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Leslie Sanford wrote: floating point seems faster.
Wow! This is the power of DSPs.
If it is really true then use they! It needs only more memory, I hope this will be not problem...
Russell
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It is true - particularly with the SSE type instruction sets. For example, a 3.6GHz P4 (single core) can exceed 8GFLOPS on an FFT http://www.fftw.org/speed/Pentium4-3.60GHz-icc/[^]
scroll down to the single-precision complex 1D transforms
Peter
"Until the invention of the computer, the machine gun was the device that enabled humans to make the most mistakes in the smallest amount of time."
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IMO there is no general answer, it depends on both the job at hand and the specifics of
the CPU.
If you need to add code to prevent integers from overflowing, you should consider floats,
since unpredictable conditional branches are very bad for performance.
If your inputs and outputs are integers, using floats will cost conversion times; most modern
CPUs have different register sets for ints and floats, and can pass data between them only
through "memory" (i.e. the data cache), adding to latency, and probably taking away some
performance.
If you need transcendental functions, floats are the obvious choice.
If you have streaming data the CPU might be optimized more for one or the other.
The Intel processor line has a long tradition of favoring integers over floats when spending
the transistor budget.
If your CPU is general-purpose (as opposed to DSP) and your algorithm needs a lot of
address calculations and indexing, you should consider float data, so the integer ALUs
are available for sequencing and addressing, the float ALU(s) for data operations.
I once found the optimum implementation of an image processing algorithm by doing half
of the pixels in integers, and the other half in floats at the same time, so all integer
and float units of the CPU were kept busy as much as possible.
Luc Pattyn [Forum Guidelines] [My Articles]
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Luc Pattyn wrote: If you need to add code to prevent integers from overflowing, you should consider floats,
since unpredictable conditional branches are very bad for performance.
This is a bit off-topic, but I've been curious about how the compiler treats predictable branches. For example, say I have a function that is passed a boolean value. Within this method is a loop in which the boolean is tested:
void Function(bool condition)
{
for(int i = 0; i < 1000; i++)
{
if(condition)
{
}
else
{
}
}
}
The obvious cure for getting the branch out of the loop would be to nest the loop inside the if and else blocks; you'd wind up with two version of the loop. I've done this in some situations, but in others, it can lead to exceedingly verbose code.
So my question is that in the above situation, we have a condition that will not change for the duration of the function call, i.e. a predictable branch. Can the compiler help us out here to keep things efficient?
Luc Pattyn wrote: If your inputs and outputs are integers, using floats will cost conversion times; most modern
CPUs have different register sets for ints and floats, and can pass data between them only
through "memory" (i.e. the data cache), adding to latency, and probably taking away some
performance.
If you need transcendental functions, floats are the obvious choice.
If you have streaming data the CPU might be optimized more for one or the other.
The Intel processor line has a long tradition of favoring integers over floats when spending
the transistor budget.
If your CPU is general-purpose (as opposed to DSP) and your algorithm needs a lot of
address calculations and indexing, you should consider float data, so the integer ALUs
are available for sequencing and addressing, the float ALU(s) for data operations.
Based on this criteria, I think I'll stick with floats. I seem to have the denormal problem under control, which was my main motivation for switching. I'm working on a VST synth plugin; the input and output to and from the plugin respectively are in floats, so it probably doesn't make sense to change to integers.
Thanks again for your insightful answers.
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Hi Leslie,
you're welcome.
on the for/if issue:
when the if is the only statement inside the for loop (and the condition is invariant as
you stated), I will turn them inside out, as it makes more sense to me to have the slow
changing (or constant) thing first:
if (condition) {
for(loop_control) { stuff }
} else {
for(loop_control) { other_stuff }
}
I can't recollect having seen a compiler do that transformation for me; of course if
condition is a build-time constant, the idle half of the code is thrown out by most compilers.
Anyway I am inclined not to rely on a compiler for the big decisions, I'll be happy if
it does a good job at peephole optimizations.
If the if is not the only statement in the for loop, my decision will depend on how much code
there is to duplicate; obviously I hate to duplicate code for lots of reasons, so I will
consider that only if maximum performance is relevant.
Greetings
Luc Pattyn [Forum Guidelines] [My Articles]
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If you are not familiar with it, you should look at the Intel compiler. They also have some high performance primitives libraries available that may be of use - see the MKL[^] and IPP[^], and some good booksk on optimization:
The Software Optimization Cookbook[^]
The Software Vectorization Handbook[^]
Peter
"Until the invention of the computer, the machine gun was the device that enabled humans to make the most mistakes in the smallest amount of time."
