If you want to make games, you will likely need math routines, if you are making a math program, you need math, and if you are making a utility, you will need math. You will need math in a good number of programs, so here are some routines that might prove useful.


1 Multiplication

1.1 DE_Times_A, 16-bit output

At 13 bytes, this code is a pretty decent balance of speed and size. It multiplies DE by A and returns a 16-bit result in HL.

   DE_Times_A:
   ;Inputs: DE,A
   ;Outputs: HL is product, B=0, A,C,DE preserved
   ;342cc~390cc, avg= 366cc
   ;size: 13 bytes
       ld b,8
       ld hl,0
   _:
       add hl,hl \ rlca \ jr nc,$+3 \ add hl,de \ djnz -_
       ret

1.2 DE_Times_A, 24-bit output

This version takes only a minor tweak to return the full 24-bit result.

   DE_Times_A:
   ;Inputs: DE,A
   ;Outputs: A:HL is product, BC=0,DE preserved
   ;343cc~423cc, avg= 383cc
   ;size: 14 bytes
       ld bc,0800h
       ld h,c
       ld l,c
   _:
       add hl,hl \ rla \ jr nc,$+4 \ add hl,de \ adc a,c
       djnz -_
       ret

1.3 DE_Times_A, Unrolled, 16-bit output

Unrolled routines are larger in most cases, but they can really save on speed. This is 25% faster at its slowest, 40% faster at its fastest:

   DE_Times_A:
   ;Inputs: DE,A
   ;Outputs: A:HL is product, BC,DE preserved
   ;min: 203cc
   ;max: 268cc
   ;avg: 235cc
   ;size: 43 bytes
       ld hl,0   \ rlca \ jr nc,$+5 \ ld h,d \ ld e,l
       add hl,hl \ rlca \ jr nc,$+3 \ add hl,de
       add hl,hl \ rlca \ jr nc,$+3 \ add hl,de
       add hl,hl \ rlca \ jr nc,$+3 \ add hl,de
       add hl,hl \ rlca \ jr nc,$+3 \ add hl,de
       add hl,hl \ rlca \ jr nc,$+3 \ add hl,de
       add hl,hl \ rlca \ jr nc,$+3 \ add hl,de
       add hl,hl \ rlca \ ret nc \ add hl,de \ ret

1.4 DE_Times_A, unrolled, 24-bit output

This version takes only a minor tweak to return the full 24-bit result. This is roughly 34% faster, being unrolled.

   DE_Times_A:
   ;Inputs: DE,A
   ;Outputs: A:HL is product, C=0, B,DE preserved
   ;207cc~300cc, avg= 253.5cc
   ;size: 14 bytes
       ld hl,0
       ld c,h
       ;or a      Uncomment to allow early exit if A=0
       ;ret z
               add a,a \ jr nc,$+5 \ ld h,d \ ld l,e
       add hl,hl \ rla \ jr nc,$+4 \ add hl,de \ adc a,c
       add hl,hl \ rla \ jr nc,$+4 \ add hl,de \ adc a,c
       add hl,hl \ rla \ jr nc,$+4 \ add hl,de \ adc a,c
       add hl,hl \ rla \ jr nc,$+4 \ add hl,de \ adc a,c
       add hl,hl \ rla \ jr nc,$+4 \ add hl,de \ adc a,c
       add hl,hl \ rla \ jr nc,$+4 \ add hl,de \ adc a,c
       add hl,hl \ rla \ ret nc \ add hl,de \ adc a,c
       ret

1.5 B_Times_DE, 16-bit output

This routine removes leading zeroes before finishing the multiplication, which take a little more code, but results in a faster average speed.

   B_Times_DE:
   ;Inputs: A,DE
   ;Outputs: HL=product, B=0, A=input B, C,DE unafected
   ;22 bytes
   ;B=0:    26cc
   ;B=1:    201cc
   ;B>1:    219cc~339cc
   ;avg=319.552734375cc    (319+283/512)
       ld hl,0
       or b
       ret z
       ld b,8
       rlca
       dec b
       jr nc,$-2
       ld h,d
       ld l,e
       ret z
   _:
       add hl,hl
       rlca
       jr nc,$+3
       add hl,de
       djnz -_
       ret

1.6 B_Times_DE, 24-bit output

This routine removes leading zeroes before finishing the multiplication, which take a little more code, but This routine uses another clever way of optimizing for speed without unrolling. The result is slightly larger and a bit faster. The idea here is to remove leading zeros before multiplying.


   B_Times_DE:
   ;Inputs: A,DE
   ;Outputs: HL=product, B=0, A=input B, C,DE unafected
   ;22 bytes
       ld hl,0
       or b
       ret z
       ld bc,800h
       rla
       dec b
       jr nc,$-2
       ld h,d
       ld l,e
       ret z
   _:
       add hl,hl
       rla
       jr nc,$+3
       add hl,de
       adc a,c
       djnz -_
       ret

1.7 DE_Times_BC, 32-bit result

   DE_Times_BC:
   ;Inputs:
   ;     DE and BC are factors
   ;Outputs:
   ;     A is 0
   ;     BC is not changed
   ;     DE:HL is the product
   ;902cc~1206cc, avg=1050cc
   ;20 bytes
          ld hl,0
          ld a,16
   Mul_Loop_1:
            add hl,hl
            rl e \ rl d
            jr nc,$+6
              add hl,bc
              jr nc,$+3
              inc de
            dec a
            jr nz,Mul_Loop_1
          ret

1.8 DE_Times_BC, pseudo-unrolled result

For 5 bytes more, you can cut out 93cc from the average. This method somehat unrolls the code by making the iterated code into a subroutine, then place a call to that subroutine that falls through to the same subroutine, essentially iterating it twice. Now do the same to this subroutine, and you have iterated 4 times, do this twice more to get the 16 iterations we need.

   DE_Times_BC:
   ;Inputs:
   ;     DE and BC are factors
   ;Outputs:
   ;     A,BC are not changed
   ;     DE:HL is the product
   ;25 bytes
   ;873cc~1289cc, avg=957cc
       ld hl,0
       call +_
   _:
       call +_
   _:
       call +_
   _:
       call +_
   _:
   ;38cc or 54cc or 64cc, avg=43.25
       add hl,hl
       rl e \ rl d
       ret nc
       add hl,bc
       ret nc
       inc de
       ret

1.9 BC_Times_DE, fully unrolled

This is very fast, averaging less than 600cc. 38% and 43% faster than the pseudo-unrolled and regular routine, but 123 bytes.

