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Re: Integer cosine function

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From mhx@iae.nl (Marcel Hendrix)
Subject Re: Integer cosine function
Newsgroups comp.lang.forth
Message-ID <04691416018434@frunobulax.edu> (permalink)
Date Tue, 19 Feb 2013 21:34:31 +0200
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Zbiggy <zbigniew2011REMOVE@gmail.REMOVE.com> writes Re: Integer cosine function

> In comp.lang.forth, Marcel Hendrix wrote:

>> My comment has nothing to do with precision/accuracy. Brad's code 
>> simply *doesn't work correctly* for the 64-bit and higher Forth's
>> we'll have in 20 years, that's all. Look at the source to see why, 
>> it's instructive.

You didn't read Brad's code, did you? 

When I say 'doesn't work correctly for a 64-bit Forth', I mean that
code like
| : ROUND  ( d -- n )     \ round to nearest
|   80000000 0 D+  NIP
| ;
only works for a 32bit 2's complement Forth. I do not say that
Brad's algorithm is wrong or inaccurate as such.

> What do you think about this then (the result given as a ratio):
>
> : power ( m n - m^n )   ?dup if 1 swap 0 do over * loop nip else drop 1 then ;

Use Horner's rule. Erase your post before somebody reads it.

> : intCosinus14 ( n -- num denom )
>  87178291200
>  over 43589145600 swap 2 power * -  over 3632428800 swap 4 power * +
>  over 121080960 swap 6 power * -    over 2162160 swap 8 power * +
>  over 24024 swap 10 power * -       over 182 swap 12 power * +
>  over 14 power -
>  nip 87178291200
> ;

You're using n^14, without scaling. This needs a 131 bit Forth.

> Yes, when "closing the circle" (around the 5-6 rad) it's losing accuracy.
> Anyway we could take advantage out of the fact, it's periodical function.

For simulation and graphics, the argument can be many times PI. Better to
work in square degrees (400 degrees = 2*pi).

