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actually merge to fold_divmod_general [pr] (#13363)
* actually merge to fold_divmod_general [pr]
* one more merge
* Revert "one more merge"
This reverts commit aa79f6781c.
* avoid that case for speed
* faster and simpler
This commit is contained in:
George Hotz
@@ -2,77 +2,86 @@ from tinygrad.uop.ops import PatternMatcher, UPat, Ops, UOp
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from tinygrad.dtype import dtypes
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from tinygrad.helpers import cdiv, cmod, CORRECT_DIVMOD_FOLDING, unwrap
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def cancel_divmod(d: UOp, x: UOp, y: UOp) -> UOp|None:
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# simple cancel div/mod case when the range of the numerator lies within a single denominator interval
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def fold_divmod_general(d: UOp) -> UOp|None:
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x, y = d.src
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# cancel_divmod: simple cancel div/mod case when the range of the numerator lies within a single denominator interval
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x_min, x_max, y_min, y_max = x.vmin, x.vmax, y.vmin, y.vmax
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assert isinstance(x_min, int) and isinstance(x_max, int) and isinstance(y_min, int) and isinstance(y_max, int)
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if y_min==y_max==0: raise ZeroDivisionError(f"{'Division' if d.op is Ops.IDIV else 'Mod'} by zero trying to rewrite {x.alu(d.op, y)}")
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if y_min*y_max > 0 and (q:=cdiv(x_min,y_min)) == cdiv(x_min,y_max) == cdiv(x_max,y_min) == cdiv(x_max,y_max):
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return x - q*y if d.op is Ops.MOD else d.const_like(q)
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return None
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def fold_divmod_const(d: UOp, x: UOp, y: UOp) -> UOp|None:
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if ((c := y.arg) < 0): return None
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# split uops for the rest of the processing
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x_peeled, const = x.pop_const()
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uops = list(x_peeled.split_uop(Ops.ADD))
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uops_no_const = list(x_peeled.split_uop(Ops.ADD))
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# remove_nested_mod: remove nested mod in case the inner mod is a multiple of the outer mod, example: (a%4 + b)%2 -> (a+b)%2
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if d.op is Ops.MOD and x.vmin >= 0:
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new_xs, changed = [], False
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for u in uops:
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if u.op is Ops.MOD and u.src[1].divides(c) is not None:
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new_xs.append(u.src[0])
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changed = True
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else: new_xs.append(u)
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if changed: return (UOp.sum(*new_xs) + const) % y
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# ** Constant Denominator Rules **
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# these rules strictly require y to be a scalar constant > 0
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if y.op is Ops.CONST and (c := y.arg) > 0:
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# remove_nested_mod: remove nested mod in case the inner mod is a multiple of the outer mod, example: (a%4 + b)%2 -> (a+b)%2
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if d.op is Ops.MOD and x.vmin >= 0:
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new_xs, changed = [], False
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for u in uops_no_const:
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if u.op is Ops.MOD and u.src[1].divides(c) is not None:
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new_xs.append(u.src[0])
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changed = True
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else: new_xs.append(u)
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if changed: return (UOp.sum(*new_xs) + const) % y
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# Shared decomposition for folding rules
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decomp = [(u.divides(f:=u.const_factor()),f) for u in uops]
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terms, factors = zip(*decomp)
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# Shared decomposition for folding rules
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decomp = [(u.divides(f:=u.const_factor()),f) for u in uops_no_const]
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terms, factors = zip(*decomp)
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# fold_binary_numerator: fold if expression has one non-constant term that takes on two values
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if len(terms)==1 and (v:=terms[0]).vmax-v.vmin == 1:
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y1 = cmod(factors[0]*v.vmin+const, c) if d.op is Ops.MOD else cdiv(factors[0]*v.vmin+const, c)
