Ajout de MIN/100.

Arthur HUGEAT
1 parent 5e2bf244bf
Showing 2 changed files with 71 additions and 35 deletions Side-by-side Diff
ifcs2018_journal.tex
images/min_100.pdf
@@ -710,15 +710,16 @@
 This section presents the results of the complementary quadratic program aimed at
 minimizing the area occupation for a targeted rejection level.
  
-The experimental setup is also composed of three cases. The raw input is the same
+The experimental setup is composed of four cases. The raw input is the same
 as in the previous section, from a PRN generator, which fixes the input data size $\Pi^I$.
-Then the targeted rejection $\mathcal{R}$ has been fixed to either 40, 60 or 80~dB.
-Hence, the three cases have been named: MIN/40, MIN/60, MIN/80.
+Then the targeted rejection $\mathcal{R}$ has been fixed to either 40, 60, 80 or 100~dB.
+Hence, the three cases have been named: MIN/40, MIN/60, MIN/80 and MIN/100.
 The number of configurations $p$ is the same as previous section.
  
 Table~\ref{tbl:gurobi_min_40} shows the results obtained by the filter solver for MIN/40.
 Table~\ref{tbl:gurobi_min_60} shows the results obtained by the filter solver for MIN/60.
 Table~\ref{tbl:gurobi_min_80} shows the results obtained by the filter solver for MIN/80.
+Table~\ref{tbl:gurobi_min_100} shows the results obtained by the filter solver for MIN/100.
  
 \renewcommand{\arraystretch}{1.4}
  
  
  
@@ -777,13 +778,32 @@
       \end{tabular}
     }
 \end{table}
+
+\begin{table}[h!tb]
+  \caption{Configurations $(C_i, \pi_i^C, \pi_i^S)$, rejections and areas (in arbitrary units) for MIN/100}
+  \label{tbl:gurobi_min_100}
+  \centering
+    {\scalefont{0.77}
+      \begin{tabular}{|c|ccccc|c|c|}
+        \hline
+         $n$  & $i = 1$     & $i = 2$     & $i = 3$     & $i = 4$     & $i = 5$     & Rejection       & Area  \\
+        \hline
+            1 & -           & -           & -           & -           & -           & -               & -     \\
+            2 & (15, 7, 17) & (51, 14, 0) & -           & -           & -           & 100~dB          & 1365  \\
+            3 & (3, 3, 15)  & (27, 9, 0)  & (27, 9, 0)  & -           & -           & 100~dB          & 1002  \\
+            4 & (3, 3, 15)  & (31, 9, 0)  & (19, 7, 0)  & (3, 3, 0)   & -           & 101~dB          & 909   \\
+            5 & (3, 3, 15)  & (23, 8, 1)  & (19, 7, 0)  & (3, 3, 0)   & (3, 3, 0)   & 101~dB          & 810   \\
+        \hline
+      \end{tabular}
+    }
+\end{table}
 \renewcommand{\arraystretch}{1}
  
-% JMF : je croyais que dans un cas le monolithique n'y arrivait juste pas : tu as retire' ce cas ?
-From these tables, we can first state that all configurations reach the targeted rejection
+From these tables, we can first state that almost configurations reach the targeted rejection
 level or even better thanks to our underestimate of the cascade rejection as the sum of the
-individual filter rejection
-% we have stages lesser is the area occupied in arbitrary unit. JMF : je ne comprends pas cette phrase
+individual filter rejection. The only exception is for the monolithic case ($n = 1$) in
+MIN/100. With our filter configurations there is no solution able to reach 100~dB of rejection.
+% we have stages lesser is the area occupied in arbitrary unit. JMF : je ne comprends pas cette phrase, AH: C'est déjà dit à la dernière phrase de ce paragraphe
 Futhermore, the area of the monolithic filter is twice as big as the two cascaded filters
 (1131 and 1760  arbitrary units v.s 547 and 903 arbitrary units for 60 and 80~dB rejection
 respectively). More generally, the more filters are cascaded, the lower the occupied area.
@@ -806,6 +826,7 @@
 Figure~\ref{fig:min_40} shows the rejection of the different configurations in the case of MIN/40.
 Figure~\ref{fig:min_60} shows the rejection of the different configurations in the case of MIN/60.
 Figure~\ref{fig:min_80} shows the rejection of the different configurations in the case of MIN/80.
+Figure~\ref{fig:min_100} shows the rejection of the different configurations in the case of MIN/100.
  
