Remove rweight #337

JasonGross · 2018-03-27T20:32:47Z

No description provided.

andres-erbsen · 2018-03-27T21:29:34Z

File "./src/Experiments/SimplyTypedArithmetic.v", line 7450, characters 14-21:
Error: The reference rweight was not found in the current environment.

andres-erbsen

Approved as long assuming you get it to build in a boring way / by doing similar transformations as in the rest of the file.

andres-erbsen · 2018-03-27T21:31:57Z

src/Experiments/SimplyTypedArithmetic.v

+          (Hc : length c = len_c)
+          (Hidxs : length idxs = len_idxs).
+  Definition weight (i : nat)
+    := 2^(-(-(limbwidth_num * i) / limbwidth_den)).


is the double negation used here to make it round up? I don't know whether the trick here works, but I would believe you if you said it does. In C I often use (n + d - 1)/d for rounding up. Edit: hah, you proved it correct below. I approve of both the trick and the fact that the code was already set up in a way to make it the right thing to do to prove it.

I got the "trick" by unfolding Qceiling (Z.pos (Z.to_pos num) / Z.to_pos den) and then removing the matches

andres-erbsen · 2018-03-27T21:34:54Z

src/Experiments/SimplyTypedArithmetic.v

-      expand_lists ().
-      subst carrymod; reflexivity.
-    Qed.
+  Local Lemma weight_0 : weight 0 = 1.


Could you get this lemma and the next from lemmas about 2^Qceiling(limbwidth*i) ? Or are your proofs intentionally duplicative because they look simpler?

I was originally trying to be as permissive as possible. I'll strengthen the hypotheses to require 0 < limbwidth_den which is required for basing it on 2^Qceiling(limbwidth*i) to actually be a simplification.

andres-erbsen · 2018-03-27T21:37:08Z

src/Experiments/SimplyTypedArithmetic.v

@@ -6419,21 +6418,21 @@ Section rcarry_mul.
  Definition rcarry_mul
    := BoundsPipeline
         (carry_mul_gen
-            @ rw @ GallinaReify.Reify s @ GallinaReify.Reify c @ GallinaReify.Reify n @ GallinaReify.Reify (length c) @ GallinaReify.Reify idxs @ GallinaReify.Reify (length idxs))
+            @ GallinaReify.Reify (Qnum limbwidth) @ GallinaReify.Reify (Z.pos (Qden limbwidth)) @ GallinaReify.Reify s @ GallinaReify.Reify c @ GallinaReify.Reify n @ GallinaReify.Reify (length c) @ GallinaReify.Reify idxs @ GallinaReify.Reify (length idxs))


It might be easier to take in (Z*Z) instead of Q for the limbwidth. either is fine by me.

Huh? limbwidth is computed in this section. I could also let-bind the numerator and denominator....

andres-erbsen · 2018-03-27T21:38:16Z

src/Experiments/SimplyTypedArithmetic.v

@@ -6591,6 +6584,7 @@ Section rcarry_mul.
                     | intros; apply eval_oppmod
                     | intros; apply eval_encodemod
                     | eassumption
+                     | apply conj


I remember having issues with non-conditional (e?)apply conj looping. if you think it's fine here then it's most likely fine

If it starts looping, I'll get rid of it. But this is really a very simple proof that goes by eauto modulo beta-iota-delta.

JasonGross · 2018-03-28T00:34:38Z

Updated to build to the end by plugging in a concrete weight function and proving a few extra lemmas.

JasonGross · 2018-03-28T00:36:07Z

@jadephilipoom Are you okay with the changes to montred that inline the weight function? I tried to do things in a way that minimally impacted your proof (so definitely feel free to later rewrite it more or whatever).

jadephilipoom · 2018-03-28T08:18:48Z

src/Experiments/SimplyTypedArithmetic.v

+    Let w_divides : forall i : nat, w (S i) / w i > 0
+      := weight_divides _ _ log2R_good.
+    Let w_1_gt1 : w 1 > 1 := weight_1_gt_1 _ _ log2R_good.
+    Let w_half_1_gt1 : w_half 1 > 1 := weight_1_gt_1 _ _ half_log2R_good.


Ugh, this is quite a lot of boilerplate. I was thinking of maybe making a record or something for saturated weight functions, and maybe this is another point for that strategy.

