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Multiply matrix 1xM by MxM real4 for sizes M=4,6,8

Started by RuiLoureiro, August 21, 2018, 04:41:40 AM

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RuiLoureiro

August 21, 2018, 04:41:40 AM Last Edit: August 24, 2018, 06:41:23 AM by RuiLoureiro
Hi all,
       Here we have 3 particular cases to multiply any vector 1x4, 1x6 or 1x8 by the square matrix
       4x4, 6x6 and 8x8 using SSE/FPU instructions. Now, using these examples, you may write
       any other particular case.

Quote
      The procedures are inside the files .inc
      By lines:
       
            invoke      Multiply1x4_4x4Lin_v1SSE, pMatX, pMatY, pMatXY
            invoke      Multiply1x4_4x4Lin_v2SSE, pMatX, pMatY, pMatXY
            invoke      Multiply1x4_4x4Lin_v3SSE, pMatX, pMatY, pMatXY
           
            invoke      Multiply1x6_6x6Lin_v2SSE, pMatX, pMatY, pMatXY
            invoke      Multiply1x6_6x6Lin_v3SSE, pMatX, pMatY, pMatXY   
       
            invoke      Multiply1x8_8x8Lin_v1SSE, pMatX, pMatY, pMatXY
            invoke      Multiply1x8_8x8Lin_v2SSE, pMatX, pMatY, pMatXY           

       By columns(by definition):
       
            invoke      Multiply1x4_4x4Col_v1SSE, pMatX, pMatY, pMatXY

            invoke      Multiply1x6_6x6Col_v1SSE, pMatX, pMatY, pMatXY

            invoke      Multiply1x8_8x8Col_v1SSE, pMatX, pMatY, pMatXY

      FPU VERSIONS:
     
            invoke      Multiply1x4_4x4Lin_v1FPU, pMatX, pMatY, pMatXY
            invoke      Multiply1x4_4x4Lin_v2FPU, pMatX, pMatY, pMatXY
            invoke      Multiply1x4_4x4Lin_v3FPU, pMatX, pMatY, pMatXY
            invoke      Multiply1x4_4x4Lin_v4FPU, pMatX, pMatY, pMatXY
           
            invoke      Multiply1x6_6x6Lin_v1FPU, pMatX, pMatY, pMatXY
            invoke      Multiply1x6_6x6Lin_v2FPU, pMatX, pMatY, pMatXY
            invoke      Multiply1x6_6x6Lin_v3FPU, pMatX, pMatY, pMatXY
            invoke      Multiply1x6_6x6Lin_v4FPU, pMatX, pMatY, pMatXY

            invoke      Multiply1x8_8x8Lin_v1FPU, pMatX, pMatY, pMatXY
            invoke      Multiply1x8_8x8Lin_v2FPU, pMatX, pMatY, pMatXY
            invoke      Multiply1x8_8x8Lin_v3FPU, pMatX, pMatY, pMatXY
            invoke      Multiply1x8_8x8Lin_v4FPU, pMatX, pMatY, pMatXY

            The same for culumns

    DOCUMENTATION:          TEXT_ABOUT_MULTIPLY_SSE_REAL4.txt

    MATRIX DEFINITION:      We must define any matrixX as this

                            ALIGN 16
                            dd ?
                            dd ?
                            dd M   ; <<--- number of columns
                            dd M   ; <<--- number of lines
              matrixX  dd (M*M) dup (?)         

    VERIFY SSE PROCEDURES:  Use multiply1xM_MxMLin_v1.exe/asm and
                                                multiply1xM_MxMCol_v1.exe/asm

    Please test it in your CPU (i5/i7/AMD).
    Use ExecuteTestmultiply1xM_MxM_SSEv1.bat and post the file Resultsmultiply1xM_MxM_v1.txt.

