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Now, i have googled this some, with not much as far as results, so I though I would ask here to see what kind of luck I would have. I am using the Analog Devices ADuC831 (8052 ISA) part to do data acquisition and transmission. I have some data that is being held as floating point (single precision IEEE 754 format). Some of this data needs to be outputted to serial on request. This is where my request comes in. Currently I am using sprintf() to format this output into my buffer. HOWEVER, the footprint of this code is making it less than desirable to use (over 1100 bytes of code space and nearly 30 bytes of memory). So I am looking to do the output on my own. And to this means, I have succeeded, to an extent. So far I have removed my need for sprintf() in printing HEX format, as well as ints and chars. My problem is with floats. I have not yet attempted standard notation: 3.1415926 But I did write an exponent formula. 3.141593E+00 I even got the rounding. HOWEVER, this is using simple multiplies and divides, by 10, to achieve it's goals. And this introduces my problem. Since a few of the numbers go out to 6 digits of precision, I am having problems with these last digits outputting correctly. For example: Value entered: 6.791775E-08 Value displayed: 6.791777E-08 Hex value on chip: 0x3391DA2E (6.7917753e-8) Clearly, the entered value is being stored correctly and the displayed value, while close, is just slightly off. So is there a way to do this without this error induced by my multiplications by 10 (and still not using sprintf()? RonB -------------------------------------------------- "It is human nature to take shortcuts in thinking" --------------------------------------------------

```
On Tue, 27 Mar 2007 15:45:49 -0500, Ron Blancarte
<r...@---TAKETHISOUT---.blancarte.com> wrote:
>Now, i have googled this some, with not much as far as results, so I
>though I would ask here to see what kind of luck I would have.
>
>I am using the Analog Devices ADuC831 (8052 ISA) part to do data
>acquisition and transmission. I have some data that is being held as
>floating point (single precision IEEE 754 format). Some of this data
>needs to be outputted to serial on request. This is where my request
>comes in. Currently I am using sprintf() to format this output into
>my buffer. HOWEVER, the footprint of this code is making it less than
>desirable to use (over 1100 bytes of code space and nearly 30 bytes of
>memory). So I am looking to do the output on my own.
>
>And to this means, I have succeeded, to an extent. So far I have
>removed my need for sprintf() in printing HEX format, as well as ints
>and chars. My problem is with floats. I have not yet attempted
>standard notation:
> 3.1415926
>But I did write an exponent formula.
> 3.141593E+00
>I even got the rounding. HOWEVER, this is using simple multiplies and
>divides, by 10, to achieve it's goals. And this introduces my
>problem. Since a few of the numbers go out to 6 digits of precision,
>I am having problems with these last digits outputting correctly. For
>example:
>
>Value entered: 6.791775E-08
>Value displayed: 6.791777E-08
>Hex value on chip: 0x3391DA2E (6.7917753e-8)
>
>Clearly, the entered value is being stored correctly and the displayed
>value, while close, is just slightly off. So is there a way to do
>this without this error induced by my multiplications by 10 (and still
>not using sprintf()?
>
Depending on exactly which development environment you are using,
check if you have the ftoa function available. Quite a lot of the
compilers for the 8 bit MCUs include this function.
Do you really need to store the information in floating point format ?
The 8051 is not particularly suitable for handling floating point.
Keeping the data in integer or fixed point format, and only converting
to floating point when necessary should help reduce your code
footprint.
Regards
Anton Erasmus
```

```
"Ron Blancarte" <r...@---TAKETHISOUT---.blancarte.com> wrote in message
news:c...@4ax.com...
> Clearly, the entered value is being stored correctly and the displayed
> value, while close, is just slightly off. So is there a way to do
> this without this error induced by my multiplications by 10 (and still
> not using sprintf()?
The correct way of doing this is to only do one normalizing multiply
or divide by a power of 10, so you only get one roundoff error. Powers
of 10 are exact in floats up to 10^10, for a wider dynamic range you
get multiple roundoff errors unless you use more precision. After
normalization you use integer arithmetic to extract the digits.
My advice would be to use integer-only arithmetic for normalization,
this way you get less roundoff error over much larger ranges.
Getting this right is non-trivial, that is why floating point printf is so
large. If you don't mind a large roundoff error then you can make
it smaller, but it is extremely hard to make it both small and accurate...
