Hello,

I have to implement atan2 on a dsPIC30F and would like to do that in
fixed point for reasonable performance. Does someone already did that?

Thanks,
--
Eric Meurville

From:	Nithin
Subject:	Re: C code for fixed point atan2
Date:	20 Jan 2005 14:42:46 -0800

Hi
You may want to look a this
http://dspguru.com/comp.dsp/tricks/alg/fxdatan2.htm

-Nithin

From:	Eric Meurville
Subject:	Re: C code for fixed point atan2
Date:	Fri, 21 Jan 2005 10:46:18 +0100

Thanks for the link but the code proposed uses floats and I would
perform the computation with integers.

EMe.

Nithin wrote:
> Hi
> You may want to look a this
> http://dspguru.com/comp.dsp/tricks/alg/fxdatan2.htm
>
> -Nithin
>

From:	Steve Underwood
Subject:	Re: C code for fixed point atan2
Date:	Fri, 21 Jan 2005 19:10:01 +0800

Hi Eric,

Look again. The example code may use floats, but the title is "fixed
point atan2 with self-normalisation". If you recast the numbers as fixed
point values it works just fine.

Regards,
Steve

Eric Meurville wrote:

> Thanks for the link but the code proposed uses floats and I would
> perform the computation with integers.
>
> EMe.
>
> Nithin wrote:
>
>> Hi
>> You may want to look a this
>> http://dspguru.com/comp.dsp/tricks/alg/fxdatan2.htm
>>
>> -Nithin
>>

From:	bungalow_steve at yahoo.com
Subject:	Re: C code for fixed point atan2
Date:	21 Jan 2005 09:18:17 -0800

Steve Underwood wrote:
> bungalow_steve@yahoo.com wrote:
> > Steve Underwood wrote:
> >
> >>Hi Eric,
> >>
> >>Look again. The example code may use floats, but the title is
"fixed
> >>point atan2 with self-normalisation". If you recast the numbers as
> >
> > fixed
> >
> >>point values it works just fine.
> >>
> >>Regards,
> >>Steve
> >>
> >>
> >>Eric Meurville wrote:
> >>
> >>
> >>>Thanks for the link but the code proposed uses floats and I would
> >>>perform the computation with integers.
> >>>
> >>>EMe.
> >>>
> >>>Nithin wrote:
> >>>
> >>>
> >>>>Hi
> >>>>You may want to look a this
> >>>>http://dspguru.com/comp.dsp/tricks/alg/fxdatan2.htm
> >>>>
> >>>>-Nithin
> >>>>
> >
> >
> > if you simply recast everything as integers, won't coeff_1 =0? and
what
> > do you do with 1e-10?
> >
>
> Who said anything about using integers. I said fixed point. You don't

> even have to think about the 1e-10. A comment tells you why it is
there,
> and it is, therefore, trivial to eliminate it with a bit of logic.
The
> logic doesn't work so well with floats, which I guess is why the
> original is kludged in that way.
>
> Regards,
> Steve

There is a fixed point data type in C?

From:	Jerry Avins
Subject:	Re: C code for fixed point atan2
Date:	Fri, 21 Jan 2005 12:49:19 -0500

bungalow_steve@yahoo.com wrote:

...

> There is a fixed point data type in C?

Fixed-point is at worst integer scaled by shifts. Compilers for some
processors that have fixed-point hardware do support a fixed-point type.
Without that, either do the job in assembler or write C-callable
assembly routines for best execution speed.

Jerry
--
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

From:	Ronald H. Nicholson Jr.
Subject:	Re: C code for fixed point atan2
Date:	Fri, 21 Jan 2005 19:21:39 +0000 (UTC)

In article <1106327897.743543.57540@z14g2000cwz.googlegroups.com>,
wrote:
>> Who said anything about using integers. I said fixed point.
....
>There is a fixed point data type in C?

Yes, indirectly. The meaning of the bits in (int/short/long) are
defined by the programmer. For instance they can represent boolean flags
instead of any scalar quantity. If LSB represents a unit quantity, then
you might have traditional integers. But the LSB can also represent a
fractional quantity, for instance, cents instead of dollars if you don't
want to lose pennies in certain types of financial arithmetic. The LSB can
also represent 1/256th's, or other 1/(2^n)th's, if you want normalization
or renormalization to be easily done using the << and >> C operators.