Good luck
RuiLoureiro

All results: :t :t :t
Thanks Siekmanski (for all your help  ;) ),
LiaoMi (gaves me a lot of work and you run it in 4 cycles-unfair  ;) ),
Jochen (8 cycles is very good for i5 ! ;) )
Code Select

Siekmanski:

***** Time table - LoopCount =1000000 *****

Intel(R) Core(TM) i7-4930K CPU @ 3.40GHz (SSE4)

18  cycles, Multiply1x4_4x4Lin_v3SSE,  MatrixX1x4   * MatrixY4x4
18  cycles, Multiply1x4_4x4Lin_v1SSE,  MatrixX1x4   * MatrixY4x4
22  cycles, Multiply1x4_4x4Lin_v2SSE,  MatrixX1x4   * MatrixY4x4

42  cycles, Multiply1x6_6x6Lin_v2SSE,  MatrixX1x6   * MatrixY6x6
45  cycles, Multiply1x6_6x6Lin_v3SSE,  MatrixX1x6   * MatrixY6x6

69  cycles, Multiply1x8_8x8Lin_v1SSE,  MatrixX1x8   * MatrixY8x8
76  cycles, Multiply1x8_8x8Lin_v2SSE,  MatrixX1x8   * MatrixY8x8

115  cycles, Multiply1x4_4x4Lin_v1FPU,  MatrixX1x4   * MatrixY4x4
117  cycles, Multiply1x4_4x4Lin_v4FPU,  MatrixX1x4   * MatrixY4x4
118  cycles, Multiply1x4_4x4Lin_v2FPU,  MatrixX1x4   * MatrixY4x4
119  cycles, Multiply1x4_4x4Lin_v3FPU,  MatrixX1x4   * MatrixY4x4

153  cycles, Multiply1x6_6x6Lin_v2FPU,  MatrixX1x6   * MatrixY6x6
157  cycles, Multiply1x6_6x6Lin_v1FPU,  MatrixX1x6   * MatrixY6x6
160  cycles, Multiply1x6_6x6Lin_v4FPU,  MatrixX1x6   * MatrixY6x6
166  cycles, Multiply1x6_6x6Lin_v3FPU,  MatrixX1x6   * MatrixY6x6

177  cycles, Multiply1x8_8x8Lin_v1FPU,  MatrixX1x8   * MatrixY8x8
182  cycles, Multiply1x8_8x8Lin_v4FPU,  MatrixX1x8   * MatrixY8x8
206  cycles, Multiply1x8_8x8Lin_v2FPU,  MatrixX1x8   * MatrixY8x8
215  cycles, Multiply1x8_8x8Lin_v3FPU,  MatrixX1x8   * MatrixY8x8

***** Time table - LoopCount =1000000 *****

Intel(R) Core(TM) i7-4930K CPU @ 3.40GHz (SSE4)

  9  cycles, Multiply1x4_4x4Col_v1SSE,  MatrixX1x4   * MatrixY4x4
25  cycles, Multiply1x6_6x6Col_v1SSE,  MatrixX1x6   * MatrixY6x6
30  cycles, Multiply1x8_8x8Col_v1SSE,  MatrixX1x8   * MatrixY8x8

114  cycles, Multiply1x4_4x4Col_v2FPU,  MatrixX1x4   * MatrixY4x4
116  cycles, Multiply1x4_4x4Col_v1FPU,  MatrixX1x4   * MatrixY4x4
117  cycles, Multiply1x4_4x4Col_v3FPU,  MatrixX1x4   * MatrixY4x4
120  cycles, Multiply1x4_4x4Col_v4FPU,  MatrixX1x4   * MatrixY4x4

152  cycles, Multiply1x6_6x6Col_v2FPU,  MatrixX1x6   * MatrixY6x6
154  cycles, Multiply1x6_6x6Col_v1FPU,  MatrixX1x6   * MatrixY6x6
163  cycles, Multiply1x6_6x6Col_v3FPU,  MatrixX1x6   * MatrixY6x6
165  cycles, Multiply1x6_6x6Col_v4FPU,  MatrixX1x6   * MatrixY6x6

194  cycles, Multiply1x8_8x8Col_v2FPU,  MatrixX1x8   * MatrixY8x8
202  cycles, Multiply1x8_8x8Col_v1FPU,  MatrixX1x8   * MatrixY8x8
204  cycles, Multiply1x8_8x8Col_v3FPU,  MatrixX1x8   * MatrixY8x8
206  cycles, Multiply1x8_8x8Col_v4FPU,  MatrixX1x8   * MatrixY8x8
+++++++++++++++++++++++++++++++++++++++++++
LiaoMi:

***** Time table - LoopCount =1000000 *****

Intel(R) Core(TM) i7-4810MQ CPU @ 2.80GHz (SSE4)

