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Re: embedded forth

From rickman <gnuarm@gmail.com>
Newsgroups comp.lang.forth
Subject Re: embedded forth
Date 2017-01-27 17:54 -0500
Organization A noiseless patient Spider
Message-ID <o6gj07$ner$1@dont-email.me> (permalink)
References (4 earlier) <o67ld7$dg5$1@cherry.spenarnc.xs4all.nl> <o68smu$otg$1@dont-email.me> <423bc49f-f47d-415d-80d6-53fb0472c929@googlegroups.com> <o6dhov$l5l$1@dont-email.me> <ef764024-296b-463c-b522-31366ded00da@googlegroups.com>

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On 1/27/2017 4:08 PM, Ilya Tarasov wrote:
> четверг, 26 января 2017 г., 22:15:18 UTC+3 пользователь rickman
> написал:
>> On 1/26/2017 3:19 AM, Ilya Tarasov wrote:
>>>> BTW, sine generation is *very* easy to do in a PLD and can be
>>>> made to run *very* fast.  I did some work on this a while back
>>>> and a DDS in an FPGA can be made using multipliers instead of a
>>>> large lookup table to minimize phase noise.  In essence you can
>>>> get any noise level in the digital logic that you require and
>>>> generate samples at 100s of MHz.  :)
>>>
>>> You may take a look on CORDIC algorithm as well. It is another
>>> example of a module, not very effective for generic MCU, but
>>> perfect for FPGA. CORDIC IP-core can provide one bit of sin/cos
>>> per clock cycle (pipelining is allowed too), so it is possible to
>>> have 16 or 32-bit sine wave with 200+ MHz clock speed. No
>>> multipliers are needed.
>>
>> When I see the claim of the CORDIC algorithm not needing
>> multipliers I have to smile.  No, technically the CORDIC algorithm
>> does not need a single multiplier.  But the algorithm performs an
>> operation that is
>
> 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. 
The difference is to calculate a sine calculation requires up to two 
multiplies if you want high resolution and minimum phase jitter.


>> functionally equivalent to a multiply, N operations on N bit
>> quantities which is order N**2 complexity.  The difference is that
>> multiplication is typically supported by hardware and is *very*
>> fast while the CORDIC algorithm must be done step by step and so is
>> much less efficient.  In FPGAs with hard IP multipliers the CORDIC
>> uses much more space than just using the hard IP.  In software the
>> CORDIC takes N steps where N is the number of bits and a multiply
>> is often a single instruction.
>
> Pipelined version require one cycle per output with N stages of
> pipeline. Size is N times larger, of course.

Yep.  Very similar to a multiplier.


>> The CORDIC algorithm saw much more use a decades or two ago when
>> dedicated multipliers were much less common.  Now the CORDIC
>> algorithm is typically used in niche applications where there is
>> some limitation on using a multiplier.
>
> For FPGA, there is a balance between cells, memory and multipliers.
> For DSP system, there DSP block are key components, it is likely you
> will count every DSP48 block and don't be able to spent some of them
> to sine wave generation. Logic cells may be free and CORDIC is a good
> solution in this case.

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.


> 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?

-- 

Rick C

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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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