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Leslie Sanford wrote: floating point seems faster
It will be - it's got a native, hardware implementation, whereas fixed point hasn't. In the best case (performance-wise) implementation of fixed point, additive operations should be transformed into single integer operations (unless you're checking for overflow, which'll add a whole lot more overhead, including branching). Multiplicative operations will require re-scaling of the output, which adds extra overhead as well.
I believe that modern CPUs do float operations in times comparable to the integer equivalents, so there's likely little or no performance hit from using floats.
I work with embedded control systems using relatively slow CPUs (ranging from 25MHz 680x0 to 150MHz PowerPC). We transitioned to using floating-point maths from fixed-point when we started using PowerPCs, because it performed as well (or better) than fixed point operations and also had a better range/precision trade-off than fixed-point.
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Can anyone help me work out a solution to this?
I have 15 different number, lets call these num1,num2,num3,num4 etc..
I want to be able to select the 5 largest numbers out of the 15.
There must be some methodical way to search through and compare the values to get the 5 largest.
Any ideas?
Cheers for your help.
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The easy way (not the most efficient one!): sort the entire input collection, then
throw away all but the top 5.
The less expensive way: create an output collection, initially empty.
loop over all items in your input collection; compare them to the output collection,
if fewer than 5 items, add; if not, compare; if larger than the smallest, remove smallest and
add new one, otherwise skip. For best performance keep the output collection sorted all the
time.
Luc Pattyn [Forum Guidelines] [My Articles]
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Are you sure the overhead of continually resorting the output collection is less than just sorting the main list once?
--
If you view money as inherently evil, I view it as my duty to assist in making you more virtuous.
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Actually you don't need to keep the output collection sorted, I was wrong there,
the only thing that matters is only the smallest item gets replaced, so a single compare
pass suffices, which means at most 10*5 compares.
Luc Pattyn [Forum Guidelines] [My Articles]
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If you need to output many items, you should use a heap to efficiently remove the smallest item. That way you get O(n lg m). (n = number of input items, m = number of output items)
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I agree for sufficient output size there is a tree-based optimum somewhere in the middle of
the SortedList and the ArbitraryList; unfortunately .NET does not provide such MinHeap.
Luc Pattyn [Forum Guidelines] [My Articles]
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At others replyed you can sort the array and then extraxt the maxs, this in 2 step. But the faster way depends probally on the length of your data array and on the number of extractions: in your case this numbers are 15 and 5, I think that you can fastly sort the array, so then it is probally a good idea to do this. But in the case of 100 and 3 probally you can find a faster way without sort the array and find directly the greather 3 numbers.
So, I want only to tell you a different way to solve this:
1) find the min value (minV)
2) find the max value and its index (maxV1, idxV1) then save it somewhere
3) replace maxV1 with minV in the original array
4) find the max value, so: maxV2 and idxV2, then store maxV2 somewhere and replace it with minV in the array
5) do this again and again...5 times
Probally this way can be faster on longer array (like 100) because in this way you have to read data from the array less times then to sort it
Russell
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I need some help programming my own magic square in matlab without using the magic function my input should look something like this : [a b]=my_magic(5,10,4,3) and the out put of a should look like a 5x5 matrix with ten starting at row 4 column 3 and b should spit out the sum
Thank You
Rami
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Here you can find the algorithms.
There are 3 different way according to the order of the square: magic square of odd order, magic square of even order and magic square of 4x order.
http://en.wikipedia.org/wiki/Magic_square[^]
Russell
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FRACTAL FORMULAS
Hey folks!
I am hoping to experiment with some simple fractal formulas in VB. I have some running ok, but some
I seem to be having trouble with. I am using VB 4.0, and am hoping someone out there in cybertopia
might be able to share insights or code snippets? I don't need anything fancy like complex graphic
rendering of the fractals, although if you are excited about this stuff and feel ambitious I'm happy to
check out any graphic stuff you might want to share.
Simply, all I'm looking for is simple number in and number out routines, i.e. you stick a number(s)
into the formula, set the iteration ceiling and then watch what ever numbers get pumped out, thats it really.
So we might have say two text boxes for inputs,
textbox1 = any number value, i.e. 129
textbox2 = any number value, i.e. 234
Then we feed those values into the fractals formula loop and for every interation the newly generated
values get dumped to some other textbox.
=================
Barry Martin - Hopalong
This one is probably one of the most interesting ones, it seems Barry Martin released a really old dos version called hopalong
and there are various exe takes on this floating about, but most of them don't work anymore because they are so old.
I had trouble with this one because I don't really understand the "sign" function, and the VB 4 sign function doesn't seem
to work in a way thats compatible with the formula, but then I'm just as likely ignorant of how to properly apply it.
2 plots resemble organic structures like cells
xnew=y-sqrt (abs(b*x-c))sign(x)
ynew = a-x
different values for constants a,b,c give different patterns and periodicities
========
For the Lorentz function, I'd like to get a really simple rudimentary one working, but I'm also curious about what would happen
if we had two parallel Lorentz functions working together, one accepting outputs from the other and then feeding back into the first one,
i.e.
