need to re-read and spellcheck
This commit is contained in:
Brett Weiland
parent
302ed29555
commit
b0b2eb6ff1
@ -29,7 +29,7 @@ def twoscomp_to_int(num, length):
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return num & (1 << length) - 1
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def debug(results):
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headers = ['multiplicand bin', 'multiplier bin', 'multiplicand dec', 'multiplier dec', 'expected bin', 'expected dec', 'booth if correct', 'booth mod if correct']
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headers = ['multiplicand bin', 'multiplier bin', 'multiplicand dec', 'multiplier dec', 'expected bin', 'expected dec', 'booth', 'mod booth']
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table = []
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for [multiplicand_bin, multiplier_bin, result_booth, result_booth_mod, length] in results:
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multiplicand = twoscomp_to_int(multiplicand_bin, length)
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@ -40,6 +40,8 @@ def debug(results):
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success_bm = [bin(result_booth_mod), "PASS"] [result_booth_mod == expected_bin]
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table.append([bin(multiplicand_bin), bin(multiplier_bin), multiplicand, multiplier, bin(expected_bin), expected, success_b, success_bm])
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with open("report/debug_table.tex", "w") as f:
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f.write(tabulate(table, headers, tablefmt="latex_longtable"))
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print("\nCHECKS: \n", tabulate(table, headers), "\n")
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@ -161,7 +163,7 @@ if __name__ == "__main__":
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})
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# generate table for operations vs operand length
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plt.title("Operations vs Operand Length")
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plt.gcf().set_size_inches(w=4.5, h=3.5)
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plt.plot(lengths, ops_booth, '^--m', label='booths algorithim')
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plt.plot(lengths, ops_mod_booth, 'v--c', label='modified booths algorithim')
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plt.gca().set_xlabel("Length of Operands")
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@ -178,6 +180,7 @@ if __name__ == "__main__":
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iters_mod_booth.append(int(length / 2))
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plt.figure()
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plt.gcf().set_size_inches(w=4.5, h=3.5)
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plt.plot(lengths, lengths, '^--m', label='booths algorithim')
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plt.plot(lengths, [int(l/2) for l in lengths], 'v--c', label='modified booths algorithim')
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plt.gca().set_xlabel("Operand Length")
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24
report/debug_table.tex
Normal file
24
report/debug_table.tex
Normal file
@ -0,0 +1,24 @@
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\begin{longtable}{llrrlrll}
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\hline
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multiplicand bin & multiplier bin & multiplicand dec & multiplier dec & expected bin & expected dec & booth & mod booth \\
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\hline
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\endhead
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0b1110 & 0b1111 & -2 & -1 & 0b10 & 2 & PASS & PASS \\
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0b101 & 0b0 & 5 & 0 & 0b0 & 0 & PASS & PASS \\
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0b111111 & 0b111111 & -1 & -1 & 0b1 & 1 & PASS & PASS \\
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0b101110 & 0b110111 & -18 & -9 & 0b10100010 & 162 & PASS & PASS \\
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0b111011 & 0b100011 & -5 & -29 & 0b10010001 & 145 & PASS & PASS \\
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0b11111 & 0b1010101 & 31 & 85 & 0b101001001011 & 2635 & PASS & PASS \\
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0b11010111 & 0b1010101 & -41 & 85 & 0b1111001001100011 & -3485 & PASS & PASS \\
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0b1010101 & 0b11010111 & 85 & -41 & 0b1111001001100011 & -3485 & PASS & PASS \\
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0b1110111 & 0b110011 & 119 & 51 & 0b1011110110101 & 6069 & PASS & PASS \\
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0b0 & 0b1110111 & 0 & 119 & 0b0 & 0 & PASS & PASS \\
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0b101010101 & 0b101010101 & 341 & 341 & 0b11100011000111001 & 116281 & PASS & PASS \\
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0b1100111011 & 0b1001110000 & -197 & -400 & 0b10011001111010000 & 78800 & PASS & PASS \\
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0b1001101110 & 0b101111010 & -402 & 378 & 0b11011010111001101100 & -151956 & PASS & PASS \\
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0b10101010101 & 0b10101010101 & 1365 & 1365 & 0b111000110111000111001 & 1863225 & PASS & PASS \\
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0b1111100111 & 0b0 & 999 & 0 & 0b0 & 0 & PASS & PASS \\
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0b101010101010 & 0b101010101010 & -1366 & -1366 & 0b111000111100011100100 & 1865956 & PASS & PASS \\
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0b111001110000 & 0b11111111 & -400 & 255 & 0b111111100111000110010000 & -102000 & PASS & PASS \\
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\hline
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\end{longtable}
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@ -27,7 +27,7 @@
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\begingroup%
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\makeatletter%
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\begin{pgfpicture}%
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\pgfpathrectangle{\pgfpointorigin}{\pgfqpoint{6.400000in}{4.800000in}}%
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\pgfpathrectangle{\pgfpointorigin}{\pgfqpoint{4.500000in}{3.500000in}}%
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\pgfusepath{use as bounding box, clip}%
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\begin{pgfscope}%
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\pgfsetbuttcap%
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@ -39,9 +39,9 @@
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\pgfsetstrokecolor{currentstroke}%
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\pgfsetdash{}{0pt}%
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\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}%
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\pgfpathlineto{\pgfqpoint{4.500000in}{3.500000in}}%
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\pgfpathlineto{\pgfqpoint{0.000000in}{3.500000in}}%
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\pgfpathlineto{\pgfqpoint{0.000000in}{0.000000in}}%
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\pgfpathclose%
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\pgfusepath{fill}%
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@ -56,11 +56,11 @@
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\pgfsetstrokecolor{currentstroke}%
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\pgfsetstrokeopacity{0.000000}%
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\pgfsetdash{}{0pt}%
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\pgfpathlineto{\pgfqpoint{0.562500in}{0.385000in}}%
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\pgfpathclose%
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\pgfusepath{fill}%
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\end{pgfscope}%
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@ -79,7 +79,7 @@
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\pgfusepath{stroke,fill}%
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}%
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\begin{pgfscope}%
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\pgfsys@transformshift{1.025455in}{0.528000in}%
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\pgfsys@transformshift{0.721023in}{0.385000in}%
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\pgfsys@useobject{currentmarker}{}%
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\end{pgfscope}%
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\end{pgfscope}%