-marcel

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Integer cosine function Brad Eckert <hwfwguy@gmail.com> - 2013-02-16 07:35 -0800
  Re: Integer cosine function mhx@iae.nl (Marcel Hendrix) - 2013-02-17 13:57 +0200
    Re: Integer cosine function Andrew Haley <andrew29@littlepinkcloud.invalid> - 2013-02-17 09:40 -0600
      Re: Integer cosine function "Elizabeth D. Rather" <erather@forth.com> - 2013-02-17 07:51 -1000
        Re: Integer cosine function mhx@iae.nl (Marcel Hendrix) - 2013-02-17 19:06 +0200
          Re: Integer cosine function anton@mips.complang.tuwien.ac.at (Anton Ertl) - 2013-02-18 14:46 +0000
          Re: Integer cosine function Zbiggy <zbigniew2011REMOVE@gmail.REMOVE.com> - 2013-02-19 20:01 +0100
            Re: Integer cosine function mhx@iae.nl (Marcel Hendrix) - 2013-02-19 21:34 +0200
              Re: Integer cosine function Zbiggy <zbigniew2011REMOVE@gmail.REMOVE.com> - 2013-02-19 21:46 +0100
            Re: Integer cosine function Hugh Aguilar <hughaguilar96@yahoo.com> - 2013-02-19 15:55 -0800
              Re: Integer cosine function Coos Haak <chforth@hccnet.nl> - 2013-02-21 00:59 +0100
        Re: Integer cosine function Brad Eckert <hwfwguy@gmail.com> - 2013-02-18 09:19 -0800
          Re: Integer cosine function rickman <gnuarm@gmail.com> - 2013-02-18 14:27 -0500
          Re: Integer cosine function Bernd Paysan <bernd.paysan@gmx.de> - 2013-02-18 20:53 +0100
            Re: Integer cosine function Hugh Aguilar <hughaguilar96@yahoo.com> - 2013-02-18 19:10 -0800
              Re: Integer cosine function Bernd Paysan <bernd.paysan@gmx.de> - 2013-02-19 13:13 +0100
              Re: Integer cosine function rickman <gnuarm@gmail.com> - 2013-02-19 23:04 -0500
            Re: Integer cosine function Gary Bergstrom <g.bergstrom@ieee.org> - 2013-02-20 10:00 -0800
              Re: Integer cosine function Bernd Paysan <bernd.paysan@gmx.de> - 2013-02-21 13:04 +0100
                Re: Integer cosine function rickman <gnuarm@gmail.com> - 2013-02-21 19:03 -0500
                Re: Integer cosine function Bernd Paysan <bernd.paysan@gmx.de> - 2013-02-22 02:45 +0100
                Re: Integer cosine function Mark Wills <markrobertwills@yahoo.co.uk> - 2013-02-22 02:32 -0800
                Re: Integer cosine function Bernd Paysan <bernd.paysan@gmx.de> - 2013-02-22 16:01 +0100
                Re: Integer cosine function Hugh Aguilar <hughaguilar96@yahoo.com> - 2013-02-22 22:07 -0800
                Re: Integer cosine function "Rod Pemberton" <do_not_have@notemailnotz.cnm> - 2013-02-23 10:27 -0500
                Re: Integer cosine function Andrew Haley <andrew29@littlepinkcloud.invalid> - 2013-02-22 03:59 -0600
                Re: Integer cosine function Mark Wills <markrobertwills@yahoo.co.uk> - 2013-02-22 02:30 -0800
                Re: Integer cosine function Bernd Paysan <bernd.paysan@gmx.de> - 2013-02-22 15:56 +0100
                Re: Integer cosine function Zbiggy <zbigniew2011REMOVE@gmail.REMOVE.com> - 2013-02-22 16:13 +0100
                Re: Integer cosine function Bernd Paysan <bernd.paysan@gmx.de> - 2013-02-22 17:45 +0100
                Re: Integer cosine function Zbiggy <zbigniew2011REMOVE@gmail.REMOVE.com> - 2013-02-22 18:44 +0100
                Re: Integer cosine function Bernd Paysan <bernd.paysan@gmx.de> - 2013-02-22 19:19 +0100
                Re: Integer cosine function Hugh Aguilar <hughaguilar96@yahoo.com> - 2013-02-22 14:43 -0800
                Re: Integer cosine function Bernd Paysan <bernd.paysan@gmx.de> - 2013-02-23 01:30 +0100
                Re: Integer cosine function Hugh Aguilar <hughaguilar96@yahoo.com> - 2013-02-22 21:51 -0800
                Re: Integer cosine function Bernd Paysan <bernd.paysan@gmx.de> - 2013-02-24 01:43 +0100
