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Re: Low precision number formats do not suit many simulations

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On 2026-04-16 08:06, Martin Brown wrote:
> On 16/04/2026 07:43, Jan Panteltje wrote:
>>> joegwinn@comcast.netwrote:
>>>>
>>> This is a new kind of floating-point number, likely good for AI, but
>>> lots of other uses will turn up.
>>>
>>> From IEEE Spectrum (March 2026 issue):
>>>
>>> AI has driven an explosion of new number formats—the ways in which
>>> numbers are represented digitally. Engineers are looking at every
>>> possible way to save computation time and energy, including shortening
>>> the number of bits used to represent data. But what works for AI
>>> doesn't necessarily work for scientific computing, be it for
>>> computational physics, biology, fluid dynamics, or engineering
>>> simulations. IEEE Spectrum spoke with Laslo Hunhold, who recently
>>> joined Barcelona-based Openchip as an AI engineer, about his efforts
>>> to develop a bespoke number format for scientific computing.
>>>
>>> .<https://spectrum.ieee.org/number-formats-ai-scientific-computing>
>>>
>>> Joe
>>
>> Do not know much about what that guy did.
>> But I noticed I can do most 'scientific things with 32 bits (in asm at 
>> that)
>> For example the Fourier transform in
>>   https://panteltje.nl/panteltje/pic/scope_pic/
>>    asm source downloadable on that site
>>   I did using 32 bit integer.
> 
> FFTs are relatively forgiving where numerical precision is concerned. 
> The basis functions are perfectly orthogonal summed over the domain.
> 
> Even something as simple as solving a cubic equation x^3 + ax^2 + bx + c 
> can easily go wrong when computing in float32 since it involves 
> computing a^6. You can work around this lack of dynamic range but it is 
> painful!
> 
> Double precision also helps a lot when accumulating summations of reals 
> or even in FFTs to do recurrence relations for sin/cos(n*w*t)
> 
> Almost all modern FP libraries today promote the float32 argument to 
> double and do the computation in double precision rounding the result 
> back to float at the end. It avoids a lot of messing about ensuring 
> nothing overflows during the intermediate calculations.
> 
>> Is that science?
>> Of course when AI wants to do a divide by zero using Albert E.'s brain 
>> fog,
>> than it will likely need infinite bits to do the wormhole dance...
>>
>> My conclusion: 32 bits is enough for most things
> 
> CDC7600 60 bits really was good enough for most orbital dynamics 
> computations which is why astronomical codes used them (and BMEWS too).
> 
> Today's CPUs double precision 64bit and float 32 bit have essentially 
> the same performance unless you are vectorising or using huge arrays so 
> that unless you *really* know what you are doing double precision is 
> preferred for most routine scientific calculations. The exception is 
> bulk raw data where you seldom have more than 4 significant figures.
> 

There are also schemes such as FDTD (finite difference time domain) EM 
simulation, where the roundoff error is pretty nearly constant--all the 
numerical noise flows out of the simulation domain at the speed of 
light!  (Providing you use the right sort of absorbing boundaries, of 
course.)

My clusterized simulator is all done in single precision floats, which 
makes a big difference in speed.

Cheers

Phil Hobbs

-- 
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC / Hobbs ElectroOptics
Optics, Electro-optics, Photonics, Analog Electronics
Briarcliff Manor NY 10510

