From 9aacd8ff7998b4ae3732ccfa8b3c73a7ab47fe63 Mon Sep 17 00:00:00 2001 From: "copybara-service[bot]" Date: Fri, 17 Jan 2025 18:43:05 +0000 Subject: [PATCH] deploy: ae28ea77c278dc12cc2289ac826aa8334b1a40c7 --- .../06/30/heir-meeting-2023-06-30/index.html | 7 +- .../07/18/heir-meeting-2023-07-18/index.html | 7 +- .../08/02/heir-meeting-2023-08-01/index.html | 7 +- .../08/16/heir-meeting-2023-08-15/index.html | 7 +- .../09/05/heir-meeting-2023-08-29/index.html | 7 +- .../09/13/heir-meeting-2023-09-12/index.html | 7 +- .../09/27/heir-meeting-2023-09-26/index.html | 7 +- .../10/25/heir-meeting-2023-10-24/index.html | 7 +- .../11/07/heir-meeting-2023-11-07/index.html | 7 +- .../11/28/heir-meeting-2023-11-28/index.html | 7 +- .../12/12/heir-meeting-2023-12-12/index.html | 7 +- .../01/11/heir-meeting-2024-01-11/index.html | 7 +- .../01/25/heir-meeting-2024-01-25/index.html | 7 +- .../02/08/heir-meeting-2024-02-08/index.html | 7 +- .../03/07/heir-meeting-2024-03-07/index.html | 7 +- .../04/04/heir-meeting-2024-04-04/index.html | 7 +- .../04/18/heir-meeting-2024-04-18/index.html | 7 +- .../05/02/heir-meeting-2024-05-02/index.html | 7 +- .../05/16/heir-meeting-2024-05-16/index.html | 7 +- .../05/30/heir-meeting-2024-05-30/index.html | 7 +- .../06/13/heir-meeting-2024-06-13/index.html | 7 +- .../06/27/heir-meeting-2024-06-27/index.html | 7 +- .../07/11/heir-meeting-2024-07-11/index.html | 7 +- .../index.html | 7 +- .../07/25/heir-meeting-2024-07-25/index.html | 7 +- .../08/08/heir-meeting-2024-08-08/index.html | 7 +- .../08/22/heir-meeting-2024-08-22/index.html | 7 +- .../09/05/heir-meeting-2024-09-05/index.html | 7 +- .../09/19/heir-meeting-2024-09-19/index.html | 7 +- .../10/04/heir-meeting-2024-10-04/index.html | 7 +- .../11/26/heir-meeting-2024-11-26/index.html | 7 +- blog/_print/index.html | 97 +- blog/index.html | 5 +- blog/index.xml | 183 +- blog/page/1/index.html | 1 - blog/page/2/index.html | 11 - blog/page/3/index.html | 13 - blog/page/4/index.html | 15 - docs/_print/index.html | 6 +- docs/dialects/_print/index.html | 6 +- docs/dialects/index.xml | 6 +- docs/dialects/lattigo/index.html | 8 +- docs/index.xml | 4657 +---------------- index.xml | 183 +- 44 files changed, 329 insertions(+), 5079 deletions(-) delete mode 100644 blog/page/1/index.html delete mode 100644 blog/page/2/index.html delete mode 100644 blog/page/3/index.html delete mode 100644 blog/page/4/index.html diff --git a/blog/2023/06/30/heir-meeting-2023-06-30/index.html b/blog/2023/06/30/heir-meeting-2023-06-30/index.html index 700fa709d..020413f7e 100644 --- a/blog/2023/06/30/heir-meeting-2023-06-30/index.html +++ b/blog/2023/06/30/heir-meeting-2023-06-30/index.html @@ -4,17 +4,16 @@ "> -

HEIR meeting 2023-06-30

Notes and recording from the second HEIR meeting.

The second HEIR meeting was 2023-05-30 (notes, and video recording).

There are some initial design discussion threads started on GitHub Discussions to get the -design rolling.

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HEIR meeting 2023-07-18

Notes from the 2023-07-18 HEIR meeting.

The third HEIR meeting was 2023-07-18 (notes).

We decided to schedule future meetings every two weeks, with alternating focus on MLIR and Hardware. See the meeting calendar to join. -(direct link to the calendar)

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HEIR meeting 2023-08-01

Notes from the 2023-08-01 HEIR meeting.

The fourth HEIR meeting was 2023-08-01 (notes and video recording).

We’re also starting on the Poly and Secret dialects in #74 (poly) and #78 (secret), so please join in the -fun!

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HEIR meeting 2023-08-15

Notes from the 2023-08-15 HEIR meeting.

Here are the notes and video recording -from the HEIR meeting on 2023-08-15.

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HEIR meeting 2023-08-29

Notes from the 2023-08-29 HEIR meeting.

Here are the notes from the HEIR meeting on 2023-08-29. There was an issue with the recording, so -there is no video recording this week.

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HEIR meeting 2023-09-12

Notes from the 2023-09-12 HEIR meeting.

Here are the notes and video recording -from the HEIR meeting on 2023-09-12.

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HEIR meeting 2023-09-26

Notes from the 2023-09-26 HEIR meeting.

Here are the notes and video recording from the HEIR meeting on 2023-09-26.

Next meeting (Oct 10) is canceled for the MLIR workshop, and I’ll post an update from that workshop on this blog, hopefully also with a video of the talk that -Alex Viand and I will be giving at the LLVM developers meeting.

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HEIR meeting 2023-10-24

Notes from the 2023-10-24 HEIR meeting.

Here are the notes and video recording from the HEIR meeting on 2023-10-24.

Also of note: our talk at FHE.org was last Thursday (recording), and the similar talk at the LLVM developers meeting talk was the previous Wednesday, though the video -has not yet been posted for that.

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HEIR meeting 2023-11-07

Notes from the 2023-11-07 HEIR meeting.

Here are the notes and video recording -from the HEIR meeting on 2023-11-07.

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HEIR meeting 2023-11-28

Notes from the 2023-11-28 HEIR meeting.

Here are the notes and video recording -from the HEIR meeting on 2023-11-28.

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HEIR meeting 2023-12-12

Notes from the 2023-12-12 HEIR meeting.

Here are the notes and video recording from the HEIR meeting on 2023-12-12.

This is the last meeting for 2023. Please respond to this poll for 2024 scheduling -preferences.

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HEIR meeting 2024-01-11

Notes from the 2024-01-11 HEIR meeting.

Here are the notes and video recording -from the HEIR meeting on 2024-01-11.

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HEIR meeting 2024-01-25

Notes from the 2024-01-25 HEIR meeting.

Here are the notes and video recording -from the HEIR meeting on 2024-01-25.

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HEIR meeting 2024-02-08

Notes from the 2024-02-08 HEIR meeting.

Here are the notes and video recording -from the HEIR meeting on 2024-02-08.

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HEIR meeting 2024-03-07

Notes from the 2024-03-07 HEIR meeting.

Here are the notes and video recording from the HEIR meeting on 2024-03-07.

Note: there will be no HEIR meeting on 2024-03-21 due to the FHE.org, HACS, and -RWC conferences. Hope to see you all there!

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HEIR meeting 2024-04-04

Notes from the 2024-04-04 HEIR meeting.

Here are the notes and video recording -from the HEIR meeting on 2024-04-04.

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HEIR meeting 2024-04-18

Notes from the 2024-04-18 HEIR meeting.

Here are the notes and video recording -from the HEIR meeting on 2024-04-18.

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HEIR meeting 2024-05-02

Notes from the 2024-05-02 HEIR meeting.

Here are the notes and video recording -from the HEIR meeting on 2024-05-02.

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HEIR meeting 2024-05-16

Notes from the 2024-05-16 HEIR meeting.

Here are the notes and video recording -from the HEIR meeting on 2024-05-16.

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HEIR meeting 2024-05-30

Notes from the 2024-05-30 HEIR meeting.

Here are the notes and video recording -from the HEIR meeting on 2024-05-30.

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HEIR meeting 2024-06-13

Notes from the 2024-06-13 HEIR meeting.

Here are the notes and video recording -from the HEIR meeting on 2024-06-13.

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HEIR meeting 2024-06-27

Notes from the 2024-06-27 HEIR meeting.

Here are the notes and video recording -from the HEIR meeting on 2024-06-27.

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HEIR meeting 2024-07-11

Notes from the 2024-07-11 HEIR meeting.