 \begin{figure}
 \centering
  
  
  
  
  
  
  
@@ -828,40 +849,51 @@
 \label{fig:min_80}
 \end{figure}
  
+\begin{figure}
+\centering
+\includegraphics[width=\linewidth]{images/min_100}
+\caption{Signal spectrum for MIN/100}
+\label{fig:min_100}
+\end{figure}
+
 We observe that all rejections given by the quadratic solver are close to the experimentally
 measured rejection. All curves prove that the constraint to reach the target rejection is
-respected with both monolithic or cascaded filters.
+respected with both monolithic (except in MIN/100 which has no monolithic solution) or cascaded filters.
  
-Table~\ref{tbl:resources_usage} shows the resource usage in the case of MIN/40, MIN/60 and
-MIN/80 \emph{i.e.} when the target rejection is fixed to 40, 60 and 80~dB. We
+Table~\ref{tbl:resources_usage} shows the resource usage in the case of MIN/40, MIN/60;
+MIN/80 and MIN/100 \emph{i.e.} when the target rejection is fixed to 40, 60, 80 and 100~dB. We
 have taken care to extract solely the resources used by
 the FIR filters and remove additional processing blocks including FIFO and PL to
 PS communication.
  
+\renewcommand{\arraystretch}{1.2}
 \begin{table}
   \caption{Resource occupation. The last column refers to available resources on a Zynq-7010 as found on the Redpitaya.}
   \label{tbl:resources_usage_comp}
   \centering
-      \begin{tabular}{|c|c|ccc|c|}
+  {\scalefont{0.90}
+      \begin{tabular}{|c|c|cccc|c|}
         \hline
-        $n$ &          & MIN/40   & MIN/60   & MIN/80   & \emph{Zynq 7010}         \\ \hline\hline
-            & LUT      & 343      & 334      & 772      & \emph{17600}             \\
-        1   & BRAM     & 1        & 1        & 1        & \emph{120}               \\
-            & DSP      & 27       & 39       & 55       & \emph{80}                \\ \hline
-            & LUT      & 1252     & 2862     & 5099     & \emph{17600}             \\
-        2   & BRAM     & 2        & 2        & 2        & \emph{120}               \\
-            & DSP      & 0        & 0        & 0        & \emph{80}                \\ \hline
-            & LUT      & 891      & 2148     & 2023     & \emph{17600}             \\
-        3   & BRAM     & 3        & 3        & 3        & \emph{120}               \\
-            & DSP      & 0        & 0        & 19       & \emph{80}                \\ \hline
-            & LUT      & 662      & 1729     & 2451     & \emph{17600}             \\
-        4   & BRAM     & 4        & 4        & 4        & \emph{120}               \\
-            & DPS      & 0        & 0        & 7        & \emph{80}                \\ \hline
-            & LUT      & -        & 1259     & 2602     & \emph{17600}             \\
-        5   & BRAM     & -        & 5        & 5        & \emph{120}               \\
-            & DPS      & -        & 0        & 0        & \emph{80}                \\ \hline
+        $n$ &          & MIN/40   & MIN/60   & MIN/80   & MIN/100  & \emph{Zynq 7010}         \\ \hline\hline
+            & LUT      & 343      & 334      & 772      & -        & \emph{17600}             \\
+        1   & BRAM     & 1        & 1        & 1        & -        & \emph{120}               \\
+            & DSP      & 27       & 39       & 55       & -        & \emph{80}                \\ \hline
+            & LUT      & 1252     & 2862     & 5099     & 640      & \emph{17600}             \\
+        2   & BRAM     & 2        & 2        & 2        & 2        & \emph{120}               \\
+            & DSP      & 0        & 0        & 0        & 66       & \emph{80}                \\ \hline
+            & LUT      & 891      & 2148     & 2023     & 2448     & \emph{17600}             \\
+        3   & BRAM     & 3        & 3        & 3        & 3        & \emph{120}               \\
+            & DSP      & 0        & 0        & 19       & 27       & \emph{80}                \\ \hline
+            & LUT      & 662      & 1729     & 2451     & 2893     & \emph{17600}             \\
+        4   & BRAM     & 4        & 4        & 4        & 4        & \emph{120}               \\
+            & DPS      & 0        & 0        & 7        & 19       & \emph{80}                \\ \hline
+            & LUT      & -        & 1259     & 2602     & 2505     & \emph{17600}             \\
+        5   & BRAM     & -        & 5        & 5        & 5        & \emph{120}               \\
+            & DPS      & -        & 0        & 0        & 19       & \emph{80}                \\ \hline
       \end{tabular}
+  }
 \end{table}
+\renewcommand{\arraystretch}{1}
  
