feat: add faster rat semantics for testing, and show equivalence against slow semantics #35
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abdoo8080
reviewed
Jan 21, 2026
abdoo8080
reviewed
Jan 21, 2026
Comment on lines
+162
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+185
| /-- The upper approximant of 'v'. | ||
| Returns the smallest 'x : X' such that 'r ≤ v x'. -/ | ||
| def upper (e s : Nat) (r : ExtRat) : PackedFloat e s := | ||
| (lower e s r.neg).neg | ||
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| /-- Lower half, return 'true' iff we are strictly in the lower half. -/ | ||
| def lh (e s : Nat) (r : ExtRat) : Bool := | ||
| (r - (lower e s r).toExtRat) < (upper e s r).toExtRat - r | ||
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| /-- Tiebreak, return 'true' iff we are exactly in the middle of the lower and upper approximants. -/ | ||
| def tb (e s : Nat) (r : ExtRat) : Bool := | ||
| r - (lower e s r).toExtRat = (upper e s r).toExtRat - r | ||
| /-- Upper half, return 'true' iff we are strictly in the upper half. -/ | ||
| def uh (e s : Nat) (r : ExtRat) : Bool := | ||
| (r - (lower e s r).toExtRat) > (upper e s r).toExtRat - r | ||
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| /-- Check if 'X' is even. -/ | ||
| def ev (e s : Nat) (x : PackedFloat e s) : Bool := | ||
| match x.toExtRat with | ||
| | .Number n => | ||
| let den := n.den | ||
| let num := n.num | ||
| num = 0 ∨ (den = 1 ∧ num.natAbs % 2 = 0) | ||
| | _ => false |
Collaborator
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These differ from the definition in the paper...
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not sure what you mean --- the paper just says "let there exist an integer such that 2 * integer equals the rat", and this should be the computational version of this?
Contributor
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While the slow / reference implementation works, the fast one doesn't seem to. Debugging what's going on... |
abdoo8080
reviewed
Jan 21, 2026
Comment on lines
198
to
213
| if _hz : r = .Number 0 then rsz e s sign | ||
| else | ||
| if _hlh : lh e s r | ||
| then lower e s | ||
| else | ||
| if _htb : tb e s r | ||
| then | ||
| if _heven : ev e s (lower e s r) | ||
| then lower e s | ||
| else upper e s | ||
| else | ||
| -- not tie break, not lower, so we are in upper half. | ||
| -- have : uh r v := by | ||
| -- have := trichotomy_lh_tb_uh r v | ||
| -- grind | ||
| upper e s |
Collaborator
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Could you flatten the ites to mirror the paper? Don't worry about introducing redundancies in the conditions.
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The fast semantics should be closer to the 'round' implementation, which will help. inspired by @abdoo8080 , who suggested that we have this for fast execution.