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`nx_ncf_synth.nx` source

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1// nx_ncf_synth.nx -- the SHARED control-flow SYNTHESIS CORE (no main; imported by the rungs + the WIRING).
2// The clean DRY home for X-AUT-NCF-001 synthesis: rungs 1-2 (nx_ncf_synth_gate, nx_ncf_loop_gate) proved the
3// CONSTRUCTS (conditional, bounded loop) self-contained; this is the importable core + the unified entry
4// `ncf_synth` that the router uses to route a NOVEL spec (input->output examples) to synthesis. Grammar:
5// affine ops, a single conditional, a bounded loop. ALL identifiers are ncf_-prefixed so importers that also
6// pull nx_pattern_classify/library never collide. license_tier: ORIGINAL
7import "nx_syscalls.nx"
8const NCF_MAGIC_8192: i64 = 8192
9const NCF_MAGIC_999999: i64 = 999999
10const NCF_MAGIC_888888: i64 = 888888
11
12const NCF_ORGAN:  *u8 = "runtime/_hdl_build/ncf_organ.nx"
13const NCF_NAME:   *u8 = "ncf_organ"
14const NCF_RESULT: *u8 = "knowledge/status/ncf_out.bin"
15const NCF_RUNNER: *u8 = "_offc/nx_sov_build_run.elf"
16
17func ncf_w(s: *u8) -> i64 { var n: i64=0; while s[n]!=(0 as u8){n=n+1} sys_write(1,s,n); return 0 }
18func ncf_n(v: i64) -> i64 { if v==0 { sys_write(1,"0" as *u8,1); return 0 } var m: i64=v; if m<0 { sys_write(1,"-" as *u8,1); m=0-m } let t: *u8=sys_mmap(24); var k: i64=0; while m>0 { t[k]=(48+(m%10)) as u8; m=m/10; k=k+1 } let o: *u8=sys_mmap(24); var w: i64=0; var q: i64=k-1; while q>=0 { o[w]=t[q]; w=w+1; q=q-1 } sys_write(1,o,w); return 0 }
19func ncf_cat(buf: *u8, off: i64, s: *u8) -> i64 { var o: i64=off; var i: i64=0; while s[i]!=(0 as u8){ buf[o]=s[i]; o=o+1; i=i+1 } return o }
20func ncf_catn(buf: *u8, off: i64, v: i64) -> i64 { var o: i64=off; if v==0 { buf[o]=48 as u8; return o+1 } var m: i64=v; if m<0 { buf[o]=45 as u8; o=o+1; m=0-m } let t: *u8=sys_mmap(24); var k: i64=0; while m>0 { t[k]=(48+(m%10)) as u8; m=m/10; k=k+1 } var i: i64=0; while i<k { buf[o]=t[k-1-i]; o=o+1; i=i+1 } return o }
21
22// ---- grammar ----
23func ncf_op_eval(op: i64, arg: i64, x: i64) -> i64 {
  if op==0 { return x }
  if op==1 { return 0 - x }
  if op==2 { return x + arg }
  if op==3 { return x * arg }
  if op==4 { return x * 0 }
  return x
30}
31func ncf_pred_eval(pred: i64, k: i64, x: i64) -> i64 {
  if pred==0 { if x<0 { return 1 } return 0 }
  if pred==1 { if x<k { return 1 } return 0 }
  if pred==2 { if x>k { return 1 } return 0 }
  return 0
36}
37func ncf_loop_eval(init: i64, bop: i64, c: i64, x: i64) -> i64 {
  var acc: i64=init; var i: i64=1
  while i<=x {
      if bop==0 { acc=acc+c }
      if bop==1 { acc=acc*c }
      if bop==2 { acc=acc+i }
      if bop==3 { acc=acc*i }
      i=i+1
  }
  return acc
47}
48
49// affine-index loop body: acc = acc + (c1*i + c0) -- covers x^2 and the quadratic/arithmetic-series family
50func ncf_loop_eval2(init: i64, c1: i64, c0: i64, x: i64) -> i64 {
  var acc: i64=init; var i: i64=1
  while i<=x { acc=acc+((c1*i)+c0); i=i+1 }
  return acc
54}
55
56// quadratic-index loop body: acc = acc + (c2*i*i + c1*i + c0) -- covers x^3 and the cubic family
57func ncf_loop_eval3(init: i64, c2: i64, c1: i64, c0: i64, x: i64) -> i64 {
  var acc: i64=init; var i: i64=1
  while i<=x { acc=acc+(((c2*i)*i)+(c1*i)+c0); i=i+1 }
  return acc
61}
62
63// TWO-STATE linear recurrence: state (a,b); each step (a,b) <- (paa*a+pab*b, pba*a+pbb*b); return a.
