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Final release - unsure what else I can optimize anymore :-)
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| Original file line number | Diff line number | Diff line change |
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| WHAT IS THIS? | ||
| ============= | ||
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| This is a real-time Mandelbrot fractal zoomer. | ||
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| COMPILE/INSTALL/RUN | ||
| =================== | ||
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| Windows | ||
| ------- | ||
| Windows users can download and run a pre-compiled Windows binary | ||
| [here](https://github.com/ttsiodras/MandelbrotSSE/releases/download/2.2/mandelSSE-win32-2.2.zip). | ||
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| After decompressing, you can simply execute either one of the two .bat | ||
| files. The 'autopilot' one zooms in a specific location, while the other | ||
| one allows you to zoom interactively using your mouse (left-click zooms in, | ||
| right-click zooms out). | ||
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| For Linux/BSD/OSX users | ||
| ----------------------- | ||
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| Make sure you have libSDL installed - then... | ||
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| $ ./configure | ||
| $ make | ||
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| You can then simply... | ||
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| $ src/mandelSSE -h | ||
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| Usage: ./src/mandelSSE [-a] [-s|-x] [-h] [WIDTH HEIGHT] | ||
| Where: | ||
| -h Show this help message | ||
| -a Run in autopilot mode (default: mouse mode) | ||
| -s Use SSE and OpenMP | ||
| -x Use XaoS algorithm (default) | ||
| If WIDTH and HEIGHT are not provided, they default to: 800 600 | ||
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| $ src/mandelSSE -a 1024 768 | ||
| (Runs in autopilot in 1024x768 window, using XaoS) | ||
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| $ src/mandelSSE -s 1024 768 | ||
| (Runs in mouse-driven SSE mode, in a 1024x768 window) | ||
| (left-click zooms-in, right-click zooms out) | ||
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| $ src/mandelSSE -x 1024 768 | ||
| (same as before, but in XaoS mode - much faster, esp during deep zooms) | ||
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| WHAT IS THIS, AGAIN? | ||
| ==================== | ||
|
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||
| When I got my hands on an SSE enabled processor (an Athlon-XP, back in 2002), | ||
| I wanted to try out SSE programming... And over the better part of a weekend, | ||
| I created a simple implementation of a Mandelbrot zoomer in SSE assembly. | ||
| I was glad to see that my code was almost 3 times faster than pure C. | ||
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||
| But that was just the beginning. | ||
| Over the last two decades, I kept coming back to this, enhancing it. | ||
|
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| - I learned how to use the GNU autotools, and made it work on most Intel | ||
| platforms: checked with Linux, Windows (MinGW) and OpenBSD. | ||
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| - After getting acquainted with OpenMP, in Nov 2009 I added OpenMP #pragmas | ||
| to run both the C and the SSE code in all cores/CPUs. The SSE code had to | ||
| be moved from a separate assembly file into inlined code - but the effort | ||
| was worth it. The resulting frame rate - on a tiny Atom 330 running Arch | ||
| Linux - sped up from 58 to 160 frames per second. | ||
|
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||
| - I then coded it in CUDA - a 75$ GPU card gave almost two orders of | ||
| magnitude of speedup! | ||
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| - Then in May 2011, I made the code switch automatically from single precision | ||
| floating point to double precision - when one zooms "deep enough". | ||
|
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| - Around 2012 I added a significant optimization: avoiding fully calculating | ||
| the Mandelbrot lake areas (black color) by drawing at 1/16 resolution and | ||
| skipping black areas in full res... | ||
|
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||
| - I learned enough VHDL in 2018 to [code the algorithm inside a Spartan3 | ||
| FPGA](https://www.youtube.com/watch?v=yFIbjiOWYFY). That was quite a | ||
| [learning exercise](https://github.com/ttsiodras/MandelbrotInVHDL). | ||
|
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||
| - In September 2020 I [ported a fixed-point arithmetic]( | ||
| https://github.com/ttsiodras/Blue_Pill_Mandelbrot/) version of the | ||
| algorithm [inside a 1.4$ microcontroller]( | ||
| https://www.youtube.com/watch?v=5875JOnFDLg). | ||
|
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||
| - And finally (?), in October 2020, I implemented what I understood to be | ||
| the XaoS algorithm - that is, re-using pixels from the previous frame | ||
| to optimally update the next one. Especially in deep-dives and large | ||
| windows, this delivers amazing speedups. | ||
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| CODERS ONLY | ||
| =========== | ||
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| SSE code | ||
| -------- | ||
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| This is the main loop (brace yourselves): | ||
