## wo: 9-byte modulo

,While working on a code golf challenge in `dc`

today, my mind turned to if and how I could solve the same challenge with the current instruction set of `wo`

. We left off in the middle of `wo5`

, with six slots to go and the promise of division. Internally, I was filling a couple of slots with additional stack manipulation instructions, with three slots still open. The goal isn’t necessarily to be able to do everything (or, perhaps, much of anything) efficiently at this point, but to leave that bit-shaving option on the table, letting the programmer do the most with the least. Since there’s no fractional input, division was a no-brainer: now you can enter fractions, you can waste a little time making a reciprocal for multiplication, and you can (of course) divide.

Part of my exercise today made use of calculating modulo. It briefly occurred to me that this could be one of my remaining three `wo5`

instructions^{1}, but I also wondered how much space one would waste simply implementing it themself in a `wo5`

program. The answer: 9 bytes. Well, 70 bits, but I guess I have to round up. Instead of implementing modulo, I’m considering a FLOOR instruction. For this demonstration, I’m going to largely comment the state of the stack, with the top to the right. I’m going to use decimal numbers and named instructions. Given that…

```
10 #Put a number on the stack
4 #And another (these don't count toward the byte count)
1
YANKPST #PST: 10, 10, 4, 10
1
YANKPST #PST: 10, 10, 10, 4, 10, 4
DIVIDE #PST: 10, 10, 10, 10, 4, 2.5
FLOOR #PST: 10, 10, 10, 10, 4, 2
1
1
YANKPST #PST: 10, 10, 10, 10, 10, 4, 1, 2
DIVIDE #PST: 10, 10, 10, 10, 10, 10, 4, .5
DIVIDE #PST: 10, 10, 10, 10, 10, 10, 10, 8
-1
DIVIDE #PST: 10, 10, 10, 10, 10, 10, 10, -8
ADD #PST: 10, 10, 10, 10, 10, 10, 10, 2
```

…14 commands at 5 bits each: 70 bits total^{2}. It shows the unwieldiness of using such limited instructions, but at the same time demonstrates that many such instructions still only take 8 bytes. There may be situations where, despite one complex need, a smaller overall word size still leads to shorter code.

This code also goes a ways to demonstrate how our stack can get away from us. *Ideally* one would either ignore or manage this, but I may be biting off more than I can chew here. I don’t necessarily know that it’ll have the same benefit that the bottom (*T*) of a 4-level RPN stack has. It may also be worth entertaining a differentiation between *popped values* and *parameters*, with, for instance, `YANKPST`

shrinking the stack where the index was taken from (the old top, essentially).

### Current Instruction Set:

- 0, 0, PRNTPST
- Print the contents of the primary stack (PST)
- 1, 1, GOTO
- Pop top of stack, go to corresponding word
- MNum: Go to word indicated by storage register R2 (more on this later)
- Nonexistent word exits
- 2, 10, ADD
- Pop two values off of the stack, push their sum
- 3, 11, SKIPZERO
- Pop one value off of the stack, if == 0, skip all words through next instruction
- 4, 100, REGISTER
- Pop two values off of the stack, set register indexed by first to value of second
- MNum: Push value of register indexed by first
- 5, 101, DOUBLE
- Pop two values off of the stack, push value created by treating the popped values as a double number
- 6, 110, CLEARPST
- Empty PST, pushing the top of stack as its only value
- 7, 111, YANKPST
- Pop a value off of the stack, push the value of the stack entry indexed by the popped value
- MNum: Could potentially cause a DROP
- Negative values indexed from bottom of stack
- 8, 1000, PICKPST
- Pop 1 value off of PST, pop the value off of PST with the index of the first value popped
- Negative numbers index from bottom
- 9, 1001, PICK$ST
- Pop 1 value off of PST, pop the value off of $ST with the index of the value popped from PST
- MNum: Fold entire SST into string on PST
- Negative numbers index from bottom
- 10, 1010, PUT$ST
- Pop one value off of PST, push onto $ST
- If value is a string, unfold entire string onto $ST
- 11, 1011, CLEAR$ST
- Clear $ST entirely ($ST, unlike PST, can be empty)
- 12, 1100, FLOOR
- Pop one value from PST, push floor of value
- 13, 1101, DIVIDE
- Pop two values from PST, push (fractional) quotient

- Alternatively (and I actually think I’m leaning this way), a register could be used to flag whether
`DIVIDE`

returns a fractional quotient or an integer quotient and remainder. ↩︎ - Without the initial stack entries:
`00011`

`01110`

`00011`

`01110`

`11010`

`11000`

`00011`

`00011`

`01110`

`11010`

`11010`

`10011`

`11010`

`00100`

. Padding the final byte with zeroes, we get`1B`

`86`

`ED`

`60`

`63`

`76`

`B5`

`3D`

`10`

. In the Jelly code page, our code is`ñ⁶ḣ`cvỌ=Ñ`

. ↩︎