Re: The problem with implementation defined behaviour.

From	Bernd Paysan <bernd.paysan@gmx.de>
Newsgroups	comp.lang.forth
Subject	Re: The problem with implementation defined behaviour.
Date	2016-04-02 21:43 +0000
Organization	A noiseless patient Spider
Message-ID	<ndpedu$3ag$1@dont-email.me> (permalink)
References	(8 earlier) <h4idndgL64APGWDLnZ2dnUU7-NnNnZ2d@supernews.com> <fbf6d82f-953c-45f1-a918-4da4a9df45b7@googlegroups.com> <2016Apr1.134404@mips.complang.tuwien.ac.at> <ndmqlj$ek8$3@dont-email.me> <lLednUgdjbXMamLLnZ2dnUU7-XudnZ2d@supernews.com>

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Am Sat, 02 Apr 2016 11:46:09 -0500 schrieb Andrew Haley:

> Bernd Paysan <bernd.paysan@gmx.de> wrote:
>> On the 4stack processor, I decided against implementing a divider unit,
>> and for Goldschmidt division: first find-first-one in the divider, then
>> shift it so that it is between 0.5 and 0.9999 (decimal point left of
>> the actual number), compute the inverse (which is now between 1 and
>> 1.9999, top bit actually not represented), multiply, and then shift
>> right.
> 
> Interesting.  How do you compute the inverse?  A lookup table, perhaps?

After normalizing the number and excluding division by zero, you use the 
top n bits (e.g. top 8 bits) to get an approximate inverse.  And then you 
continue either with Goldschmidt or Newton-Raphson (both are quite 
similar algorithms) to double the precision of that approximation per 
round.  Both use the same number of multiplications (two per iteration), 
but Goldschmidt can use the multiplications in parallel, which means the 
cost is much closer to one multiplication on pipelined architectures; so 
the latency is one multiplication per iteration.

Rounding can be tricky to get exactly what you want, so I compute the 
remainder, too, and adjust off-by-one results if necessary.  If you are 
careful with your initial approximation table, most results are rounded 
good enough.

-- 
Bernd Paysan
"If you want it done right, you have to do it yourself"
net2o ID: kQusJzA;7*?t=uy@X}1GWr!+0qqp_Cn176t4(dQ*
http://bernd-paysan.de/