64// The first construct with MULTIPLE accumulators -- covers Fibonacci/Lucas/Pell (order-2 recurrences) that
65// NO single-accumulator construct (rungs 1-4) can express. This is small-program synthesis, not curve-fitting.
66func ncf_loop_eval4(a0: i64, b0: i64, paa: i64, pab: i64, pba: i64, pbb: i64, x: i64) -> i64 {
  var a: i64=a0; var b: i64=b0; var i: i64=1
  while i<=x { let na: i64=(paa*a)+(pab*b); let nb: i64=(pba*a)+(pbb*b); a=na; b=nb; i=i+1 }
  return a
70}
71
72// GENERALIZED k-order linear recurrence (companion / shift-register form): a(n) = sum_t c[t]*a(n-k+t), with
73// the k-element window initialized from the spec's first k outputs. ONE construct, parameterized by order k --
74// it SUBSUMES the two-state rung (k=2 = Fibonacci) and covers ANY order (k=3 Tribonacci, k=4 Tetranacci, ...)
75// without a hand-authored rung per order. form = [k, c0..c_{k-1}, v0..v_{k-1}]. (Assumes xs = 0,1,..,n-1.)
76func ncf_pow3(k: i64) -> i64 { var r: i64=1; var t: i64=0; while t<k { r=r*3; t=t+1 } return r }
77func ncf_recur_eval(form: *i64, x: i64) -> i64 {
  let k: i64=form[0]
  if x<k { return form[1+k+x] }
  let w: *i64=sys_mmap(128) as *i64
  var j: i64=0; while j<k { w[j]=form[1+k+j]; j=j+1 }
  var nn: i64=k
  while nn<=x {
      var nv: i64=0; var t: i64=0
      while t<k { nv=nv+(form[1+t]*w[t]); t=t+1 }
      var s: i64=0; while s<k-1 { w[s]=w[s+1]; s=s+1 }
      w[k-1]=nv; nn=nn+1
  }
  return w[k-1]
90}
91
92// ---- searchers ----
93func ncf_search_linear(xs: *i64, ys: *i64, n: i64) -> i64 {
  var op1: i64=0
  while op1<5 {
      var a1: i64=0-4
      while a1<=4 {
          var ok: i64=1; var i: i64=0
          while i<n { if ncf_op_eval(op1,a1,xs[i])!=ys[i] { ok=0; i=n } else { i=i+1 } }
          if ok==1 { return 1 }
          a1=a1+1
      }
      op1=op1+1
  }
  var p: i64=0
  while p<5 {
      var qq: i64=0
      while qq<5 {
          var a: i64=0-3
          while a<=3 {
              var b: i64=0-3
              while b<=3 {
                  var ok2: i64=1; var j: i64=0
                  while j<n { let r1: i64=ncf_op_eval(p,a,xs[j]); if ncf_op_eval(qq,b,r1)!=ys[j] { ok2=0; j=n } else { j=j+1 } }
                  if ok2==1 { return 1 }
                  b=b+1
              }
              a=a+1
          }
          qq=qq+1
      }
      p=p+1
  }
  return 0
125}
126func ncf_search_branch(xs: *i64, ys: *i64, n: i64, form: *i64) -> i64 {
  var pred: i64=0
  while pred<3 {
      var k: i64=0-3
      while k<=3 {
          var top: i64=0
          while top<5 {
              var ta: i64=0-3
              while ta<=3 {
                  var eop: i64=0
                  while eop<5 {
                      var ea: i64=0-3
                      while ea<=3 {
                          var ok: i64=1; var i: i64=0
                          while i<n {
