i*ones(length(j)),'k'); +end + +% Labels and Printing +xlh = xlabel(['Divisor (d)']); +xlh.Position(2) = xlh.Position(2) - 0.1; +xlh.FontSize = 18; +ylh = ylabel(['P = 4 \cdot w_i']); +ylh.Position(1) = ylh.Position(1)-0.02; +ylh.FontSize = 18; + +% Containment Values (placed manually although not bad) +m2 = [5/6 1.0 5/4 11/8 11/8]; +m1 = [1/4 1/4 1/2 1/2 1/2]; +m0 = [-1/4 -1/4 -1/2 -1/2 -1/2]; +m1b = [-5/6 -1 -5/4 -11/8 -11/8]; +x2 = Dmin:ulpd:Dmax; +s2 = stairs(x2, m2); +s2.Color = '#8f08d1'; +s2.LineWidth = 3.0; +s1 = stairs(x2, m1); +s1.Color = '#8f08d1'; +s1.LineWidth = 3.0; +s0 = stairs(x2, m0); +s0.Color = '#8f08d1'; +s0.LineWidth = 3.0; +s1b = stairs(x2, m1b); +s1b.Color = '#8f08d1'; +s1b.LineWidth = 3.0; + +% Place manually Quotient (ugh) +j = Dmin+ulpd/2:ulpd:Dmax; +i = rho*beta*Dmaximum-ulpp*3/4:-ulpp:-rho*beta*Dmaximum; +text(j(1), i(1), '2') +text(j(1), i(2), '2') +text(j(1), i(3), '2') +text(j(1), i(4), '2') +text(j(1), i(5), '2') +text(j(1), i(6), '2') +text(j(1), i(7), '2') +text(j(1), i(8), '2') +text(j(1), i(9), '2') +text(j(1), i(10), '2') +text(j(1), i(11), '2') +text(j(1), i(12), '2') +text(j(1), i(13), '2') +text(j(1), i(14), '2') +error1 = text(j(1), i(15), 'Full Precision', 'FontSize', 16); +text(j(1), i(16), '1') +text(j(1), i(17), '1') +text(j(1), i(18), '1') +text(j(1), i(19), '1') +text(j(1), i(20), '0') +text(j(1), i(21), '0') +text(j(1), i(22), '0') +text(j(1), i(23), '0') +text(j(1), i(24), '-1') +text(j(1), i(25), '-1') +text(j(1), i(26), '-1') +text(j(1), i(27), '-1') +error2 = text(j(1), i(28), 'Full Precision', 'FontSize', 16); +text(j(1), i(29), '-2') +text(j(1), i(30), '-2') +text(j(1), i(31), '-2') +text(j(1), i(32), '-2') +text(j(1), i(33), '-2') +text(j(1), i(34), '-2') +text(j(1), i(35), '-2') +text(j(1), i(36), '-2') +text(j(1), i(37), '-2') +text(j(1), i(38), '-2') +text(j(1), i(39), '-2') +text(j(1), i(40), '-2') +text(j(1), i(41), '-2') +text(j(1), i(42), '-2') + +text(j(2), i(1), '2') +text(j(2), i(2), '2') +text(j(2), i(3), '2') +text(j(2), i(4), '2') +text(j(2), i(5), '2') +text(j(2), i(6), '2') +text(j(2), i(7), '2') +text(j(2), i(8), '2') +text(j(2), i(9), '2') +text(j(2), i(10), '2') +text(j(2), i(11), '2') +text(j(2), i(12), '2') +text(j(2), i(13), '2') +text(j(2), i(14), '1') +text(j(2), i(15), '1') +text(j(2), i(16), '1') +text(j(2), i(17), '1') +text(j(2), i(18), '1') +text(j(2), i(19), '1') +text(j(2), i(20), '0') +text(j(2), i(21), '0') +text(j(2), i(22), '0') +text(j(2), i(23), '0') +text(j(2), i(24), '-1') +text(j(2), i(25), '-1') +text(j(2), i(26), '-1') +text(j(2), i(27), '-1') +text(j(2), i(28), '-1') +text(j(2), i(29), '-1') +text(j(2), i(30), '-2') +text(j(2), i(31), '-2') +text(j(2), i(32), '-2') +text(j(2), i(33), '-2') +text(j(2), i(34), '-2') +text(j(2), i(35), '-2') +text(j(2), i(36), '-2') +text(j(2), i(37), '-2') +text(j(2), i(38), '-2') +text(j(2), i(39), '-2') +text(j(2), i(40), '-2') +text(j(2), i(41), '-2') +text(j(2), i(42), '-2') + +text(j(3), i(1), '2') +text(j(3), i(2), '2') +text(j(3), i(3), '2') +text(j(3), i(4), '2') +text(j(3), i(5), '2') +text(j(3), i(6), '2') +text(j(3), i(7), '2') +text(j(3), i(8), '2') +text(j(3), i(9), '2') +text(j(3), i(10), '2') +text(j(3), i(11), '2') +text(j(3), i(12), '1') +text(j(3), i(13), '1') +text(j(3), i(14), '1') +text(j(3), i(15), '1') +text(j(3), i(16), '1') +text(j(3), i(17), '1') +text(j(3), i(18), '0') +text(j(3), i(19), '0') +text(j(3), i(20), '0') +text(j(3), i(21), '0') +text(j(3), i(22), '0') +text(j(3), i(23), '0') +text(j(3), i(24), '0') +text(j(3), i(25), '0') +text(j(3), i(26), '-1') +text(j(3), i(27), '-1') +text(j(3), i(28), '-1') +text(j(3), i(29), '-1') +text(j(3), i(30), '-1') +text(j(3), i(31), '-1') +text(j(3), i(32), '-2') +text(j(3), i(33), '-2') +text(j(3), i(34), '-2') +text(j(3), i(35), '-2') +text(j(3), i(36), '-2') +text(j(3), i(37), '-2') +text(j(3), i(38), '-2') +text(j(3), i(39), '-2') +text(j(3), i(40), '-2') +text(j(3), i(41), '-2') +text(j(3), i(42), '-2') + +text(j(4), i(1), '2') +text(j(4), i(2), '2') +text(j(4), i(3), '2') +text(j(4), i(4), '2') +text(j(4), i(5), '2') +text(j(4), i(6), '2') +text(j(4), i(7), '2') +text(j(4), i(8), '2') +text(j(4), i(9), '2') +text(j(4), i(10), '2') +text(j(4), i(11), '1') +text(j(4), i(12), '1') +text(j(4), i(13), '1') +text(j(4), i(14), '1') +text(j(4), i(15), '1') +text(j(4), i(16), '1') +text(j(4), i(17), '1') +text(j(4), i(18), '0') +text(j(4), i(19), '0') +text(j(4), i(20), '0') +text(j(4), i(21), '0') +text(j(4), i(22), '0') +text(j(4), i(23), '0') +text(j(4), i(24), '0') +text(j(4), i(25), '0') +text(j(4), i(26), '-1') +text(j(4), i(27), '-1') +text(j(4), i(28), '-1') +text(j(4), i(29), '-1') +text(j(4), i(30), '-1') +text(j(4), i(31), '-1') +text(j(4), i(32), '-1') +text(j(4), i(33), '-2') +text(j(4), i(34), '-2') +text(j(4), i(35), '-2') +text(j(4), i(36), '-2') +text(j(4), i(37), '-2') +text(j(4), i(38), '-2') +text(j(4), i(39), '-2') +text(j(4), i(40), '-2') +text(j(4), i(41), '-2') +text(j(4), i(42), '-2') + + + +print -dpng pd_bad.png + + + + + diff --git a/pipelined/srt/stine/srt4_pd3.m b/pipelined/srt/stine/srt4_pd3.m new file mode 100644 index 00000000..695b3c7f --- /dev/null +++ b/pipelined/srt/stine/srt4_pd3.m @@ -0,0 +1,855 @@ +% +% Clear all variables and screen +clear +clf +% Define the number of bits (input Dividend) +n = 4; +% +% Define Divisor Range +% Normalized Floating Point [Dmin,Dmax] = [1,2] +% Normalized Fixed Point [Dmin, Dmax] =[1/2,1] +% +Dminimum = 1.0/2; +Dmaximum = 2.0/2; +% Define an ulp +ulp = 2^(-n); +% radix = beta +beta = 4; +% rho = redundancy factor -> SHOULD ALWAYS BE >= THAN 1/2 +% +% SD representations have alpha < beta - 1 +% +% alpha = ceil(beta/2) minimially redundant +% alpha = beta -1 maximally redundant (rho = 1) +% alpha = (beta-1)/2 nonredundant +% alpha > beta - 1 over-redundant +% +rho = 2/3; +% Calculation of max digit set +alpha = rho*(beta-1); +% Da contains digit set +q = []; +for i = -alpha:alpha + q = [q; i]; +end +% 4r(i-1)/D values +hold on +% figure(1) +grid off +for i = 1:length(q) + x = -rho+q(i):ulp:rho+q(i); + % Plot redundancy (overlap) Positive + z = [rho+q(i),rho+q(i)]; + y = [x(length(x))-q(i),0]; + % Plot redundancy (overlap) Negative + if (i ~= length(q)) + w = [-rho+q(i+1)-q(i+1),0]; + u = [-rho+q(i+1),-rho+q(i+1)]; + % plot(u,w,'b') + end + % plot(x,x-q(i)) + % plot(z,y,'r') + +end +% title('Robertson Diagram for Radix-4 SRT Divison') + +% +% Plot Atkins P-D plot +% Normalized Floating Point [Dmin,Dmax] = [1,2] +% Normalized Fixed Point [Dmin, Dmax] =[1/2,1] +% +Dmin = Dminimum; +Dmax = Dmaximum; +for i = 1:length(q) + D = Dmin:ulp:Dmax; + P1 = (rho+q(i))*D; + P2 = (-rho+q(i))*D; + hold on + p1 = plot(D,P1,'b'); + p2 = plot(D,P2,'r'); + axis([Dmin Dmax -beta*rho*Dmaximum beta*rho*Dmaximum]) + xticks(D) + p1.LineWidth = 2.0; + p2.LineWidth = 2.0; +end + +% Let's make x axis binary +j = []; +for i=1:length(D) + j = [j disp_bin(D(i), 1, 4)]; +end +yk = []; +yk2 = []; +for i=-2.5:0.5:2.5; + yk = [yk disp_bin(i, 3, 4)]; + yk2 = [yk2 i]; +end +xtickangle(90) +xticklabels(j) +yticklabels(yk) + +Np = 4; +Nd = 4; +Dmin = Dminimum; +Dmax = Dmaximum; +ulpd = 2^(-Nd); +ulpp = 2^(-Np); + +% Let's draw allow points on PD plot +% Positive Portions +index = 1; +i = 0:ulpp:rho*beta*Dmaximum; +for j = Dmin:ulpd:Dmax + plot(j*ones(1,length(i)),i,'k'); +end + +j = Dmin:ulpd:Dmax; +for i = 0:ulpp:rho*beta*Dmaximum + plot(j,i*ones(length(j)),'k'); +end + +% Negative Portions +index = 1; +i = 0:-ulpp:rho*-beta*Dmaximum; +for j = Dmin:ulpd:Dmax + plot(j*ones(1,length(i)),i,'k'); +end + +j = Dmin:ulpd:Dmax; +for i = 0:-ulpp:-rho*beta*Dmaximum + plot(j,i*ones(length(j)),'k'); +end + +% Labels and Printing +xlh = xlabel(['Divisor (d)']); +xlh.Position(2) = xlh.Position(2) - 0.1; +%xlh.FontSize = 18; +ylh = ylabel(['P = 4 \cdot w_i']); +ylh.Position(1) = ylh.Position(1)-0.02; +%ylh.FontSize = 18; + +% Containment Values (placed manually although not bad) +m2 = [3/4 7/8 15/16 1.0 9/8 19/16 5/4 6/4 6/4]; +m1 = [1/4 1/4 1/4 1/4 3/8 3/8 1/2 1/2 1/2]; +m0 = [-1/4 -3/8 -3/8 -3/8 -1/2 -1/2 -1/2 -1/2 -1/2]; +m1b = [-13/16 -15/16 -1 -9/8 -5/4 -5/4 -11/8 -6/4 -6/4]; +x2 = Dmin:ulpd:Dmax; +s2 = stairs(x2, m2); +s2.Color = '#8f08d1'; +s2.LineWidth = 3.0; +s1 = stairs(x2, m1); +s1.Color = '#8f08d1'; +s1.LineWidth = 3.0; +s0 = stairs(x2, m0); +s0.Color = '#8f08d1'; +s0.LineWidth = 3.0; +s1b = stairs(x2, m1b); +s1b.Color = '#8f08d1'; +s1b.LineWidth = 3.0; + +% Place manually Quotient (ugh) +j = Dmin+ulpd/2:ulpd:Dmax; +i = rho*beta*Dmaximum-ulpp:-ulpp:-rho*beta*Dmaximum; + +% 1 +text(j(1), i(1), '2') +text(j(1), i(2), '2') +text(j(1), i(3), '2') +text(j(1), i(4), '2') +text(j(1), i(5), '2') +text(j(1), i(6), '2') +text(j(1), i(7), '2') +text(j(1), i(8), '2') +text(j(1), i(9), '2') +text(j(1), i(10), '2') +text(j(1), i(11), '2') +text(j(1), i(12), '2') +text(j(1), i(13), '2') +text(j(1), i(14), '2') +text(j(1), i(15), '2') +text(j(1), i(16), '2') +text(j(1), i(17), '2') +text(j(1), i(18), '2') +text(j(1), i(19), '2') +text(j(1), i(20), '2') +text(j(1), i(21), '2') +text(j(1), i(22), '2') +text(j(1), i(23), '2') +text(j(1), i(24), '2') +text(j(1), i(25), '2') +text(j(1), i(26), '2') +text(j(1), i(27), '2') +text(j(1), i(28), '2') +text(j(1), i(29), '2') +text(j(1), i(30), '2') +text(j(1), i(31), '1') +text(j(1), i(32), '1') +text(j(1), i(33), '1') +text(j(1), i(34), '1') +text(j(1), i(35), '1') +text(j(1), i(36), '1') +text(j(1), i(37), '1') 