Here are the notes and video recording -from the HEIR meeting on 2024-07-11.

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HEIR meeting 2024-07-18 (mod_arith dialect)

Notes from the 2024-07-18 HEIR meeting.

Here are the notes and video recording from the HEIR meeting on 2024-07-18. This special discussion was focused on the -modular arithmetic dialect.

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HEIR meeting 2024-07-25

Notes from the 2024-07-25 HEIR meeting.

Here are the notes and video recording -from the HEIR meeting on 2024-07-25.

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HEIR meeting 2024-08-08

Notes from the 2024-08-08 HEIR meeting.

Here are the notes and video recording -from the HEIR meeting on 2024-08-08.

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HEIR meeting 2024-08-22

Notes from the 2024-08-22 HEIR meeting.

Here are the notes and video recording -from the HEIR meeting on 2024-08-22.

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HEIR meeting 2024-09-05

Notes from the 2024-09-05 HEIR meeting.

Here are the notes and video recording -from the HEIR meeting on 2024-09-05.

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HEIR meeting 2024-09-19

Notes from the 2024-09-19 HEIR meeting.

Here are the notes and video recording -from the HEIR meeting on 2024-09-19.

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HEIR meeting 2024-10-04

Notes from the 2024-10-04 HEIR meeting.

Here are the notes and video recording -from the HEIR meeting on 2024-10-04.

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HEIR meeting 2024-11-26

Notes from the 2024-11-26 HEIR meeting.

Here are the notes, video recording, and a transcription of the recording -from the HEIR meeting on 2024-11-26.

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This is the multi-page printable view of this section. -Click here to print.

Return to the regular view of this page.

Blog

HEIR as a Platform for Research (and new YouTube Channel)

Notes from the 2024-12-05 HEIR meeting.
By Jeremy Kun | +

This is the multi-page printable view of this section. +Click here to print.

Return to the regular view of this page.

Blog

HEIR as a Platform for Research (and new YouTube Channel)

Notes from the 2024-12-05 HEIR meeting.
By Jeremy Kun |

On 2024-12-05, the HEIR team presented a talk aimed at giving researchers a high-level overview of the HEIR project, brainstorming where new research might be needed, and discussing how the HEIR team could help with research projects.

The video recording of this talk is on YouTube, and this is the first video posted on the -new HEIR YouTube channel.

HEIR meeting 2024-11-26

Notes from the 2024-11-26 HEIR meeting.
By Jeremy Kun | -

Here are the +new HEIR YouTube channel.

2 - HEIR meeting 2024-11-26

Notes from the 2024-11-26 HEIR meeting.

Here are the notes, video recording, and @@ -16,84 +15,68 @@ notes and video recording -from the HEIR meeting on 2024-10-31.

HEIR meeting 2024-10-04

Notes from the 2024-10-04 HEIR meeting.
By Asra Ali | -

Here are the +from the HEIR meeting on 2024-10-31.

4 - HEIR meeting 2024-10-04

Notes from the 2024-10-04 HEIR meeting.

Here are the notes and video recording -from the HEIR meeting on 2024-10-04.

HEIR meeting 2024-09-19

Notes from the 2024-09-19 HEIR meeting.
By Asra Ali | -

Here are the +from the HEIR meeting on 2024-10-04.

5 - HEIR meeting 2024-09-19

Notes from the 2024-09-19 HEIR meeting.

Here are the notes and video recording -from the HEIR meeting on 2024-09-19.

HEIR meeting 2024-09-05

Notes from the 2024-09-05 HEIR meeting.
By Asra Ali | -

Here are the +from the HEIR meeting on 2024-09-19.

6 - HEIR meeting 2024-09-05

Notes from the 2024-09-05 HEIR meeting.

Here are the notes and video recording -from the HEIR meeting on 2024-09-05.

HEIR meeting 2024-08-22

Notes from the 2024-08-22 HEIR meeting.
By Asra Ali | -

Here are the +from the HEIR meeting on 2024-09-05.

7 - HEIR meeting 2024-08-22

Notes from the 2024-08-22 HEIR meeting.

Here are the notes and video recording -from the HEIR meeting on 2024-08-22.

HEIR meeting 2024-08-08

Notes from the 2024-08-08 HEIR meeting.
By Asra Ali | -

Here are the +from the HEIR meeting on 2024-08-22.

8 - HEIR meeting 2024-08-08

Notes from the 2024-08-08 HEIR meeting.

Here are the notes and video recording -from the HEIR meeting on 2024-08-08.

HEIR meeting 2024-07-25

Notes from the 2024-07-25 HEIR meeting.
By Asra Ali | -

Here are the +from the HEIR meeting on 2024-08-08.

9 - HEIR meeting 2024-07-25

Notes from the 2024-07-25 HEIR meeting.

Here are the notes and video recording -from the HEIR meeting on 2024-07-25.

HEIR meeting 2024-07-18 (mod_arith dialect)

Notes from the 2024-07-18 HEIR meeting.
By Asra Ali | -

Here are the +from the HEIR meeting on 2024-07-25.

10 - HEIR meeting 2024-07-18 (mod_arith dialect)

Notes from the 2024-07-18 HEIR meeting.

Here are the notes and video recording from the HEIR meeting on 2024-07-18. This special discussion was focused on the -modular arithmetic dialect.

HEIR meeting 2024-07-11

Notes from the 2024-07-11 HEIR meeting.
By Asra Ali | -

Here are the +modular arithmetic dialect.

11 - HEIR meeting 2024-07-11

Notes from the 2024-07-11 HEIR meeting.

Here are the notes and video recording -from the HEIR meeting on 2024-07-11.

HEIR meeting 2024-06-27

Notes from the 2024-06-27 HEIR meeting.
By Asra Ali | -

Here are the +from the HEIR meeting on 2024-07-11.

12 - HEIR meeting 2024-06-27

Notes from the 2024-06-27 HEIR meeting.

Here are the notes and video recording -from the HEIR meeting on 2024-06-27.

HEIR meeting 2024-06-13

Notes from the 2024-06-13 HEIR meeting.
By Asra Ali | -

Here are the +from the HEIR meeting on 2024-06-27.

13 - HEIR meeting 2024-06-13

Notes from the 2024-06-13 HEIR meeting.

Here are the notes and video recording -from the HEIR meeting on 2024-06-13.

HEIR meeting 2024-05-30

Notes from the 2024-05-30 HEIR meeting.
By Asra Ali | -

Here are the +from the HEIR meeting on 2024-06-13.

14 - HEIR meeting 2024-05-30

Notes from the 2024-05-30 HEIR meeting.

Here are the notes and video recording -from the HEIR meeting on 2024-05-30.

HEIR meeting 2024-05-16

Notes from the 2024-05-16 HEIR meeting.
By Jeremy Kun | -

Here are the +from the HEIR meeting on 2024-05-30.

15 - HEIR meeting 2024-05-16

Notes from the 2024-05-16 HEIR meeting.

Here are the notes and video recording -from the HEIR meeting on 2024-05-16.

HEIR meeting 2024-05-02

Notes from the 2024-05-02 HEIR meeting.
By Jeremy Kun | -

Here are the +from the HEIR meeting on 2024-05-16.

16 - HEIR meeting 2024-05-02

Notes from the 2024-05-02 HEIR meeting.

Here are the notes and video recording -from the HEIR meeting on 2024-05-02.

HEIR meeting 2024-04-18

Notes from the 2024-04-18 HEIR meeting.
By Jeremy Kun | -

Here are the +from the HEIR meeting on 2024-05-02.

17 - HEIR meeting 2024-04-18

Notes from the 2024-04-18 HEIR meeting.

Here are the notes and video recording -from the HEIR meeting on 2024-04-18.

HEIR meeting 2024-04-04

Notes from the 2024-04-04 HEIR meeting.
By Jeremy Kun | -

Here are the +from the HEIR meeting on 2024-04-18.

18 - HEIR meeting 2024-04-04

Notes from the 2024-04-04 HEIR meeting.

Here are the notes and video recording -from the HEIR meeting on 2024-04-04.

HEIR meeting 2024-03-07

Notes from the 2024-03-07 HEIR meeting.
By Jeremy Kun | -

Here are the +from the HEIR meeting on 2024-04-04.

19 - HEIR meeting 2024-03-07

Notes from the 2024-03-07 HEIR meeting.