                              var r: i64=0
                              if ncf_pred_eval(pred,k,xs[i])==1 { r=ncf_op_eval(top,ta,xs[i]) } else { r=ncf_op_eval(eop,ea,xs[i]) }
                              if r!=ys[i] { ok=0; i=n } else { i=i+1 }
                          }
                          if ok==1 { form[0]=pred; form[1]=k; form[2]=top; form[3]=ta; form[4]=eop; form[5]=ea; return 1 }
                          ea=ea+1
                      }
                      eop=eop+1
                  }
                  ta=ta+1
              }
              top=top+1
          }
          k=k+1
      }
      pred=pred+1
  }
  return 0
159}
160func ncf_search_loop(xs: *i64, ys: *i64, n: i64, form: *i64) -> i64 {
  var init: i64=0
  while init<3 {
      var bop: i64=0
      while bop<4 {
          var c: i64=0-2
          while c<=3 {
              var ok: i64=1; var i: i64=0
              while i<n { if ncf_loop_eval(init,bop,c,xs[i])!=ys[i] { ok=0; i=n } else { i=i+1 } }
              if ok==1 { form[0]=init; form[1]=bop; form[2]=c; return 1 }
              c=c+1
          }
          bop=bop+1
      }
      init=init+1
  }
  return 0
177}
178
179// search the affine-index loop: form=[init,c1,c0]; covers x^2 etc. (the construct rung-2 simple loop cannot)
180func ncf_search_loop2(xs: *i64, ys: *i64, n: i64, form: *i64) -> i64 {
  var init: i64=0-2
  while init<=4 {
      var c1: i64=0-3
      while c1<=4 {
          var c0: i64=0-3
          while c0<=3 {
              var ok: i64=1; var i: i64=0
              while i<n { if ncf_loop_eval2(init,c1,c0,xs[i])!=ys[i] { ok=0; i=n } else { i=i+1 } }
              if ok==1 { form[0]=init; form[1]=c1; form[2]=c0; return 1 }
              c0=c0+1
          }
          c1=c1+1
      }
      init=init+1
  }
  return 0
197}
198
199// search the quadratic-index loop: form=[init,c2,c1,c0]; covers x^3 (the affine-index loop cannot -- it is quadratic-in-x)
200func ncf_search_loop3(xs: *i64, ys: *i64, n: i64, form: *i64) -> i64 {
  var init: i64=0-2
  while init<=3 {
      var c2: i64=0-2
      while c2<=4 {
          var c1: i64=0-4
          while c1<=3 {
              var c0: i64=0-2
              while c0<=3 {
                  var ok: i64=1; var i: i64=0
                  while i<n { if ncf_loop_eval3(init,c2,c1,c0,xs[i])!=ys[i] { ok=0; i=n } else { i=i+1 } }
                  if ok==1 { form[0]=init; form[1]=c2; form[2]=c1; form[3]=c0; return 1 }
                  c0=c0+1
              }
              c1=c1+1
          }
          c2=c2+1
      }
      init=init+1
  }
  return 0
221}
222
223// search the two-state recurrence: form=[a0,b0,paa,pab,pba,pbb]; covers order-2 recurrences (Fibonacci etc.)
224// that single-accumulator loops cannot. Coefficients in {0,1,2}, inits in {0,1,2} -- the classic family.
