hkramski
GitHub
commit
2a7ff83875
10 changed files with 939 additions and 3 deletions
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@ -13,7 +13,7 @@ Der Chaostreff Ludwigsburg ist ein lockeres Zusammentreffen von Hackern, die sic
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#### Wann und Wo trefft ihr euch?
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Der nächste RL-Termin steht auf Grund von Covid-19 noch nicht fest. Aktuell trifft man uns auf https://matrix.complb.de
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(#chaostreff:matrix.complb.de) und jeden Mittwoch per Jitsi (https://complb.de/covid1920200315/)
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(#chaostreff:matrix.complb.de) und zwei Mal im Monat bei Jitsi (https://complb.de/stammtisch20200506/)
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Du erreichst uns außerdem per Mail über chaostreff AT complb PUNKt de
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259
post/CCC_Why_what_is_SIMD.md
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259
post/CCC_Why_what_is_SIMD.md
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# ARMv7-l SIMD and using NEON
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## Motivation for SIMD
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<img src="pics/Adaline.jpg">
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[(WikiCommons:Adaline)](https://commons.wikimedia.org/wiki/File:Adaline.jpg)
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$\hat{y} = f(W\times \hat{x}+B)$
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For a time series:
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$X = \left[\hat{x_0},\hat{x_1},\dots,\hat{x_n}\right]$
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We get:
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$Y = f(W\times X+B)$
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### That is what Thensorflow, numpy and lots of others are good about ...
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## Matrix Mutlipication
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Eor each element in the resulting matrix a scalar product of a specific column of the matrix W and a specifc row of matrix X is required.
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<img src="pics/mxm.png">
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Now that takes a while:
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Simple approach in C
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~~~
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for (c = 0; c < m; c++) {
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for (d = 0; d < q; d++) {
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for (k = 0; k < p; k++) {
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sum = sum + first[c][k]*second[k][d];
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}
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multiply[c][d] = sum;
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sum = 0;
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}
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}
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~~~
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That requires for matrixs (100,100) x (100,1000) 100*100*1000 = 10 MFLOPS. What can be done to optimize the speed?
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## Techniques to optimize the calculation
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### Only splitting the Matrix
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Two reasons:
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1. optimize cache usage (**not today**)
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2. using **SIMD power**
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<img src="pics/matrix.png">
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# SIMD (single instruction multiple data)
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### Just a few words to Inlining Assembler in C (or C++)
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Assembler [examples see](https://www.ibiblio.org/gferg/ldp/GCC-Inline-Assembly-HOWTO.html)
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The most simple one, works on x86:
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~~~
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#include <stdio.h>
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int main(void)
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{
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int foo = 10, bar = 15;
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asm volatile ("addl %%ebx,%%eax"
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:"=a"(foo)
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:"a"(foo), "b"(bar));
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printf("foo+bar=%d\n", foo);
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return 0;
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}
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~~~
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From the gcc manual
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~~~
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asm asm-qualifiers ( AssemblerTemplate
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: OutputOperands
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[ : InputOperands
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[ : Clobbers ] ])
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~~~
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## My sources
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All points are from the link above The
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[NEON TM Version: 1.0 Programmer’s Guide](https://static.docs.arm.com/den0018/a/DEN0018A_neon_programmers_guide_en.pdf)
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- general idea behind SIMD (not talking about MIMD)
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- ARM NEON comparision with others (1.2 - pp 1-4)
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- the instruction timing is not clear - depends as all calculations mainly on data fetching time.
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- Fundamentals of NEON technology (1.4 - pp 1-10)
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- 1.4.1 Registers q, d, s
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- 1.4.2 Datatypes
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### What is it
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With a single instruction a vector (or other structurs) can be calculated in parallel.
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One assembler instruction multi/adds vectors of 4x4:
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<img src="pics/matrix-simd.png">
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Each of the 9 patches requires 4 x 4 = 16 SIMD instruction (compared to 4 x 4 x 4 = 64 ops ) fmla.f32. (multipy/Add)
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## Remark about this document
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This study is only for a better understanding of the SIMD instructions and SIMD performance of
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the ARMV7-A core (actually this one is a CORTEX-A53, but the OS supports only the 32 bit
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alternative.)
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## Documents and Sources
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[ARM ® and Thumb ® -2 Instruction Set](http://infocenter.arm.com/help/topic/com.arm.doc.qrc0001m/QRC0001_UAL.pdf)
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[ARM Architecture Reference Manual ARMv7-A and ARMv7-R](https://static.docs.arm.com/ddi0406/c/DDI0406C_C_arm_architecture_reference_manual.pdf)
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The
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[NEON TM Version: 1.0 Programmer’s Guide](https://static.docs.arm.com/den0018/a/DEN0018A_neon_programmers_guide_en.pdf) provides all the information required to realy do SIMD on ARMV7-A and R.
