Fit the arithmetic to three digits

Say you want the next number in a random sequence: (21s + 17) mod 1000.

The direct way works out 21s by adding s to itself 21 times. Every STO keeps only three digits, so the mod 1000 takes care of itself, but you're looping 21 times for one number.

cell  contents  notes
 10      040    INP 40  cells 10-19: 21s by adding s 21 times; STO keeps three digits each time
 11      141    CLA 41
 12      642    STO 42
 13      143    CLA 43
 14      240    ADD 40
 15      643    STO 43
 16      142    CLA 42
 17      200    ADD 00
 18      642    STO 42
 19      313    TAC 13
 20      143    CLA 43  cells 20-24: then add 17
 21      244    ADD 44
 22      643    STO 43
 23      543    OUT 43
 24      900    HRS 00
 40      000
 41     -021
 42      000
 43      000
 44      017

Step through the natural way in Cardigan

With a little rearranging, nothing in the formula needs more than four digits. 21s is 20s + s, and 20s mod 1000 is 10 times (2s mod 100). SFT 22 keeps the last two digits, which is your mod 100. SFT 10 multiplies by ten. And the final STO does the mod 1000 for you.

cell  contents  notes
 10      040    INP 40  cells 10-19: 21s + 17 as 10 (2s mod 100) + s + 17
 11      140    CLA 40
 12      240    ADD 40  2s
 13      422    SFT 22  2s mod 100
 14      410    SFT 10  10 (2s mod 100), never past 990
 15      240    ADD 40
 16      241    ADD 41
 17      642    STO 42  STO keeps three digits: the mod 1000
 18      542    OUT 42
 19      900    HRS 00
 40      000
 41      017
 42      000

Step through the CARDIAC way in Cardigan

Both turn 999 into 996. The loop takes 20 cells and runs 155 instructions; the rearranged version takes 13 cells and runs 10.

From the tips in cardiac-code on GitHub. All the tips.