225func ncf_search_loop4(xs: *i64, ys: *i64, n: i64, form: *i64) -> i64 {
  var a0: i64=0
  while a0<=2 {
      var b0: i64=0
      while b0<=2 {
          var paa: i64=0
          while paa<=2 {
              var pab: i64=0
              while pab<=2 {
                  var pba: i64=0
                  while pba<=2 {
                      var pbb: i64=0
                      while pbb<=2 {
                          var ok: i64=1; var i: i64=0
                          while i<n { if ncf_loop_eval4(a0,b0,paa,pab,pba,pbb,xs[i])!=ys[i] { ok=0; i=n } else { i=i+1 } }
                          if ok==1 { form[0]=a0; form[1]=b0; form[2]=paa; form[3]=pab; form[4]=pba; form[5]=pbb; return 1 }
                          pbb=pbb+1
                      }
                      pba=pba+1
                  }
                  pab=pab+1
              }
              paa=paa+1
          }
          b0=b0+1
      }
      a0=a0+1
  }
  return 0
254}
255
256// search the generalized recurrence: try orders k=2..4 (smallest first = minimal order); init window = first k
257// outputs (read, not searched); odometer over constant coeffs in {0,1,2}. Covers Fibonacci/Lucas/Pell/Tribonacci/
258// Tetranacci -- the whole constant-coefficient linear-recurrence family from ONE construct.
259func ncf_search_recur(xs: *i64, ys: *i64, n: i64, form: *i64) -> i64 {
  var k: i64=2
  while k<=4 {
      if n>k {
          let combos: i64=ncf_pow3(k)
          var combo: i64=0
          while combo<combos {
              form[0]=k
              var tmp: i64=combo; var t: i64=0
              while t<k { form[1+t]=tmp%3; tmp=tmp/3; t=t+1 }
              var j: i64=0; while j<k { form[1+k+j]=ys[j]; j=j+1 }
              var ok: i64=1; var i: i64=0
              while i<n { if ncf_recur_eval(form,xs[i])!=ys[i] { ok=0; i=n } else { i=i+1 } }
              if ok==1 { return 1 }
              combo=combo+1
          }
      }
      k=k+1
  }
  return 0
279}
280
281// UNIFIED ENTRY: try conditional, then loop; returns 0=UNHANDLED(stays NOVEL->tutor, no fake), 1=branch, 2=loop.
282func ncf_synth(xs: *i64, ys: *i64, n: i64, form: *i64) -> i64 {
  if ncf_search_branch(xs,ys,n,form)==1 { return 1 }
  if ncf_search_loop(xs,ys,n,form)==1 { return 2 }
  if ncf_search_loop2(xs,ys,n,form)==1 { return 3 }
  if ncf_search_loop3(xs,ys,n,form)==1 { return 4 }
  if ncf_search_loop4(xs,ys,n,form)==1 { return 5 }
  if ncf_search_recur(xs,ys,n,form)==1 { return 6 }
  return 0
290}
291
292// evaluate a synthesized FORM at x (the organ's logic, in-process) -- dispatches by construct kind. Lets a caller
293// verify held-out generalization without a god-build (ncf_emit faithfully emits this form, proven in the gates).