 If we keep the previous estimation of cost of one DSP in terms of LUT (1 DSP $\approx$ 100 LUT)
 the real resource consumption decreases as a function of the number of stages in the cascaded
  
  
  
  
@@ -873,22 +905,26 @@
 Finally, table~\ref{tbl:area_time_comp} shows the computation time to solve
 the quadratic program.
  
+\renewcommand{\arraystretch}{1.2}
 \begin{table}[h!tb]
 \caption{Time to solve the quadratic program with Gurobi}
 \label{tbl:area_time_comp}
 \centering
-\begin{tabular}{|c|c|c|c|}\hline
-$n$ & Time (MIN/40)           & Time (MIN/60)               & Time (MIN/80)  \\\hline\hline
-1   & 0.07~s                  & 0.02~s                      & 0.01~s         \\
-2   & 7.8~s                   & 16~s                        & 14~s           \\
-3   & 4.7~s                   & 14~s                        & 28~s           \\
-4   & 39~s                    & 20~s                        & 193~s          \\
-5   & 126~s                   & 12~s                        & 170~s          \\\hline
+{\scalefont{0.90}
+\begin{tabular}{|c|c|c|c|c|}\hline
+$n$ & Time (MIN/40)           & Time (MIN/60)               & Time (MIN/80) & Time (MIN/100)               \\\hline\hline
+1   & 0.07~s                  & 0.02~s                      & 0.01~s        & -                            \\
+2   & 7.8~s                   & 16~s                        & 14~s          & 1.8~s                        \\
+3   & 4.7~s                   & 14~s                        & 28~s          & 39~s                         \\
+4   & 39~s                    & 20~s                        & 193~s         & 522~s  ($\approx$ 9~min)     \\
+5   & -                       & 12~s                        & 170~s         & 1048~s ($\approx$ 17~min)    \\\hline
 \end{tabular}
+}
 \end{table}
+\renewcommand{\arraystretch}{1}
  