13  cycles, Multiply1x4_4x4Lin_v1SSE,  MatrixX1x4   * MatrixY4x4
14  cycles, Multiply1x4_4x4Lin_v3SSE,  MatrixX1x4   * MatrixY4x4
16  cycles, Multiply1x4_4x4Lin_v2SSE,  MatrixX1x4   * MatrixY4x4

30  cycles, Multiply1x6_6x6Lin_v2SSE,  MatrixX1x6   * MatrixY6x6
33  cycles, Multiply1x6_6x6Lin_v3SSE,  MatrixX1x6   * MatrixY6x6

47  cycles, Multiply1x8_8x8Lin_v1SSE,  MatrixX1x8   * MatrixY8x8
50  cycles, Multiply1x8_8x8Lin_v2SSE,  MatrixX1x8   * MatrixY8x8

86  cycles, Multiply1x4_4x4Lin_v1FPU,  MatrixX1x4   * MatrixY4x4
89  cycles, Multiply1x4_4x4Lin_v2FPU,  MatrixX1x4   * MatrixY4x4
90  cycles, Multiply1x4_4x4Lin_v4FPU,  MatrixX1x4   * MatrixY4x4
94  cycles, Multiply1x4_4x4Lin_v3FPU,  MatrixX1x4   * MatrixY4x4

106  cycles, Multiply1x6_6x6Lin_v2FPU,  MatrixX1x6   * MatrixY6x6
108  cycles, Multiply1x6_6x6Lin_v4FPU,  MatrixX1x6   * MatrixY6x6
111  cycles, Multiply1x6_6x6Lin_v1FPU,  MatrixX1x6   * MatrixY6x6
114  cycles, Multiply1x6_6x6Lin_v3FPU,  MatrixX1x6   * MatrixY6x6

120  cycles, Multiply1x8_8x8Lin_v1FPU,  MatrixX1x8   * MatrixY8x8
121  cycles, Multiply1x8_8x8Lin_v4FPU,  MatrixX1x8   * MatrixY8x8
140  cycles, Multiply1x8_8x8Lin_v3FPU,  MatrixX1x8   * MatrixY8x8
145  cycles, Multiply1x8_8x8Lin_v2FPU,  MatrixX1x8   * MatrixY8x8

***** Time table - LoopCount =1000000 *****

Intel(R) Core(TM) i7-4810MQ CPU @ 2.80GHz (SSE4)

  7  cycles, Multiply1x4_4x4Col_v1SSE,  MatrixX1x4   * MatrixY4x4
16  cycles, Multiply1x6_6x6Col_v1SSE,  MatrixX1x6   * MatrixY6x6
21  cycles, Multiply1x8_8x8Col_v1SSE,  MatrixX1x8   * MatrixY8x8

86  cycles, Multiply1x4_4x4Col_v2FPU,  MatrixX1x4   * MatrixY4x4
86  cycles, Multiply1x4_4x4Col_v1FPU,  MatrixX1x4   * MatrixY4x4
88  cycles, Multiply1x4_4x4Col_v3FPU,  MatrixX1x4   * MatrixY4x4
91  cycles, Multiply1x4_4x4Col_v4FPU,  MatrixX1x4   * MatrixY4x4
105  cycles, Multiply1x6_6x6Col_v3FPU,  MatrixX1x6   * MatrixY6x6
105  cycles, Multiply1x6_6x6Col_v2FPU,  MatrixX1x6   * MatrixY6x6
108  cycles, Multiply1x6_6x6Col_v1FPU,  MatrixX1x6   * MatrixY6x6
113  cycles, Multiply1x6_6x6Col_v4FPU,  MatrixX1x6   * MatrixY6x6
132  cycles, Multiply1x8_8x8Col_v2FPU,  MatrixX1x8   * MatrixY8x8
135  cycles, Multiply1x8_8x8Col_v3FPU,  MatrixX1x8   * MatrixY8x8
138  cycles, Multiply1x8_8x8Col_v4FPU,  MatrixX1x8   * MatrixY8x8
139  cycles, Multiply1x8_8x8Col_v1FPU,  MatrixX1x8   * MatrixY8x8
---------------------------------------------------------------------------
LiaoMi:
***** Time table - LoopCount =1000000 *****

AMD Ryzen 7 1700 Eight-Core Processor           (SSE4)

  8  cycles, Multiply1x4_4x4Lin_v3SSE,  MatrixX1x4   * MatrixY4x4
10  cycles, Multiply1x4_4x4Lin_v1SSE,  MatrixX1x4   * MatrixY4x4
12  cycles, Multiply1x4_4x4Lin_v2SSE,  MatrixX1x4   * MatrixY4x4

