28 lines
1.7 KiB
TeX
28 lines
1.7 KiB
TeX
%root:main.tex
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\begin{algorithm}[t]
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\caption{$\approxq(\circuit, \vct{p}, \conf, \error)$}
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\label{alg:mon-sam}
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\begin{algorithmic}[1]
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\Require \circuit: Circuit
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\Require $\vct{p} = (\prob_1,\ldots, \prob_\numvar)$ $\in [0, 1]^N$
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\Require $\conf$ $\in [0, 1]$
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\Require $\error$ $\in [0, 1]$
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\Ensure \vari{acc} $\in \mathbb{R}$
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\State $\accum \gets 0$\label{alg:mon-sam-global1}
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\State $\numsamp \gets \ceil{\frac{2 \log{\frac{2}{\conf}}}{\error^2}}$\label{alg:mon-sam-global2}
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\State $(\circuit_\vari{mod}, \vari{size}) \gets $ \onepass($\circuit$)\label{alg:mon-sam-onepass}\Comment{$\onepass$ is \Cref{alg:one-pass-iter}}
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\For{$\vari{i} \in 1 \text{ to }\numsamp$}\label{alg:sampling-loop}\Comment{Perform the required number of samples}
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\State $(\vari{M}, \vari{sgn}_\vari{i}) \gets $ \sampmon($\circuit_\vari{mod}$)\label{alg:mon-sam-sample}\Comment{\sampmon is \Cref{alg:sample}. Note that $\vari{sgn}_\vari{i}$ is the \emph{sign} of the monomial's coefficient and \emph{not} the coefficient itself}
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\If{$\vari{M}$ has at most one variable from each block}\label{alg:check-duplicate-block}
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\State $\vari{Y}_\vari{i} \gets \prod_{X_j\in\vari{M}}p_j$\label{alg:mon-sam-assign1}\Comment{\vari{M} is the sampled monomial's set of variables (cref. \cref{subsec:sampmon-remarks})}
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\State $\vari{Y}_\vari{i} \gets \vari{Y}_\vari{i} \times\; \vari{sgn}_\vari{i}$\label{alg:mon-sam-product}
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\State $\accum \gets \accum + \vari{Y}_\vari{i}$\Comment{Store the sum over all samples}\label{alg:mon-sam-add}
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\EndIf
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\EndFor
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\State $\vari{acc} \gets \vari{acc} \times \frac{\vari{size}}{\numsamp}$\label{alg:mon-sam-global3}
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\State \Return \vari{acc}
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\end{algorithmic}
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\end{algorithm} |