274 lines
7.3 KiB
Forth
274 lines
7.3 KiB
Forth
## Helpers
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~~~
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:s:shout (s-) '!_ s:prepend s:put nl 'Stack_:_ s:put dump-stack nl ;
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{{
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'Depth var
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:message (-)
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'abort_with__trail__invoked s:shout nl
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'Do__reset__to_clear_stack. s:put nl ;
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:put-name (a-) fetch d:lookup-xt
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dup n:-zero? [ d:name s:put nl ] [ drop ] choose ;
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---reveal---
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:trail repeat pop put-name again ;
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:abort (-?) depth !Depth message trail ;
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:s:abort (s-) 's:abort_:_ s:prepend s:put nl abort ;
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}}
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{{
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:f:dump-astack (-)_dump_alternative_stack
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f:adepth [ [ f:pop ] times ] sip 'fa_ s:put [ f:dup f:put sp f:push ] times ;
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:dump-stacks (-) dump-stack nl f:dump-stack nl f:dump-astack ;
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---reveal---
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:s (-)___Stack dump-stacks ;
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}}
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{{
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:f:reset (-|float:?-) f:depth [ f:drop ] times ;
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:f:areset (-|alt:?-) f:depth [ f:pop f:drop ] times ;
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:reset.nf (?-|float:?-) reset f:reset f:areset ;
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---reveal---
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:r (?-)__Reset reset.nf ;
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}}
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~~~
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## Description
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This implements a means of encoding floating point values
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into signed integer cells. The technique is described in
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the paper titled "Encoding floating point numbers to shorter
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integers" by Kiyoshi Yoneda and Charles Childers.
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This will extend the `f:` vocabulary and adds a new `e:` vocabulary.
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Here `e:` stands for encoded.
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## Code & Commentary
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Define some constants. The range is slightly reduced from
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the standard integer range as the smallest value is used
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for NaN.
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~~~
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n:MAX n:dec 'e:MAX const
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n:MAX n:dec n:negate 'e:MIN const
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n:MIN 'e:NAN const
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n:MAX 'e:INF const
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n:MAX n:negate 'e:-INF const
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~~~
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~~~
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:e:n? (e-f) e:MIN n:inc e:MAX n:dec n:between? ;
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:e:max? (e-f) e:MAX eq? ;
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:e:min? (e-f) e:MIN eq? ;
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:e:zero? (e-f) n:zero? ;
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:e:nan? (e-f) e:NAN eq? ;
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:e:inf? (e-f) e:INF eq? ;
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:e:-inf? (e-f) e:-INF eq? ;
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:e:clip (e-e) e:MIN e:MAX n:limit ;
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~~~
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Since 32-bit cell takes about 9 decimal digits, if you set
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`[ .1e5 ] f:E1 set-hook`
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you will have 4 decimal digits left for the integer part of the encoded number,
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which corresponds to 8 decimal digits decoded.
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Encode/decode words to secure dynamic range.
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This portion is the essence of the method.
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~~~
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:f:E1 (-|f:-n)_e-unit_in_float hook .1.e5 ; (decimal_digits_to_shift_left
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:f:-shift (|f:n-n)_shift_left f:E1 f:* ;
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:f:+shift (|f:n-n)_shift_right f:E1 f:/ ;
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:f:signed-sqrt (|f:n-n) f:dup f:sign f:abs f:sqrt n:to-float f:* ;
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:f:+encode (|f:n-n) f:signed-sqrt f:-shift ;
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:f:-encode (|f:n-n) f:dup f:sign f:+shift f:dup f:* n:to-float f:* ;
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:f:signed-square (|f:n-n) f:dup f:sign f:dup f:* n:to-float f:* ;
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~~~
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Deal with special cases.
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~~~
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:f:to-e (-e|f:n-)
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f:dup f:nan? [ f:drop drop e:NAN ] if;
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f:dup f:inf? [ f:drop drop e:INF ] if;
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f:dup f:-inf? [ f:drop drop e:-INF ] if;
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f:+encode f:round f:to-number e:clip (e
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e:MIN [ f:drop ] case
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e:MAX [ f:drop ] case ;
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:e:to-f (e-|f:-n)
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e:NAN [ drop f:NAN ] case
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e:INF [ drop f:INF ] case
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e:-INF [ drop f:-INF ] case
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n:to-float f:-encode ;
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~~~
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```
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r .-1234.56789 f:to-e s e:to-f s
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```
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~~~
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:f:store (a-|f:n-) [ f:to-e ] dip store ;
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:f:fetch (a-|f:-n) fetch e:to-f ;
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~~~
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~~~
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:f:dump-stack f:depth dup [ f:push ] times [ f:pop f:dup f:put sp ] times ;
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~~~
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~~~
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:e:put (e-)
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e:MAX [ 'e:MAX s:put ] case
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e:MIN [ 'e:MIN s:put ] case
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#0 [ 'e:0 s:put ] case
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e:NAN [ 'e:NAN s:put ] case
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e:INF [ 'e:INF s:put ] case
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e:-INF [ 'e:-INF s:put ] case
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e:to-f f:put ;
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~~~
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```
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r .-1234.56789 f:to-e e:put
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```
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## Higher precision variables
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Here are words to encode floating point numbers into two cells.