Here are the notes and video recording @@ -103,81 +86,67 @@ notes and video recording -from the HEIR meeting on 2024-02-22.

HEIR meeting 2024-02-08

Notes from the 2024-02-08 HEIR meeting.
By Jeremy Kun | -

Here are the +from the HEIR meeting on 2024-02-22.

21 - HEIR meeting 2024-02-08

Notes from the 2024-02-08 HEIR meeting.

Here are the notes and video recording -from the HEIR meeting on 2024-02-08.

HEIR meeting 2024-01-25

Notes from the 2024-01-25 HEIR meeting.
By Jeremy Kun | -

Here are the +from the HEIR meeting on 2024-02-08.

22 - HEIR meeting 2024-01-25

Notes from the 2024-01-25 HEIR meeting.

Here are the notes and video recording -from the HEIR meeting on 2024-01-25.

HEIR meeting 2024-01-11

Notes from the 2024-01-11 HEIR meeting.
By Jeremy Kun | -

Here are the +from the HEIR meeting on 2024-01-25.

23 - HEIR meeting 2024-01-11

Notes from the 2024-01-11 HEIR meeting.

Here are the notes and video recording -from the HEIR meeting on 2024-01-11.

HEIR meeting 2023-12-12

Notes from the 2023-12-12 HEIR meeting.
By Jeremy Kun | -

Here are the +from the HEIR meeting on 2024-01-11.

24 - HEIR meeting 2023-12-12

Notes from the 2023-12-12 HEIR meeting.

Here are the notes and video recording from the HEIR meeting on 2023-12-12.

This is the last meeting for 2023. Please respond to this poll for 2024 scheduling -preferences.

HEIR meeting 2023-11-28

Notes from the 2023-11-28 HEIR meeting.
By Jeremy Kun | -

Here are the +preferences.

25 - HEIR meeting 2023-11-28

Notes from the 2023-11-28 HEIR meeting.

Here are the notes and video recording -from the HEIR meeting on 2023-11-28.

HEIR meeting 2023-11-07

Notes from the 2023-11-07 HEIR meeting.
By Jeremy Kun | -

Here are the +from the HEIR meeting on 2023-11-28.

26 - HEIR meeting 2023-11-07

Notes from the 2023-11-07 HEIR meeting.

Here are the notes and video recording -from the HEIR meeting on 2023-11-07.

HEIR meeting 2023-10-24

Notes from the 2023-10-24 HEIR meeting.
By Jeremy Kun | -

Here are the +from the HEIR meeting on 2023-11-07.

27 - HEIR meeting 2023-10-24

Notes from the 2023-10-24 HEIR meeting.

Here are the notes and video recording from the HEIR meeting on 2023-10-24.

Also of note: our talk at FHE.org was last Thursday (recording), and the similar talk at the LLVM developers meeting talk was the previous Wednesday, though the video -has not yet been posted for that.

HEIR meeting 2023-09-26

Notes from the 2023-09-26 HEIR meeting.
By Jeremy Kun | -

Here are the +has not yet been posted for that.

28 - HEIR meeting 2023-09-26

Notes from the 2023-09-26 HEIR meeting.

Here are the notes and video recording from the HEIR meeting on 2023-09-26.

Next meeting (Oct 10) is canceled for the MLIR workshop, and I’ll post an update from that workshop on this blog, hopefully also with a video of the talk that -Alex Viand and I will be giving at the LLVM developers meeting.

HEIR meeting 2023-09-12

Notes from the 2023-09-12 HEIR meeting.
By Jeremy Kun | -

Here are the +Alex Viand and I will be giving at the LLVM developers meeting.

29 - HEIR meeting 2023-09-12

Notes from the 2023-09-12 HEIR meeting.

Here are the notes and video recording -from the HEIR meeting on 2023-09-12.

HEIR meeting 2023-08-29

Notes from the 2023-08-29 HEIR meeting.
By Jeremy Kun | -

Here are the +from the HEIR meeting on 2023-09-12.

30 - HEIR meeting 2023-08-29

Notes from the 2023-08-29 HEIR meeting.

Here are the notes from the HEIR meeting on 2023-08-29. There was an issue with the recording, so -there is no video recording this week.

HEIR meeting 2023-08-15

Notes from the 2023-08-15 HEIR meeting.
By Jeremy Kun | -

Here are the +there is no video recording this week.

31 - HEIR meeting 2023-08-15

Notes from the 2023-08-15 HEIR meeting.

Here are the notes and video recording -from the HEIR meeting on 2023-08-15.

HEIR meeting 2023-08-01

Notes from the 2023-08-01 HEIR meeting.
By Jeremy Kun | -

The fourth HEIR meeting was 2023-08-01 +from the HEIR meeting on 2023-08-15.

32 - HEIR meeting 2023-08-01

Notes from the 2023-08-01 HEIR meeting.

The fourth HEIR meeting was 2023-08-01 (notes and video recording).

We’re also starting on the Poly and Secret dialects in #74 (poly) and #78 (secret), so please join in the -fun!

HEIR meeting 2023-07-18

Notes from the 2023-07-18 HEIR meeting.
By Jeremy Kun | -

The third HEIR meeting was 2023-07-18 +fun!

33 - HEIR meeting 2023-07-18

Notes from the 2023-07-18 HEIR meeting.

The third HEIR meeting was 2023-07-18 (notes).

We decided to schedule future meetings every two weeks, with alternating focus on MLIR and Hardware. See the meeting calendar to join. -(direct link to the calendar)

HEIR meeting 2023-06-30

Notes and recording from the second HEIR meeting.
By Jeremy Kun | -

The second HEIR meeting was 2023-05-30 +(direct link to the calendar)

34 - HEIR meeting 2023-06-30

Notes and recording from the second HEIR meeting.

The second HEIR meeting was 2023-05-30 (notes, and video recording).

There are some initial design discussion threads started on diff --git a/blog/index.html b/blog/index.html index 03cca4ebb..d2aa5b8af 100644 --- a/blog/index.html +++ b/blog/index.html @@ -1,11 +1,10 @@ Blog | HEIR -

Blog

HEIR as a Platform for Research (and new YouTube Channel)

Notes from the 2024-12-05 HEIR meeting.

HEIR meeting 2024-11-26

Notes from the 2024-11-26 HEIR meeting.

HEIR meeting 2024-10-31

Notes from the 2024-10-31 HEIR meeting.

HEIR meeting 2024-10-04

Notes from the 2024-10-04 HEIR meeting.

HEIR meeting 2024-09-19

Notes from the 2024-09-19 HEIR meeting.

HEIR meeting 2024-09-05

Notes from the 2024-09-05 HEIR meeting.

HEIR meeting 2024-08-22

Notes from the 2024-08-22 HEIR meeting.

HEIR meeting 2024-08-08

Notes from the 2024-08-08 HEIR meeting.

HEIR meeting 2024-07-25

Notes from the 2024-07-25 HEIR meeting.

HEIR meeting 2024-07-18 (mod_arith dialect)

Notes from the 2024-07-18 HEIR meeting.

HEIR meeting 2024-07-11

Notes from the 2024-07-11 HEIR meeting.

HEIR meeting 2024-06-27

Notes from the 2024-06-27 HEIR meeting.

HEIR meeting 2024-06-13

Notes from the 2024-06-13 HEIR meeting.

HEIR meeting 2024-05-30

Notes from the 2024-05-30 HEIR meeting.

HEIR meeting 2024-05-16

Notes from the 2024-05-16 HEIR meeting.

HEIR meeting 2024-05-02

Notes from the 2024-05-02 HEIR meeting.

HEIR meeting 2024-04-18

Notes from the 2024-04-18 HEIR meeting.

HEIR meeting 2024-04-04

Notes from the 2024-04-04 HEIR meeting.

HEIR meeting 2024-03-07

Notes from the 2024-03-07 HEIR meeting.

HEIR meeting 2024-02-22

Notes from the 2024-02-22 HEIR meeting.

HEIR meeting 2024-02-08

Notes from the 2024-02-08 HEIR meeting.

HEIR meeting 2024-01-25

Notes from the 2024-01-25 HEIR meeting.

HEIR meeting 2024-01-11

Notes from the 2024-01-11 HEIR meeting.

HEIR meeting 2023-12-12

Notes from the 2023-12-12 HEIR meeting.