   BC_Times_DE:
   ;BC*DE->BCHL
   ;out: E=0, A,D are destroyed
   ;Assuming B==0,C==0     128cc
   ;Assuming B==0,C!=0     317cc~414cc, avg 365.5c
   ;         B!=0,C==0     317cc~422cc, avg 367.5c
   ;Assuming B!=0,C!=0     527cc~695cc, avg 598.5
   ;Overall average: 78209011/131072=596.68740081787109375
   ;123 bytes
       ld a,b
       ld hl,0
       ld b,h
       or a
       jr z,+_
               add a,a \ jr nc,$+5 \ ld h,d \ ld l,e
       add hl,hl \ rla \ jr nc,$+4 \ add hl,de \ adc a,b
       add hl,hl \ rla \ jr nc,$+4 \ add hl,de \ adc a,b
       add hl,hl \ rla \ jr nc,$+4 \ add hl,de \ adc a,b
       add hl,hl \ rla \ jr nc,$+4 \ add hl,de \ adc a,b
       add hl,hl \ rla \ jr nc,$+4 \ add hl,de \ adc a,b
       add hl,hl \ rla \ jr nc,$+4 \ add hl,de \ adc a,b
       add hl,hl \ rla \ jr nc,$+4 \ add hl,de \ adc a,b
   _:
       push hl
       ld h,b
       ld l,b
       ld b,a
       ld a,c
       ld c,b
       or a
       jr z,+_
               add a,a \ jr nc,$+5 \ ld h,d \ ld l,e
       add hl,hl \ rla \ jr nc,$+4 \ add hl,de \ adc a,c
       add hl,hl \ rla \ jr nc,$+4 \ add hl,de \ adc a,c
       add hl,hl \ rla \ jr nc,$+4 \ add hl,de \ adc a,c
       add hl,hl \ rla \ jr nc,$+4 \ add hl,de \ adc a,c
       add hl,hl \ rla \ jr nc,$+4 \ add hl,de \ adc a,c
       add hl,hl \ rla \ jr nc,$+4 \ add hl,de \ adc a,c
       add hl,hl \ rla \ jr nc,$+4 \ add hl,de \ adc a,c
   _:
       pop de
       ld c,d
       ld d,e
       ld e,0
       add hl,de
       ret nc
       adc a,c
       ld c,a
       ret nc
       inc b
       ret

source: Zeda's Pastebin/BC_Times_DE

1.10 C_Times_D

   C_Time_D:
   ;Outputs:
   ;     A is the result
   ;     B is 0
        ld b,8          ;7           7
        xor a           ;4           4
          rlca          ;4*8        32
          rlc c         ;8*8        64
          jr nc,$+3     ;(12|11)    96|88
            add a,d     ;--
          djnz $-6      ;13*7+8     99
        ret             ;10         10
   ;304+b (b is number of bits)
   ;308 is average speed.
   ;12 bytes


1.11 mul32, 64-bit output

With these sizes, we need to use RAM to hold intermediate values. mul16 needs to perform DE*BC => DEHL

   mul32:
   ;;uses karatsuba multiplication
   ;;var_x * var_y
   ;;z0 holds the 64-bit result
   ;;708cc+6a+13b+42c +3mul
   ;;Avg: 2464.110153
   ;;Max:2839cc, 92cc faster
   ;;Min:2178cc (early can make it faster, though), 167cc faster
       ld de,(var_x)   ;\
       ld bc,(var_y)   ; |compute z0,z2
       push bc         ; | var_y
       call mul16      ; |
       ld (var_z0),hl  ; |
       ld bc,(var_y+2) ; |
       ld (var_z0+2),de; |
       ld de,(var_x+2) ; |
       push bc         ; | var_y+2
       call mul16      ; |
       ld (var_z2),hl  ; |
       ld (var_z2+2),de;/      208cc
       xor a           ;\
       ld hl,(var_x)   ; |
       ld de,(var_x+2) ; |
       add hl,de       ; |
       rra             ; |
       pop de          ; |
       ex (sp),hl      ; |
       add hl,de       ; |
       pop bc          ; |
       ex de,hl        ; |     109cc
       push de         ; |if bit0=1, add DE<<16 to result
       push bc         ; |
       push af         ; |c flag means add BC<<16 to result
       call mul16      ; |
       ex de,hl        ; |
       pop af          ; |
       pop bc          ; |
       jr nc,$+3       ; |     86+6a
       add hl,bc       ; |
       pop bc          ; |
       rla             ; |
       jr nc,$+4       ; |     26+13b
       add hl,bc       ; |
       adc a,0         ; |z1 = AHLDE-z2-z1
       ex de,hl \ ld bc,(var_z0) \ sbc hl,bc
       ex de,hl \ ld bc,(var_z0+2) \ sbc hl,bc
       sbc a,0
       ex de,hl \ ld bc,(var_z2) \ sbc hl,bc
       ex de,hl \ ld bc,(var_z2+2) \ sbc hl,bc
       sbc a,0         ; |z1 = AHLDE
       ld b,h \ ld c,l ;/ z1 = ABCDE
       ld hl,(var_z0+2);\
       add hl,de       ; |Add:
       ld (var_z0+2),hl; |z2z0
       ld hl,(var_z2)  ; | z1
       adc hl,bc       ; |----
       ld (var_z2),hl  ; |
       ret nc          ; |     279+42c
       ld hl,(var_z2+2); |
       inc hl          ; |
       ld (var_z2+2),hl; |
       ret             ;/

source Zeda's Pastebin/mul32

1.12 BCDE_Times_A

   BCDE_Times_A:
   ;Inputs: BC:DE,A
   ;Outputs: A:HL:IX is the 40-bit product, BC,DE unaffected
   ;503cc~831cc
   ;667cc average
   ;29 bytes
       ld ix,0
       ld hl,0
       call +_
   _:
       call +_
   _:
       call +_
   _:
       add ix,ix \ adc hl,hl \ rla \ ret nc
       add ix,de \ adc hl,bc \ adc a,0
       ret

source: Zeda's Pastebin/BCDE_Times_A

1.13 H_Times_E

This is the fastest and smallest rolled 8-bit multiplication routine here, and it returns the full 16-bit result.

