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Re: embedded forth

From rickman <gnuarm@gmail.com>
Newsgroups comp.lang.forth
Subject Re: embedded forth
Date 2017-01-27 23:58 -0500
Organization A noiseless patient Spider
Message-ID <o6h8a0$6ns$1@dont-email.me> (permalink)
References (6 earlier) <423bc49f-f47d-415d-80d6-53fb0472c929@googlegroups.com> <o6dhov$l5l$1@dont-email.me> <ef764024-296b-463c-b522-31366ded00da@googlegroups.com> <o6gj07$ner$1@dont-email.me> <7f7415ad-9ba0-4d9a-ba9d-d08fad5c344e@googlegroups.com>

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On 1/27/2017 7:28 PM, Ilya Tarasov wrote:
>>> The idea of CORDIC is to limit one of multiplication operands by
>>> the power of 2, so multiplier can be replaced by shifter.
>>
>> Dig into the algorithm.  It is iterative over the bits.  Each
>> operation is equivalent to the stepwise operations in a multiply.
>> Not much difference.  I don't have an implementation handy, so
>> there may be some simplification, but I think a stepwise multiply
>> is actually simpler.
>
> I think you slightly miss the interpretation. Yes, it based on vector
> rotating, represented by phase increment/decrement, which require a
> pair of multiplication. We can implement, for example sin(a+b) with
> sin table and multipliers, where a - coarse-grained angle, and b -
> fine-grained. With 1 and 0.01 degree step this gives us [0, 0.01, ...
> 89.99, 90] as an argument. CORDIC doing principally same thing, but
> rotating by angles with tangent is a power of 2. Mathematically this
> is a multiplication, but implementation can be done with shifs only.

What you aren't grasping is that what you call "shifts only" is 
virtually the same as multiplication.  When you multiply two numbers 
examining one multiplier bit at a time, the product gets shifted each 
time and the multiplicand is conditionally added each time.  Where is 
the difference?

It was touted long and loud that the CORDIC was so much more efficient 
than a multiplier when in fact it is essentially the same thing.


>> The difference is to calculate a sine calculation requires up to
>> two multiplies if you want high resolution and minimum phase
>> jitter.
>
> With CORDIC we can measure phase shift between Rubidium and Cesium
> atomic clocks :) They has about 1E-11 and 1E-14 precision
> respectively. Pure Forth system.
>
>> Multipliers are function blocks like anything else.  There are
>> FPGAs with over 10,000 multipliers.  Think those need to be
>> rationed?  Pick the chip that suits your needs.
>
> Xilinx Virtex US+ - more than 12,000. Price is very high. DSP blocks
> started from 8 in Spartan-6LX4. When designer choose an FPGA, it is
> not so good to have twice a size just for implementing function
> generators coupled with MAC blocks.

Uh, it is seldom a chip is selected because of the multiplier.  You have 
to be doing some serious math to burn all the multipliers.  You ignore 
the large LUT count of a CORDIC done at speed.  It is essentially order 
N^2 which is a *lot* of FPGA fabric.


>>> If you know another effective algorithm with hardware multipliers
>>> and exact result (not approximated), please give me a link.
>>
>> There's no such thing as "exact" digital trig solutions unless you
>> have an infinitely long word.  What do you mean by exact?
>
> All bits, up to least significant, are true. For example, Taylor
> series don't provide this property.

That is not a huge problem.  Just look up sine generation using trig 
identities.  If you want a lot of resolution you use multiplies.  If you 
need less resolution a look up table will suffice.  I recall a lot of 
work was done on this in the 70s when chips were much more limited and 
they needed to cut down the size of the calculations.  CORDIC would have 
been way too much logic so they coded the trig lookups and multiplies as 
tables.  Something like sin(a)cos(b) + cos(a)sin(b), where a would be 
the msbs of the phase and b is the lsbs.  By using separate tables for 
the various trig portions with multiplies, you can get as much 
resolution as you desire.  Two multiplies is nothing to get this 
solution and can run very fast.

I evaluated this in a spread sheet and found that once you are working 
in the area of 18 bit resolution, the linear interpolations are 
virtually perfect because they are over such a short section.  I was 
able to achieve over 100 dB of SNR with an 18 bit phase word.

When using CORDIC, how do you change the frequency?

-- 

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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