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Re: embedded forth

From rickman <gnuarm@gmail.com>
Newsgroups comp.lang.forth
Subject Re: embedded forth
Date 2017-02-14 18:13 -0500
Organization A noiseless patient Spider
Message-ID <o802qq$oud$1@dont-email.me> (permalink)
References (5 earlier) <e90a34e0-376e-4910-bd6a-96d8f16bf0bf@googlegroups.com> <o6mla6$f0l$1@dont-email.me> <e8b3a38a-d6b7-41b3-a760-fe07881bdf17@googlegroups.com> <o7ovau$66h$1@dont-email.me> <dc91cd2f-ba4b-4e8e-990b-b004bdb8dbc6@googlegroups.com>

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On 2/14/2017 2:36 PM, Gary Bergstrom wrote:
> On Sunday, February 12, 2017 at 1:30:36 AM UTC-5, rickman wrote:
>> On 1/30/2017 2:11 AM, Ilya Tarasov wrote:
>>>
>>>> I don't know why you label this an approximation.  The level of
>>>> accuracy is controlled by the tradeoff of how many of the total
>>>> phase bits you assign to a and b.  Any level of accuracy
>>>> required can be obtained.  You need to appreciate fully how
>>>> close to a straight line the small section of a sine function
>>>> is over very short angles.  It is not at all hard to get the
>>>> accuracy within a single lsb.
>>>
>>> Because of 'for small b'. This is a limitation. Approximation is
>>> not a disadvantage by default, but we may face a problem
>>> attempting to improve precision. Exact formula don't require any
>>> kind of improvement, because it provide any accuracy by default.
>>> If it is not exact, we must always answer a question 'how small b
>>> must be to obtain desired accuracy?'. Also, different ways to
>>> approximation may be applied - what about playing with polynom
>>> order?
>>
>> I did a little digging and found why there seemed to be something
>> about CORDIC that didn't quite sit.  The algorithm for CORDIC
>> iterates calculations on the sine and cosine of an angle by
>> rotating the vector, adding and subtracting from the angle until
>> the angle is zero... or approximately zero.  The way the math
>> works, the sine and cosine will always be *exact*, that is true.
>> But it will just be for the wrong angle!
>>
>> Yep, the angle is adjusted by adding and subtracting table values
>> until it is close to zero.  But each table value has a built in
>> error of up to ±0.5 lsbs.  For a 32 bit value there will be at
>> least 32 iterations which means the errors can combine to as much
>> as ±16 counts in the lsb of the phase angle.  This is on top of the
>> potential ±1 lsb due to the angle not resolving fully.  This has a
>> quirk where in the next to last iteration the angle can have
>> resolved perfectly and the final step throws it off by 1.
>>
>> Of course the rounding errors are likely uncorrelated so the
>> typical error will be 0.5*sqrt(32) or around 2.8 plus the
>> resolution error.  The analysis I've done with the trig approach
>> indicates maximum errors in the range of ±1.5 lsbs and a lower
>> typical and average.
>>
>> Is this wrong?
>
> It's been a while since I did Cordic routines, but if you're going
> from table values, given an exact angle and reading out a table value
> for the sin/cos terms to add/substract you don't have an error in the
> angle as the tables are created for specific angles, not approximate
> angles.

That is not accurate.  The tables are created for rotations so the math 
in the matrix operations are simple shifts and adds.  This does *not* 
give exact binary multiples for the actual angles.


> On the other hand, there is only so much information in the
> amplitude. Try to make a sine wave oscillator run continuously by
> rotating for a few 100 or 1000 million cycles and your amplitudes
> won't be very accurate anymore. About doing a minimax polynomial: My
> lowly DSP56k cpu can be made to evaluate an nth order polynomial in
> n+5 cycles.  If you're going for a processor rather than a hardware
> solution, it's difficult to beat this sort of speed. But if you don't
> have a multiply (who doesn't?) or you're deeply embedded within a
> logic array, then Cordic can make a lot of sense. Generating near
> zero distortion audio sine waves is an interesting hobby.