294func ncf_eval(kind: i64, form: *i64, x: i64) -> i64 {
  if kind==1 { if ncf_pred_eval(form[0],form[1],x)==1 { return ncf_op_eval(form[2],form[3],x) } return ncf_op_eval(form[4],form[5],x) }
  if kind==2 { return ncf_loop_eval(form[0],form[1],form[2],x) }
  if kind==3 { return ncf_loop_eval2(form[0],form[1],form[2],x) }
  if kind==4 { return ncf_loop_eval3(form[0],form[1],form[2],form[3],x) }
  if kind==5 { return ncf_loop_eval4(form[0],form[1],form[2],form[3],form[4],form[5],x) }
  if kind==6 { return ncf_recur_eval(form,x) }
  return 0
302}
303
304// ---- materialize ----
305func ncf_cat_ret(buf: *u8, off: i64, op: i64, arg: i64, ind: *u8) -> i64 {
  var o: i64=off
  o=ncf_cat(buf,o,ind); o=ncf_cat(buf,o,"return " as *u8)
  if op==0 { o=ncf_cat(buf,o,"x" as *u8) }
  if op==1 { o=ncf_cat(buf,o,"0 - x" as *u8) }
  if op==2 { o=ncf_cat(buf,o,"x + " as *u8); o=ncf_catn(buf,o,arg) }
  if op==3 { o=ncf_cat(buf,o,"x * " as *u8); o=ncf_catn(buf,o,arg) }
  if op==4 { o=ncf_cat(buf,o,"x * 0" as *u8) }
  o=ncf_cat(buf,o,"\n" as *u8)
  return o
315}
316func ncf_cat_pred(buf: *u8, off: i64, pred: i64, k: i64) -> i64 {
  var o: i64=off
  if pred==0 { o=ncf_cat(buf,o,"x < 0" as *u8) }
  if pred==1 { o=ncf_cat(buf,o,"x < " as *u8); o=ncf_catn(buf,o,k) }
  if pred==2 { o=ncf_cat(buf,o,"x > " as *u8); o=ncf_catn(buf,o,k) }
  return o
322}
323func ncf_cat_body(buf: *u8, off: i64, bop: i64, c: i64) -> i64 {
  var o: i64=off
  if bop==0 { o=ncf_cat(buf,o,"        acc = acc + " as *u8); o=ncf_catn(buf,o,c) }
  if bop==1 { o=ncf_cat(buf,o,"        acc = acc * " as *u8); o=ncf_catn(buf,o,c) }
  if bop==2 { o=ncf_cat(buf,o,"        acc = acc + i" as *u8) }
  if bop==3 { o=ncf_cat(buf,o,"        acc = acc * i" as *u8) }
  o=ncf_cat(buf,o,"\n" as *u8)
  return o
331}
332// emit a branch organ; held-out main computes (f(ha)*scale)+f(hb) -> NCF_RESULT. ha emitted as 0-|ha| if <0.
333// affine-index loop body source: acc = acc + ((c1 * i) +/- c0)
334func ncf_cat_body2(buf: *u8, off: i64, c1: i64, c0: i64) -> i64 {
  var o: i64=off
  o=ncf_cat(buf,o,"        acc = acc + ((" as *u8); o=ncf_catn(buf,o,c1); o=ncf_cat(buf,o," * i)" as *u8)
  if c0<0 { o=ncf_cat(buf,o," - " as *u8); o=ncf_catn(buf,o,0-c0) } else { o=ncf_cat(buf,o," + " as *u8); o=ncf_catn(buf,o,c0) }
  o=ncf_cat(buf,o,")\n" as *u8)
  return o
340}
341// quadratic-index loop body source: acc = acc (+/-)(c2 * i * i) (+/-)(c1 * i) (+/-) c0 with explicit signs
342func ncf_cat_body3(buf: *u8, off: i64, c2: i64, c1: i64, c0: i64) -> i64 {
  var o: i64=off
  o=ncf_cat(buf,o,"        acc = acc" as *u8)
  if c2<0 { o=ncf_cat(buf,o," - ((" as *u8); o=ncf_catn(buf,o,0-c2); o=ncf_cat(buf,o," * i) * i)" as *u8) } else { o=ncf_cat(buf,o," + ((" as *u8); o=ncf_catn(buf,o,c2); o=ncf_cat(buf,o," * i) * i)" as *u8) }