 The time needed to solve this configuration is significantly shorter than the time
-needed in the previous section. Indeed the worst time in this case is only 3~minutes,
+needed in the previous section. Indeed the worst time in this case is only 17~minutes,
 compared to 3~days in the previous section: this problem is more easily solved than the
 previous one.
...	...	@@ -710,15 +710,16 @@
710	710	This section presents the results of the complementary quadratic program aimed at
711	711	minimizing the area occupation for a targeted rejection level.
712	712
713		-The experimental setup is also composed of three cases. The raw input is the same
	713	+The experimental setup is composed of four cases. The raw input is the same
714	714	as in the previous section, from a PRN generator, which fixes the input data size $\Pi^I$.
715		-Then the targeted rejection $\mathcal{R}$ has been fixed to either 40, 60 or 80~dB.
716		-Hence, the three cases have been named: MIN/40, MIN/60, MIN/80.
	715	+Then the targeted rejection $\mathcal{R}$ has been fixed to either 40, 60, 80 or 100~dB.
	716	+Hence, the three cases have been named: MIN/40, MIN/60, MIN/80 and MIN/100.
717	717	The number of configurations $p$ is the same as previous section.
718	718
719	719	Table~\ref{tbl:gurobi_min_40} shows the results obtained by the filter solver for MIN/40.
720	720	Table~\ref{tbl:gurobi_min_60} shows the results obtained by the filter solver for MIN/60.
721	721	Table~\ref{tbl:gurobi_min_80} shows the results obtained by the filter solver for MIN/80.
	722	+Table~\ref{tbl:gurobi_min_100} shows the results obtained by the filter solver for MIN/100.
722	723
723	724	\renewcommand{\arraystretch}{1.4}
724	725
725	726
726	727
...	...	@@ -777,13 +778,32 @@
777	778	\end{tabular}
778	779	}
779	780	\end{table}
	781	+
	782	+\begin{table}[h!tb]
	783	+ \caption{Configurations $(C_i, \pi_i^C, \pi_i^S)$, rejections and areas (in arbitrary units) for MIN/100}
	784	+ \label{tbl:gurobi_min_100}
	785	+ \centering
	786	+ {\scalefont{0.77}
	787	+ \begin{tabular}{\|c\|ccccc\|c\|c\|}
	788	+ \hline
	789	+ $n$ & $i = 1$ & $i = 2$ & $i = 3$ & $i = 4$ & $i = 5$ & Rejection & Area \\
	790	+ \hline
	791	+ 1 & - & - & - & - & - & - & - \\
	792	+ 2 & (15, 7, 17) & (51, 14, 0) & - & - & - & 100~dB & 1365 \\
	793	+ 3 & (3, 3, 15) & (27, 9, 0) & (27, 9, 0) & - & - & 100~dB & 1002 \\
	794	+ 4 & (3, 3, 15) & (31, 9, 0) & (19, 7, 0) & (3, 3, 0) & - & 101~dB & 909 \\
	795	+ 5 & (3, 3, 15) & (23, 8, 1) & (19, 7, 0) & (3, 3, 0) & (3, 3, 0) & 101~dB & 810 \\
	796	+ \hline
	797	+ \end{tabular}
	798	+ }
	799	+\end{table}
780	800	\renewcommand{\arraystretch}{1}
781	801
782		-% JMF : je croyais que dans un cas le monolithique n'y arrivait juste pas : tu as retire' ce cas ?
783		-From these tables, we can first state that all configurations reach the targeted rejection
	802	+From these tables, we can first state that almost configurations reach the targeted rejection
784	803	level or even better thanks to our underestimate of the cascade rejection as the sum of the
785		-individual filter rejection
786		-% we have stages lesser is the area occupied in arbitrary unit. JMF : je ne comprends pas cette phrase
