; A segmented Sieve of Eratosthenes for the complete 16-bit address range.
;
; The sieve uses a 256-byte sliding window. Each entry in PrimeStates contains:
;   prime, high byte of next multiple, low byte of next multiple
;
; Once a prime becomes active at p*p, adding an 8-bit prime to offsets in a
; 256-byte window must wrap exactly once before the next window. The wrapped
; low byte becomes that prime's starting offset in the following window.
;
; Output is hexadecimal (0002 through FFFD), separated by spaces.

#Include Libraries/print.asm

#Program

start:
  RSTA
  SETD Page
  STA

nextPage:
  ; Clear all 256 flags. A wrapping to zero terminates the loop.
  SETD Segment
  RSTA
  RSTB
clearSegment:
  STB
  INCD
  INCA
  BRA segmentCleared
  BRI clearSegment

segmentCleared:
  ; Zero and one are not prime.
  SETD Page
  LDA
  BRA excludeZeroAndOne
  BRI markSegment
excludeZeroAndOne:
  SETD Segment
  INIA 0x01
  STA
  INCD
  STA

markSegment:
  ; Process the 54 primes not greater than sqrt(0xFFFF).
  SETD PrimeStates
  INIA 0d54
primeLoop:
  CALL processPrime
  DPUP 0d03
  DECA
  BRA scanSegment
  BRI primeLoop

scanSegment:
  ; A is the low byte of the candidate and wraps after 0xFF.
  SETD Segment
  RSTA
scanLoop:
  LDB
  BRB emitPrime
scanNext:
  INCD
  INCA
  BRA advancePage
  BRI scanLoop

emitPrime:
  CALL printCandidateHex
  BRI scanNext

advancePage:
  SETD Page
  LDA
  INCA
  STA
  BRA finished
  BRI nextPage

finished:
  CALL lineFeed
  HALT

; DP points at a PrimeStates entry on entry and is preserved by CALL.
processPrime:
  PSHD
  INCD
  LDA
  SETD Page
  LDB
  XOR
  BRQ primeIsActive
  POPD
  RET

primeIsActive:
  ; Recover and retain the state-entry pointer for the final update.
  POPD
  PSHD

  ; Load the prime into B and its current offset into A.
  LDA
  PSHA
  DPUP 0d02
  LDA
  POPB

  ; Form Segment + offset. Segment is page-aligned in Data Memory.
  SETD Segment
  PSHB
  PSHD
  POPB
  CCF
  ADD
  PSHQ
  POPD
  POPB

markPrimeLoop:
  INIA 0x01
  STA

  ; Add the prime to the low byte of DP using the stack as a 16-bit
  ; address adapter. Carry means that the next multiple is in the next page.
  PSHD
  POPA
  CCF
  ADD
  PSHQ
  POPD
  BRC primeFinished
  BRI markPrimeLoop

primeFinished:
  ; Q is the wrapped offset for the next page.
  POPD
  INCD
  LDA
  INCA
  STA
  INCD
  STQ
  RET

; A contains the candidate's low byte. Page contains its high byte.
printCandidateHex:
  PSHA
  SETD Page
  LDA
  CALL printByteHex
  POPA
  CALL printByteHex
  CALL blankSpace
  RET

#Data

; print.asm deliberately pads its data to one page, so this begins at 0x0100.
Segment:
  0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00
  0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00
  0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00
  0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00
  0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00
  0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00
  0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00
  0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00
  0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00
  0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00
  0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00
  0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00
  0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00
  0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00
  0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00
  0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00

Page:
  0x00

PrimeStates:
  0x02 0x00 0x04
  0x03 0x00 0x09
  0x05 0x00 0x19
  0x07 0x00 0x31
  0x0B 0x00 0x79
  0x0D 0x00 0xA9
  0x11 0x01 0x21
  0x13 0x01 0x69
  0x17 0x02 0x11
  0x1D 0x03 0x49
  0x1F 0x03 0xC1
  0x25 0x05 0x59
  0x29 0x06 0x91
  0x2B 0x07 0x39
  0x2F 0x08 0xA1
  0x35 0x0A 0xF9
  0x3B 0x0D 0x99
  0x3D 0x0E 0x89
  0x43 0x11 0x89
  0x47 0x13 0xB1
  0x49 0x14 0xD1
  0x4F 0x18 0x61
  0x53 0x1A 0xE9
  0x59 0x1E 0xF1
  0x61 0x24 0xC1
  0x65 0x27 0xD9
  0x67 0x29 0x71
  0x6B 0x2C 0xB9
  0x6D 0x2E 0x69
  0x71 0x31 0xE1
  0x7F 0x3F 0x01
  0x83 0x43 0x09
  0x89 0x49 0x51
  0x8B 0x4B 0x79
  0x95 0x56 0xB9
  0x97 0x59 0x11
  0x9D 0x60 0x49
  0xA3 0x67 0xC9
  0xA7 0x6C 0xF1
  0xAD 0x74 0xE9
  0xB3 0x7D 0x29
  0xB5 0x7F 0xF9
  0xBF 0x8E 0x81
  0xC1 0x91 0x81
  0xC5 0x97 0x99
  0xC7 0x9A 0xB1
  0xD3 0xAD 0xE9
  0xDF 0xC2 0x41
  0xE3 0xC9 0x49
  0xE5 0xCC 0xD9
  0xE9 0xD4 0x11
  0xEF 0xDF 0x21
  0xF1 0xE2 0xE1
  0xFB 0xF6 0x19