  if c1<0 { o=ncf_cat(buf,o," - (" as *u8); o=ncf_catn(buf,o,0-c1); o=ncf_cat(buf,o," * i)" as *u8) } else { o=ncf_cat(buf,o," + (" as *u8); o=ncf_catn(buf,o,c1); o=ncf_cat(buf,o," * i)" as *u8) }
  if c0<0 { o=ncf_cat(buf,o," - " as *u8); o=ncf_catn(buf,o,0-c0) } else { o=ncf_cat(buf,o," + " as *u8); o=ncf_catn(buf,o,c0) }
  o=ncf_cat(buf,o,"\n" as *u8)
  return o
350}
351func ncf_cat_arg(buf: *u8, off: i64, v: i64) -> i64 {
  var o: i64=off
  if v<0 { o=ncf_cat(buf,o,"0 - " as *u8); o=ncf_catn(buf,o,0-v) } else { o=ncf_catn(buf,o,v) }
  return o
355}
356func ncf_emit_main(buf: *u8, off: i64, ha: i64, hb: i64, scale: i64) -> i64 {
  var o: i64=off
  o=ncf_cat(buf,o,"func main() -> i64 {\n    let p: *i64 = sys_mmap(8) as *i64\n    p[0] = (f(" as *u8)
  o=ncf_cat_arg(buf,o,ha)
  o=ncf_cat(buf,o,") * " as *u8); o=ncf_catn(buf,o,scale); o=ncf_cat(buf,o,") + f(" as *u8)
  o=ncf_cat_arg(buf,o,hb)
  o=ncf_cat(buf,o,")\n    let fd: i64 = sys_openat_wr(\"knowledge/status/ncf_out.bin\" as *u8, 420)\n    if fd >= 0 { sys_write(fd, p as *u8, 8); sys_close(fd) }\n    return 0\n}\n" as *u8)
  return o
364}
365func ncf_emit_branch(form: *i64, ha: i64, hb: i64, scale: i64) -> i64 {
  let buf: *u8=sys_mmap(NCF_MAGIC_8192); var o: i64=0
  o=ncf_cat(buf,o,"// SYNTHESIZED CONTROL FLOW (a branch) + GOD-BUILT via nx_ncf_synth. license_tier: ORIGINAL\n" as *u8)
  o=ncf_cat(buf,o,"import \"nx_syscalls.nx\"\nfunc f(x: i64) -> i64 {\n    if " as *u8)
  o=ncf_cat_pred(buf,o,form[0],form[1])
  o=ncf_cat(buf,o," {\n" as *u8)
  o=ncf_cat_ret(buf,o,form[2],form[3],"        " as *u8)
  o=ncf_cat(buf,o,"    }\n" as *u8)
  o=ncf_cat_ret(buf,o,form[4],form[5],"    " as *u8)
  o=ncf_cat(buf,o,"}\n" as *u8)
  o=ncf_emit_main(buf,o,ha,hb,scale)
  let fd: i64=sys_openat_wr(NCF_ORGAN,420)
  if fd<0 { return 0-1 }
  sys_write(fd,buf,o); sys_close(fd)
  return 0
380}
381func ncf_emit_loop(form: *i64, ha: i64, hb: i64, scale: i64) -> i64 {
  let buf: *u8=sys_mmap(NCF_MAGIC_8192); var o: i64=0
  o=ncf_cat(buf,o,"// SYNTHESIZED CONTROL FLOW (a bounded loop) + GOD-BUILT via nx_ncf_synth. license_tier: ORIGINAL\n" as *u8)
  o=ncf_cat(buf,o,"import \"nx_syscalls.nx\"\nfunc f(x: i64) -> i64 {\n    var acc: i64 = " as *u8)
  o=ncf_catn(buf,o,form[0])
  o=ncf_cat(buf,o,"\n    var i: i64 = 1\n    while i <= x {\n" as *u8)
  o=ncf_cat_body(buf,o,form[1],form[2])
  o=ncf_cat(buf,o,"        i = i + 1\n    }\n    return acc\n}\n" as *u8)
  o=ncf_emit_main(buf,o,ha,hb,scale)
  let fd: i64=sys_openat_wr(NCF_ORGAN,420)
  if fd<0 { return 0-1 }
  sys_write(fd,buf,o); sys_close(fd)
  return 0
394}
395func ncf_emit_loop2(form: *i64, ha: i64, hb: i64, scale: i64) -> i64 {
