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en:pfw:dlshift_drshift

## Shifting doubles: DLSHIFT and DRSHIFT

an.02apr2024

The code is for 32bit cells, to keep it readable. For other cell widths adjust the number 32 everywhere.

## Coded with LSHIFT and RSHIFT

```decimal
: DLSHIFT ( lo hi n -- lo' hi' )    \ n in [0,32*2]
tuck lshift >r          \ hi'
2dup 32 -
2dup   lshift >r        \ lower lo to upper hi
negate rshift >r        \ upper lo to lower hi
lshift                  \ lo'
2r> r> or or   ;        \ compose hi'

: DRSHIFT ( lo hi n -- lo' hi' )    \ n in [0,32*2]
tuck 2dup rshift >r     \ hi'
32 -
2dup   rshift >r        \ upper hi to lower lo
negate lshift >r        \ lower hi to upper lo
rshift 2r> or or        \ compose lo'
r> ;                    \ hi'```

## Possibly a problem

We assume for single cell LSHIFT and RSHIFT:

1. x n shift –> x, for n=0
2. x n shift –> 0, for n not in [0,32-1]. More precise: for n in [-32,-1] or in [32,32*2].

Test your forth. If 2. does not hold:

`: LSHIFT ( x n -- x' ) dup 32 u< if lshift exit then 2drop 0 ;`

## Test code

```decimal
: DU.HEX ( ud -- ) base @ >r hex
<# 32 2/ 0 do # loop #>   type space r> base ! ;
: (TEST) ( ud ud -- ) 2over 2over du.hex du.hex
cr ." #shifts dlshift--------- drshift---------"
32 2* 2 +   -2
do cr i 3 and 0= if cr then i 7 .r space
2over 2over i dlshift du.hex i drshift du.hex
loop 2drop 2drop ;

: TEST1 ( -- ) -1. 2dup  (test) ;
: TEST2 ( -- ) 0 -1 dup 1 rshift xor 1. (test) ;```

## Test results (noForth t)

```@)test1 FFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFF
#shifts dlshift--------- drshift---------
-2 0000000000000000 0000000000000000
-1 0000000000000000 0000000000000000

0 FFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFF
1 FFFFFFFFFFFFFFFE 7FFFFFFFFFFFFFFF
2 FFFFFFFFFFFFFFFC 3FFFFFFFFFFFFFFF
3 FFFFFFFFFFFFFFF8 1FFFFFFFFFFFFFFF

4 FFFFFFFFFFFFFFF0 0FFFFFFFFFFFFFFF
5 FFFFFFFFFFFFFFE0 07FFFFFFFFFFFFFF
6 FFFFFFFFFFFFFFC0 03FFFFFFFFFFFFFF
7 FFFFFFFFFFFFFF80 01FFFFFFFFFFFFFF

8 FFFFFFFFFFFFFF00 00FFFFFFFFFFFFFF
9 FFFFFFFFFFFFFE00 007FFFFFFFFFFFFF
A FFFFFFFFFFFFFC00 003FFFFFFFFFFFFF
B FFFFFFFFFFFFF800 001FFFFFFFFFFFFF

C FFFFFFFFFFFFF000 000FFFFFFFFFFFFF
D FFFFFFFFFFFFE000 0007FFFFFFFFFFFF
E FFFFFFFFFFFFC000 0003FFFFFFFFFFFF
F FFFFFFFFFFFF8000 0001FFFFFFFFFFFF

10 FFFFFFFFFFFF0000 0000FFFFFFFFFFFF
11 FFFFFFFFFFFE0000 00007FFFFFFFFFFF
12 FFFFFFFFFFFC0000 00003FFFFFFFFFFF
13 FFFFFFFFFFF80000 00001FFFFFFFFFFF

14 FFFFFFFFFFF00000 00000FFFFFFFFFFF
15 FFFFFFFFFFE00000 000007FFFFFFFFFF
16 FFFFFFFFFFC00000 000003FFFFFFFFFF
17 FFFFFFFFFF800000 000001FFFFFFFFFF

18 FFFFFFFFFF000000 000000FFFFFFFFFF
19 FFFFFFFFFE000000 0000007FFFFFFFFF
1A FFFFFFFFFC000000 0000003FFFFFFFFF
1B FFFFFFFFF8000000 0000001FFFFFFFFF

1C FFFFFFFFF0000000 0000000FFFFFFFFF
1D FFFFFFFFE0000000 00000007FFFFFFFF
1E FFFFFFFFC0000000 00000003FFFFFFFF
1F FFFFFFFF80000000 00000001FFFFFFFF

20 FFFFFFFF00000000 00000000FFFFFFFF
21 FFFFFFFE00000000 000000007FFFFFFF
22 FFFFFFFC00000000 000000003FFFFFFF
23 FFFFFFF800000000 000000001FFFFFFF

24 FFFFFFF000000000 000000000FFFFFFF
25 FFFFFFE000000000 0000000007FFFFFF
26 FFFFFFC000000000 0000000003FFFFFF
27 FFFFFF8000000000 0000000001FFFFFF

28 FFFFFF0000000000 0000000000FFFFFF
29 FFFFFE0000000000 00000000007FFFFF
2A FFFFFC0000000000 00000000003FFFFF
2B FFFFF80000000000 00000000001FFFFF

2C FFFFF00000000000 00000000000FFFFF
2D FFFFE00000000000 000000000007FFFF
2E FFFFC00000000000 000000000003FFFF
2F FFFF800000000000 000000000001FFFF

30 FFFF000000000000 000000000000FFFF
31 FFFE000000000000 0000000000007FFF
32 FFFC000000000000 0000000000003FFF
33 FFF8000000000000 0000000000001FFF

34 FFF0000000000000 0000000000000FFF
35 FFE0000000000000 00000000000007FF
36 FFC0000000000000 00000000000003FF
37 FF80000000000000 00000000000001FF

38 FF00000000000000 00000000000000FF
39 FE00000000000000 000000000000007F
3A FC00000000000000 000000000000003F
3B F800000000000000 000000000000001F

3C F000000000000000 000000000000000F
3D E000000000000000 0000000000000007
3E C000000000000000 0000000000000003
3F 8000000000000000 0000000000000001

40 0000000000000000 0000000000000000
41 0000000000000000 0000000000000000 OK.0```
```@)test2 0000000000000001 8000000000000000
#shifts dlshift--------- drshift---------
-2 0000000000000000 0000000000000000
-1 0000000000000000 0000000000000000