23  cycles, Multiply1x6_6x6Lin_v2SSE,  MatrixX1x6   * MatrixY6x6
25  cycles, Multiply1x6_6x6Lin_v3SSE,  MatrixX1x6   * MatrixY6x6

38  cycles, Multiply1x8_8x8Lin_v1SSE,  MatrixX1x8   * MatrixY8x8
43  cycles, Multiply1x8_8x8Lin_v2SSE,  MatrixX1x8   * MatrixY8x8

104  cycles, Multiply1x4_4x4Lin_v1FPU,  MatrixX1x4   * MatrixY4x4
109  cycles, Multiply1x4_4x4Lin_v2FPU,  MatrixX1x4   * MatrixY4x4
109  cycles, Multiply1x4_4x4Lin_v4FPU,  MatrixX1x4   * MatrixY4x4
110  cycles, Multiply1x4_4x4Lin_v3FPU,  MatrixX1x4   * MatrixY4x4

142  cycles, Multiply1x6_6x6Lin_v2FPU,  MatrixX1x6   * MatrixY6x6
144  cycles, Multiply1x6_6x6Lin_v1FPU,  MatrixX1x6   * MatrixY6x6
148  cycles, Multiply1x6_6x6Lin_v4FPU,  MatrixX1x6   * MatrixY6x6
156  cycles, Multiply1x6_6x6Lin_v3FPU,  MatrixX1x6   * MatrixY6x6

164  cycles, Multiply1x8_8x8Lin_v4FPU,  MatrixX1x8   * MatrixY8x8
167  cycles, Multiply1x8_8x8Lin_v1FPU,  MatrixX1x8   * MatrixY8x8
199  cycles, Multiply1x8_8x8Lin_v2FPU,  MatrixX1x8   * MatrixY8x8
206  cycles, Multiply1x8_8x8Lin_v3FPU,  MatrixX1x8   * MatrixY8x8

***** Time table - LoopCount =1000000 *****

AMD Ryzen 7 1700 Eight-Core Processor           (SSE4)

  4  cycles, Multiply1x4_4x4Col_v1SSE,  MatrixX1x4   * MatrixY4x4
16  cycles, Multiply1x6_6x6Col_v1SSE,  MatrixX1x6   * MatrixY6x6
19  cycles, Multiply1x8_8x8Col_v1SSE,  MatrixX1x8   * MatrixY8x8

105  cycles, Multiply1x4_4x4Col_v3FPU,  MatrixX1x4   * MatrixY4x4
107  cycles, Multiply1x4_4x4Col_v4FPU,  MatrixX1x4   * MatrixY4x4
107  cycles, Multiply1x4_4x4Col_v2FPU,  MatrixX1x4   * MatrixY4x4
112  cycles, Multiply1x4_4x4Col_v1FPU,  MatrixX1x4   * MatrixY4x4

144  cycles, Multiply1x6_6x6Col_v3FPU,  MatrixX1x6   * MatrixY6x6
144  cycles, Multiply1x6_6x6Col_v4FPU,  MatrixX1x6   * MatrixY6x6
149  cycles, Multiply1x6_6x6Col_v1FPU,  MatrixX1x6   * MatrixY6x6
151  cycles, Multiply1x6_6x6Col_v2FPU,  MatrixX1x6   * MatrixY6x6

185  cycles, Multiply1x8_8x8Col_v3FPU,  MatrixX1x8   * MatrixY8x8
192  cycles, Multiply1x8_8x8Col_v1FPU,  MatrixX1x8   * MatrixY8x8
193  cycles, Multiply1x8_8x8Col_v2FPU,  MatrixX1x8   * MatrixY8x8
195  cycles, Multiply1x8_8x8Col_v4FPU,  MatrixX1x8   * MatrixY8x8

++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Jochen:
***** Time table - LoopCount =1000000 *****

Intel(R) Core(TM) i5-2450M CPU @ 2.50GHz (SSE4)

21  cycles, Multiply1x4_4x4Lin_v3SSE,  MatrixX1x4   * MatrixY4x4
21  cycles, Multiply1x4_4x4Lin_v1SSE,  MatrixX1x4   * MatrixY4x4
25  cycles, Multiply1x4_4x4Lin_v2SSE,  MatrixX1x4   * MatrixY4x4