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@ -87,7 +87,7 @@
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\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
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\pgfsetstrokecolor{textcolor}%
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\pgfsetfillcolor{textcolor}%
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\pgftext[x=1.025455in,y=0.430778in,,top]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{4}$}}%
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\pgftext[x=0.721023in,y=0.287778in,,top]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{4}$}}%
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\end{pgfscope}%
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\begin{pgfscope}%
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\pgfsetbuttcap%
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@ -104,7 +104,7 @@
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\pgfusepath{stroke,fill}%
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}%
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\begin{pgfscope}%
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\pgfsys@transformshift{1.589091in}{0.528000in}%
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\pgfsys@transformshift{1.513636in}{0.385000in}%
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\pgfsys@useobject{currentmarker}{}%
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\end{pgfscope}%
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\end{pgfscope}%
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@ -112,7 +112,7 @@
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\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
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\pgfsetstrokecolor{textcolor}%
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\pgfsetfillcolor{textcolor}%
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\pgftext[x=1.513636in,y=0.287778in,,top]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{6}$}}%
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\end{pgfscope}%
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\begin{pgfscope}%
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\pgfsetbuttcap%
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@ -129,7 +129,7 @@
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\pgfusepath{stroke,fill}%
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}%
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\begin{pgfscope}%
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\pgfsys@transformshift{2.152727in}{0.528000in}%
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\pgfsys@useobject{currentmarker}{}%
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@ -137,7 +137,7 @@
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\pgftext[x=2.306250in,y=0.287778in,,top]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{8}$}}%
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\end{pgfscope}%
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\begin{pgfscope}%
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\pgfsetbuttcap%
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@ -154,7 +154,7 @@
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\pgfusepath{stroke,fill}%
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}%
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\begin{pgfscope}%
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@ -162,7 +162,7 @@
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\end{pgfscope}%
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\begin{pgfscope}%
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\pgfsetbuttcap%
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@ -179,7 +179,7 @@
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\pgfusepath{stroke,fill}%
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}%
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\begin{pgfscope}%
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@ -187,113 +187,13 @@
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\end{pgfscope}%
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\pgfsetlinewidth{0.803000pt}%
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}%
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}%
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}%
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}%
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\begin{pgfscope}%
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@ -310,7 +210,7 @@
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\pgfusepath{stroke,fill}%
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}%
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\begin{pgfscope}%
|
||||
\pgfsys@transformshift{0.800000in}{0.696000in}%
|
||||
\pgfsys@transformshift{0.562500in}{0.507500in}%
|
||||
\pgfsys@useobject{currentmarker}{}%
|
||||
\end{pgfscope}%
|
||||
\end{pgfscope}%
|
||||
@ -318,7 +218,7 @@
|
||||
\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
|
||||
\pgfsetstrokecolor{textcolor}%
|
||||
\pgfsetfillcolor{textcolor}%
|
||||
\pgftext[x=0.633333in, y=0.647775in, left, base]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{2}$}}%
|
||||
\pgftext[x=0.395833in, y=0.459275in, left, base]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{2}$}}%
|
||||
\end{pgfscope}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsetbuttcap%
|
||||
@ -335,7 +235,7 @@
|
||||
\pgfusepath{stroke,fill}%
|
||||
}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsys@transformshift{0.800000in}{1.368000in}%
|
||||
\pgfsys@transformshift{0.562500in}{0.997500in}%
|
||||
\pgfsys@useobject{currentmarker}{}%
|
||||
\end{pgfscope}%
|
||||
\end{pgfscope}%
|
||||
@ -343,7 +243,7 @@
|
||||
\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
|
||||
\pgfsetstrokecolor{textcolor}%
|
||||
\pgfsetfillcolor{textcolor}%
|
||||
\pgftext[x=0.633333in, y=1.319775in, left, base]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{4}$}}%
|
||||
\pgftext[x=0.395833in, y=0.949275in, left, base]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{4}$}}%
|
||||
\end{pgfscope}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsetbuttcap%
|
||||
@ -360,7 +260,7 @@
|
||||
\pgfusepath{stroke,fill}%
|
||||
}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsys@transformshift{0.800000in}{2.040000in}%
|
||||
\pgfsys@transformshift{0.562500in}{1.487500in}%
|
||||
\pgfsys@useobject{currentmarker}{}%
|
||||
\end{pgfscope}%
|
||||
\end{pgfscope}%
|
||||
@ -368,7 +268,7 @@
|
||||
\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
|
||||
\pgfsetstrokecolor{textcolor}%
|
||||
\pgfsetfillcolor{textcolor}%
|
||||
\pgftext[x=0.633333in, y=1.991775in, left, base]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{6}$}}%
|
||||
\pgftext[x=0.395833in, y=1.439275in, left, base]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{6}$}}%
|
||||
\end{pgfscope}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsetbuttcap%
|
||||
@ -385,7 +285,7 @@
|
||||
\pgfusepath{stroke,fill}%
|
||||
}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsys@transformshift{0.800000in}{2.712000in}%
|
||||
\pgfsys@transformshift{0.562500in}{1.977500in}%
|
||||
\pgfsys@useobject{currentmarker}{}%
|
||||
\end{pgfscope}%
|
||||
\end{pgfscope}%
|
||||
@ -393,7 +293,7 @@
|
||||
\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
|
||||
\pgfsetstrokecolor{textcolor}%
|
||||
\pgfsetfillcolor{textcolor}%
|
||||
\pgftext[x=0.633333in, y=2.663775in, left, base]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{8}$}}%
|
||||
\pgftext[x=0.395833in, y=1.929275in, left, base]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{8}$}}%
|
||||
\end{pgfscope}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsetbuttcap%
|
||||
@ -410,7 +310,7 @@
|
||||
\pgfusepath{stroke,fill}%
|
||||
}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsys@transformshift{0.800000in}{3.384000in}%
|
||||
\pgfsys@transformshift{0.562500in}{2.467500in}%
|
||||
\pgfsys@useobject{currentmarker}{}%
|
||||
\end{pgfscope}%
|
||||
\end{pgfscope}%
|
||||
@ -418,7 +318,7 @@
|
||||
\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
|
||||
\pgfsetstrokecolor{textcolor}%
|
||||
\pgfsetfillcolor{textcolor}%
|
||||
\pgftext[x=0.563888in, y=3.335775in, left, base]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{10}$}}%
|
||||
\pgftext[x=0.326388in, y=2.419275in, left, base]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{10}$}}%
|
||||
\end{pgfscope}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsetbuttcap%
|
||||
@ -435,7 +335,7 @@
|
||||
\pgfusepath{stroke,fill}%
|
||||
}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsys@transformshift{0.800000in}{4.056000in}%
|
||||
\pgfsys@transformshift{0.562500in}{2.957500in}%
|
||||
\pgfsys@useobject{currentmarker}{}%
|
||||
\end{pgfscope}%
|
||||
\end{pgfscope}%
|
||||
@ -443,16 +343,16 @@
|
||||
\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
|
||||