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The document explains the register structure of the single, double and 128 bit registers as well as the instructions.
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Besides other examples (Swapping color channel, FIR,
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cross product),
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there is also an example for matrix matrix multiplication.
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The example examined here is based on this document and the 4 x 4 matrix multiplication given (chapter 7.1, pp. 115.)
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## About the example: my_sgemm
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The matrix matrix multiplication calculates patches of 4 x 4 at one time the rest of the
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calculation is straight forward.
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~~~
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for (i ...)
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for (j ...)
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for (k ...)
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~~~
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the inner loop calls the optimized 4 x 4 multiplication.
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## Shape of the matrixes
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All matrixes in C are column-based. matrix_a is regular and matrix_b is transposed. (Therefore, all scalar products
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of columns [B] with rows of [A] are column $\times$ column multipilications.)
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The calculation is performing
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$C = A \times B^\mathsf{T} + C$
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Assuming the matrix A contains n rows and m columns, then
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the element A[i,j] has in the c-array representing the matrix the index i * m + j.
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If we want to extract a patch out of the matrix:
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A[k:k+4,l:l+4], the for rows of the matrix could be calculated by,
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- first row starts at k*m+l
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- the next row starts with some offset o = m-4.
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- same for the thrid and forth rows.
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## The assembler SIMD part for the 4 x 4 multiplication
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Purpose of the 4x4 matrix multiplication: It multiplies of a small 4 x 4 patch of some large
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colom-based matrixes, important to know: matrix_a is regular,
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matrix_b is transposed.
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~~~
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static inline void my_sgemm_4x4(float *matrix_a, float *matrix_b,
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float *output,
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int off_a, int off_b, int off_o ) {
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/** \code */
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asm volatile (
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"# Start manual code \n\t"
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"# Matrix Multiplication \n\n\t"
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~~~
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Macro section
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This macro performs the actual multiplication. It provides the output row for one column of matrix_a and the matrix_b (q8 - q11). The rows are stored in col0 and col1 (which corresponts to two 128 bit registers), the colums are stored in
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q8-q11. res_q gives the resulting output row.
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~~~
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".macro mul_col_f32 res_q, col0_d, col1_d\n\t"
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"vmla.f32 \\res_q, q8, \\col0_d[0]\n\t"
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"vmla.f32 \\res_q, q9, \\col0_d[1]\n\t"
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"vmla.f32 \\res_q, q10, \\col1_d[0]\n\t"
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"vmla.f32 \\res_q, q11, \\col1_d[1]\n\t"
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".endm\n\n\t"
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~~~
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End macro section
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Start loading the 128 registers with 4 single floats. q12-q15 are first loaded
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with the current state of the output.
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After each register is loaded some
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offset has to be added, since the next row starts with some offset. The same
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mechanismus applies to all matrixes.
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load current state of output -> q12 - q15 */
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~~~
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"vld1.32 {q12}, [%6]!\n\t"
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"add %6, %6, %5\n\t" /* add some offset until start of next row */
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"vld1.32 {q13}, [%6]!\n\t"
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"add %6, %6, %5\n\t"
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"vld1.32 {q14}, [%6]!\n\t"
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"add %6, %6, %5\n\t"
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"vld1.32 {q15}, [%6]!\n\t"
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~~~
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load matrix_b (transposed!) -> q8 - q11 */
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~~~
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"vld1.32 {q8}, [%2]!\n\t"
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"add %2, %2, %4\n\t"
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"vld1.32 {q9}, [%2]!\n\t"
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"add %2, %2, %4\n\t"
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"vld1.32 {q10}, [%2]!\n\t"
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"add %2, %2, %4\n\t"
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"vld1.32 {q11}, [%2]!\n\t"
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~~~
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load matrix_a -> q0 - q3
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~~~
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"vld1.32 {q0}, [%1]!\n\t"
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"add %1, %1, %3\n\t"
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"vld1.32 {q1}, [%1]!\n\t"
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"add %1,%1, %3\n\t"
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"vld1.32 {q2}, [%1]!\n\t"
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"add %1, %1, %3\n\t"
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"vld1.32 {q3}, [%1]!\n\t"
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~~~
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End load registers
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Start doing the actual matrix multiplication as defined in macro
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~~~
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"mul_col_f32 q12, d0, d1\n\t"
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"mul_col_f32 q13, d2, d3\n\t"
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"mul_col_f32 q14, d4, d5\n\t"
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"mul_col_f32 q15, d6, d7\n\n\t"
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~~~
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store the result [q12 - 115] into output
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~~~
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"vst1.32 {q12}, [%0]!\n\t"
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"add %0, %0, %5\n\t"
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"vst1.32 {q13}, [%0]!\n\t"
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"add %0, %0, %5\n\t"
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"vst1.32 {q14}, [%0]!\n\t"
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"add %0, %0, %5\n\t"
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"vst1.32 {q15}, [%0]!\n\t"
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~~~
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start argument section of inline assembler
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~~~
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:"+r"((long) output)
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:"r"(&matrix_a[0]),"r"(&matrix_b[0]),"r"(off_a),"r"(off_b),
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"r"(off_o),"r"(&output[0]));
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/** \endcode */
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return;
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}
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~~~
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BIN
post/CompLB-Kramski-Home-Recording-20200519_v01.2.pdf
Normal file
BIN
post/CompLB-Kramski-Home-Recording-20200519_v01.2.pdf
Normal file
Binary file not shown.