HEIR meeting 2023-11-28

Notes from the 2023-11-28 HEIR meeting.

HEIR meeting 2023-11-07

Notes from the 2023-11-07 HEIR meeting.

HEIR meeting 2023-10-24

Notes from the 2023-10-24 HEIR meeting.

HEIR meeting 2023-09-26

Notes from the 2023-09-26 HEIR meeting.

HEIR meeting 2023-09-12

Notes from the 2023-09-12 HEIR meeting.

HEIR meeting 2023-08-29

Notes from the 2023-08-29 HEIR meeting.

HEIR meeting 2023-08-15

Notes from the 2023-08-15 HEIR meeting.

HEIR meeting 2023-08-01

Notes from the 2023-08-01 HEIR meeting.

HEIR meeting 2023-07-18

Notes from the 2023-07-18 HEIR meeting.

HEIR meeting 2023-06-30

Notes and recording from the second HEIR meeting.

Hello, World!

We’re starting a compiler toolchain for homomorphic encryption compilers.

Last modified August 25, 2024: add pre-commit hook for markdown formatter (290c3617)
\ No newline at end of file diff --git a/blog/index.xml b/blog/index.xml index d27fb007c..3fc4d0f3c 100644 --- a/blog/index.xml +++ b/blog/index.xml @@ -4,188 +4,9 @@ high-level overview of the HEIR project, brainstorming where new research might be needed, and discussing how the HEIR team could help with research projects.</p> <p>The <a href="https://youtu.be/t_XHw7LVy8s">video recording of this talk</a> is on YouTube, and this is the first video posted on the -<a href="https://www.youtube.com/@HEIRCompiler">new HEIR YouTube channel</a>.</p>Blog: HEIR meeting 2024-11-26https://heir.dev/blog/2024/11/26/heir-meeting-2024-11-26/Tue, 26 Nov 2024 00:00:00 +0000https://heir.dev/blog/2024/11/26/heir-meeting-2024-11-26/ -<p>Here are the -<a href="https://docs.google.com/document/d/10WTpdVaLz4mgmTwlJ3lVMGD4qmiNEl2Uvt3R3h0XFmc/edit?hl=en&amp;forcehl=1&amp;tab=t.0#heading=h.w3lar3vbuip1">notes</a>, -<a href="https://drive.google.com/file/d/13yvX_ap09tTqwJsdABDf3WDl79GF3bJx/view?usp=sharing">video recording</a>, -and -<a href="https://docs.google.com/document/d/1s5iXtOSpIDJX3JOEB5gQqUPm5lo1gLpRUM10pBfAdoo/edit?usp=sharing">a transcription of the recording</a> -from the HEIR meeting on 2024-11-26.</p>Blog: HEIR meeting 2024-10-04https://heir.dev/blog/2024/10/04/heir-meeting-2024-10-04/Fri, 04 Oct 2024 00:00:00 +0000https://heir.dev/blog/2024/10/04/heir-meeting-2024-10-04/ -<p>Here are the -<a href="https://docs.google.com/document/d/1tlC-g3JKOB9wxfQMEJnKQk0C0eBdtBCzZX8ck7J37fI/edit?usp=sharing">notes</a> -and -<a href="https://drive.google.com/file/d/1OFfrwWesFpxVHw2DFuNAxSB8seLG_tr1/view?usp=sharing">video recording</a> -from the HEIR meeting on 2024-10-04.</p>Blog: HEIR meeting 2024-09-19https://heir.dev/blog/2024/09/19/heir-meeting-2024-09-19/Thu, 19 Sep 2024 00:00:00 +0000https://heir.dev/blog/2024/09/19/heir-meeting-2024-09-19/ -<p>Here are the -<a href="https://docs.google.com/document/d/1aGIiZPWpk7UMg5FD8ZYHmNhKVZ6NdhfmGMvyHrrlolM/edit?usp=sharing">notes</a> -and -<a href="https://drive.google.com/file/d/1i-HqUi8pb2ywUJ-OT4fWExYCmeRLu2Cn/view?usp=sharing">video recording</a> -from the HEIR meeting on 2024-09-19.</p>Blog: HEIR meeting 2024-09-05https://heir.dev/blog/2024/09/05/heir-meeting-2024-09-05/Thu, 05 Sep 2024 00:00:00 +0000https://heir.dev/blog/2024/09/05/heir-meeting-2024-09-05/ -<p>Here are the -<a href="https://docs.google.com/document/d/1tohVmC2pn_XDn3gjCFeo3K4Wfyf7VWu3oK1vimEsFD4/edit?usp=sharing">notes</a> -and -<a href="https://drive.google.com/file/d/1XGheLF7kvJfwAMJJQ-XbDpa4Ld15kj4t/view?usp=sharing">video recording</a> -from the HEIR meeting on 2024-09-05.</p>Blog: HEIR meeting 2024-08-22https://heir.dev/blog/2024/08/22/heir-meeting-2024-08-22/Thu, 22 Aug 2024 00:00:00 +0000https://heir.dev/blog/2024/08/22/heir-meeting-2024-08-22/ -<p>Here are the -<a href="https://docs.google.com/document/d/1iEkzpO6lCVbShMcRenO3j3DptOEP-0bLu_9V4K7c39M/edit?usp=sharing">notes</a> -and -<a href="https://drive.google.com/file/d/1wFrGF7lMiYZmqbr5WQO17HomfoFoOeaj/view?usp=sharing">video recording</a> -from the HEIR meeting on 2024-08-22.</p>Blog: HEIR meeting 2024-08-08https://heir.dev/blog/2024/08/08/heir-meeting-2024-08-08/Thu, 08 Aug 2024 00:00:00 +0000https://heir.dev/blog/2024/08/08/heir-meeting-2024-08-08/ -<p>Here are the -<a href="https://docs.google.com/document/d/1FLSiaPlX38GNHqqqi_Mz3gMuVSlS4sUcwBWqpt6Fkew/edit?usp=sharing">notes</a> -and -<a href="https://drive.google.com/file/d/1sHoRvNlS14RB-r3Rk0y2RyWOERVGNc-t/view?usp=sharing">video recording</a> -from the HEIR meeting on 2024-08-08.</p>Blog: HEIR meeting 2024-07-25https://heir.dev/blog/2024/07/25/heir-meeting-2024-07-25/Thu, 25 Jul 2024 00:00:00 +0000https://heir.dev/blog/2024/07/25/heir-meeting-2024-07-25/ -<p>Here are the -<a href="https://docs.google.com/document/d/1tIrxc4V5OlAeqx_Z1rl_kuMmkd-HUAKEv90q3i-5QSU/edit?usp=sharing">notes</a> -and -<a href="https://drive.google.com/file/d/1_1CbRJeNr5NqcwEMXnfkxOqy9u5wJPyq/view?usp=sharing">video recording</a> -from the HEIR meeting on 2024-07-25.</p>Blog: HEIR meeting 2024-07-18 (mod_arith dialect)https://heir.dev/blog/2024/07/18/heir-meeting-2024-07-18-mod_arith-dialect/Thu, 18 Jul 2024 00:00:00 +0000https://heir.dev/blog/2024/07/18/heir-meeting-2024-07-18-mod_arith-dialect/ -<p>Here are the -<a href="https://docs.google.com/document/d/1o2-I03DJtNJQDupSHn8LtOXLmxsd3WO1fjvqLbT-SIc/edit?usp=sharing">notes</a> -and -<a href="https://drive.google.com/file/d/1bCMuuKnBVf6HP7R2SiZgo1C1vsG6FzF2/view?usp=sharing">video recording</a> -from the HEIR meeting on 2024-07-18. This special discussion was focused on the -modular arithmetic dialect.</p>Blog: HEIR meeting 2024-07-11https://heir.dev/blog/2024/07/11/heir-meeting-2024-07-11/Thu, 11 Jul 2024 00:00:00 +0000https://heir.dev/blog/2024/07/11/heir-meeting-2024-07-11/ -<p>Here are the -<a href="https://docs.google.com/document/d/1kP1kFKV6qrLVPv4CnIhmqO-7nMDFkCpvhzwIppJEDfU/edit?usp=sharing">notes</a> -and -<a href="https://drive.google.com/file/d/1-f5ZJ5h28FIgk_-LisNsYa77iuWPIAjU/view?usp=sharing">video recording</a> -from the HEIR meeting on 2024-07-11.</p>Blog: HEIR meeting 2024-06-27https://heir.dev/blog/2024/06/27/heir-meeting-2024-06-27/Thu, 27 Jun 2024 00:00:00 +0000https://heir.dev/blog/2024/06/27/heir-meeting-2024-06-27/ -<p>Here are the -<a href="https://docs.google.com/document/d/1lc4U2JzHapu99_sigOAYwpjNnfd9_QGrX1HAQ0hle_o/edit?usp=sharing">notes</a> -and -<a href="https://drive.google.com/file/d/1-wMytGj3AHi55sA2jb81AsHOU8EcIq6d/view?usp=sharing">video recording</a> -from the HEIR meeting on 2024-06-27.