# FUN_18002f980 (giant) — recursive FFT plan/permuation generator

Signature: `ulonglong *FUN_18002f980(plan*, log2, src, flags, depth, uVar2, scratch)`

Role: builds the FFT stage plan (bit-reverse ordering + sign-flip masks),
NOT a numeric executor (no FP math inside; all integer indexing).

## Factor split (top)
```
iVar2 = DAT_181c5e0fc[log2]      // per-log2 factor (4/8/9/13... from static table)
iVar19 = log2 - iVar2            // reduced log2 for subproblem
if iVar19 < 0x12:  pu = FUN_18002e360(iVar19, scr)   // small-plan path (radix2/3 generator)
else:             pu = FUN_18002f980(plan, iVar19, scr, ..., depth+1)   // recurse
*(plan + 0x78 + depth*8) = pu   // store sub-plan ptr per depth
*(plan + 0x38)      = param_6   // (entry stores callback/context)
*(plan + 0x1c)      = (1<<iVar19)*0x10 + 0x3f & ~0x3f   // size budget
```

## Stage iteration
```
iVar25 = 1 << iVar19
uVar3  = DAT_181c5e15c[log2]     // 2nd factor table (stage exponent bundle)
iVar33 = 1 << (uVar3 - iVar2)    // butterfly count/base
loop groups:
  for (uVar26=1; ...) {
    iVar44 = 1 << (iVar16+2);  iVar32 = 1 << (iVar16+2 + dirflag)
    if (iVar12 == log2) -> radix-8 permute block
      local_900[k]=src[±idx*8]  (and ^= DAT_181c5e1e0 for negative/reflected)
      processed 16 qwords = 8 complex pairs; groups x butterflies
    next stage: uVar26 <<= 2; iVar16 -= 2            // radix-4 sweep
    else branch radix-3: uVar26 <<= 3; iVar16 -= 3
    ...
  }
while (iVar12 < log2)
outer while (uVar24 < (iVar25-1+iVar33)/iVar33)
```

## Key masive consts
- DAT_181c5e1e0  = sign-flip XOR mask (bit for im part) applied to mirrored indices.
- DAT_181c5e0fc / 181c5e15c / 181c5e3fc = per-log2 factor tables (read as int, index log2).
- Base small planner FUN_18002e360: iVar6=1<<log2; if <9 return; else select radix2/3
  for log2==4 || >10 -> 2 else 3; loops similarly, returns param_4 (plan tail).
- Return: puVar10 + (1<<log2)*2  (aligned plan tail after current stage block).

## Notes for reimplementation
- Exact ordering must be transcribed from the index algebra (the branches accumulate a
  combination of ± vs complemented indices; XOR selects conjugate/negate for 2x recalc).
- The 7 giants are per-(data type, direct/inverse, maybe r2c/c2r) variants (identical
  structure; different base-call FUN_18002e360 vs FUN_180023860).
- Stage kernels executed at runtime are the dispatched vector kernels (see roadmap),
  driven from this plan's ordering; the transform itself therefore reproduces a
  specific FFT: split-radix 2/4/8-style in-place butterflies with fused reorder.
## Twiddle source (DAT_182616800 = sin-table)
- 1024 doubles = exact sin(k*2*pi/1024) (double precision), first half-period 0..512 (rest garbage of neighboring data).
- Copied to scratch by FUN_180039b00( log2N, dst ): step lVar18 = 1 << (10 - log2N) for N<=1024.
- So for N = 2^m: twiddle angles sampled from table with stride 2^(10-m). For N>1024 separate (two-pass) branch (unresolved).
- Stage kernels (FUN_18000bfc0/18000c5e0) consume these with 0x40-complex chunks, cplx-mul=180008440, acc=FUN_1800437c0/180044700.

## ============ UPDATE 2026-08-20 (P3: code extracted from rt snap, objdump) ============
Raw code extracted from /tmp/snap_rt.bin via handoff/extract_fft.py → /tmp/fft/*.bin.

### cplx_mul 0x180008440 = IN-PLACE ELEMENTWISE DOUBLE MULTIPLY (not complex!):
  signature (rcx=dst, rdx=src, r8d=count): dst[i] *= src[i]  (double).
  kernel 0x18003fa20: scalar path mulsd, vector path mulpd (4-wide). Corrects the
  "cplx-mul=180008440" label — the complex multiply is done via SEPARATE re/im passes
  (interleaved layout), 0x8440 is the scalar elementwise multiply.