\pgfsetstrokecolor{textcolor}%
|
||||
\pgfsetfillcolor{textcolor}%
|
||||
\pgftext[x=0.563888in, y=4.007775in, left, base]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{12}$}}%
|
||||
\pgftext[x=0.326388in, y=2.909275in, left, base]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{12}$}}%
|
||||
\end{pgfscope}%
|
||||
\begin{pgfscope}%
|
||||
\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
|
||||
\pgfsetstrokecolor{textcolor}%
|
||||
\pgfsetfillcolor{textcolor}%
|
||||
\pgftext[x=0.508333in,y=2.376000in,,bottom,rotate=90.000000]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}Number of iterations}}%
|
||||
\pgftext[x=0.270833in,y=1.732500in,,bottom,rotate=90.000000]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}Number of iterations}}%
|
||||
\end{pgfscope}%
|
||||
\begin{pgfscope}%
|
||||
\pgfpathrectangle{\pgfqpoint{0.800000in}{0.528000in}}{\pgfqpoint{4.960000in}{3.696000in}}%
|
||||
\pgfpathrectangle{\pgfqpoint{0.562500in}{0.385000in}}{\pgfqpoint{3.487500in}{2.695000in}}%
|
||||
\pgfusepath{clip}%
|
||||
\pgfsetbuttcap%
|
||||
\pgfsetroundjoin%
|
||||
@ -460,27 +360,27 @@
|
||||
\definecolor{currentstroke}{rgb}{0.750000,0.000000,0.750000}%
|
||||
\pgfsetstrokecolor{currentstroke}%
|
||||
\pgfsetdash{{5.550000pt}{2.400000pt}}{0.000000pt}%
|
||||
\pgfpathmoveto{\pgfqpoint{1.025455in}{1.368000in}}%
|
||||
\pgfpathlineto{\pgfqpoint{1.025455in}{1.368000in}}%
|
||||
\pgfpathlineto{\pgfqpoint{2.152727in}{2.040000in}}%
|
||||
\pgfpathlineto{\pgfqpoint{2.152727in}{2.040000in}}%
|
||||
\pgfpathlineto{\pgfqpoint{2.152727in}{2.040000in}}%
|
||||
\pgfpathlineto{\pgfqpoint{3.280000in}{2.712000in}}%
|
||||
\pgfpathlineto{\pgfqpoint{3.280000in}{2.712000in}}%
|
||||
\pgfpathlineto{\pgfqpoint{3.280000in}{2.712000in}}%
|
||||
\pgfpathlineto{\pgfqpoint{3.280000in}{2.712000in}}%
|
||||
\pgfpathlineto{\pgfqpoint{3.280000in}{2.712000in}}%
|
||||
\pgfpathlineto{\pgfqpoint{4.407273in}{3.384000in}}%
|
||||
\pgfpathlineto{\pgfqpoint{4.407273in}{3.384000in}}%
|
||||
\pgfpathlineto{\pgfqpoint{4.407273in}{3.384000in}}%
|
||||
\pgfpathlineto{\pgfqpoint{5.534545in}{4.056000in}}%
|
||||
\pgfpathlineto{\pgfqpoint{5.534545in}{4.056000in}}%
|
||||
\pgfpathlineto{\pgfqpoint{5.534545in}{4.056000in}}%
|
||||
\pgfpathlineto{\pgfqpoint{5.534545in}{4.056000in}}%
|
||||
\pgfpathmoveto{\pgfqpoint{0.721023in}{0.997500in}}%
|
||||
\pgfpathlineto{\pgfqpoint{0.721023in}{0.997500in}}%
|
||||
\pgfpathlineto{\pgfqpoint{1.513636in}{1.487500in}}%
|
||||
\pgfpathlineto{\pgfqpoint{1.513636in}{1.487500in}}%
|
||||
\pgfpathlineto{\pgfqpoint{1.513636in}{1.487500in}}%
|
||||
\pgfpathlineto{\pgfqpoint{2.306250in}{1.977500in}}%
|
||||
\pgfpathlineto{\pgfqpoint{2.306250in}{1.977500in}}%
|
||||
\pgfpathlineto{\pgfqpoint{2.306250in}{1.977500in}}%
|
||||
\pgfpathlineto{\pgfqpoint{2.306250in}{1.977500in}}%
|
||||
\pgfpathlineto{\pgfqpoint{2.306250in}{1.977500in}}%
|
||||
\pgfpathlineto{\pgfqpoint{3.098864in}{2.467500in}}%
|
||||
\pgfpathlineto{\pgfqpoint{3.098864in}{2.467500in}}%
|
||||
\pgfpathlineto{\pgfqpoint{3.098864in}{2.467500in}}%
|
||||
\pgfpathlineto{\pgfqpoint{3.891477in}{2.957500in}}%
|
||||
\pgfpathlineto{\pgfqpoint{3.891477in}{2.957500in}}%
|
||||
\pgfpathlineto{\pgfqpoint{3.891477in}{2.957500in}}%
|
||||
\pgfpathlineto{\pgfqpoint{3.891477in}{2.957500in}}%
|
||||
\pgfusepath{stroke}%
|
||||
\end{pgfscope}%
|
||||
\begin{pgfscope}%
|
||||
\pgfpathrectangle{\pgfqpoint{0.800000in}{0.528000in}}{\pgfqpoint{4.960000in}{3.696000in}}%
|
||||
\pgfpathrectangle{\pgfqpoint{0.562500in}{0.385000in}}{\pgfqpoint{3.487500in}{2.695000in}}%
|
||||
\pgfusepath{clip}%
|
||||
\pgfsetbuttcap%
|
||||
\pgfsetmiterjoin%
|
||||
@ -499,76 +399,76 @@
|
||||
\pgfusepath{stroke,fill}%
|
||||
}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsys@transformshift{1.025455in}{1.368000in}%
|
||||
\pgfsys@transformshift{0.721023in}{0.997500in}%
|
||||
\pgfsys@useobject{currentmarker}{}%
|
||||
\end{pgfscope}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsys@transformshift{1.025455in}{1.368000in}%
|
||||
\pgfsys@transformshift{0.721023in}{0.997500in}%
|
||||
\pgfsys@useobject{currentmarker}{}%
|
||||
\end{pgfscope}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsys@transformshift{2.152727in}{2.040000in}%
|
||||
\pgfsys@transformshift{1.513636in}{1.487500in}%
|
||||
\pgfsys@useobject{currentmarker}{}%
|
||||
\end{pgfscope}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsys@transformshift{2.152727in}{2.040000in}%
|
||||
\pgfsys@transformshift{1.513636in}{1.487500in}%
|
||||
\pgfsys@useobject{currentmarker}{}%
|
||||
\end{pgfscope}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsys@transformshift{2.152727in}{2.040000in}%
|
||||
\pgfsys@transformshift{1.513636in}{1.487500in}%
|
||||
\pgfsys@useobject{currentmarker}{}%
|
||||
\end{pgfscope}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsys@transformshift{3.280000in}{2.712000in}%
|
||||
\pgfsys@transformshift{2.306250in}{1.977500in}%
|
||||
\pgfsys@useobject{currentmarker}{}%
|
||||
\end{pgfscope}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsys@transformshift{3.280000in}{2.712000in}%
|
||||
\pgfsys@transformshift{2.306250in}{1.977500in}%
|
||||
\pgfsys@useobject{currentmarker}{}%
|
||||
\end{pgfscope}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsys@transformshift{3.280000in}{2.712000in}%
|
||||
\pgfsys@transformshift{2.306250in}{1.977500in}%
|
||||
\pgfsys@useobject{currentmarker}{}%
|
||||
\end{pgfscope}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsys@transformshift{3.280000in}{2.712000in}%
|
||||
\pgfsys@transformshift{2.306250in}{1.977500in}%
|
||||
\pgfsys@useobject{currentmarker}{}%
|
||||
\end{pgfscope}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsys@transformshift{3.280000in}{2.712000in}%
|
||||
\pgfsys@transformshift{2.306250in}{1.977500in}%
|
||||
\pgfsys@useobject{currentmarker}{}%
|
||||
\end{pgfscope}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsys@transformshift{4.407273in}{3.384000in}%
|
||||
\pgfsys@transformshift{3.098864in}{2.467500in}%
|
||||
\pgfsys@useobject{currentmarker}{}%
|
||||
\end{pgfscope}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsys@transformshift{4.407273in}{3.384000in}%
|
||||
\pgfsys@transformshift{3.098864in}{2.467500in}%
|
||||
\pgfsys@useobject{currentmarker}{}%
|
||||
\end{pgfscope}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsys@transformshift{4.407273in}{3.384000in}%
|
||||
\pgfsys@transformshift{3.098864in}{2.467500in}%
|
||||
\pgfsys@useobject{currentmarker}{}%
|
||||
\end{pgfscope}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsys@transformshift{5.534545in}{4.056000in}%
|
||||
\pgfsys@transformshift{3.891477in}{2.957500in}%
|
||||
\pgfsys@useobject{currentmarker}{}%
|
||||
\end{pgfscope}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsys@transformshift{5.534545in}{4.056000in}%
|
||||
\pgfsys@transformshift{3.891477in}{2.957500in}%
|
||||
\pgfsys@useobject{currentmarker}{}%
|
||||
\end{pgfscope}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsys@transformshift{5.534545in}{4.056000in}%
|
||||
\pgfsys@transformshift{3.891477in}{2.957500in}%
|
||||
\pgfsys@useobject{currentmarker}{}%
|
||||
\end{pgfscope}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsys@transformshift{5.534545in}{4.056000in}%
|
||||
\pgfsys@transformshift{3.891477in}{2.957500in}%
|
||||
\pgfsys@useobject{currentmarker}{}%
|
||||
\end{pgfscope}%
|
||||
\end{pgfscope}%
|
||||
\begin{pgfscope}%
|
||||
\pgfpathrectangle{\pgfqpoint{0.800000in}{0.528000in}}{\pgfqpoint{4.960000in}{3.696000in}}%
|
||||
\pgfpathrectangle{\pgfqpoint{0.562500in}{0.385000in}}{\pgfqpoint{3.487500in}{2.695000in}}%
|
||||
\pgfusepath{clip}%
|
||||
\pgfsetbuttcap%
|
||||
\pgfsetroundjoin%
|
||||
@ -576,27 +476,27 @@
|
||||
\definecolor{currentstroke}{rgb}{0.000000,0.750000,0.750000}%
|
||||
\pgfsetstrokecolor{currentstroke}%
|
||||
\pgfsetdash{{5.550000pt}{2.400000pt}}{0.000000pt}%
|
||||
\pgfpathmoveto{\pgfqpoint{1.025455in}{0.696000in}}%
|
||||
\pgfpathlineto{\pgfqpoint{1.025455in}{0.696000in}}%
|
||||
\pgfpathlineto{\pgfqpoint{2.152727in}{1.032000in}}%
|
||||
\pgfpathlineto{\pgfqpoint{2.152727in}{1.032000in}}%
|
||||
\pgfpathlineto{\pgfqpoint{2.152727in}{1.032000in}}%
|
||||
\pgfpathlineto{\pgfqpoint{3.280000in}{1.368000in}}%
|
||||
\pgfpathlineto{\pgfqpoint{3.280000in}{1.368000in}}%
|
||||
\pgfpathlineto{\pgfqpoint{3.280000in}{1.368000in}}%
|
||||
\pgfpathlineto{\pgfqpoint{3.280000in}{1.368000in}}%
|
||||
\pgfpathlineto{\pgfqpoint{3.280000in}{1.368000in}}%
|
||||
\pgfpathlineto{\pgfqpoint{4.407273in}{1.704000in}}%
|
||||
\pgfpathlineto{\pgfqpoint{4.407273in}{1.704000in}}%
|
||||
\pgfpathlineto{\pgfqpoint{4.407273in}{1.704000in}}%
|
||||
\pgfpathlineto{\pgfqpoint{5.534545in}{2.040000in}}%
|
||||
\pgfpathlineto{\pgfqpoint{5.534545in}{2.040000in}}%
|
||||
\pgfpathlineto{\pgfqpoint{5.534545in}{2.040000in}}%
|
||||
\pgfpathlineto{\pgfqpoint{5.534545in}{2.040000in}}%
|
||||
\pgfpathmoveto{\pgfqpoint{0.721023in}{0.507500in}}%
|
||||
\pgfpathlineto{\pgfqpoint{0.721023in}{0.507500in}}%
|
||||
\pgfpathlineto{\pgfqpoint{1.513636in}{0.752500in}}%
