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https://github.com/ttsiodras/mandelbrotsse
Real-time Mandelbrot zoom via SSE, AVX, OpenMP, CUDA, XaoS...
https://github.com/ttsiodras/mandelbrotsse
avx cuda openmp sse
Last synced: 4 days ago
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Real-time Mandelbrot zoom via SSE, AVX, OpenMP, CUDA, XaoS...
- Host: GitHub
- URL: https://github.com/ttsiodras/mandelbrotsse
- Owner: ttsiodras
- License: gpl-2.0
- Created: 2020-11-01T23:06:28.000Z (about 4 years ago)
- Default Branch: master
- Last Pushed: 2023-06-13T20:05:27.000Z (over 1 year ago)
- Last Synced: 2023-06-14T01:06:47.706Z (over 1 year ago)
- Topics: avx, cuda, openmp, sse
- Language: C++
- Homepage:
- Size: 479 KB
- Stars: 79
- Watchers: 3
- Forks: 3
- Open Issues: 1
-
Metadata Files:
- Readme: README
- Changelog: ChangeLog
- License: COPYING
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README
WHAT IS THIS?
=============
This is a real-time Mandelbrot fractal zoomer.
COMPILE/INSTALL/RUN
===================
Windows
-------
Windows users can download and run a pre-compiled Windows binary
[here](https://github.com/ttsiodras/MandelbrotSSE/releases/download/2.11/mandelSSE-win32-2.11.zip).
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/hold zooms in,
right-click/hold zooms out).
For those of you that want to build from source code, there are
cross-compilation instructions later in this document.
For Linux/BSD/OSX users
-----------------------
Make sure you have libSDL2 installed. In Debian and its derivatives,
like Ubuntu, just `sudo apt install libsdl2-dev`.
Then, build the code - with...
$ ./configure
$ make
Usage
-----
You can then try these:
$ src/mandelSSE
(Runs in autopilot mode, in a 1024x768 window)
$ src/mandelSSE -m 1280 720
(Runs in mouse-driven mode, in a 1280x720 window)
(left-click/hold zooms-in, right-click/hold zooms out)
Option `-h` gives you additional information about how to control
the Mandelbrot zoomer:
$ ./src/mandelSSE -h
Usage: ./src/mandelSSE [-a|-m] [-h] [-b] [-v|-s|-d] [-i iter] [-p pct] [-f rate] [WIDTH HEIGHT]
Where:
-h Show this help message
-m Run in mouse-driven mode
-a Run in autopilot mode (default)
-b Run in benchmark mode (implies autopilot)
-v Force use of AVX
-s Force use of SSE
-d Force use of non-AVX, non-SSE code
-i iter The maximum number of iterations of the Mandelbrot loop (default: 2048)
-p pct The percentage of pixels computed per frame (default: 0.75)
(the rest are copied from the previous frame)
-f fps Enforce upper bound of frames per second (default: 60)
(use 0 to run at full possible speed)
If WIDTH and HEIGHT are not provided, they default to: 1024 768
For ultimate rendering speed, you can disable the frame limiter (option `-f`).
By default, you are limited to 60fps:
$ src/mandelSSE -m -f 0 1280 720
The benchmarking mode (-b) does this automatically.
If you want to benchmark your CPU only (and not display anything)
tell SDL you don't care about displaying the fractal:
$ SDL_VIDEODRIVER=dummy src/mandelSSE -b 512 384
Be mindful of your CPU's thermal throttling if you are benchmarking :-)
Note that you can force AVX (-v), SSE (-s) or dumb floating point (-d)
to see the speed impact made by our usage of special Intel instructions.
You can also control:
- the percentage of pixels actually computed per frame, with option `-p`.
If you e.g. pass `-p 0.5`, then 100-0.5 = 99.5% of the pixels will be
copied from the previous frame, and only 0.5% will be actually derived
through the Mandelbrot computations. Amazingly, this is enough for
a decent quality fly-through zoom in the fractal.
By default, this is set to 0.75.
- the number of Mandelbrot iterations (option `-i`). By default this is
set to 2048 to allow for decent zoom levels, but if you want to see
insane speeds, set this to something low, like 128; and disable the
frame limiter; i.e. use `-f 0 -i 128`.
WHAT IS THIS, AGAIN?
====================
Long story.
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.
But that was just the beginning.
Over the last two decades, I kept coming back to this, enhancing it.
- I learned how to use the GNU autotools, and made it work on most Intel
platforms: checked with Linux, Windows (MinGW) and OpenBSD.
A decade later, I also tested it on Raspbian and Armbian; it works
fine in ARM machines as well. Autotools also allow me to cross-compile
for Windows (more on that below).
- 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.
- I then coded it in CUDA - a 75$ GPU card gave me almost two orders of
magnitude of speedup!
- Then in May 2011, I made the code switch automatically from single precision
floating point to double precision - when one zooms "deep enough".
- 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 the full resolution render.
- 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 experience](https://github.com/ttsiodras/MandelbrotInVHDL).
- 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).
- 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 delivered
amazing speedups; between 2 and 3 orders of magnitude.
- In July 2022, I optimised further with AVX instructions (+80% speed
in CoreLoopDouble). I also ported the code to libSDL2, which stopped
video tearing.
FOR CODERS ONLY
===============
My SSE code
-----------
This used to be my main loop, right after I ported to SSE back in 2002:
; 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
; at this point, xmm2 has all 1s in the non-overflowed pixels
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
inc ecx
cmp ecx, ITERATIONS
jnz short loop1
The new AVX code (inside CoreLoopDoubleAVX) follows the same motif;
except that it also includes periodicity checking, and uses the YMM
registers.
The comments should help you follow what's happening... Basically,
we compute 4 pixels at a time.
XaoS
----
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.
The devil, as ever, is in the details.
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.
I do the same for the Y coordinates. In both cases, we are talking
about a 1-dimensional array, of MAXX or MAXY length.
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.
This works perfectly - the zoom becomes nice and smooth, and is
also improved with a full Mandelbrot render the moment the user
stops zoooming.
The code has a lot of comments explaining the inner-workings in detail.
Have a look!
Cross compiling for Windows via MinGW
-------------------------------------
After decompressing the SDL 2.0.22 tarball, install MinGW:
$ sudo apt install gcc-mingw-w64
Then download the source code of libSDL and compile it as follows:
$ cd SDL-2.0.22
$ ./configure --host=x86_64-w64-mingw32 \
--disable-video-x11 --disable-x11-shared \
--prefix=/usr/local/packages/SDL-2.0.22-win32
$ make
$ sudo make install
Finally, come back to this source folder, and configure it like this:
$ ./configure --host=x86_64-w64-mingw32 \
--with-sdl-prefix=/usr/local/packages/SDL-2.0.22-win32 \
--disable-sdltest
$ make
$ cp src/mandelSSE.exe \
/usr/local/packages/SDL-2.0.22-win32/bin/SDL2.dll \
/some/path/for/Windows/
You can also get the "ingredients" (DLLs for SDL2, OpenMP, libstd++, etc)
from the packaged release
[here](https://github.com/ttsiodras/MandelbrotSSE/releases/download/2.11/mandelSSE-win32-2.11.zip).
MISC
====
Since it reports frame rate at the end (option `-b`), you can use this as
a benchmark for AVX instructions - it puts the AVX registers under quite a load.
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).