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Re: What Floating-Point Precisions Would Physicists Prefer?

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On Thu, 06 Aug 2015 11:18:07 -0700, Quadibloc wrote:

> 
> Yes. I remember trying to invert a matrix as a first-year computing assignment, 
> and getting a bad result. 
>

Well, the matrix has to be ill-conditioned.  The classic example is the
Hilbert matrix:

https://en.wikipedia.org/wiki/Hilbert_matrix


> 
> If you do it right, you don't have to waste bits
>

The problem with precision is that it has historically been
very expensive to go to higher bit lengths.  With today's cheap
hardware this is no longer the case, but the compromise, both
in hardware and in standards, has settled on 64 (or 128) bits
for floating point.

Another area of concern is compiler optimization.  Some compilers,
such as the Intel C/C++ compiler, has a default level of optimization
that is directed toward computational speed.  To achieve this
it will turn on a math processor feature called "denormal flush-to-zero."

Digital floating point numbers are always "normalized," that is,
the first bit of the mantissa is always an implied "1."  However,
numbers that are close to zero cannot be normalized and they must
have a different format, called a "denormal" number.  Calculating
with the denormal format takes a LOT of time and to increase speed
an option exists to just transform, or flush, these numbers to
zero.  Doing this increases computational speed but it can also
reduce accuracy.

Other compiler optimizations can influence accuracy in other ways
as well.

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Thread

What Floating-Point Precisions Would Physicists Prefer? Quadibloc <jsavard@ecn.ab.ca> - 2015-08-04 20:41 -0700
  Re: What Floating-Point Precisions Would Physicists Prefer? Fabian Russell <root@localhost.localdomain> - 2015-08-05 05:14 +0000
    Re: What Floating-Point Precisions Would Physicists Prefer? Quadibloc <jsavard@ecn.ab.ca> - 2015-08-05 04:38 -0700
      Re: What Floating-Point Precisions Would Physicists Prefer? Fabian Russell <root@localhost.localdomain> - 2015-08-05 14:22 +0000
        nano-M-sets noTthaTguY <abu.kuanysh05@gmail.com> - 2015-08-05 13:14 -0700
          Re: nano-M-sets Fabian Russell <root@localhost.localdomain> - 2015-08-05 21:23 +0000
            Re: nano-M-sets Poutnik <poutnik4nntp@gmail.com> - 2015-08-06 08:16 +0200
              Re: nano-M-sets Fabian Russell <root@localhost.localdomain> - 2015-08-06 17:34 +0000
                Re: nano-M-sets Quadibloc <jsavard@ecn.ab.ca> - 2015-08-06 11:23 -0700
                Re: nano-M-sets Fabian Russell <root@localhost.localdomain> - 2015-08-06 18:39 +0000
                Re: nano-M-sets Poutnik <poutnik4nntp@gmail.com> - 2015-08-06 21:07 +0200
                Re: nano-M-sets Fabian Russell <root@localhost.localdomain> - 2015-08-06 19:14 +0000
                Re: nano-M-sets Poutnik <poutnik4nntp@gmail.com> - 2015-08-07 07:41 +0200
                Re: nano-M-sets Quadibloc <jsavard@ecn.ab.ca> - 2015-08-06 14:17 -0700
                Re: nano-M-sets Fabian Russell <root@localhost.localdomain> - 2015-08-06 21:36 +0000
                Re: nano-M-sets Poutnik <poutnik4nntp@gmail.com> - 2015-08-07 08:08 +0200
                Re: nano-M-sets Poutnik <poutnik4nntp@gmail.com> - 2015-08-06 21:05 +0200
        Re: What Floating-Point Precisions Would Physicists Prefer? Quadibloc <jsavard@ecn.ab.ca> - 2015-08-06 11:18 -0700
          Re: What Floating-Point Precisions Would Physicists Prefer? Fabian Russell <root@localhost.localdomain> - 2015-08-06 19:03 +0000
            Re: What Floating-Point Precisions Would Physicists Prefer? Quadibloc <jsavard@ecn.ab.ca> - 2015-08-06 14:11 -0700
              Re: What Floating-Point Precisions Would Physicists Prefer? Fabian Russell <root@localhost.localdomain> - 2015-08-06 21:51 +0000
                Re: What Floating-Point Precisions Would Physicists Prefer? Quadibloc <jsavard@ecn.ab.ca> - 2015-08-06 15:18 -0700
                Re: What Floating-Point Precisions Would Physicists Prefer? Fabian Russell <root@localhost.localdomain> - 2015-08-07 01:11 +0000
                Re: What Floating-Point Precisions Would Physicists Prefer? noTthaTguY <abu.kuanysh05@gmail.com> - 2015-08-07 10:25 -0700
                Re: What Floating-Point Precisions Would Physicists Prefer? Quadibloc <jsavard@ecn.ab.ca> - 2015-08-07 11:41 -0700
                Re: What Floating-Point Precisions Would Physicists Prefer? "hanson" <hanson@quick.net> - 2015-08-07 16:21 -0700
  Re: What Floating-Point Precisions Would Physicists Prefer? Timo <timo@physics.uq.edu.au> - 2015-08-05 04:47 -0700
    Re: What Floating-Point Precisions Would Physicists Prefer? Poutnik <Poutnik4NNTP@gmail.com> - 2015-08-05 14:36 +0200

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