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Re: Floating point vs fixed arithmetics (signed 64-bit)

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Tim Wescott wrote:

> On Tue, 27 Mar 2012 13:56:49 -0500, Walter Banks wrote:
>
> > "David T. Ashley" wrote:
> >
> >> On Tue, 27 Mar 2012 18:52:09 +0300, upsidedown@downunder.com wrote:
> >>
> >> >On Tue, 27 Mar 2012 11:28:18 -0400, David T. Ashley
> >> ><dashley@gmail.com> wrote:
> >> >
> >> >
> >> >>Without FPU support, assuming that the processor has basic integer
> >> >>multiplication instructions, integer operations are ALWAYS faster
> >> >>than floating-point operations.  Usually _far_ faster.  And always
> >> >>more precise.
> >> >
> >> >Floating point instructions MUL/DIV are trivial, just multiply/divide
> >> >the mantissa and add/sub the exponent.
> >> >
> >> >With FP add/sub you have to denormalize one operand and then normalize
> >> >the result, which can be quite time consuming, without sufficient HW
> >> >support.
> >> >
> >> >This can be really time consuming, if the HW is designed by an idiot.
> >>
> >> Your observations are valid.  But I have yet to see a practical example
> >> of something that can be done faster and with equal accuracy in
> >> floating point vs. using integer operations.
> >>
> >> I concur with your observations.  After reading your first paragaph ...
> >> yeah, floating-point multiplication is pretty simple so long as the
> >> floating point format is sane.
> >>
> >> Before reading your post, I my mental model was that floating-point
> >> operations might be 20 times as slow as integer operations.  Now I'm
> >> thinking maybe 2-3 times.
> >
> > I did a fixed point support package for our 8 bit embedded systems
> > compilers and one interesting metric came out of the project.
> >
> > Given a number of bits in a number and similar error checking fixed or
> > float took very similar amounts of execution time and code size in
> > applications.
> >
> > For example 32 bit float and 32 bit fixed point. They are not exact but
> > they are close. In the end much to my surprise the choice is dynamic
> > range or resolution.
> >
> > There are other factors IEEE754 has potentially much more error checking
> > but not all libraries a written to support it, and not applications need
> > it.
>
> That's interesting, because in my experience fixed-point fractional
> arithmetic (i.e., 0x7fffffff = 1 - 2^-31, 0x80000001 = -1 + 2^-31), with
> saturation-on-add, is significantly faster (3x to 10x) than floating
> point on all the machines I've tried it except for those with floating-
> point hardware.
>
> I have a portable version that works on just about anything that's ANSI-C
> compatible, and when I really need speed I rewrite the arithmetic
> routines in assembly for about a 2x increase.
>
> The only processor that came close to matching it was the TMS320F2812,
> where we used the ANSI-C compatible version that was just about matched
> by the floating-point package that came with the tool set (and I _know_
> that TI cut corners with that floating point package).  That's the _only_
> processor in my experience where the floating point could keep up with
> the ANSI-C version, and I would expect that had I written an assembly
> version it would have been faster yet.

What you saw was what I was expecting. My points in the post was to be
careful in assuming that fixed is going to be dramatically better. At least for
8 bits the variable size in bits is a significant factor when all math is
multiprecision.

One of the keys in our metrics was the target was 8 bit processors
and there was an exchange between precision and dynamic range
but the bit sizes remained the same.

Real applications are probably dominated by scaling and precision
reducing the number of bits used by fixed point for the same application.

It didn't make sense until I realized that it was 8 bit processors using
software mults and divides and 32 bit floating point uses for the most
part 24bit mults and divides and a few adds/subtracts for the exponents.
32 bit fixed point uses 32 bit mults/divides adding to the cycle count.

My experience with 32 bit processors is similar to yours although
I don't have metrics to back it up.


Walter..