I'm not clear on what the amplitude error you are referring to would be. 
  Both methods track time with a phase incrementer and use the circuits 
being discussed to convert that to a sine value.  The only error in the 
phase over many cycles would be the limitation of the size of the phase 
step value.  The amplitude would be true to the accuracy of the sine 
conversion.

-- 

Rick C

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Thread

embedded forth Dale Scott <dalescottnet@gmail.com> - 2017-01-21 11:27 -0800
  Re: embedded forth Paul Rubin <no.email@nospam.invalid> - 2017-01-21 11:31 -0800
  Re: embedded forth stephen@mpeforth.com - 2017-01-22 00:52 -0800
  Re: embedded forth anton@mips.complang.tuwien.ac.at (Anton Ertl) - 2017-01-22 17:09 +0000
    Re: embedded Forth Dale Scott <dalescottnet@gmail.com> - 2017-01-22 09:43 -0800
      Re: embedded Forth stephen@mpeforth.com - 2017-01-22 12:19 -0800
      Re: embedded Forth albert@cherry.spenarnc.xs4all.nl (Albert van der Horst) - 2017-01-22 21:25 +0100
      Re: embedded Forth john <anon@example.com> - 2017-01-22 21:04 +0000
        Re: embedded Forth "Elizabeth D. Rather" <erather@forth.com> - 2017-01-22 12:30 -1000
        Re: embedded Forth hughaguilar96@gmail.com - 2017-01-22 20:45 -0800
      Re: embedded Forth stephen@mpeforth.com - 2017-01-22 14:08 -0800
        Re: embedded Forth Paul Rubin <no.email@nospam.invalid> - 2017-01-22 14:55 -0800
          Re: embedded Forth Dale Scott <dalescottnet@gmail.com> - 2017-01-22 20:41 -0800
            Re: embedded Forth Paul Rubin <no.email@nospam.invalid> - 2017-01-22 21:19 -0800
      Re: embedded Forth hughaguilar96@gmail.com - 2017-01-22 21:36 -0800
        Re: embedded Forth Dale Scott <dalescottnet@gmail.com> - 2017-01-22 22:09 -0800
          Re: embedded Forth rickman <gnuarm@gmail.com> - 2017-01-23 04:15 -0500
            Re: embedded Forth Dale Scott <dalescottnet@gmail.com> - 2017-01-23 08:41 -0800
              Re: embedded Forth rickman <gnuarm@gmail.com> - 2017-01-23 14:32 -0500
                Re: embedded Forth Dale Scott <dalescottnet@gmail.com> - 2017-01-23 11:53 -0800
                Re: embedded Forth rickman <gnuarm@gmail.com> - 2017-01-23 15:10 -0500
              Re: embedded Forth Paul Rubin <no.email@nospam.invalid> - 2017-01-23 14:34 -0800
                Re: embedded Forth Andrew Haley <andrew29@littlepinkcloud.invalid> - 2017-01-24 03:14 -0600
        Re: embedded Forth rickman <gnuarm@gmail.com> - 2017-01-23 03:43 -0500
          Re: embedded Forth john <anon@example.com> - 2017-01-23 10:32 +0000
          keep secrets (was Re: embedded Forth) "Wolfgang Allinger" <all2001@spambog.com> - 2017-01-23 08:58 -0300
            Re: keep secrets (was Re: embedded Forth) Rod Pemberton <NeedNotReplyHere@xrsevnneqk.cem> - 2017-01-23 07:47 -0500
              Re: keep secrets (was Re: embedded Forth) "Wolfgang Allinger" <all2001@spambog.com> - 2017-01-23 18:18 -0300
                Re: keep secrets (was Re: embedded Forth) rickman <gnuarm@gmail.com> - 2017-01-23 19:15 -0500
            Re: keep secrets (was Re: embedded Forth) rickman <gnuarm@gmail.com> - 2017-01-23 14:38 -0500
              Re: keep secrets (was Re: embedded Forth) "Wolfgang Allinger" <all2001@spambog.com> - 2017-01-23 18:43 -0300
                Re: keep secrets (was Re: embedded Forth) rickman <gnuarm@gmail.com> - 2017-01-23 19:48 -0500