http://electrooptical.net
http://hobbs-eo.com

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AI�s Math Tricks Don�t Work for Scientific Computing - Low-precision number formats don�t suit many simulations joegwinn@comcast.net - 2026-04-15 18:33 -0400
  Re: AI’s Math Tricks Don’t Work for Scientific Computing - Low-precision number formats don’t suit many simulations Phil Hobbs <pcdhSpamMeSenseless@electrooptical.net> - 2026-04-15 20:17 -0400
    reply john larkin <jl@glen--canyon.com> - 2026-04-16 02:18 -0700
      Re: reply joegwinn@comcast.net - 2026-04-16 11:36 -0400
        Re: reply john larkin <jl@glen--canyon.com> - 2026-04-16 09:31 -0700
          Re: reply joegwinn@comcast.net - 2026-04-16 14:49 -0400
            Re: reply john larkin <jl@glen--canyon.com> - 2026-04-16 18:25 -0700
              Re: reply joegwinn@comcast.net - 2026-04-17 11:52 -0400
          Re: 68020 Buzz McCool <buzz_mccool@yahoo.com> - 2026-04-23 09:12 -0700
            Re: 68020 Phil Hobbs <pcdhSpamMeSenseless@electrooptical.net> - 2026-04-23 17:25 -0400
            Re: 68020 Don Y <blockedofcourse@foo.invalid> - 2026-04-23 15:39 -0700
              Re: 68020 Martin Brown <'''newspam'''@nonad.co.uk> - 2026-04-24 09:40 +0100
                Re: 68020 Don Y <blockedofcourse@foo.invalid> - 2026-04-24 02:26 -0700
                Re: 68020 john larkin <jl@glen--canyon.com> - 2026-04-24 10:03 -0700
      Re: reply Nioclás Pól Caileán de Ghloucester <thanks-to@Taf.com> - 2026-04-16 19:14 +0000
      Re: reply bitrex <user@example.net> - 2026-04-16 16:46 -0400
    Re: AI’s Math Tricks Don’t Work for Scientific Computing - Low-precision number formats don’t suit many simulations Martin Brown <'''newspam'''@nonad.co.uk> - 2026-04-16 10:45 +0100
      Re: AI�s Math Tricks Don�t Work for Scientific Computing - Low-precision number formats don�t suit many simulations joegwinn@comcast.net - 2026-04-16 18:38 -0400
  Re: AIs Math Tricks Dont Work for Scientific Computing - Low-precision number formats dont suit many simulations Don Y <blockedofcourse@foo.invalid> - 2026-04-15 18:29 -0700
  Re: Low precision number formats do not suit many simulations Jan Panteltje <alien@comet.invalid> - 2026-04-16 06:43 +0000
    Re: Low precision number formats do not suit many simulations Bill Sloman <bill.sloman@ieee.org> - 2026-04-16 21:28 +1000
    Re: Low precision number formats do not suit many simulations Martin Brown <'''newspam'''@nonad.co.uk> - 2026-04-16 13:06 +0100
      Re: Low precision number formats do not suit many simulations Don Y <blockedofcourse@foo.invalid> - 2026-04-16 06:34 -0700
      Re: Low precision number formats do not suit many simulations joegwinn@comcast.net - 2026-04-16 11:44 -0400
        Re: Low precision number formats do not suit many simulations Don Y <blockedofcourse@foo.invalid> - 2026-04-16 08:59 -0700
          Re: Low precision number formats do not suit many simulations joegwinn@comcast.net - 2026-04-16 14:51 -0400
            Re: Low precision number formats do not suit many simulations Don Y <blockedofcourse@foo.invalid> - 2026-04-16 14:29 -0700
              Re: Low precision number formats do not suit many simulations John R Walliker <jrwalliker@gmail.com> - 2026-04-16 23:44 +0100
                Re: Low precision number formats do not suit many simulations joegwinn@comcast.net - 2026-04-16 19:00 -0400
                Re: Low precision number formats do not suit many simulations Don Y <blockedofcourse@foo.invalid> - 2026-04-16 16:48 -0700
                Re: Low precision number formats do not suit many simulations Don Y <blockedofcourse@foo.invalid> - 2026-04-16 16:41 -0700
              Re: Low precision number formats do not suit many simulations Nioclás Pól Caileán de Ghloucester <thanks-to@Taf.com> - 2026-04-17 19:56 +0000
                Re: Low precision number formats do not suit many simulations Don Y <blockedofcourse@foo.invalid> - 2026-04-17 16:24 -0700
                Re: Low precision number formats do not suit many simulations Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-04-17 18:06 -0700
                Re: Low precision number formats do not suit many simulations Nioclás Pól Caileán de Ghloucester <thanks-to@Taf.com> - 2026-04-18 19:29 +0000
                Re: Low precision number formats do not suit many simulations Don Y <blockedofcourse@foo.invalid> - 2026-04-18 15:10 -0700
          Re: Low precision number formats do not suit many simulations Arie de Muijnck <noreply@ademu.nl> - 2026-04-17 02:01 +0200
            Re: Low precision number formats do not suit many simulations Don Y <blockedofcourse@foo.invalid> - 2026-04-16 17:30 -0700
      Re: Low precision number formats do not suit many simulations Phil Hobbs <pcdhSpamMeSenseless@electrooptical.net> - 2026-04-17 15:53 -0400
  test test john larkin <jl@glen--canyon.com> - 2026-04-16 02:16 -0700
    Re: test test john larkin <jl@glen--canyon.com> - 2026-04-16 07:45 -0700
      Re: test test Jan Panteltje <alien@comet.invalid> - 2026-04-16 15:59 +0000
        Re: test test Nioclás Pól Caileán de Ghloucester <thanks-to@Taf.com> - 2026-04-16 19:24 +0000
      Re: test test joegwinn@comcast.net - 2026-04-16 12:09 -0400

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