mirror of https://github.com/status-im/leopard.git
First commit
This commit is contained in:
catid
commit
d867f3a7da
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*.suo
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msvc/LHC_RS.VC.db
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*.opendb
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msvc/LHC_RS.vcxproj.user
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*.log
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*.obj
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*.tlog
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*.idb
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*.pdb
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*.exe
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*.ilk
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*.iobj
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*.ipdb
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*.vspx
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# Lin-Han-Chung RS Codes
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This is an attempt at implementing a fast version of the algorithm described here:
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~~~
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S.-J. Lin, T. Y. Al-Naffouri, Y. S. Han, and W.-H. Chung,
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"Novel Polynomial Basis with Fast Fourier Transform and Its Application to Reed-Solomon Erasure Codes"
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IEEE Trans. on Information Theory, pp. 6284-6299, November, 2016.
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~~~
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Available here: [http://ct.ee.ntust.edu.tw/it2016-2.pdf](http://ct.ee.ntust.edu.tw/it2016-2.pdf)
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I wasn't able to figure out how to speed up the critical piece of code:
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~~~
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// z = x + y (mod Q)
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static inline GFSymbol AddModQ(GFSymbol a, GFSymbol b)
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{
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const unsigned sum = (unsigned)a + b;
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// Partial reduction step, allowing for Q to be returned
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return static_cast<GFSymbol>(sum + (sum >> kGFBits));
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}
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// vx[] += vy[] * z
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static void muladd_mem(GFSymbol * vx, const GFSymbol * vy, GFSymbol z, unsigned symbolCount)
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{
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for (unsigned i = 0; i < symbolCount; ++i)
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{
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const GFSymbol a = vy[i];
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if (a == 0)
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continue;
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const GFSymbol sum = static_cast<GFSymbol>(AddModQ(GFLog[a], z));
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vx[i] ^= GFExp[sum];
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}
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}
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~~~
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This routine basically takes all the runtime. Since it involves normal addition via `AddModQ()`, it is pretty slow and is hard to vectorize.
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Math over GF(2^^16) is a lot faster because multiplies can be decomposed linearly into separate operations that can be done via vector instructions.
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So unfortunately it looks like while this field does have an FFT, the field does not permit fast math.
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Maybe someone else can figure out how to speed this up?
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Binary file not shown.
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static inline void FWHT_4(GFSymbol* data)
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{
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#if 1
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GFSymbol t0 = data[0];
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GFSymbol t1 = data[1];
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GFSymbol t2 = data[2];
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GFSymbol t3 = data[3];
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FWHT_2(t0, t1);
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FWHT_2(t2, t3);
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FWHT_2(t0, t2);
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FWHT_2(t1, t3);
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data[0] = t0;
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data[1] = t1;
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data[2] = t2;
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data[3] = t3;
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#else
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LHC_M128 * LHC_RESTRICT data64 = reinterpret_cast<LHC_M128 *>(data);
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const LHC_M128 mask = _mm_set_epi32(0xffff, 0xffff, 0xffff, 0xffff);
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// Load 8 bytes of data into low half of register
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// input = { t0 t1 t2 t3 0 0 0 0 }
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LHC_M128 input = _mm_loadl_epi64(data64);
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// FWHT_2(t0, t1); FWHT_2(t2, t3);
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// t0t2 = { t0 0 t2 0 0 0 0 0 }
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LHC_M128 t0t2 = _mm_and_si128(input, mask);
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// t1t3 = { t1 0 t3 0 0 0 0 0 }
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input = _mm_srli_epi32(input, 16);
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// {input, sum} = {t0t2 - t1t3, t0t2 - t1t3}
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LHC_M128 sum = _mm_add_epi32(t0t2, input);
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input = _mm_sub_epi32(t0t2, input);
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if (CpuHasSSSE3)
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{
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// Reduce to 16-bit values
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// input = { t0 + t1, t2 + t3, 0, 0, t0 - t1, t2 - t3, 0, 0 }