   H_Times_E:
   ;Inputs:
   ;     H,E
   ;Outputs:
   ;     HL is the product
   ;     D,B are 0
   ;     A,E,C are preserved
   ;Size:  12 bytes
   ;Speed: 311+6b, b is the number of bits set in the input HL
   ;      average is 335 cycles
   ;      max required is 359 cycles
        ld d,0     ;1600    7      7
        ld l,d     ;6A      4      4
        ld b,8     ;0608    7      7
                   ;            
        add hl,hl  ;29      11*8   88
        jr nc,$+3  ;3001 12*8-5b   96-5b
        add hl,de  ;19      11*b   11b
        djnz $-4   ;10FA  13*8-5   99
                   ;            
        ret        ;C9      10     10

== H_Times_E == (Unrolled)

   H_Times_E:
   ;Inputs:
   ;     H,E
   ;Outputs:
   ;     HL is the product
   ;     D,B are 0
   ;     A,E,C are preserved
   ;Size:  38 bytes
   ;Speed: 198+6b+9p-7s, b is the number of bits set in the input H, p is if it is odd, s is the upper bit of h
   ;   average is 226.5 cycles (108.5 cycles saved)
   ;   max required is 255 cycles (104 cycles saved)
        ld d,0      ;1600   7   7
        ld l,d      ;6A     4   4
        ld b,8      ;0608   7   7
              ;      
        sla h   ;   8
        jr nc,$+3   ;3001  12-b
        ld l,e   ;6B    --
   
        add hl,hl   ;29    11
        jr nc,$+3   ;3001  12+6b
        add hl,de   ;19    --
   
        add hl,hl   ;29    11
        jr nc,$+3   ;3001  12+6b
        add hl,de   ;19    --
   
        add hl,hl   ;29    11
        jr nc,$+3   ;3001  12+6b
        add hl,de   ;19    --
   
        add hl,hl   ;29    11
        jr nc,$+3   ;3001  12+6b
        add hl,de   ;19    --
   
        add hl,hl   ;29    11
        jr nc,$+3   ;3001  12+6b
        add hl,de   ;19    --
   
        add hl,hl   ;29    11
        jr nc,$+3   ;3001  12+6b
        add hl,de   ;19    --
   
        add hl,hl   ;29   11
        ret nc      ;D0   11+15p
        add hl,de   ;19   --
        ret         ;C9   --

1.14 L_Squared (fast)

The following provides an optimized algorithm to square an 8-bit number, but it only returns the lower 8 bits.

   L_sqrd:
   ;Input: L
   ;Output: L*L->A
   ;151 t-states
   ;37 bytes
   	ld h,l
   ;First iteration, get the lowest 3 bits
   	sla l
   	rr h
   	sbc a,a
   	or l
   ;second iteration, get the next 2 bits
   	ld c,a
   	rr h
   	sbc a,a
   	xor l
   	and $F8
   	add a,c
   ;third iteration, get the next 2 bits
   	ld c,a
   	sla l
   	rr h
   	sbc a,a
   	xor l
   	and $E0
   	add a,c
   ;fourth iteration, get the last bit
   	ld c,a
   	ld a,l
   	add a,a
   	rrc h
   	xor h
   	and $80
   	xor c
   	neg
   	ret

2 Absolute Value

Here are a handful of optimised routines for the absolute value of a number:

2.1 absHL

   absHL:
        bit 7,h
        ret z
        xor a \ sub l \ ld l,a
        sbc a,a \ sub h \ ld h,a
        ret

2.2 absDE

   absDE:
        bit 7,d
        ret z
        xor a \ sub e \ ld e,a
        sbc a,a \ sub d \ ld d,a
        ret

2.3 absBC

   absBC:
        bit 7,b
        ret z
        xor a \ sub c \ ld c,a
        sbc a,a \ sub b \ ld b,a
        ret

2.4 absA

   absA:
        or a
        ret p
        neg
        ret

2.5 abs[reg8]

   abs[reg8]:
       xor a
       sub [reg8]
       ret m
       ld [reg8],a
       ret

3 Division

3.1 C_Div_D

This is a simple 8-bit division routine:


   C_Div_D:
   ;Inputs:
   ;     C is the numerator
   ;     D is the denominator
   ;Outputs:
   ;     A is the remainder
   ;     B is 0
   ;     C is the result of C/D
   ;     D,E,H,L are not changed
   ;
        ld b,8
        xor a
          sla c
          rla
          cp d
          jr c,$+4
            inc c
            sub d
          djnz $-8
        ret

3.2 BC_Div_DE

This divides BC by DE, storing the result in AC, remainder in HL

   BC_Div_DE:
   ;Inputs: BC,DE
   ;Outputs: DE unaffected, HL is remainder, AC is quotient, B=0
   ;20 bytes
   ;1098cc~1258cc, avg=1178cc
       ld hl,0
       ld a,b
       ld b,16
   _:
       sll c \ rla \ adc hl,hl \ sbc hl,de \ jr nc,$+4 \ add hl,de \ dec c
       djnz -_
       ret

3.3 DEHL_Div_C

This divides the 32-bit value in DEHL by C:

   DEHL_Div_C:
   ;Inputs:
   ;     DEHL is a 32 bit value where DE is the upper 16 bits
   ;     C is the value to divide DEHL by
   ;Outputs:
   ;    A is the remainder
   ;    B is 0
   ;    C is not changed
   ;    DEHL is the result of the division
   ;
        ld b,32
        xor a
          add hl,hl
          rl e \ rl d
          rla
          cp c
          jr c,$+4
            inc l
            sub c
          djnz $-11
        ret

3.4 DEHLIX_Div_C

   DEHLIX_Div_C:
   ;Inputs:
   ;     DEHLIX is a 48 bit value where DE is the upper 16 bits
   ;     C is the value to divide DEHL by
   ;Outputs:
   ;    A is the remainder
   ;    B is 0
   ;    C is not changed
   ;    DEHLIX is the result of the division
   ;
        ld b,48
        xor a
          add ix,ix
          adc hl,hl
          rl e \ rl d
          rla
          cp c
          jr c,$+5
            inc ixl
            sub c
          djnz $-15
        ret


3.5 HL_Div_C

   HL_Div_C:
   ;Inputs:
   ;     HL is the numerator
   ;     C is the denominator
   ;Outputs:
   ;     A is the remainder
   ;     B is 0
   ;     C is not changed
   ;     DE is not changed
   ;     HL is the quotient
   ;
          ld b,16
          xor a
            add hl,hl
            rla
            cp c
            jr c,$+4
              inc l
              sub c
            djnz $-7
          ret

3.6 HLDE_Div_C

   HLDE_Div_C:
   ;Inputs:
   ;     HLDE is a 32 bit value where HL is the upper 16 bits
   ;     C is the value to divide HLDE by
   ;Outputs:
   ;    A is the remainder
   ;    B is 0
   ;    C is not changed
   ;    HLDE is the result of the division
   ;
        ld b,32
        xor a
          sll e \ rl d
          adc hl,hl
          rla
          cp c
          jr c,$+4
            inc e
            sub c
          djnz $-12
        ret

3.7 RoundHL_Div_C

Returns the result of the division rounded to the nearest integer.

