b32cb2b842
FossilOrigin-Name: 40562e92ecedb75ae91988859932a4f046bbea251f397508400857910f05f0e3
76 lines
1.9 KiB
Forth
76 lines
1.9 KiB
Forth
# Float
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## Description
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This implements a means of encoding floating point values into signed integer cells. The technique is described in the paper titled "Encoding floating point numbers to shorter integers" by Kiyoshi Yoneda and Charles Childers.
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This will extend the `f:` vocabulary and adds a new `u:` vocabulary.
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## Code & Commentary
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Define some constants. The range is slightly reduced from the standard integer range as the smallest value is used for NaN.
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~~~
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n:MAX n:dec 'u:MAX const
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n:MAX n:dec n:negate 'u:MIN const
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n:MIN 'u:NAN const
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n:MAX 'u:INF const
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n:MAX n:negate 'u:-INF const
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~~~
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~~~
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:u:n? (u-f)
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u:MIN n:inc u:MAX n:dec n:between? ;
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:u:max? (u-f) u:MAX eq? ;
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:u:min? (u-f) u:MIN eq? ;
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:u:zero? (u-f) n:zero? ;
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:u:nan? (u-f) u:NAN eq? ;
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:u:inf? (u-f) u:INF eq? ;
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:u:-inf? (u-f) u:-INF eq? ;
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:u:clip (u-u) u:MIN u:MAX n:limit ;
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~~~
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~~~
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{{
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:f:U1 (-|f:-b) .1.e9 ;
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:f:BALANCE (-|f:-b) .1. ;
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:f:scale (-|f:a-b) f:U1 f:* ;
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:f:descale (-|f:a-b) f:U1 f:/ ;
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:f:encode (-|f:a-b)__n/(s_+_n_)
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f:BALANCE f:over f:+ f:/ ;
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:f:decode (-|f:a-b)_su/(1_-_u_)
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.1. f:over f:- f:/ f:BALANCE f:* ;
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---reveal---
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:f:to-u (-u|f:a-)
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f:dup f:encode f:scale f:round f:to-number u:clip
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f:dup f:nan? [ drop u:NAN ] if
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f:dup f:inf? [ drop u:INF ] if
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f:dup f:-inf? [ drop u:-INF ] if
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f:drop ;
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:u:to-f (u-|f:-b)
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n:to-float f:descale f:decode ;
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:u:to-f (u-|f:-b)
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dup n:to-float f:descale f:decode
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dup u:nan? [ f:drop f:NAN ] if
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dup u:inf? [ f:drop f:INF ] if
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dup u:-inf? [ f:drop f:-INF ] if
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drop ;
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}}
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~~~
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```
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:tab #9 c:put #9 c:put #9 c:put ;
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.103.333 f:to-u dup n:put tab u:to-f f:put nl
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..000412 f:to-u dup n:put sp sp tab u:to-f f:put nl
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.129192.232415 f:to-u dup n:put tab u:to-f f:put nl
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f:NAN f:to-u dup n:put sp sp sp sp sp u:to-f f:put nl
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f:INF f:to-u dup n:put sp sp sp sp sp u:to-f f:put nl
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```
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