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Author Topic: Kalles Fraktaler 3.0  (Read 1280 times)
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greentexas
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« on: November 24, 2016, 02:18:39 PM »

I wonder whether there will be a Kalles Fraktaler 3.0. I haven't seen a new version released in a couple months, so maybe this is a sign of a 3.0 update. Is there a 3.0 update in the work?
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Kalles Fraktaler
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« Reply #1 on: November 24, 2016, 04:30:05 PM »

No I am sorry there is not.

Some months ago I tried to update the arbitrary precision calculations to use Lattice multiplication, which I belive both Fractal Extreme and Mandel Machine are doing, and also to use _umul128 in order to fully utilize 64-bit integers.
However since my program allows for zoom depths to e100000 I found out that the Lattice multiplication gets much slower because of the huge amount of memory needed, even though it is static stack memory. So that was a dead end.
I also recall Botond Kosa mentioning something about that as a reason why MM doesn't go deeper (than e3010 or something)

I have also tried SIMD, using parallel double calculcations, and found that it did indeed speed up things about 4 times.
However... that is only applicable to some e600, because after that other datatypes than double are used.
Mandel Machine is analyzing the values and change to smaller hardware datatypes, which can use SIMD, when values are getting "big enough".
But "big enough" is too ambigous, and MM do have unsolvable glitches, probably because the prediction of "big enough" easily fails.

So I am not able to improve KF and I have now stopped trying smiley
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Want to create DEEP Mandelbrot fractals 100 times faster than the commercial programs, for FREE? One hour or one minute? Three months or one day? Try Kalles Fraktaler http://www.chillheimer.de/kallesfraktaler
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greentexas
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« Reply #2 on: November 28, 2016, 12:49:01 AM »

It's a bit sad that you've had to put Kalles Fraktaler to bed. cry That's why your last movie was called "Final". But I know you'll still be active on Fractal Forums and Youtube, just not showcasing KF.
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PolynomialZen
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« Reply #3 on: February 10, 2017, 07:40:19 AM »

Thanks for letting us know about your decision and kudos for sharing years of efforts with the community.

Regardless ... you probably looked at things like the following when exploring SIMD but have you considered approaches like

https://hal.archives-ouvertes.fr/hal-01312858/document

or

https://github.com/lumianph/gpuprec

or others listed https://www.google.ca/search?client=safari&rls=en&q=extended+precision+gpu+programming&ie=UTF-8&oe=UTF-8&gfe_rd=cr&ei=bVudWIaTOOfo8AeU5LqYAg
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claude
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« Reply #4 on: February 10, 2017, 03:26:18 PM »

double-double / quad-double techniques like CAMPARY and qd/GQD don't scale in the end - if more than 1022-1070 bits of precision are needed (around 20 doubles) at sizes around 1.0 the least-significant limbs gradually underflow to 0.

They might still be useful at small zoom levels.

So for high precision the special routines of ARPREC or MPFR are needed, and GARPREC for GPU is not released yet.
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PolynomialZen
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« Reply #5 on: February 10, 2017, 06:48:17 PM »

Apologies for my ignorance since I have not studied the code in sufficient detail. Nevertheless, what is the range of SDs (significant digits) required in KF's program from start down to e100000? I understand KF gets by with a LOT less than 100000 SDs and uses no GPUs. The GPU acceleration attempts for the Mandelbrot sets I have seen in the last few years are not based on perturbation but use the traditional (brute force) methodology.
« Last Edit: February 10, 2017, 10:32:22 PM by PolynomialZen » Logged
claude
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« Reply #6 on: February 10, 2017, 07:13:07 PM »

When using perturbation, there still needs to be a full-precision reference orbit (more than one if you have glitch correction enabled).  The rest of the per-pixel calculations can be done with double down to 1e-308 or more (depending if series approximation skips beyond the region where more precision is needed), long double down to around 1e-4932, or double plus extended exponent range for unlimited zoom depth (or rather, zoom depth limited by the memory needed to store the high precision reference).

Full-precision means "enough precision to distinguish neighbouring pixels", which can be calculated from zoom depth and image size.

The number of decimal digits needed is around the exponent, so 308 decimal digits for the reference at the limit of double precision pixels, 4932 at long double limit.  To convert to bnary bits of precision, multiply the exponent by log210 = 3.32....    This gives 1024 and 16384 at the limits, corresponding to 11 bits signed exponent for double, and 15 bits signed exponent for long double.

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greentexas
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« Reply #7 on: March 01, 2017, 02:04:35 PM »

You made a very important point, claude. I've noticed that after around 10300, rendering seems to slow down, even with "lbdl.dll". I rendered a trivial image at e10000 that used 17,000 iterations, and it took a long time to render.
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