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i(21), '1') +text(j(8), i(22), '1') +text(j(8), i(23), '1') +text(j(8), i(24), '1') +text(j(8), i(25), '1') +text(j(8), i(26), '1') +text(j(8), i(27), '1') +text(j(8), i(28), '1') +text(j(8), i(29), '1') +text(j(8), i(30), '1') +text(j(8), i(31), '1') +text(j(8), i(32), '1') +text(j(8), i(33), '1') +text(j(8), i(34), '1') +text(j(8), i(35), '0') +text(j(8), i(36), '0') +text(j(8), i(37), '0') +text(j(8), i(38), '0') +text(j(8), i(39), '0') +text(j(8), i(40), '0') +text(j(8), i(41), '0') +text(j(8), i(42), '0') + +text(j(8), i(43), '0') +text(j(8), i(44), '0') +text(j(8), i(45), '0') +text(j(8), i(46), '0') +text(j(8), i(47), '0') +text(j(8), i(48), '0') +text(j(8), i(49), '0') +text(j(8), i(50), '0') +text(j(8), i(51), '-1') +text(j(8), i(52), '-1') +text(j(8), i(53), '-1') +text(j(8), i(54), '-1') +text(j(8), i(55), '-1') +text(j(8), i(56), '-1') +text(j(8), i(57), '-1') +text(j(8), i(58), '-1') +text(j(8), i(59), '-1') +text(j(8), i(60), '-1') +text(j(8), i(61), '-1') +text(j(8), i(62), '-1') +text(j(8), i(63), '-1') +text(j(8), i(64), '-1') +text(j(8), i(65), '-1') +text(j(8), i(66), '-1') +text(j(8), i(67), '-2') +text(j(8), i(68), '-2') +text(j(8), i(69), '-2') +text(j(8), i(70), '-2') +text(j(8), i(71), '-2') +text(j(8), i(72), '-2') +text(j(8), i(73), '-2') +text(j(8), i(74), '-2') +text(j(8), i(75), '-2') +text(j(8), i(76), '-2') +text(j(8), i(77), '-2') +text(j(8), i(78), '-2') +text(j(8), i(79), '-2') +text(j(8), i(80), '-2') +text(j(8), i(81), '-2') +text(j(8), i(82), '-2') +text(j(8), i(83), '-2') +text(j(8), i(84), '-2') + +orient('landscape') +print -dpng 'pd_csa.png' + + + + + diff --git a/pipelined/srt/stine/srt4div b/pipelined/srt/stine/srt4div index b44c6dc0d18016698d3b7391786f51596957c3b8..a780abd4b2470ec6896cf7e6eea3e02760e63785 100755 GIT binary patch delta 494 zcmbPmiE+Xu#tj^doR&fiU|_jfkTIP}WM_9q!wtoUuQxH<>^?J3{+rh{#C$Wj`4>>k?}L~x2hs9Ee)1bd2{tvLo|A_+^C(^6-DF_HB3!`^G|H7v zppD6ymyJ1}orj%cv!c>Zj>#Uj9*jDhC)&PcV$$cCypc(4^E8JwER6b_on2d*87nrQ z^f<@LXta5TA2%~Q=OR{aCR35ks{>0}Hp_<{WCH4Z7%`s_sH`z6pOevN^2cO-P8}tX gs~H${HfyG|Gc%@4-k5IAcy{v3bbCgo$(k9@0UVCK&j0`b delta 467 zcmbPmiE+Xu#tj^doRUHeU?90!kTIP}#M4CO%ii5tZM$79XNg&Q-{07kwrq0`v%Rd~ zCw>9f13<#}#3%l^gP-^XC;wB>t4|VOVDRWXzJm#9$P3pG|NndRvX(%_K<2(M1c`Nv zzS3i0==R;<(e3)8^W1)BpiG(vf8K!?PM^VAJdw5hdk@yK9j@gAiWYu|mihcZo0B__ zzgPfP?s@@iAkcaqs9B64>oR62o}2tK-JX$o IvS!9}08pi?%K!iX diff --git a/pipelined/srt/stine/srt4div.c b/pipelined/srt/stine/srt4div.c index e40ace57..65fdac53 100755 --- a/pipelined/srt/stine/srt4div.c +++ b/pipelined/srt/stine/srt4div.c @@ -207,7 +207,7 @@ int main(int argc, char* argv[]) { } // Output Results - RQ = N/D; + RQ = flr(N/D, prec); // Since q_{computed} = q / radix, multiply by radix RD = Q * radix; printf("true = %1.18lf, computed = %1.18lf, \n", RQ, RD);