   RoundHL_Div_C:
   ;Inputs:
   ;     HL is the numerator
   ;     C is the denominator
   ;Outputs:
   ;     A is twice the remainder of the unrounded value 
   ;     B is 0
   ;     C is not changed
   ;     DE is not changed
   ;     HL is the rounded quotient
   ;     c flag set means no rounding was performed
   ;            reset means the value was rounded
   ;
          ld b,16
          xor a
            add hl,hl
            rla
            cp c
            jr c,$+4
              inc l
              sub c
            djnz $-7
          add a,a
          cp c
          jr c,$+3
            inc hl
          ret


3.8 Speed Optimised HL_div_10

By adding 9 bytes to the code, we save 87 cycles: (min speed = 636 t-states)

   DivHLby10:
   ;Inputs:
   ;     HL
   ;Outputs:
   ;     HL is the quotient
   ;     A is the remainder
   ;     DE is not changed
   ;     BC is 10
   
    ld bc,$0D0A
    xor a
    add hl,hl \ rla
    add hl,hl \ rla
    add hl,hl \ rla
   
    add hl,hl \ rla
    cp c
    jr c,$+4
      sub c
      inc l
    djnz $-7
    ret


3.9 Speed Optimised EHL_Div_10

By adding 20 bytes to the routine, we actually save 301 t-states. The speed is quite fast at a minimum of 966 t-states and a max of 1002:

   DivEHLby10:
   ;Inputs:
   ;     EHL
   ;Outputs:
   ;     EHL is the quotient
   ;     A is the remainder
   ;     D is not changed
   ;     BC is 10
   
    ld bc,$050a
    xor a
    sla e \ rla
    sla e \ rla
    sla e \ rla
   
    sla e \ rla
    cp c
    jr c,$+4
      sub c
      inc e
    djnz $-8
   
    ld b,16
   
    add hl,hl
    rla
    cp c
    jr c,$+4
    sub c
    inc l
    djnz $-7
    ret


3.10 Speed Optimised DEHL_Div_10

The minimum speed is now 1350 t-states. The cost was 15 bytes, the savings were 589 t-states

   DivDEHLby10:
   ;Inputs:
   ;     DEHL
   ;Outputs:
   ;     DEHL is the quotient
   ;     A is the remainder
   ;     BC is 10
   
    ld bc,$0D0A
    xor a
    ex de,hl
    add hl,hl \ rla
    add hl,hl \ rla
    add hl,hl \ rla
   
    add hl,hl \ rla
    cp c
    jr c,$+4
      sub c
      inc l
    djnz $-7
   
    ex de,hl
    ld b,16
   
    add hl,hl
    rla
    cp c
    jr c,$+4
    sub c
    inc l
    djnz $-7
    ret


3.11 A_Div_C (small)

This routine should only be used when C is expected to be greater than 16. In this case, the naive way is actually the fastest and smallest way:

    ld b,-1
    sub c
    inc b
    jr nc,$-2
    add a,c

Now B is the quotient, A is the remainder. It takes at least 26 t-states and at most 346 if you ensure that c>16

3.12 E_div_10 (tiny+fast)

This is how it would appear inline, since it is so small at 10 bytes (and 81 t-states). It divides E by 10, returning the result in H :

   e_div_10:
   ;returns result in H
        ld d,0
        ld h,d \ ld l,e
        add hl,hl
        add hl,de
        add hl,hl
        add hl,hl
        add hl,de
        add hl,hl



4 Square Root

4.1 RoundSqrtE

Returns the square root of E, rounded to the nearest integer:

   ;===============================================================
   sqrtE:
   ;===============================================================
   ;Input:
   ;     E is the value to find the square root of
   ;Outputs:
   ;     A is E-D^2
   ;     B is 0
   ;     D is the rounded result
   ;     E is not changed
   ;     HL is not changed
   ;Destroys:
   ;     C
   ;
           xor a               ;1      4         4
           ld d,a              ;1      4         4
           ld c,a              ;1      4         4
           ld b,4              ;2      7         7
   sqrtELoop:
           rlc d               ;2      8        32
           ld c,d              ;1      4        16
           scf                 ;1      4        16
           rl c                ;2      8        32
   
           rlc e               ;2      8        32
           rla                 ;1      4        16
           rlc e               ;2      8        32
           rla                 ;1      4        16
   
           cp c                ;1      4        16
           jr c,$+4            ;4    12|15      48+3x
             inc d             ;--    --        --
             sub c             ;--    --        --
           djnz sqrtELoop      ;2    13|8       47
           cp d                ;1      4         4
           jr c,$+3            ;3    12|11     12|11
             inc d             ;--    --        --
           ret                 ;1     10        10
   ;===============================================================
   ;Size  : 29 bytes
   ;Speed : 347+3x cycles plus 1 if rounded down
   ;   x is the number of set bits in the result.
   ;===============================================================


4.2 SqrtE

This returns the square root of E (rounded down).

