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Qround.v: Add more rounding functions - #291
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| (** Properties about how [Qfloor] and [Qceiling] interact with [Qplus] *) | ||
| Lemma Qfloor_add_Z_r : forall (x:Q) (z:Z), Qfloor (x + inject_Z z) = (Qfloor x + z)%Z. |
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Note that this property (and the related properties below) are all defined at the bottom of the file so that their proofs can take advantage of Qfloor_comp and Qceiling_comp. If you'd prefer, I can rearrange these proofs, although I may need to inline some of the details of Q{floor,ceiling}_comp to accommodate this.
| now apply (Qplus_le_compat _ _ _ _ (Qle_refl x)). | ||
| Qed. | ||
| Lemma Qround_to_even_resp_le : forall x y, x <= y -> (Qround_to_even x <= Qround_to_even y)%Z. |
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The implementation of this proof is particularly verbose. If you have ideas on how to make this cleaner, I'd love to hear them!
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Would anyone be able to give this a review (@andres-erbsen, perhaps)? |
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This adds three additional rounding functions to
Qround.v(Qtruncate,Qround_away, andQround_to_even) to complement the existingQfloorandQceilingfunctions. It also proves some corresponding properties (e.g., that each function respects<=).Fixes#283.