0 0000000000000001 8000000000000000
1 0000000000000002 4000000000000000
2 0000000000000004 2000000000000000
3 0000000000000008 1000000000000000

4 0000000000000010 0800000000000000
5 0000000000000020 0400000000000000
6 0000000000000040 0200000000000000
7 0000000000000080 0100000000000000

8 0000000000000100 0080000000000000
9 0000000000000200 0040000000000000
A 0000000000000400 0020000000000000
B 0000000000000800 0010000000000000

C 0000000000001000 0008000000000000
D 0000000000002000 0004000000000000
E 0000000000004000 0002000000000000
F 0000000000008000 0001000000000000

10 0000000000010000 0000800000000000
11 0000000000020000 0000400000000000
12 0000000000040000 0000200000000000
13 0000000000080000 0000100000000000

14 0000000000100000 0000080000000000
15 0000000000200000 0000040000000000
16 0000000000400000 0000020000000000
17 0000000000800000 0000010000000000

18 0000000001000000 0000008000000000
19 0000000002000000 0000004000000000
1A 0000000004000000 0000002000000000
1B 0000000008000000 0000001000000000

1C 0000000010000000 0000000800000000
1D 0000000020000000 0000000400000000
1E 0000000040000000 0000000200000000
1F 0000000080000000 0000000100000000

20 0000000100000000 0000000080000000
21 0000000200000000 0000000040000000
22 0000000400000000 0000000020000000
23 0000000800000000 0000000010000000

24 0000001000000000 0000000008000000
25 0000002000000000 0000000004000000
26 0000004000000000 0000000002000000
27 0000008000000000 0000000001000000

28 0000010000000000 0000000000800000
29 0000020000000000 0000000000400000
2A 0000040000000000 0000000000200000
2B 0000080000000000 0000000000100000

2C 0000100000000000 0000000000080000
2D 0000200000000000 0000000000040000
2E 0000400000000000 0000000000020000
2F 0000800000000000 0000000000010000

30 0001000000000000 0000000000008000
31 0002000000000000 0000000000004000
32 0004000000000000 0000000000002000
33 0008000000000000 0000000000001000

34 0010000000000000 0000000000000800
35 0020000000000000 0000000000000400
36 0040000000000000 0000000000000200
37 0080000000000000 0000000000000100

38 0100000000000000 0000000000000080
39 0200000000000000 0000000000000040
3A 0400000000000000 0000000000000020
3B 0800000000000000 0000000000000010

3C 1000000000000000 0000000000000008
3D 2000000000000000 0000000000000004
3E 4000000000000000 0000000000000002
3F 8000000000000000 0000000000000001

40 0000000000000000 0000000000000000
41 0000000000000000 0000000000000000  OK.0```

## Coded with D2* and D2/

an.02apr2024

```decimal
: DLSHIFT ( lo hi n -- lo' hi' )    \ n in [0,32*2]
dup 32 2* u<
if 0 ?do d2* loop exit
then 2drop drop 0. ;
: DRSHIFT ( lo hi n -- lo' hi' )    \ n in [0,32*2]
dup 32 2* u<
if 0 ?do d2/  [ -1 1 rshift ] literal and loop exit
then 2drop drop 0. ;```

Remember that D2/ is in fact an arithmetic shift.