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y2 = cmod(factors[0]*v.vmax+const, c) if d.op is Ops.MOD else cdiv(factors[0]*v.vmax+const, c)
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return (y2-y1)*(v-v.vmin) + y1
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# fold_binary_numerator: fold if expression has one non-constant term that takes on two values
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if len(terms)==1 and (v:=terms[0]).vmax-v.vmin == 1:
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y1 = cmod(factors[0]*v.vmin+const, c) if d.op is Ops.MOD else cdiv(factors[0]*v.vmin+const, c)
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y2 = cmod(factors[0]*v.vmax+const, c) if d.op is Ops.MOD else cdiv(factors[0]*v.vmax+const, c)
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return (y2-y1)*(v-v.vmin) + y1
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# fold_divmod_congruence: fold if a is congruent to an expression whose range is between 0 and c
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if not (x.vmin<0 and CORRECT_DIVMOD_FOLDING):
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rems = [min((r:=f%c), r-c, key=abs) for f in factors]
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if (rem:=sum(r*v for r,v in zip(rems,terms))+const%c).vmin//c==rem.vmax//c:
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if d.op is Ops.MOD: return rem - rem.vmin//c*c
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return sum((f-r)//c * v for f,r,v in zip(factors,rems,terms)) + (const-const%c+rem.vmin//c*c)//c
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# fold_divmod_congruence: fold if a is congruent to an expression whose range is between 0 and c
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if not (x.vmin<0 and CORRECT_DIVMOD_FOLDING):
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rems = [min((r:=f%c), r-c, key=abs) for f in factors]
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if (rem:=sum(r*v for r,v in zip(rems,terms))+const%c).vmin//c==rem.vmax//c:
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if d.op is Ops.MOD: return rem - rem.vmin//c*c
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return sum((f-r)//c * v for f,r,v in zip(factors,rems,terms)) + (const-const%c+rem.vmin//c*c)//c
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# gcd_with_remainder: factor out common gcd from numerator
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if x.vmin >= 0:
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gcd = UOp.gcd(*uops, y).simplify()
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if gcd.op is Ops.CONST and gcd.arg > 1:
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new_x = unwrap(x_peeled.divide_exact(gcd)).simplify() + (const%c)//gcd.arg
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if new_x.vmin >= 0:
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ret = new_x.alu(d.op, x.ufix(c//gcd.arg))
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return ret*gcd + const%gcd.arg if d.op is Ops.MOD else ret+const//c
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return None
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# gcd_with_remainder: factor out common gcd from numerator
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# Note: this rule uses uops_no_const to exclude the additive constant from the GCD calculation
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if x.vmin >= 0:
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gcd = UOp.gcd(*uops_no_const, y).simplify()
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if gcd.op is Ops.CONST and gcd.arg > 1:
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new_x = unwrap(x_peeled.divide_exact(gcd)).simplify() + (const%c)//gcd.arg
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if new_x.vmin >= 0:
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ret = new_x.alu(d.op, x.ufix(c//gcd.arg))
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return ret*gcd + const%gcd.arg if d.op is Ops.MOD else ret+const//c
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def fold_divmod_variable(d: UOp, x: UOp, y: UOp) -> UOp|None:
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uops = list(x.split_uop(Ops.ADD))
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# nest_div_by_smallest_factor: try and nest the div and see if it allows the numerator to be simplified
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if d.op is Ops.IDIV and x.vmin >= 0:
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div = min([c] + [abs(f) for u, f in zip(uops_no_const, factors) if u.op not in (Ops.CONST, Ops.VCONST) and abs(f) > 1 and (c%f)==0])
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# NOTE: this is recursive!
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if div < c and (newxs := fold_divmod_general(x//div)) is not None and newxs.vmin >= 0:
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return newxs // (c // div)
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# 1. divide_by_gcd: x//y -> (x//gcd)//(y//gcd) or x%y -> gcd*(x//gcd)%(y//gcd)
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gcd = UOp.gcd(*uops, y).simplify()
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# ** Variable Denominator / Fallback Rules **
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# These rules apply to variables OR constants that failed the checks above.
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# Reconstruct all uops including const for these checks.