|
||||
\pgfpathlineto{\pgfqpoint{1.513636in}{0.752500in}}%
|
||||
\pgfpathlineto{\pgfqpoint{1.513636in}{0.752500in}}%
|
||||
\pgfpathlineto{\pgfqpoint{2.306250in}{0.997500in}}%
|
||||
\pgfpathlineto{\pgfqpoint{2.306250in}{0.997500in}}%
|
||||
\pgfpathlineto{\pgfqpoint{2.306250in}{0.997500in}}%
|
||||
\pgfpathlineto{\pgfqpoint{2.306250in}{0.997500in}}%
|
||||
\pgfpathlineto{\pgfqpoint{2.306250in}{0.997500in}}%
|
||||
\pgfpathlineto{\pgfqpoint{3.098864in}{1.242500in}}%
|
||||
\pgfpathlineto{\pgfqpoint{3.098864in}{1.242500in}}%
|
||||
\pgfpathlineto{\pgfqpoint{3.098864in}{1.242500in}}%
|
||||
\pgfpathlineto{\pgfqpoint{3.891477in}{1.487500in}}%
|
||||
\pgfpathlineto{\pgfqpoint{3.891477in}{1.487500in}}%
|
||||
\pgfpathlineto{\pgfqpoint{3.891477in}{1.487500in}}%
|
||||
\pgfpathlineto{\pgfqpoint{3.891477in}{1.487500in}}%
|
||||
\pgfusepath{stroke}%
|
||||
\end{pgfscope}%
|
||||
\begin{pgfscope}%
|
||||
\pgfpathrectangle{\pgfqpoint{0.800000in}{0.528000in}}{\pgfqpoint{4.960000in}{3.696000in}}%
|
||||
\pgfpathrectangle{\pgfqpoint{0.562500in}{0.385000in}}{\pgfqpoint{3.487500in}{2.695000in}}%
|
||||
\pgfusepath{clip}%
|
||||
\pgfsetbuttcap%
|
||||
\pgfsetmiterjoin%
|
||||
@ -615,71 +515,71 @@
|
||||
\pgfusepath{stroke,fill}%
|
||||
}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsys@transformshift{1.025455in}{0.696000in}%
|
||||
\pgfsys@transformshift{0.721023in}{0.507500in}%
|
||||
\pgfsys@useobject{currentmarker}{}%
|
||||
\end{pgfscope}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsys@transformshift{1.025455in}{0.696000in}%
|
||||
\pgfsys@transformshift{0.721023in}{0.507500in}%
|
||||
\pgfsys@useobject{currentmarker}{}%
|
||||
\end{pgfscope}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsys@transformshift{2.152727in}{1.032000in}%
|
||||
\pgfsys@transformshift{1.513636in}{0.752500in}%
|
||||
\pgfsys@useobject{currentmarker}{}%
|
||||
\end{pgfscope}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsys@transformshift{2.152727in}{1.032000in}%
|
||||
\pgfsys@transformshift{1.513636in}{0.752500in}%
|
||||
\pgfsys@useobject{currentmarker}{}%
|
||||
\end{pgfscope}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsys@transformshift{2.152727in}{1.032000in}%
|
||||
\pgfsys@transformshift{1.513636in}{0.752500in}%
|
||||
\pgfsys@useobject{currentmarker}{}%
|
||||
\end{pgfscope}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsys@transformshift{3.280000in}{1.368000in}%
|
||||
\pgfsys@transformshift{2.306250in}{0.997500in}%
|
||||
\pgfsys@useobject{currentmarker}{}%
|
||||
\end{pgfscope}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsys@transformshift{3.280000in}{1.368000in}%
|
||||
\pgfsys@transformshift{2.306250in}{0.997500in}%
|
||||
\pgfsys@useobject{currentmarker}{}%
|
||||
\end{pgfscope}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsys@transformshift{3.280000in}{1.368000in}%
|
||||
\pgfsys@transformshift{2.306250in}{0.997500in}%
|
||||
\pgfsys@useobject{currentmarker}{}%
|
||||
\end{pgfscope}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsys@transformshift{3.280000in}{1.368000in}%
|
||||
\pgfsys@transformshift{2.306250in}{0.997500in}%
|
||||
\pgfsys@useobject{currentmarker}{}%
|
||||
\end{pgfscope}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsys@transformshift{3.280000in}{1.368000in}%
|
||||
\pgfsys@transformshift{2.306250in}{0.997500in}%
|
||||
\pgfsys@useobject{currentmarker}{}%
|
||||
\end{pgfscope}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsys@transformshift{4.407273in}{1.704000in}%
|
||||
\pgfsys@transformshift{3.098864in}{1.242500in}%
|
||||
\pgfsys@useobject{currentmarker}{}%
|
||||
\end{pgfscope}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsys@transformshift{4.407273in}{1.704000in}%
|
||||
\pgfsys@transformshift{3.098864in}{1.242500in}%
|
||||
\pgfsys@useobject{currentmarker}{}%
|
||||
\end{pgfscope}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsys@transformshift{4.407273in}{1.704000in}%
|
||||
\pgfsys@transformshift{3.098864in}{1.242500in}%
|
||||
\pgfsys@useobject{currentmarker}{}%
|
||||
\end{pgfscope}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsys@transformshift{5.534545in}{2.040000in}%
|
||||
\pgfsys@transformshift{3.891477in}{1.487500in}%
|
||||
\pgfsys@useobject{currentmarker}{}%
|
||||
\end{pgfscope}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsys@transformshift{5.534545in}{2.040000in}%
|
||||
\pgfsys@transformshift{3.891477in}{1.487500in}%
|
||||
\pgfsys@useobject{currentmarker}{}%
|
||||
\end{pgfscope}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsys@transformshift{5.534545in}{2.040000in}%
|
||||
\pgfsys@transformshift{3.891477in}{1.487500in}%
|
||||
\pgfsys@useobject{currentmarker}{}%
|
||||
\end{pgfscope}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsys@transformshift{5.534545in}{2.040000in}%
|
||||
\pgfsys@transformshift{3.891477in}{1.487500in}%
|
||||
\pgfsys@useobject{currentmarker}{}%
|
||||
\end{pgfscope}%
|
||||
\end{pgfscope}%
|
||||
@ -690,8 +590,8 @@
|
||||
\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
|
||||
\pgfsetstrokecolor{currentstroke}%
|
||||
\pgfsetdash{}{0pt}%
|
||||
\pgfpathmoveto{\pgfqpoint{0.800000in}{0.528000in}}%
|
||||
\pgfpathlineto{\pgfqpoint{0.800000in}{4.224000in}}%
|
||||
\pgfpathmoveto{\pgfqpoint{0.562500in}{0.385000in}}%
|
||||
\pgfpathlineto{\pgfqpoint{0.562500in}{3.080000in}}%
|
||||
\pgfusepath{stroke}%
|
||||
\end{pgfscope}%
|
||||
\begin{pgfscope}%
|
||||
@ -701,8 +601,8 @@
|
||||
\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
|
||||
\pgfsetstrokecolor{currentstroke}%
|
||||
\pgfsetdash{}{0pt}%
|
||||
\pgfpathmoveto{\pgfqpoint{5.760000in}{0.528000in}}%
|
||||
\pgfpathlineto{\pgfqpoint{5.760000in}{4.224000in}}%
|
||||
\pgfpathmoveto{\pgfqpoint{4.050000in}{0.385000in}}%
|
||||
\pgfpathlineto{\pgfqpoint{4.050000in}{3.080000in}}%
|
||||
\pgfusepath{stroke}%
|
||||
\end{pgfscope}%
|
||||
\begin{pgfscope}%
|
||||
@ -712,8 +612,8 @@
|
||||
\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
|
||||
\pgfsetstrokecolor{currentstroke}%
|
||||
\pgfsetdash{}{0pt}%
|
||||
\pgfpathmoveto{\pgfqpoint{0.800000in}{0.528000in}}%
|
||||
\pgfpathlineto{\pgfqpoint{5.760000in}{0.528000in}}%
|
||||
\pgfpathmoveto{\pgfqpoint{0.562500in}{0.385000in}}%
|
||||
\pgfpathlineto{\pgfqpoint{4.050000in}{0.385000in}}%
|
||||
\pgfusepath{stroke}%
|
||||
\end{pgfscope}%
|
||||
\begin{pgfscope}%
|
||||
@ -723,8 +623,8 @@
|
||||
\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
|
||||
\pgfsetstrokecolor{currentstroke}%
|
||||
\pgfsetdash{}{0pt}%
|
||||
\pgfpathmoveto{\pgfqpoint{0.800000in}{4.224000in}}%
|
||||
\pgfpathlineto{\pgfqpoint{5.760000in}{4.224000in}}%
|
||||
\pgfpathmoveto{\pgfqpoint{0.562500in}{3.080000in}}%
|
||||
\pgfpathlineto{\pgfqpoint{4.050000in}{3.080000in}}%
|
||||
\pgfusepath{stroke}%
|
||||
\end{pgfscope}%
|
||||
\begin{pgfscope}%
|
||||
@ -738,16 +638,16 @@
|
||||
\pgfsetstrokecolor{currentstroke}%
|
||||
\pgfsetstrokeopacity{0.800000}%
|
||||
\pgfsetdash{}{0pt}%
|
||||
\pgfpathmoveto{\pgfqpoint{0.897222in}{3.725543in}}%
|
||||
\pgfpathlineto{\pgfqpoint{2.990205in}{3.725543in}}%
|
||||
\pgfpathquadraticcurveto{\pgfqpoint{3.017983in}{3.725543in}}{\pgfqpoint{3.017983in}{3.753321in}}%
|
||||
\pgfpathlineto{\pgfqpoint{3.017983in}{4.126778in}}%
|
||||
\pgfpathquadraticcurveto{\pgfqpoint{3.017983in}{4.154556in}}{\pgfqpoint{2.990205in}{4.154556in}}%
|
||||
\pgfpathlineto{\pgfqpoint{0.897222in}{4.154556in}}%
|
||||
\pgfpathquadraticcurveto{\pgfqpoint{0.869444in}{4.154556in}}{\pgfqpoint{0.869444in}{4.126778in}}%
|
||||
\pgfpathlineto{\pgfqpoint{0.869444in}{3.753321in}}%
|
||||
\pgfpathquadraticcurveto{\pgfqpoint{0.869444in}{3.725543in}}{\pgfqpoint{0.897222in}{3.725543in}}%
|
||||
\pgfpathlineto{\pgfqpoint{0.897222in}{3.725543in}}%
|
||||
\pgfpathmoveto{\pgfqpoint{0.659722in}{2.581543in}}%
|
||||
\pgfpathlineto{\pgfqpoint{2.752705in}{2.581543in}}%
|
||||
\pgfpathquadraticcurveto{\pgfqpoint{2.780483in}{2.581543in}}{\pgfqpoint{2.780483in}{2.609321in}}%
|
||||
\pgfpathlineto{\pgfqpoint{2.780483in}{2.982778in}}%
|
||||
\pgfpathquadraticcurveto{\pgfqpoint{2.780483in}{3.010556in}}{\pgfqpoint{2.752705in}{3.010556in}}%
|
||||
\pgfpathlineto{\pgfqpoint{0.659722in}{3.010556in}}%
|
||||
\pgfpathquadraticcurveto{\pgfqpoint{0.631944in}{3.010556in}}{\pgfqpoint{0.631944in}{2.982778in}}%
|
||||
\pgfpathlineto{\pgfqpoint{0.631944in}{2.609321in}}%
|
||||
\pgfpathquadraticcurveto{\pgfqpoint{0.631944in}{2.581543in}}{\pgfqpoint{0.659722in}{2.581543in}}%
|
||||
\pgfpathlineto{\pgfqpoint{0.659722in}{2.581543in}}%
|
||||
\pgfpathclose%
|
||||
\pgfusepath{stroke,fill}%
|
||||
\end{pgfscope}%
|
||||
@ -758,9 +658,9 @@
|
||||
\definecolor{currentstroke}{rgb}{0.750000,0.000000,0.750000}%
|
||||
\pgfsetstrokecolor{currentstroke}%
|
||||
\pgfsetdash{{5.550000pt}{2.400000pt}}{0.000000pt}%
|
||||
\pgfpathmoveto{\pgfqpoint{0.925000in}{4.050389in}}%
|
||||
\pgfpathlineto{\pgfqpoint{1.063889in}{4.050389in}}%
|
||||
\pgfpathlineto{\pgfqpoint{1.202778in}{4.050389in}}%
|
||||
\pgfpathmoveto{\pgfqpoint{0.687500in}{2.906389in}}%
|
||||