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| ; x' = x^2 - y^2 + a | ||
| ; y' = 2xy + b | ||
| ; | ||
| mov ecx, 0 | ||
| movaps xmm5, [fours] ; 4. 4. 4. 4. ; xmm5 | ||
| movaps xmm6, [re] ; a0 a1 a2 a3 ; xmm6 | ||
| movaps xmm7, [im] ; b0 b1 b2 b3 ; xmm7 | ||
| xorps xmm0, xmm0 ; 0. 0. 0. 0. | ||
| xorps xmm1, xmm1 ; 0. 0. 0. 0. | ||
| xorps xmm3, xmm3 ; 0. 0. 0. 0. ; xmm3 | ||
| loop1: | ||
| movaps xmm2, xmm0 ; x0 x1 x2 x3 ; xmm2 | ||
| mulps xmm2, xmm1 ; x0*y0 x1*y1 x2*y2 x3*y3 ; xmm2 | ||
| mulps xmm0, xmm0 ; x0^2 x1^2 x2^2 x3^2 ; xmm0 | ||
| mulps xmm1, xmm1 ; y0^2 y1^2 y2^2 y3^2 ; xmm1 | ||
| movaps xmm4, xmm0 | ||
| addps xmm4, xmm1 ; x0^2+y0^2 x1... ; xmm4 | ||
| subps xmm0, xmm1 ; x0^2-y0^2 x1... ; xmm0 | ||
| addps xmm0, xmm6 ; x0' x1' x2' x3' ; xmm0 | ||
| movaps xmm1, xmm2 ; x0*y0 x1*y1 x2*y2 x3*y3 ; xmm1 | ||
| addps xmm1, xmm1 ; 2x0*y0 2x1*y1 2x2*y2 2x3*y3 ; xmm1 | ||
| addps xmm1, xmm7 ; y0' y1' y2' y3' ; xmm1 | ||
| cmpltps xmm4, xmm5 ; <4 <4 <4 <4 ? ; xmm2 | ||
| movaps xmm2, xmm4 | ||
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| ; at this point, xmm2 has all 1s in the non-overflowed pixels | ||
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| movmskps eax, xmm4 ; (lower 4 bits reflect comparisons) | ||
| andps xmm4, [ones] ; so, prepare to increase the non-over | ||
| addps xmm3, xmm4 ; by updating the 4 bailout counters | ||
| or eax, eax ; have all 4 pixels overflowed ? | ||
| jz short nomore ; yes, we're done | ||
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| inc ecx | ||
| cmp ecx, 119 | ||
| jnz short loop1 | ||
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| XaoS | ||
| ---- | ||
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| The idea behind the XaoS algorithm is simple: don't redraw the pixels; | ||
| instead re-use as many as you can from the previous frame. | ||
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| The devil, as ever, is in the details. | ||
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| The way I implemented this is as follows: the topmost scaline goes | ||
| from X coordinate `xld` to `xru` - in `xstep` steps (see code | ||
| for details). I store these computed coordinates in array `xcoord`; | ||
| and in the next frame, I compare the new coordinates with the old | ||
| ones. For each pixel, I basically find the closest X coordinate match. | ||
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| I do the same for the Y coordinates. In both cases, we are talking | ||
| about a 1-dimensional array, of MAXX or MAXY length. | ||
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| After I have the matches, I sort them - based on distance to the | ||
| coordinates of the previous frame. The `mandel` function then forces | ||
| a redraw for the worst N columns/rows - where N comes as a percentage | ||
| parameter in the function call. Simply put, if the pixel's | ||
| X and Y coordinates fall on "slots" that are close enough to the | ||
| old frame's `xcoord` and `ycoord`, the pixel color is taken | ||
| from the previous frame without doing the expensive Mandelbrot | ||
| calculation. | ||
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| This works perfectly - the zoom becomes nice and smooth, and is | ||
| also improved with a full Mandelbrot render the moment the user | ||
| stops zoooming. | ||
|
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| The code has a lot of comments explaining the inner-workings in detail. | ||
| Have a look! | ||
|
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| Cross compiling for Windows via MinGW | ||
| ------------------------------------- | ||
| After decompressing the SDL 1.2.15 tarball, install MinGW: | ||
|
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| $ sudo apt install gcc-mingw-w64 | ||
|
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| Then compile libSDL: | ||
|
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| $ cd SDL-1.2.15 | ||
| $ ./configure --host=x86_64-w64-mingw32 --disable-dga \ | ||
| --disable-video-dga --disable-video-x11-dgamouse \ | ||
| --disable-video-x11 --disable-x11-shared \ | ||
| --prefix=/usr/local/packages/SDL-1.2.15-win32 | ||
| $ make | ||
| $ sudo make install | ||
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| Finally, come back to this source folder, and compile the XaoS | ||
| version: | ||
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| $ ./configure --host=x86_64-w64-mingw32 \ | ||
| --disable-sse --disable-sse2 --disable-ssse3 \ | ||
| --with-sdl-prefix=/usr/local/packages/SDL-1.2.15-win32 \ | ||
| --disable-sdltest | ||
| $ make | ||
| $ cp src/mandelSSE.exe \ | ||
| /usr/local/packages/SDL-1.2.15-win32/bin/SDL.dll \ | ||
| /some/path/for/Windows/ | ||
|
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| This will suffice for "-x" (XaoS) execution; if you want SSE/OpenMP, | ||
| turn the --disable above into --enable... and remember to copy the | ||
| libgomp DLL, too. | ||
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| MISC | ||
| ==== | ||
| Since it reports frame rate at the end, you can use this as a benchmark | ||
| for SSE instructions - it puts the SSE registers under quite a load. | ||
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| I've also coded a | ||
| [CUDA version](https://www.thanassis.space/mandelcuda-1.0.tar.bz2), | ||
| which you can play with, if you have an NVIDIA card. | ||
| Some details about it, in the blog post I wrote back in 2009 about | ||
| it [here](https://www.thanassis.space/mandelSSE.html). |
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