Lorentz function (1) outputs cycle iteration values to Lorentz (2)
And then Lorentz(2) inputs to Lorent(1) and so on.....
By the way, does anyone know if a single Lorentz function can operate on more than the default # of inputs
Lorentz Function
xnew = x+d*a*(y-x)
ynew = y+d*(x*(c-2)-y)
znew = z+d*(x*y-b*z)
where a,b,c,d are contants, i.e. values of 10,8/3,28,0.003
========
I tried coding this one also, but instead of getting a rich set of chaotic values all I got were two values
that repeated exactly the same over and over again????
Mandlebrot
z ; iterate via ; z^2 + c
==========
For this one I tried implementing this but for some reason, when I coded this to VB, it only generated
the same values over and over again.... no chaotically generated values......
(folds and remaps oval onto itself
)
Michael Henons;
Germaine to stellar orbits
xnew = y + 1 - 1.4 * x^2
ynew = 0.3 * x
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cyndy_northrup wrote: I tried coding this one also, but instead of getting a rich set of chaotic values all I got were two values
that repeated exactly the same over and over again????
cyndy_northrup wrote: For this one I tried implementing this but for some reason, when I coded this to VB, it only generated
the same values over and over again.... no chaotically generated values......
Your problem seems to be a problem to update the old values with the new ones found:
cyndy_northrup wrote: xnew = y + 1 - 1.4 * x^2
ynew = 0.3 * x
are you updating x and y?
'step 1:
xnew = y + 1 - 1.4 * x^2
ynew = 0.3 * x
'store xnew,ynew somewhere
x=xnew;
y=ynew;
'goto step 1
Russell
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yes!
unfortunatelty, i cant seem to get vb to do this properly it just repeats the same numbers?
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ok, but it could be acceptable that the numbers repeats itself, it is only a sequence.
If you want to draw the images related to the fractals I'm thinking than you are not on the right way:
take the mandelbrot formula z(n+1)=z(n)^2+c
you do not have to prepare the sequence of z to draw the image, you have to study its convergence!
Fixing c, start from z=0 then you have to see if z(n) will escapes to infinity. You have to do this for many values of c (complex).
The image is only the real and imag part of c and the color is the first value of n that gives |z(n)|>2.
All this is true if my memory is well working
Russell
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I don't know what your problem is, and I am not going to cover all those fractals.
Mandelbrot needs complex numbers (z = z*z + c needs a complex z and a complex c);
and the Mandelbrot set requires you iterate this formula with some constant c, a
variable initial value z0 of z (that's the point on the drawing), and then you calculate
how many iterations it takes to satisfy abs(z)>=2 to determine the "height" or color
of point z0.
There are several articles on Mandelbrot here on CodeProject; maybe on the others too.
The basic info probably is available on Wikipedia, if not just Google.
BTW: fractals make most sense when you plot them, just showing some numbers is
hiding their beauty for sure.
Luc Pattyn [Forum Guidelines] [My Articles]
this weeks tips:
- make Visual display line numbers: Tools/Options/TextEditor/...
- show exceptions with ToString() to see all information
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i have a 16 bit variable(unsigned short).
now i want a best algorithm (function) which will do the following.
1.if contiguous bits at LSB are high then the function should return 1.
for example, consider the following bit patterns
0000000001111111
or
0000111111111111
or
0000000000000001
2.if continuous bits at MSB are high then the function should return 2.
for example,
1110000000000000 and so on.
3.other wise it should return 0 for the examoples such as
1010000000000011
0000011101010011 and so on
thanks in advance.
any more clarifications required, please get back.
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Test the int with this constant variables if you want to not use a for loop with SHIFTs and bit-comparing.
To return 1:
1111111111111110
1111111111111100
1111111111111000
...
1100000000000000
1000000000000000
to return 2:
0000000000000001
0000000000000011
...
0111111111111111
else return 0
Russell
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There might be some nifty bit processing, but this should work with no more than about 6 comparisons (32 bits - 62 options)
8-bit version:
int fn(int x)
{
switch (x)
case 0x01:
case 0x03:
case 0x07:
case 0x0F:
case 0x1F:
case 0x3F:
case 0x7F:
return 1;
case 0x80:
case 0xC0:
case 0xE0:
case 0xF0:
case 0xF8:
case 0xFC:
case 0xFE:
return 1;
default:
return 0;
}
I think compilers are quite good at optimizing this sort of code, but I have never tested it so I'd be interested in comments.
Peter
"Until the invention of the computer, the machine gun was the device that enabled humans to make the most mistakes in the smallest amount of time."
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