Wilco
```

Wilco Dijkstra wrote: > "Ron Blancarte" <r...@---TAKETHISOUT---.blancarte.com> wrote in message > news:c...@4ax.com... > >>Clearly, the entered value is being stored correctly and the displayed >>value, while close, is just slightly off. So is there a way to do >>this without this error induced by my multiplications by 10 (and still >>not using sprintf()? > > The correct way of doing this is to only do one normalizing multiply > or divide by a power of 10, so you only get one roundoff error. Powers > of 10 are exact in floats up to 10^10, for a wider dynamic range you > get multiple roundoff errors unless you use more precision. After > normalization you use integer arithmetic to extract the digits. Agreed. > My advice would be to use integer-only arithmetic for normalization, > this way you get less roundoff error over much larger ranges. Hmmm, I don't understand the recommendation here. I would say multiply or divide by the proper (exact) power of 10 to get a number in the range -9999999..9999999, add a rounding factor (-0.5 or +0.5), convert to a 32-bit integer, convert that to a 7-digit character string, then format. -- Thad

```
On Tue, 27 Mar 2007 23:19:29 +0200 (while OU was sucking), Anton
Erasmus wrote:
>On Tue, 27 Mar 2007 15:45:49 -0500, Ron Blancarte
><r...@---TAKETHISOUT---.blancarte.com> wrote:
>
>>Now, i have googled this some, with not much as far as results, so I
>>though I would ask here to see what kind of luck I would have.
>>
>>I am using the Analog Devices ADuC831 (8052 ISA) part to do data
>>acquisition and transmission. I have some data that is being held as
>>floating point (single precision IEEE 754 format). Some of this data
>>needs to be outputted to serial on request. This is where my request
>>comes in. Currently I am using sprintf() to format this output into
>>my buffer. HOWEVER, the footprint of this code is making it less than
>>desirable to use (over 1100 bytes of code space and nearly 30 bytes of
>>memory). So I am looking to do the output on my own.
>>
>>And to this means, I have succeeded, to an extent. So far I have
>>removed my need for sprintf() in printing HEX format, as well as ints
>>and chars. My problem is with floats. I have not yet attempted
>>standard notation:
>> 3.1415926
>>But I did write an exponent formula.
>> 3.141593E+00
>>I even got the rounding. HOWEVER, this is using simple multiplies and
>>divides, by 10, to achieve it's goals. And this introduces my
>>problem. Since a few of the numbers go out to 6 digits of precision,
>>I am having problems with these last digits outputting correctly. For
>>example:
>>
>>Value entered: 6.791775E-08
>>Value displayed: 6.791777E-08
>>Hex value on chip: 0x3391DA2E (6.7917753e-8)
>>
>>Clearly, the entered value is being stored correctly and the displayed
>>value, while close, is just slightly off. So is there a way to do
>>this without this error induced by my multiplications by 10 (and still
>>not using sprintf()?
>>
>
>Depending on exactly which development environment you are using,
>check if you have the ftoa function available. Quite a lot of the
>compilers for the 8 bit MCUs include this function.
>Do you really need to store the information in floating point format ?
>The 8051 is not particularly suitable for handling floating point.
>Keeping the data in integer or fixed point format, and only converting
>to floating point when necessary should help reduce your code
>footprint.
Well I hvae to pick my poison. Since this is for a measurement
application, that does involve trig, I will take my chances with FP in
this case. Besides, that portion of my code is not the problem.
Around half of my code (in size) is a command handler, of which this
output is part of. I have been able to take chunks out of it slowly,
cutting nearly 8k out of it, with some optimization and pulling out
standard functions (like replacing strcmp with my own version).
And unfortunatly Keil doesn't appear to have the ftoa() funciton
included w/ it. So that is out.
RonB
--------------------------------------------------
"It is human nature to take shortcuts in thinking"
--------------------------------------------------
```

```
On Tue, 27 Mar 2007 15:45:49 -0500, Ron Blancarte
<r...@---TAKETHISOUT---.blancarte.com> wrote:
>I am using the Analog Devices ADuC831 (8052 ISA) part to do data
>acquisition and transmission. I have some data that is being held as
>floating point (single precision IEEE 754 format). Some of this data
>needs to be outputted to serial on request.
Is this serial port connected to a bigger system, such as a PC ?
Could you run your own receiver program on this system ?
If this is the case and you don't want to send binary data directly
over the UART, simply split the 32 bit float into eight 4 bit fields,
convert each field to hex and send over the serial line. At the
receiver end of the line, do the opposite conversion. Since the
receiving system would most likely also use IEEE 754 floats, no extra
conversion on the receiver end is needed and the value can be
displayed using printf on the receiving device.
Paul
```

```
> And unfortunatly Keil doesn't appear to have the ftoa() funciton
> included w/ it. So that is out.
