tinygrad/tinygrad/codegen/uopgraph.py

from __future__ import annotations
from typing import Optional, Tuple, Dict, List, cast, TYPE_CHECKING, Any, DefaultDict, Callable
import functools, itertools, operator
from collections import defaultdict
from tinygrad.dtype import dtypes, PtrDType, ImageDType
from tinygrad.ops import UnaryOps, BinaryOps, TernaryOps, UOp, UOps, UPat, PatternMatcher, symbolic_flat
from tinygrad.ops import graph_rewrite, is_irreducible, split_uop, identity_element, uop_given_valid, parse_valid, is_increasing, simplify_valid
from tinygrad.helpers import DEBUG, getenv, flatten, dedup, TRANSCENDENTAL, AMX, prod, partition, all_same
from tinygrad.codegen.transcendental import xexp2, xlog2, xsin, TRANSCENDENTAL_SUPPORTED_DTYPES

if TYPE_CHECKING: from tinygrad.renderer import Renderer

# ***** float4/image store handling *****

def fold_expanded(ex, buf):
  if buf.dtype.base != dtypes.float and buf.dtype.base != dtypes.half and not isinstance(buf.dtype, ImageDType): return None
  new_srcs = dedup(list(ex.src))
  old_new_srcs = new_srcs[:]
  is_load, is_image = new_srcs[0].op is UOps.LOAD, isinstance(buf.dtype, ImageDType)

  # first, extract all the relevant offsets
  offsets_rootsrc: DefaultDict[Any, dict] = defaultdict(dict)
  for i,s in enumerate(new_srcs):
    if s.dtype.count != 1 or (is_image and s.src[1].dtype.count == 2): continue
    idx = s.src[1]
    if idx.arg is BinaryOps.ADD and idx.src[1].op is UOps.CONST: root_src, arg = idx.src[0], idx.src[1].arg
    elif idx.op is UOps.CONST: root_src, arg = "CONST", idx.arg
    else: root_src, arg = idx, 0
    # add gates for gated
    if len(s.src) >= 4: root_src = (s.src[3], root_src)
    assert arg not in offsets_rootsrc[root_src]
    offsets_rootsrc[root_src][arg] = i

  # then rewrite everything we can
  lengths = [4] if is_image else ([8,4,2] if buf.dtype.base == dtypes.half and getenv("ALLOW_HALF8") else ([16,8,4,2] if AMX else [4,2]))
  used = set()
  for rootsrc, offsets in offsets_rootsrc.items():
    for o in offsets:
      for fold_length in lengths:
        if all((rootsrc,o+i) not in used and o+i in offsets for i in range(fold_length)):
          load_1 = new_srcs[offsets[o]]
          new_src = list(load_1.src)
          if new_src[1].divides(fold_length) is None: continue
          # for images, we rewrite the index. it must evenly divide 4 from the above check
          if is_image:
            new_src[1] = UOp(UOps.VECTORIZE, dtypes.int.vec(2), ((new_src[1] // 4) % buf.dtype.shape[1], (new_src[1] // (4 * buf.dtype.shape[1]))))
          # vectorize the store/loadconst
          if not is_load or len(new_src) >= 4:
            new_src[2] = UOp(UOps.VECTORIZE, new_src[2].dtype.vec(fold_length), tuple(new_srcs[offsets[o+i]].src[2] for i in range(fold_length)))
          # generate the folded new_srcs
          if is_load:
            new_load = UOp(UOps.LOAD, load_1.dtype.vec(fold_length), tuple(new_src))
            for i in range(fold_length): new_srcs[offsets[o+i]] = new_load.gep(i)
          else:
            for i in range(fold_length): new_srcs[offsets[o+i]] = UOp(UOps.STORE, dtypes.void, tuple(new_src)) if i == 0 else None
          for i in range(fold_length): used.add((rootsrc,o+i))

  # dedup expand for LOAD
  if is_load and len(old_new_srcs) != len(ex.src): new_srcs = [new_srcs[old_new_srcs.index(s)] for s in ex.src]
  # remove Nones for STORE
  return UOp(ex.op, ex.dtype, tuple(x for x in new_srcs if x is not None), ex.arg) if len(used) else None

def fix_unfoldable_image_load(load:UOp, buf:UOp):
  if not isinstance(buf.dtype, ImageDType) or load.src[1].dtype.count == 2: return None
  id4 = load.src[1] % 4
  new_src = list(load.src)
  # TODO: copied logic from above
  new_src[1] = UOp(UOps.VECTORIZE, dtypes.int.vec(2), ((load.src[1] // 4) % buf.dtype.shape[1], (load.src[1] // (4 * buf.dtype.shape[1]))))
  if len(new_src) >= 4:
    new_src[2] = UOp(UOps.VECTORIZE, new_src[2].dtype.vec(4), tuple(new_src[2] for _ in range(4)))
  vec_load = UOp(UOps.LOAD, load.dtype.vec(4), tuple(new_src))
  return functools.reduce(lambda ret, i: id4.ne(i).where(ret, vec_load.gep(i)), range(4), load.const_like(float('nan')))

float4_folding = PatternMatcher([
  (UPat(UOps.VECTORIZE, src=UPat(UOps.LOAD, src=(UPat.var("buf"), UPat()), allow_any_len=True), name="ex"), fold_expanded),
  (UPat((UOps.BARRIER, UOps.SINK), src=UPat(UOps.STORE, src=(UPat.var("buf"), UPat(), UPat()), allow_any_len=True), name="ex"), fold_expanded),
])

