floating pt. to fixed pt. conversion

Hi,

are there any good tutorials to convert floating point C code to fixed
point C code.

Regards,
Shaekhar

shekhar85 <chandrashekharla@n_o_s_p_a_m.gmail.com> wrote:
 
> are there any good tutorials to convert floating point C 
> code to fixed point C code.

What kind of tutorial do you want?

Converting the code is easy.  Making sure that the algoritm
works the same way in fixed point is a completely different
question.

What kind of problems are you asking about?

-- glen
 

Hi Shaekhar

> are there any good tutorials to convert floating point C code to fixed
> point C code.

I have some routine for conversion ...

unsigned int MaskBit(unsigned char Bit)
{
    // Local Variable
    unsigned int x;

    // Init Mask
    x = 0;

   // Loop for Mask dimension
   while(Bit)
   {
        // Rotate Left
        x <<= 1;

       // Add Mask Bit
       x |= 1;

       // Decrement bit number
       Bit--;
    }

    // Return with MaskBit
    return x;
}

float Fixed2Float(unsigned int Value, unsigned char Data, unsigned char 
Binary, unsigned char Signed)
{
    // Signed conversione ...
    if((Signed != 0) && (Value >> (Data - 1)))
    {
         // Positive Value
         Value = (~Value + 1) & MaskBit(Data);

        // Negative Value
        return (float)(-1.0 * ((float)(Value) / (float)(1 << Binary)));
    }
    else
    {
         // Positive Value
         return (float)(+1.0 * ((float)(Value) / (float)(1 << Binary)));
     }
}

unsigned int Float2Fixed(float Value, unsigned char Data, unsigned char 
Binary)
{
     // Convert to Fixed Point
     return ((unsigned int)((Value) * (float)(1 << Binary) + ((Value) < 0 
? -0.5 : 0.5))) & MaskBit(Data);
}

Reagrds

Kappasm

On Aug 16, 2:43&#4294967295;am, glen herrmannsfeldt <g...@ugcs.caltech.edu> wrote:
> shekhar85 <chandrashekharla@n_o_s_p_a_m.gmail.com> wrote:
> > are there any good tutorials to convert floating point C
> > code to fixed point C code.
>
> Converting the code is easy. &#4294967295;Making sure that the algorithm
> works the same way in fixed point is a completely different
> question.

and you might have an ice cube's chance in hell in getting them to
work exactly the same.  sometimes algs written in float have great
difficulty working in fixed (like with FFT in it) without a great deal
of roundoff error or the risk of overflow deep in side.  on the other
hand, sometimes an alg works in fixed but not so well in float (like a
CIC filter).

to answer the OP's concern, doing algs in fixed-point in C requires
care in the size of word and what happens to the size of the result of
an operation.  and then there are the scaling factors you need to
worry about.

i thought maybe Randy Yates had a tutorial.  no?

r b-j


r b-j

On 08/15/2010 10:15 PM, shekhar85 wrote:
> Hi,
>
> are there any good tutorials to convert floating point C code to fixed
> point C code.

I probably over-complicate things, but this is a pretty broad subject, 
and one that would be hard to write a tutorial _for_.

As RBJ pointed out, some algorithms almost demand floating point, or 
huge increases in numerical precision (such as the FFT), while some 
algorithms depend on fixed-point tricks (such as CIC).

I do most of my signal processing for control systems and for low-level 
communications, where the incoming data path size is known and the 
filters are simple; these applications boil down to IIR and FIR 
filtering for the most part, and for the most part do just fine in 
fixed-point math.  Here, the big difference between a 32-bit floating 
point number and a 32-bit fixed point number is that when I'm paying 
proper attention to scaling the floating point number throws away 7 
perfectly good and valuable bits worth of precision, and gives me back a 
10^76 variation in magnitude that I don't need in the least.

But I've always converted between floating point and fixed point 
algorithms by understanding the underlying math, and rewriting the 
algorithm to match the different representation.  I suppose you could 
come up with specific recipes for specific situations (IIR, FIR, etc.), 
but I'm not sure if you could easily cover all the useful ones in a 
document that's smaller and easier than one that just teaches you the math.