BIN
post/Logo_Chaostreff_LB.zip
Normal file
BIN
post/Logo_Chaostreff_LB.zip
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Binary file not shown.
8
post/logo.md
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8
post/logo.md
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@ -0,0 +1,8 @@
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---
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date: "2020-05-02"
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tages: ["chaostreff", "logo", "misc"]
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title: "Logo-Paket Chaostreff LB"
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---
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Das Logo-Zip gibt es hier [Download](https://complb.de/logo/Logo_Chaostreff_LB.zip)
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300
post/matrix_matrix.c
Normal file
300
post/matrix_matrix.c
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@ -0,0 +1,300 @@
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#include <stdio.h>
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#include <string.h>
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#include <math.h>
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#include <sys/time.h>
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/**
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* gcc -o mm -g -march=armv7 -mfpu=neon-vfpv4 matrix_matrix.c
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* or cross compile
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* arm-linux-gnueabihf-gcc -o mm -g -march=armv7 -mfpu=neon-vfpv4 matrix_matrix.c
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*
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* test with a = np.arange(4*n*m + 4m).reshape(4*n,4*m)
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* a.dot(a.T)
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*
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* this file contains all the elements to show ARM7VL usage of
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* SIMD architecture
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*
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*/
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void simple_transpose( float *, int, int, float *);
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static inline void my_sgemm_4x4(float *, float *, float *,
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int, int, int );
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/**
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* help routine (only for documentation demonstration
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*
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* transpose some matrix matrix_a (size n_rows, n_cols)
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* to matrix output
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*
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*/
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void simple_transpose( float *matrix_a, int n_rows_a, int n_cols_a,
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float *output ) {
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for (int ra = 0; ra < n_rows_a; ra++)
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for (int ca = 0; ca < n_cols_a; ca++ )
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output[n_rows_a*ca+ra] = matrix_a[n_cols_a*ra+ca];
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//output[ra][ca] = matrix_a[ca][ra];
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return;
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}
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/**
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* Kernal function including the optimization and the
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* 4 x 4 multiplication of 4 x4 fragments of large column based
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* matrixes matrix_a and matrix_b
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*
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* arguments:
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* - (float *) matrix_a: square matrix of size 4 x 4,
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* - (float *) matrix_b: square matrix of size 4 x 4,
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* - (float *) output: 4 x 4 result (return value)
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* - (int) off_a,b,o: offset between to elements last element of one row
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* and 1 element of next row matrix_a, matrix_b and output
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*
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* details documented here 
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*/