# ***** image load valid simplification *****

def simplify_buffer_load(load:UOp) -> Optional[UOp]:
  if not isinstance(load.src[0].dtype, PtrDType) or len(load.src) != 4: return None
  buf, start_idx, invalid_val, valid = load.src
  if (idx:=uop_given_valid(valid, start_idx)) is None: return load.replace(src=(buf, start_idx, invalid_val, valid.const_like(False)))
  return None if idx is start_idx else load.replace(src=((buf, idx, invalid_val, valid)))

def simplify_image_load(load:UOp) -> Optional[UOp]:
  if not isinstance(buf_dtype:=load.src[0].dtype, ImageDType) or len(load.src) != 4: return None
  buf, start_idx, invalid_val, valid = load.src
  if (idx:=uop_given_valid(valid, start_idx)) is None: return load.replace(src=(buf, start_idx, invalid_val, valid.const_like(False)))

  # can drop valid if idx is out of bound when valid is False
  drop_stmt = []
  for stmt in split_uop(valid, BinaryOps.AND):
    X, is_upper_bound, c = parse_valid(stmt)

    # for X0 + X1 + ... >= 1, check if it's out of bound when Xi = 0 for all i
    if not is_upper_bound and c == 1 and all(is_irreducible(u) and u.vmin == 0 for u in split_uop(X, BinaryOps.ADD)):
      testidx = functools.reduce(lambda nowidx,u: nowidx.substitute({u:u.const_like(0)}), split_uop(X, BinaryOps.ADD), idx)
      testidx = graph_rewrite(testidx, sym)
      if testidx.src[0].vmax < 0 or testidx.src[1].vmax < 0:
        drop_stmt.append(stmt)
        continue

    # if X <= c, check if it's out of bound when X = c+1
    # if X >= c, check if it's out of bound when X = c-1
    test_value = c + 1 if is_upper_bound else c - 1
    for i,b in zip(idx.src, (buf_dtype.shape[1], buf_dtype.shape[0])):
      if is_increasing(i):
        rw = graph_rewrite(i.substitute({X:X.const_like(test_value)}), sym)
        if rw.vmin >= b or rw.vmax < 0:
          drop_stmt.append(stmt)
          break

  if not drop_stmt and idx is start_idx: return None
  new_valid = functools.reduce(operator.and_, ss) if (ss:=[s for s in split_uop(valid, BinaryOps.AND) if s not in drop_stmt]) else None
  return load.replace(src=((buf, idx, invalid_val, new_valid) if new_valid is not None else (buf, idx)))

# ***** optional patterns *****

transcendental_patterns = [
  (UPat(UOps.ALU, dtype=TRANSCENDENTAL_SUPPORTED_DTYPES, src=(UPat.var("d"),), arg=UnaryOps.EXP2), xexp2),
  (UPat(UOps.ALU, dtype=TRANSCENDENTAL_SUPPORTED_DTYPES, src=(UPat.var("d"),), arg=UnaryOps.LOG2), xlog2),
  (UPat(UOps.ALU, dtype=TRANSCENDENTAL_SUPPORTED_DTYPES, src=(UPat.var("d"),), arg=UnaryOps.SIN), xsin),
]

powers_of_two = {2**i:i for i in range(64)}
@functools.lru_cache(None)
def get_extra_patterns(ops, force_transcendental=False):
  pat = [(p[0], cast(Callable, p[1])) for p in transcendental_patterns if p[0].arg not in ops or force_transcendental]
  # rewrite MOD to AND (which should always be supported, but not for generic in tests)
  if BinaryOps.AND in ops:
    pat += [(UPat(UOps.ALU, arg=BinaryOps.MOD, src=(UPat.var('base'), UPat.cvar("const"))),
            lambda base,const: base & (const.arg-1) if const.arg in powers_of_two else None)]
  # rewrite MUL/IDIV to SHL+SHR
  if BinaryOps.SHL in ops and BinaryOps.SHR in ops:
    pat += [
    (UPat(UOps.ALU, arg=BinaryOps.MUL, dtype=dtypes.ints, src=[UPat.cvar("const"), UPat.var("mul")]), lambda mul, const:
      UOp(UOps.ALU, mul.dtype, (mul, UOp.const(dtypes.int, powers_of_two[const.arg])), BinaryOps.SHL) if const.arg in powers_of_two else None),
    (UPat(UOps.ALU, arg=BinaryOps.IDIV, src=(UPat.var("div"), UPat.cvar("const"))), lambda div, const:
      UOp(UOps.ALU, div.dtype, (div, UOp.const(dtypes.int, powers_of_two[const.arg])), BinaryOps.SHR) if const.arg in powers_of_two else None)]
  if UnaryOps.NEG in ops:
    pat += [(UPat.var('x')*-1, lambda x: x.alu(UnaryOps.NEG))]
    if BinaryOps.SUB in ops: pat += [(UPat.var('x')+UPat.var('y').alu(UnaryOps.NEG), lambda x,y: x.alu(BinaryOps.SUB, y))]
  if TernaryOps.MULACC in ops:
    pat += [(UPat.var('a')*UPat.var('b')+UPat.var('c'), lambda a,b,c: a.alu(TernaryOps.MULACC, b, c))]
  return PatternMatcher(pat)