                Re: keep secrets (was Re: embedded Forth) "Elizabeth D. Rather" <erather@forth.com> - 2017-01-23 16:30 -1000
                Re: keep secrets (was Re: embedded Forth) rickman <gnuarm@gmail.com> - 2017-01-23 22:23 -0500
  Re: embedded forth rickman <gnuarm@gmail.com> - 2017-01-22 13:44 -0500
    Re: embedded forth Paul Rubin <no.email@nospam.invalid> - 2017-01-22 13:38 -0800
      Re: embedded forth rickman <gnuarm@gmail.com> - 2017-01-23 00:45 -0500
        Re: embedded forth Dale Scott <dalescottnet@gmail.com> - 2017-01-22 22:44 -0800
          Re: embedded forth Paul Rubin <no.email@nospam.invalid> - 2017-01-23 00:48 -0800
          Re: embedded forth rickman <gnuarm@gmail.com> - 2017-01-23 03:51 -0500
      Re: embedded forth john <anon@example.com> - 2017-01-23 10:02 +0000
    Re: embedded forth anton@mips.complang.tuwien.ac.at (Anton Ertl) - 2017-01-23 09:01 +0000
      Re: embedded forth albert@cherry.spenarnc.xs4all.nl (Albert van der Horst) - 2017-01-23 13:05 +0100
        Re: embedded forth rickman <gnuarm@gmail.com> - 2017-01-23 14:40 -0500
          Re: embedded forth Mark Wills <markwills1970@gmail.com> - 2017-01-24 01:12 -0800
          Re: embedded forth albert@cherry.spenarnc.xs4all.nl (Albert van der Horst) - 2017-01-24 14:38 +0100
            Re: embedded forth rickman <gnuarm@gmail.com> - 2017-01-24 19:51 -0500
              Re: embedded forth albert@cherry.spenarnc.xs4all.nl (Albert van der Horst) - 2017-01-25 11:34 +0100
                Re: embedded forth rickman <gnuarm@gmail.com> - 2017-01-25 22:13 -0500
                Re: embedded forth albert@cherry.spenarnc.xs4all.nl (Albert van der Horst) - 2017-01-26 11:36 +0100
                Re: embedded forth rickman <gnuarm@gmail.com> - 2017-01-26 14:07 -0500
              Re: embedded forth Ilya Tarasov <ilya74.tarasov@gmail.com> - 2017-01-26 00:19 -0800
                Re: embedded forth rickman <gnuarm@gmail.com> - 2017-01-26 14:15 -0500
                Re: embedded forth Ilya Tarasov <ilya74.tarasov@gmail.com> - 2017-01-27 13:08 -0800
                Re: embedded forth rickman <gnuarm@gmail.com> - 2017-01-27 17:54 -0500
                Re: embedded forth Paul Rubin <no.email@nospam.invalid> - 2017-01-27 15:29 -0800
                Re: embedded forth Ilya Tarasov <ilya74.tarasov@gmail.com> - 2017-01-27 16:28 -0800
                Re: embedded forth rickman <gnuarm@gmail.com> - 2017-01-27 23:58 -0500
                Re: embedded forth Ilya Tarasov <ilya74.tarasov@gmail.com> - 2017-01-28 11:58 -0800
                Re: embedded forth rickman <gnuarm@gmail.com> - 2017-01-28 15:36 -0500
                Re: embedded forth Ilya Tarasov <ilya74.tarasov@gmail.com> - 2017-01-28 15:05 -0800
                Re: embedded forth Paul Rubin <no.email@nospam.invalid> - 2017-01-28 15:57 -0800
                Re: embedded forth rickman <gnuarm@gmail.com> - 2017-01-28 21:51 -0500
                Re: embedded forth Ilya Tarasov <ilya74.tarasov@gmail.com> - 2017-01-29 09:53 -0800
                Re: embedded forth albert@cherry.spenarnc.xs4all.nl (Albert van der Horst) - 2017-01-29 19:32 +0100
                Re: embedded forth Ilya Tarasov <ilya74.tarasov@gmail.com> - 2017-01-29 11:53 -0800
                Re: embedded forth rickman <gnuarm@gmail.com> - 2017-01-30 01:10 -0500