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static inline void my_sgemm_4x4(float *matrix_a, float *matrix_b,
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float *output,
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int off_a, int off_b, int off_o ) {
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/** \code */
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asm volatile (
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"# Start manual code \n\t"
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"# Matrix Multiplication \n\n\t"
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/* Maco section */
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".macro mul_col_f32 res_q, col0_d, col1_d\n\t"
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"vmla.f32 \\res_q, q8, \\col0_d[0]\n\t"
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"vmla.f32 \\res_q, q9, \\col0_d[1]\n\t"
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"vmla.f32 \\res_q, q10, \\col1_d[0]\n\t"
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"vmla.f32 \\res_q, q11, \\col1_d[1]\n\t"
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".endm\n\n\t"
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/* end macro section */
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/* load current state of output -> q12 - q15 */
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"vld1.32 {q12}, [%6]!\n\t"
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"add %6, %6, %5\n\t" /* add some offset until start of next row */
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"vld1.32 {q13}, [%6]!\n\t"
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"add %6, %6, %5\n\t"
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"vld1.32 {q14}, [%6]!\n\t"
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"add %6, %6, %5\n\t"
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"vld1.32 {q15}, [%6]!\n\t"
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/* load matrix_b (transposed!) -> q8 - q11 */
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"vld1.32 {q8}, [%2]!\n\t"
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"add %2, %2, %4\n\t"
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"vld1.32 {q9}, [%2]!\n\t"
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"add %2, %2, %4\n\t"
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"vld1.32 {q10}, [%2]!\n\t"
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"add %2, %2, %4\n\t"
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"vld1.32 {q11}, [%2]!\n\t"
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/* load matrix_a -> q0 - q3 */
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"vld1.32 {q0}, [%1]!\n\t"
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"add %1, %1, %3\n\t"
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"vld1.32 {q1}, [%1]!\n\t"
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"add %1,%1, %3\n\t"
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"vld1.32 {q2}, [%1]!\n\t"
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"add %1, %1, %3\n\t"
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"vld1.32 {q3}, [%1]!\n\t"
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/* end load registers
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* start doing the actual matrix multiplication as defined in macro */
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"mul_col_f32 q12, d0, d1\n\t"
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"mul_col_f32 q13, d2, d3\n\t"
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"mul_col_f32 q14, d4, d5\n\t"
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"mul_col_f32 q15, d6, d7\n\n\t"
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/* store the result [q12 - 115] into output */
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"vst1.32 {q12}, [%0]!\n\t"
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"add %0, %0, %5\n\t"
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"vst1.32 {q13}, [%0]!\n\t"
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"add %0, %0, %5\n\t"
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"vst1.32 {q14}, [%0]!\n\t"
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"add %0, %0, %5\n\t"
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"vst1.32 {q15}, [%0]!\n\t"
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/* start argument section of inline assembler */
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:"+r"((long) output)
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:"r"(&matrix_a[0]),"r"(&matrix_b[0]),"r"(off_a),"r"(off_b),
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"r"(off_o),"r"(&output[0]));
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/** \endcode */
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return;
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}
