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firestar5683
112 lines
5.9 KiB
Python
112 lines
5.9 KiB
Python
import functools
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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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# NOTE: this cache is only on index UOps
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@functools.cache
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def fold_divmod_general(d: UOp, correct_divmod_folding: bool) -> 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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# split uops for the rest of the processing
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x_peeled, const = x.pop_const()
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uops_no_const = list(x_peeled.split_uop(Ops.ADD))
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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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u = u.src[0]
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changed = True
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new_xs.append(u)
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if changed and (new_x:=(UOp.sum(*new_xs) + const)).vmin >= 0: return new_x % 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_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_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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# 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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# 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, correct_divmod_folding)) is not None and newxs.vmin >= 0:
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return newxs // (c // div)
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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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# 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 all_uops:
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if (q:=u.divide_exact(y)) is not None: quo.append(q)
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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))
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else: rem.append(u)
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if not quo: return None
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new_x = sum(rem)+x.const_like(0)
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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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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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if c.vmin>0 and d.vmin>0 and ((x.vmin>=0 and a.vmin>=0) or (x.vmax<=0 and a.vmax<=0)) else None), # (x//c+a)//d -> (x+a*c)//(c*d)
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(UPat.var("x", dtypes.index) // UPat.var("d"), lambda x,d: -(x//(-d)) if d.vmax < 0 else None),
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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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((UPat.var("x", dtypes.index)+UPat.cvar("c", vec=False)).named("n")//UPat.cvar("d", vec=False),
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lambda x,c,n,d: ((x+c.arg%d.arg)//d + c.arg//d.arg) if c.arg%d.arg!=c.arg and x.vmin>=0 and n.vmin>=0 and d.arg>0 else None),
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((UPat.var("x", dtypes.index)+UPat.cvar("c", vec=False)).named("n")//UPat.cvar("d", vec=False),
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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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(UPat((Ops.IDIV, Ops.MOD), dtypes.index, name="d"), lambda d: fold_divmod_general(d, bool(CORRECT_DIVMOD_FOLDING))),
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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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(UPat.var("x", dtypes.index) % UPat.var("d"), lambda x,d: (x%(-d)) if d.vmax < 0 else None),
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]) |