soothe2-re/notes_giant_fft.md

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.