SCIENTIA SINICA Informationis, Volume 48 , Issue 1 : 100-114(2018) https://doi.org/10.1360/N112017-00065

A shortest path routing mechanism based on ${S_3}$ for TriBA-Net

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  • ReceivedMar 30, 2017
  • AcceptedMay 27, 2017
  • PublishedDec 28, 2017


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  • Figure 1

    (Color online) Plan of ${\rm{}}{{\rm~TG}^L}$

  • Figure 2

    (Color online) Diagram of using ${s_3}=~({123})$ to transform ${\rm~TG}^2$

  • Figure 3

    (Color online) The shortest path routing approach in ${\rm~FM}_0$ mode

  • Figure 4

    (Color online) Distance evaluation from vertex to tip

  • Figure 5

    (Color online) Flow modes of communication data in TriBA-Net

  • Figure 6

    (Color online) Port naming of nodes in TriBA-Net

  • Figure 7

    (Color online) Optimized route comparison circuit

  • Figure 8

    (Color online) Curve of average latency versus injection rate. (a) Uniform; (b) Bitreversal; (c) Shuffle

  • Figure 9

    (Color online) Curve of throughput versus injection rate. (a) Uniform; (b) Bitreversal; (c) Shuffle

  • Table 1   Truth table of equivalent transformation of layer codes
    Current mode (uvw) 000 001 010 011 100 101
    Current code (ab) Transformed code ($x′′x′$)
    01 01 10 01 10 11 11
    10 10 01 11 11 10 01
    11 11 11 10 01 01 10

    Algorithm 1 SPR0

    Require:$s′′_Ls′_L \cdots s′′_1s′_1$, starting point identifier;

    $t′′_Lt′_L \cdots t′′_1t′_1$,

    ending point identifier;


    size of ${\rm~FRG}^l$;

    Output:Direction of forwarding at $s′′_Ls′_L \cdots s′′_1s′_1$;

    LenPA $ \leftarrow s′_{l - 1} \cdots s′_1 + 1 + t′′_{l - 1} \cdots t′′_1$;

    LenPB $ \leftarrow ( {\bar s′′_{l - 1} \cdots \bar s′′_1 + \bar s′_{l - 1} \cdots \bar s′_1} ) + ( {\bar t′′_{l - 1} \cdots \bar t′′_1 + \bar t′_{l - 1} \cdots \bar t′_1} ) + {2^{l - 1}} + 1$;

    if LenPA LenPB then

    return $~2;~~//~{\rm~Port}~2$;


    return $~3;~//~{\rm~Port}~3$;

    end if


    Algorithm 2 SPR4T

    Require:$s′′_Ls′_L \cdots s′′_1s′_1$, starting point identifier;

    $t′′_Lt′_L \cdots t′′_1t′_1$,

    ending point identifier;


    size of TriBA-Net;

    Output:Direction of forwarding at $s′′_Ls′_L \cdots s′′_1s′_1$;

    if $l~=~0$ then

    return $0;~~//~{\rm~Port}~0$;


    for $l~=~L~\to~1$

    if$s′′_ls′_l \ne t′′_lt′_l$ then


    end if

    end for

    $i \leftarrow {\rm FM}( {s′′_ls′_l \cdots s′′_1s′_1, t′′_lt′_l \cdots t′′_1t′_1} )$;

    ${\bar u_{\rm EQ}} \leftarrow {{\rm Convert}_i}( {s′′_ls′_l \cdots s′′_1s′_1} )$;

    ${\bar v_{\rm EQ}} \leftarrow {{\rm Convert}_i}( {t′′_lt′_l \cdots t′′_1t′_1} )$;

    return $~s_i^{~-~1}(~{{\rm~SPR0}(~{{{\bar~u}_{\rm~EQ}},{{\bar~v}_{\rm~EQ}},l}~)}~)$;

    end if

  • Table 2   Configuration of the parameters of the simulator
    Configuration Topology Network size Switching Flit size Buffer Packet size Virtual channel
    Parameter TriBA-Net 27 nodes Wormhole 32 bits 4 flits 4 flits 4
  • Table 3   Router hardware overhead list
    Slices LUTs Flips-Flops
    SPORT router 139 269 114
    SPR4T router 118 229 103
  • Table 4   Comparison of power consumption between SPR4T and SPORT routers
    Uniform (nW) Bitreversal (nW)
    SPORT router 32.28 30.42
    SPR4T router 29.54 27.78