Hey there, it's ya gender non-specific diminutive Zeda, here, and today we'll be looking at the Fisher-Yates algorithm and just how freaking efficient it can be for shuffling a list. For reference, it takes one second to shuffle a 999-element list at 6MHz, and if that ain't the way your deity intended it, I don't know what is.

First, how do we shuffle L1 in BASIC?

`rand(dim(L1->L2`

SortA(L2,L1

This is a super clever algorithm, but slow as heck as the lists get bigger. Plus, it uses an extra list of the same size, wasting precious RAM. So how does the Fisher-Yates algorithm work? You start at the last element. Randomly choose an element up to and including the current element and swap them. Now move down one element and repeat (so now the last element is off limits, then the last two, et cetera). Repeat this until there is one element left.

This is easy to perform in-place, and it performs n-1 swaps, making it significantly faster than the BASIC algorithm above. In fact, let's implement it in BASIC:

`dim(L1->N`

For(K,N,2,-1

randInt(1,K->A

L1(K->B

L1(A->L1(K

B->L1(A

End

This takes approximately 37.5 seconds to sort a 999 element list. I don't even have the RAM needed to test the regular method, but extrapolating, it would take the "normal" method approximately 73 seconds for 999 elements. So basically, the Fisher-Yates algorithm is actually faster even in TI-BASIC (after about 400 elements, though).

So without further ado, the assembly code!

`;Randomizes a TI-list in Ans`

_RclAns= 4AD7h

seed1 = $80F8

seed2 = $80FC

seed1_0=seed1

seed1_1=seed1+2

seed2_0=seed2

seed2_1=seed2+2

#define bcall(x) rst 28h \ .dw x

.db $BB,$6D

.org $9D95

; Put it into 15MHz mode if possible!

in a,(2)

add a,a

sbc a,a

out (20h),a

; Initialize the random seed

ld hl,seed1

ld b,7

ld a,r

_:

xor (hl)

ld (hl),a

inc hl

djnz -_

or 99

or (hl)

ld (hl),a

; Locate Ans, verify that it is a list or complex list

bcall(_RclAns)

ex de,hl

ld c,(hl)

inc hl

ld b,(hl)

inc hl

ld (list_base),hl

dec a

jr z,+_

sub 12

ret nz

dec a

_:

;A is 0 if a real list, -1 if complex

;HL points to the first element

;BC is the number of elements

and $29 ;make it either NOP or ADD HL,HL

ld (get_complex_element),a

sub 29h

sbc a,a

;FF if real, 00 if complex

cpl

and 9

add a,9

ld (element_size),a

shuffle_loop:

push bc

push bc

call rand

pop bc

ex de,hl

call mul16

dec bc

;swap elements DE and BC

call get_element

push hl

ld d,b

ld e,c

call get_element

pop de

call swap_elements

pop bc

dec bc

ld a,c

dec a

jr nz,shuffle_loop

inc b

dec b

jr nz,shuffle_loop

ret

swap_elements:

;HL and DE point to the elements

element_size = $+2

ld bc,255

_:

ld a,(de)

ldi

dec hl

ld (hl),a

inc hl

djnz -_

ret

get_element:

;Input:

; DE is the element to locate

;Output:

; HL points to the element

ld l,e

ld h,d

add hl,hl

add hl,hl

add hl,hl

add hl,de

get_complex_element:

nop

list_base = $+1

ld de,0

add hl,de

ret

rand:

;Tested and passes all CAcert tests

;Uses a very simple 32-bit LCG and 32-bit LFSR

;it has a period of 18,446,744,069,414,584,320

;roughly 18.4 quintillion.

;LFSR taps: 0,2,6,7 = 11000101

;291cc

;Thanks to Runer112 for his help on optimizing the LCG and suggesting to try the much simpler LCG. On their own, the two are terrible, but together they are great.

ld hl,(seed1)

ld de,(seed1+2)

ld b,h

ld c,l

add hl,hl \ rl e \ rl d

add hl,hl \ rl e \ rl d

inc l

add hl,bc

ld (seed1_0),hl

ld hl,(seed1_1)

adc hl,de

ld (seed1_1),hl

ex de,hl

;;lfsr

ld hl,(seed2)

ld bc,(seed2+2)

add hl,hl \ rl c \ rl b

ld (seed2_1),bc

sbc a,a

and %11000101

xor l

ld l,a

ld (seed2_0),hl

ex de,hl

add hl,bc

ret

mul16:

;BC*DE

ld hl,0

ld a,16

mul16_loop:

add hl,hl

rl e

rl d

jr nc,+_

add hl,bc

jr nc,+_

inc de

_:

dec a

jr nz,mul16_loop

ret

It isn't perfect, but it is pretty good and importantly, it is fast! The biggest problem is in the random number generator, but even that is still pretty good for this application.