nx_ncf_cube_gate.nx source

1// nx_ncf_cube_gate.nx -- X-AUT-NCF-001 RUNG 4: SYNTHESIZE A QUADRATIC-INDEX LOOP (acc += c2*i*i + c1*i + c0), 2// covering x^3 and the cubic family -- exactly the case rung 3 (affine-index) honestly REFUSED. Escalation: 3// the rung-3 affine-index loop PROVABLY FAILS on x^3 (its sum is quadratic-in-x); the quadratic-index loop 4// SUCCEEDS (x^3 = sum(3i^2 - 3i + 1)). Uses the shared lib nx_ncf_synth, so the WIRING auto-widens (x^3 now 5// routes). Construct ladder: linear < conditional < simple-loop < affine-index-loop < QUADRATIC-INDEX-LOOP. 6// T1 linear FAILS. T2 affine-index loop (rung 3) FAILS on x^3 -> the quadratic-index body is necessary. 7// T3 quadratic-index loop SYNTHESIZES x^3 = acc=0; for i { acc += 3i^2 - 3i + 1 }. 8// T4 MATERIALIZE+GOD-BUILD+run HELD-OUT {5->125, 6->216} -> 125216. T5 unified ncf_synth routes x^3 (kind=4). 9// expect_exit: 0 license_tier: ORIGINAL 10import "nx_ncf_synth.nx" 11import "nx_syscalls.nx" 12 13func main() -> i64 { 14 ncf_w("=== nx_ncf_cube: SYNTHESIZE A QUADRATIC-INDEX LOOP (X-AUT-NCF-001 rung 4) -- covers x^3, rung-3 cannot ===\n" as *u8) 15 var pass: i64=0; var total: i64=0 16 17 // SPEC = x^3: examples {0..4}, HELD-OUT {5->125, 6->216}. 18 let xs: *i64=sys_mmap(64) as *i64; let ys: *i64=sys_mmap(64) as *i64 19 xs[0]=0; xs[1]=1; xs[2]=2; xs[3]=3; xs[4]=4 20 ys[0]=0; ys[1]=1; ys[2]=8; ys[3]=27; ys[4]=64 21 let n: i64=5 22 23 let sp: *i64=sys_mmap(8) as *i64; sp[0]=0-1 24 let sfd: i64=sys_openat_wr(NCF_RESULT,420); if sfd>=0 { sys_write(sfd,sp as *u8,8); sys_close(sfd) } 25 26 // T1: linear FAILS. 27 let lin: i64=ncf_search_linear(xs,ys,n) 28 total=total+1; if lin==0 { pass=pass+1; ncf_w(" [PASS] " as *u8) } else { ncf_w(" [FAIL] " as *u8) } 29 ncf_w("T1 NEG-CONTROL: linear-only FAILS on x^3, lin_found=" as *u8); ncf_n(lin); ncf_w("\n" as *u8) 30 31 // T2: rung-3 AFFINE-INDEX loop FAILS (the escalation -- affine-index sum is quadratic-in-x, x^3 is cubic). 32 let aform: *i64=sys_mmap(64) as *i64 33 let affine: i64=ncf_search_loop2(xs,ys,n,aform) 34 total=total+1; if affine==0 { pass=pass+1; ncf_w(" [PASS] " as *u8) } else { ncf_w(" [FAIL] " as *u8) } 35 ncf_w("T2 NEG-CONTROL: rung-3 AFFINE-INDEX loop FAILS on x^3 -> quadratic-index body NECESSARY, affine_found=" as *u8); ncf_n(affine); ncf_w("\n" as *u8) 36 37 // T3: quadratic-index loop SYNTHESIZES x^3. 38 let form: *i64=sys_mmap(64) as *i64 39 let q: i64=ncf_search_loop3(xs,ys,n,form) 40 total=total+1; if q==1 { pass=pass+1; ncf_w(" [PASS] " as *u8) } else { ncf_w(" [FAIL] " as *u8) } 41 ncf_w("T3 SYNTHESIS: quadratic-index loop FOUND acc=" as *u8); ncf_n(form[0]); ncf_w("; for i { acc += " as *u8); ncf_n(form[1]); ncf_w("*i*i + " as *u8); ncf_n(form[2]); ncf_w("*i + " as *u8); ncf_n(form[3]); ncf_w(" } for x^3\n" as *u8) 42 43 // T4: MATERIALIZE -> GOD-BUILD -> run HELD-OUT -> verify (x^3(5)=125, x^3(6)=216 -> 125216). 44 var emitted: i64=0; if q==1 { if ncf_emit(4,form,5,6,1000)==0 { emitted=1 } } 45 var built: i64=0; if emitted==1 { if ncf_god_build(NCF_NAME)==0 { built=1 } } 46 let produced: i64=ncf_read(NCF_RESULT) 47 total=total+1; if produced==125216 { pass=pass+1; ncf_w(" [PASS] " as *u8) } else { ncf_w(" [FAIL] " as *u8) } 48 ncf_w("T4 MATERIALIZE+GOD-BUILD: synthesized quadratic-index loop compiled (nx_cc->nxasm, no gcc) + ran HELD-OUT -> produced=" as *u8); ncf_n(produced); ncf_w(" (expect 125216)\n" as *u8) 49 50 // T5: the UNIFIED ncf_synth now routes x^3 to the quadratic-index construct (kind=4) = auto-widens the wiring. 51 let uform: *i64=sys_mmap(64) as *i64 52 let kind: i64=ncf_synth(xs,ys,n,uform) 53 total=total+1; if kind==4 { pass=pass+1; ncf_w(" [PASS] " as *u8) } else { ncf_w(" [FAIL] " as *u8) } 54 ncf_w("T5 UNIFIED: ncf_synth(x^3) -> kind=" as *u8); ncf_n(kind); ncf_w(" (4=quadratic-index loop) = the wiring now auto-routes x^3 (was the old NOVEL->tutor boundary)\n" as *u8) 55 56 ncf_w("\n HONEST SCOPE: covers cubics of the form init + sum(c2*i*i + c1*i + c0); x^4 (quartic) + non-polynomial (Fibonacci, needs two-state) still escalate = the next rungs. Ladder: linear < conditional < simple-loop < affine-index < quadratic-index.\n" as *u8) 57 ncf_w("NCF-CUBE verdict=" as *u8) 58 if pass==total { ncf_w("GREEN passes=" as *u8); ncf_n(pass); ncf_w("/" as *u8); ncf_n(total); ncf_w(" -- the team SYNTHESIZED + GOD-BUILT a quadratic-index loop (author-share>0): X-AUT-NCF-001 rung 4\n" as *u8); sys_exit(0); return 0 } 59 ncf_w("RED passes=" as *u8); ncf_n(pass); ncf_w("/" as *u8); ncf_n(total); ncf_w("\n" as *u8); sys_exit(1); return 1 60}