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

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

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

Abstract

The routing algorithm of a Network-on-Chip (NoC) is essential to its performance and power consumption. This paper presents a novel shortest path routing algorithm for TriBA-Net. First, the algorithm designs a coding scheme based on the topological features of TriBA-Net. The set of words 1, 3, and 2, used in the coding scheme, has the same meaning as the well-known group ${S_3}$ on 3-letters. Second, a communication model, which contains 6 types of flow modes, has been proposed for reflecting the status of the path within two hops. Finally, the algorithm is simplified by the cyclic permutation characteristic of the ${S_3}$ group. Whats more, the implementation of the SPR4T router is completed under the XC6VLX550TL chip. Experimental results show that under the uniform traffic pattern in the 27-node TriBA-Net performance test, SPR4T routing algorithm has a 7.5% higher saturation injection rate and a 7.7% higher throughput rate, with the obvious savings of hardware overhead and lower power consumption when compared to the SPORT routing algorithm.


Funded by

国家自然科学基金(61300011)

国家自然科学基金(61300010)


References

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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

  • 1   Table 1Truth table of equivalent transformation of layer codes
    Current mode (uvw) 000 001 010 011 100 101
    Current code (ab) Transformed code ($xx$)
    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;

    $l$,

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

    else

    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;

    $l$,

    size of TriBA-Net;

    Output:Direction of forwarding at $s_Ls_L~\cdots~s_1s_1$;

    if $l~=~0$ then

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

    else

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

    if $s_ls_l~\ne~t_lt_l$ then

    $~{\rm~break}$;

    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

  • 2   Table 2Configuration 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
  • 3   Table 3Router hardware overhead list
    Slices LUTs Flips-Flops
    SPORT router 139 269 114
    SPR4T router 118 229 103
  • 4   Table 4Comparison of power consumption between SPR4T and SPORT routers
    Uniform (nW) Bitreversal (nW)
    SPORT router 32.28 30.42
    SPR4T router 29.54 27.78

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