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/**
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* matrix matrix multiplication of some matrix_a and some matrix_b
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* (works only for size 4*n x 4*m)
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* the order is column based and output = a x b.transpose()
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*
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* the multiplication based on patch-wise standard multiplication algorithm
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* each patch of size 4 x 4
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*/
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void my_sgemm(float *matrix_a, int n_rows_a, int n_cols_a,
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float *matrix_b, int n_rows_b, int n_cols_b,
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float *output ) {
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int offset_a = 4*(n_cols_a-4);
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int offset_b = 4*(n_cols_b-4);
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for(int i=0;i<n_rows_a;i = i+4 ) {
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||||
for(int j=0;j<n_cols_b;j = j+4 ) {
|
||||
for(int k=0;k<n_cols_a;k = k+4 ) {
|
||||
my_sgemm_4x4(&matrix_a[n_cols_a*i+k],
|
||||
&matrix_b[n_cols_b*k+j],
|
||||
&output[n_cols_b*i+j],
|
||||
offset_a, offset_b, offset_b);
|
||||
}
|
||||
}
|
||||
}
|
||||
return;
|
||||
}
|
||||
|
||||
/**
|
||||
* standard algorithm for matrix matrix multiplication
|
||||
* output = matrix_a.dot(matrix_bb.transpose())
|
||||
* - arguments:
|
||||
* - (float *) a: column-based matrix size n_colums_a x n_rows_b
|
||||
* - (int) n_rows_a, n_cols_a: size of matrix a
|
||||
* - (float *) b: column-based matrix size n_colums_a x n_rows_b
|
||||
* - (int) n_rows_b, n_cols_b: size of matrix b
|
||||
* - (float *) output: column-based matrix = a.dot(b.T)
|
||||
* - return: void
|
||||
*/
|
||||
|
||||
void simple_mm( float *a, int n_rows_a, int n_cols_a,
|
||||
float *b, int n_rows_b, int n_cols_b,
|
||||
float *output ) {
|
||||
for(int i=0;i<n_rows_a;i++)
|
||||
for(int j=0;j<n_cols_b;j++) {
|
||||
output[n_cols_b*i+j]=0;
|
||||
for(int k=0;k<n_cols_a;k++) {
|
||||
output[n_cols_b*i+j]+=a[n_cols_a*i+k]*b[n_cols_b*k+j];
|
||||
}
|
||||
}
|
||||
return;
|
||||
}
|
||||
|
||||
/**
|
||||
* int main():
|
||||
* calls simple and optimized function and compare speed
|
||||
* size defined by macros (N_ROWS_x, N_COLS_B: 4 * n, 4 * m)
|
||||
* Matrix defined as:
|
||||
* matrix_a = np.arange(N_ROWS_A*N_COLS_B).reshape(N_ROWS_A,N_COLS_A)
|
||||
* matrix_b = a.T
|
||||
* 1. call optimized my_sgemm
|
||||
* 2. call simple_mm
|
||||
* compare times, check identity
|
||||
* print results
|
||||
* size of example matrix
|
||||
*/
|
||||
|
||||
#define N_COLS_A 256
|
||||
#define N_ROWS_A 256
|
||||
#define N_COLS_B N_ROWS_A
|
||||
#define N_ROWS_B N_COLS_A
|
||||
|
||||
int main() {
|
||||
float matrix_a[N_ROWS_A][N_COLS_A];
|
||||
float matrix_b[N_ROWS_B][N_COLS_B];
|
||||
float matrix_aa[N_ROWS_A][N_COLS_A];
|
||||
float matrix_bb[N_ROWS_B][N_COLS_B];
|
||||
float buffer[N_ROWS_A][N_COLS_B];
|
||||
float reference[N_ROWS_A][N_COLS_B];
|
||||
struct timeval t1, t2, t3;
|
||||
long int durationf, durations;
|
||||
|
||||
/**
|
||||
* matrix_a = np.arange(N_ROWS_A*N_COLS_B).reshape(N_ROWS_A,N_COLS_A)
|
||||
*/
|
||||
|
||||
for (int ra = 0; ra < N_ROWS_A; ra++) {
|
||||
for (int ca = 0; ca < N_COLS_A; ca++) {
|
||||
matrix_a[ra][ca] = N_COLS_A*ra+ca;
|
||||
matrix_aa[ra][ca] = N_COLS_A*ra+ca;
|
||||
}
|
||||
}
|
||||
|
||||
/**
|
||||
* calculate matrix_b as matrix_a.T
|
||||
*
|
||||
*/
|
||||
|
||||
simple_transpose(&matrix_a[0][0], N_ROWS_A, N_COLS_A,
|
||||
&matrix_b[0][0]);
|
||||
|
||||
simple_transpose(&matrix_aa[0][0], N_ROWS_A, N_COLS_A,
|
||||
&matrix_bb[0][0]);
|
||||
|
||||
/**
|
||||
* set outputs buffer (outpot of my_sgemm) and referece (simple_mm)
|
||||
* to zero
|
||||
*/
|
||||
|
||||
for (int ra = 0; ra < N_ROWS_A; ra++)
|
||||
for (int cb = 0; cb < N_COLS_B; cb++) {
|
||||
buffer[ra][cb] = 0.0;
|
||||
reference[ra][cb] = 0.0;
|
||||
}
|
||||
|
||||
/**
|
||||
* 1. set timer to t1 (start of optimized algorithm)
|
||||
* 2. call optimized algorithm
|
||||
*/
|
||||
|
||||
gettimeofday(&t1, NULL);
|
||||
|
||||
my_sgemm(&matrix_aa[0][0], N_ROWS_A, N_COLS_A,
|
||||
&matrix_bb[0][0], N_ROWS_B, N_COLS_B,
|
||||
&buffer[0][0]);
|
||||
|
||||
/**
|
||||
* 3. set timer to t2 (end of optimized and start of simple algorithm)
|
||||
* 4. call optimized algorithm
|
||||
*/
|
||||
|
||||
gettimeofday(&t2, NULL);
|
||||
|
||||
simple_mm(&matrix_a[0][0], N_ROWS_A, N_COLS_A,
|
||||
&matrix_b[0][0], N_ROWS_B, N_COLS_B,
|
||||
&reference[0][0]);
|
||||
|
||||
/**
|
||||
* 3. set timer to t3 (end of simple algorithm)
|
||||
*/
|