# ***** threefry *****

def threefry2x32(x: UOp, key: UOp):
  # split x into two uint32, since x in a uint64
  x0, x1 = (x & 0xffffffff).cast(dtypes.uint32), ((x // 2**32) & 0xffffffff).cast(dtypes.uint32)

  rotations = [[13, 15, 26, 6], [17, 29, 16, 24]]
  key0, key1 = (key & 0xffffffff).cast(dtypes.uint32), ((key // 2**32) & 0xffffffff).cast(dtypes.uint32)
  ks = [key1, key0 ^ key1 ^ 0x1BD11BDA, key0]
  xr = [x0 + ks[-1], x1 + ks[0]]
  for i in range(5):
    for r in rotations[i % 2]: xr[0], xr[1] = (x0 := xr[0] + xr[1]), x0 ^ ((xr[1] * 2**r) + (xr[1] // 2**(32 - r)))
    xr = [(xr[0] + ks[i % 3]), (xr[1] + ks[(i + 1) % 3] + i + 1)]

  return xr[1].cast(dtypes.uint64) * 2**32 | xr[0].cast(dtypes.uint64)

# ***** main rewriter *****

def loop_collapse(compval, idx, multconst, rng:UOp, reduce, idx2=None, idx3=None, extra=None, vec=None, ne=None, mval:UOp=UOp.const(dtypes.int32, 1)):
  if getenv("DISABLE_LOOP_COLLAPSE") or rng not in reduce.src: return None  # must be the right REDUCE
  loop_start, loop_end = rng.src
  mval_arg = mval.arg
  if loop_start.arg != 0:
    # TODO: support and test this with other mvals and loop_starts
    if DEBUG >= 1: print(f"WARNING, NOT FOLDING: mval:{mval.arg} loop_start:{loop_start.arg}")
    return None
  if idx2 is not None: idx = idx + idx2
  if idx3 is not None: idx = idx + idx3
  if vec is not None:
    # idx, mval, loop_start, loop_end
    def dvec(x): return UOp(UOps.VECTORIZE, x.dtype.vec(vec.dtype.count), src=(x,)*vec.dtype.count)
    idx, mval, loop_start, loop_end = dvec(idx), dvec(mval), dvec(loop_start), dvec(loop_end)
  if mval_arg > 0 and ne is not None:
    comprange = UOp.minimum(loop_end, UOp.maximum((idx-compval)//mval + (loop_end-loop_start), loop_start))
  elif mval_arg < 0 and ne is None:
    comprange = UOp.minimum(loop_end, UOp.maximum((idx-compval-mval)//mval + (loop_end-loop_start), loop_start))
  else:
    return None
  new_reduce_op = comprange.cast(multconst.dtype) * multconst
  ret = UOp(UOps.REDUCE, reduce.dtype, (new_reduce_op,) + tuple(x for x in reduce.src[1:] if x is not rng), reduce.arg)
  if extra is not None: ret = ret + UOp(UOps.REDUCE, reduce.dtype, (extra,) + reduce.src[1:], reduce.arg)
  return ret

def index_collapse(idx,rng,buf,ld,reduce,add=UOp.const(dtypes.int, 0),mul=UOp.const(dtypes.int, 1)):
  if rng not in reduce.src: return None
  return UOp(reduce.op, reduce.dtype, (UOp(ld.op, ld.dtype, (buf, add+mul*idx, ld.const_like(0), idx.ge(rng.src[0]) & idx.lt(rng.src[1]))),)+
             tuple(x for x in reduce.src[1:] if x is not rng), reduce.arg)