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all_uops = uops_no_const + ([x.const_like(const)] if const != 0 else [])
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# divide_by_gcd: x//y -> (x//gcd)//(y//gcd)
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gcd = UOp.gcd(*all_uops, y).simplify()
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if not (gcd.op is Ops.CONST and gcd.arg==1):
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ret = unwrap(x.divide_exact(gcd)).alu(d.op, unwrap(y.divide_exact(gcd)))
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return ret*gcd if d.op is Ops.MOD else ret
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# 2. factor_remainder: (d*x+y)//d -> x+y//d or (d*x+y)%d
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# for mod we go further and take the remainder of all factors to reduce their size
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# These only work for floordiv (and the corresponding remainder)! Thats why we check the sign of x,y and new_x
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# factor_remainder: (d*x+y)//d -> x+y//d
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if y.vmin<0 or x.vmin<0: return None
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quo, rem = [], []
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for u in uops:
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for u in all_uops:
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if (q:=u.divide_exact(y)) is not None: quo.append(q)
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# if this is mod and y is a const, we can make the remainder factor sm
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elif d.op is Ops.MOD and y.op is Ops.CONST and (c:=u.const_factor())%y.arg!=c:
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rem.append(u.divides(c)*(c%y.arg))
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quo.append(u.const_like(0)) # we append this so we can check if something changed
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quo.append(u.const_like(0))
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else: rem.append(u)
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if not quo: return None
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@@ -80,16 +89,6 @@ def fold_divmod_variable(d: UOp, x: UOp, y: UOp) -> UOp|None:
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if new_x.vmin<0: return None
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return new_x%y if d.op is Ops.MOD else new_x//y+sum(quo)
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def nest_div_by_smallest_factor(d: UOp, x: UOp, y: UOp) -> UOp|None:
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# we try and nest the div and see if it allows the numerator to be simplified
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if ((c := y.arg) < 0): return None
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factors = [u.const_factor() for u in x.split_uop(Ops.ADD) if u.op not in (Ops.CONST, Ops.VCONST)]
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div = min([y.arg]+[abs(f) for f in factors if abs(f) > 1 and (c%f)==0])
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newxs = fold_divmod_const(newx:=(x//div), x, y.const_like(div))
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if newxs is None: newxs = fold_divmod_variable(newx, x, y.const_like(div))
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if div==y.arg or newxs is None or x.vmin<0 or newx.vmin<0: return None
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return newxs//(c//div)
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div_and_mod_symbolic = PatternMatcher([
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# ** 1. Fast Inline Rules **
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((UPat.var("x")//UPat.cvar("c") + UPat.cvar("a"))//UPat.cvar("d"), lambda x,c,a,d: (x+a*c)//(c*d)
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@@ -102,11 +101,7 @@ div_and_mod_symbolic = PatternMatcher([
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lambda x,c,n,d: (-(-(c.arg%d.arg + x - (d.arg-1))//d) + c.arg//d.arg) if x.vmax<=0 and n.vmin>=0 and d.arg>0 else None),
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# ** 2. Slow Rules **
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# NOTE: if you move this one below `fold_divmod_const` you get more uops in test/external/external_benchmark_schedule.py
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(UPat((Ops.IDIV, Ops.MOD), dtypes.index, name="d", src=(UPat.var("x"), UPat.var("y"))), cancel_divmod),
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(UPat((Ops.IDIV, Ops.MOD), dtypes.index, name="d", src=(UPat.var("x"), UPat.cvar("y", vec=False))), fold_divmod_const),
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(UPat((Ops.IDIV, Ops.MOD), dtypes.index, name="d", src=(UPat.var("x"), UPat.var("y"))), fold_divmod_variable),
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(UPat(Ops.IDIV, dtypes.index, name="d", src=(UPat.var("x"), UPat.cvar("y", vec=False))), nest_div_by_smallest_factor),
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(UPat((Ops.IDIV, Ops.MOD), dtypes.index, name="d"), fold_divmod_general),
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# NOTE: these have to go at the bottom or TestSymbolicOps.test_var loops
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(UPat.var("x", dtypes.index) % UPat.var("d"), lambda x,d: -((-x)%d) if x.vmax <= 0 else None),
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