||||
|
||||
gettimeofday(&t3, NULL);
|
||||
|
||||
/**
|
||||
* calculate durations for optimized and simple algorithm
|
||||
*/
|
||||
|
||||
durationf = 1e6*(t2.tv_sec - t1.tv_sec)+(t2.tv_usec - t1.tv_usec);
|
||||
durations = 1e6*(t3.tv_sec - t2.tv_sec)+(t3.tv_usec - t2.tv_usec);
|
||||
|
||||
/**
|
||||
* output (6 x 6 patch of result (both algorithm)
|
||||
*/
|
||||
|
||||
printf("my_sgemm\n");
|
||||
for (int ra=0; ra<6; ra++ ) {
|
||||
for (int cb=0; cb<6; cb++ ) printf("%.2e ", buffer[ra][cb]);
|
||||
printf("\n");
|
||||
}
|
||||
printf("reference\n");
|
||||
for (int ra=0; ra<6; ra++ ) {
|
||||
for (int cb=0; cb<6; cb++ ) printf("%.2e ", reference[ra][cb]);
|
||||
printf("\n");
|
||||
}
|
||||
|
||||
/**
|
||||
* calculate mean sqare error
|
||||
*/
|
||||
|
||||
float mse = 0.0F;
|
||||
for (int ra=0; ra<N_ROWS_A; ra++ ) {
|
||||
for (int cb=0; cb<N_COLS_B; cb++ ) {
|
||||
mse += (reference[ra][cb]-buffer[ra][cb]) *
|
||||
(reference[ra][cb]-buffer[ra][cb]);
|
||||
}
|
||||
}
|
||||
|
||||
/**
|
||||
* print mse and ration of times optimized_time / simple_time
|
||||
*/
|
||||
|
||||
printf("MSE: %.5f [durationrate f/s %.5f]\n",mse,
|
||||
(float)durationf/(float)durations);
|
||||
return 0;
|
||||
}
|
||||
318
post/motivation_matrix_mult.ipynb
Normal file
318
post/motivation_matrix_mult.ipynb
Normal file
|
|
@ -0,0 +1,318 @@
|
|||
{
|
||||
"cells": [
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"# Motivation\n",
|
||||
"## How to solve matrix-matrix multiplication"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 1,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"import numpy as np\n",
|
||||
"import pandas as pd"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"Simple approach in C\n",
|
||||
"\n",
|
||||
"~~~\n",
|
||||
" for (c = 0; c < m; c++) {\n",
|
||||
" for (d = 0; d < q; d++) {\n",
|
||||
" for (k = 0; k < p; k++) {\n",
|
||||
" sum = sum + first[c][k]*second[k][d];\n",
|
||||
" }\n",
|
||||
" \n",
|
||||
" multiply[c][d] = sum;\n",
|
||||
" sum = 0;\n",
|
||||
" }\n",
|
||||
" }\n",
|
||||
"~~~"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 2,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"def mymatrixmult(A,B):\n",
|
||||
" y = np.zeros((A.shape[0], B.shape[1]))\n",
|
||||
" for i in range(A.shape[0]):\n",
|
||||
" for j in range(B.shape[1]):\n",
|
||||
" for k in range(A.shape[0]):\n",
|
||||
" y[i][j] += A[i][k]*B[k][j]\n",
|
||||
" return y\n",
|
||||
" \n",
|
||||
"m = np.arange(40000).reshape(200,200)\n",
|
||||
"m1 = m/np.average(m)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"### Takes a while (200**3) = 8 MFLOPS"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 3,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"array([[6.61708085e-03, 1.65675784e-02, 2.65180759e-02, ...,\n",
|
||||
" 1.96686509e+00, 1.97681559e+00, 1.98676609e+00],\n",
|
||||
" [1.65675784e-02, 4.65190759e-02, 7.64705735e-02, ...,\n",
|
||||
" 5.91701260e+00, 5.94696409e+00, 5.97691559e+00],\n",
|
||||
" [2.65180759e-02, 7.64705735e-02, 1.26423071e-01, ...,\n",
|
||||
" 9.86716010e+00, 9.91711260e+00, 9.96706510e+00],\n",
|
||||
" ...,\n",
|
||||
" [1.96686509e+00, 5.91701260e+00, 9.86716010e+00, ...,\n",
|
||||
" 7.80145924e+02, 7.84096071e+02, 7.88046219e+02],\n",
|
||||
" [1.97681559e+00, 5.94696409e+00, 9.91711260e+00, ...,\n",
|
||||
" 7.84096071e+02, 7.88066220e+02, 7.92036368e+02],\n",
|
||||
" [1.98676609e+00, 5.97691559e+00, 9.96706510e+00, ...,\n",
|
||||
" 7.88046219e+02, 7.92036368e+02, 7.96026518e+02]])"
|
||||
]
|
||||
},
|
||||
"execution_count": 3,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"mymatrixmult(m1, m1.T)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 4,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"array([[6.61708085e-03, 1.65675784e-02, 2.65180759e-02, ...,\n",
|
||||
" 1.96686509e+00, 1.97681559e+00, 1.98676609e+00],\n",
|
||||
" [1.65675784e-02, 4.65190759e-02, 7.64705735e-02, ...,\n",
|
||||
" 5.91701260e+00, 5.94696409e+00, 5.97691559e+00],\n",
|
||||
" [2.65180759e-02, 7.64705735e-02, 1.26423071e-01, ...,\n",
|
||||
" 9.86716010e+00, 9.91711260e+00, 9.96706510e+00],\n",
|
||||
" ...,\n",
|
||||
" [1.96686509e+00, 5.91701260e+00, 9.86716010e+00, ...,\n",
|
||||
" 7.80145924e+02, 7.84096071e+02, 7.88046219e+02],\n",
|
||||
" [1.97681559e+00, 5.94696409e+00, 9.91711260e+00, ...,\n",
|
||||
" 7.84096071e+02, 7.88066220e+02, 7.92036368e+02],\n",
|
||||
" [1.98676609e+00, 5.97691559e+00, 9.96706510e+00, ...,\n",
|
||||
" 7.88046219e+02, 7.92036368e+02, 7.96026518e+02]])"
|
||||
]
|
||||
},
|
||||
"execution_count": 4,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"m1.dot(m1.T)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"### Now numpy: (2000**3) = 8 GFLOPS"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 5,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"M = np.arange(4000000).reshape(2000,2000) \n",
|
||||
"M1 = M/np.average(M) "