Thread

The problem with implementation defined behaviour. Albert van der Horst <albert@spenarnc.xs4all.nl> - 2016-03-29 14:39 +0000
  Re: The problem with implementation defined behaviour. anton@mips.complang.tuwien.ac.at (Anton Ertl) - 2016-03-29 16:20 +0000
    Re: The problem with implementation defined behaviour. "Elizabeth D. Rather" <erather@forth.com> - 2016-03-29 09:16 -1000
      Re: The problem with implementation defined behaviour. Bernd Paysan <bernd.paysan@gmx.de> - 2016-03-30 00:06 +0000
        Re: The problem with implementation defined behaviour. mhx@iae.nl - 2016-03-29 22:09 -0700
          Re: The problem with implementation defined behaviour. "Elizabeth D. Rather" <erather@forth.com> - 2016-03-29 21:37 -1000
          Re: The problem with implementation defined behaviour. Paul Rubin <no.email@nospam.invalid> - 2016-03-30 00:48 -0700
            Re: The problem with implementation defined behaviour. Paul Rubin <no.email@nospam.invalid> - 2016-03-30 00:48 -0700
          Re: The problem with implementation defined behaviour. anton@mips.complang.tuwien.ac.at (Anton Ertl) - 2016-03-30 07:59 +0000
            Re: The problem with implementation defined behaviour. mhx@iae.nl - 2016-03-30 10:16 -0700
              Re: The problem with implementation defined behaviour. Bernd Paysan <bernd.paysan@gmx.de> - 2016-03-30 23:43 +0000
                Re: The problem with implementation defined behaviour. mhx@iae.nl - 2016-03-31 06:01 -0700
                Re: The problem with implementation defined behaviour. Bernd Paysan <bernd.paysan@gmx.de> - 2016-04-01 21:36 +0000
                Re: The problem with implementation defined behaviour. mhx@iae.nl - 2016-04-01 14:57 -0700
                Re: The problem with implementation defined behaviour. Bernd Paysan <bernd.paysan@gmx.de> - 2016-04-01 21:59 +0000
                Re: The problem with implementation defined behaviour. mhx@iae.nl - 2016-04-02 00:51 -0700
                Re: The problem with implementation defined behaviour. anton@mips.complang.tuwien.ac.at (Anton Ertl) - 2016-04-01 08:25 +0000
                Re: The problem with implementation defined behaviour. Bernd Paysan <bernd.paysan@gmx.de> - 2016-04-01 21:32 +0000
                division performance (was: The problem with implementation defined ...) anton@mips.complang.tuwien.ac.at (Anton Ertl) - 2016-04-05 11:12 +0000
                Re: division performance (was: The problem with implementation defined ...) Bernd Paysan <bernd.paysan@gmx.de> - 2016-04-05 20:45 +0000
                Re: division performance (was: The problem with implementation defined ...) anton@mips.complang.tuwien.ac.at (Anton Ertl) - 2016-04-06 10:03 +0000
                Re: division performance (was: The problem with implementation defined ...) Bernd Paysan <bernd.paysan@gmx.de> - 2016-04-08 22:53 +0000
                Re: division performance (was: The problem with implementation defined ...) anton@mips.complang.tuwien.ac.at (Anton Ertl) - 2016-04-09 10:14 +0000
                Re: division performance (was: The problem with implementation defined ...) anton@mips.complang.tuwien.ac.at (Anton Ertl) - 2016-04-09 13:43 +0000
              Re: The problem with implementation defined behaviour. anton@mips.complang.tuwien.ac.at (Anton Ertl) - 2016-03-31 10:55 +0000
                Re: The problem with implementation defined behaviour. mhx@iae.nl - 2016-03-31 06:38 -0700
                Re: The problem with implementation defined behaviour. anton@mips.complang.tuwien.ac.at (Anton Ertl) - 2016-03-31 16:21 +0000
                Re: The problem with implementation defined behaviour. Paul Rubin <no.email@nospam.invalid> - 2016-03-31 11:49 -0700
                Re: The problem with implementation defined behaviour. "Elizabeth D. Rather" <erather@forth.com> - 2016-03-31 10:11 -1000
                Re: The problem with implementation defined behaviour. mhx@iae.nl - 2016-04-01 03:53 -0700
                Re: The problem with implementation defined behaviour. anton@mips.complang.tuwien.ac.at (Anton Ertl) - 2016-04-01 11:44 +0000
                Re: The problem with implementation defined behaviour. Bernd Paysan <bernd.paysan@gmx.de> - 2016-04-01 21:53 +0000
                Re: The problem with implementation defined behaviour. Andrew Haley <andrew29@littlepinkcloud.invalid> - 2016-04-02 11:46 -0500
                Re: The problem with implementation defined behaviour. Bernd Paysan <bernd.paysan@gmx.de> - 2016-04-02 21:43 +0000
                Re: The problem with implementation defined behaviour. Andrew Haley <andrew29@littlepinkcloud.invalid> - 2016-04-03 03:17 -0500
                Re: The problem with implementation defined behaviour. hughaguilar96@gmail.com - 2016-04-01 23:54 -0700
          Re: The problem with implementation defined behaviour. Albert van der Horst <albert@spenarnc.xs4all.nl> - 2016-03-30 12:58 +0000
          Re: The problem with implementation defined behaviour. Bernd Paysan <bernd.paysan@gmx.de> - 2016-03-30 22:22 +0000
        Re: The problem with implementation defined behaviour. Albert van der Horst <albert@spenarnc.xs4all.nl> - 2016-03-30 12:55 +0000
      Re: The problem with implementation defined behaviour. anton@mips.complang.tuwien.ac.at (Anton Ertl) - 2016-03-30 07:44 +0000
        Re: The problem with implementation defined behaviour. Albert van der Horst <albert@spenarnc.xs4all.nl> - 2016-03-30 13:08 +0000
          Re: The problem with implementation defined behaviour. anton@mips.complang.tuwien.ac.at (Anton Ertl) - 2016-03-30 13:43 +0000
        Re: The problem with implementation defined behaviour. Bernd Paysan <bernd.paysan@gmx.de> - 2016-03-30 22:06 +0000
      Re: The problem with implementation defined behaviour. trevor <tgritchie@blueyonder.co.uk> - 2016-03-30 13:13 +0100
        Re: The problem with implementation defined behaviour. Albert van der Horst <albert@spenarnc.xs4all.nl> - 2016-03-30 13:56 +0000
      Re: The problem with implementation defined behaviour. Albert van der Horst <albert@spenarnc.xs4all.nl> - 2016-03-30 12:49 +0000

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