  let buf: *u8=sys_mmap(NCF_MAGIC_8192); var o: i64=0
  o=ncf_cat(buf,o,"// SYNTHESIZED CONTROL FLOW (affine-index loop) + GOD-BUILT via nx_ncf_synth. license_tier: ORIGINAL\n" as *u8)
  o=ncf_cat(buf,o,"import \"nx_syscalls.nx\"\nfunc f(x: i64) -> i64 {\n    var acc: i64 = " as *u8)
  o=ncf_catn(buf,o,form[0])
  o=ncf_cat(buf,o,"\n    var i: i64 = 1\n    while i <= x {\n" as *u8)
  o=ncf_cat_body2(buf,o,form[1],form[2])
  o=ncf_cat(buf,o,"        i = i + 1\n    }\n    return acc\n}\n" as *u8)
  o=ncf_emit_main(buf,o,ha,hb,scale)
  let fd: i64=sys_openat_wr(NCF_ORGAN,420)
  if fd<0 { return 0-1 }
  sys_write(fd,buf,o); sys_close(fd)
  return 0
408}
409func ncf_emit_loop3(form: *i64, ha: i64, hb: i64, scale: i64) -> i64 {
  let buf: *u8=sys_mmap(NCF_MAGIC_8192); var o: i64=0
  o=ncf_cat(buf,o,"// SYNTHESIZED CONTROL FLOW (quadratic-index loop) + GOD-BUILT via nx_ncf_synth. license_tier: ORIGINAL\n" as *u8)
  o=ncf_cat(buf,o,"import \"nx_syscalls.nx\"\nfunc f(x: i64) -> i64 {\n    var acc: i64 = " as *u8)
  o=ncf_catn(buf,o,form[0])
  o=ncf_cat(buf,o,"\n    var i: i64 = 1\n    while i <= x {\n" as *u8)
  o=ncf_cat_body3(buf,o,form[1],form[2],form[3])
  o=ncf_cat(buf,o,"        i = i + 1\n    }\n    return acc\n}\n" as *u8)
  o=ncf_emit_main(buf,o,ha,hb,scale)
  let fd: i64=sys_openat_wr(NCF_ORGAN,420)
  if fd<0 { return 0-1 }
  sys_write(fd,buf,o); sys_close(fd)
  return 0
422}
423// materialize the two-state recurrence: two registers a,b with a parallel update via temps.
424func ncf_emit_loop4(form: *i64, ha: i64, hb: i64, scale: i64) -> i64 {
  let buf: *u8=sys_mmap(NCF_MAGIC_8192); var o: i64=0
  o=ncf_cat(buf,o,"// SYNTHESIZED CONTROL FLOW (two-state linear recurrence) + GOD-BUILT via nx_ncf_synth. license_tier: ORIGINAL\n" as *u8)
  o=ncf_cat(buf,o,"import \"nx_syscalls.nx\"\nfunc f(x: i64) -> i64 {\n    var a: i64 = " as *u8)
  o=ncf_catn(buf,o,form[0])
  o=ncf_cat(buf,o,"\n    var b: i64 = " as *u8)
  o=ncf_catn(buf,o,form[1])
  o=ncf_cat(buf,o,"\n    var i: i64 = 1\n    while i <= x {\n        let na: i64 = (" as *u8)
  o=ncf_catn(buf,o,form[2]); o=ncf_cat(buf,o," * a) + (" as *u8); o=ncf_catn(buf,o,form[3]); o=ncf_cat(buf,o," * b)\n        let nb: i64 = (" as *u8)
  o=ncf_catn(buf,o,form[4]); o=ncf_cat(buf,o," * a) + (" as *u8); o=ncf_catn(buf,o,form[5]); o=ncf_cat(buf,o," * b)\n        a = na\n        b = nb\n        i = i + 1\n    }\n    return a\n}\n" as *u8)
  o=ncf_emit_main(buf,o,ha,hb,scale)
  let fd: i64=sys_openat_wr(NCF_ORGAN,420)
  if fd<0 { return 0-1 }
  sys_write(fd,buf,o); sys_close(fd)
  return 0
439}
440// materialize the order-k recurrence: a k-element shift-register window, linear update, base cases for x<k.
