%� Assemble the cube root function

�assemble
:
(4� Prompt for one number, so you can see that the
)� function is working
2�
<�"Find cube root of ";A%
F� A%>-1
PE� The USR function takes the *address* of the machine code as its
Q1� parameter, not the parameter to pass to it!
R2� This is subtly different from FNcube_root...
dresult%=�(cube_root)
n$� (result%*result%*result%)=A% �
x) �"Cube root is ";result%;" exactly" 
��
�7 �"Cube root is between ";result%-1;" and ";result%
��
�:
�� Then do our speed test
�<�'"Speed test... find cubes of all numbers from 1-10000"
�:
��=0:� A%=1 � 10000
�v%=�cube_root(A%)
�!�:� �/100;" seconds in BASIC"
�:
��=0:� A%=1 � 10000
�v%=�(cube_root)

$�:� �/100;" seconds in ARM code"

:

�

":

,� �cube_root(n%)

6check%=1:result%=0

@<ȕ (result%<n%):check%+=1:result%=check%*check%*check%:�

J=n%

T:

^� �assemble

h� code 256

rP%=code:[OPT 2

|:

�L.cube_root                    ; Enter with R0 = no. to find cube root of

�>          MOV       R1,#0     ; R1 = starting search value

�.cube_search

�>          ADD       R1,R1,#1  ; Increase search value by 1

�"          MUL       R2,R1,R1  

�5          MUL       R2,R1,R2  ; Cube search value

�E          CMP       R2,R0     ; Compare it to our original number

�P          BLT       cube_search ; Loop around if it's less than our original

�          :

�J          MOV       R0,R1     ; Move search value into return register

�          :

�3          MOV       PC,R14    ; Return to BASIC

�]
�
�

00000000  0d 00 0a 25 f4 20 41 73  73 65 6d 62 6c 65 20 74  |...%. Assemble t|
00000010  68 65 20 63 75 62 65 20  72 6f 6f 74 20 66 75 6e  |he cube root fun|
00000020  63 74 69 6f 6e 0d 00 14  0d f2 61 73 73 65 6d 62  |ction.....assemb|
00000030  6c 65 0d 00 1e 05 3a 0d  00 28 34 f4 20 50 72 6f  |le....:..(4. Pro|
00000040  6d 70 74 20 66 6f 72 20  6f 6e 65 20 6e 75 6d 62  |mpt for one numb|
00000050  65 72 2c 20 73 6f 20 79  6f 75 20 63 61 6e 20 73  |er, so you can s|
00000060  65 65 20 74 68 61 74 20  74 68 65 0d 00 29 19 f4  |ee that the..)..|
00000070  20 66 75 6e 63 74 69 6f  6e 20 69 73 20 77 6f 72  | function is wor|
00000080  6b 69 6e 67 0d 00 32 05  f5 0d 00 3c 1c e8 22 46  |king..2....<.."F|
00000090  69 6e 64 20 63 75 62 65  20 72 6f 6f 74 20 6f 66  |ind cube root of|
000000a0  20 22 3b 41 25 0d 00 46  0b fd 20 41 25 3e 2d 31  | ";A%..F.. A%>-1|
000000b0  0d 00 50 45 f4 20 54 68  65 20 55 53 52 20 66 75  |..PE. The USR fu|
000000c0  6e 63 74 69 6f 6e 20 74  61 6b 65 73 20 74 68 65  |nction takes the|
000000d0  20 2a 61 64 64 72 65 73  73 2a 20 6f 66 20 74 68  | *address* of th|
000000e0  65 20 6d 61 63 68 69 6e  65 20 63 6f 64 65 20 61  |e machine code a|
000000f0  73 20 69 74 73 0d 00 51  31 f4 20 70 61 72 61 6d  |s its..Q1. param|
00000100  65 74 65 72 2c 20 6e 6f  74 20 74 68 65 20 70 61  |eter, not the pa|
00000110  72 61 6d 65 74 65 72 20  74 6f 20 70 61 73 73 20  |rameter to pass |
00000120  74 6f 20 69 74 21 0d 00  52 32 f4 20 54 68 69 73  |to it!..R2. This|
00000130  20 69 73 20 73 75 62 74  6c 79 20 64 69 66 66 65  | is subtly diffe|
00000140  72 65 6e 74 20 66 72 6f  6d 20 46 4e 63 75 62 65  |rent from FNcube|
00000150  5f 72 6f 6f 74 2e 2e 2e  0d 00 64 18 72 65 73 75  |_root.....d.resu|
00000160  6c 74 25 3d ba 28 63 75  62 65 5f 72 6f 6f 74 29  |lt%=.(cube_root)|
00000170  0d 00 6e 24 e7 20 28 72  65 73 75 6c 74 25 2a 72  |..n$. (result%*r|
00000180  65 73 75 6c 74 25 2a 72  65 73 75 6c 74 25 29 3d  |esult%*result%)=|
00000190  41 25 20 8c 0d 00 78 29  20 f1 22 43 75 62 65 20  |A% ...x) ."Cube |
000001a0  72 6f 6f 74 20 69 73 20  22 3b 72 65 73 75 6c 74  |root is ";result|
000001b0  25 3b 22 20 65 78 61 63  74 6c 79 22 20 0d 00 82  |%;" exactly" ...|
000001c0  05 cc 0d 00 8c 37 20 f1  22 43 75 62 65 20 72 6f  |.....7 ."Cube ro|
000001d0  6f 74 20 69 73 20 62 65  74 77 65 65 6e 20 22 3b  |ot is between ";|
000001e0  72 65 73 75 6c 74 25 2d  31 3b 22 20 61 6e 64 20  |result%-1;" and |
000001f0  22 3b 72 65 73 75 6c 74  25 0d 00 96 05 cd 0d 00  |";result%.......|
00000200  a0 05 3a 0d 00 aa 1c f4  20 54 68 65 6e 20 64 6f  |..:..... Then do|
00000210  20 6f 75 72 20 73 70 65  65 64 20 74 65 73 74 0d  | our speed test.|
00000220  00 b4 3c f1 27 22 53 70  65 65 64 20 74 65 73 74  |..<.'"Speed test|
00000230  2e 2e 2e 20 66 69 6e 64  20 63 75 62 65 73 20 6f  |... find cubes o|
00000240  66 20 61 6c 6c 20 6e 75  6d 62 65 72 73 20 66 72  |f all numbers fr|
00000250  6f 6d 20 31 2d 31 30 30  30 30 22 0d 00 be 05 3a  |om 1-10000"....:|
00000260  0d 00 c8 16 d1 3d 30 3a  e3 20 41 25 3d 31 20 b8  |.....=0:. A%=1 .|
00000270  20 31 30 30 30 30 0d 00  d2 15 76 25 3d a4 63 75  | 10000....v%=.cu|
00000280  62 65 5f 72 6f 6f 74 28  41 25 29 0d 00 dc 21 ed  |be_root(A%)...!.|
00000290  3a f1 20 91 2f 31 30 30  3b 22 20 73 65 63 6f 6e  |:. ./100;" secon|
000002a0  64 73 20 69 6e 20 42 41  53 49 43 22 0d 00 e6 05  |ds in BASIC"....|
000002b0  3a 0d 00 f0 16 d1 3d 30  3a e3 20 41 25 3d 31 20  |:.....=0:. A%=1 |
000002c0  b8 20 31 30 30 30 30 0d  00 fa 13 76 25 3d ba 28  |. 10000....v%=.(|
000002d0  63 75 62 65 5f 72 6f 6f  74 29 0d 01 04 24 ed 3a  |cube_root)...$.:|
000002e0  f1 20 91 2f 31 30 30 3b  22 20 73 65 63 6f 6e 64  |. ./100;" second|
000002f0  73 20 69 6e 20 41 52 4d  20 63 6f 64 65 22 0d 01  |s in ARM code"..|
00000300  0e 05 3a 0d 01 18 05 e0  0d 01 22 05 3a 0d 01 2c  |..:.......".:..,|
00000310  14 dd 20 a4 63 75 62 65  5f 72 6f 6f 74 28 6e 25  |.. .cube_root(n%|
00000320  29 0d 01 36 16 63 68 65  63 6b 25 3d 31 3a 72 65  |)..6.check%=1:re|
00000330  73 75 6c 74 25 3d 30 0d  01 40 3c c8 95 20 28 72  |sult%=0..@<.. (r|
00000340  65 73 75 6c 74 25 3c 6e  25 29 3a 63 68 65 63 6b  |esult%<n%):check|
00000350  25 2b 3d 31 3a 72 65 73  75 6c 74 25 3d 63 68 65  |%+=1:result%=che|
00000360  63 6b 25 2a 63 68 65 63  6b 25 2a 63 68 65 63 6b  |ck%*check%*check|
00000370  25 3a ce 0d 01 4a 07 3d  6e 25 0d 01 54 05 3a 0d  |%:...J.=n%..T.:.|
00000380  01 5e 0f dd 20 f2 61 73  73 65 6d 62 6c 65 0d 01  |.^.. .assemble..|
00000390  68 0e de 20 63 6f 64 65  20 32 35 36 0d 01 72 12  |h.. code 256..r.|
000003a0  50 25 3d 63 6f 64 65 3a  5b 4f 50 54 20 32 0d 01  |P%=code:[OPT 2..|
000003b0  7c 05 3a 0d 01 86 4c 2e  63 75 62 65 5f 72 6f 6f  ||.:...L.cube_roo|
000003c0  74 20 20 20 20 20 20 20  20 20 20 20 20 20 20 20  |t               |
000003d0  20 20 20 20 20 3b 20 45  6e 74 65 72 20 77 69 74  |     ; Enter wit|
000003e0  68 20 52 30 20 3d 20 6e  6f 2e 20 74 6f 20 66 69  |h R0 = no. to fi|
000003f0  6e 64 20 63 75 62 65 20  72 6f 6f 74 20 6f 66 0d  |nd cube root of.|
00000400  01 90 3e 20 20 20 20 20  20 20 20 20 20 4d 4f 56  |..>          MOV|
00000410  20 20 20 20 20 20 20 52  31 2c 23 30 20 20 20 20  |       R1,#0    |
00000420  20 3b 20 52 31 20 3d 20  73 74 61 72 74 69 6e 67  | ; R1 = starting|
00000430  20 73 65 61 72 63 68 20  76 61 6c 75 65 0d 01 9a  | search value...|
00000440  10 2e 63 75 62 65 5f 73  65 61 72 63 68 0d 01 a4  |..cube_search...|
00000450  3e 20 20 20 20 20 20 20  20 20 20 41 44 44 20 20  |>          ADD  |
00000460  20 20 20 20 20 52 31 2c  52 31 2c 23 31 20 20 3b  |     R1,R1,#1  ;|
00000470  20 49 6e 63 72 65 61 73  65 20 73 65 61 72 63 68  | Increase search|
00000480  20 76 61 6c 75 65 20 62  79 20 31 0d 01 ae 22 20  | value by 1..." |
00000490  20 20 20 20 20 20 20 20  20 4d 55 4c 20 20 20 20  |         MUL    |
000004a0  20 20 20 52 32 2c 52 31  2c 52 31 20 20 0d 01 b8  |   R2,R1,R1  ...|
000004b0  35 20 20 20 20 20 20 20  20 20 20 4d 55 4c 20 20  |5          MUL  |
000004c0  20 20 20 20 20 52 32 2c  52 31 2c 52 32 20 20 3b  |     R2,R1,R2  ;|
000004d0  20 43 75 62 65 20 73 65  61 72 63 68 20 76 61 6c  | Cube search val|
000004e0  75 65 0d 01 c2 45 20 20  20 20 20 20 20 20 20 20  |ue...E          |
000004f0  43 4d 50 20 20 20 20 20  20 20 52 32 2c 52 30 20  |CMP       R2,R0 |
00000500  20 20 20 20 3b 20 43 6f  6d 70 61 72 65 20 69 74  |    ; Compare it|
00000510  20 74 6f 20 6f 75 72 20  6f 72 69 67 69 6e 61 6c  | to our original|
00000520  20 6e 75 6d 62 65 72 0d  01 cc 50 20 20 20 20 20  | number...P     |
00000530  20 20 20 20 20 42 4c 54  20 20 20 20 20 20 20 63  |     BLT       c|
00000540  75 62 65 5f 73 65 61 72  63 68 20 3b 20 4c 6f 6f  |ube_search ; Loo|
00000550  70 20 61 72 6f 75 6e 64  20 69 66 20 69 74 27 73  |p around if it's|
00000560  20 6c 65 73 73 20 74 68  61 6e 20 6f 75 72 20 6f  | less than our o|
00000570  72 69 67 69 6e 61 6c 0d  01 d6 0f 20 20 20 20 20  |riginal....     |
00000580  20 20 20 20 20 3a 0d 01  e0 4a 20 20 20 20 20 20  |     :...J      |
00000590  20 20 20 20 4d 4f 56 20  20 20 20 20 20 20 52 30  |    MOV       R0|
000005a0  2c 52 31 20 20 20 20 20  3b 20 4d 6f 76 65 20 73  |,R1     ; Move s|
000005b0  65 61 72 63 68 20 76 61  6c 75 65 20 69 6e 74 6f  |earch value into|
000005c0  20 72 65 74 75 72 6e 20  72 65 67 69 73 74 65 72  | return register|
000005d0  0d 01 ea 0f 20 20 20 20  20 20 20 20 20 20 3a 0d  |....          :.|
000005e0  01 f4 33 20 20 20 20 20  20 20 20 20 20 4d 4f 56  |..3          MOV|
000005f0  20 20 20 20 20 20 20 50  43 2c 52 31 34 20 20 20  |       PC,R14   |
00000600  20 3b 20 52 65 74 75 72  6e 20 74 6f 20 42 41 53  | ; Return to BAS|
00000610  49 43 0d 01 fe 05 5d 0d  02 08 05 e1 0d ff        |IC....].......|
0000061e