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*** Memory Management of Strassen Heap Based Matrix Multiplication algorithms ***
[ Abstract ]
Memory Management of Strassen Heap Based Matrix Multiplication algorithms is evaluated for matrix sizes:
8192 x 8192
16384 x 16384
32768 x 32768
65536 x 65536
Single Precision Floating point data type.
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[ Abbreviations ]
VM - Virtual Memory
PM - Physical Memory
IM - Input Matrices
HM - Heap Matrices
SM - Swaped Memory ( to VM )
TM - Total Memory TM = ( IM + HM )
MS - Memory Saved MS = ( HM - SM )
FP - Floating Point
DT - Data Type
SP - Single Precision FP DT ( float - 4 bytes )
DP - Double Precision FP DT ( double - 8 bytes )
EP - Extended Precision FP DT ( long double - 10/12 bytes )
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[ Case 1 - 8192 x 8192 ] [ Input Matrices ( IM ) ] Matrix A: 8192 x 8192 SP data type Memory used: 256MB x 1 = 256 MB Matrix B: 8192 x 8192 SP data type Memory used: 256MB x 1 = 256 MB Matrix C: 8192 x 8192 SP data type Memory used: 256MB x 1 = 256 MB Total : = 768 MB IM [ Heap Matrices ( HM ) ] A[2] : 4096 x 4096 SP data type Memory used: 64MB x 2 = 128 MB B[2] : 4096 x 4096 SP data type Memory used: 64MB x 2 = 128 MB M[7] : 4096 x 4096 SP data type Memory used: 64MB x 7 = 448 MB Total : = 704 MB HM Total Memory ( TM ): 1472 MB TM [ Swaped Memory ( SM ) ] A[2] : 4096 x 4096 SP data type Memory used: 64MB x 2 = 128 MB B[2] : 4096 x 4096 SP data type Memory used: 64MB x 2 = 128 MB Total : = 256 MB SM 704 MB HM - 256 MB SM --------- Memory Saved: 448 MB MS
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[ Case 2 - 16384 x 16384 ] [ Input Matrices ( IM ) ] Matrix A: 16384 x 16384 SP data type Memory used: 1024MB x 1 = 1024 MB Matrix B: 16384 x 16384 SP data type Memory used: 1024MB x 1 = 1024 MB Matrix C: 16384 x 16384 SP data type Memory used: 1024MB x 1 = 1024 MB Total : = 3072 MB IM [ Heap Matrices ( HM ) ] A[2] : 8192 x 8192 SP data type Memory used: 256MB x 2 = 512 MB B[2] : 8192 x 8192 SP data type Memory used: 256MB x 2 = 512 MB M[7] : 8192 x 8192 SP data type Memory used: 256MB x 7 = 1792 MB Total : = 2816 MB HM Total Memory ( TM ): 5888 MB TM [ Swaped Memory ( SM ) ] A[2] : 8192 x 8192 SP data type Memory used: 256MB x 2 = 512 MB B[2] : 8192 x 8192 SP data type Memory used: 256MB x 2 = 512 MB Total : = 1024 MB SM 2816 MB HM - 1024 MB SM --------- Memory Saved: 1792 MB MS
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[ Case 3 - 32768 x 32768 ] [ Input Matrices ( IM ) ] Matrix A: 32768 x 32768 SP data type Memory used: 4096MB x 1 = 4096 MB Matrix B: 32768 x 32768 SP data type Memory used: 4096MB x 1 = 4096 MB Matrix C: 32768 x 32768 SP data type Memory used: 4096MB x 1 = 4096 MB Total : = 12288 MB IM [ Heap Matrices ( HM ) ] A[2] : 16384 x 16384 SP data type Memory used: 1024MB x 2 = 2048 MB B[2] : 16384 x 16384 SP data type Memory used: 1024MB x 2 = 2048 MB M[7] : 16384 x 16384 SP data type Memory used: 1024MB x 7 = 7168 MB Total : = 11264 MB HM Total Memory ( TM ): 23552 MB TM [ Swaped Memory ( SM ) ] A[2] : 16384 x 16384 SP data type Memory used: 1024MB x 2 = 2048 MB B[2] : 16384 x 16384 SP data type Memory used: 1024MB x 2 = 2048 MB Total : = 4096 MB SM 11264 MB HM - 4096 MB SM --------- Memory Saved: 7168 MB MS
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[ Case 4 - 65536 x 65536 ] [ Input Matrices ( IM ) ] Matrix A: 65536 x 65536 SP data type Memory used: 16384MB x 1 = 16384 MB Matrix B: 65536 x 65536 SP data type Memory used: 16384MB x 1 = 16384 MB Matrix C: 65536 x 65536 SP data type Memory used: 16384MB x 1 = 16384 MB Total : = 49152 MB IM [ Heap Matrices ( HM ) ] A[2] : 32768 x 32768 SP data type Memory used: 4096MB x 2 = 8192 MB B[2] : 32768 x 32768 SP data type Memory used: 4096MB x 2 = 8192 MB M[7] : 32768 x 32768 SP data type Memory used: 4096MB x 7 = 28672 MB Total : = 45056 MB HM Total Memory ( TM ): 94208 MB TM [ Swaped Memory ( SM ) ] A[2] : 32768 x 32768 SP data type Memory used: 4096MB x 2 = 8192 MB B[2] : 32768 x 32768 SP data type Memory used: 4096MB x 2 = 8192 MB Total : = 16384 MB SM 45056 MB HM - 16384 MB SM --------- Memory Saved: 28672 MB MS
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