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Unobjectionable rewrite rules for saturated arithmetic #1777

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Unobjectionable rewrite rules for saturated arithmetic #1777

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32 changes: 32 additions & 0 deletions src/Rewriter/Rules.v
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Original file line number Diff line number Diff line change
Expand Up @@ -289,18 +289,35 @@ Definition arith_rewrite_rulesT (max_const_val : Z) : list (bool * Prop)
; (forall s y x,
Z.add_get_carry_full s (- y) x
= dlet vb := Z.sub_get_borrow_full s x y in (fst vb, - snd vb))
; (forall s y x k,
Z.add_get_carry_full s x (-y * k)
= dlet vb := Z.sub_get_borrow_full s x (y * k) in (fst vb, - snd vb))
; (forall s y x k,
Z.add_get_carry_full s (-y * k) x
= dlet vb := Z.sub_get_borrow_full s x (y * k) in (fst vb, - snd vb))
Comment on lines +292 to +297
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@jadephilipoom perhaps we should standardize on Z.add_get_carry_full and get rid of other variants?

Originally posted by @andres-erbsen in #1609 (comment)

; (forall s y x,
Z.add_with_get_carry_full s 0 x (- y)
= dlet vb := Z.sub_get_borrow_full s x y in (fst vb, - snd vb))
; (forall s y x,
Z.add_with_get_carry_full s 0 (- y) x
= dlet vb := Z.sub_get_borrow_full s x y in (fst vb, - snd vb))

; (forall s c x,
Z.add_with_get_carry_full s (- c) x 0
= dlet vb := Z.sub_with_get_borrow_full s c x 0 in (fst vb, - snd vb))

; (forall s c y x,
Z.add_with_get_carry_full s (- c) (- y) x
= dlet vb := Z.sub_with_get_borrow_full s c x y in (fst vb, - snd vb))
; (forall s c y x,
Z.add_with_get_carry_full s (- c) x (- y)
= dlet vb := Z.sub_with_get_borrow_full s c x y in (fst vb, - snd vb))
; (forall s c y x k,
Z.add_with_get_carry_full s c x (-y * k)
= dlet vb := Z.sub_with_get_borrow_full s (-c) x (y * k) in (fst vb, - snd vb))
; (forall s c y x k,
Z.add_with_get_carry_full s c (-y * k) x
= dlet vb := Z.sub_with_get_borrow_full s (-c) x (y * k) in (fst vb, - snd vb))
; (forall b x, (* inline negation when the rewriter wouldn't already inline it *)
ident.gets_inlined b x = false
-> -x = dlet v := x in -v)
Expand Down Expand Up @@ -396,6 +413,16 @@ Definition arith_with_casts_rewrite_rulesT (adc_no_carry_to_add : bool) : list (
y ∈ ry -> y = Z.ones (Z.succ (Z.log2 y))
-> cstZ rv (cstZ ry ('y) &' cstZ rx x) = cstZ rx x)
]%Z%zrange
; mymap
do_again
[ (forall x y, cstZ r[0~>1] x * y = Z.zselect (cstZ r[0~>1] x) (cstZ r[0~>0] (' 0)) y)
; (forall x y, y * cstZ r[0~>1] x = Z.zselect (cstZ r[0~>1] x) (cstZ r[0~>0] (' 0)) y)
; (forall c M rv r0 rM, 0 ∈ r0 -> M ∈ rM -> M ∈ rv -> 2^Z.log2 (M+1) = M + 1 -> 1 <= M ->
cstZ rv (Z.zselect (cstZ r[0~>1] c) (cstZ r0 ('0)) (cstZ rM ('M)))
= (dlet vc := cstZZ rv r[0~>1] (Z.sub_with_get_borrow_full ('(M+1)) (cstZ r[0~>1] c) 0 0) in
cstZ rv (fst vc)))
; (forall rv c x y, cstZ rv (Z.zselect c x y) = dlet v := cstZ rv (Z.zselect c x y) in cstZ rv v)
]
Comment on lines +416 to +425
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@andres-erbsen turn mul_split with negated intput into negated mul_split first

Originally posted by @andres-erbsen in #1609 (comment)

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@andres-erbsen Is this something that should be done before merging?

; mymap
do_again
[ (* [do_again], so that we can trigger add/sub rules on the output *)
Expand All @@ -416,6 +443,11 @@ Definition arith_with_casts_rewrite_rulesT (adc_no_carry_to_add : bool) : list (
adc_no_carry_to_add = true -> s ∈ rs -> (n rx - n ry - n rc <= r[0~>s-1])%zrange
-> cstZZ rv r[0~>0] (Z.sub_with_get_borrow_full (cstZ rs ('s)) (cstZ rc c) (cstZ rx x) (cstZ ry y))
= (cstZ rv (cstZ rx x - cstZ ry y - cstZ rc c), (cstZ r[0~>0] ('0))))
(* 0-0-c passes through the carry *)
; (forall rv rs s c rx ry,
s ∈ rs -> 0 ∈ rx -> 0 ∈ ry -> -1 / s = -1
-> cstZZ rv r[0~>1] (Z.sub_with_get_borrow_full (cstZ rs ('s)) (cstZ r[0~>1] c) (cstZ rx ('0)) (cstZ ry ('0)))
= (cstZ rv (-(cstZ r[0~>1]c) mod 's), (cstZ r[0~>1] c)))
]%Z%zrange
; mymap
dont_do_again
Expand Down
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