                Re: embedded forth Ilya Tarasov <ilya74.tarasov@gmail.com> - 2017-01-29 23:11 -0800
                Re: embedded forth Paul Rubin <no.email@nospam.invalid> - 2017-01-29 23:34 -0800
                Re: embedded forth albert@cherry.spenarnc.xs4all.nl (Albert van der Horst) - 2017-01-30 12:42 +0100
                Re: embedded forth albert@cherry.spenarnc.xs4all.nl (Albert van der Horst) - 2017-01-30 12:36 +0100
                Re: embedded forth ctmalan@gmail.com - 2017-01-30 11:02 -0800
                Re: embedded forth Paul Rubin <no.email@nospam.invalid> - 2017-01-30 11:04 -0800
                Re: embedded forth Andrew Haley <andrew29@littlepinkcloud.invalid> - 2017-01-31 04:34 -0600
                Re: embedded forth Ilya Tarasov <ilya74.tarasov@gmail.com> - 2017-01-30 12:15 -0800
                Re: embedded forth rickman <gnuarm@gmail.com> - 2017-01-30 10:15 -0500
                Re: embedded forth Ilya Tarasov <ilya74.tarasov@gmail.com> - 2017-01-30 12:20 -0800
                Re: embedded forth Paul Rubin <no.email@nospam.invalid> - 2017-01-30 14:09 -0800
                Re: embedded forth albert@cherry.spenarnc.xs4all.nl (Albert van der Horst) - 2017-01-31 03:04 +0100
                Re: embedded forth Paul Rubin <no.email@nospam.invalid> - 2017-01-30 20:19 -0800
                Re: embedded forth rickman <gnuarm@gmail.com> - 2017-01-30 17:10 -0500
                Re: embedded forth Ilya Tarasov <ilya74.tarasov@gmail.com> - 2017-01-30 14:38 -0800
                Re: embedded forth rickman <gnuarm@gmail.com> - 2017-01-30 23:09 -0500
                Re: embedded forth Ilya Tarasov <ilya74.tarasov@gmail.com> - 2017-01-31 09:32 -0800
                Re: embedded forth rickman <gnuarm@gmail.com> - 2017-02-08 18:22 -0500
                Re: embedded forth Ilya Tarasov <ilya74.tarasov@gmail.com> - 2017-02-09 01:46 -0800
                Re: embedded forth rickman <gnuarm@gmail.com> - 2017-02-09 05:11 -0500
                Re: embedded forth rickman <gnuarm@gmail.com> - 2017-02-12 01:30 -0500
                Re: embedded forth Ilya Tarasov <ilya74.tarasov@gmail.com> - 2017-02-12 10:21 -0800
                Re: embedded forth rickman <gnuarm@gmail.com> - 2017-02-12 19:37 -0500
                Re: embedded forth Ilya Tarasov <ilya74.tarasov@gmail.com> - 2017-02-14 13:26 -0800
                Re: embedded forth Gary Bergstrom <forthprgrmr@gmail.com> - 2017-02-14 11:36 -0800
                Re: embedded forth rickman <gnuarm@gmail.com> - 2017-02-14 18:13 -0500
                Re: embedded forth rickman <gnuarm@gmail.com> - 2017-01-28 21:51 -0500
                Re: embedded forth Ilya Tarasov <ilya74.tarasov@gmail.com> - 2017-01-29 10:20 -0800
                Re: embedded forth Cecil Bayona <cbayona@cbayona.com> - 2017-01-29 12:38 -0600
                Re: embedded forth Ilya Tarasov <ilya74.tarasov@gmail.com> - 2017-01-29 11:49 -0800
                Re: embedded forth rickman <gnuarm@gmail.com> - 2017-02-04 04:22 -0500
                Re: embedded forth Ilya Tarasov <ilya74.tarasov@gmail.com> - 2017-02-04 17:54 -0800
                Re: embedded forth hughaguilar96@gmail.com - 2017-02-04 20:26 -0800
                Re: embedded forth Ilya Tarasov <ilya74.tarasov@gmail.com> - 2017-02-05 07:53 -0800
                Re: embedded forth hughaguilar96@gmail.com - 2017-02-05 11:08 -0800
