Subject: Re: [boost] [boostcon][proto] Suggestion for LIAW session: fixed-pointnumbers
From: Ravi (lists_ravi_at_[hidden])
Date: 2011-03-16 02:21:00
On Tuesday 15 March 2011 21:10:52 Gruenke, Matt wrote:
> > All of the others required non-obvious rules to represent the cases when
> > the MSB is to the right of the binary point or the LSB is much to the
> > left of the binary point.
>
> I'm not sure we're talking about the same thing, here. The template
> parameters of the results returned by my operators were determined by
> those of the operands.
In the system you proposed, what are the template parameters for the fixed-
point number with the following range?
{ 0, 1, ..., 15 } x 2^{-11}
Or, the fixed-point number holding values in the following range?
{ 0, 1, ..., 15 } x 2^{11}
> > > * inverse returns a type with one fewer frac bits than the
> > >
> > > operand had int bits and one more int bits than the
> > > operand had frac bits. This sacrifice of precision is
> > > necessary to avoid overflow.
> >
> > This one is tricky; the behavior you propose is completely unacceptable
> > for signal processing.
>
> Which one? Inverse? If you need more headroom, you can always add it
> before the operation (hint: it's free). I think I included inversion more
> for completeness. Is it something you use often? Since integer division
> is usually so slow, I expect that most people will just opt for floating
> point when they get into that territory.
Fixed-point numbers are used in plenty of places where speed is not an issue
-- modeling signal processing circuits in software is one example, and
firmware in embedded control systems with no floating point unit is another.
In such cases, falling back to floating-point is not an option. Implementing
dividers in hardware is a tricky task, especially since most dividers are
serial, but with some parallelization or statistical rounding. Getting
division and CORDIC working correctly are pretty much the only non-trivial
challenges in low-to-medium speed fixed-point circuit design. At high speeds,
carry propagation latency can be tricky as well.
Regards,
Ravi