# TODO: there's a lot shared with no_vectorized_wmma here
def gep_through_wmma(gep:UOp, wmma:UOp):
  out_sz = prod(x[1] for x in wmma.arg[6][-1])
  wmma_idxs = gep.arg[::out_sz]
  for i in range(out_sz):
    if tuple(x-i for x in gep.arg[i::out_sz]) != wmma_idxs: return None
  tsrcs = []
  for s,sz in zip(wmma.src, wmma.arg[6]):
    src_args = []
    ssz = prod(x[1] for x in sz)
    for w in wmma_idxs: src_args += list(range((w//out_sz)*ssz, (w//out_sz)*ssz + ssz))
    tsrcs.append(s.gep(tuple(src_args)))
  return UOp(UOps.WMMA, gep.dtype, tuple(tsrcs), wmma.arg)

def no_vectorized_wmma(wmma:UOp):
  out_sz = prod(x[1] for x in wmma.arg[6][-1])
  if wmma.dtype.count == out_sz: return None
  tsrcs = []
  for s,sz in zip(wmma.src, wmma.arg[6]):
    ssz = prod(x[1] for x in sz)
    tsrcs.append([s.gep(tuple(range(grp, grp+ssz))) for grp in range(0, s.dtype.count, ssz)])
  wmmas = [UOp(UOps.WMMA, wmma.dtype.scalar().vec(out_sz), tsrc, wmma.arg) for tsrc in zip(*tsrcs)]
  wmma_ex = flatten([[e.gep(i) for i in range(out_sz)] for e in wmmas])
  return UOp(UOps.VECTORIZE, wmma.dtype, tuple(wmma_ex))