	804	+individual filter rejection. The only exception is for the monolithic case ($n = 1$) in
	805	+MIN/100. With our filter configurations there is no solution able to reach 100~dB of rejection.
	806	+% we have stages lesser is the area occupied in arbitrary unit. JMF : je ne comprends pas cette phrase, AH: C'est déjà dit à la dernière phrase de ce paragraphe
787	807	Futhermore, the area of the monolithic filter is twice as big as the two cascaded filters
788	808	(1131 and 1760 arbitrary units v.s 547 and 903 arbitrary units for 60 and 80~dB rejection
789	809	respectively). More generally, the more filters are cascaded, the lower the occupied area.
...	...	@@ -806,6 +826,7 @@
806	826	Figure~\ref{fig:min_40} shows the rejection of the different configurations in the case of MIN/40.
807	827	Figure~\ref{fig:min_60} shows the rejection of the different configurations in the case of MIN/60.
808	828	Figure~\ref{fig:min_80} shows the rejection of the different configurations in the case of MIN/80.
	829	+Figure~\ref{fig:min_100} shows the rejection of the different configurations in the case of MIN/100.
809	830
810	831	\begin{figure}
811	832	\centering
812	833
813	834
814	835
815	836
816	837
817	838
818	839
...	...	@@ -828,40 +849,51 @@
828	849	\label{fig:min_80}
829	850	\end{figure}
830	851
	852	+\begin{figure}
	853	+\centering
	854	+\includegraphics[width=\linewidth]{images/min_100}
	855	+\caption{Signal spectrum for MIN/100}
	856	+\label{fig:min_100}
	857	+\end{figure}
	858	+
831	859	We observe that all rejections given by the quadratic solver are close to the experimentally
832	860	measured rejection. All curves prove that the constraint to reach the target rejection is
833		-respected with both monolithic or cascaded filters.
	861	+respected with both monolithic (except in MIN/100 which has no monolithic solution) or cascaded filters.
834	862
835		-Table~\ref{tbl:resources_usage} shows the resource usage in the case of MIN/40, MIN/60 and
836		-MIN/80 \emph{i.e.} when the target rejection is fixed to 40, 60 and 80~dB. We
	863	+Table~\ref{tbl:resources_usage} shows the resource usage in the case of MIN/40, MIN/60;
	864	+MIN/80 and MIN/100 \emph{i.e.} when the target rejection is fixed to 40, 60, 80 and 100~dB. We
837	865	have taken care to extract solely the resources used by
838	866	the FIR filters and remove additional processing blocks including FIFO and PL to
839	867	PS communication.
840	868
	869	+\renewcommand{\arraystretch}{1.2}
841	870	\begin{table}
842	871	\caption{Resource occupation. The last column refers to available resources on a Zynq-7010 as found on the Redpitaya.}
843	872	\label{tbl:resources_usage_comp}
844	873	\centering
845		- \begin{tabular}{\|c\|c\|ccc\|c\|}
	874	+ {\scalefont{0.90}
	875	+ \begin{tabular}{\|c\|c\|cccc\|c\|}
846	876	\hline
847		- $n$ & & MIN/40 & MIN/60 & MIN/80 & \emph{Zynq 7010} \\ \hline\hline
848		- & LUT & 343 & 334 & 772 & \emph{17600} \\
849		- 1 & BRAM & 1 & 1 & 1 & \emph{120} \\
850		- & DSP & 27 & 39 & 55 & \emph{80} \\ \hline
851		- & LUT & 1252 & 2862 & 5099 & \emph{17600} \\
852		- 2 & BRAM & 2 & 2 & 2 & \emph{120} \\
853		- & DSP & 0 & 0 & 0 & \emph{80} \\ \hline