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// input = { t0, t2, 0, 0, t1, t3, 0, 0 }
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input = _mm_hadd_epi16(sum, input);
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// FWHT_2(t0, t2); FWHT_2(t1, t3);
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// Spread the values out
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// input = { t0, 0, t2, 0, t1, 0, t3, 0 }
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input = _mm_shufflelo_epi16(input, _MM_SHUFFLE(3, 1, 2, 0));
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input = _mm_shufflehi_epi16(input, _MM_SHUFFLE(3, 1, 2, 0));
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// Compute 32-bit sums with overflows
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// sum = { t0 + t2, t1 + t3, undef, undef } (32-bit overflows)
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sum = _mm_hadd_epi32(input, input);
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// Compute 32-bit difs with overflows
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// input = { t0 - t2, t1 - t3, undef, undef } (32-bit overflows)
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input = _mm_hsub_epi32(input, input);
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// Reduce to 16-bit values
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// input = { t0 + t2, t1 + t3, t0 + t2, t1 + t3, t0 - t2, t1 - t3, t0 - t2, t1 - t3 } (16-bit reduced)
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input = _mm_hadd_epi16(sum, input);
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// input = { t0 + t2, t1 + t3, t0 - t2, t1 - t3, undef, undef, undef, undef }
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input = _mm_shuffle_epi32(input, _MM_SHUFFLE(3, 1, 2, 0));
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// Store 8 bytes of data
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_mm_storel_epi64(data64, input);
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}
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else
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{
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LHC_DEBUG_BREAK; // FIXME
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// FWHT_2(t0, t2); FWHT_2(t1, t3);
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}
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#endif
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}
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File diff suppressed because it is too large
Load Diff
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Microsoft Visual Studio Solution File, Format Version 12.00
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# Visual Studio 14
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VisualStudioVersion = 14.0.25420.1
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MinimumVisualStudioVersion = 10.0.40219.1
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EndProject
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Global
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GlobalSection(SolutionConfigurationPlatforms) = preSolution
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Debug|Win32 = Debug|Win32
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Debug|x64 = Debug|x64
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Release|Win32 = Release|Win32
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Release|x64 = Release|x64
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EndGlobalSection
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GlobalSection(ProjectConfigurationPlatforms) = postSolution
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{32176592-2F30-4BD5-B645-EB11C8D3453E}.Debug|Win32.ActiveCfg = Debug|Win32
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{32176592-2F30-4BD5-B645-EB11C8D3453E}.Debug|Win32.Build.0 = Debug|Win32
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{32176592-2F30-4BD5-B645-EB11C8D3453E}.Debug|x64.ActiveCfg = Debug|x64
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{32176592-2F30-4BD5-B645-EB11C8D3453E}.Debug|x64.Build.0 = Debug|x64
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{32176592-2F30-4BD5-B645-EB11C8D3453E}.Release|Win32.ActiveCfg = Release|Win32
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{32176592-2F30-4BD5-B645-EB11C8D3453E}.Release|Win32.Build.0 = Release|Win32
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{32176592-2F30-4BD5-B645-EB11C8D3453E}.Release|x64.ActiveCfg = Release|x64
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{32176592-2F30-4BD5-B645-EB11C8D3453E}.Release|x64.Build.0 = Release|x64
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EndGlobalSection
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GlobalSection(SolutionProperties) = preSolution
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HideSolutionNode = FALSE
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EndGlobalSection
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EndGlobal
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<?xml version="1.0" encoding="utf-8"?>
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<ProjectConfiguration Include="Debug|Win32">
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<Configuration>Debug</Configuration>
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<Platform>Win32</Platform>
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<ProjectConfiguration Include="Debug|x64">
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<Configuration>Debug</Configuration>
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<Platform>x64</Platform>
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</ProjectConfiguration>
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<ProjectConfiguration Include="Release|Win32">
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<Configuration>Release</Configuration>
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<Platform>Win32</Platform>
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</ProjectConfiguration>
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<ProjectConfiguration Include="Release|x64">
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<Configuration>Release</Configuration>
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<Platform>x64</Platform>
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<ClCompile Include="..\lhc_rs.cpp" />
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<PropertyGroup Label="Globals">
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<ProjectGuid>{32176592-2F30-4BD5-B645-EB11C8D3453E}</ProjectGuid>
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<RootNamespace>GF65536</RootNamespace>
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<ProjectName>LHC_RS</ProjectName>
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