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Thread

Floating point vs fixed arithmetics (signed 64-bit) kishor <kiishor@gmail.com> - 2012-03-26 02:22 -0700
  Re: Floating point vs fixed arithmetics (signed 64-bit) "Boudewijn Dijkstra" <sp4mtr4p.boudewijn@indes.com> - 2012-03-26 12:08 +0200
  Re: Floating point vs fixed arithmetics (signed 64-bit) Arlet Ottens <usenet+5@c-scape.nl> - 2012-03-26 13:14 +0200
    Re: Floating point vs fixed arithmetics (signed 64-bit) David Brown <david@westcontrol.removethisbit.com> - 2012-03-26 13:24 +0200
      Re: Floating point vs fixed arithmetics (signed 64-bit) kishor <kiishor@gmail.com> - 2012-03-26 05:24 -0700
        Re: Floating point vs fixed arithmetics (signed 64-bit) Fredrik Östman <Fredrik_Oestman@work.invalid> - 2012-03-26 12:38 +0000
          Re: Floating point vs fixed arithmetics (signed 64-bit) kishor <kiishor@gmail.com> - 2012-03-26 06:33 -0700
            Re: Floating point vs fixed arithmetics (signed 64-bit) Arlet Ottens <usenet+5@c-scape.nl> - 2012-03-26 15:49 +0200
            Re: Floating point vs fixed arithmetics (signed 64-bit) David Brown <david@westcontrol.removethisbit.com> - 2012-03-26 15:45 +0200
            Re: Floating point vs fixed arithmetics (signed 64-bit) Fredrik Östman <Fredrik_Oestman@work.invalid> - 2012-03-26 14:34 +0000
        Re: Floating point vs fixed arithmetics (signed 64-bit) Arlet Ottens <usenet+5@c-scape.nl> - 2012-03-26 15:34 +0200
          Re: Floating point vs fixed arithmetics (signed 64-bit) Tim Wescott <tim@seemywebsite.com> - 2012-03-26 12:25 -0500
            Re: Floating point vs fixed arithmetics (signed 64-bit) Arlet Ottens <usenet+5@c-scape.nl> - 2012-03-26 20:19 +0200
              Re: Floating point vs fixed arithmetics (signed 64-bit) Rich Webb <bbew.ar@mapson.nozirev.ten> - 2012-03-26 16:45 -0400
                Re: Floating point vs fixed arithmetics (signed 64-bit) Tim Wescott <tim@seemywebsite.com> - 2012-03-26 17:15 -0500
                Re: Floating point vs fixed arithmetics (signed 64-bit) Rich Webb <bbew.ar@mapson.nozirev.ten> - 2012-03-26 19:09 -0400
                Re: Floating point vs fixed arithmetics (signed 64-bit) kishor <kiishor@gmail.com> - 2012-03-27 04:59 -0700
                Re: Floating point vs fixed arithmetics (signed 64-bit) David Brown <david@westcontrol.removethisbit.com> - 2012-03-27 15:25 +0200
                Re: Floating point vs fixed arithmetics (signed 64-bit) David T. Ashley <dashley@gmail.com> - 2012-03-29 13:17 -0400
  Re: Floating point vs fixed arithmetics (signed 64-bit) "Paul E. Bennett" <Paul_E.Bennett@topmail.co.uk> - 2012-03-27 11:28 +0100
  Re: Floating point vs fixed arithmetics (signed 64-bit) David T. Ashley <dashley@gmail.com> - 2012-03-27 11:28 -0400
    Re: Floating point vs fixed arithmetics (signed 64-bit) upsidedown@downunder.com - 2012-03-27 18:52 +0300
      Re: Floating point vs fixed arithmetics (signed 64-bit) David T. Ashley <dashley@gmail.com> - 2012-03-27 13:02 -0400
        Re: Floating point vs fixed arithmetics (signed 64-bit) Walter Banks <walter@bytecraft.com> - 2012-03-27 13:56 -0500
          Re: Floating point vs fixed arithmetics (signed 64-bit) Tim Wescott <tim@seemywebsite.com> - 2012-03-27 14:17 -0500
            Re: Floating point vs fixed arithmetics (signed 64-bit) Walter Banks <walter@bytecraft.com> - 2012-03-27 15:35 -0500
              Re: Floating point vs fixed arithmetics (signed 64-bit) Tim Wescott <tim@seemywebsite.please> - 2012-03-27 22:36 -0500
          Re: Floating point vs fixed arithmetics (signed 64-bit) David Brown <david@westcontrol.removethisbit.com> - 2012-03-28 09:00 +0200