</p>Blog: HEIR meeting 2024-06-13https://heir.dev/blog/2024/06/13/heir-meeting-2024-06-13/Thu, 13 Jun 2024 00:00:00 +0000https://heir.dev/blog/2024/06/13/heir-meeting-2024-06-13/ -<p>Here are the -<a href="https://docs.google.com/document/d/1rkPxOdbJY5J6qhsciZ0rfdj5_9PG_Ng-6USBUvLrEeU/edit?usp=sharing">notes</a> -and -<a href="https://drive.google.com/file/d/19oQOYlvfeHoSwWqOC4hXZTBuaPIf1zQl/view?usp=sharing">video recording</a> -from the HEIR meeting on 2024-06-13.</p>Blog: HEIR meeting 2024-05-30https://heir.dev/blog/2024/05/30/heir-meeting-2024-05-30/Thu, 30 May 2024 00:00:00 +0000https://heir.dev/blog/2024/05/30/heir-meeting-2024-05-30/ -<p>Here are the -<a href="https://docs.google.com/document/d/1mvigwMRTeVQvdpm2hwiewfU8jcJT94ArQBNvngvgkTc/edit?usp=sharing">notes</a> -and -<a href="https://drive.google.com/file/d/1CTIyd7HRiNV857VO2EonquWZZlBhysLM/view?usp=sharing">video recording</a> -from the HEIR meeting on 2024-05-30.</p>Blog: HEIR meeting 2024-05-16https://heir.dev/blog/2024/05/16/heir-meeting-2024-05-16/Thu, 16 May 2024 00:00:00 +0000https://heir.dev/blog/2024/05/16/heir-meeting-2024-05-16/ -<p>Here are the -<a href="https://docs.google.com/document/d/15MwanXaBap6qNzYj7g1m6zRcqK363O-3iCCcNcGY1Ds/edit?usp=sharing">notes</a> -and -<a href="https://drive.google.com/file/d/1gOf_Tb8k9UNx7i0OvjjikkYUG3HrPjoS/view?usp=sharing">video recording</a> -from the HEIR meeting on 2024-05-16.</p>Blog: HEIR meeting 2024-05-02https://heir.dev/blog/2024/05/02/heir-meeting-2024-05-02/Thu, 02 May 2024 00:00:00 +0000https://heir.dev/blog/2024/05/02/heir-meeting-2024-05-02/ -<p>Here are the -<a href="https://docs.google.com/document/d/1uEDeIN0iTUmmtlacZg0c2j7VbAHO3A9e0_8mnunUv10/edit?usp=sharing">notes</a> -and -<a href="https://drive.google.com/file/d/1u1q74rUKdXFi08tAKFRKjI-bojuorQK8/view?usp=drivesdk">video recording</a> -from the HEIR meeting on 2024-05-02.</p>Blog: HEIR meeting 2024-04-18https://heir.dev/blog/2024/04/18/heir-meeting-2024-04-18/Thu, 18 Apr 2024 00:00:00 +0000https://heir.dev/blog/2024/04/18/heir-meeting-2024-04-18/ -<p>Here are the -<a href="https://docs.google.com/document/d/1BJjfYI2yjR3YEg_ugjDuS-trAkYMlKbU7jpH_M1GF3Q/edit?usp=sharing">notes</a> -and -<a href="https://drive.google.com/file/d/1WSsUp9CmjDmEVtGMYk2QXIpZCEetf_Ot/view?usp=sharing">video recording</a> -from the HEIR meeting on 2024-04-18.</p>Blog: HEIR meeting 2024-04-04https://heir.dev/blog/2024/04/04/heir-meeting-2024-04-04/Thu, 04 Apr 2024 00:00:00 +0000https://heir.dev/blog/2024/04/04/heir-meeting-2024-04-04/ -<p>Here are the -<a href="https://docs.google.com/document/d/121_0mzqYIWYMc7rcW2Et5qS-ux4ut3b-kno1dI9sQq8/edit?usp=sharing">notes</a> -and -<a href="https://drive.google.com/file/d/1_Ksjx8s8nD4cLsuZp5_KitYI2mPN72Je/view?usp=sharing">video recording</a> -from the HEIR meeting on 2024-04-04.</p>Blog: HEIR meeting 2024-03-07https://heir.dev/blog/2024/03/07/heir-meeting-2024-03-07/Thu, 07 Mar 2024 00:00:00 +0000https://heir.dev/blog/2024/03/07/heir-meeting-2024-03-07/ -<p>Here are the -<a href="https://docs.google.com/document/d/1felxN5mFBV5LheP79is30jHRxlKLW0NQEo6FPDKxDKM/edit?usp=sharing">notes</a> -and -<a href="https://drive.google.com/file/d/1oVJG-fM72nNLiR1eXkzdeaqdDOEpTfK0/view?usp=sharing">video recording</a> -from the HEIR meeting on 2024-03-07.</p> -<p>Note: there will be no HEIR meeting on 2024-03-21 due to the FHE.org, HACS, and -RWC conferences. Hope to see you all there!</p>Blog: HEIR meeting 2024-02-22https://heir.dev/blog/2024/02/22/heir-meeting-2024-02-22/Thu, 22 Feb 2024 00:00:00 +0000https://heir.dev/blog/2024/02/22/heir-meeting-2024-02-22/ +<a href="https://www.youtube.com/@HEIRCompiler">new HEIR YouTube channel</a>.</p>Blog: HEIR meeting 2024-02-22https://heir.dev/blog/2024/02/22/heir-meeting-2024-02-22/Thu, 22 Feb 2024 00:00:00 +0000https://heir.dev/blog/2024/02/22/heir-meeting-2024-02-22/ <p>Here are the <a href="https://docs.google.com/document/d/1ktK2Y2-OnadvsIIa94HRch_oHCaQ0D6gbT3CElKmGak/edit?usp=sharing">notes</a> and <a href="https://drive.google.com/file/d/1RDONadr54-7uX5ko5dmUX3s1l7QHeHbM/view?usp=sharing">video recording</a> -from the HEIR meeting on 2024-02-22.</p>Blog: HEIR meeting 2024-02-08https://heir.dev/blog/2024/02/08/heir-meeting-2024-02-08/Thu, 08 Feb 2024 00:00:00 +0000https://heir.dev/blog/2024/02/08/heir-meeting-2024-02-08/ -<p>Here are the -<a href="https://docs.google.com/document/d/1w0Cc3YfbSNO4PYVdGjb8KpE5rql8zgoDG2X0Yseon_4/edit?usp=sharing">notes</a> -and -<a href="https://drive.google.com/file/d/1rTsc-sWdRCqJWONrgGo5FV7CQd1S_OV-/view?usp=sharing">video recording</a> -from the HEIR meeting on 2024-02-08.</p>Blog: HEIR meeting 2024-01-25https://heir.dev/blog/2024/01/25/heir-meeting-2024-01-25/Thu, 25 Jan 2024 00:00:00 +0000https://heir.dev/blog/2024/01/25/heir-meeting-2024-01-25/ -<p>Here are the -<a href="https://docs.google.com/document/d/1yrkAVR_348vT3SD7apb9QDoFIgz0bjHn-SzT2GOacfs/edit?usp=sharing">notes</a> -and -<a href="https://drive.google.com/file/d/11JTfRy_3LvHjJQe0nJuqe8WGa8F9oHu1/view?usp=sharing">video recording</a> -from the HEIR meeting on 2024-01-25.</p>Blog: HEIR meeting 2024-01-11https://heir.dev/blog/2024/01/11/heir-meeting-2024-01-11/Thu, 11 Jan 2024 00:00:00 +0000https://heir.dev/blog/2024/01/11/heir-meeting-2024-01-11/ -<p>Here are the -<a href="https://docs.google.com/document/d/133yuywcbI1AWnbsJezq8QlCpgXfX5HMk7YjXQBSTwoE/edit?usp=sharing">notes</a> -and -<a href="https://drive.google.com/file/d/1gLwcshtNda6M6YMWSsyGrNDvlQ8QiL0O/view?usp=sharing">video recording</a> -from the HEIR meeting on 2024-01-11.</p>Blog: HEIR meeting 2023-12-12https://heir.dev/blog/2023/12/12/heir-meeting-2023-12-12/Tue, 12 Dec 2023 00:00:00 +0000https://heir.dev/blog/2023/12/12/heir-meeting-2023-12-12/ -<p>Here are the -<a href="https://docs.google.com/document/d/1ekGrOBLoB_F3qjC43r6NzJbWpgT9RILTJyVu5Ax3PCQ/edit?usp=sharing">notes</a> -and -<a href="https://drive.google.com/file/d/1DaYj9euovyf8vuCi260RQYfEkItn4SEc/view?usp=sharing">video recording</a> -from the HEIR meeting on 2023-12-12.</p> -<p>This is the last meeting for 2023. Please respond to -<a href="https://app.rallly.co/invite/fHNdzrbisHVA">this poll</a> for 2024 scheduling -preferences.