\pgfpathlineto{\pgfqpoint{0.826389in}{2.906389in}}%
|
||||
\pgfpathlineto{\pgfqpoint{0.965278in}{2.906389in}}%
|
||||
\pgfusepath{stroke}%
|
||||
\end{pgfscope}%
|
||||
\begin{pgfscope}%
|
||||
@ -781,7 +681,7 @@
|
||||
\pgfusepath{stroke,fill}%
|
||||
}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsys@transformshift{1.063889in}{4.050389in}%
|
||||
\pgfsys@transformshift{0.826389in}{2.906389in}%
|
||||
\pgfsys@useobject{currentmarker}{}%
|
||||
\end{pgfscope}%
|
||||
\end{pgfscope}%
|
||||
@ -789,7 +689,7 @@
|
||||
\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
|
||||
\pgfsetstrokecolor{textcolor}%
|
||||
\pgfsetfillcolor{textcolor}%
|
||||
\pgftext[x=1.313889in,y=4.001778in,left,base]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}booths algorithim}}%
|
||||
\pgftext[x=1.076389in,y=2.857778in,left,base]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}booths algorithim}}%
|
||||
\end{pgfscope}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsetbuttcap%
|
||||
@ -798,9 +698,9 @@
|
||||
\definecolor{currentstroke}{rgb}{0.000000,0.750000,0.750000}%
|
||||
\pgfsetstrokecolor{currentstroke}%
|
||||
\pgfsetdash{{5.550000pt}{2.400000pt}}{0.000000pt}%
|
||||
\pgfpathmoveto{\pgfqpoint{0.925000in}{3.856716in}}%
|
||||
\pgfpathlineto{\pgfqpoint{1.063889in}{3.856716in}}%
|
||||
\pgfpathlineto{\pgfqpoint{1.202778in}{3.856716in}}%
|
||||
\pgfpathmoveto{\pgfqpoint{0.687500in}{2.712716in}}%
|
||||
\pgfpathlineto{\pgfqpoint{0.826389in}{2.712716in}}%
|
||||
\pgfpathlineto{\pgfqpoint{0.965278in}{2.712716in}}%
|
||||
\pgfusepath{stroke}%
|
||||
\end{pgfscope}%
|
||||
\begin{pgfscope}%
|
||||
@ -821,7 +721,7 @@
|
||||
\pgfusepath{stroke,fill}%
|
||||
}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsys@transformshift{1.063889in}{3.856716in}%
|
||||
\pgfsys@transformshift{0.826389in}{2.712716in}%
|
||||
\pgfsys@useobject{currentmarker}{}%
|
||||
\end{pgfscope}%
|
||||
\end{pgfscope}%
|
||||
@ -829,7 +729,7 @@
|
||||
\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
|
||||
\pgfsetstrokecolor{textcolor}%
|
||||
\pgfsetfillcolor{textcolor}%
|
||||
\pgftext[x=1.313889in,y=3.808105in,left,base]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}modified booths algorithim}}%
|
||||
\pgftext[x=1.076389in,y=2.664105in,left,base]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}modified booths algorithim}}%
|
||||
\end{pgfscope}%
|
||||
\end{pgfpicture}%
|
||||
\makeatother%
|
||||
|
||||
@ -27,7 +27,7 @@
|
||||
\begingroup%
|
||||
\makeatletter%
|
||||
\begin{pgfpicture}%
|
||||
\pgfpathrectangle{\pgfpointorigin}{\pgfqpoint{6.400000in}{4.800000in}}%
|
||||
\pgfpathrectangle{\pgfpointorigin}{\pgfqpoint{4.500000in}{3.500000in}}%
|
||||
\pgfusepath{use as bounding box, clip}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsetbuttcap%
|
||||
@ -39,9 +39,9 @@
|
||||
\pgfsetstrokecolor{currentstroke}%
|
||||
\pgfsetdash{}{0pt}%
|
||||
\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}%
|
||||
\pgfpathlineto{\pgfqpoint{6.400000in}{0.000000in}}%
|
||||
\pgfpathlineto{\pgfqpoint{6.400000in}{4.800000in}}%
|
||||
\pgfpathlineto{\pgfqpoint{0.000000in}{4.800000in}}%
|
||||
\pgfpathlineto{\pgfqpoint{4.500000in}{0.000000in}}%
|
||||
\pgfpathlineto{\pgfqpoint{4.500000in}{3.500000in}}%
|
||||
\pgfpathlineto{\pgfqpoint{0.000000in}{3.500000in}}%
|
||||
\pgfpathlineto{\pgfqpoint{0.000000in}{0.000000in}}%
|
||||
\pgfpathclose%
|
||||
\pgfusepath{fill}%
|
||||
@ -56,11 +56,11 @@
|
||||
\pgfsetstrokecolor{currentstroke}%
|
||||
\pgfsetstrokeopacity{0.000000}%
|
||||
\pgfsetdash{}{0pt}%
|
||||
\pgfpathmoveto{\pgfqpoint{0.800000in}{0.528000in}}%
|
||||
\pgfpathlineto{\pgfqpoint{5.760000in}{0.528000in}}%
|
||||
\pgfpathlineto{\pgfqpoint{5.760000in}{4.224000in}}%
|
||||
\pgfpathlineto{\pgfqpoint{0.800000in}{4.224000in}}%
|
||||
\pgfpathlineto{\pgfqpoint{0.800000in}{0.528000in}}%
|
||||
\pgfpathmoveto{\pgfqpoint{0.562500in}{0.385000in}}%
|
||||
\pgfpathlineto{\pgfqpoint{4.050000in}{0.385000in}}%
|
||||
\pgfpathlineto{\pgfqpoint{4.050000in}{3.080000in}}%
|
||||
\pgfpathlineto{\pgfqpoint{0.562500in}{3.080000in}}%
|
||||
\pgfpathlineto{\pgfqpoint{0.562500in}{0.385000in}}%
|
||||
\pgfpathclose%
|
||||
\pgfusepath{fill}%
|
||||
\end{pgfscope}%
|
||||
@ -79,7 +79,7 @@
|
||||
\pgfusepath{stroke,fill}%
|
||||
}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsys@transformshift{1.025455in}{0.528000in}%
|
||||
\pgfsys@transformshift{0.721023in}{0.385000in}%
|
||||
\pgfsys@useobject{currentmarker}{}%
|
||||
\end{pgfscope}%
|
||||
\end{pgfscope}%
|
||||
@ -87,7 +87,7 @@
|
||||
\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
|
||||
\pgfsetstrokecolor{textcolor}%
|
||||
\pgfsetfillcolor{textcolor}%
|
||||
\pgftext[x=1.025455in,y=0.430778in,,top]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{4}$}}%
|
||||
\pgftext[x=0.721023in,y=0.287778in,,top]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{4}$}}%
|
||||
\end{pgfscope}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsetbuttcap%
|
||||
@ -104,7 +104,7 @@
|
||||
\pgfusepath{stroke,fill}%
|
||||
}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsys@transformshift{1.589091in}{0.528000in}%
|
||||
\pgfsys@transformshift{1.513636in}{0.385000in}%
|
||||
\pgfsys@useobject{currentmarker}{}%
|
||||
\end{pgfscope}%
|
||||
\end{pgfscope}%
|
||||
@ -112,7 +112,7 @@
|
||||
\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
|
||||
\pgfsetstrokecolor{textcolor}%
|
||||
\pgfsetfillcolor{textcolor}%
|
||||
\pgftext[x=1.589091in,y=0.430778in,,top]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{5}$}}%
|
||||
\pgftext[x=1.513636in,y=0.287778in,,top]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{6}$}}%
|
||||
\end{pgfscope}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsetbuttcap%
|
||||
@ -129,7 +129,7 @@
|
||||
\pgfusepath{stroke,fill}%
|
||||
}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsys@transformshift{2.152727in}{0.528000in}%
|
||||
\pgfsys@transformshift{2.306250in}{0.385000in}%
|
||||
\pgfsys@useobject{currentmarker}{}%
|
||||
\end{pgfscope}%
|
||||
\end{pgfscope}%
|
||||
@ -137,7 +137,7 @@
|
||||
\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
|
||||
\pgfsetstrokecolor{textcolor}%
|
||||
\pgfsetfillcolor{textcolor}%
|
||||
\pgftext[x=2.152727in,y=0.430778in,,top]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{6}$}}%
|
||||
\pgftext[x=2.306250in,y=0.287778in,,top]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{8}$}}%
|
||||
\end{pgfscope}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsetbuttcap%
|
||||
@ -154,7 +154,7 @@
|
||||
\pgfusepath{stroke,fill}%
|
||||
}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsys@transformshift{2.716364in}{0.528000in}%
|
||||
\pgfsys@transformshift{3.098864in}{0.385000in}%
|
||||
\pgfsys@useobject{currentmarker}{}%
|
||||
\end{pgfscope}%
|
||||
\end{pgfscope}%
|
||||
@ -162,7 +162,7 @@
|
||||
\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
|
||||
\pgfsetstrokecolor{textcolor}%
|
||||
\pgfsetfillcolor{textcolor}%
|
||||
\pgftext[x=2.716364in,y=0.430778in,,top]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{7}$}}%
|
||||
\pgftext[x=3.098864in,y=0.287778in,,top]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{10}$}}%
|
||||
\end{pgfscope}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsetbuttcap%
|
||||
@ -179,7 +179,7 @@
|
||||
\pgfusepath{stroke,fill}%
|
||||
}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsys@transformshift{3.280000in}{0.528000in}%
|
||||
\pgfsys@transformshift{3.891477in}{0.385000in}%
|
||||
\pgfsys@useobject{currentmarker}{}%
|
||||
\end{pgfscope}%
|
||||
\end{pgfscope}%
|
||||
@ -187,113 +187,13 @@
|
||||
\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
|
||||
\pgfsetstrokecolor{textcolor}%
|
||||
\pgfsetfillcolor{textcolor}%
|
||||
\pgftext[x=3.280000in,y=0.430778in,,top]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{8}$}}%
|
||||
\end{pgfscope}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsetbuttcap%
|
||||
\pgfsetroundjoin%
|
||||
\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
|
||||
\pgfsetfillcolor{currentfill}%
|
||||
\pgfsetlinewidth{0.803000pt}%
|
||||
\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
|
||||
\pgfsetstrokecolor{currentstroke}%
|
||||
\pgfsetdash{}{0pt}%
|
||||
\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{%
|
||||
\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}%
|
||||
\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}%
|
||||
\pgfusepath{stroke,fill}%
|
||||
}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsys@transformshift{3.843636in}{0.528000in}%
|
||||
\pgfsys@useobject{currentmarker}{}%
|
||||
\end{pgfscope}%
|
||||
\pgftext[x=3.891477in,y=0.287778in,,top]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{12}$}}%
|
||||
\end{pgfscope}%
|
||||
\begin{pgfscope}%
|
||||
\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
|
||||
\pgfsetstrokecolor{textcolor}%
|
||||
\pgfsetfillcolor{textcolor}%
|
||||
\pgftext[x=3.843636in,y=0.430778in,,top]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{9}$}}%
|
||||
