[Codegen] TargetLowering::prepareUREMEqFold(): `x u% C1 ==/!= C2` (PR35479)
Summary: The current lowering is: ``` Name: (X % C1) == C2 -> X * C3 <= C4 || false Pre: (C2 == 0 || C1 u<= C2) && (C1 u>> countTrailingZeros(C1)) * C3 == 1 %zz = and i8 C3, 0 ; trick alive into making C3 avaliable in precondition %o0 = urem i8 %x, C1 %r = icmp eq i8 %o0, C2 => %zz = and i8 C3, 0 ; and silence it from complaining about said reg %C4 = -1 /u C1 %n0 = mul i8 %x, C3 %n1 = lshr i8 %n0, countTrailingZeros(C1) ; rotate right %n2 = shl i8 %n0, ((8-countTrailingZeros(C1)) %u 8) ; rotate right %n3 = or i8 %n1, %n2 ; rotate right %is_tautologically_false = icmp ule i8 C1, C2 %C4_fixed = select i1 %is_tautologically_false, i8 -1, i8 %C4 %res = icmp ule i8 %n3, %C4_fixed %r = xor i1 %res, %is_tautologically_false ``` https://rise4fun.com/Alive/2xC https://rise4fun.com/Alive/jpb5 However, we can support non-tautological cases `C1 u> C2` too. Said handling consists of two parts: * `C2 u<= (-1 %u C1)`. It just works. We only have to change `(X % C1) == C2` into `((X - C2) % C1) == 0` ``` Name: (X % C1) == C2 -> (X - C2) * C3 <= C4 iff C2 u<= (-1 %u C1) Pre: (C1 u>> countTrailingZeros(C1)) * C3 == 1 && C2 u<= (-1 %u C1) %zz = and i8 C3, 0 ; trick alive into making C3 avaliable in precondition %o0 = urem i8 %x, C1 %r = icmp eq i8 %o0, C2 => %zz = and i8 C3, 0 ; and silence it from complaining about said reg %C4 = (-1 /u C1) %n0 = sub i8 %x, C2 %n1 = mul i8 %n0, C3 %n2 = lshr i8 %n1, countTrailingZeros(C1) ; rotate right %n3 = shl i8 %n1, ((8-countTrailingZeros(C1)) %u 8) ; rotate right %n4 = or i8 %n2, %n3 ; rotate right %is_tautologically_false = icmp ule i8 C1, C2 %C4_fixed = select i1 %is_tautologically_false, i8 -1, i8 %C4 %res = icmp ule i8 %n4, %C4_fixed %r = xor i1 %res, %is_tautologically_false ``` https://rise4fun.com/Alive/m4P https://rise4fun.com/Alive/SKrx * `C2 u> (-1 %u C1)`. We also have to change `(X % C1) == C2` into `((X - C2) % C1) == 0`, and we have to decrement C4: ``` Name: (X % C1) == C2 -> (X - C2) * C3 <= C4 iff C2 u> (-1 %u C1) Pre: (C1 u>> countTrailingZeros(C1)) * C3 == 1 && C2 u> (-1 %u C1) %zz = and i8 C3, 0 ; trick alive into making C3 avaliable in precondition %o0 = urem i8 %x, C1 %r = icmp eq i8 %o0, C2 => %zz = and i8 C3, 0 ; and silence it from complaining about said reg %C4 = (-1 /u C1)-1 %n0 = sub i8 %x, C2 %n1 = mul i8 %n0, C3 %n2 = lshr i8 %n1, countTrailingZeros(C1) ; rotate right %n3 = shl i8 %n1, ((8-countTrailingZeros(C1)) %u 8) ; rotate right %n4 = or i8 %n2, %n3 ; rotate right %is_tautologically_false = icmp ule i8 C1, C2 %C4_fixed = select i1 %is_tautologically_false, i8 -1, i8 %C4 %res = icmp ule i8 %n4, %C4_fixed %r = xor i1 %res, %is_tautologically_false ``` https://rise4fun.com/Alive/d40 https://rise4fun.com/Alive/8cF I believe this concludes `x u% C1 ==/!= C2` lowering. In fact, clang is may now be better in this regard than gcc: as it can be seen from `@t32_6_4` test, we do lower `x % 6 == 4` via this pattern, while gcc does not: https://godbolt.org/z/XNU2z9 And all the general alive proofs say this is legal. And manual checking agrees: https://rise4fun.com/Alive/WA2 Fixes [[ https://bugs.llvm.org/show_bug.cgi?id=35479 | PR35479 ]]. Reviewers: RKSimon, craig.topper, spatel Reviewed By: RKSimon Subscribers: nick, hiraditya, llvm-commits Tags: #llvm Differential Revision: https://reviews.llvm.org/D70053
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