</p>Blog: HEIR meeting 2023-11-28https://heir.dev/blog/2023/11/28/heir-meeting-2023-11-28/Tue, 28 Nov 2023 00:00:00 +0000https://heir.dev/blog/2023/11/28/heir-meeting-2023-11-28/ -<p>Here are the -<a href="https://docs.google.com/document/d/1-kkkG__qlAtsp50YXxHC7Dq__Qvgb4BcLZCopzJOzE4/edit?usp=sharing">notes</a> -and -<a href="https://drive.google.com/file/d/1ykxaqlfVExqGC6saiSnfM2A7_TpWqKiE/view">video recording</a> -from the HEIR meeting on 2023-11-28.</p>Blog: HEIR meeting 2023-11-07https://heir.dev/blog/2023/11/07/heir-meeting-2023-11-07/Tue, 07 Nov 2023 00:00:00 +0000https://heir.dev/blog/2023/11/07/heir-meeting-2023-11-07/ -<p>Here are the -<a href="https://docs.google.com/document/d/1nOlAhul4DwZU8UQPpTF1i3OldSY9EmwaWG3EPSZIhHs/edit?usp=sharing">notes</a> -and -<a href="https://drive.google.com/file/d/1I7aIipm54CCcDcLyRYXI_gARfT1z93cN/view?usp=sharing">video recording</a> -from the HEIR meeting on 2023-11-07.</p>Blog: HEIR meeting 2023-10-24https://heir.dev/blog/2023/10/25/heir-meeting-2023-10-24/Wed, 25 Oct 2023 00:00:00 +0000https://heir.dev/blog/2023/10/25/heir-meeting-2023-10-24/ -<p>Here are the -<a href="https://docs.google.com/document/d/1MYjjkytck0fxySbrh49hxBJgNM78NXSD0ZwzAgEPOUw/edit?usp=sharing">notes</a> -and -<a href="https://drive.google.com/file/d/1zrSCQJXta40KbBiCjcIWOP3gd1tuc3MU/view?usp=sharing">video recording</a> -from the HEIR meeting on 2023-10-24.</p> -<p>Also of note: our talk at FHE.org was last Thursday -(<a href="https://www.youtube.com/watch?v=kqDFdKUTNA4">recording</a>), and the similar talk -at the LLVM developers meeting talk was the previous Wednesday, though the video -has not yet been posted for that.</p>Blog: HEIR meeting 2023-09-26https://heir.dev/blog/2023/09/27/heir-meeting-2023-09-26/Wed, 27 Sep 2023 00:00:00 +0000https://heir.dev/blog/2023/09/27/heir-meeting-2023-09-26/ -<p>Here are the -<a href="https://docs.google.com/document/d/1pkG8eaSUddAySJWjQHIFqe0hyYkO0wH9X0JtnR6wlWo/edit?usp=sharing">notes</a> -and -<a href="https://drive.google.com/file/d/1xaH-G3SZPVv_gEpUkfhFuvUTUwU2ZKLY/view?usp=sharing">video recording</a> -from the HEIR meeting on 2023-09-26.</p> -<p>Next meeting (Oct 10) is canceled for the MLIR workshop, and I&rsquo;ll post an update -from that workshop on this blog, hopefully also with a video of the talk that -Alex Viand and I will be giving at the LLVM developers meeting.</p>Blog: HEIR meeting 2023-09-12https://heir.dev/blog/2023/09/13/heir-meeting-2023-09-12/Wed, 13 Sep 2023 00:00:00 +0000https://heir.dev/blog/2023/09/13/heir-meeting-2023-09-12/ -<p>Here are the -<a href="https://docs.google.com/document/d/1gOH1V6ORQwJDDo6I4jrDgCqqNFTsfcQbfpdUR6tv_60/edit?usp=sharing">notes</a> -and -<a href="https://drive.google.com/file/d/1zFtpBcCCq5d6UD8Nm8r3rfg3sgy-guz7/view?usp=sharing">video recording</a> -from the HEIR meeting on 2023-09-12.</p>Blog: HEIR meeting 2023-08-29https://heir.dev/blog/2023/09/05/heir-meeting-2023-08-29/Tue, 05 Sep 2023 00:00:00 +0000https://heir.dev/blog/2023/09/05/heir-meeting-2023-08-29/ -<p>Here are the -<a href="https://docs.google.com/document/d/1Lax8Inby5Mg8BZLkcV_5hUiWH-roL22rtszfc0PBGmE/edit?usp=sharing">notes</a> -from the HEIR meeting on 2023-08-29. There was an issue with the recording, so -there is no video recording this week.</p>Blog: HEIR meeting 2023-08-15https://heir.dev/blog/2023/08/16/heir-meeting-2023-08-15/Wed, 16 Aug 2023 16:15:47 +0000https://heir.dev/blog/2023/08/16/heir-meeting-2023-08-15/ -<p>Here are the -<a href="https://docs.google.com/document/d/1vZsKJH4wCAZCtyh3o9nNMLRFwlWQiVdvUMvwJnA4cIc/edit?usp=sharing">notes</a> -and -<a href="https://drive.google.com/file/d/1DDNepYCSqgi-JlBLBzHrsL5CjjiwqcA_/view?usp=sharing">video recording</a> -from the HEIR meeting on 2023-08-15.</p>Blog: HEIR meeting 2023-08-01https://heir.dev/blog/2023/08/02/heir-meeting-2023-08-01/Wed, 02 Aug 2023 15:46:42 -0700https://heir.dev/blog/2023/08/02/heir-meeting-2023-08-01/ -<p>The fourth HEIR meeting was 2023-08-01 -(<a href="https://docs.google.com/document/d/1gid-MARMUStb3dB9jsXEV_CnPDpf_9cyPXy9uXtZk08/edit?usp=sharing">notes</a> -and -<a href="https://drive.google.com/file/d/1U6HDdKJo3-UHibFPgNrDakU8EpCt5xHZ/view?usp=sharing">video recording</a>).</p> -<p>We&rsquo;re also starting on the Poly and Secret dialects in -<a href="https://github.com/google/heir/pull/74">#74 (poly)</a> and -<a href="https://github.com/google/heir/pull/78">#78 (secret)</a>, so please join in the -fun!</p>Blog: HEIR meeting 2023-07-18https://heir.dev/blog/2023/07/18/heir-meeting-2023-07-18/Tue, 18 Jul 2023 10:43:16 -0700https://heir.dev/blog/2023/07/18/heir-meeting-2023-07-18/ -<p>The third HEIR meeting was 2023-07-18 -(<a href="https://docs.google.com/document/d/1DXdyUCmevqY8RJI3kM8oO5nWDEITFIVBPIbucONOB-k/edit?usp=sharing">notes</a>).</p> -<p>We decided to schedule future meetings every two weeks, with alternating focus -on MLIR and Hardware. See the <a href="https://heir.dev/community/">meeting calendar</a> to -join. -(<a href="https://calendar.google.com/calendar/u/0/embed?src=c85ecb3cda4bfb7daa3da95d5aeb19672930501b49d17896e65fa3f963f17a80@group.calendar.google.com&amp;ctz=America/Los_Angeles">direct link to the calendar</a>)</p>Blog: HEIR meeting 2023-06-30https://heir.dev/blog/2023/06/30/heir-meeting-2023-06-30/Fri, 30 Jun 2023 12:42:22 -0700https://heir.dev/blog/2023/06/30/heir-meeting-2023-06-30/ -<p>The second HEIR meeting was 2023-05-30 -(<a href="https://docs.google.com/document/d/1wxaEtpEDdO2yv5YKmFTc8FVlqHxm49gHzEdcnBFBKWs/edit?usp=sharing">notes</a>, -and -<a href="https://drive.google.com/file/d/1S893iJdeL08BAonLenmkUGNC34PX1qpg/view?usp=sharing">video recording</a>).</p> -<p>There are some initial design discussion threads started on -<a href="https://github.com/google/heir/discussions">GitHub Discussions</a> to get the -design rolling.</p> -<ul> -<li><a href="https://github.com/google/heir/discussions/53">High-Level FHE Dialect</a></li> -<li><a href="https://github.com/google/heir/discussions/54">Scheme Dialects</a></li> -<li><a href="https://github.com/google/heir/discussions/55">Poly/Math Dialects</a></li> -</ul> \ No newline at end of file +from the HEIR meeting on 2024-02-22.</p> \ No newline at end of file diff --git a/blog/page/1/index.html b/blog/page/1/index.html deleted file mode 100644 index d34bb9b27..000000000 --- a/blog/page/1/index.html +++ /dev/null @@ -1 +0,0 @@ -https://heir.dev/blog/ \ No newline at end of file diff --git a/blog/page/2/index.html b/blog/page/2/index.html deleted file mode 100644 index 9a18e37dc..000000000 --- a/blog/page/2/index.html +++ /dev/null @@ -1,11 +0,0 @@ -Blog | HEIR - -