A moderate amount of digging on the web will get you loads of C source code
for just about all those classic runtime C lib functions that you're
missing. That stuff has been in the public domain for years.
There are efficient and not so efficient versions of sprintf() and ftoa() to
be found so you'll want to evaluate several to find the one that suits your
needs. The bonus is that you're getting source code so you can customize to
your heart's content.
JJS
```

```
"Thad Smith" <T...@acm.org> wrote in message
news:4609b2ec$0$47168$8...@auth.newsreader.octanews.com...
> Wilco Dijkstra wrote:
>> "Ron Blancarte" <r...@---TAKETHISOUT---.blancarte.com> wrote in message
>> news:c...@4ax.com...
>>
>>>Clearly, the entered value is being stored correctly and the displayed
>>>value, while close, is just slightly off. So is there a way to do
>>>this without this error induced by my multiplications by 10 (and still
>>>not using sprintf()?
>>
>> The correct way of doing this is to only do one normalizing multiply
>> or divide by a power of 10, so you only get one roundoff error. Powers
>> of 10 are exact in floats up to 10^10, for a wider dynamic range you
>> get multiple roundoff errors unless you use more precision. After
>> normalization you use integer arithmetic to extract the digits.
>
> Agreed.
>
>> My advice would be to use integer-only arithmetic for normalization,
>> this way you get less roundoff error over much larger ranges.
>
> Hmmm, I don't understand the recommendation here. I would say multiply or divide by the
> proper (exact) power of 10 to get a number in the range -9999999..9999999, add a
> rounding factor (-0.5 or +0.5), convert to a 32-bit integer, convert that to a 7-digit
> character string, then format.
What I mean is that if you do the normalization multiply/divide using
integer arithmetic, you get more precision, eg. 32 bits rathern than 24
when using float. This gives you larger powers of 10 that can be
represented exactly and a more accurate result after normalization
(and more control over rounding). Integer arithmetic makes even more
sense if you use emulated floating point.
Wilco
```

```
fcvt and ecvt might also bear thinking about.
"John Speth" <j...@yahoo.com> wrote in message
news:eudu8n$s8b$1...@aioe.org...
>> And unfortunatly Keil doesn't appear to have the ftoa() funciton
>> included w/ it. So that is out.
>
> A moderate amount of digging on the web will get you loads of C source
> code for just about all those classic runtime C lib functions that you're
> missing. That stuff has been in the public domain for years.
>
> There are efficient and not so efficient versions of sprintf() and ftoa()
> to be found so you'll want to evaluate several to find the one that suits
> your needs. The bonus is that you're getting source code so you can
> customize to your heart's content.
>
> JJS
>
>
```

```
"Wilco Dijkstra" <W...@ntlworld.com> writes:
> "Thad Smith" <T...@acm.org> wrote in message
> > Wilco Dijkstra wrote:
> >> "Ron Blancarte" <r...@---TAKETHISOUT---.blancarte.com> wrote in message
> >>
> >>>Clearly, the entered value is being stored correctly and the displayed
> >>>value, while close, is just slightly off. So is there a way to do
> >>>this without this error induced by my multiplications by 10 (and still
> >>>not using sprintf()?
> >>
> >> The correct way of doing this is to only do one normalizing multiply
> >> or divide by a power of 10, so you only get one roundoff error. Powers
> >> of 10 are exact in floats up to 10^10, for a wider dynamic range you
> >> get multiple roundoff errors unless you use more precision. After
> >> normalization you use integer arithmetic to extract the digits.
> >
> > Agreed.
> >
> >> My advice would be to use integer-only arithmetic for normalization,
> >> this way you get less roundoff error over much larger ranges.
> >
> > Hmmm, I don't understand the recommendation here. I would say multiply or divide by the
> > proper (exact) power of 10 to get a number in the range -9999999..9999999, add a
> > rounding factor (-0.5 or +0.5), convert to a 32-bit integer, convert that to a 7-digit
> > character string, then format.
>
> What I mean is that if you do the normalization multiply/divide using
> integer arithmetic, you get more precision, eg. 32 bits rathern than 24
> when using float. This gives you larger powers of 10 that can be
> represented exactly and a more accurate result after normalization
> (and more control over rounding). Integer arithmetic makes even more
> sense if you use emulated floating point.
And don't forget to look at the accuracy of the data
before getting wound around the axle of precision.
If the source of the data is an 8-bit ADC, for
instance, no amount of fancy footwork is going to
get you three decimal place accuracy. If the
problem is ill-conditioned, not much of anything
will help.
```