task8
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ex3/ex3_results.txt
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ex3/ex3_results.txt
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-------------- Task 1 --------------
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-------------------------------------------------------------
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STREAM version $Revision: 5.10 $
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-------------------------------------------------------------
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This system uses 8 bytes per array element.
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-------------------------------------------------------------
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Array size = 80000000 (elements), Offset = 0 (elements)
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Memory per array = 610.4 MiB (= 0.6 GiB).
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Total memory required = 1831.1 MiB (= 1.8 GiB).
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Each kernel will be executed 20 times.
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The *best* time for each kernel (excluding the first iteration)
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will be used to compute the reported bandwidth.
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-------------------------------------------------------------
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Your clock granularity/precision appears to be 1 microseconds.
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Each test below will take on the order of 116886 microseconds.
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(= 116886 clock ticks)
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Increase the size of the arrays if this shows that
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you are not getting at least 20 clock ticks per test.
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-------------------------------------------------------------
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WARNING -- The above is only a rough guideline.
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For best results, please be sure you know the
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precision of your system timer.
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-------------------------------------------------------------
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Function Best Rate MB/s Avg time Min time Max time
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Copy: 29569.4 0.048585 0.043288 0.059164
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Scale: 17644.0 0.082248 0.072546 0.102548
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Add: 21030.1 0.100620 0.091298 0.124700
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Triad: 21230.7 0.100758 0.090435 0.120631
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-------------------------------------------------------------
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Solution Validates: avg error less than 1.000000e-13 on all three arrays
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-------------------------------------------------------------
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./flops.exe
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FLOPS C Program (Double Precision), V2.0 18 Dec 1992
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Module Error RunTime MFLOPS
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(usec)
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1 4.0146e-13 0.0024 5827.9076
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2 -1.4166e-13 0.0007 10037.8942
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3 4.7184e-14 0.0039 4371.9185
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4 -1.2557e-13 0.0034 4355.5711
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5 -1.3800e-13 0.0066 4415.6439
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6 3.2380e-13 0.0065 4441.6299
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7 -8.4583e-11 0.0053 2277.1707
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8 3.4867e-13 0.0069 4367.6094
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Iterations = 512000000
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NullTime (usec) = 0.0000
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MFLOPS(1) = 7050.6178
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MFLOPS(2) = 3461.6233
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MFLOPS(3) = 4175.0442
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MFLOPS(4) = 4389.7311
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-------------- Task 2 --------------
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Memory needed (double 64-bit, 8 bytes):
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(A) (2N + 1) * 8 bytes
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(B) (M*N + M + N) * 8 bytes
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(C) (M*L + L*N + M*N) * 8 bytes
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(D) (N + N + p) * 8 bytes
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Floating point operations:
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(A) 2N
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(B) M * 2N
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(C) M * 2L * N
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(D) 2 * N * p (Horner Schema)
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Read/Write operations:
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(A) Read: 2N Write: 1
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(B) Read: M*2N Write: M*N
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(C) Read: M*2L*N Write: M*L*N
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(D) Read: 2*N*p Write: N*P
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-------------- Task 3 --------------
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Functions implemented in task_3.cpp
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-------------- Task 4 --------------
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----- Benchmark (A) -----
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Memory allocated : 0.745 GByte
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Duration per loop : 0.036 sec
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GFLOPS : 2.579
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GiByte/s : 20.630
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-------------------------
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----- Benchmark (B) -----
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Memory allocated : 0.715 GByte
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Duration per loop : 0.105 sec
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GFLOPS : 1.704
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GiByte/s : 6.818
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-------------------------
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----- Benchmark (C) -----
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Memory allocated : 0.026 GByte
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Duration per loop : 0.459 sec
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GFLOPS : 4.062
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GiByte/s : 0.057
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-------------------------
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----- Benchmark (D) -----
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Memory allocated : 0.015 GByte
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Duration per loop : 0.310 sec
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GFLOPS : 1.201
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GiByte/s : 0.048
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-------------------------
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-------------- Task 5 --------------
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----- Benchmark norm -----
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||x|| = 897124.301552
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Memory allocated : 0.373 GByte
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Duration per loop : 0.022 sec
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GFLOPS : 4.222
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GiByte/s : 16.890
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-------------------------
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What do you observe? Why?