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Words defined up to this point store
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floating point numbers, which are often 64-bit or 2-cell numbers,
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into signed integers, which are always 32-bit or 1-cell numbers.
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The encoding causes loss in both precision and dynamic range.
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Words defined below encode floating point numbers into
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two integers occupying two 32-bit cells.
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Two different ways are implemented:
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- `w1` uses fixed point encoding.
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Splits a floating point number into the integer and the fraction
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parts to store them in two cells.
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This is faster with a narrower dynamic range.
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- `w2` uses sqrt-encoding described in doc/SqrtEncoding.pdf .
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This is slower with a relatively wider dynamic range,
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but likely not as wide as the original floating point.
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Since Retro's cells are 32-bit,
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it is more convenient to handle floating point numbers
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encoded into single cells than into pairs of cells.
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For instance, consider using the `array:` words for vectors.
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Hence in many cases the words found by doing
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'e: d:words-with
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are suitable.
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However, sometimes a higher precision is desired at a higher cost.
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These are the same as `f:+encode` and `f:-encode` except that they come
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without `f:-shift` and `f:+shift` .
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~~~
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:f:+encode.w2 (|f:n-n) f:dup f:sign f:abs f:sqrt n:to-float f:* ;
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:f:-encode.w2 (|f:n-n) f:dup f:sign f:dup f:* n:to-float f:* ;
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~~~
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```
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r .-12345.6789 f:+encode.w2 s f:-encode.w2 s
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```
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Split encoded floating point numbers into the integer and the fraction parts.
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The sign goes to the integer part.
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The fractional part is that of the absolute value.
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~~~
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{{
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:f:+shift9 .1.e-9 f:* ;
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:f:-shift9 .1.e9 f:* ;
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---reveal---
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:f:+split (-|f:n-fi)_absFrac.-shift9_signedInt
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f:dup f:sign (s|f:_n
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f:abs f:dup f:floor f:swap f:over (s|f:_abs.int_abs_abs.int
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f:- f:-shift9 (s|f:_abs.int_abs.frac.-shift9
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f:swap n:to-float f:* (_|f:_abs.frac.-shift9_signedInt
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;
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:f:-split (-|f:fi-n)
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f:dup f:sign f:abs (s|f:_abs.frac.-shift9_abs.int
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f:swap f:+shift9 f:+ n:to-float f:* (_|f:_n
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;
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}}
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~~~
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```
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r .-123456789.0987654321 f:+split s f:-split s
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```
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From float to double cells w2 .
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And its inverse.
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~~~
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:f:to-w1 (-fi|f:n-)_frac_sInt f:+split f:to-number f:to-number swap ;
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:w1:to-f (fi-|f:-n) swap n:to-float n:to-float f:-split ;
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:f:to-w2 (-fi|f:n-)_frac_sInt f:+encode.w2 f:to-w1 ;
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:w2:to-f (fi-|f:-n) w1:to-f f:-encode.w2 ;
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~~~
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```
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r .-123456789.0987654321 f:to-w2 s w2:to-f s
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```
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`f:var1` and `f:var2` take initial values.
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~~~
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{{
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:f:SATURATE1 (|f:-n) n:MAX n:to-float ;
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:f:overflow-check1 (|f:n-n)
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f:dup f:abs f:SATURATE1 f:gt?
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[ f:put nl 'f:var1_overflow s:abort ] if ;
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---reveal---
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:f:var1 (s-|f:n-) f:overflow-check1 f:to-w1 rot d:create , , ;
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:f:@1 (a-|f:-n) fetch-next [ fetch ] dip w1:to-f ;
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:f:!1 (a-|f:n-) f:overflow-check1 f:to-w1 rot store-next store ;
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}}
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~~~
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```
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r
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.-123456789.0987654321 'FVar1 f:var1
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&FVar1 f:@1 s
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r
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.-98765.4321 &FVar1 f:!1
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&FVar1 f:@1 s
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```
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.-9876543210.123456789 &FVar1 f:@1 (This_test_should__abort
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.1.e20 &FVar1 f:!1 (This_test_should__abort
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~~~
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{{
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:f:SATURATE2 (|f:-n) n:MAX n:to-float f:dup f:* ;
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:f:overflow-check2 (|f:n-n)
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f:dup f:abs f:SATURATE2 f:gt?
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[ f:put nl 'f:var2_overflow s:abort ] if ;
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---reveal---
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:f:var2 (s-|f:n-) f:overflow-check2 f:to-w2 rot d:create , , ;
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:f:@2 (a-|f:-n) fetch-next [ fetch ] dip w2:to-f ;
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:f:!2 (a-|f:n-) f:overflow-check2 f:to-w2 rot store-next store ;
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}}
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~~~
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```
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r
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.-123456789.0987654321 'FVar2 f:var2
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&FVar2 f:@2 s
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r
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.-9876543210.123456789 &FVar2 f:!2
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&FVar2 f:@2 s
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```
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.1.e20 &FVar2 f:!2 (This_test_should_abort
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