nx_param_joint.nx source

1// nx_param_joint.nx -- X-PRM-004 (PRMJOINT-pairs-swept): the JOINT pair-sweep rung for COUPLED 2// knobs. The terrace lesson (params.tsv procgen_coupled_knobs): greedy single-variable tuning 3// ZEROES peaks that are only reachable by moving two coupled knobs TOGETHER -- coordinate ascent 4// stalls on the terrace because every single-knob step from the start goes DOWN into the coupling 5// valley. This organ is the generic pair-sweep harness + the proof: 6// POS (coupled): a terrace fitness whose peak (a>=H AND b>=H)=100 sits behind a valley (single 7// moves =5 < start=10). JOINT grid-sweep finds 100; GREEDY coordinate-ascent stalls at 10. 8// joint_wins = (coupled_joint > coupled_greedy). 9// NEG (separable): f=a+b has NO coupling, so greedy is already optimal -- JOINT must NOT beat it 10// (no_false_win = (sep_joint == sep_greedy)). Proves the harness only claims a win on REAL 11// coupling, never a spurious one. 12// Honest scope: the fitness here is a synthetic terrace MODEL of coupled knobs (capability proof); 13// wiring the live grader WIN floor as the fitness is the follow-on (cf. nx_param_tune rung2 note). 14// Sovereign (nx_cc->nxasm_x86, no gcc). license_tier: ORIGINAL 15import "nx_syscalls.nx" 16const K_MAGIC_1000000000: i64 = 1000000000 17 18func pj_w(fd: i64, s: *u8) -> i64 { var n: i64 = 0; while s[n] != (0 as u8) { n = n + 1 } sys_write(fd, s, n); return 0 } 19func pj_n(fd: i64, v: i64) -> i64 { let bb: *u8 = sys_mmap(28); var m: i64=v; if m<0 {sys_write(fd,"-" as *u8,1); m=0-m}; let t: *u8 = sys_mmap(28); var k: i64=0; if m==0 {t[0]=48;k=1}; while m>0 {t[k]=(48+(m%10)) as u8; m=m/10; k=k+1}; var i: i64=0; while i<k {bb[i]=t[k-1-i]; i=i+1}; sys_write(fd, bb, k); return 0 } 20 21// COUPLED terrace: peak only when BOTH knobs are high; single moves fall into a valley below start. 22func pj_fit_coupled(a: i64, b: i64) -> i64 { 23 let h: i64 = 8 24 if a >= h { if b >= h { return 100 } } // the peak -- needs BOTH 25 if a >= h { return 5 } // moved a only -> valley 26 if b >= h { return 5 } // moved b only -> valley 27 return 10 // start terrace (both low) 28} 29// SEPARABLE: no coupling -- each knob contributes independently (greedy is already optimal here). 30func pj_fit_sep(a: i64, b: i64) -> i64 { return a + b } 31 32func pj_eval(coupled: i64, a: i64, b: i64) -> i64 { 33 if coupled == 1 { return pj_fit_coupled(a, b) } 34 return pj_fit_sep(a, b) 35} 36 37// JOINT pair-sweep: evaluate the FULL (a,b) grid, return the global best. 38func pj_joint(coupled: i64, lo: i64, hi: i64) -> i64 { 39 var best: i64 = 0 - K_MAGIC_1000000000 40 var a: i64 = lo 41 while a <= hi { 42 var b: i64 = lo 43 while b <= hi { 44 let f: i64 = pj_eval(coupled, a, b) 45 if f > best { best = f } 46 b = b + 1 47 } 48 a = a + 1 49 } 50 return best 51} 52 53// GREEDY coordinate ascent from (lo,lo): optimize a (hold b=lo), then b (hold best a). The single- 54// variable strategy -- this is what X-PRM-003 does per-knob; on coupled knobs it stalls on the terrace. 55func pj_greedy(coupled: i64, lo: i64, hi: i64) -> i64 { 56 var besta: i64 = lo 57 var bestfa: i64 = pj_eval(coupled, lo, lo) 58 var a: i64 = lo 59 while a <= hi { let f: i64 = pj_eval(coupled, a, lo); if f > bestfa { bestfa = f; besta = a } a = a + 1 } 60 var bestb: i64 = lo 61 var bestfb: i64 = pj_eval(coupled, besta, lo) 62 var b: i64 = lo 63 while b <= hi { let f: i64 = pj_eval(coupled, besta, b); if f > bestfb { bestfb = f; bestb = b } b = b + 1 } 64 return pj_eval(coupled, besta, bestb) 65} 66 67func main() -> i64 { 68 let lo: i64 = 0 69 let hi: i64 = 10 70 71 let cj: i64 = pj_joint(1, lo, hi) // coupled, joint sweep 72 let cg: i64 = pj_greedy(1, lo, hi) // coupled, greedy 73 let sj: i64 = pj_joint(0, lo, hi) // separable, joint sweep 74 let sg: i64 = pj_greedy(0, lo, hi) // separable, greedy 75 76 var joint_wins: i64 = 0 77 if cj > cg { joint_wins = 1 } 78 var no_false_win: i64 = 0 79 if sj == sg { no_false_win = 1 } 80 81 pj_w(1, "PRMJOINT param=procgen_coupled_knobs coupled_joint=" as *u8); pj_n(1, cj) 82 pj_w(1, " coupled_greedy=" as *u8); pj_n(1, cg) 83 pj_w(1, " joint_wins=" as *u8); pj_n(1, joint_wins) 84 pj_w(1, " sep_joint=" as *u8); pj_n(1, sj) 85 pj_w(1, " sep_greedy=" as *u8); pj_n(1, sg) 86 pj_w(1, " no_false_win=" as *u8); pj_n(1, no_false_win) 87 88 var ok: i64 = 1 89 if joint_wins != 1 { ok = 0 } 90 if no_false_win != 1 { ok = 0 } 91 if cj != 100 { ok = 0 } 92 if cg != 10 { ok = 0 } 93 if ok == 1 { pj_w(1, " verdict=GREEN\n" as *u8); return 0 } 94 pj_w(1, " verdict=RED\n" as *u8) 95 return 1 96}