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-> Faster per loop than scalar product, only loads elements of 1 vector, instead of 2.
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-------------- Task 6 --------------
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Benchmarks using cBLAS
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----- Benchmark (A) -----
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Memory allocated : 0.745 GByte
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Duration per loop : 0.023 sec
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GFLOPS : 4.006
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GiByte/s : 32.052
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-------------------------
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----- Benchmark (B) -----
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Memory allocated : 0.715 GByte
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Duration per loop : 0.026 sec
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GFLOPS : 7.010
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GiByte/s : 28.045
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-------------------------
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----- Benchmark (C) -----
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Memory allocated : 0.026 GByte
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Duration per loop : 0.020 sec
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GFLOPS : 91.320
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GiByte/s : 1.278
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-------------------------
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-------------- Task 7 --------------
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A =
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4.000000 1.000000 0.250000 0.111111 0.062500
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1.000000 4.000000 1.000000 0.250000 0.111111
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0.250000 1.000000 4.000000 1.000000 0.250000
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0.111111 0.250000 1.000000 4.000000 1.000000
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0.062500 0.111111 0.250000 1.000000 4.000000
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b =
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0.000000 1.000000
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0.000000 1.000000
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0.000000 1.000000
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0.000000 1.000000
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0.000000 1.000000
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L + U =
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4.000000 1.000000 0.250000 0.111111 0.062500
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0.250000 3.750000 0.937500 0.222222 0.095486
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0.062500 0.250000 3.750000 0.937500 0.222222
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0.027778 0.059259 0.250000 3.749370 0.937050
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0.015625 0.025463 0.059259 0.249922 3.749234
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x =
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0.000000 0.196259
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0.000000 0.148391
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0.000000 0.151272
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0.000000 0.148391
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0.000000 0.196259
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Check solution:
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A * x =
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0.000000 1.000000
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0.000000 1.000000
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0.000000 1.000000
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0.000000 1.000000
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0.000000 1.000000
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N = | 1 | 2 | 4 | 8 | 16 | 32
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---------|--------|--------|--------|--------|--------|-------
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Nrhs = 2 | 0.0047 | 0.0045 | 0.0046 | 0.0130 | 0.0203 | 0.0476
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Nrhs = 4 | 0.0027 | 0.0031 | 0.0033 | 0.0046 | 0.0085 | 0.0250
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Nrhs = 8 | 0.0035 | 0.0035 | 0.0045 | 0.0061 | 0.0119 | 0.0300
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Nrhs = 16 | 0.0085 | 0.0062 | 0.0221 | 0.0113 | 0.0599 | 0.0757
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Nrhs = 32 | 0.0122 | 0.0165 | 0.0112 | 0.0123 | 0.0238 | 0.0834
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Nrhs = 64 | 0.0072 | 0.0078 | 0.0164 | 0.0133 | 0.0421 | 0.0666
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Nrhs = 128 | 0.0073 | 0.0189 | 0.0269 | 0.0199 | 0.0337 | 0.1041
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Nrhs = 256 | 0.0107 | 0.0135 | 0.0279 | 0.0351 | 0.0582 | 0.1438
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Nrhs = 512 | 0.0276 | 0.0174 | 0.0237 | 0.1027 | 0.1113 | 0.2417
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For fixed n, the solution time per rhs does not slow down consistently and scales very well.
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Its faster than expected.
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-------------- Task 8 --------------
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There are 1 processes running.
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Intervalls: 100 x 100
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Start Jacobi solver for 10201 d.o.f.s
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aver. Jacobi rate : 0.997922 (1000 iter)
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final error: 0.124971 (rel) 0.000194029 (abs)
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JacobiSolve: timing in sec. : 0.079399
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ASCI file square_100.txt opened
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17361 2 34320 3
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Start Jacobi solver for 17361 d.o.f.s
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aver. Jacobi rate : 0.998401 (1000 iter)
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final error: 0.201744 (rel) 0.000265133 (abs)
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JacobiSolve: timing in sec. : 0.18853
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