          Re: Floating point vs fixed arithmetics (signed 64-bit) j.m.granville@gmail.com - 2012-03-30 04:08 -0700
            Re: Floating point vs fixed arithmetics (signed 64-bit) Mark Borgerson <mborgerson@comcast.net> - 2012-04-02 22:52 -0700
              Re: Floating point vs fixed arithmetics (signed 64-bit) John Devereux <john@devereux.me.uk> - 2012-04-03 11:33 +0100
                Re: Floating point vs fixed arithmetics (signed 64-bit) Anders.Montonen@kapsi.spam.stop.fi.invalid - 2012-04-03 12:05 +0000
                Re: Floating point vs fixed arithmetics (signed 64-bit) John Devereux <john@devereux.me.uk> - 2012-04-03 16:34 +0100
                Re: Floating point vs fixed arithmetics (signed 64-bit) Paul <paul@pcserviceselectronics.co.uk> - 2012-04-04 09:35 +0100
            Re: Floating point vs fixed arithmetics (signed 64-bit) Tim Wescott <tim@seemywebsite.com> - 2012-04-03 13:52 -0500
              Re: Floating point vs fixed arithmetics (signed 64-bit) Mark Borgerson <mborgerson@comcast.net> - 2012-04-04 16:50 -0700
                Re: Floating point vs fixed arithmetics (signed 64-bit) John Devereux <john@devereux.me.uk> - 2012-04-05 11:48 +0100
        Re: Floating point vs fixed arithmetics (signed 64-bit) David Brown <david@westcontrol.removethisbit.com> - 2012-03-28 09:17 +0200
          Re: Floating point vs fixed arithmetics (signed 64-bit) Tim Wescott <tim@seemywebsite.com> - 2012-03-28 12:20 -0500
            Re: Floating point vs fixed arithmetics (signed 64-bit) Andrew Reilly <areilly---@bigpond.net.au> - 2012-03-28 22:44 +0000
              Re: Floating point vs fixed arithmetics (signed 64-bit) Tim Wescott <tim@seemywebsite.com> - 2012-03-28 18:35 -0500
                Re: Floating point vs fixed arithmetics (signed 64-bit) David Brown <david@westcontrol.removethisbit.com> - 2012-03-29 10:58 +0200
                Re: Floating point vs fixed arithmetics (signed 64-bit) Mark Borgerson <mborgerson@comcast.net> - 2012-03-29 07:56 -0700
                Re: Floating point vs fixed arithmetics (signed 64-bit) Tim Wescott <tim@seemywebsite.com> - 2012-03-29 16:52 -0500
                Re: Floating point vs fixed arithmetics (signed 64-bit) Mark Borgerson <mborgerson@comcast.net> - 2012-03-29 21:19 -0700
                Re: Floating point vs fixed arithmetics (signed 64-bit) Tim Wescott <tim@seemywebsite.please> - 2012-03-30 00:42 -0500
              Re: Floating point vs fixed arithmetics (signed 64-bit) upsidedown@downunder.com - 2012-03-29 07:19 +0300
                Re: Floating point vs fixed arithmetics (signed 64-bit) Andrew Reilly <areilly---@bigpond.net.au> - 2012-03-29 11:53 +0000
                Re: Floating point vs fixed arithmetics (signed 64-bit) Walter Banks <walter@bytecraft.com> - 2012-03-29 09:40 -0500
                Re: Floating point vs fixed arithmetics (signed 64-bit) upsidedown@downunder.com - 2012-03-29 23:46 +0300
                Re: Floating point vs fixed arithmetics (signed 64-bit) Walter Banks <walter@bytecraft.com> - 2012-03-29 09:28 -0500
                Re: Floating point vs fixed arithmetics (signed 64-bit) David Brown <david@westcontrol.removethisbit.com> - 2012-03-29 16:58 +0200
            Re: Floating point vs fixed arithmetics (signed 64-bit) David Brown <david@westcontrol.removethisbit.com> - 2012-03-29 10:09 +0200
            Re: Floating point vs fixed arithmetics (signed 64-bit) Clifford Heath <cjh@no.spam.please.net> - 2012-04-01 18:08 +1000
          Re: Floating point vs fixed arithmetics (signed 64-bit) dp <dp@tgi-sci.com> - 2012-03-28 02:38 -0700
      Re: Floating point vs fixed arithmetics (signed 64-bit) upsidedown@downunder.com - 2012-03-28 22:59 +0300

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