Posts in 2024

- - \ No newline at end of file diff --git a/blog/page/3/index.html b/blog/page/3/index.html deleted file mode 100644 index 3b0d0c29f..000000000 --- a/blog/page/3/index.html +++ /dev/null @@ -1,13 +0,0 @@ -Blog | HEIR - -

Posts in 2024

Posts in 2023

  • HEIR meeting 2023-12-12

    Tuesday, December 12, 2023 in Blog

    Here are the notes and video recording from the HEIR meeting on 2023-12-12. -This is the last meeting for 2023. Please respond to this poll for 2024 scheduling preferences.

    Read more

  • HEIR meeting 2023-11-28

    Tuesday, November 28, 2023 in Blog

    Here are the notes and video recording from the HEIR meeting on 2023-11-28.

    Read more

  • HEIR meeting 2023-11-07

    Tuesday, November 07, 2023 in Blog

    Here are the notes and video recording from the HEIR meeting on 2023-11-07.

    Read more

  • HEIR meeting 2023-10-24

    Wednesday, October 25, 2023 in Blog

    Here are the notes and video recording from the HEIR meeting on 2023-10-24. -Also of note: our talk at FHE.org was last Thursday (recording), and the similar talk at the LLVM developers meeting talk was the previous Wednesday, though the video has not …

    Read more

  • HEIR meeting 2023-09-26

    Wednesday, September 27, 2023 in Blog

    Here are the notes and video recording from the HEIR meeting on 2023-09-26. -Next meeting (Oct 10) is canceled for the MLIR workshop, and I’ll post an update from that workshop on this blog, hopefully also with a video of the talk that Alex …

    Read more

  • HEIR meeting 2023-09-12

    Wednesday, September 13, 2023 in Blog

    Here are the notes and video recording from the HEIR meeting on 2023-09-12.

    Read more

  • HEIR meeting 2023-08-29

    Tuesday, September 05, 2023 in Blog

    Here are the notes from the HEIR meeting on 2023-08-29. There was an issue with the recording, so there is no video recording this week.

    Read more

- - \ No newline at end of file diff --git a/blog/page/4/index.html b/blog/page/4/index.html deleted file mode 100644 index b966b50f1..000000000 --- a/blog/page/4/index.html +++ /dev/null @@ -1,15 +0,0 @@ -Blog | HEIR - -

Posts in 2023

  • HEIR meeting 2023-08-15

    Wednesday, August 16, 2023 in Blog

    Here are the notes and video recording from the HEIR meeting on 2023-08-15.

    Read more

  • HEIR meeting 2023-08-01

    Wednesday, August 02, 2023 in Blog

    The fourth HEIR meeting was 2023-08-01 (notes and video recording). -We’re also starting on the Poly and Secret dialects in #74 (poly) and #78 (secret), so please join in the fun!

    Read more

  • HEIR meeting 2023-07-18

    Tuesday, July 18, 2023 in Blog

    The third HEIR meeting was 2023-07-18 (notes). -We decided to schedule future meetings every two weeks, with alternating focus on MLIR and Hardware. See the meeting calendar to join. (direct link to the calendar)

    Read more

  • HEIR meeting 2023-06-30

    Friday, June 30, 2023 in Blog

    The second HEIR meeting was 2023-05-30 (notes, and video recording). -There are some initial design discussion threads started on GitHub Discussions to get the design rolling. -High-Level FHE Dialect Scheme Dialects Poly/Math Dialects

    Read more

  • Hello, World!

    Tuesday, June 13, 2023 in Blog

    Hello, world! We’re starting a project to unify homomorphic encryption compiler IRs. -Our initial meeting was 2023-05-30 (read-only copy of the minutes). Stay tuned for future updates while we work out a meeting schedule.

    Read more

- - \ No newline at end of file diff --git a/docs/_print/index.html b/docs/_print/index.html index 4c1c90a8a..c96a8ac67 100644 --- a/docs/_print/index.html +++ b/docs/_print/index.html @@ -1631,10 +1631,10 @@ ::mlir::IntegerAttr # galoisElement >

This type represents the Galois key for the RLWE encryption scheme.

galoisElement: Enabling the automorphism X -> X^{galoisElement}.

Parameters:

ParameterC++ typeDescription
galoisElement::mlir::IntegerAttrAn Attribute containing a integer value

RLWEKeyGeneratorType

Syntax: !lattigo.rlwe.key_generator

This type represents the key generator for the RLWE encryption scheme.

RLWEPlaintextType

Syntax: !lattigo.rlwe.plaintext

This type represents the plaintext for the RLWE encryption scheme.

RLWEPublicKeyType

Syntax: !lattigo.rlwe.public_key

This type represents the public key for the RLWE encryption scheme.

RLWERelinearizationKeyType

Syntax: !lattigo.rlwe.relinearization_key

This type represents the relinearization key for the RLWE encryption scheme.

RLWESecretKeyType

Syntax: !lattigo.rlwe.secret_key

This type represents the secret key for the RLWE encryption scheme.

Lattigo ops

lattigo.bgv.add (heir::lattigo::BGVAddOp)

Add two ciphertexts in the Lattigo BGV dialect

Syntax:

operation ::= `lattigo.bgv.add` operands attr-dict `:` functional-type(operands, results)
-

This operation adds two ciphertext values in the Lattigo BGV dialect.

Interfaces: OpAsmOpInterface

Operands:

OperandDescription
evaluator
lhs
rhs

Results:

ResultDescription
output

lattigo.bgv.decode (heir::lattigo::BGVDecodeOp)

Decode a plaintext value in the Lattigo BGV dialect

Syntax:

operation ::= `lattigo.bgv.decode` operands attr-dict `:` functional-type(operands, results)
+

This operation adds two ciphertext values in the Lattigo BGV dialect.

Interfaces: OpAsmOpInterface

Operands:

OperandDescription
evaluator
lhs
rhsor

Results:

ResultDescription
output

lattigo.bgv.decode (heir::lattigo::BGVDecodeOp)

Decode a plaintext value in the Lattigo BGV dialect

Syntax:

operation ::= `lattigo.bgv.decode` operands attr-dict `:` functional-type(operands, results)

This operation decodes a plaintext value using the specified encoder in the Lattigo BGV dialect.

Interfaces: OpAsmOpInterface

Operands:

OperandDescription
encoder
plaintext
valueany type

Results:

ResultDescription
decodedany type

lattigo.bgv.encode (heir::lattigo::BGVEncodeOp)

Encode a plaintext value in the Lattigo BGV dialect

Syntax:

operation ::= `lattigo.bgv.encode` operands attr-dict `:` functional-type(operands, results)

This operation encodes a plaintext value using the specified encoder in the Lattigo BGV dialect.