                Re: embedded forth hughaguilar96@gmail.com - 2017-02-05 11:39 -0800
                Re: embedded forth Ilya Tarasov <ilya74.tarasov@gmail.com> - 2017-02-08 06:46 -0800
                Re: embedded forth luser droog <mijoryx@yahoo.com> - 2017-02-13 19:17 -0800
                Re: embedded forth Ilya Tarasov <ilya74.tarasov@gmail.com> - 2017-02-15 06:23 -0800
                Re: embedded forth hughaguilar96@gmail.com - 2017-02-15 11:09 -0800
                Re: embedded forth Ilya Tarasov <ilya74.tarasov@gmail.com> - 2017-02-15 15:24 -0800
                Re: embedded forth jkn_gg@nicorp.f9.co.uk - 2017-02-16 09:49 -0800
                Re: embedded forth hughaguilar96@gmail.com - 2017-02-17 09:12 -0800
                Re: embedded forth Ilya Tarasov <ilya74.tarasov@gmail.com> - 2017-02-17 12:47 -0800
                Re: embedded forth hughaguilar96@gmail.com - 2017-02-17 16:18 -0800
                Re: embedded forth luser droog <mijoryx@yahoo.com> - 2017-02-16 08:43 -0800
                Re: embedded forth Alex <alex@rivadpm.com> - 2017-02-05 20:47 +0000
                Re: embedded forth hughaguilar96@gmail.com - 2017-02-05 13:36 -0800
                Re: embedded forth Alex <alex@rivadpm.com> - 2017-02-05 23:18 +0000
                Re: embedded forth hughaguilar96@gmail.com - 2017-02-05 21:10 -0800
                Re: embedded forth Alex <alex@rivadpm.com> - 2017-02-06 11:12 +0000
                Re: embedded forth hughaguilar96@gmail.com - 2017-02-05 21:15 -0800
                Re: embedded forth hughaguilar96@gmail.com - 2017-02-05 22:45 -0800
                Re: embedded forth albert@cherry.spenarnc.xs4all.nl (Albert van der Horst) - 2017-02-06 12:04 +0100
                Re: embedded forth Ilya Tarasov <ilya74.tarasov@gmail.com> - 2017-02-08 03:08 -0800
                Re: embedded forth rickman <gnuarm@gmail.com> - 2017-02-08 06:39 -0500
                Re: embedded forth Ilya Tarasov <ilya74.tarasov@gmail.com> - 2017-02-08 07:15 -0800
                Re: embedded forth rickman <gnuarm@gmail.com> - 2017-02-08 15:49 -0500
                Re: embedded forth Ilya Tarasov <ilya74.tarasov@gmail.com> - 2017-02-09 01:14 -0800
                Re: embedded forth rickman <gnuarm@gmail.com> - 2017-02-09 05:19 -0500
                Re: embedded forth Ilya Tarasov <ilya74.tarasov@gmail.com> - 2017-02-09 03:48 -0800
                Re: embedded forth rickman <gnuarm@gmail.com> - 2017-02-05 16:08 -0500
                Re: embedded forth rickman <gnuarm@gmail.com> - 2017-02-07 21:59 -0500
                Re: embedded forth albert@cherry.spenarnc.xs4all.nl (Albert van der Horst) - 2017-01-28 11:10 +0100
                Re: embedded forth rickman <gnuarm@gmail.com> - 2017-01-28 06:15 -0500
                Re: embedded forth albert@cherry.spenarnc.xs4all.nl (Albert van der Horst) - 2017-01-28 19:48 +0100
                Re: embedded forth rickman <gnuarm@gmail.com> - 2017-01-28 14:37 -0500
                Re: embedded forth mhx@iae.nl - 2017-01-28 07:48 -0800
                Re: embedded forth albert@cherry.spenarnc.xs4all.nl (Albert van der Horst) - 2017-01-28 19:53 +0100
                Re: embedded forth mhx@iae.nl - 2017-01-28 15:49 -0800
        Re: embedded forth "Wolfgang Allinger" <all2001@spambog.com> - 2017-01-23 18:46 -0300

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