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 7,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"array([[6.66167083e-04, 1.66566758e-03, 2.66516808e-03, ...,\n",
|
||||
" 1.99666867e+00, 1.99766817e+00, 1.99866767e+00],\n",
|
||||
" [1.66566758e-03, 4.66516908e-03, 7.66467058e-03, ...,\n",
|
||||
" 5.99167016e+00, 5.99466966e+00, 5.99766917e+00],\n",
|
||||
" [2.66516808e-03, 7.66467058e-03, 1.26641731e-02, ...,\n",
|
||||
" 9.98667166e+00, 9.99167116e+00, 9.99667067e+00],\n",
|
||||
" ...,\n",
|
||||
" [1.99666867e+00, 5.99167016e+00, 9.98667166e+00, ...,\n",
|
||||
" 7.98001466e+03, 7.98400966e+03, 7.98800466e+03],\n",
|
||||
" [1.99766817e+00, 5.99466966e+00, 9.99167116e+00, ...,\n",
|
||||
" 7.98400966e+03, 7.98800666e+03, 7.99200366e+03],\n",
|
||||
" [1.99866767e+00, 5.99766917e+00, 9.99667067e+00, ...,\n",
|
||||
" 7.98800466e+03, 7.99200366e+03, 7.99600267e+03]])"
|
||||
]
|
||||
},
|
||||
"execution_count": 7,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"M1.dot(M1.T)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 15,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"array([[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11],\n",
|
||||
" [ 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23],\n",
|
||||
" [ 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35],\n",
|
||||
" [ 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47],\n",
|
||||
" [ 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59],\n",
|
||||
" [ 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71],\n",
|
||||
" [ 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83],\n",
|
||||
" [ 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95],\n",
|
||||
" [ 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107],\n",
|
||||
" [108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119],\n",
|
||||
" [120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131],\n",
|
||||
" [132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143]])"
|
||||
]
|
||||
},
|
||||
"execution_count": 15,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"n = 12\n",
|
||||
"np.arange(n*n).reshape(n,n)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"## Splitting the matrix\n",
|
||||
"\n",
|
||||
"Two reasons:\n",
|
||||
"1. optimize cache usage\n",
|
||||
"2. using SIMD power\n",
|
||||
"\n",
|
||||
"<img src=\"pics/matrix.png\">"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"## ?\n",
|
||||
"\n",
|
||||
"No idea, about the following: $y = tanh(M)$"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 8,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"y = np.tanh(M1.dot(M1.T))"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 24,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"(1000, 1000)"
|
||||
]
|
||||
},
|
||||
"execution_count": 24,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"y.shape"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 51,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"16.0"
|
||||
]
|
||||
},
|
||||
"execution_count": 51,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"((4*128)**3)*16/((128)**3*64)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"# das wichtig"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": []
|
||||
}
|
||||
],
|
||||
"metadata": {
|
||||
"kernelspec": {
|
||||
"display_name": "Python 3",
|
||||
"language": "python",
|
||||
"name": "python3"
|
||||
},
|
||||
"language_info": {
|
||||
"codemirror_mode": {
|
||||
"name": "ipython",
|
||||
"version": 3
|
||||
},
|
||||
"file_extension": ".py",
|
||||
"mimetype": "text/x-python",
|
||||
"name": "python",
|
||||
"nbconvert_exporter": "python",
|
||||
"pygments_lexer": "ipython3",
|
||||
"version": "3.6.9"
|
||||
}
|
||||
},
|
||||
"nbformat": 4,
|
||||
"nbformat_minor": 4
|
||||
}
|
||||
27
post/stammtisch20200506.md
Normal file
27
post/stammtisch20200506.md
Normal file
|
|
@ -0,0 +1,27 @@
|
|||
---
|
||||
date: "2020-05-06"
|
||||
tages: ["chaostreff", "veranstaltung", "protokoll"]
|
||||
title: "Kurzprotokoll 06.05.2020"
|
||||
---
|
||||
|
||||
|
||||
Chaostreff-relevante Punkte:
|
||||
|
||||
1. Der Chaostreff findet nun regelmäßig an folgenden Terminen statt:
|
||||
1. 1. Mittwoch im Monat, ab 19:42, Ort: Jitsi
|
||||
2. 3. Dienstag im Monat, ab 19:42, Ort: Jitsi
|
||||
|
||||
Jitsi-Link: https://meet.jit.si/chaoslb
|
||||
|
||||
|
||||
Einige Themen mit und ohne Links:
|
||||
|
||||
1. Es gab einen spannenden Vortrag von fritzthekit/eduard zu SIMD und sauschnellen Matrixberechnungen auf einem
|
||||
Raspberry Pi. Links zum [Jupyter-Notebook](motivation_matrix_mult.ipynb), [C-Code](matrix_matrix.c) und zur [Präsentation als Markdown](CCC_Why_what_is_SIMD.md)
|
||||
2. Go für kleine Plätze [TinyGo](https://tinygo.org/)
|
||||
3. Zooms Datenschutzbeurteilungen waren ein Thema (die jetzt doch irgendwie halb DSGVO-konform sind)
|
||||
4. Iridium Browser [Link](https://iridiumbrowser.de/)
|
||||
5. ...