-- 

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Do you need to implement control loops in software?
"Applied Control Theory for Embedded Systems" was written for you.
See details at http://www.wescottdesign.com/actfes/actfes.html

robert bristow-johnson wrote:

> On Aug 16, 2:43 am, glen herrmannsfeldt <g...@ugcs.caltech.edu> wrote:
> 
>>shekhar85 <chandrashekharla@n_o_s_p_a_m.gmail.com> wrote:
>>
>>>are there any good tutorials to convert floating point C
>>>code to fixed point C code.
>>
>>Converting the code is easy.  Making sure that the algorithm
>>works the same way in fixed point is a completely different
>>question.
> 
> 
> and you might have an ice cube's chance in hell in getting them to
> work exactly the same.  sometimes algs written in float have great
> difficulty working in fixed (like with FFT in it) without a great deal
> of roundoff error or the risk of overflow deep in side.  on the other
> hand, sometimes an alg works in fixed but not so well in float (like a
> CIC filter).
> 
> to answer the OP's concern, doing algs in fixed-point in C requires
> care in the size of word and what happens to the size of the result of
> an operation.  and then there are the scaling factors you need to
> worry about.
> 
> i thought maybe Randy Yates had a tutorial.  no?

I think a conversion of an algorithm from floating point to integer 
implementation could be done as a routine fully automated procedure. You 
have to track all variables, their variances and derivatives of the 
result from the variables, numerically. Of course that won't avoid the 
special cases, however the converted algorithm will be generally 
working. I am surprised if this is not yet implemented in matlabi, etc.


Vladimir Vassilevsky
DSP and Mixed Signal Design Consultant
http://www.abvolt.com

On Aug 16, 2:22&#4294967295;pm, Vladimir Vassilevsky <nos...@nowhere.com> wrote:
> robert bristow-johnson wrote:
> > On Aug 16, 2:43 am, glen herrmannsfeldt <g...@ugcs.caltech.edu> wrote:
>
> >>shekhar85 <chandrashekharla@n_o_s_p_a_m.gmail.com> wrote:
>
> >>>are there any good tutorials to convert floating point C
> >>>code to fixed point C code.
>
> >>Converting the code is easy. &#4294967295;Making sure that the algorithm
> >>works the same way in fixed point is a completely different
> >>question.
>
> > and you might have an ice cube's chance in hell in getting them to
> > work exactly the same. &#4294967295;sometimes algs written in float have great
> > difficulty working in fixed (like with FFT in it) without a great deal
> > of roundoff error or the risk of overflow deep in side. &#4294967295;on the other
> > hand, sometimes an alg works in fixed but not so well in float (like a
> > CIC filter).
>
> > to answer the OP's concern, doing algs in fixed-point in C requires
> > care in the size of word and what happens to the size of the result of
> > an operation. &#4294967295;and then there are the scaling factors you need to
> > worry about.
>
> > i thought maybe Randy Yates had a tutorial. &#4294967295;no?
>
> I think a conversion of an algorithm from floating point to integer
> implementation could be done as a routine fully automated procedure. You
> have to track all variables, their variances and derivatives of the
> result from the variables, numerically. Of course that won't avoid the
> special cases, however the converted algorithm will be generally
> working. I am surprised if this is not yet implemented in matlabi, etc.
>
> Vladimir Vassilevsky
> DSP and Mixed Signal Design Consultanthttp://www.abvolt.com

What happens when you come across a sqrt, atan2, log, pow, etc? Would
fixed point versions be installed automatically? If automatic
conversion code exists, please post a link.

