nx_vtransform_gate.nx source

1// nx_vtransform_gate.nx -- proves + MEASURES the sovereign 4x4 transform+quantize (nx_vtransform), V-R2. 2// Native nx_cc->nxasm, no node. 3// 1) energy compaction: a flat residual -> all energy in 1 coeff (DC); a smooth residual -> few coeffs 4// 2) lossless round-trip at q=1: fwd -> quant -> dequant -> inv == the original residual 5// 3) quantization compaction (MEASURED): a smooth residual at q=16 -> nonzero coeffs << 16 (the entropy cost) 6// 4) bounded lossy round-trip at q=8: reconstructed within a bounded error of the original 7// 5) anti-tautology: a high-frequency (checkerboard) residual does NOT collapse to DC (transform is real) 8// license_tier: ORIGINAL 9import "nx_syscalls.nx" 10import "nx_gate_emit_lib.nx" 11import "nx_vtransform.nx" 12 13func g_abs(v: i64) -> i64 { if v < 0 { return 0 - v } return v } 14func bcopy(d: *i64, s: *i64) -> i64 { var i: i64=0; while i<16 { d[i]=s[i]; i=i+1 } return 0 } 15func beq(a: *i64, b: *i64) -> i64 { var i: i64=0; while i<16 { if a[i]!=b[i] { return 0 } i=i+1 } return 1 } 16func maxerr(a: *i64, b: *i64) -> i64 { var m: i64=0; var i: i64=0; while i<16 { let e: i64=g_abs(a[i]-b[i]); if e>m { m=e } i=i+1 } return m } 17 18func main() -> i64 { 19 g_puts("nx_vtransform gate (sovereign 4x4 transform+quantize of the residual, MEASURED)\n" as *u8) 20 var pass: i64 = 0; var total: i64 = 0 21 22 let orig: *i64 = sys_mmap(16*8) as *i64 23 let blk: *i64 = sys_mmap(16*8) as *i64 24 25 // 1) energy compaction -- flat residual (all 8) -> only DC nonzero 26 var i: i64 = 0; while i < 16 { orig[i] = 8; i = i + 1 } 27 bcopy(blk, orig); vt_fwd(blk) 28 var r1: i64 = 1 29 if blk[0] != 128 { r1 = 0 } // DC = 8 * 16 30 var nzf: i64 = vt_nonzero(blk) 31 if nzf != 1 { r1 = 0 } // every other coeff zero 32 g_puts(" [measure] flat residual -> DC=" as *u8); g_pn(blk[0]); g_puts(", nonzero coeffs=" as *u8); g_pn(nzf); g_puts(" / 16\n" as *u8) 33 pass = pass + g_check("energy compaction: flat residual -> all energy in DC" as *u8, r1); total=total+1 34 35 // 2) lossless round-trip at q=1 36 i = 0; while i < 16 { orig[i] = (i*i - 7*i + 3); i = i + 1 } // an arbitrary residual 37 bcopy(blk, orig) 38 vt_fwd(blk); vt_quant(blk, 1); vt_dequant(blk, 1); vt_inv(blk) 39 pass = pass + g_check("lossless round-trip at q=1 (fwd->quant->dequant->inv == orig)" as *u8, beq(blk, orig)); total=total+1 40 41 // 3) quantization compaction on a smooth (motion-comp-like) residual 42 i = 0; while i < 16 { let rr: i64 = i / 4; let cc: i64 = i % 4; orig[i] = 3 + rr + cc; i = i + 1 } // gentle gradient 43 bcopy(blk, orig) 44 vt_fwd(blk) 45 let nz_before: i64 = vt_nonzero(blk) 46 let nz_after: i64 = vt_quant(blk, 16) 47 g_puts(" [measure] smooth residual: nonzero " as *u8); g_pn(nz_before); g_puts(" -> after quant(16) " as *u8); g_pn(nz_after); g_puts(" / 16\n" as *u8) 48 pass = pass + g_check("quantization compaction: nonzero coeffs drop sharply" as *u8, nz_after < nz_before); total=total+1 49 50 // 4) bounded lossy round-trip at q=8 51 bcopy(blk, orig) 52 vt_fwd(blk); vt_quant(blk, 8); vt_dequant(blk, 8); vt_inv(blk) 53 let me: i64 = maxerr(blk, orig) 54 g_puts(" [measure] lossy round-trip q=8: max pixel error=" as *u8); g_pn(me); g_puts("\n" as *u8) 55 pass = pass + g_check("bounded lossy round-trip (max error small)" as *u8, me <= 8); total=total+1 56 57 // 5) anti-tautology: a checkerboard (high-freq) residual does NOT collapse to DC 58 i = 0; while i < 16 { let rr: i64 = i/4; let cc: i64 = i%4; if ((rr+cc) & 1) == 0 { orig[i]=20 } else { orig[i]=0-20 } i=i+1 } 59 bcopy(blk, orig); vt_fwd(blk) 60 var r5: i64 = 1 61 if blk[0] != 0 { r5 = 0 } // checkerboard has ZERO DC... 62 if vt_nonzero(blk) == 0 { r5 = 0 } // ...but real energy in a high-freq coeff (not faked away) 63 g_puts(" [measure] checkerboard: DC=" as *u8); g_pn(blk[0]); g_puts(", high-freq coeff present (nonzero=" as *u8); g_pn(vt_nonzero(blk)); g_puts(")\n" as *u8) 64 pass = pass + g_check("anti-tautology: high-freq residual keeps high-freq energy" as *u8, r5); total=total+1 65 66 g_puts("---- vtransform gate: passed " as *u8); g_pn(pass); g_puts(" / " as *u8); g_pn(total); g_puts(" ----\n" as *u8) 67 if pass == total { g_puts("verdict=GREEN\n" as *u8); sys_exit(0); return 0 } 68 g_puts("verdict=RED\n" as *u8); sys_exit(1); return 1 69}