SignalChapter 11: Capstones

82SIEVE

The task

X is from 2 to 120. P must receive only the primes: 2, 3, 5, 7, 11, 13, and so on.

b is an SC-2D: 10 lines, and every jump takes 3 cycles. Use DIV or MOD to test a divisor.

c is an SC-2L: every instruction takes 2 cycles, for half the energy.

The board

The board as the puzzle screen lays it out. Cyan pins read, lemon pins write, violet pins go both ways. On a narrow screen, scroll the board sideways to see all of it.

Key idea

A number up to 120 that is not prime has a divisor of 2, 3, 5, or 7, so a chain of MOD filters keeps the primes; which core tests which divisor sets the score.

Hints

Each hint goes a step further than the one before. Open them one at a time.

Hint 1Show

A number up to 120 that is not prime has a divisor of 2, 3, 5, or 7.

Hint 2Show

Each core can drop the numbers that one or two of those divide with MOD.

Hint 3Show

2, 3, 5, and 7 divide themselves, but they are prime, so let them through.

Solution

Reveal the Full SolutionThe complete program for SIEVE. Open it only when you want the answer.

The reference program

The game's own solution. It passes every test and scores exactly par on every benchmark.

aSC-2 standard

S: IN P0
MOV B, A
MOD 2
JNZ T1
MOV A, B
SUB 2
JG S
T1: MOV A, B
MOD 3
JNZ K
MOV A, B
SUB 3
JG S
K: MOV A, B
OUT P1

bSC-2D signal processor

S: IN P0
MOV B, A
MOD 5
JNZ K
MOV A, B
SUB 5
JG S
K: MOV A, B
OUT P1

cSC-2L low power

S: IN P0
MOV B, A
MOD 7
JNZ K
MOV A, B
SUB 7
JG S
K: MOV A, B
OUT P1

CYCLES: 353; at par
ENERGY: 2486; at par
NODES: 3; at par
INSTRUCTIONS: 33; at par

Another way: Sieve relay

A second program that also passes. It beats par on ENERGY and INSTRUCTIONS and gives some back on CYCLES.

Less energy than par, but slower. The SC-2D only relays, and the low power SC-2L tests both 7 and 5.

aSC-2 standard

S: IN P0
MOV B, A
MOD 2
JNZ T1
MOV A, B
SUB 2
JG S
T1: MOV A, B
MOD 3
JNZ K
MOV A, B
SUB 3
JG S
K: MOV A, B
OUT P1

bSC-2D signal processor

IN P0
OUT P1

cSC-2L low power

S: IN P0
MOV B, A
MOD 7
JNZ T1
MOV A, B
SUB 7
JG S
T1: MOV A, B
MOD 5
JNZ K
MOV A, B
SUB 5
JG S
K: MOV A, B
OUT P1

CYCLES: 392; over par
ENERGY: 2296; under par
NODES: 3; at par
INSTRUCTIONS: 32; under par

Another way: Sieve seven on b

A second program that also passes. It beats par on CYCLES and gives some back on ENERGY.

Faster than par, at more energy. b, the SC-2D, tests 7, and c, the SC-2L, tests 5.

aSC-2 standard

S: IN P0
MOV B, A
MOD 2
JNZ T1
MOV A, B
SUB 2
JG S
T1: MOV A, B
MOD 3
JNZ K
MOV A, B
SUB 3
JG S
K: MOV A, B
OUT P1

bSC-2D signal processor

S: IN P0
MOV B, A
MOD 7
JNZ K
MOV A, B
SUB 7
JG S
K: MOV A, B
OUT P1

cSC-2L low power

S: IN P0
MOV B, A
MOD 5
JNZ K
MOV A, B
SUB 5
JG S
K: MOV A, B
OUT P1

CYCLES: 346; under par
ENERGY: 2493; over par
NODES: 3; at par
INSTRUCTIONS: 33; at par