Add a generalized version of Barrett Reduction #44
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In this version, we split up the integer division so that we are less likely to overflow in intermediate computations. This is still not the version in HAC 14.42; that version also does early reduction modulo b^(k+1). This is work towards #43
| then r | ||
| else if r <? 2 * n | ||
| then r - n | ||
| else r - 2 * n. |
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The following seems slightly more natural to me (and it would match implementations that use conditional subtraction):
let r := if r<?n then r else r-n in
let r := if r<?n then r else r-n in
r
(the current form is fine as well)
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Changed (I added a few spaces, though)
andres-erbsen
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LGTM (ready to be merged by author)
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LGTM as is, see suggestions. |
As per @andres-erbsen's suggestion
As per Andres's suggestions.
JasonGross
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Builds locally in 8.4pl1 and 8.6, so I'm going to merge it. |
JasonGross
referenced
this pull request
in JasonGross/fiat-crypto
Feb 21, 2022
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, [#57, mit-plv#96]) index 0: mit-plv#345 != #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?
JasonGross
referenced
this pull request
in JasonGross/fiat-crypto
Feb 21, 2022
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, [#57, mit-plv#96]) index 0: mit-plv#345 != #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?
JasonGross
added a commit
that referenced
this pull request
Feb 22, 2022
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?
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In this version, we split up the integer division so that we are less
likely to overflow in intermediate computations.
This is still not the version in HAC 14.42; that version also does early
reduction modulo b^(k+1).
This is work towards #43