# this is symbolic 2.0
sym = symbolic_flat+PatternMatcher([
  # self ASSIGN is just self
  (UPat(UOps.ASSIGN, src=(UPat.var('x'), UPat.var('x'))), lambda x: x),
  # ASSIGN to global is just self
  (UPat(UOps.ASSIGN, src=(UPat(UOps.DEFINE_GLOBAL), UPat.var("x"))), lambda x: x),
  # VECTORIZE/GEP: the expander rule allows tuple GEP creation, this is just for removal
  (UPat(UOps.VECTORIZE, src=UPat(UOps.GEP, src=(UPat(name="x"),)), name="vec"),
   lambda vec,x: x if x.dtype == vec.dtype and tuple(y.arg[0] for y in vec.src) == tuple(range(len(vec.src))) else None),
  # reorder ALU/VECTORIZE
  (UPat(UOps.ALU, src=(UPat(UOps.VECTORIZE, src=UPat(name='x')), UPat(UOps.VECTORIZE, src=UPat(name='y'))), name='alu'),
   lambda x,y,alu: UOp(UOps.VECTORIZE, alu.dtype, (UOp(UOps.ALU, alu.dtype.scalar(), (x,y), alu.arg),)*alu.dtype.count)),
  # VECTORIZE of a single element is just that element
  (UPat(UOps.VECTORIZE, src=(UPat(name='x'),)), lambda x: x),
  # VECTORIZE void is SINK
  (UPat(UOps.VECTORIZE, dtype=dtypes.void, src=UPat(UOps.BARRIER, name='b')), lambda b: b),
  (UPat(UOps.VECTORIZE, dtype=dtypes.void, name='x'), lambda x: UOp(UOps.SINK, dtypes.void, x.src)),
  # GEP/VECTORIZE, GEP/GEP, GEP/CONST, GEP/VCONST
  (UPat(UOps.GEP, src=(UPat(UOps.GEP, name='g2'),), name='g1'),
   lambda g1, g2: g2.src[0].gep(tuple(g2.arg[g1.arg[i]] for i in range(g1.dtype.count)))),
  (UPat(UOps.GEP, src=(UPat(UOps.VECTORIZE, name="vec"),), name="gep"),
   lambda gep, vec: UOp(UOps.VECTORIZE, gep.dtype, tuple(vec.src[i] for i in gep.arg)) if len(gep.arg) > 1 else vec.src[gep.arg[0]]),
  (UPat(UOps.GEP, src=(UPat.cvar("c", vec=False),), name="gep"), lambda gep, c: gep.const_like(c.arg)),
  (UPat(UOps.GEP, src=(UPat(UOps.VCONST, name="c"),), name="gep"), lambda gep, c: gep.const_like(tuple(c.arg[x] for x in gep.arg))),
  # push all GEPs through ALUs (fix arange stuff)
  (UPat(UOps.GEP, src=(UPat((UOps.ALU, UOps.CAST, UOps.BITCAST), name='alu'),), name='gep'),
   lambda gep,alu: UOp(alu.op, alu.dtype.scalar().vec(gep.dtype.count), tuple(x.gep(gep.arg) for x in alu.src), alu.arg)),
  # push some GEPs through WMMAs
  (UPat(UOps.GEP, src=(UPat(UOps.WMMA, name="wmma"),), name="gep"), gep_through_wmma),
  # tensor core with a 0 input is acc
  (UPat(UOps.WMMA, src=(UPat.const(None, 0.0), UPat.var(), UPat.var("acc"))), lambda acc: acc),
  (UPat(UOps.WMMA, src=(UPat.var(), UPat.const(None, 0.0), UPat.var("acc"))), lambda acc: acc),
  # tensor core cleanups
  (UPat.var("add") + UPat(UOps.WMMA, name="wmma"),
    lambda add, wmma: UOp(wmma.op, wmma.dtype, (wmma.src[0], wmma.src[1], wmma.src[2]+add), wmma.arg)),
  # threefry
  (UPat(UOps.ALU, dtype=dtypes.uint64, src=(UPat.var("x"), UPat.var("key")), arg=BinaryOps.THREEFRY), threefry2x32),
  # arange loop folding
  (UPat(UOps.REDUCE, src=(UPat.any(m2:=UPat.any(
    m1:=(UPat.var("idx") + UPat.cvar("mval") * UPat(UOps.RANGE, name="rng")),
    m1 + UPat.var("idx2"), m1 + UPat.var("idx2") + UPat.var("idx3"), UPat(UOps.VECTORIZE, name="vec", src=m1))
    .lt(UPat.cvar("compval")).where(UPat.cvar("multconst"), UPat.const(None, 0)), m2 + UPat.var("extra")),),
    arg=BinaryOps.ADD, name="reduce", allow_any_len=True), loop_collapse),
  # arange loop folding (new ge)
  (UPat(UOps.REDUCE, src=(UPat.any(m2:=UPat.any(
    m1:=(UPat.var("idx") + UPat.any(UPat.cvar("mval") * UPat(UOps.RANGE, name="rng"), UPat(UOps.RANGE, name="rng"))),
    m1 + UPat.var("idx2"), m1 + UPat.var("idx2") + UPat.var("idx3"), UPat(UOps.VECTORIZE, name="vec", src=m1))
    .lt(UPat.cvar("compval")).ne(UPat(UOps.CONST, name="ne", arg=True))
    .where(UPat.cvar("multconst"), UPat.const(None, 0)), m2 + UPat.var("extra")),),
    arg=BinaryOps.ADD, name="reduce", allow_any_len=True), loop_collapse),
  # indexing, with cast or where
  (UPat(UOps.REDUCE, src=(UPat.var("idx").eq(UPat(UOps.RANGE, name="rng")).cast()*
    UPat(UOps.LOAD, src=(UPat.var("buf"), UPat.any(UPat.var("add")+UPat.var("mul")*UPat(UOps.RANGE, name="rng"), UPat(UOps.RANGE, name="rng"))),
         name="ld"),), arg=BinaryOps.ADD, name="reduce", allow_any_len=True), index_collapse),
  (UPat(UOps.REDUCE, src=(UPat.var("idx").eq(UPat(UOps.RANGE, name="rng")).where(
    UPat(UOps.LOAD, src=(UPat.var("buf"), UPat.any(UPat.var("add")+UPat.var("mul")*UPat(UOps.RANGE, name="rng"), UPat(UOps.RANGE, name="rng"))),
         name="ld"), UPat.const(None, 0.0)),), arg=BinaryOps.ADD, name="reduce", allow_any_len=True), index_collapse),
  # GEP/CAST const rules
  (UPat(UOps.CAST, name="root", src=UPat.cvar("c")), lambda root, c: root.const_like(c.arg)),
  # ** self folding **
  # cast NOOP (NOTE: it's str to deal with PtrDType)
  (UPat(UOps.CAST, name="root"), lambda root: root.src[0] if str(root.dtype) == str(root.src[0].dtype) else None),
  (UPat(UOps.REDUCE, src=(UPat.var("x"),)), lambda x: x),  # a REDUCE without ranges is a NOOP
  # ** load/store folding **
  (UPat.store(UPat.var("buf"), UPat.var("idx"), UPat.load(UPat.var("buf"), UPat.var("idx"))), lambda buf,idx:UOp(UOps.NOOP)),
  # x!=0 -> (bool)x
  (UPat.var("x").ne(0), lambda x: x.cast(dtypes.bool.vec(x.dtype.count))),
  # TODO: can do the invert of this (flip alt/load) when we fix double ops
  (UPat.store(UPat.var("buf"), UPat.var("idx"), UPat.var("gate").where(UPat.var("alt"), UPat.load(UPat.var("buf"), UPat.var("idx")))),
   lambda buf, idx, gate, alt: UOp.store(buf, idx, alt, gate)),
  # fold gated LOAD/STORE
  (UPat.load(UPat(), UPat(), UPat(), UPat.const(dtypes.bool, True), name="ld"), lambda ld: ld.replace(src=ld.src[:2])),
  (UPat.load(UPat(), UPat(), UPat(), UPat.const(dtypes.bool, True), UPat.var("bar"), name="ld"), lambda ld,bar: ld.replace(src=ld.src[:2]+(bar,))),
  (UPat.load(UPat(), UPat(), UPat.var("var"), UPat.const(dtypes.bool, False)), lambda var: var),
  (UPat.load(UPat(), UPat(), UPat.var("var"), UPat.const(dtypes.bool, False), UPat()), lambda var: var),
  (UPat.store(UPat(), UPat(), UPat(), UPat.const(dtypes.bool, True), name="store"), lambda store: store.replace(src=store.src[:3])),
  (UPat.store(UPat(), UPat(), UPat(), UPat.const(dtypes.bool, False)), lambda: UOp(UOps.NOOP)),
  # remove NOOPs from SINK
  (UPat(UOps.SINK, name="root"),
    lambda root: UOp(UOps.SINK, root.dtype, a, root.arg) if len(a:=tuple(x for x in root.src if x.op is not UOps.NOOP)) != len(root.src) else None),
  # remove EXPANDs from SINK/BARRIER
  (UPat(UOps.BARRIER, src=(UPat((UOps.VECTORIZE, UOps.SINK), name='sink'),)), lambda sink: UOp(UOps.BARRIER, dtypes.void, sink.src)),
  (UPat(UOps.SINK, name="root"),
    lambda root: UOp(UOps.SINK, root.dtype, tuple(flatten(x.src if x.op in {UOps.SINK, UOps.EXPAND} else (x,) for x in root.src)), root.arg)
      if any(x.op in {UOps.SINK, UOps.EXPAND} for x in root.src) else None),
])