\end{pgfscope}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsetbuttcap%
|
||||
\pgfsetroundjoin%
|
||||
\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
|
||||
\pgfsetfillcolor{currentfill}%
|
||||
\pgfsetlinewidth{0.803000pt}%
|
||||
\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
|
||||
\pgfsetstrokecolor{currentstroke}%
|
||||
\pgfsetdash{}{0pt}%
|
||||
\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{%
|
||||
\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}%
|
||||
\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}%
|
||||
\pgfusepath{stroke,fill}%
|
||||
}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsys@transformshift{4.407273in}{0.528000in}%
|
||||
\pgfsys@useobject{currentmarker}{}%
|
||||
\end{pgfscope}%
|
||||
\end{pgfscope}%
|
||||
\begin{pgfscope}%
|
||||
\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
|
||||
\pgfsetstrokecolor{textcolor}%
|
||||
\pgfsetfillcolor{textcolor}%
|
||||
\pgftext[x=4.407273in,y=0.430778in,,top]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{10}$}}%
|
||||
\end{pgfscope}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsetbuttcap%
|
||||
\pgfsetroundjoin%
|
||||
\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
|
||||
\pgfsetfillcolor{currentfill}%
|
||||
\pgfsetlinewidth{0.803000pt}%
|
||||
\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
|
||||
\pgfsetstrokecolor{currentstroke}%
|
||||
\pgfsetdash{}{0pt}%
|
||||
\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{%
|
||||
\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}%
|
||||
\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}%
|
||||
\pgfusepath{stroke,fill}%
|
||||
}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsys@transformshift{4.970909in}{0.528000in}%
|
||||
\pgfsys@useobject{currentmarker}{}%
|
||||
\end{pgfscope}%
|
||||
\end{pgfscope}%
|
||||
\begin{pgfscope}%
|
||||
\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
|
||||
\pgfsetstrokecolor{textcolor}%
|
||||
\pgfsetfillcolor{textcolor}%
|
||||
\pgftext[x=4.970909in,y=0.430778in,,top]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{11}$}}%
|
||||
\end{pgfscope}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsetbuttcap%
|
||||
\pgfsetroundjoin%
|
||||
\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
|
||||
\pgfsetfillcolor{currentfill}%
|
||||
\pgfsetlinewidth{0.803000pt}%
|
||||
\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
|
||||
\pgfsetstrokecolor{currentstroke}%
|
||||
\pgfsetdash{}{0pt}%
|
||||
\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{%
|
||||
\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}%
|
||||
\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}%
|
||||
\pgfusepath{stroke,fill}%
|
||||
}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsys@transformshift{5.534545in}{0.528000in}%
|
||||
\pgfsys@useobject{currentmarker}{}%
|
||||
\end{pgfscope}%
|
||||
\end{pgfscope}%
|
||||
\begin{pgfscope}%
|
||||
\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
|
||||
\pgfsetstrokecolor{textcolor}%
|
||||
\pgfsetfillcolor{textcolor}%
|
||||
\pgftext[x=5.534545in,y=0.430778in,,top]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{12}$}}%
|
||||
\end{pgfscope}%
|
||||
\begin{pgfscope}%
|
||||
\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
|
||||
\pgfsetstrokecolor{textcolor}%
|
||||
\pgfsetfillcolor{textcolor}%
|
||||
\pgftext[x=3.280000in,y=0.251766in,,top]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}Length of Operands}}%
|
||||
\pgftext[x=2.306250in,y=0.108766in,,top]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}Length of Operands}}%
|
||||
\end{pgfscope}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsetbuttcap%
|
||||
@ -310,7 +210,7 @@
|
||||
\pgfusepath{stroke,fill}%
|
||||
}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsys@transformshift{0.800000in}{0.696000in}%
|
||||
\pgfsys@transformshift{0.562500in}{0.507500in}%
|
||||
\pgfsys@useobject{currentmarker}{}%
|
||||
\end{pgfscope}%
|
||||
\end{pgfscope}%
|
||||
@ -318,7 +218,7 @@
|
||||
\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
|
||||
\pgfsetstrokecolor{textcolor}%
|
||||
\pgfsetfillcolor{textcolor}%
|
||||
\pgftext[x=0.633333in, y=0.647775in, left, base]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{0}$}}%
|
||||
\pgftext[x=0.395833in, y=0.459275in, left, base]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{0}$}}%
|
||||
\end{pgfscope}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsetbuttcap%
|
||||
@ -335,7 +235,7 @@
|
||||
\pgfusepath{stroke,fill}%
|
||||
}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsys@transformshift{0.800000in}{1.256000in}%
|
||||
\pgfsys@transformshift{0.562500in}{0.915833in}%
|
||||
\pgfsys@useobject{currentmarker}{}%
|
||||
\end{pgfscope}%
|
||||
\end{pgfscope}%
|
||||
@ -343,7 +243,7 @@
|
||||
\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
|
||||
\pgfsetstrokecolor{textcolor}%
|
||||
\pgfsetfillcolor{textcolor}%
|
||||
\pgftext[x=0.633333in, y=1.207775in, left, base]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{2}$}}%
|
||||
\pgftext[x=0.395833in, y=0.867608in, left, base]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{2}$}}%
|
||||
\end{pgfscope}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsetbuttcap%
|
||||
@ -360,7 +260,7 @@
|
||||
\pgfusepath{stroke,fill}%
|
||||
}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsys@transformshift{0.800000in}{1.816000in}%
|
||||
\pgfsys@transformshift{0.562500in}{1.324167in}%
|
||||
\pgfsys@useobject{currentmarker}{}%
|
||||
\end{pgfscope}%
|
||||
\end{pgfscope}%
|
||||
@ -368,7 +268,7 @@
|
||||
\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
|
||||
\pgfsetstrokecolor{textcolor}%
|
||||
\pgfsetfillcolor{textcolor}%
|
||||
\pgftext[x=0.633333in, y=1.767775in, left, base]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{4}$}}%
|
||||
\pgftext[x=0.395833in, y=1.275941in, left, base]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{4}$}}%
|
||||
\end{pgfscope}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsetbuttcap%
|
||||
@ -385,7 +285,7 @@
|
||||
\pgfusepath{stroke,fill}%
|
||||
}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsys@transformshift{0.800000in}{2.376000in}%
|
||||
\pgfsys@transformshift{0.562500in}{1.732500in}%
|
||||
\pgfsys@useobject{currentmarker}{}%
|
||||
\end{pgfscope}%
|
||||
\end{pgfscope}%
|
||||
@ -393,7 +293,7 @@
|
||||
\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
|
||||
\pgfsetstrokecolor{textcolor}%
|
||||
\pgfsetfillcolor{textcolor}%
|
||||
\pgftext[x=0.633333in, y=2.327775in, left, base]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{6}$}}%
|
||||
\pgftext[x=0.395833in, y=1.684275in, left, base]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{6}$}}%
|
||||
\end{pgfscope}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsetbuttcap%
|
||||
@ -410,7 +310,7 @@
|
||||
\pgfusepath{stroke,fill}%
|
||||
}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsys@transformshift{0.800000in}{2.936000in}%
|
||||
\pgfsys@transformshift{0.562500in}{2.140833in}%
|
||||
\pgfsys@useobject{currentmarker}{}%
|
||||
\end{pgfscope}%
|
||||
\end{pgfscope}%
|
||||
@ -418,7 +318,7 @@
|
||||
\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
|
||||
\pgfsetstrokecolor{textcolor}%
|
||||
\pgfsetfillcolor{textcolor}%
|
||||
\pgftext[x=0.633333in, y=2.887775in, left, base]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{8}$}}%
|
||||
\pgftext[x=0.395833in, y=2.092608in, left, base]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{8}$}}%
|
||||
\end{pgfscope}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsetbuttcap%
|
||||
@ -435,7 +335,7 @@
|
||||
\pgfusepath{stroke,fill}%
|
||||
}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsys@transformshift{0.800000in}{3.496000in}%
|
||||
\pgfsys@transformshift{0.562500in}{2.549167in}%
|
||||
\pgfsys@useobject{currentmarker}{}%
|
||||
\end{pgfscope}%
|
||||
\end{pgfscope}%
|
||||
@ -443,7 +343,7 @@
|
||||
\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
|
||||
\pgfsetstrokecolor{textcolor}%
|
||||
\pgfsetfillcolor{textcolor}%
|
||||
\pgftext[x=0.563888in, y=3.447775in, left, base]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{10}$}}%
|
||||
\pgftext[x=0.326388in, y=2.500941in, left, base]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{10}$}}%
|
||||
\end{pgfscope}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsetbuttcap%
|
||||
@ -460,7 +360,7 @@
|
||||
\pgfusepath{stroke,fill}%
|
||||
}%
|
||||
\begin{pgfscope}%
|
||||
\pgfsys@transformshift{0.800000in}{4.056000in}%
|
||||
\pgfsys@transformshift{0.562500in}{2.957500in}%
|
||||
\pgfsys@useobject{currentmarker}{}%
|
||||
\end{pgfscope}%
|
||||
\end{pgfscope}%
|
||||
@ -468,16 +368,16 @@
|
||||
\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
|
||||
\pgfsetstrokecolor{textcolor}%
|
||||
\pgfsetfillcolor{textcolor}%
|
||||
\pgftext[x=0.563888in, y=4.007775in, left, base]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{12}$}}%
|
||||
