nx_nofloat_muon_ns_gate.nx source

1// nx_nofloat_muon_ns_gate.nx -- gate for integer Newton-Schulz orthogonalization (Muon core). 2// HONEST claim (Muon NS = APPROXIMATE orthogonalization, SVs -> ~1, not exactly 1): 3// T1 a non-orthogonal matrix is orthogonalized -- X X^T -> I error drops hard (>5x) after NS 4// T2 MONOTONE: more iterations reduce the error (err@5 < err@1) -- the iteration converges, not diverges 5// T3 the result's X X^T diagonal lands near 1.0 (each in [0.6,1.4]*Q16) -- Muon-style approx-orthogonal 6// T4 DETERMINISTIC: two runs bit-identical -- the NOVEL EXCEED (float NS is order-dependent, ours is not) 7// license_tier: ORIGINAL No hw writes (Rule 26). expect_exit: 0 8import "nx_nofloat_muon_ns.nx" 9import "nx_gate_verdict.nx" 10import "nx_syscalls.nx" 11 12const MG_N: i64 = 4 13const MG_Q: i64 = 65536 14 15func mg_set_test(g: *i64, n: i64) -> i64 { 16 var i: i64 = 0 17 while i < n*n { g[i] = 0; i = i + 1 } 18 // symmetric tridiagonal [[2,1,0,0],[1,2,1,0],[0,1,2,1],[0,0,1,2]] * Q (clearly non-orthogonal) 19 g[0]=2*MG_Q; g[1]=1*MG_Q; g[4]=1*MG_Q; g[5]=2*MG_Q; g[6]=1*MG_Q; g[9]=1*MG_Q; g[10]=2*MG_Q; g[11]=1*MG_Q; g[14]=1*MG_Q; g[15]=2*MG_Q 20 return 0 21} 22 23func main() -> i64 { 24 let ctr: *i64 = gv_ctr() 25 gv_head("nx_nofloat_muon_ns gate -- integer Newton-Schulz orthogonalization (Muon core, novel exceed)" as *u8) 26 let n: i64 = MG_N 27 let g: *i64 = sys_mmap(64*8) as *i64 28 let x: *i64 = sys_mmap(64*8) as *i64 29 30 mg_set_test(g, n) 31 let err_before: i64 = mn_ortho_err(g, n) 32 mn_orthogonalize_it(g, x, n, 5) 33 let err5: i64 = mn_ortho_err(x, n) 34 35 // T1: error drops >5x 36 var t1: i64 = 0 37 if err5 * 5 < err_before { t1 = 1 } 38 gv_check("T1 non-orthogonal matrix orthogonalized (X X^T->I error drops >5x)" as *u8, t1, ctr) 39 40 // T2: monotone -- err@5 < err@1 (iteration converges) 41 let x1: *i64 = sys_mmap(64*8) as *i64 42 mg_set_test(g, n) 43 mn_orthogonalize_it(g, x1, n, 1) 44 let err1: i64 = mn_ortho_err(x1, n) 45 var t2: i64 = 0 46 if err5 < err1 { t2 = 1 } 47 gv_check("T2 MONOTONE convergence (err@5-iters < err@1-iter, not diverging)" as *u8, t2, ctr) 48 49 // T3: X X^T diagonal near 1.0 (each in [0.6,1.4]*Q16) -- Muon-style approximate orthogonality 50 let xt: *i64 = sys_mmap(64*8) as *i64 51 let gg: *i64 = sys_mmap(64*8) as *i64 52 mn_transpose(x, xt, n) 53 mn_mm(x, xt, gg, n) 54 var t3: i64 = 1 55 var i: i64 = 0 56 let lo: i64 = (MG_Q * 6) / 10 57 let hi: i64 = (MG_Q * 14) / 10 58 while i < n { 59 let dv: i64 = gg[i*n+i] 60 if dv < lo { t3 = 0 } 61 if dv > hi { t3 = 0 } 62 i = i + 1 63 } 64 gv_check("T3 X X^T diagonal near 1.0 (each in [0.6,1.4] Q16) = approx-orthogonal" as *u8, t3, ctr) 65 66 // T4: deterministic 67 let xa: *i64 = sys_mmap(64*8) as *i64 68 let xb: *i64 = sys_mmap(64*8) as *i64 69 mg_set_test(g, n) 70 mn_orthogonalize_it(g, xa, n, 5) 71 mg_set_test(g, n) 72 mn_orthogonalize_it(g, xb, n, 5) 73 var t4: i64 = 0 74 var d: i64 = 0 75 var k: i64 = 0 76 while k < n*n { if xa[k] != xb[k] { d = 1 } k = k + 1 } 77 if d == 0 { t4 = 1 } 78 gv_check("T4 DETERMINISTIC bit-identical (the exceed: float NS is order-dependent, ours is not)" as *u8, t4, ctr) 79 80 let rc: i64 = gv_verdict("NOFLOAT-MUON-NS-GATE" as *u8, ctr, "integer Newton-Schulz orthogonalization (Muon core): directional, monotone-convergent, approx-orthogonal, bit-exact deterministic" as *u8) 81 sys_exit(rc) 82 return rc 83}