# *** uop expander ***

def _expand_arg_to_idx(args:Tuple[Tuple[int, int], ...], rpk:Dict[int, int]) -> int:
  idx, mul = 0, 1
  for axis,m in args[::-1]:
    idx += rpk[axis] * mul
    mul *= m
  return idx

def _choices_from_args(args:Tuple[Tuple[int, int], ...]) -> List[Dict[int, int]]:
  return [dict(x) for x in itertools.product(*[zip(itertools.repeat(axis), range(m)) for axis,m in args])]

@functools.lru_cache(None)
def _swizzle_args(cargs:Tuple[Tuple[int, int], ...], eargs:Tuple[Tuple[int, int], ...], exclude_args:Tuple[int, ...]) -> List[int]:
  return [_expand_arg_to_idx(eargs, {**rpk, **{x:0 for x in exclude_args}} if exclude_args else rpk) for rpk in _choices_from_args(cargs)]

def do_expand(root:UOp):
  expands = [x for x in root.src if x.op is UOps.EXPAND]
  if len(expands) == 0: return None
  # NOTE: we 0 out the reduce axis for WMMA. in theory they should all be the same, but is this always correct?
  exclude_args = tuple(dedup(root.arg[-1] + tuple(y[0] for y in flatten(root.arg[-2])))) if root.op is UOps.WMMA else ()
  if all_same(expands_args:=[x.arg for x in expands]) and len(exclude_args) == 0:
    # if there's only one expand arg, it's okay to use it (optimization)
    expand_args = expands[0].arg
  else:
    # otherwise, we sort them and GEP
    expand_args = tuple(x for x in sorted(dedup(flatten(expands_args))) if x[0] not in exclude_args)
  expand_sz = prod([x[1] for x in expand_args])
  new_srcs = []
  for i,src in enumerate(root.src):
    if src.op is UOps.EXPAND:
      if root.op is UOps.IF and i == 0:
        # IF means OR on first arg to IF
        new_srcs.append(functools.reduce(operator.__or__, [src.src[0].gep(i) for i in range(expand_sz)]))
      elif expand_args == src.arg:
        # just remove the expand
        new_srcs.append(src.src[0])
      else:
        lst = _swizzle_args(expand_args, src.arg, exclude_args)
        # if the base dtype is > 1, put those at the end
        if src.dtype.count > 1: lst = flatten([[i*src.dtype.count+j for j in range(src.dtype.count)] for i in lst])
        new_srcs.append(src.src[0].gep(tuple(lst)))
    else:
      # non-EXPAND input
      if (root.op in {UOps.LOAD, UOps.STORE} and i == 0) or (root.op is UOps.REDUCE and i != 0):
        # for the first arg of LOAD/STORE and the RANGE args of REDUCE, just pass them through ignoring EXPANDS
        new_srcs.append(src)
      elif src.dtype.count > 1:
        # put any input dtype > 1 grouped together
        new_srcs.append(UOp(UOps.VECTORIZE,
                            src.dtype.scalar().vec(expand_sz*src.dtype.count), tuple(src.gep(i) for i in range(src.dtype.count))*expand_sz))
      else:
        # repeat the arg
        new_srcs.append(src.broadcast(expand_sz))

  new_arg = root.arg
  if root.op is UOps.GEP:
    assert root.dtype.count == 1
    # is this right?
    new_arg = tuple(range(root.arg[0], new_srcs[0].dtype.count, new_srcs[0].dtype.count // expand_sz))
  nsrc = UOp(root.op, root.dtype.scalar().vec(root.dtype.count*expand_sz), tuple(new_srcs), new_arg)
  return UOp(UOps.EXPAND, root.dtype, (nsrc,), expand_args)

acc_number = 0
def do_reduce(root:UOp):
  global acc_number
  reduce_parented, reduce_unparented = partition(root.src[1:], lambda x: x in root.src[0].sparents)
  ret = root.src[0]
  if len(reduce_parented):
    acc = UOp(UOps.DEFINE_ACC, root.dtype,
              (root.const_like(identity_element(root.arg, root.dtype.scalar())),) + tuple(reduce_parented), (acc_number,))
    acc_number += 1
    ret = UOp(UOps.ASSIGN, root.dtype, (acc, acc.alu(root.arg, ret)))
  # for MAX, we can just ignore the unparented
  if root.arg is BinaryOps.ADD:
    for r in reduce_unparented:ret = ret * (r.src[1]-r.src[0]).cast(ret.dtype.scalar()).broadcast(ret.dtype.count)
  return ret