                Re: Integer cosine function anton@mips.complang.tuwien.ac.at (Anton Ertl) - 2013-02-25 17:55 +0000
                Re: Integer cosine function Bernd Paysan <bernd.paysan@gmx.de> - 2013-02-25 21:01 +0100
                Re: Integer cosine function Hugh Aguilar <hughaguilar96@yahoo.com> - 2013-02-25 23:22 -0800
                Re: Integer cosine function Bernd Paysan <bernd.paysan@gmx.de> - 2013-02-26 15:11 +0100
                Re: Integer cosine function rickman <gnuarm@gmail.com> - 2013-02-27 08:05 -0500
                Re: Integer cosine function "Rod Pemberton" <do_not_have@notemailnotz.cnm> - 2013-02-27 22:14 -0500
                Re: Integer cosine function rickman <gnuarm@gmail.com> - 2013-02-27 22:56 -0500
                Re: Integer cosine function "Rod Pemberton" <do_not_have@notemailnotz.cnm> - 2013-03-01 21:37 -0500
                Re: Integer cosine function rickman <gnuarm@gmail.com> - 2013-03-07 13:12 -0500
                Re: Integer cosine function Brad Eckert <hwfwguy@gmail.com> - 2013-02-28 08:00 -0800
                Re: Integer cosine function "Rod Pemberton" <do_not_have@notemailnotz.cnm> - 2013-03-01 21:38 -0500
                Re: Integer cosine function Gerry Jackson <gerry@jackson9000.fsnet.co.uk> - 2013-02-28 16:55 +0000
                Re: Integer cosine function "Rod Pemberton" <do_not_have@notemailnotz.cnm> - 2013-03-01 21:38 -0500
                Re: Integer cosine function Gerry Jackson <gerry@jackson9000.fsnet.co.uk> - 2013-03-04 11:08 +0000
                Re: Integer cosine function Mark Wills <markrobertwills@yahoo.co.uk> - 2013-03-04 03:39 -0800
                Re: Integer cosine function "Rod Pemberton" <do_not_have@notemailnotz.cnm> - 2013-03-04 20:49 -0500
                Re: Integer cosine function stephenXXX@mpeforth.com (Stephen Pelc) - 2013-03-05 10:20 +0000
                Re: Integer cosine function Mark Wills <markrobertwills@yahoo.co.uk> - 2013-03-07 00:12 -0800
                Re: Integer cosine function "Rod Pemberton" <do_not_have@notemailnotq.cpm> - 2013-03-08 04:21 -0500
                Re: Integer cosine function "Rod Pemberton" <do_not_have@notemailnotz.cnm> - 2013-03-04 20:50 -0500
                Re: Integer cosine function Gerry Jackson <gerry@jackson9000.fsnet.co.uk> - 2013-03-05 07:16 +0000
                Re: Integer cosine function "Rod Pemberton" <do_not_have@notemailnotq.cpm> - 2013-03-06 17:56 -0500
                Re: Integer cosine function Mark Wills <markrobertwills@yahoo.co.uk> - 2013-03-07 00:24 -0800
                Re: Integer cosine function Mark Wills <markrobertwills@yahoo.co.uk> - 2013-03-07 07:34 -0800
                Re: Integer cosine function Lars Brinkhoff <lars.spam@nocrew.org> - 2013-02-28 12:57 +0100
                Re: Integer cosine function Bernd Paysan <bernd.paysan@gmx.de> - 2013-02-28 17:07 +0100
                Re: Integer cosine function Hugh Aguilar <hughaguilar96@yahoo.com> - 2013-02-28 19:37 -0800
                Re: Integer cosine function stephenXXX@mpeforth.com (Stephen Pelc) - 2013-03-01 10:56 +0000
                Re: Integer cosine function anton@mips.complang.tuwien.ac.at (Anton Ertl) - 2013-03-01 13:52 +0000
                Re: Integer cosine function Hugh Aguilar <hughaguilar96@yahoo.com> - 2013-03-05 17:48 -0800
                Re: Integer cosine function rickman <gnuarm@gmail.com> - 2013-03-13 17:44 -0400
                Re: Integer cosine function "Rod Pemberton" <do_not_have@notemailnotz.cnm> - 2013-03-01 21:36 -0500
                Re: Integer cosine function Elizabeth D Rather <erather@forth.com> - 2013-03-01 19:14 -1000
                Re: Integer cosine function mhx@iae.nl (Marcel Hendrix) - 2013-03-02 09:34 +0200