Probably if the lists are the same lengths, then we want to compare them element-wise rather than all at once. It's way too verbose to keep expanding them, so we only do that when lists are not the same length. We now get error messages such as ``` Unable to unify: [inr [378, 381, 384]] == [inr [101, 106, 108]] Could not unify the values at index 0: [mit-plv#378, mit-plv#381, mit-plv#384] != [mit-plv#101, mit-plv#106, mit-plv#108] index 0: mit-plv#378 != mit-plv#101 (slice 0 44, [mit-plv#377]) != (slice 0 44, [mit-plv#98]) index 0: mit-plv#377 != mit-plv#98 (add 64, [mit-plv#345, mit-plv#375]) != (add 64, [mit-plv#57, mit-plv#96]) index 0: mit-plv#345 != mit-plv#57 (slice 0 44, [mit-plv#337]) != (slice 0 44, [#44]) index 0: mit-plv#337 != #44 (add 64, [#41, mit-plv#334]) != (add 64, [#25, #41]) index 1: mit-plv#334 != #25 (mul 64, [#1, mit-plv#331]) != (mul 64, [#0, #1, #22]) [(add 64, [mit-plv#329, mit-plv#329])] != [#0, (const 20, [])] [(add 64, [(mul 64, [#7, mit-plv#328]), (mul 64, [#7, mit-plv#328])])] != [#0, (const 20, [])] [(add 64, [(mul 64, [(const 2, []), (add 64, [#0, mit-plv#327])]), (mul 64, [(const 2, []), (add 64, [#0, mit-plv#327])])])] != [#0, (const 20, [])] [(add 64, [(mul 64, [(const 2, []), (add 64, [#0, (mul 64, [#0, mit-plv#326])])]), (mul 64, [(const 2, []), (add 64, [#0, (mul 64, [#0, mit-plv#326])])])])] != [#0, (const 20, [])] [(add 64, [(mul 64, [(const 2, []), (add 64, [#0, (mul 64, [#0, (const 4, [])])])]), (mul 64, [(const 2, []), (add 64, [#0, (mul 64, [#0, (const 4, [])])])])])] != [#0, (const 20, [])] [(add 64, [(mul 64, [(const 2, []), (add 64, [(old 64 0, []), (mul 64, [(old 64 0, []), (const 4, [])])])]), (mul 64, [(const 2, []), (add 64, [(old 64 0, []), (mul 64, [(old 64 0, []), (const 4, [])])])])])] != [(old 64 0, []), (const 20, [])] ``` The second to last line is generally the one to look at; the last line adds a bit more detail to it. Perhaps we should instead list out the values of indices rather than expanding one additional level?

Probably if the lists are the same lengths, then we want to compare them element-wise rather than all at once. It's way too verbose to keep expanding them, so we only do that when lists are not the same length. We now get error messages such as ``` Unable to unify: [inr [378, 381, 384]] == [inr [101, 106, 108]] Could not unify the values at index 0: [#378, #381, #384] != [#101, #106, #108] index 0: #378 != #101 (slice 0 44, [#377]) != (slice 0 44, [#98]) index 0: #377 != #98 (add 64, [#345, #375]) != (add 64, [#57, #96]) index 0: #345 != #57 (slice 0 44, [#337]) != (slice 0 44, [#44]) index 0: #337 != #44 (add 64, [#41, #334]) != (add 64, [#25, #41]) index 1: #334 != #25 (mul 64, [#1, #331]) != (mul 64, [#0, #1, #22]) [(add 64, [#329, #329])] != [#0, (const 20, [])] [(add 64, [(mul 64, [#7, #328]), (mul 64, [#7, #328])])] != [#0, (const 20, [])] [(add 64, [(mul 64, [(const 2, []), (add 64, [#0, #327])]), (mul 64, [(const 2, []), (add 64, [#0, #327])])])] != [#0, (const 20, [])] [(add 64, [(mul 64, [(const 2, []), (add 64, [#0, (mul 64, [#0, #326])])]), (mul 64, [(const 2, []), (add 64, [#0, (mul 64, [#0, #326])])])])] != [#0, (const 20, [])] [(add 64, [(mul 64, [(const 2, []), (add 64, [#0, (mul 64, [#0, (const 4, [])])])]), (mul 64, [(const 2, []), (add 64, [#0, (mul 64, [#0, (const 4, [])])])])])] != [#0, (const 20, [])] [(add 64, [(mul 64, [(const 2, []), (add 64, [(old 64 0, []), (mul 64, [(old 64 0, []), (const 4, [])])])]), (mul 64, [(const 2, []), (add 64, [(old 64 0, []), (mul 64, [(old 64 0, []), (const 4, [])])])])])] != [(old 64 0, []), (const 20, [])] ``` The second to last line is generally the one to look at; the last line adds a bit more detail to it. Perhaps we should instead list out the values of indices rather than expanding one additional level?

JasonGross requested a review from andres-erbsen March 27, 2018 20:32

JasonGross added this to To Do in Pipeline without CPS via automation Mar 27, 2018

andres-erbsen approved these changes Mar 27, 2018

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JasonGross added 2 commits March 27, 2018 19:40

Move mod_ops out of Positional

40b951a

Inline weight into *mod, remove rweight

05000d2

JasonGross force-pushed the no-rweight branch from 4f53619 to 05000d2 Compare March 28, 2018 00:34

JasonGross requested a review from jadephilipoom March 28, 2018 00:36

jadephilipoom approved these changes Mar 28, 2018

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JasonGross merged commit f17f20e into mit-plv:master Mar 29, 2018

Pipeline without CPS automation moved this from To Do to Done Mar 29, 2018

JasonGross deleted the no-rweight branch March 29, 2018 00:06

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Remove rweight #337

Remove rweight #337

JasonGross commented Mar 27, 2018

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JasonGross commented Mar 28, 2018

JasonGross commented Mar 28, 2018

jadephilipoom Mar 28, 2018

Remove rweight #337

Remove rweight #337

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JasonGross commented Mar 28, 2018

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