   ;===============================================================
   sqrtE:
   ;===============================================================
   ;Input:
   ;     E is the value to find the square root of
   ;Outputs:
   ;     A is E-D^2
   ;     B is 0
   ;     D is the result
   ;     E is not changed
   ;     HL is not changed
   ;Destroys:
   ;     C=2D+1 if D is even, 2D-1 if D is odd
   
           xor a               ;1      4         4
           ld d,a              ;1      4         4
           ld c,a              ;1      4         4
           ld b,4              ;2      7         7
   sqrtELoop:
           rlc d               ;2      8        32
           ld c,d              ;1      4        16
           scf                 ;1      4        16
           rl c                ;2      8        32
   
           rlc e               ;2      8        32
           rla                 ;1      4        16
           rlc e               ;2      8        32
           rla                 ;1      4        16
   
           cp c                ;1      4        16
           jr c,$+4            ;4    12|15      48+3x
             inc d             ;--    --        --
             sub c             ;--    --        --
           djnz sqrtELoop      ;2    13|8       47
           ret                 ;1     10        10
   ;===============================================================
   ;Size  : 25 bytes
   ;Speed : 332+3x cycles
   ;   x is the number of set bits in the result. This will not
   ;   exceed 4, so the range for cycles is 332 to 344. To put this
   ;   into perspective, under the slowest conditions (4 set bits
   ;   in the result at 6MHz), this can execute over 18000 times
   ;   in a second.
   ;===============================================================


4.3 SqrtHL

This returns the square root of HL (rounded down). It is faster than division, interestingly:

   SqrtHL4:
   ;39 bytes
   ;Inputs:
   ;     HL
   ;Outputs:
   ;     BC is the remainder
   ;     D is not changed
   ;     E is the square root
   ;     H is 0
   ;Destroys:
   ;     A
   ;     L is a value of either {0,1,4,5}
   ;       every bit except 0 and 2 are always zero
   
        ld bc,0800h   ;3  10      ;10
        ld e,c        ;1  4       ;4
        xor a         ;1  4       ;4
   SHL4Loop:          ;           ;
        add hl,hl     ;1  11      ;88
        rl c          ;2  8       ;64
        adc hl,hl     ;2  15      ;120
        rl c          ;2  8       ;64
        jr nc,$+4     ;2  7|12    ;96+3y   ;y is the number of overflows. max is 2
        set 0,l       ;2  8       ;--
        ld a,e        ;1  4       ;32
        add a,a       ;1  4       ;32
        ld e,a        ;1  4       ;32
        add a,a       ;1  4       ;32
        bit 0,l       ;2  8       ;64
        jr nz,$+5     ;2  7|12    ;144-6y
        sub c         ;1  4       ;32
        jr nc,$+7     ;2  7|12    ;96+15x  ;number of bits in the result
            ld a,c    ;1  4       ;
            sub e     ;1  4       ;
            inc e     ;1  4       ;
            sub e     ;1  4       ;
            ld c,a    ;1  4       ;
        djnz SHL4Loop ;2  13|8    ;99
        bit 0,l       ;2  8       ;8
        ret z         ;1  11|19   ;11+8z
        inc b         ;1          ;
        ret           ;1          ;
   ;1036+15x-3y+8z
   ;x is the number of set bits in the result
   ;y is the number of overflows (max is 2)
   ;z is 1 if 'b' is returned as 1
   ;max is 1154 cycles
   ;min is 1032 cycles


4.4 SqrtL

This returns the square root of L, rounded down:


   SqrtL:
   ;Inputs:
   ;     L is the value to find the square root of
   ;Outputs:
   ;      C is the result
   ;      B,L are 0
   ;     DE is not changed
   ;      H is how far away it is from the next smallest perfect square
   ;      L is 0
   ;      z flag set if it was a perfect square
   ;Destroyed:
   ;      A
        ld bc,400h       ; 10    10
        ld h,c           ; 4      4
   sqrt8Loop:            ;
        add hl,hl        ;11     44
        add hl,hl        ;11     44
        rl c             ; 8     32
        ld a,c           ; 4     16
        rla              ; 4     16
        sub a,h          ; 4     16
        jr nc,$+5        ;12|19  48+7x
          inc c
          cpl
          ld h,a
        djnz sqrt8Loop   ;13|8   47
        ret              ;10     10
   ;287+7x
   ;19 bytes



5 ConvFloat (or ConvOP1)

This converts a floating point number pointed to by DE to a 16 bit-value. This is like bcall(_ConvOP1) without the limit of 9999 and a bit more flexible (since the number doesn't need to be at OP1):


   ConvOP1: 
   ;;Output: HL is the 16-bit result. 
       ld de,OP1 
   ConvFloat: 
   ;;Input: DE points to the float. 
   ;;Output: HL is the 16-bit result. 
   ;;Errors: DataType if the float is negative or complex 
   ;;        Domain if the integer exceeds 16 bits. 
   ;;Timings:  Assume no errors were called. 
   ;;  Input is on: 
   ;;  (0,1)         => 59cc                        Average=59 
   ;;  0 or [1,10)   => 120cc or 129cc                     =124.5 
   ;;  [10,100)      => 176cc or 177cc                     =176.5 
   ;;  [100,1000)    => 309cc, 310cc, 318cc, or 319cc.     =314 
   ;;  [1000,10000)  => 376cc to 378cc                     =377 
   ;;  [10000,65536) => 514cc to 516cc, or 523cc to 525cc  =519.5 
   ;;Average case:  496.577178955078125cc 
   ;;vs 959.656982421875cc 
   ;;87 bytes 
       ld a,(de) 
       or a 
       jr nz,ErrDataType 
       inc de 
       ld hl,0 
       ld a,(de) 
       inc de 
       sub 80h 
       ret c 
       jr z,final 
       cp 5 
       jp c,enterloop 
   ErrDomain: 
   ;Throws a domain error. 
       bcall(_ErrDomain) 
   ErrDataType: 
   ;Throws a data type error. 
       bcall(_ErrDataType) 
   loop: 
       ld a,b 
       ld b,h 
       ld c,l 
       add hl,hl 
       add hl,bc 
       add hl,hl 
       add hl,hl 
       add hl,hl 
       add hl,bc 
       add hl,hl 
       add hl,hl 
   enterloop: 
       ld b,a 
       ex de,hl 
       ld a,(hl) \ and $F0 \ rra \ ld c,a \ rra \ rra \ sub c \ add a,(hl) 
       inc hl 
       ex de,hl 
       add a,l 
       ld l,a 
       jr nc,$+3 
       inc h 
       dec b 
       ret z 
       djnz loop 
       ld b,h 
       ld c,l 
       xor a 
   ;check overflow in this mul by 10! 
       add hl,hl \ adc a,a 
       add hl,hl \ adc a,a 
       add hl,bc \ adc a,0 
       add hl,hl \ adc a,a 
       jr nz,ErrDomain 
   final: 
       ld a,(de) 
       rrca 
       rrca 
       rrca 
       rrca 
       and 15 
       add a,l 
       ld l,a 
       ret nc 
       inc h 
       ret nz
       jr ErrDomain

source: Cemetech/Useful Routines

6 ConvStr16

This will convert a string of base-10 digits to a 16-bit value. Useful for parsing numbers in a string:

   ;===============================================================
   ConvRStr16:
   ;===============================================================
   ;Input: 
   ;     DE points to the base 10 number string in RAM. 
   ;Outputs: 
   ;     HL is the 16-bit value of the number 
   ;     DE points to the byte after the number 
   ;     BC is HL/10 
   ;     z flag reset (nz)
   ;     c flag reset (nc)
   ;Destroys: 
   ;     A (actually, add 30h and you get the ending token) 
   ;Size:  23 bytes 
   ;Speed: 104n+42+11c
   ;       n is the number of digits 
   ;       c is at most n-2 
   ;       at most 595 cycles for any 16-bit decimal value 
   ;===============================================================
        ld hl,0          ;  10 : 210000 
   ConvLoop:             ; 
        ld a,(de)        ;   7 : 1A 
        sub 30h          ;   7 : D630 
        cp 10            ;   7 : FE0A 
        ret nc           ;5|11 : D0 
        inc de           ;   6 : 13 
                         ; 
        ld b,h           ;   4 : 44 
        ld c,l           ;   4 : 4D 
        add hl,hl        ;  11 : 29 
        add hl,hl        ;  11 : 29 
        add hl,bc        ;  11 : 09 
        add hl,hl        ;  11 : 29 
                         ; 
        add a,l          ;   4 : 85 
        ld l,a           ;   4 : 6F 
        jr nc,ConvLoop   ;12|23: 30EE 
        inc h            ; --- : 24 
        jr ConvLoop      ; --- : 18EB


7 gcdHL_DE

This computes the Greatest Common Divisor of HL and DE, using the binary gcd algorithm.

   gcdHL_DE:
   ;gcd(HL,DE)->HL
   ;binary GCD algorithm
       ld a,h \ or l \ ret z
       ex de,hl
       ld a,h \ or l \ ret z
       sbc hl,de
       add hl,de
       ret z
       ld b,1
       ld a,e \ or l \ rra \ jr c,+_
       inc b
       rr h \ rr l
       rr d \ rr e
       ld a,e \ or l \ rra \ jr nc,$-12
   _:
       srl h \ rr l \ jr nc,$-4 \ adc hl,hl
       ex de,hl
   _:
       srl h \ rr l \ jr nc,$-4 \ adc hl,hl
       xor a \ sbc hl,de
       jr z,+_
       jr nc,-_ \ sub l \ ld l,a \ sbc a,a \ sub h \ ld h,a
       jp -_-1
   _:
       ex de,hl
       dec b
       ret z
       add hl,hl
       djnz $-1
       ret

8 Modulus

8.1 DEHL_mod_3

See below.

8.2 HLDE_mod_3

See below.

8.3 HL_mod_3

See below.

8.4 A_mod_3

Computes A mod 3 (essentially, the remainder of A after division by 3):

   DEHL_mod_3:
   HLDE_mod_3:
   ;Inputs: 
   ;  HL:DE  unsigned integer 
   ;Outputs: 
   ;  A = HLDE mod 3 
   ;  Z flag is set if divisible by 3 
   ;Destroys: 
   ;  C 
   ; 27 bytes, 103cc,118cc,104cc,119cc, avg=114.75cc
        add hl,de
        jr nc,$+3
        dec hl
   HL_mod_3:
   ;Inputs: 
   ;  HL  unsigned integer 
   ;Outputs: 
   ;  A = HL mod 3 
   ;  Z flag is set if divisible by 3 
   ;Destroys: 
   ;  C 
   ; 23 bytes, 80cc or 95cc, avg 91.25cc
       ld a,h
       add a,l
       sbc a,0   ;conditional decrement
   A_mod_3: 
   ;Inputs: 
   ;  A  unsigned integer 
   ;Outputs: 
   ;  A = A mod 3 
   ;  Z flag is set if divisible by 3 
   ;Destroys: 
   ;  C 
   ; 19 bytes,  65cc or 80cc, avg=76.25cc
       ld c,a                     ;add nibbles  
       rrca / rrca / rrca / rrca  
       add a,c  
       adc a,0                    ;n mod 15 (+1) in both nibbles  
       ld c,a                     ;add half nibbles  
       rrca / rrca  
       add a,c  
       adc a,1  
       ret z  
       and 3 
       dec a 
       ret

source: Cemetech/Fast 8-bit mod 3


8.5 A_mod_10:

This is not a typical method used, but it is small and fast at 196 to 201 t-states, 12 bytes

   ld bc,05A0h
   Loop:
        sub c
        jr nc,$+3
          add a,c
        srl c
        djnz Loop
        ret

9 Random Numbers

9.1 rand8_LCG

This is one of many variations of PRNGs. This routine is not particularly useful for many games, but is fairly useful for shuffling a deck of cards. It uses SMC, but that can be fixed by defining randSeed elsewhere and using ld a,(randSeed) at the beginning.

   rand8_LCG:
   ;f(n+1)=13f(n)+83
   ;97 cycles
   randSeed=$+1
       ld a,3
       ld c,a
       add a,a
       add a,c
       add a,a
       add a,a
       add a,c
       add a,83
       ld (randSeed),a
       ret

9.2 rand16_LCG

Similar to the rand8_LCG, this generates a a sequence of pseudo-random values that has a cycle of 65536 (so it will hit every single 16-bit integer):

   rand16_LCG:
   ;f(n+1)=241f(n)+257   ;65536
   ;181 cycles, add 17 if called
   ;Outputs:
   ;     BC was the previous pseudorandom value
   ;     HL is the next pseudorandom value
   ;Notes:
   ;     You can also use B,C,H,L as pseudorandom 8-bit values
   ;     this will generate all 8-bit values
   randSeed=$+1
       ld hl,235
       ld c,l
       ld b,h
       add hl,hl
       add hl,bc
       add hl,hl
       add hl,bc
       add hl,hl
       add hl,bc
       add hl,hl
       add hl,hl
       add hl,hl
       add hl,hl
       add hl,bc
       inc h
       inc hl
       ld (randSeed),hl
       ret

9.3 rand; best quality:speed

This routine uses a combined LFSR and LCG to offer an extremely fast and proven high quality pseudo random numbers.

   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. 
   ;;291cc 
   ;;58 bytes 
   seed1_0=$+1 
       ld hl,12345 
   seed1_1=$+1 
       ld de,6789 
       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 
   seed2_0=$+1 
       ld hl,9876 
   seed2_1=$+1 
       ld bc,54321 
       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

source: Cemetech/Useful Routines

9.4 rand; very fast

The cycle for this is more limited, but is still quite large and well suited to games.

   rand:
   ;collab with Runer112
   ;;Output:
   ;;    HL is a pseudo-random int
   ;;    A and BC are also, but much weaker and smaller cycles
   ;;    Preserves DE
   ;;148cc, super fast
   ;;26 bytes
   ;;period length: 4,294,901,760
   seed1=$+1
       ld hl,9999
       ld b,h
       ld c,l
       add hl,hl
       add hl,hl
       inc l
       add hl,bc
       ld (seed1),hl
   seed2=$+1
       ld hl,987
       add hl,hl
       sbc a,a
       and %00101101
       xor l
       ld l,a
       ld (seed2),hl
       add hl,bc
       ret

source: Zeda's Pastebin/rand

9.5 randInt

This returns a random integer on [0,A-1].

   rand:
   ;;Input: A is the range.
   ;;Output: Returns in A a random number from 0 to B-1.
   ;;  B=0
   ;;  DE is not changed
   ;;Destroys:
   ;;  HL
   ;;Speed:
   ;;  322cc to 373cc, 347.5cc average
       push af
       call rand
       ex de,hl
       pop af
       ld hl,0
       ld b,h
       add a,a \ jr nc,$+5 \ ld h,d \ ld l,e
       add hl,hl \ rla \ jr nc,$+4 \ add hl,de \ adc a,b
       add hl,hl \ rla \ jr nc,$+4 \ add hl,de \ adc a,b
       add hl,hl \ rla \ jr nc,$+4 \ add hl,de \ adc a,b
       add hl,hl \ rla \ jr nc,$+4 \ add hl,de \ adc a,b
       add hl,hl \ rla \ jr nc,$+4 \ add hl,de \ adc a,b
       add hl,hl \ rla \ jr nc,$+4 \ add hl,de \ adc a,b
       add hl,hl \ rla \ ret nc \ add hl,de \ adc a,b
       ret

source: Zeda's Pastebin/rand

10 Fixed Point Math

Fixed Point numbers are similar to Floating Point numbers in that they give the user a way to work with non-integers. For some terminology, an 8.8 Fixed Point number is 16 bits where the upper 8 bits is the integer part, the lower 8 bits is the fractional part. Both Floating Point and Fixed Point are abbreviated 'FP', but one can tell if Fixed Point is being referred to by context. The way one would interpret an 8.8 FP number would be to take the upper 8 bits as the integer part and divide the lower 8-bits by 256 (2[sup]8[/sup]) so if HL is an 8.8 FP number that is $1337, then its value is 19+55/256 = 19.21484375. In most cases, integers are enough for working in Z80 Assembly, but if that doesn't work, you will rarely need more than 16.16 FP precision (which is 32 bits in all). FP algorithms are generally pretty similar to their integer counterparts, so it isn't too difficult to convert.

10.1 FPLog88

This is an 8.8 fixed point natural log routine. This is extremely accurate. In the very worst case, it is off by 2/256, but on average, it is off by less than 1/256 (the smallest unit for an 8.8 FP number).

   FPLog88:
   ;Input:
   ;     HL is the 8.8 Fixed Point input. H is the integer part, L is the fractional part.
   ;Output:
   ;     HL is the natural log of the input, in 8.8 Fixed Point format.
        ld a,h
        or l
        dec hl
        ret z
        inc hl
        push hl
        ld b,15
        add hl,hl
        jr c,$+4
        djnz $-3
        ld a,b
        sub 8
        jr nc,$+4
        neg
        ld b,a
        pop hl
        push af
        jr nz,lnx
        jr nc,$+7
        add hl,hl
        djnz $-1
        jr lnx
        sra h
        rr l
        djnz $-4
   lnx:
        dec h        ;subtract 1 so that we are doing ln((x-1)+1) = ln(x)
        push hl      ;save for later
        add hl,hl    ;we are doing the 4x/(4+4x) part
        add hl,hl
        ld d,h
        ld e,l
        inc h
        inc h
        inc h
        inc h
        call FPDE_Div_HL  ;preserves DE, returns AHL as the 16.8 result
        pop de       ;DE is now x instead of 4x
        inc h        ;now we are doing x/(3+Ans)
        inc h
        inc h
        call FPDE_Div_HL
        inc h        ;now we are doing x/(2+Ans)
        inc h
        call FPDE_Div_HL
        inc h        ;now we are doing x/(1+Ans)
        call FPDE_Div_HL  ;now it is computed to pretty decent accuracy
        pop af       ;the power of 2 that we divided the initial input by
        ret z        ;if it was 0, we don't need to add/subtract anything else
        ld b,a
        jr c,SubtLn2
        push hl
        xor a
        ld de,$B172  ;this is approximately ln(2) in 0.16 FP format
        ld h,a
        ld l,a
        add hl,de
        jr nc,$+3
        inc a
        djnz $-4
        pop de
        rl l         ;returns c flag if we need to round up
        ld l,h
        ld h,a
        jr nc,$+3
        inc hl
        add hl,de
        ret
   SubtLn2:
        ld de,$00B1
          or a
          sbc hl,de
          djnz $-3
        ret
   
   
   FPDE_Div_HL:
   ;Inputs:
   ;     DE,HL are 8.8 Fixed Point numbers
   ;Outputs:
   ;     DE is preserved
   ;     AHL is the 16.8 Fixed Point result (rounded to the least significant bit)
        di
        push de
        ld b,h
        ld c,l
        ld a,16
        ld hl,0
   Loop1:
        sla e
        rl d
        adc hl,hl
        jr nc,$+8
        or a
        sbc hl,bc
        jp incE
        sbc hl,bc
        jr c,$+5
   incE:
        inc e
        jr $+3
        add hl,bc
        dec a
        jr nz,Loop1
        ex af,af'
        ld a,8
   Loop2:
        ex af,af'
        sla e
        rl d
        rl a
        ex af,af'
        add hl,hl
        jr nc,$+8
        or a
        sbc hl,bc
        jp incE_2
        sbc hl,bc
        jr c,$+5
   incE_2:
        inc e
        jr $+3
        add hl,bc
        dec a
        jr nz,Loop2
   ;round
        ex af,af'
        add hl,hl
        jr c,$+6
        sbc hl,de
        jr c,$+9
        inc e
        jr nz,$+6
        inc d
        jr nz,$+3
        inc a
        ex de,hl
        pop de
        ret

10.2 FPDE_Div_BC88

This performs Fixed Point division for DE/BC where DE and BC are 8.8 FP numbers. This returns a little extra precision for the integer part (16-bit integer part, 8-bit fractional part).