### twiddle loader FUN_180039b00 (log2N=ecx, dst=rdx):
  N = 1<<log2N;  count = N/4 (sar $2 after N/2 sar).
  if log2N > 10: separate two-pass branch (0x180039dc9).
  else stride = 1 << (10-log2N); copy sin_table[0x182616800 + k*stride*8] -> dst[k], k=0..N/4-1.
  sin_table DAT_182616800 = sin(k·2π/1024) for k=0..256 (257 valid doubles, then garbage).
  => twiddle[k] = sin(k·stride·2π/1024), the quarter-period sample set.

### stage kernels FUN_18000bfc0 / 18000c5e0 (butterfly):
  prologue stack 0x470 (scratch 0x200×2 doubles). Per 0x40-complex chunk:
    0x180140c40(src, scratch, scratch+0x200, 0x40)  — load/format twiddle into scratch
    0x8440(dst, scratch, 0x40)                       — dst *= scratch   (elementwise)
    0x8440(dst, scratch+0x200, 0x40)                 — dst *= scratch+0x200
  then butterfly arithmetic + acc (FUN_1800437c0/044700). Full loop still to transcribe.

### dispatcher 0x535a70 → 0x140a10 (scalar) / 0x140a70 (vector) (per NOTES:166).
Second-level dispatch: 0x140a10/140a70 read global index [0x1826159a0] (=4 at capture)
then jump through tables:
  scalar 0x182617548 = {0x180141380, 0x1801413a0, ..., 0x1801414a0}  (12 entries, [4]=0x180141400)
  vector 0x182617588 = {0x180141440, ..., 0x180141560}              ([4]=0x1801414c0)
These are the per-size/per-type stage kernels (0x1801413xx/1415xx family).

### FOURTH level — final kernels (runtime-filled pointer tables):
0x180141400 = jmp *[0x1826181d8]; the tables hold (at capture):
  0x1826181d8=0x1802a24c0, 0x182618200=0x1802a4d80, 0x182618228=0x1802a7540,
  0x182618250=0x1802b4540, 0x182618278=0x1802c1540, 0x1826182a0=0x1802ce4a0.
These 6 are the final split-radix FFT kernels (stack frames 0x328/0x350/0x7c8/0x7c8/0x7f8/0xd48).
- **CRITICAL for bit-exact**: kernel 0x1802a24c0 prologue sets MXCSR rounding mode (vstmxcsr/
  vldmxcsr, round-to-nearest 0x1f80) AND x87 control word (fnstcw/fldcw) before the FP loop,
  then restores. So the transform runs under an explicitly-forced rounding mode.

### STATUS / scope
Full bit-exact FFT = plan generator (0x2f980 split-radix index algebra) + runtime dispatch
(3-level tables) + 6 final kernels (each 0x800-0x1200 bytes of vectorized split-radix butterfly)
+ twiddle. This is the P3 2-4 week body. Architecture fully mapped; transcription not yet done.

### Final kernel 0x1802a24c0 — own vectorized sin/cos, NOT twiddle table
The big-N kernels compute trig ON THE FLY via an AVX polynomial (vfmadd231ps/213ps chain) with
range reduction done by float-bit tricks (vpaddd/vpsubd/vpsrad $0x17 = 23-bit shift = exponent
extract, vpcmpgtd, vblendvps). Polynomial constants (rodata, float, broadcast x8):
  0x181f81fa0 = 0.333366   0x181f81fc0 = -0.250047  0x181f81fe0 = 0.198225
  0x181f82000 = -0.164625  0x181f82020 = 0.169649   0x181f82040 = -0.151772
  0x181f82100 = 0.666667   0x181f821c0 = 0.693147 (= ln 2)  0x181f822c0 = 0.75
  (0.693147 = ln 2 ⇒ exp-based sin/cos, SVML-like vector math library.)
=> Small-N path uses the twiddle sin-table (0x39b00); big-N path uses this own polynomial.
Transcribing this bit-exactly = reimplementing a vector math sin/cos (Cody-Waite + poly + exp),
plus the split-radix butterfly + integer reorder — the multi-week P3 body.