/articles/toma

\begin{algorithm}[htb]

\DontPrintSemicolon

\caption{\label{alg:texrec_pascal} Optimized implementation of the back-projection kernel relaying on the texture engine to perform interpolation}

%\begin{algorithmic}

\KwIn {Texture, projection constants~($\cmem{c}_*$),  dimensions~($n_*$), cache sizes~($s_*$), and other parameters~($v_*$)}

\KwShMem {$\shmem{\vfloat{s}}[64][4]$, $\shmem{\vfloat{r}}[16][16]$}

\KwOut {Reconstructed slice $\gmem{\vfloat{r}}$}

\Begin {

\tcc{Computing sequential numbers of 4x4 square, quadrant, and pixel within quadrant}

$square \eq \vy{m_t} \imod 4$ \;

$quadrant \eq \vx{m_t} \idiv 4$ \;

$pixel \eq \vx{m_t} \imod 4$ \;

\tcc{Computing projection and pixel offsets}

$m_p \eq \vy{m_t} \idiv 4$ \;

$\vx{m_t'} \eq 4 \mul square + 2 \mul (quadrant \imod 2) +  (pixel \imod 2) $ \;

$\vy{m_t'} \eq 2 \mul (quadrant \idiv 2) +  (pixel \idiv 2) $ \;

\tcc{Computing pixel coordinates}

$\vdata{m}'_g \eq \vdata{m}_b \vmul \vdata{n}_t + \vdata{m}'_t$ \;

$\vdata{f}'_g \eq \vdata{m}'_g - \vdata{v}_a$ \;

\tcc{Computing partial sums}

$\vfloat{s}[4] \eq \{0\}$ \;

\ForToBy{p}{m_p}{n_p}{4}{

    $c_s \eq \vy{\cmem{c_s}[p]}$ \;

    $h \eq \cmem{c_a}[p] + \vx{f'_g} \mul \cmem{c_c}[p] - \vy{f'_g} \mul \cmem{c_s}[p] + \fconstf{0.5}$ \;

	\ForTo{q}{0}{4}{

       $\vfloat{s}[q] \aeq $ \KwTex{$h - 4 \mul q \mul c_s$, $p + \fconstf{0.5}$} \;

    }

}

\tcc{Reduction}

$\vdata{m}_t'' =  \vlist{\vx{m_t} \imod 4, 4 \mul \vy{m_t} + \vx{m_t} \idiv 4}$ \;

\ForTo{q}{0}{4}{

    \tcc{Moving partial sums to shared memory}

    $\shmem{\vfloat{s}}[\vx{n_t} \mul \vy{m_t'} + \vx{m_t'}][m_p] \eq \vfloat{s}[q]$ \;

    \KwSyncThreads \;

    \tcc{Performing reduction}

    $\vfloat{r} \eq \shmem{\vfloat{s}}[\vy{m_t'}][\vx{m_t'}]$ \;

    \CFor{i \eq 2}{i \geq 1}{i \deq 2}{

        $\vfloat{r} \aeq$ \KwShflXor{$\vfloat{r}$, $i$, $4$} \;   

    }

    \tcc{Grouping results in shared memory to coalesce global memory writes}

    \If{$\vx{m_t''} \ifeq 0$} {

        $\shmem{\vfloat{r}}[4 \mul q + \vy{m_t''} \idiv 16][\vy{m_t''} \imod 16] \eq\vfloat{r}$ \;

    }

    \KwSyncThreads \;

}

$\gmem{\vfloat{r}}[\vy{m_g}][\vx{m_g}] \eq \shmem{\vfloat{r}}[\vy{m_t}][\vx{m_t}]$  \;

}

\end{algorithm}