47  cycles, Multiply1x6_6x6Lin_v2SSE,  MatrixX1x6   * MatrixY6x6
50  cycles, Multiply1x6_6x6Lin_v3SSE,  MatrixX1x6   * MatrixY6x6

81  cycles, Multiply1x8_8x8Lin_v1SSE,  MatrixX1x8   * MatrixY8x8
85  cycles, Multiply1x8_8x8Lin_v2SSE,  MatrixX1x8   * MatrixY8x8

94  cycles, Multiply1x4_4x4Lin_v4FPU,  MatrixX1x4   * MatrixY4x4
94  cycles, Multiply1x4_4x4Lin_v1FPU,  MatrixX1x4   * MatrixY4x4
97  cycles, Multiply1x4_4x4Lin_v3FPU,  MatrixX1x4   * MatrixY4x4
98  cycles, Multiply1x4_4x4Lin_v2FPU,  MatrixX1x4   * MatrixY4x4

114  cycles, Multiply1x6_6x6Lin_v2FPU,  MatrixX1x6   * MatrixY6x6
119  cycles, Multiply1x6_6x6Lin_v4FPU,  MatrixX1x6   * MatrixY6x6
126  cycles, Multiply1x6_6x6Lin_v1FPU,  MatrixX1x6   * MatrixY6x6
126  cycles, Multiply1x6_6x6Lin_v3FPU,  MatrixX1x6   * MatrixY6x6

139  cycles, Multiply1x8_8x8Lin_v4FPU,  MatrixX1x8   * MatrixY8x8
143  cycles, Multiply1x8_8x8Lin_v1FPU,  MatrixX1x8   * MatrixY8x8
157  cycles, Multiply1x8_8x8Lin_v2FPU,  MatrixX1x8   * MatrixY8x8
158  cycles, Multiply1x8_8x8Lin_v3FPU,  MatrixX1x8   * MatrixY8x8

***** Time table - LoopCount =1000000 *****

Intel(R) Core(TM) i5-2450M CPU @ 2.50GHz (SSE4)

  8  cycles, Multiply1x4_4x4Col_v1SSE,  MatrixX1x4   * MatrixY4x4
22  cycles, Multiply1x6_6x6Col_v1SSE,  MatrixX1x6   * MatrixY6x6
33  cycles, Multiply1x8_8x8Col_v1SSE,  MatrixX1x8   * MatrixY8x8

94  cycles, Multiply1x4_4x4Col_v3FPU,  MatrixX1x4   * MatrixY4x4
94  cycles, Multiply1x4_4x4Col_v2FPU,  MatrixX1x4   * MatrixY4x4
95  cycles, Multiply1x4_4x4Col_v1FPU,  MatrixX1x4   * MatrixY4x4
101  cycles, Multiply1x4_4x4Col_v4FPU,  MatrixX1x4   * MatrixY4x4

118  cycles, Multiply1x6_6x6Col_v2FPU,  MatrixX1x6   * MatrixY6x6
124  cycles, Multiply1x6_6x6Col_v3FPU,  MatrixX1x6   * MatrixY6x6
127  cycles, Multiply1x6_6x6Col_v4FPU,  MatrixX1x6   * MatrixY6x6
129  cycles, Multiply1x6_6x6Col_v1FPU,  MatrixX1x6   * MatrixY6x6

155  cycles, Multiply1x8_8x8Col_v3FPU,  MatrixX1x8   * MatrixY8x8
155  cycles, Multiply1x8_8x8Col_v2FPU,  MatrixX1x8   * MatrixY8x8
162  cycles, Multiply1x8_8x8Col_v4FPU,  MatrixX1x8   * MatrixY8x8
162  cycles, Multiply1x8_8x8Col_v1FPU,  MatrixX1x8   * MatrixY8x8

Siekmanski

#1
August 21, 2018, 05:39:33 PM
Hi Rui,

The results,
Creative coders use backward thinking techniques as a strategy.

LiaoMi

#2
August 24, 2018, 12:08:28 AM
Hi RuiLoureiro,

AMD Ryzen 7 1700 Eight-Core Processor (SSE4)
+
Intel(R) Core(TM) i7-4810MQ CPU @ 2.80GHz (SSE4)

jj2007

#3
August 24, 2018, 12:12:38 AM
Hi Rui,
Core i5 here.
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