John

On 08/16/2010 11:22 AM, Vladimir Vassilevsky wrote:
>
>
> robert bristow-johnson wrote:
>
>> On Aug 16, 2:43 am, glen herrmannsfeldt <g...@ugcs.caltech.edu> wrote:
>>
>>> shekhar85 <chandrashekharla@n_o_s_p_a_m.gmail.com> wrote:
>>>
>>>> are there any good tutorials to convert floating point C
>>>> code to fixed point C code.
>>>
>>> Converting the code is easy. Making sure that the algorithm
>>> works the same way in fixed point is a completely different
>>> question.
>>
>>
>> and you might have an ice cube's chance in hell in getting them to
>> work exactly the same. sometimes algs written in float have great
>> difficulty working in fixed (like with FFT in it) without a great deal
>> of roundoff error or the risk of overflow deep in side. on the other
>> hand, sometimes an alg works in fixed but not so well in float (like a
>> CIC filter).
>>
>> to answer the OP's concern, doing algs in fixed-point in C requires
>> care in the size of word and what happens to the size of the result of
>> an operation. and then there are the scaling factors you need to
>> worry about.
>>
>> i thought maybe Randy Yates had a tutorial. no?
>
> I think a conversion of an algorithm from floating point to integer
> implementation could be done as a routine fully automated procedure. You
> have to track all variables, their variances and derivatives of the
> result from the variables, numerically. Of course that won't avoid the
> special cases, however the converted algorithm will be generally
> working. I am surprised if this is not yet implemented in matlabi, etc.

I don't know -- I think there'd be too many variables for it to work 
well in every case.

Perhaps it could be done to work well in the linear shift-invariant 
case, however.

-- 

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Do you need to implement control loops in software?
"Applied Control Theory for Embedded Systems" was written for you.
See details at http://www.wescottdesign.com/actfes/actfes.html

Tim Wescott <tim@seemywebsite.com> wrote:
> On 08/15/2010 10:15 PM, shekhar85 wrote:

>> are there any good tutorials to convert floating point C code 
>> to fixed point C code.
 
> I probably over-complicate things, but this is a pretty broad 
> subject, and one that would be hard to write a tutorial _for_.

Well, there are tutorials on fixed point (non-integer) math.
It does seem that some have a hard time with it, even though we
all learned it in about fourth grade.  For addition, align the
radix point, for multiplication add the number of places to the
right of the radix point, and use that for the product.  It works
in decimal, binary, and any other base you want to use.

PL/I is one of the few languages with direct support for fixed
point with the radix point other than to the immediate right
of the least significant digit.  (both binary and decimal.)
PL/I allows the scale factor (radix point position) to be either
positive or negative.  In 32 bit binary, it is usual to allow
between -31 and 31 bits to the right of the binary point,
or between -15 and +15 to the right of the decimal point
(for fixed decimal arithmetic).
 
> As RBJ pointed out, some algorithms almost demand floating point, or 
> huge increases in numerical precision (such as the FFT), while some 
> algorithms depend on fixed-point tricks (such as CIC).

As I have said here before, floating point for quantities with
relative uncertainty, fixed point for absolute uncertainty.

Knuth says fixed point for typesetting and financial calculations,
two that, more or less obviously, have absolute uncertainty.
Knuth has an example of a typesetting machine that he was told was
at 5333 DPI, but turned out to be 5333+1/3 DPI.  Programming for 5333
was visibly wrong, though you might think that the error is small.

(snip) 
> But I've always converted between floating point and fixed point 
> algorithms by understanding the underlying math, and rewriting the 
> algorithm to match the different representation.  I suppose you could 
> come up with specific recipes for specific situations (IIR, FIR, etc.), 
> but I'm not sure if you could easily cover all the useful ones in a 
> document that's smaller and easier than one that just teaches you 
> the math.


Understand the math, understand the uncertainties in the input
and output data, and what happens in between.

-- glen

John wrote:

> On Aug 16, 2:22 pm, Vladimir Vassilevsky <nos...@nowhere.com> wrote:
> 

>>I think a conversion of an algorithm from floating point to integer
>>implementation could be done as a routine fully automated procedure. You
>>have to track all variables, their variances and derivatives of the
>>result from the variables, numerically. Of course that won't avoid the
>>special cases, however the converted algorithm will be generally
>>working. I am surprised if this is not yet implemented in matlabi, etc.
>>
> 
> What happens when you come across a sqrt, atan2, log, pow, etc? Would
> fixed point versions be installed automatically? 

The trivial approach is borrow the function from a software floating 
point library as is. The better solution could be having approximations 
for standard functions accurate to a given number of bits.

> If automatic
> conversion code exists, please post a link.

I don't know if there is such a tool, however I don't think that float 
to fixed point conversion is more difficult problem, then, say, 
analytical integration.


Vladimir Vassilevsky
DSP and Mixed Signal Design Consultant
http://www.abvolt.com