import random from z3 import Int, Solver, sat from tinygrad import dtypes, Device from tinygrad.ops import UOp, Ops, UPat, graph_rewrite, PatternMatcher from tinygrad.codegen.devectorizer import fast_idiv random.seed(42) z3_renderer = PatternMatcher([ (UPat((Ops.DEFINE_VAR, Ops.SPECIAL), name="x"), lambda x: UOp(Ops.NOOP, arg=x.arg[0])), # Because fast_idiv only works for non-negative integers we can emulate machine arithmetic with modulo operations. (UPat(Ops.SHR, src=UPat(Ops.NOOP), name="x"), lambda x: UOp(Ops.NOOP, arg=f"(({x.src[0].arg}/(2**{x.src[1].arg}))%{dtypes.max(x.dtype)+1})")), (UPat(Ops.MUL, src=UPat(Ops.NOOP), name="x"), lambda x: UOp(Ops.NOOP, arg=f"(({x.src[0].arg}*{x.src[1].arg})%{dtypes.max(x.dtype)+1})")), (UPat((Ops.CONST, Ops.VCONST), name="x"), lambda x: UOp(Ops.NOOP, arg=str(x.arg))), (UPat(Ops.CAST, src=UPat(Ops.NOOP), name="x"), lambda x: UOp(Ops.NOOP, arg=f"{x.src[0].arg}")), ]) def render(self) -> str: ret = graph_rewrite(self.simplify(), z3_renderer) return ret.arg if ret.op is Ops.NOOP else str(ret) if __name__ == "__main__": x = Int('x') for _ in range(10_000): dt = random.choice(dtypes.ints) u = UOp(Ops.DEFINE_VAR, dt, arg=('x', 0, random.randint(1, dtypes.max(dt))), src=()) d = random.randint(1, max(1, u.arg[2])) expr = fast_idiv(Device[Device.DEFAULT].renderer, u, d) if expr is None: continue solver = Solver() solver.add(x>=u.arg[1], x<=u.arg[2]) if solver.check(eval(render(expr)) != x/d) == sat: assert False, f"Failed: {render(expr)} != x//{d} at x={solver.model()[x]}\nx={u}\nd={d}"