Normalize for any input or output, and renormalize after any multiply
or divide, and the (int/short/long) C data types can be used to represent
fixed point or scaled integer values of the appropriate range and accuracy.

IMHO. YMMV.
--
Ron Nicholson rhn AT nicholson DOT com http://www.nicholson.com/rhn/
#include // only my own opinions, etc.

From:	Steve Underwood
Subject:	Re: C code for fixed point atan2
Date:	Mon, 24 Jan 2005 15:02:52 +0800

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Ronald H. Nicholson Jr. wrote:

>In article <1106327897.743543.57540@z14g2000cwz.googlegroups.com>,
> wrote:
>
>
>>>Who said anything about using integers. I said fixed point.
>>>
>>>
>...
>
>
>>There is a fixed point data type in C?
>>
>>
>
>Yes, indirectly. The meaning of the bits in (int/short/long) are
>defined by the programmer. For instance they can represent boolean flags
>instead of any scalar quantity. If LSB represents a unit quantity, then
>you might have traditional integers. But the LSB can also represent a
>fractional quantity, for instance, cents instead of dollars if you don't
>want to lose pennies in certain types of financial arithmetic. The LSB can
>also represent 1/256th's, or other 1/(2^n)th's, if you want normalization
>or renormalization to be easily done using the << and >> C operators.
>
>Normalize for any input or output, and renormalize after any multiply
>or divide, and the (int/short/long) C data types can be used to represent
>fixed point or scaled integer values of the appropriate range and accuracy.
>
>IMHO. YMMV.
>
>
I think it is interesting to note that various older languages - Algol,
Coral, PL/1 - had explicit support for fixed point arithmetic. I think
Ada still does (its years since I touched it), but it seems to be
missing for other currently popular languages. Its value was somewhat
limited in the older languages. It was generally rather implementation
dependant, so code tended not to be very portable. It is, however,
something of a pity that you now have to use vanilla integers, and do
all the fiddley bits yourself. You may end up with the same result, but
the code lacks clarity.

That said, if you can't see that any language supporting integers also
supports fixed point you've failed arithmetic 101. :-)

Regards,
Steve

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Ronald H. Nicholson Jr. wrote:

In article <1106327897.743543.57540@z14g2000cwz.googlegroups.com>,
 <bungalow_steve@yahoo.com> wrote:

Who said anything about using integers. I said fixed point.

...

There is a fixed point data type in C?


Yes, indirectly.  The meaning of the bits in (int/short/long) are
defined by the programmer.  For instance they can represent boolean flags
instead of any scalar quantity.  If LSB represents a unit quantity, then
you might have traditional integers.  But the LSB can also represent a
fractional quantity, for instance, cents instead of dollars if you don't
want to lose pennies in certain types of financial arithmetic. The LSB can
also represent 1/256th's, or other 1/(2^n)th's, if you want normalization
or renormalization to be easily done using the << and >> C operators.

Normalize for any input or output, and renormalize after any multiply
or divide, and the (int/short/long) C data types can be used to represent
fixed point or scaled integer values of the appropriate range and accuracy.

IMHO. YMMV.

I think it is interesting to note that various older languages - Algol,
Coral, PL/1 - had explicit support for fixed point arithmetic. I think
Ada still does (its years since I touched it), but it seems to be
missing for other currently popular languages. Its value was somewhat
limited in the older languages. It was generally rather implementation
dependant, so code tended not to be very portable. It is, however,
something of a pity that you now have to use vanilla integers, and do
all the fiddley bits yourself. You may end up with the same result, but
the code lacks clarity.

That said, if you can't see that any language supporting integers also
supports fixed point you've failed arithmetic 101. :-)

Regards,

Steve

--------------020006080406080906020401--

From:	glen herrmannsfeldt
Subject:	Re: C code for fixed point atan2
Date:	Fri, 21 Jan 2005 13:37:56 -0800

Ronald H. Nicholson Jr. wrote:
(someone asked)

>>There is a fixed point data type in C?

> Yes, indirectly. The meaning of the bits in (int/short/long) are
> defined by the programmer. For instance they can represent boolean flags
> instead of any scalar quantity. If LSB represents a unit quantity, then
> you might have traditional integers. But the LSB can also represent a
> fractional quantity,

It would be much easier with a multiply that returned a 2N bit
product, and a divide that took a 2N bit dividend. That is the
way it is done in hardware, mostly for this reason. (The other
reason is to allow implementing multiple precision arithmetic.)

-- glen

From:	bungalow_steve at yahoo.com
Subject:	Re: C code for fixed point atan2
Date:	21 Jan 2005 09:39:40 -0800

Microchip might be implementing more terms in the polynomial, I suspect
if you implemented the code in integer math on the dsPIC the entire
function would execute in less time then a single floating point add.
If I remember correctly the integer divide is the killer, 18 cycles,
but even with that, your talking at most 25-30 cycles for the entire
integer algorithm compared with over 100 cycles for a single floating
addition.

From:	bungalow_steve at yahoo.com
Subject:	Re: C code for fixed point atan2
Date:	21 Jan 2005 06:45:00 -0800

Steve Underwood wrote:
> Hi Eric,
>
> Look again. The example code may use floats, but the title is "fixed
> point atan2 with self-normalisation". If you recast the numbers as
fixed
> point values it works just fine.
>
> Regards,
> Steve
>
>
> Eric Meurville wrote:
>
> > Thanks for the link but the code proposed uses floats and I would
> > perform the computation with integers.
> >
> > EMe.
> >
> > Nithin wrote:
> >
> >> Hi
> >> You may want to look a this
> >> http://dspguru.com/comp.dsp/tricks/alg/fxdatan2.htm
> >>
> >> -Nithin
> >>

if you simply recast everything as integers, won't coeff_1 =0? and what
do you do with 1e-10?

From:	Steve Underwood
Subject:	Re: C code for fixed point atan2
Date:	Sat, 22 Jan 2005 00:14:35 +0800

bungalow_steve@yahoo.com wrote:
> Steve Underwood wrote:
>
>>Hi Eric,
>>
>>Look again. The example code may use floats, but the title is "fixed
>>point atan2 with self-normalisation". If you recast the numbers as
>
> fixed
>
>>point values it works just fine.
>>
>>Regards,
>>Steve
>>
>>
>>Eric Meurville wrote:
>>
>>
>>>Thanks for the link but the code proposed uses floats and I would
>>>perform the computation with integers.
>>>
>>>EMe.
>>>
>>>Nithin wrote:
>>>
>>>
>>>>Hi
>>>>You may want to look a this
>>>>http://dspguru.com/comp.dsp/tricks/alg/fxdatan2.htm
>>>>
>>>>-Nithin
>>>>
>
>
> if you simply recast everything as integers, won't coeff_1 =0? and what
> do you do with 1e-10?
>

Who said anything about using integers. I said fixed point. You don't
even have to think about the 1e-10. A comment tells you why it is there,
and it is, therefore, trivial to eliminate it with a bit of logic. The
logic doesn't work so well with floats, which I guess is why the
original is kludged in that way.

Regards,
Steve

From:	Eric Meurville
Subject:	Re: C code for fixed point atan2
Date:	Fri, 21 Jan 2005 16:55:34 +0100

I agree, this code is definetely floating point. Nevertheless, its
performance on dsPIC30F is 3 times better than Microchip native math
library.

bungalow_steve@yahoo.com wrote:
> Steve Underwood wrote:
>
>>Hi Eric,
>>
>>Look again. The example code may use floats, but the title is "fixed
>>point atan2 with self-normalisation". If you recast the numbers as
>
> fixed
>
>>point values it works just fine.
>>
>>Regards,
>>Steve
>>
>>
>>Eric Meurville wrote:
>>
>>
>>>Thanks for the link but the code proposed uses floats and I would
>>>perform the computation with integers.
>>>
>>>EMe.
>>>
>>>Nithin wrote:
>>>
>>>
>>>>Hi
>>>>You may want to look a this
>>>>http://dspguru.com/comp.dsp/tricks/alg/fxdatan2.htm
>>>>
>>>>-Nithin
>>>>
>
>
> if you simply recast everything as integers, won't coeff_1 =0? and what
> do you do with 1e-10?
>

--
Eric Meurville