All FFT's need double precision

Article: PhysX87: Software Deficiency
By: Vincent Diepeveen (diep.delete@this.xs4all.nl), July 19, 2010 2:02 pm
Room: Moderated Discussions
David Kanter (dkanter@realworldtech.com) on 7/19/10 wrote:
---------------------------

All FFT's need double precision or integer transforms. To build it in single precision ain't easy, to say polite. Overflow here, overflow there, round off error here, round off error there.

In fact integer transforms are better, wasn't it that the chip misses a 64 bits integer multiplication in SIMD.

It only has 32 x 32 == 64 bits.

What you want is either 1 or 2 instructions, preferably 2 instructions that can run in parallel where you do:

[v1 , v2] * [w1 , w2] == lower64 bits [ v1w1 , v2w2 ]

and the same instruction for the highbits.

If the SIMD would these 2 instructions, which can get executed in parallel of each other; then that would boost science everywhere. Not only would the FFT run faster than with double precision fft's, also these FFT's have no round off error; and as MOST scientists just do their calculation a single time, that would dramatically improve science everywhere.

What happens as we speak is that many scientists waste their time to round off errors; in fact many enhancements to quantum mechanica are based upon round off errors. So they 'explain' a random phenomena that simply doesn't exist; it's just a round off error they saw.

The confusion all this causes in science is SO BIG.

The calculation of results really is a DIFFERENT science from the theories that people want to prove with their calculation. It's a special expertise.

Now what happens is that if you move to single precision floating point, the mess is even bigger. Quadratic bigger.

To calculate single precision double precision results is very tough.

Karatsuba is an example of trying this in an efficient manner. It needs a lot of shifting instructions and 3 multiplies.

That is, provided your calculation can calculate in single precision half the number of bits from double precision.

All these claims of 'double precision' Fermi running at 50% of the speed of the single precision has to get proven first.

I'm very sceptical until i see it.

A gpu chip delivering 500 Gflop double precision would be kick butt of course. Let's sit and wait a few months.

It's about how fast it can multiply in double precision of course. In fact i'd prefer very big integers, i already explained why.

But let's suppose it has an integer multiplication of 16 x 16 bits getting 32 bits.

How many do we need of those (besides a lot of shifting instructions and additions and substracts)?

Well the answer is: quite a lot.

Let's say we lose factor 10 or so practical.

So speaking about single precision is utter nonsense except for a bunch of simulators, or in my case parameter tuning (making steps towards terminator chip - still looking for investors by the way).

Yet realize majority of system time at supercomputers goes to matrix calculations, not seldom in FFT type forms; so i'd say just focus upon that for number crunching.

What i'm doing is hardly getting funded - until one nation shows up with a real terminator chip and ships it to planet Mars to explore, as we don't want to sentence human beings to there.

Vincent
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            You are just quoting SINGLE precision flops? OMG what planet do you live? Vincent Diepeveen2010/07/19 10:26 AM
              The prior poster was talking about SP (NT)David Kanter2010/07/19 11:34 AM
                All FFT's need double precisionVincent Diepeveen2010/07/19 02:02 PM
                  All FFT's need double precisionDavid Kanter2010/07/19 02:09 PM
                    All FFT's need double precisionVincent Diepeveen2010/07/19 04:06 PM
                  All FFT's need double precision - notMichael S2010/07/20 01:16 AM
                    All FFT's need double precision - notUngo2010/07/21 12:04 AM
                      All FFT's need double precision - notMichael S2010/07/21 02:35 PM
                      All FFT's need double precision - notEduardoS2010/07/21 02:52 PM
                        All FFT's need double precision - notAnon2010/07/21 05:23 PM
                          All FFT's need double precision - notRicardo B2010/07/26 07:46 AM
                        I'm on a boat!anon2010/07/22 11:42 AM
                        All FFT's need double precision - notVincent Diepeveen2010/07/24 11:39 PM
                          All FFT's need double precision - notslacker2010/07/25 03:27 AM
                            All FFT's need double precision - notRicardo B2010/07/26 07:40 AM
                          All FFT's need double precision - notEduardoS2010/07/25 08:37 AM
                            All FFT's need double precision - notMichael S2010/07/25 10:43 AM
                    All FFT's need double precision - notVincent Diepeveen2010/07/24 11:19 PM
      A bit off baseEduardoS2010/07/08 04:08 PM
        A bit off baseGroo2010/07/08 06:11 PM
          A bit off basejohn mann2010/07/08 06:58 PM
            All right...let's cool it...David Kanter2010/07/08 07:54 PM
    A bit off baseVincent Diepeveen2010/07/19 03:36 PM
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