\pgftext[x=0.326388in, y=2.909275in, left, base]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}$\mathdefault{12}$}}%
|
||||
\end{pgfscope}%
|
||||
\begin{pgfscope}%
|
||||
\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
|
||||
\pgfsetstrokecolor{textcolor}%
|
||||
\pgfsetfillcolor{textcolor}%
|
||||
\pgftext[x=0.508333in,y=2.376000in,,bottom,rotate=90.000000]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}Number of Additions and Subtractions}}%
|
||||
\pgftext[x=0.270833in,y=1.732500in,,bottom,rotate=90.000000]{\color{textcolor}{\rmfamily\fontsize{10.000000}{12.000000}\selectfont\catcode`\^=\active\def^{\ifmmode\sp\else\^{}\fi}\catcode`\%=\active\def%{\%}Number of Additions and Subtractions}}%
|
||||
\end{pgfscope}%
|
||||
\begin{pgfscope}%
|
||||
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|
||||
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|
||||
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|
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|
||||
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|
||||
@ -485,27 +385,27 @@
|
||||
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||||
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||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
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|
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|
||||
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|
||||
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|
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
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|
||||
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|
||||
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|
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|
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|
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|
||||
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|
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@ -524,76 +424,76 @@
|
||||
\pgfusepath{stroke,fill}%
|
||||
}%
|
||||
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|
||||
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|
||||
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|
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
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|
||||
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|
||||
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|
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|
||||
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|
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|
||||
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|
||||
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|
||||
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|
||||
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|
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
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|
||||
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|
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|
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|
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|
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@ -601,27 +501,27 @@
|
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|
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
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|
||||
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|
||||
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|
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|
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
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|
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|
||||
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|
||||
@ -640,71 +540,71 @@
|
||||
\pgfusepath{stroke,fill}%
|
||||
}%
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
\end{pgfscope}%
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
\end{pgfscope}%
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
\end{pgfscope}%
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
\end{pgfscope}%
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
\end{pgfscope}%
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
\end{pgfscope}%
|
||||
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|
||||
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|
||||
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|
||||
\pgfsys@useobject{currentmarker}{}%
|
||||
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|
||||
\end{pgfscope}%
|
||||
@ -715,8 +615,8 @@
|
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|
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|
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|
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|
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|
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|
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|
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|
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\end{pgfscope}%
|
||||
\begin{pgfscope}%
|
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@ -726,8 +626,8 @@
|
||||
\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
|
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|
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|
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|
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|
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|
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@ -737,8 +637,8 @@
|
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|
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|
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|
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|
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|
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@ -748,17 +648,11 @@
|
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(./speed_table.tex [8]) (./result_table.tex) [9] [10] (./report.aux)
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) [10] [11] (./report.aux)
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@ -8,6 +8,12 @@
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\usepackage{float}
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\usepackage{listings}
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\usepackage{xcolor}
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\usepackage{caption}
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\usepackage{subcaption}
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\usepackage{layouts}
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\usepackage{pdflscape}
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\usepackage{rotating}
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\usepackage{longtable}
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\usepackage{pgf}
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@ -53,7 +59,19 @@ Bit 1 & Bit 0 & Action \\
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\bottomrule
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\end{tabular}
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\end{table}
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After all iterations are complete, the result is arithmaticlly shifted once to the left, and the process repeats for the number of bits in an operand.\\
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After all iterations are complete, the result is arithmaticlly shifted once to the left, and the process repeats for the number of bits in an operand. The pseudo code for this algorithim is below:\\
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\begin{verbatim}
|
||||
Booth:
|
||||
result = multiplier << 1
|
||||
loop (operand length) times:
|
||||
if last two bits are 01:
|
||||
result(upper half) += multiplicand
|
||||
if last two bits are 10:
|
||||
result(upper half) += twos_comp(multiplicand)
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remove extra bits from result
|
||||
arithmatic shift result right
|
||||
result >> 1
|
||||
\end{verbatim}
|
||||
|
||||
Modified booth's algorithim functions similar to Booth's algorithim, but checks the last \textit{three} bits instead. As such, there are a larger selection of actions for each iteration:
|
||||
\begin{table}[H]
|
||||
@ -74,17 +92,51 @@ Bit 2 & Bit 1 & Bit 0 & Action \\
|
||||
\end{tabular}
|
||||
\end{table}
|
||||
Because some operations require doubling the multiplicand, an extra bit is added to the most significant side of the workspace to avoid overflow. After each iteration, the result is arithmaticlly shifted right twice. The number of iterations is only half of the length of the operands. After all iterations, the workspace is shifted right once, and the second most significant bit is set to the first most significant bit as the result register does not include the extra bit.