def do_contract(con:UOp):
  ex = con.src[0]
  # CONTRACT without EXPAND repeats the element VECTORIZED
  if ex.op is not UOps.EXPAND: return UOp(UOps.VECTORIZE, con.dtype, con.src*con.dtype.count)
  # CONTRACT may remove several axes from EXPAND
  assert con.dtype.count == prod([x[1] for x in con.arg]), "dtype is wrong"
  idxs = []
  for rpk in _choices_from_args(new_ex_args:=tuple(x for x in ex.arg if x not in con.arg)):
    idxs += [_expand_arg_to_idx(ex.arg, {**rpk, **lrpk}) for lrpk in _choices_from_args(con.arg)]
  return UOp(UOps.EXPAND, con.dtype, (ex.src[0].gep(tuple(idxs)),), new_ex_args)

def no_vectorized_alu(alu):
  if alu.dtype.count == 1: return None
  alus = tuple(UOp(alu.op, alu.dtype.scalar(), tuple(s.gep(i) for s in alu.src), alu.arg) for i in range(alu.dtype.count))
  return UOp(UOps.VECTORIZE, alu.dtype, alus)

def create_gate(root:UOp) -> Optional[UOp]:
  @functools.lru_cache(None)
  def _gate_srcs(u:UOp, gate:UOp) -> UOp:
    if u.op is UOps.BARRIER: return u
    if u.op is UOps.LOAD and u.src[-1].op is UOps.BARRIER:
      return UOp(u.op, u.dtype, u.src[:-1]+(UOp(UOps.IF, dtypes.void, (gate, u.src[-1])),), u.arg)
    return u if (replace_source:=tuple(_gate_srcs(x, gate) for x in u.src)) == u.src else UOp(u.op, u.dtype, replace_source, u.arg)
  return None if len(root.src) == 3 or (ret:=_gate_srcs(root, root.src[3])) is root else ret

expander = PatternMatcher([
  (UPat(UOps.VECTORIZE, src=UPat(UOps.CONST), name="vec"), lambda vec: UOp.const(vec.dtype, tuple(x.arg for x in vec.src))),
  (UPat(UOps.VECTORIZE, src=UPat(UOps.GEP, src=(UPat(name="x"),)), name="vec"), lambda vec,x: x.gep(tuple(y.arg[0] for y in vec.src))),
  # create gate MUST BE BEFORE expander
  (UPat(UOps.STORE, name="root"), create_gate),
  # double expand
  (UPat(UOps.EXPAND, name="outer", src=(UPat(UOps.EXPAND, name="inner"),)),
   lambda outer, inner: UOp(UOps.EXPAND, outer.dtype, (inner.src[0],), inner.arg+outer.arg)),
  # do expansion
  (UPat((UOps.ALU, UOps.CAST, UOps.BITCAST, UOps.GEP, UOps.WMMA, UOps.LOAD, UOps.STORE,
         UOps.VECTORIZE, UOps.REDUCE, UOps.IF), name="root", custom_early_reject=set([(UOps.EXPAND, None)])), do_expand),
  (UPat(UOps.CONTRACT, name="con"), do_contract),
  # remove EXPANDs from SINK
  (UPat(UOps.SINK, name="root"),
   lambda root: UOp(UOps.SINK, root.dtype, a, root.arg)
    if len(a:=tuple(flatten(x.src if x.op is UOps.EXPAND else (x,) for x in root.src))) != len(root.src) else None),
  # BARRIERs aren't actually expanded
  (UPat(UOps.BARRIER, src=(UPat(UOps.EXPAND, name="ex"),)),
   lambda ex: UOp(UOps.EXPAND, dtypes.void, (UOp(UOps.BARRIER, dtypes.void, ex.src),)*len(ex.src), ex.arg)),
  # empty EXPAND is NOOP
  (UPat(UOps.EXPAND, src=(UPat.var('x'),), arg=()), lambda x: x),
  # EXPAND GEP (needed for WMMA, generalize this) -> vectorized ALU
  (UPat(UOps.EXPAND, name="ex", src=tuple(UPat.var('x').gep(i)+UPat.var('y').gep(i) for i in range(256 if AMX else 8))),
    lambda ex,x,y: UOp(UOps.EXPAND, ex.dtype, tuple((x+y).gep(i) for i in range(256 if AMX else 8)), ex.arg)),
])

def no_vectorized_load_store(ls:UOp):
  idx = ls.src[1]
  if idx.dtype.count == 1: return None
  # ugh, the meaning of a dtype.count idx is overloaded
  if ls.op is UOps.LOAD and idx.dtype.count != ls.dtype.count: return None
  if ls.op is UOps.STORE and idx.dtype.count != ls.src[2].dtype.count: return None
  tv = [UOp(ls.op, ls.dtype.scalar(), (ls.src[0],) + tuple(j.gep(i) for j in ls.src[1:])) for i in range(idx.dtype.count)]
  return UOp(UOps.VECTORIZE, ls.dtype, tuple(tv))