                Re: Integer cosine function kenney@cix.compulink.co.uk - 2013-03-02 09:06 -0600
                Re: Integer cosine function Brad Eckert <hwfwguy@gmail.com> - 2013-02-26 08:53 -0800
                Re: Integer cosine function "Rod Pemberton" <do_not_have@notemailnotz.cnm> - 2013-02-26 16:59 -0500
                Re: Integer cosine function albert@spenarnc.xs4all.nl (Albert van der Horst) - 2013-02-27 00:52 +0000
                Re: Integer cosine function "Rod Pemberton" <do_not_have@notemailnotz.cnm> - 2013-02-27 04:07 -0500
                Re: Integer cosine function "WJ" <w_a_x_man@yahoo.com> - 2013-03-05 20:51 +0000
                Re: Integer cosine function Hugh Aguilar <hughaguilar96@yahoo.com> - 2013-03-05 17:58 -0800
                Re: Integer cosine function Bernd Paysan <bernd.paysan@gmx.de> - 2013-03-06 16:39 +0100
                Re: Integer cosine function Hugh Aguilar <hughaguilar96@yahoo.com> - 2013-03-06 14:21 -0800
                Re: Integer cosine function Bernd Paysan <bernd.paysan@gmx.de> - 2013-03-07 00:11 +0100
                Re: Integer cosine function albert@spenarnc.xs4all.nl (Albert van der Horst) - 2013-03-06 23:44 +0000
                Re: Integer cosine function Hugh Aguilar <hughaguilar96@yahoo.com> - 2013-03-06 16:24 -0800
                Re: Integer cosine function Bernd Paysan <bernd.paysan@gmx.de> - 2013-03-07 01:59 +0100
                Re: Integer cosine function Hugh Aguilar <hughaguilar96@yahoo.com> - 2013-03-06 19:48 -0800
                Re: Integer cosine function Bernd Paysan <bernd.paysan@gmx.de> - 2013-03-07 16:22 +0100
                Re: Integer cosine function "WJ" <w_a_x_man@yahoo.com> - 2013-03-06 23:37 +0000
                Re: Integer cosine function "Rod Pemberton" <do_not_have@notemailnotz.cnm> - 2013-02-23 09:54 -0500
                Re: Integer cosine function "WJ" <w_a_x_man@yahoo.com> - 2013-03-05 21:03 +0000
                Re: Integer cosine function Hugh Aguilar <hughaguilar96@yahoo.com> - 2013-03-05 15:59 -0800
                Re: Integer cosine function Hugh Aguilar <hughaguilar96@yahoo.com> - 2013-03-05 16:38 -0800
                Re: Integer cosine function Andrew Haley <andrew29@littlepinkcloud.invalid> - 2013-02-22 12:07 -0600
                Re: Integer cosine function Bernd Paysan <bernd.paysan@gmx.de> - 2013-02-22 19:39 +0100
                Re: Integer cosine function "Elizabeth D. Rather" <erather@forth.com> - 2013-02-22 09:23 -1000
                Re: Integer cosine function Andrew Haley <andrew29@littlepinkcloud.invalid> - 2013-02-23 04:44 -0600
                Re: Integer cosine function Hugh Aguilar <hughaguilar96@yahoo.com> - 2013-02-22 13:00 -0800
                Re: Integer cosine function Bernd Paysan <bernd.paysan@gmx.de> - 2013-02-23 01:09 +0100
                Re: Integer cosine function rickman <gnuarm@gmail.com> - 2013-02-22 21:16 -0500
                Re: Integer cosine function rickman <gnuarm@gmail.com> - 2013-02-22 20:28 -0500
  Re: Integer cosine function Gary Bergstrom <g.bergstrom@ieee.org> - 2013-02-27 07:59 -0800
    Re: Integer cosine function Brad Eckert <hwfwguy@gmail.com> - 2013-02-27 08:48 -0800
      Re: Integer cosine function Gary Bergstrom <g.bergstrom@ieee.org> - 2013-02-27 10:23 -0800
      Re: Integer cosine function Gary Bergstrom <g.bergstrom@ieee.org> - 2013-03-15 10:14 -0700
        Re: Integer cosine function Brad Eckert <hwfwguy@gmail.com> - 2013-03-15 13:19 -0700
          Re: Integer cosine function Brad Eckert <hwfwguy@gmail.com> - 2013-03-15 13:28 -0700
            Re: Integer cosine function Gary Bergstrom <g.bergstrom@ieee.org> - 2013-03-15 21:13 -0700

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