retroforth/example/FloatVar.forth
crc dfba89dca9 improved example/FloatVar.forth from Kiyoshi
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2019-02-21 11:42:52 +00:00

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Forth

Here are words to encode floating point numbers into two cells.
Words in file FloatingPointEncoding.forth encode
floating point numbers, which are often 64-bit or 2-cell numbers,
into signed integers, which are always 32-bit or 1-cell numbers.
The encoding causes loss in both precision and dynamic range.
Words defined in this file encodes floating point numbers into
two integers occupying two 32-bit cells.
Two different ways are implemented:
- `w1` used fixed point encoding.
Splits a floating point number into the integer and the fraction
parts to store them in two cells.
This is faster with a narrower dynamic range.
- `w2` uses sqrt-encoding described in doc/SqrtEncoding.pdf .
This is slower with a relatively wider dynamic range,
but likely not as wide as the original floating point.
Since Retro's cells are 32-bit,
it is more convenient to handle floating point numbers
encoded into single cells than into pairs of cells.
For instance, consider using the `set:` class words for vectors.
Hence in many cases the words found by doing
'u: d:words-with
are suitable.
However, sometimes a higher precision is desired at a higher cost.
~~~
:d:-found? (s-f) d:lookup n:zero? ;
:st (-) dump-stack nl f:dump-stack ;
's:abort d:-found? [ 'example/Abort.forth include ] if
~~~
Encode/decode words to secure dynamic range.
This is the essence of the method.
~~~
:f:encode.w2 (|f:n-n) f:dup f:sign f:abs f:sqrt n:to-float f:* ;
:f:-encode.w2 (|f:n-n) f:dup f:sign f:dup f:* n:to-float f:* ;
~~~
```
.-12345.6789 f:encode.w2 st
f:-encode.w2 st
```
Split encoded floating point numbers into the integer and the fraction parts.
The sign goes to the integer part.
The fractional part is that of the absolute value.
~~~
{{
:f:shift9 .1.e-9 f:* ;
:f:-shift9 .1.e9 f:* ;
---reveal---
:f:split (-|f:n-fi)_absFrac.-shift9_signedInt
f:dup f:sign (s|f:_n
f:abs f:dup f:floor f:swap f:over (s|f:_abs.int_abs_abs.int
f:- f:-shift9 (s|f:_abs.int_abs.frac.-shift9
f:swap n:to-float f:* (_|f:_abs.frac.-shift9_signedInt
;
:f:-split (-|f:fi-n)
f:dup f:sign f:abs (s|f:_abs.frac.-shift9_abs.int
f:swap f:shift9 f:+ n:to-float f:* (_|f:_n
;
}}
~~~
```
.-123456789.0987654321 f:split st
f:-split st
```
From float to double cells w2 .
And its inverse.
~~~
:f:to-w1 (-fi|f:n-)_frac_sInt f:split f:to-number f:to-number swap ;
:w1:to-f (fi-|f:-n) swap n:to-float n:to-float f:-split ;
:f:to-w2 (-fi|f:n-)_frac_sInt f:encode.w2 f:to-w1 ;
:w2:to-f (fi-|f:-n) w1:to-f f:-encode.w2 ;
:st (-) dump-stack nl f:dump-stack ;
:f:sign (-n|f:a-)
f:dup .0 f:eq? [ #0 f:drop ] if;
.0 f:gt? [ #1 ] [ #-1 ] choose ;
~~~
```
.-123456789.0987654321 f:to-w2 st
w2:to-f st
```
`f:var1` and `f:var2` take initial values.
~~~
{{
:f:SATURATE1 (|f:-n) n:MAX n:to-float ;
:f:overflow-check1 (|f:n-n)
f:dup f:abs f:SATURATE1 f:gt?
[ f:put nl 'f:var1_overflow s:abort ] if ;
---reveal---
:f:var1 (s-|f:n-) f:overflow-check1 f:to-w1 rot d:create , , ;
:f:fetch1 (a-|f:-n) fetch-next [ fetch ] dip w1:to-f ;
:f:store1 (a-|f:n-) f:overflow-check1 f:to-w1 rot store-next store ;
}}
~~~
```
.-123456789.0987654321 'FVar1 f:var1
&FVar1 f:fetch1 st
.-98765.4321 &FVar1 f:store1
&FVar1 f:fetch1 st
```
.-9876543210.123456789 &FVar1 f:store1 (This_test_should__abort
.1.e20 &FVar1 f:store1 (This_test_should__abort
~~~
{{
:f:SATURATE2 (|f:-n) n:MAX n:to-float f:dup f:* ;
:f:overflow-check2 (|f:n-n)
f:dup f:abs f:SATURATE2 f:gt?
[ f:put nl 'f:var2_overflow s:abort ] if ;
---reveal---
:f:var2 (s-|f:n-) f:overflow-check2 f:to-w2 rot d:create , , ;
:f:fetch2 (a-|f:-n) fetch-next [ fetch ] dip w2:to-f ;
:f:store2 (a-|f:n-) f:overflow-check2 f:to-w2 rot store-next store ;
}}
~~~
```
.-123456789.0987654321 'FVar2 f:var2
&FVar2 f:fetch2 st
.-9876543210.123456789 &FVar2 f:store2
&FVar2 f:fetch2 st
```
.1.e20 &FVar2 f:store2 (This_test_should_abort