|
||||
|
||||
|
||||
Nächster Stammtisch ist am 19.05.2020 mit einem Vortrag von Harvey.
|
||||
24
post/stammtisch20200519.md
Normal file
24
post/stammtisch20200519.md
Normal file
|
|
@ -0,0 +1,24 @@
|
|||
---
|
||||
date: "2020-05-19"
|
||||
tages: ["chaostreff", "veranstaltung"]
|
||||
title: "Kurzprotokoll 19.05.2020"
|
||||
---
|
||||
|
||||
Chaostreff-relevante Punkte:
|
||||
1. Ein gemeinsamer Abend mit dem CCCS wäre auch mal nett. Wir gehen in die Terminfindung.
|
||||
2. Wohin kann das Repo der Chaostreff-Website migriert werden? In der Diskussion sind die Gitea-Instanz vom CCCS und Codeberg.
|
||||
|
||||
Einige Themen mit und ohne Links:
|
||||
1. Der Vortrag von Harvey war mit 10 Menschen gut besucht und - wie immer - sehr informativ und unterhaltsam [Folien](CompLB-Kramski-Home-Recording-20200519_v01.2.pdf)
|
||||
2. GoTo-Meeting wird von Datenschützern als Videokonferenzsystem verwendet: [Link](https://www.gotomeeting.com/de-de)
|
||||
3. Gitea als Git-Webfrontend: [Link](https://gitea.io/en-us/)
|
||||
4. Codeberg als Github-Alternative: [Link](https://codeberg.org/)
|
||||
5. gotop als schicke top/htop-Alternative - wird nicht mehr gepflegt, es gibt aber ein Fork und eine Fortführung in Rust: [Link](https://github.com/cjbassi/gotop)
|
||||
6. Online-Abstimmung bei den Grünen: Mit welcher Technik realisieren Parteien, z.B. die Grünen, Online-Abstimmungen?
|
||||
7. Multigeiger: [Link](https://github.com/ecocurious2/MultiGeiger)
|
||||
8. ...
|
||||
|
||||
|
||||
Der nächste Chaostreff findet am 03.06.2020 statt.
|
||||
|
||||
Bleibt gesund und hackt Sachen!
|
||||
4
vas.md
4
vas.md
|
|
@ -12,5 +12,5 @@ ansehen.
|
|||
1. 01.04.2020 - Harvey/Heinz: _Shell-Health-Check_ oder _Wie ich (wieder) lernte, die Shell zu lieben_ [Folien](https://complb.de/stammtisch20200401/CompLB-Kramski-Shell-Check-20200325_v02.pdf)
|
||||
2. 22.04.2020 - ampoff/Steffen: _Die National Software Reference Library_ [Folien](https://complb.de/stammtisch20200422/nsrl_short.pdf)
|
||||
3. 06.05.2020 - fritzthekit - _SIMD und neuronale Netze_
|
||||
4. 20.05.2020 - Harvey/Heinz: _Mit Spielfilm-Mitschnitten gegen den Stream schwimmen_
|
||||
5. t.b.a. - ampoff/Steffen: _Ansible und AWX_ oder _einenSchmissigenTitelFinden_
|
||||
4. 19.05.2020 - Harvey/Heinz: _Mit Spielfilm-Mitschnitten gegen den Stream schwimmen_ [Folien](https://complb.de/stammtisch2020519/CompLB-Kramski-Home-Recording-20200519_v01.2.pdf)
|
||||
5. 16.06.2020 - ampoff/Steffen: _Ansible und AWX_ oder _Langweilige Tasks automatisieren, mehr Zeit für alles andere_
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue