Day 13: More Program Control
Assembly already has the advantage over high-level languages in terms of speed and efficiency, but another plus is the ability of programs to overwrite themselves. As you are well aware, you can define and read/write a variable in the program code:
LD A, (data) ADD A, C ADC A, B LD (data), A RET data: .DB 35
Notice that a variable is just a label with some numbers after it, which is pretty much identical to any other label you have in the program. Therefore, any label can be treated as a variable, even if it was never intended to be one.
LD A, 26 LD (Blegh), A RET Blegh: CP 7 RET
What happens here? The
LD (Blegh), A will change the instruction
CP 7 to something else entirely. Taking a lower-level perspective,
FE07C9 is changed to 1A07C9. This new op code sequence represents
LD A, (DE) ; $1A RLCA ; $07 RET ; $C9
The entire operation of the program has been totally changed! The code has modified itself, or less reflexively, self-modifying code.
An arbitrary example like this shows SMC’s primary disadvantage: really hard to interpret code. The main purpose of SMC is to extend the processor’s limited capabilities. Example: When using an index register, the offset is a constant number. With SMC, that offset can be altered.
IX_Offset .EQU $+2 INC (IX + 0) ; $DD $34 $00 LD A, (IX_Offset) ADD A, 3 LD (IX_Offset), A
Or you can change the target of a JR or DJNZ.
LD A, B ADD A, A LD (Jump), A Jump .EQU $+1 JR $00 INC IX ; JR $00 INC IX ; JR $02 INC IX ; JR $04 INC IX ; JR $06 INC IX ; JR $08 INC IX ; JR $0A
It can also be used to save a register faster than the stack:
LD (save_a), A LD (save_hl), HL ; Do some math on A and HL ... save_a .EQU $+1 LD A, $00 save_hl .EQU $+1 LD HL, $0000
A PUSH without a POP
When you use RET, the processor pops the top value of the stack into PC. Supposing that you pushed a value and followed it with a RET, you would jump to the address corresponding to that value.
Where would this be useful? Assume a scenario wherein a main module
jumps to one of about twenty routines. Once any one of these routines is
finished, they should return to a specific address in the main module
referenced by the label Start. This would have to be done by placing a
JP Start at the end of each routine, which would come out to 60 bytes of
On the other hand, if the main module were to push the value of Start before jumping to a routine, then the routine would only need a RET to return. This would save 40 bytes of code.
Start: LD HL, Start PUSH HL . . . JP Z, Routine01 . . . JP Z, Routine02 . . . JP C, Routine03 . . . ; This is for exiting the program POP AF ; Remove Start from the stack RET Routine01: ; Do stuff RET ; Go back to Start Routine02: ; Do stuff RET ; Go back to Start Routine03: ; Do stuff RET ; Go back to Start
A lookup table is just an array, that all. But where a lookup table differs from your ordinary array is that a LUT contains pre-calculated data that is not intended to change. Sometimes you have to perform a function that cannot be calculated easily or at all. The use of a LUT lets you get around this. It may also be used for trivial functions where speed is a necessity.
To construct a LUT, first identify the function’s domain (the range of possible input values). For each domain value, calculate the result of the function, format it accordingly, and enter it into the LUT.
Example: a LUT used to calculate sin(x), 0° <= x < 90° (in 8.8 fixed-point format):
The input value must now be transformed into the value it represents in the LUT. This is done as with any other array.
LD H, 0 LD L, A LD DE, sine_table ADD HL, DE LD A, (HL) INC HL LD H, (HL) LD L, A RET sine_table: ; The lookup table .DW $0000, $0004, $0009, $000D, $0012, $0016, $001B, $001F, $0024 .DW $0028, $002C, $0031, $0035, $003A, $003E, $0042, $0047, $004B .DW $004F, $0053, $0058, $005C, $0060, $0064, $0068, $006C, $0070 .DW $0074, $0078, $007C, $0080, $0084, $0088, $008B, $008F, $0093 .DW $0096, $009A, $009E, $00A1, $00A5, $00A8, $00AB, $00AF, $00B2 .DW $00B5, $00B8, $00BB, $00BE, $00C1, $00C4, $00C7, $00CA, $00CC .DW $00CF, $00D2, $00D4, $00D7, $00D9, $00DB, $00DE, $00E0, $00E2 .DW $00E4, $00E6, $00E8, $00EA, $00EC, $00ED, $00EF, $00F1, $00F2 .DW $00F3, $00F5, $00F6, $00F7, $00F8, $00F9, $00FA, $00FB, $00FC .DW $00FD, $00FE, $00FE, $00FF, $00FF, $00FF, $0100, $0100, $0100
The most prohibitive drawback to using lookup tables is their giant size, but there’s nothing that can be done about that (actually, in the case of trigonometry, you could use the symmetry of the sine function to have a LUT with only the entries for one-quarter of a circle).
A vector table is a lookup table where each table entry is a 16-bit address. The input value is converted to an address, then a jump to that address is done. This is how the switch() type of control structure works. If you want to relate a value to a subroutine, then a vector table will do it faster and easier than a large, confusing CP/JP block.
Here is an example vector table:
VectTbl: .DW ClearScreen .DW PutSprite .DW DrawLine .DW EndPrgm .DW BlackScreen
The elements of the vector table are accessed just as a lookup table
LD H, 0 LD L, A LD HL, HL LD DE, VectTbl ADD HL, DE LD A, (HL) INC HL LD H, (HL) LD L, A JP (HL)
Similar to vector tables, jump tables work by holding entire jump instructions instead of just addresses.
JumpTbl: JP ClearScreen JP PutSprite JP DrawLine JP EndPrgm JP BlackScreen
To call or jump to a routine in the jump table, you use an address of
JumpTbl + 3 * n
n is the number of the routine you want. Supposing you wanted to
run DrawLine, then you would use
CALL JumpTbl + 3 * 2
Jump tables are very useful for shells (the
bcall addresses are part
of one big jump table (or vector table, does it really make a
difference?)). Suppose you made this new shell called
“StratocumulusOS”1 that was so freakin’ awesome it made MirageOS
look like the
dog it is (well that remains to be seen ;)), and all its library functions were
referenced through a jump table that the shell stored at, oh, let’s say $8000.
Now if someone makes a program for StratocumulusOS and uses the libraries
CALL stratocumulus_routines + 3 * 3
This will call $8009 which will then jump to $9436. But, one month later you release StratocumulusOS v1.1 which, owing to a truly brilliant optimization on your part, has a much smaller library size; as well, you store the routines somewhere else (but the jump table is still stored at $8000):
When that original v1.0 program is run under v1.1, then that CALL
$8009 will still jump to the right routine.
If you don’t mind the size difference, you can also use a jump table as a replacement for a vector table. In this case, you have to multiply A by three (since each jump is three bytes in size).
For reasons of security, the TI-83 Plus will crash if PC is ever $C000 or greater. This is a mega-bitch, because it means the executable part of a program can never exceed 8811 bytes. You can get a partial reprieve by copying code to the scrap RAM areas. But if this code references an address within itself with 16-bit addresses, you have to relocate them.
LD A, 40 Loop: INC (HL) INC HL DEC A JP NZ, Loop
Say that this piece of code were to be relocated to $9900. The problem is that when assembled, TASM will determine the value of Loop in the JP as relative to $9D95, when it should be relative to $9900. You have to handle situations like this. It’s easy: first you subtract $9D95 from the value of Loop, giving the offset from $9D95. Then you add the offset to $9900 to get the correct address. This is the fixed code:
LD A, 40 Loop: INC (HL) INC HL DEC A JP NZ, Loop - $9D95 + $9900
If there need to be a lot of relocations you would do well to make some macros.