;; Chained `uextend` and `sextend`.
(rule (simplify (uextend ty (uextend _intermediate_ty x)))
      (uextend ty x))
(rule (simplify (sextend ty (sextend _intermediate_ty x)))
      (sextend ty x))

;; Once something has be `uextend`ed, further `sextend`ing is the same as `uextend`
(rule (simplify (sextend ty (uextend _intermediate_ty x)))
      (uextend ty x))

;; `icmp` is zero or one, so sign-extending is the same as zero-extending
(rule (simplify (sextend ty x@(icmp _ _ _ _)))
      (uextend ty x))

;; Masking out any of the top bits of the result of `uextend` is a no-op. (This
;; is like a cheap version of known-bits analysis.)
(rule (simplify (band wide x @ (uextend _ (value_type narrow)) (iconst_u _ mask)))
      ; Check that `narrow_mask` has a subset of the bits that `mask` does.
      (if-let $true (let ((narrow_mask u64 (ty_mask narrow))) (u64_eq narrow_mask (u64_and mask narrow_mask))))
      x)

;; Masking out the sign-extended bits of an `sextend` turns it into a `uextend`.
(rule (simplify (band wide (sextend _ x @ (value_type narrow)) (iconst_u _ mask)))
      (if-let $true (u64_eq mask (ty_mask narrow)))
      (uextend wide x))

;; 32-bit integers zero-extended to 64-bit integers are never negative
(rule (simplify
       (slt ty
             (uextend $I64 x @ (value_type $I32))
             (iconst_u _ 0)))
      (subsume (iconst_u ty 0)))
(rule (simplify
       (sge ty
             (uextend $I64 x @ (value_type $I32))
             (iconst_u _ 0)))
      (subsume (iconst_u ty 1)))

;; Sign-extending can't change whether a number is zero nor how it signed-compares to zero
(rule (simplify (eq _ (sextend _ x@(value_type ty)) (iconst_s _ 0)))
      (eq ty x (iconst_s ty 0)))
(rule (simplify (ne _ (sextend _ x@(value_type ty)) (iconst_s _ 0)))
      (ne ty x (iconst_s ty 0)))
(rule (simplify (icmp _ cc (sextend _ x@(value_type ty)) (iconst_s _ 0)))
      (if (signed_cond_code cc))
      (icmp ty cc x (iconst_s ty 0)))

;; A reduction-of-an-extend back to the same original type is the same as not
;; actually doing the extend in the first place.
(rule (simplify (ireduce ty (sextend _ x @ (value_type ty)))) (subsume x))
(rule (simplify (ireduce ty (uextend _ x @ (value_type ty)))) (subsume x))

;; A reduction-of-an-extend that's not just to the original type is either:
;; a reduction of the original if the final type is smaller, or
(rule (simplify (ireduce (ty_int ty_final) (sextend _ inner@(value_type ty_initial))))
      (if-let $true (u64_lt (ty_bits_u64 ty_final) (ty_bits_u64 ty_initial)))
      (ireduce ty_final inner))
(rule (simplify (ireduce (ty_int ty_final) (uextend _ inner@(value_type ty_initial))))
      (if-let $true (u64_lt (ty_bits_u64 ty_final) (ty_bits_u64 ty_initial)))
      (ireduce ty_final inner))
;; an extension of the original if the final type is larger.
(rule (simplify (ireduce (ty_int ty_final) (sextend _ inner@(value_type ty_initial))))
      (if-let $true (u64_lt (ty_bits_u64 ty_initial) (ty_bits_u64 ty_final)))
      (sextend ty_final inner))
(rule (simplify (ireduce (ty_int ty_final) (uextend _ inner@(value_type ty_initial))))
      (if-let $true (u64_lt (ty_bits_u64 ty_initial) (ty_bits_u64 ty_final)))
      (uextend ty_final inner))

;; `band`, `bor`, and `bxor` can't affect any bits that aren't set in the one of
;; the inputs, so they can be pushed down inside `uextend`s
(rule (simplify (band bigty (uextend _ x@(value_type smallty)) (uextend _ y@(value_type smallty))))
      (uextend bigty (band smallty x y)))
(rule (simplify (bor bigty (uextend _ x@(value_type smallty)) (uextend _ y@(value_type smallty))))
      (uextend bigty (bor smallty x y)))
(rule (simplify (bxor bigty (uextend _ x@(value_type smallty)) (uextend _ y@(value_type smallty))))
      (uextend bigty (bxor smallty x y)))

;; Matches values where `ireducing` them will not actually introduce another
;; instruction, since other rules will collapse them with the reduction.
(decl pure multi will_simplify_with_ireduce (Value) Value)
(rule (will_simplify_with_ireduce x@(uextend _ _)) x)
(rule (will_simplify_with_ireduce x@(sextend _ _)) x)
(rule (will_simplify_with_ireduce x@(iconst _ _)) x)
(rule (will_simplify_with_ireduce x@(unary_op _ _ a))
      (if-let _ (will_simplify_with_ireduce a))
      x)
(rule (will_simplify_with_ireduce x@(binary_op _ _ a b))
      (if-let _ (will_simplify_with_ireduce a))
      (if-let _ (will_simplify_with_ireduce b))
      x)

;; Matches values where the high bits of the input don't affect lower bits of
;; the output, and thus the inputs can be reduced before the operation rather
;; than doing the wide operation then reducing afterwards.
(decl pure multi reducible_modular_op (Value) Value)
(rule (reducible_modular_op x@(ineg _ _)) x)
(rule (reducible_modular_op x@(bnot _ _)) x)
(rule (reducible_modular_op x@(iadd _ _ _)) x)
(rule (reducible_modular_op x@(isub _ _ _)) x)
(rule (reducible_modular_op x@(imul _ _ _)) x)
(rule (reducible_modular_op x@(bor  _ _ _)) x)
(rule (reducible_modular_op x@(bxor _ _ _)) x)
(rule (reducible_modular_op x@(band _ _ _)) x)

;; Replace `(small)(x OP y)` with `(small)x OP (small)y` in cases where that's
;; legal and it reduces the total number of instructions since the reductions
;; to the arguments simplify further.
(rule (simplify (ireduce smallty val@(unary_op _ op x)))
      (if-let _ (reducible_modular_op val))
      (if-let _ (will_simplify_with_ireduce x))
      (unary_op smallty op (ireduce smallty x)))
(rule (simplify (ireduce smallty val@(binary_op _ op x y)))
      (if-let _ (reducible_modular_op val))
      (if-let _ (will_simplify_with_ireduce x))
      (if-let _ (will_simplify_with_ireduce y))
      (binary_op smallty op (ireduce smallty x) (ireduce smallty y)))