SuperPi on GPU, were going CUDA

[Lestat]

While using "the SuperPi" algorithm [Gauss-Legendre http://en.wikipedia.org/wiki/Gauss-Legendre_algorithm] it is absolutely multi-threadable. Other algorithms probably too.
The reason is simple: there are only about 10 matematical operations each loop - the rest is computing it with custom-written methematical operations using very high precision [eg. adding 30MB to compute a result of simple addition ].

I've done it a little while ago, looks like this: [FORTRAN77, oldschool , but original SuperPi was also written in FORTRAN ]

program pi_calc
:banana::banana::banana::banana::banana::banana:implicit none
      integer i
      real*8 a(1:21),b(1:21),t(1:21),p(1:21)
      real*8 pi      
      a(1)=1
      b(1)=1/sqrt(2.0)
      t(1)=0.25
      p(1)=1

      do i=1,20,1
      :banana::banana:a(i+1)=(a(i)+b(i))/2
        b(i+1)=sqrt(a(i)*(b(i)))
        t(i+1)=t(i)-p(i)*(a(i)-a(i+1))**2
        p(i+1)=2*p(i)
        pi=(a(i)+b(i))**2/(4*t(i))
        write(*,*)i,pi
      enddo

      stop
      end

"do ____ enddo" - loop of course, the main algorithm
"**" - power
output:
1 2.91421352106
2 3.14057922577
3 3.14159262165
4 3.14159262902
5 3.14159262902
6 3.14159262902
.............................................

That program without custom-written mathematical formulas only calculates ~15 digits and in fact not all digits are correct, the accuracy is not so great . But with that formulas it is a "classic SuperPi" - 1M with 19 iterations etc .
As we can see the idea is really simple, only ~10 mathematical operations per loop.
The thing is to implement mathematical operations which can handle veeeery accurate precision [30M of digits or as we like].

So there is:
addition [add bits with carry, simple and multithreadable with some error margin [if carry will happen too many times ], division by 2 [simple binary "shift left"] - very fast in fact, not worth optimizing;
square root - I don't know the algorithm, but this is probably the slowest in that program - if it really is slowest hmm... I dunno if this is easy multithreadable
multiplication - probably faster than sqrt but non-comparable slower than addidtion for sure - the simple algorithm is as we all know to multiplicate in row and add - it will be very time-eating [30MB * 30MB means ~10^12 operations, I dunno if it is coded that way, probably there is faster algorithm, because 10^12 cycles in 1 second means a terahertz] - this is absolutely multithreadable [perfect scaling I can say]. IIRC 32-bit CPU can multiply 32-bit * 32-bit in 6 cycles which will be more real, but still somehow slow. No, wait - there must be faster algorithm [or it is not the most time-eating], because with doubling the accuracy we are slowing the calculations a little more than twice. Or maybe there is some trick to increase number of digits with each loop, but I don't think so [every loop takes +- the same amount of time].
division - also not that simple to write with threads ["not that simple" means "I don't know how to do it" ]

So the main problems: write a multi-threaded sqrt and division [power is not that demanding as it is only ^2 which in fact means multiplication].

Sorry if that was too long and I bored You , but I personally find it interesting to know what it is all about [especially when we are benching it hours and hours, and all we can see are those 19-24 loops, nothing more .
Well, we all can now at least understand what means "not convergent in sqr" - we know what sqrt it is and why it should be convergent .

i have no idea what you just said dude but i just got an ice cream headache from trying to understand that

Last time I checked it had to be an NVIDIA card or the drivers will not load.

I didn't say you can't run CUDA with just one card -- I said you can't run a CUDA task that lasts longer than 5 seconds on a primary display or it will get aborted by the OS (Windows XP, don't know about Vista but probably the same applies).

As for the formula, best known PI algorithm is Chudnovsky at the moment as used in PiFast43.

hell vista does the "the display driver has stopped and has been restarted" all on its own,, you dont need CUDA to make Vista screw up your display adapter!!