|
||||
Pseudo code for this algorithim is listed below:
|
||||
\begin{verbatim}
|
||||
Modified booth:
|
||||
multiplicand(MSB) = multiplicand(second MSB)
|
||||
result = multiplier << 1
|
||||
loop (operand length / 2) times:
|
||||
if last two bits are 001 or 010:
|
||||
result(upper half) += multiplicand
|
||||
if last two bits are 011:
|
||||
result(upper half) += multiplicand * 2
|
||||
if last two bits are 100:
|
||||
result(upper half) += twos_comp(multiplicand) * 2
|
||||
if last two bits are 101 or 110:
|
||||
result(upper half) += twos_comp(multiplicand)
|
||||
remove extra bits from result
|
||||
arithmatic shift result right twice
|
||||
result >> 1
|
||||
result(second MSB) = result(MSB)
|
||||
result(MSB) = 0
|
||||
\end{verbatim}
|
||||
|
||||
\par
|
||||
\section*{Simulation Implimentation}
|
||||
Both algorithims were simulated in Python in attempts to utalize its high level nature for rapid development. The table for Booth's algorithim was preformed with a simple if-then loop, while a switch case was used in modified booth's algorithim. Simple integers were used to represent registers.
|
||||
\par
|
||||
One objective of this paper is to analyze and compare the peformance of these two algorithms for various operand lengths. As such, the length of operands had to be constantly accounted for. Aritmatic bitwise operations, including finding two's compliment, were all implimented using functions that took length as an input. Further more, extra bits were cleared after each iteration.
|
||||
\par
|
||||
To track down issues and test the validity of the multipliers, a debug function was written. To allow Python to natively work with the operands, each value is calculated from its two's compliment format. The converted numbers are then multiplied, and the result is compared to both Booth's Algorithim and Modified Booth's Algorithim. To ensure that the debugging function itself doesn't malfunction, all converted operands and expected results are put into a single large table for checking. The exported version of this table can be seen in table X. % TODO
|
||||
To track down issues and test the validity of the multipliers, a debug function was written. To allow Python to natively work with the operands, each value is calculated from its two's compliment format. The converted numbers are then multiplied, and the result is compared to both Booth's Algorithim and Modified Booth's Algorithim. To ensure that the debugging function itself doesn't malfunction, all converted operands and expected results are put into a single large table for checking. The exported version of this table can be seen on the last page, in table \ref{debug_table}. % TODO
|
||||
\section*{Analysis}
|
||||
Modified Booth's algorithim only requires half the iterations as Booth's algorithim. As such, it can be expected that the benifit of modified Booth's algorithim increases two fold with bit length. This can be shown by comparing the two curves in figure X.
|
||||
Modified Booth's algorithim only requires half the iterations as Booth's algorithim. As such, it can be expected that the benifit of modified Booth's algorithim increases two fold with bit length. This can be shown by comparing the two curves in figure \ref{igraph}.
|
||||
\begin{figure}[H]
|
||||
\centering
|
||||
\input{iterations.pgf}\\
|
||||
\captionof{figure}{Add and Subtract operations of various Operand Lengths}
|
||||
\label{igraph}
|
||||
\end{figure}
|
||||
|
||||
\par
|
||||
Despite this, the nature of both algorithims dictate that modified booth's algorithim is not explicitly faster. Iteration count translates to the \textit{maxiumum} number of additions and subtractions. Figure X shows the performance of the two algorithims given different input lengths, while table x shows the actual data made to generate the plot. There are some interesting things to note. When operands contain repeating zeros or ones, both operations preform similarly, as only shifting is required. Operands containing entirely ones or zeros result in idential preformance. On the contrary, alternating bits within operands demonstrate where the two algorithims differ, as almost no bits can be skipped over. Operands made entirely of alternating bits result in the maximum performance diffrence, in which modified booth's algorithim is potentially two times faster.
|
||||
Despite this, the nature of both algorithims dictate that modified booth's algorithim is not explicitly faster. Iteration count translates to the \textit{maxiumum} number of additions and subtractions. Figure \ref{pgraph} shows the performance of the two algorithims given different input lengths, while table x shows the actual data made to generate the plot. There are some interesting things to note. When operands contain repeating zeros or ones, both operations preform similarly, as only shifting is required. Operands containing entirely ones or zeros result in idential preformance. On the contrary, alternating bits within operands demonstrate where the two algorithims differ, as almost no bits can be skipped over. Operands made entirely of alternating bits result in the maximum performance diffrence, in which modified booth's algorithim is potentially two times faster.
|
||||
\begin{figure}[H]
|
||||
\centering
|
||||
\input{performance.pgf}\\
|
||||
\captionof{figure}{Add and Subtract operations of various Operand Lengths}
|
||||
\label{pgraph}
|
||||
\end{figure}
|
||||
\par
|
||||
All of this needs to be considered when designing an ALU. Modified booth's algorithim may improve speed, but requires substantially more hardware to impliment. One must consider if die space is to be allocated to optimize multiplication. In many applications, fast multiplication is unnessesary; many early single-chip processors and microcontrollers didn't impliment multiplication, as they were intended for simple embeded applications.
|
||||
\section*{Conclusion}
|
||||
@ -96,6 +148,21 @@ Hardware multipliers can help accellerate applications in which multiplication i
|
||||
\newpage
|
||||
\section*{Appendix}
|
||||
|
||||
% efficiency gets comparitively better over length
|
||||
% not much for the smaller operands
|
||||
% lots of repeated 1s and 0s very good for both algorithims
|
||||
\begin{figure}[h]
|
||||
\centering
|
||||
\input{speed_table.tex}
|
||||
\captionof{table}{Number of additions and subtractions for various inputs}
|
||||
\label{speed_table}
|
||||
\end{figure}
|
||||
\begin{figure}[H]
|
||||
\input{result_table.tex}
|
||||
\captionof{table}{Results of multiplication according to simulated multipliers}
|
||||
\label{result_table}
|
||||
\end{figure}
|
||||
|
||||
\lstdefinestyle{mystyle}{
|
||||
backgroundcolor=\color{backcolour},
|
||||
commentstyle=\color{codegreen},
|
||||
@ -115,16 +182,17 @@ Hardware multipliers can help accellerate applications in which multiplication i
|
||||
tabsize=2
|
||||
}
|
||||
|
||||
|
||||
\lstset{style=mystyle}
|
||||
\newpage
|
||||
\subsection*{Code listing}
|
||||
\lstinputlisting[language=Python]{../booth_multiplier.py}
|
||||
% efficiency gets comparitively better over length
|
||||
% not much for the smaller operands
|
||||
% lots of repeated 1s and 0s very good for both algorithims
|
||||
\begin{center}
|
||||
\input{performance.pgf}\\
|
||||
\input{iterations.pgf}\\
|
||||
\input{speed_table.tex}\\
|
||||
\input{result_table.tex}\\
|
||||
\end{center}
|
||||
|
||||
\begin{sidewaysfigure}
|
||||
\captionof{table}{Simulator self checking}
|
||||
\label{debug_table}
|
||||
\input{debug_table.tex}
|
||||
\end{sidewaysfigure}
|
||||
|
||||
|
||||
|
||||
\end{document}
|
||||
|
||||
35
sudocode
Normal file
35
sudocode
Normal file
@ -0,0 +1,35 @@
|
||||
Booth:
|
||||
result = multiplier << 1
|
||||
loop (operand length) times:
|
||||
if last two bits are 01:
|
||||
result(upper half) += multiplicand
|
||||
if last two bits are 10:
|
||||
result(upper half) += twos_comp(multiplicand)
|
||||
remove extra bits from result
|
||||
arithmatic shift result right
|
||||
result >> 1
|
||||
|
||||
Modified booth:
|
||||
multiplicand(MSB) = multiplicand(second MSB)
|
||||
result = multiplier << 1
|
||||
loop (operand length / 2) times:
|
||||
if last two bits are 001 or 010:
|
||||
result(upper half) += multiplicand
|
||||
if last two bits are 011:
|
||||
result(upper half) += multiplicand * 2
|
||||
if last two bits are 100:
|
||||
result(upper half) += twos_comp(multiplicand) * 2
|
||||
if last two bits are 101 or 110:
|
||||
result(upper half) += twos_comp(multiplicand)
|
||||
remove extra bits from result
|
||||
arithmatic shift result right twice
|
||||
result >> 1
|
||||
result(second MSB) = result(MSB)
|
||||
result(MSB) = 0
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
Loading…
x
Reference in New Issue
Block a user