def no_vectorized_acc(acc:UOp):
  if acc.dtype.count == 1: return None
  alus = tuple(UOp(acc.op, acc.dtype.scalar(),
    tuple(s.gep(i) if j == 0 else s for j,s in enumerate(acc.src)), acc.arg+(i,)) for i in range(acc.dtype.count))
  return UOp(UOps.VECTORIZE, acc.dtype, alus)

def delete_redundant_gates(root:UOp) -> Optional[UOp]:
  @functools.lru_cache(None)
  def find_gate(x:UOp) -> Optional[UOp]:
    if x.op is UOps.IF: return x
    return next((ret for s in x.src if (ret:=find_gate(s)) is not None), None)
  if len(root.src) == 3 or (gate:=find_gate(root)) is None or gate.src[0] is not root.src[3]: return None
  return UOp(UOps.STORE, root.dtype, root.src[:3], root.arg)

just_reduce = PatternMatcher([
  # do reduce
  (UPat(UOps.REDUCE, name="root"), do_reduce),
])

devectorize = PatternMatcher([
  # no ALU on vectorized dtypes
  (UPat((UOps.ALU, UOps.CAST, UOps.BITCAST, UOps.ASSIGN), name="alu"), no_vectorized_alu),
  (UPat(UOps.WMMA, name="wmma"), no_vectorized_wmma),
  (UPat(UOps.DEFINE_ACC, name="acc"), no_vectorized_acc),
  (UPat((UOps.LOAD, UOps.STORE), name="ls"), no_vectorized_load_store),
])

reducer = PatternMatcher([
  (UPat(UOps.CONST, name='c'),
   lambda c: UOp(UOps.VECTORIZE, c.dtype, (UOp.const(c.dtype.scalar(), c.arg),)*c.dtype.count) if c.dtype.count > 1 else None),
  (UPat(UOps.VCONST, name='c'), lambda c: UOp(UOps.VECTORIZE, c.dtype, tuple(UOp.const(c.dtype.scalar(), x) for x in c.arg))),
  (UPat(UOps.GEP, name='gep'), lambda gep: UOp(UOps.VECTORIZE, gep.dtype, tuple(gep.src[0].gep(x) for x in gep.arg)) if len(gep.arg) > 1 else None),
  # delete_redundant_gates (after expand, is this still needed?)
  (UPat(UOps.STORE, name="root"), delete_redundant_gates),
  # late fixup of unfoldable image loads
  (UPat(UOps.LOAD, src=(UPat.var("buf"), UPat()), allow_any_len=True, name="load"), fix_unfoldable_image_load),
  # simplify valid
  (UPat(UOps.ALU, name="valid", arg=BinaryOps.AND), simplify_valid),
  # image load valid idx simplification
  (UPat(UOps.LOAD, name="load"), simplify_image_load),
  # buffer load valid idx simplification
  (UPat(UOps.LOAD, name="load"), simplify_buffer_load),
])

def idx_load_store(x:UOp):
  idx = x.src[0].index(x.src[1])
  v = x.dtype.count if x.op is UOps.LOAD else x.src[2].dtype.count
  if v > 1 and not isinstance(x.src[0].dtype, ImageDType): idx = idx.cast(idx.dtype.base.vec(v).ptr(idx.dtype.local))
  return UOp(x.op, x.dtype, (idx,)+x.src[2:], x.arg)

indexing = PatternMatcher([
  # use indexing for LOAD/STORE
  (UPat((UOps.LOAD, UOps.STORE), src=(UPat((UOps.DEFINE_GLOBAL, UOps.DEFINE_LOCAL)),), allow_any_len=True, name="x"), idx_load_store),
])

# *** uop graph ***

linearize_cnt = 0
def full_graph_rewrite(sink:UOp, opts:Optional[Renderer]=None) -> UOp:
  global linearize_cnt, acc_number
  assert sink.op is UOps.SINK, f"sink isn't sink, it's {sink.op}"

  # do graph rewrite
  acc_number = 0
  sink = graph_rewrite(sink, sym)

  # expand
  linearize_cnt += 1
  if linearize_cnt != (de:=getenv("DEBUG_EXPAND", 0)) and de != -1:
    sink = graph_rewrite(sink, sym+expander)
    if getenv("DO_REDUCE", 1):
      sink = graph_rewrite(sink, sym+just_reduce)
      sink = graph_rewrite(sink, sym+(devectorize+float4_folding if opts is not None and opts.supports_float4 else devectorize))
      sink = graph_rewrite(sink, sym+reducer)
      sink = graph_rewrite(sink, sym+indexing+get_extra_patterns(tuple(opts.code_for_op.keys()) if opts is not None else (), TRANSCENDENTAL>=2))

  if opts is not None and opts.extra_matcher is not None: sink = graph_rewrite(sink, opts.extra_matcher)
  return sink