nx_resid_entropy_gate.nx source

1// nx_resid_entropy_gate.nx -- proves + MEASURES the wired residual entropy coder (nx_resid_entropy): a realistic 2// Laplacian LPC residual is range-coded LOSSLESSLY, far below a fixed N-bit/sample representation and near the Shannon 3// entropy bound. This is the voice codec's v2 q/bit lever, MEASURED (a real bitrate cut at identical quality), not a 4// vs-Opus claim. 5import "nx_syscalls_x86_64.nx" 6import "nx_resid_entropy.nx" 7import "nx_quality_metric.nx" 8 9func g_puts(s: *u8) -> i64 { var n: i64=0; while s[n]!=(0 as u8){n=n+1} sys_write(1,s,n); return 0 } 10func g_pn(v: i64) -> i64 { 11 let b: *u8 = sys_mmap(28); var x: i64 = v 12 if x < 0 { b[0]=45; sys_write(1,b,1); x = 0 - x } 13 if x == 0 { b[0]=48; sys_write(1,b,1); return 0 } 14 var d: i64=0; var y: i64=x 15 while y>0 { d=d+1; y=y/10 } 16 var i: i64=d-1; y=x 17 while i>=0 { b[i]=(48+(y%10)) as u8; y=y/10; i=i-1 } 18 sys_write(1,b,d); return 0 19} 20func g_check(name: *u8, cond: i64) -> i64 { 21 if cond==1 { g_puts(" PASS " as *u8) } else { g_puts(" FAIL " as *u8) } 22 g_puts(name); g_puts("\n" as *u8); return cond 23} 24 25func main() -> i64 { 26 g_puts("nx_resid_entropy gate (range-code the LPC residual, MEASURED q/bit)\n" as *u8) 27 var pass: i64 = 0; var total: i64 = 0 28 let n: i64 = 256 29 let ALPHA: i64 = 17 // residual symbols for |r| up to 8 (re_zz(8)=16) 30 31 let freq: *i64 = sys_mmap(ALPHA*8) as *i64 32 let cum: *i64 = sys_mmap((ALPHA+1)*8) as *i64 33 let ft: i64 = re_build_model(ALPHA, freq, cum) 34 35 // realistic Laplacian residual: magnitude counts halve (128 zeros, 64 ±1, 32 ±2, ...) -- the shape of real LPC residuals 36 let resid: *i64 = sys_mmap(n*8) as *i64 37 var idx: i64 = 0 38 var mag: i64 = 0 39 while idx < n { 40 if mag > 8 { mag = 8 } 41 var cnt: i64 = 128 >> mag 42 if cnt < 1 { cnt = 1 } 43 var k: i64 = 0 44 while k < cnt { 45 if idx < n { 46 if mag == 0 { resid[idx] = 0 } else { if (k & 1) == 0 { resid[idx] = mag } else { resid[idx] = 0 - mag } } 47 idx = idx + 1 48 } 49 k = k + 1 50 } 51 mag = mag + 1 52 if mag > 8 { if idx < n { resid[idx] = 0; idx = idx + 1 } } 53 } 54 55 // range-code + round-trip 56 let out: *u8 = sys_mmap(2048) as *u8 57 let rc_bytes: i64 = re_encode(resid, n, ALPHA, cum, ft, out, 2048) 58 let dec: *i64 = sys_mmap(n*8) as *i64 59 re_decode(out, rc_bytes, n, ALPHA, cum, ft, dec) 60 var exact: i64 = 1 61 var i: i64 = 0 62 while i < n { if dec[i] != resid[i] { exact = 0 } i = i + 1 } 63 64 // fixed N-bit baseline (ceil(log2(17)) = 5 bits/sample) and the Shannon entropy bound from the actual histogram 65 let fixed_bytes: i64 = (n * 5 + 7) / 8 66 let hist: *i64 = sys_mmap(ALPHA*8) as *i64 67 i = 0; while i < ALPHA { hist[i] = 0; i = i + 1 } 68 i = 0; while i < n { var z: i64 = re_zz(resid[i]); if z >= ALPHA { z = ALPHA - 1 } hist[z] = hist[z] + 1; i = i + 1 } 69 var ent_bits_q16: i64 = 0 // sum cnt * log2(n/cnt) in Q16 70 i = 0 71 while i < ALPHA { if hist[i] > 0 { ent_bits_q16 = ent_bits_q16 + hist[i] * (qm_log2_q16(n) - qm_log2_q16(hist[i])) } i = i + 1 } 72 let entropy_bytes: i64 = (ent_bits_q16 >> 16) / 8 73 74 g_puts(" [measure] residual n=" as *u8); g_pn(n); g_puts(" samples: range-coded=" as *u8); g_pn(rc_bytes) 75 g_puts(" B vs fixed-5bit=" as *u8); g_pn(fixed_bytes); g_puts(" B vs Shannon-bound=" as *u8); g_pn(entropy_bytes); g_puts(" B\n" as *u8) 76 g_puts(" [measure] bitrate cut vs fixed = " as *u8); g_pn((fixed_bytes - rc_bytes) * 100 / fixed_bytes); g_puts("%\n" as *u8) 77 78 pass = pass + g_check("residual round-trips LOSSLESSLY through the range coder" as *u8, exact); total=total+1 79 pass = pass + g_check("range-coded residual < fixed-5bit (real q/bit cut)" as *u8, rc_bytes < fixed_bytes); total=total+1 80 pass = pass + g_check("range-coded within 30% of the Shannon entropy bound (near-optimal)" as *u8, rc_bytes * 10 <= entropy_bytes * 13); total=total+1 81 82 g_puts("---- resid_entropy gate: passed " as *u8); g_pn(pass); g_puts(" / " as *u8); g_pn(total); g_puts(" ----\n" as *u8) 83 if pass == total { g_puts("verdict=GREEN\n" as *u8); sys_exit(0); return 0 } 84 g_puts("verdict=RED\n" as *u8); sys_exit(1); return 1 85}