   FPDE_Div_BC88:
   ;Inputs:
   ;     DE,BC are 8.8 Fixed Point numbers
   ;Outputs:
   ;     ADE is the 16.8 Fixed Point result (rounded to the least significant bit)
        di
        ld a,16
        ld hl,0
   Loop1:
        sla e
        rl d
        adc hl,hl
        jr nc,$+8
        or a
        sbc hl,bc
        jp incE
        sbc hl,bc
        jr c,$+5
   incE:
        inc e
        jr $+3
        add hl,bc
        dec a
        jr nz,Loop1
        ex af,af'
        ld a,8
   Loop2:
        ex af,af'
        sla e
        rl d
        rla
        ex af,af'
        add hl,hl
        jr nc,$+8
        or a
        sbc hl,bc
        jp incE_2
        sbc hl,bc
        jr c,$+5
   incE_2:
        inc e
        jr $+3
        add hl,bc
        dec a
        jr nz,Loop2
   ;round
        ex af,af'
        add hl,hl
        jr c,$+5
        sbc hl,de
        ret c
        inc e
        ret nz
        inc d
        ret nz
        inc a
        ret

10.3 Log_2_88

These computes log base 2 of the fixed point 8.8 number. This is much faster and smaller than the natural log routine above.

10.3.1 (size optimised)

   Log_2_88_size:
   ;Inputs:
   ;     HL is an unsigned 8.8 fixed point number.
   ;Outputs:
   ;     HL is the signed 8.8 fixed point value of log base 2 of the input.
   ;Example:
   ;     pass HL = 3.0, returns 1.58203125 (actual is ~1.584962501...)
   ;averages about 39 t-states slower than original
   ;62 bytes
        ex de,hl
        ld hl,0
        ld a,d
        ld c,8
        or a
        jr z,DE_lessthan_1
        srl d
        jr z,logloop-1
        inc l
        rr e
        jr $-7
   DE_lessthan_1:
        ld a,e
        dec hl
        or a
        ret z
        inc l
        dec l
        add a,a
        jr nc,$-2
        ld e,a
   
        inc d
   logloop:
        add hl,hl
        push hl
        ld h,d
        ld l,e
        ld a,e
        ld b,8
   
        add hl,hl
        rla
        jr nc,$+5
          add hl,de
          adc a,0
        djnz $-7
   
        ld e,h
        ld d,a
        pop hl
        rr a           ;this is right >_>
        jr z,$+7
          srl d
          rr e
          inc l
        dec c
        jr nz,logloop
        ret

10.3.2 (speed optimised)

   Log_2_88_speed:
   ;Inputs:
   ;     HL is an unsigned 8.8 fixed point number.
   ;Outputs:
   ;     HL is the signed 8.8 fixed point value of log base 2 of the input.
   ;Example:
   ;     pass HL = 3.0, returns 1.58203125 (actual is ~1.584962501...)
   ;saves at least 688 t-states over regular (about 17% speed boost)
   ;98 bytes
        ex de,hl
        ld hl,0
        ld a,d
        ld c,8
        or a
        jr z,DE_lessthan_1
        srl d
        jr z,logloop-1
        inc l
        rr e
        jp $-7
   DE_lessthan_1:
        ld a,e
        dec hl
        or a
        ret z
        inc l
        dec l
        add a,a
        jr nc,$-2
        ld e,a
   
        inc d
   logloop:
        add hl,hl
        push hl
        ld h,d
        ld l,e
        ld a,e
        ld b,7
   
        add hl,hl
        rla
        jr nc,$+3
          add hl,de
   
        add hl,hl
        rla
        jr nc,$+3
          add hl,de
   
        add hl,hl
        rla
        jr nc,$+3
          add hl,de
   
        add hl,hl
        rla
        jr nc,$+3
          add hl,de
   
        add hl,hl
        rla
        jr nc,$+3
          add hl,de
   
        add hl,hl
        rla
        jr nc,$+3
          add hl,de
   
        add hl,hl
        rla
        jr nc,$+5
          add hl,de
          adc a,0
   
        add hl,hl
        rla
        jr nc,$+5
          add hl,de
          adc a,0
   
        ld e,h
        ld d,a
        pop hl
        rr a
        jr z,$+7
          srl d
          rr e
          inc l
        dec c
        jr nz,logloop
        ret

10.3.3 (balanced)

(this only saves about 40 cycles over the size optimised one)

   Log_2_88:
   ;Inputs:
   ;     HL is an unsigned 8.8 fixed point number.
   ;Outputs:
   ;     HL is the signed 8.8 fixed point value of log base 2 of the input.
   ;Example:
   ;     pass HL = 3.0, returns 1.58203125 (actual is ~1.584962501...)
   ;70 bytes
        ex de,hl
        ld hl,0
        ld a,d
        ld c,8
        or a
        jr z,DE_lessthan_1
        srl d
        jr z,logloop-1
        inc l
        rr e
        jp $-7
   DE_lessthan_1:
        ld a,e
        dec hl
        or a
        ret z
        inc l
        dec l
        add a,a
        jr nc,$-2
        ld e,a
   
        inc d
   logloop:
        add hl,hl
        push hl
        ld h,d
        ld l,e
        ld a,e
        ld b,7
   
        add hl,hl
        rla
        jr nc,$+3
          add hl,de
        djnz $-5
   
        adc a,0
        add hl,hl
        rla
        jr nc,$+5
          add hl,de
          adc a,0
        ld e,h
        ld d,a
        pop hl
        rr a
        jr z,$+7
          srl d
          rr e
          inc l
        dec c
        jr nz,logloop
        ret