441func ncf_emit_recur(form: *i64, ha: i64, hb: i64, scale: i64) -> i64 {
  let k: i64=form[0]
  let buf: *u8=sys_mmap(NCF_MAGIC_8192); var o: i64=0
  o=ncf_cat(buf,o,"// SYNTHESIZED CONTROL FLOW (order-k linear recurrence) + GOD-BUILT via nx_ncf_synth. license_tier: ORIGINAL\n" as *u8)
  o=ncf_cat(buf,o,"import \"nx_syscalls.nx\"\nfunc f(x: i64) -> i64 {\n    let w: *i64 = sys_mmap(128) as *i64\n" as *u8)
  var j: i64=0
  while j<k { o=ncf_cat(buf,o,"    w[" as *u8); o=ncf_catn(buf,o,j); o=ncf_cat(buf,o,"] = " as *u8); o=ncf_catn(buf,o,form[1+k+j]); o=ncf_cat(buf,o,"\n" as *u8); j=j+1 }
  o=ncf_cat(buf,o,"    if x < " as *u8); o=ncf_catn(buf,o,k); o=ncf_cat(buf,o," { return w[x] }\n" as *u8)
  o=ncf_cat(buf,o,"    var nn: i64 = " as *u8); o=ncf_catn(buf,o,k); o=ncf_cat(buf,o,"\n    while nn <= x {\n        let nv: i64 = " as *u8)
  var t: i64=0
  while t<k {
      o=ncf_cat(buf,o,"(" as *u8); o=ncf_catn(buf,o,form[1+t]); o=ncf_cat(buf,o," * w[" as *u8); o=ncf_catn(buf,o,t); o=ncf_cat(buf,o,"])" as *u8)
      if t<k-1 { o=ncf_cat(buf,o," + " as *u8) }
      t=t+1
  }
  o=ncf_cat(buf,o,"\n        var s: i64 = 0\n        while s < " as *u8); o=ncf_catn(buf,o,k-1); o=ncf_cat(buf,o," { w[s] = w[s+1]; s = s + 1 }\n" as *u8)
  o=ncf_cat(buf,o,"        w[" as *u8); o=ncf_catn(buf,o,k-1); o=ncf_cat(buf,o,"] = nv\n        nn = nn + 1\n    }\n    return w[" as *u8); o=ncf_catn(buf,o,k-1); o=ncf_cat(buf,o,"]\n}\n" as *u8)
  o=ncf_emit_main(buf,o,ha,hb,scale)
  let fd: i64=sys_openat_wr(NCF_ORGAN,420)
  if fd<0 { return 0-1 }
  sys_write(fd,buf,o); sys_close(fd)
  return 0
463}
464// emit whichever construct was synthesized (kind from ncf_synth)
465func ncf_emit(kind: i64, form: *i64, ha: i64, hb: i64, scale: i64) -> i64 {
  if kind==1 { return ncf_emit_branch(form,ha,hb,scale) }
  if kind==2 { return ncf_emit_loop(form,ha,hb,scale) }
  if kind==3 { return ncf_emit_loop2(form,ha,hb,scale) }
  if kind==4 { return ncf_emit_loop3(form,ha,hb,scale) }
  if kind==5 { return ncf_emit_loop4(form,ha,hb,scale) }
  if kind==6 { return ncf_emit_recur(form,ha,hb,scale) }
  return 0-1
473}
474
475// ---- GOD-BUILD + read ----
476func ncf_god_build(name: *u8) -> i64 {
  let pid: i64=sys_fork()
  if pid==0 {
      let dn: i64=sys_openat_wr("/dev/null\x00" as *u8,420)
      if dn>=0 { sys_dup3(dn,1,0); sys_dup3(dn,2,0) }
      let argv: *i64=sys_mmap(64) as *i64
      argv[0]=NCF_RUNNER as i64; argv[1]=name as i64; argv[2]=0
      let envp: *i64=sys_mmap(16) as *i64
      envp[0]="PATH=/usr/bin:/bin" as *u8 as i64; envp[1]=0
      sys_execve(NCF_RUNNER,argv,envp)
      sys_exit(127)
  }
  let st: *i64=sys_mmap(16) as *i64
  sys_wait4(pid,st,0)
  return (st[0]>>8)&0xff
491}
492func ncf_read(path: *u8) -> i64 {
  let lenp: *i64=sys_mmap(16) as *i64
  let buf: *u8=sys_read_file(path,lenp)
  if (buf as i64)==0 { return 0-NCF_MAGIC_999999 }
  if lenp[0]<8 { return 0-NCF_MAGIC_888888 }
  let p: *i64=buf as *i64
  return p[0]
499}
nx_ncf_synth.nx source

`nx_ncf_synth.nx` source
