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Re: [avr-libc-dev] Bug in math library
From: |
Paul Schlie |
Subject: |
Re: [avr-libc-dev] Bug in math library |
Date: |
Sun, 09 Jan 2005 00:01:53 -0500 |
User-agent: |
Microsoft-Entourage/11.1.0.040913 |
exp = 0 is a sufficient zero test if demoralized numbers aren't supported,
(which seem like a reasonable simplifying assumption for avr applications)
As an aside, it may be worth considering that it's likely beneficial to
further simplify avr's implementation by simply treating +/- 0, +/- inf
more simply and consistently as the non-accumulating bounds of otherwise
normally represented values, thereby eliminating the arithmetic and
algebraic anomalies otherwise introduced, which typically then require
checking to transform the computed results into useful values, which as
it's often never done comprehensively, often results in latent bugs in
embedded applications, which typically don't simply print out results for
a human to read, and typically never expect sticky +/-inf, or NAN behaviors
or results.
Alternatively by defining: +/-0 = +/-2^-127, +/-inf = +/-2^-127
(+inf -> +0 -> -0 -> -inf) = 1/(+0 -> +inf -> -inf -> -0)
x = x + +/-0, +inf = +inf + (x : x >= -0), -inf = -inf - (x : x >= -0)
Some interesting simplifying useful properties result:
1 = (+0 -> +inf)*(+inf -> +0) = (+2^-127 -> +2^+127)*(+2^-127 -> +2^+127)
= (+0 -> +inf)/(+0 -> +inf) = (+2^-127 -> +2^+127)/(+2^+127 -> +2^-127)
Thereby 0/0 = 1, not NAN, as although 0/X is thought of as being 0, as 0
becomes divided by an increasingly smaller, or multiplied by an increasingly
larger value, the result approaches 1 as the value reaches it's respective
reciprocal bounds. Finally by defining that functions returning a float
will return the real component of the result value, all operations on floats
become well defined, and never yield NAN. (including typical examples of
square-root of a negative number, which would then more conveniently yield
0, not NAN; as it there was an interest in checking for negative square
roots for example, it should be done prior to it's call, not afterward,
etc.)
> From: Colin O'Flynn <address@hidden>
> Organization: NewAE
> Reply-To: <address@hidden>
> Date: Sat, 8 Jan 2005 17:46:14 -0400
> To: Marek Michalkiewicz <address@hidden>
> Cc: <address@hidden>
> Subject: Re: [avr-libc-dev] Bug in math library
>
>> Not necessary - already sent there (see Cc: in headers).
>
> Oh - guess my mail client screwed up, don't see the CC's.
>
> Anyway the other thing I thought of - if the hidden bit is set when zero
> detected, it might be easier to just check for 0x01 being present in that
> register.
>
> However it is that sort of thing that will probably get broken in the
> future... to be completely safe I would need to do this:
>
> clr __tmp_reg__
> OR __tmp_reg__, rB2
> OR __tmp_reg__, rB1
> OR __tmp_reg__, rB0
>
> Then the Z flag would be set if all those registers are zero. It is an
> increase from 1 to 4 instructions.
>
> Regards,
>
> -Colin
>
> _______________________________________________
> AVR-libc-dev mailing list
> address@hidden
> http://lists.nongnu.org/mailman/listinfo/avr-libc-dev
- [avr-libc-dev] Bug in math library, Colin O'Flynn, 2005/01/08
- Re: [avr-libc-dev] Bug in math library, Marek Michalkiewicz, 2005/01/08
- Message not available
- Message not available
- Re: [avr-libc-dev] Bug in math library, Colin O'Flynn, 2005/01/08
- Re: [avr-libc-dev] Bug in math library, Colin O'Flynn, 2005/01/08
- Re: [avr-libc-dev] Bug in math library, Marek Michalkiewicz, 2005/01/08
- Re: [avr-libc-dev] Bug in math library, Colin O'Flynn, 2005/01/09
- Re: [avr-libc-dev] Bug in math library,
Paul Schlie <=
- Re: [avr-libc-dev] Bug in math library, Paul Schlie, 2005/01/09
- Re: [avr-libc-dev] Bug in math library, Bob Paddock, 2005/01/09
- Re: [avr-libc-dev] Bug in math library, Colin O'Flynn, 2005/01/09
- Re: [avr-libc-dev] Bug in math library, Paul Schlie, 2005/01/09
- Re: [avr-libc-dev] Bug in math library, Colin O'Flynn, 2005/01/09
- Re: [avr-libc-dev] Bug in math library, Joerg Wunsch, 2005/01/09