854		- & LUT & 891 & 2148 & 2023 & \emph{17600} \\
855		- 3 & BRAM & 3 & 3 & 3 & \emph{120} \\
856		- & DSP & 0 & 0 & 19 & \emph{80} \\ \hline
857		- & LUT & 662 & 1729 & 2451 & \emph{17600} \\
858		- 4 & BRAM & 4 & 4 & 4 & \emph{120} \\
859		- & DPS & 0 & 0 & 7 & \emph{80} \\ \hline
860		- & LUT & - & 1259 & 2602 & \emph{17600} \\
861		- 5 & BRAM & - & 5 & 5 & \emph{120} \\
862		- & DPS & - & 0 & 0 & \emph{80} \\ \hline
	877	+ $n$ & & MIN/40 & MIN/60 & MIN/80 & MIN/100 & \emph{Zynq 7010} \\ \hline\hline
	878	+ & LUT & 343 & 334 & 772 & - & \emph{17600} \\
	879	+ 1 & BRAM & 1 & 1 & 1 & - & \emph{120} \\
	880	+ & DSP & 27 & 39 & 55 & - & \emph{80} \\ \hline
	881	+ & LUT & 1252 & 2862 & 5099 & 640 & \emph{17600} \\
	882	+ 2 & BRAM & 2 & 2 & 2 & 2 & \emph{120} \\
	883	+ & DSP & 0 & 0 & 0 & 66 & \emph{80} \\ \hline
	884	+ & LUT & 891 & 2148 & 2023 & 2448 & \emph{17600} \\
	885	+ 3 & BRAM & 3 & 3 & 3 & 3 & \emph{120} \\
	886	+ & DSP & 0 & 0 & 19 & 27 & \emph{80} \\ \hline
	887	+ & LUT & 662 & 1729 & 2451 & 2893 & \emph{17600} \\
	888	+ 4 & BRAM & 4 & 4 & 4 & 4 & \emph{120} \\
	889	+ & DPS & 0 & 0 & 7 & 19 & \emph{80} \\ \hline
	890	+ & LUT & - & 1259 & 2602 & 2505 & \emph{17600} \\
	891	+ 5 & BRAM & - & 5 & 5 & 5 & \emph{120} \\
	892	+ & DPS & - & 0 & 0 & 19 & \emph{80} \\ \hline
863	893	\end{tabular}
	894	+ }
864	895	\end{table}
	896	+\renewcommand{\arraystretch}{1}
865	897
866	898	If we keep the previous estimation of cost of one DSP in terms of LUT (1 DSP $\approx$ 100 LUT)
867	899	the real resource consumption decreases as a function of the number of stages in the cascaded
868	900
869	901
870	902
871	903
...	...	@@ -873,22 +905,26 @@
873	905	Finally, table~\ref{tbl:area_time_comp} shows the computation time to solve
874	906	the quadratic program.
875	907
	908	+\renewcommand{\arraystretch}{1.2}
876	909	\begin{table}[h!tb]
877	910	\caption{Time to solve the quadratic program with Gurobi}
878	911	\label{tbl:area_time_comp}
879	912	\centering
880		-\begin{tabular}{\|c\|c\|c\|c\|}\hline
881		-$n$ & Time (MIN/40) & Time (MIN/60) & Time (MIN/80) \\\hline\hline
882		-1 & 0.07~s & 0.02~s & 0.01~s \\
883		-2 & 7.8~s & 16~s & 14~s \\
884		-3 & 4.7~s & 14~s & 28~s \\
885		-4 & 39~s & 20~s & 193~s \\
886		-5 & 126~s & 12~s & 170~s \\\hline
	913	+{\scalefont{0.90}
	914	+\begin{tabular}{\|c\|c\|c\|c\|c\|}\hline
	915	+$n$ & Time (MIN/40) & Time (MIN/60) & Time (MIN/80) & Time (MIN/100) \\\hline\hline
	916	+1 & 0.07~s & 0.02~s & 0.01~s & - \\
	917	+2 & 7.8~s & 16~s & 14~s & 1.8~s \\
	918	+3 & 4.7~s & 14~s & 28~s & 39~s \\
	919	+4 & 39~s & 20~s & 193~s & 522~s ($\approx$ 9~min) \\
	920	+5 & - & 12~s & 170~s & 1048~s ($\approx$ 17~min) \\\hline
887	921	\end{tabular}
	922	+}
888	923	\end{table}
	924	+\renewcommand{\arraystretch}{1}
889	925
890	926	The time needed to solve this configuration is significantly shorter than the time
891		-needed in the previous section. Indeed the worst time in this case is only 3~minutes,
	927	+needed in the previous section. Indeed the worst time in this case is only 17~minutes,
892	928	compared to 3~days in the previous section: this problem is more easily solved than the
893	929	previous one.
894	930