Interfaces: OpAsmOpInterface

Operands:

OperandDescription
encoder
valueany type
plaintext

Results:

ResultDescription
encoded

lattigo.bgv.mul (heir::lattigo::BGVMulOp)

Multiply two ciphertexts in the Lattigo BGV dialect

Syntax:

operation ::= `lattigo.bgv.mul` operands attr-dict `:` functional-type(operands, results)
-

This operation multiplies two ciphertext values in the Lattigo BGV dialect.

Interfaces: OpAsmOpInterface

Operands:

OperandDescription
evaluator
lhs
rhs

Results:

ResultDescription
output

lattigo.bgv.new_encoder (heir::lattigo::BGVNewEncoderOp)

Create a new encoder in the Lattigo BGV dialect

Syntax:

operation ::= `lattigo.bgv.new_encoder` operands attr-dict `:` functional-type(operands, results)
+

This operation multiplies two ciphertext values in the Lattigo BGV dialect.

Interfaces: OpAsmOpInterface

Operands:

OperandDescription
evaluator
lhs
rhsor

Results:

ResultDescription
output

lattigo.bgv.new_encoder (heir::lattigo::BGVNewEncoderOp)

Create a new encoder in the Lattigo BGV dialect

Syntax:

operation ::= `lattigo.bgv.new_encoder` operands attr-dict `:` functional-type(operands, results)

This operation creates a new encoder for encoding plaintext values in the Lattigo BGV dialect.

Interfaces: OpAsmOpInterface

Operands:

OperandDescription
params

Results:

ResultDescription
encoder

lattigo.bgv.new_evaluator (heir::lattigo::BGVNewEvaluatorOp)

Create a new evaluator in the Lattigo BGV dialect

Syntax:

operation ::= `lattigo.bgv.new_evaluator` operands attr-dict `:` functional-type(operands, results)

This operation creates a new evaluator for performing operations on ciphertexts in the Lattigo BGV dialect.

By default, the evaluator is created with the provided parameters and could execute operations which does not relying on evaluation keys.

To support operations that require evaluation keys, @@ -1645,7 +1645,7 @@

This operation rescales a ciphertext value in the Lattigo BGV dialect.

Interfaces: OpAsmOpInterface

Operands:

OperandDescription
evaluator
input

Results:

ResultDescription
output

lattigo.bgv.rotate_columns (heir::lattigo::BGVRotateColumnsOp)

Rotate columns of a ciphertext in the Lattigo BGV dialect

Syntax:

operation ::= `lattigo.bgv.rotate_columns` operands attr-dict `:` functional-type(operands, results)

This operation rotates the columns of a ciphertext value in the Lattigo BGV dialect.

Lattigo exposes the SIMD slot of BGV as a N/2 x 2 matrix, where N/2 is the column.

offset is valid in (-N/2, N/2).

Interfaces: OpAsmOpInterface

Attributes:

AttributeMLIR TypeDescription
offset::mlir::IntegerAttrAn Attribute containing a integer value

Operands:

OperandDescription
evaluator
input

Results:

ResultDescription
output

lattigo.bgv.rotate_rows (heir::lattigo::BGVRotateRowsOp)

Rotate rows of a ciphertext in the Lattigo BGV dialect

Syntax:

operation ::= `lattigo.bgv.rotate_rows` operands attr-dict `:` functional-type(operands, results)

This operation swap the rows of a ciphertext value in the Lattigo BGV dialect.

Lattigo exposes the SIMD slot of BGV as a N/2 x 2 matrix, where 2 is the row.

Interfaces: OpAsmOpInterface

Operands:

OperandDescription
evaluator
input

Results:

ResultDescription
output

lattigo.bgv.sub (heir::lattigo::BGVSubOp)

Subtract two ciphertexts in the Lattigo BGV dialect

Syntax:

operation ::= `lattigo.bgv.sub` operands attr-dict `:` functional-type(operands, results)
-

This operation subtracts one ciphertext value from another in the Lattigo BGV dialect.

Interfaces: OpAsmOpInterface

Operands:

OperandDescription
evaluator
lhs
rhs

Results:

ResultDescription
output

lattigo.rlwe.decrypt (heir::lattigo::RLWEDecryptOp)

Decrypts a ciphertext using RLWE

Syntax:

operation ::= `lattigo.rlwe.decrypt` operands attr-dict `:` functional-type(operands, results)
+

This operation subtracts one ciphertext value from another in the Lattigo BGV dialect.

Interfaces: OpAsmOpInterface

Operands:

OperandDescription
evaluator
lhs
rhsor

Results:

ResultDescription
output

lattigo.rlwe.decrypt (heir::lattigo::RLWEDecryptOp)

Decrypts a ciphertext using RLWE

Syntax:

operation ::= `lattigo.rlwe.decrypt` operands attr-dict `:` functional-type(operands, results)

This operation decrypts a ciphertext using RLWE

Interfaces: OpAsmOpInterface

Operands:

OperandDescription
decryptor
ciphertext

Results:

ResultDescription
plaintext

lattigo.rlwe.encrypt (heir::lattigo::RLWEEncryptOp)

Encrypts a plaintext using RLWE

Syntax:

operation ::= `lattigo.rlwe.encrypt` operands attr-dict `:` functional-type(operands, results)

This operation encrypts a plaintext using RLWE

Interfaces: OpAsmOpInterface

Operands:

OperandDescription
encryptor
plaintext

Results:

ResultDescription
ciphertext

lattigo.rlwe.gen_galois_key (heir::lattigo::RLWEGenGaloisKeyOp)

Generates a new RLWE Galois key

Syntax:

operation ::= `lattigo.rlwe.gen_galois_key` operands attr-dict `:` functional-type(operands, results)

This operation generates a new RLWE Galois key

galoisElement: Enabling the automorphism X -> X^{galoisElement}.

Interfaces: OpAsmOpInterface

Attributes:

AttributeMLIR TypeDescription
galoisElement::mlir::IntegerAttrAn Attribute containing a integer value

Operands:

OperandDescription
keyGenerator
secretKey

Results:

ResultDescription
galoisKey

lattigo.rlwe.gen_key_pair (heir::lattigo::RLWEGenKeyPairOp)

Generates a new RLWE key pair

Syntax:

operation ::= `lattigo.rlwe.gen_key_pair` operands attr-dict `:` functional-type(operands, results)
diff --git a/docs/dialects/_print/index.html b/docs/dialects/_print/index.html
index cb746695b..04564b1ea 100644
--- a/docs/dialects/_print/index.html
+++ b/docs/dialects/_print/index.html
@@ -231,10 +231,10 @@
   ::mlir::IntegerAttr   # galoisElement
 >

This type represents the Galois key for the RLWE encryption scheme.

galoisElement: Enabling the automorphism X -> X^{galoisElement}.

Parameters:

ParameterC++ typeDescription
galoisElement::mlir::IntegerAttrAn Attribute containing a integer value

RLWEKeyGeneratorType

Syntax: !lattigo.rlwe.key_generator

This type represents the key generator for the RLWE encryption scheme.

RLWEPlaintextType

Syntax: !lattigo.rlwe.plaintext

This type represents the plaintext for the RLWE encryption scheme.

RLWEPublicKeyType

Syntax: !lattigo.rlwe.public_key

This type represents the public key for the RLWE encryption scheme.

RLWERelinearizationKeyType

Syntax: !lattigo.rlwe.relinearization_key

This type represents the relinearization key for the RLWE encryption scheme.

RLWESecretKeyType

Syntax: !lattigo.rlwe.secret_key

This type represents the secret key for the RLWE encryption scheme.

Lattigo ops

lattigo.bgv.add (heir::lattigo::BGVAddOp)

Add two ciphertexts in the Lattigo BGV dialect

Syntax:

operation ::= `lattigo.bgv.add` operands attr-dict `:` functional-type(operands, results)
-

This operation adds two ciphertext values in the Lattigo BGV dialect.

Interfaces: OpAsmOpInterface

Operands:

OperandDescription
evaluator
lhs
rhs

Results:

ResultDescription
output

lattigo.bgv.decode (heir::lattigo::BGVDecodeOp)

Decode a plaintext value in the Lattigo BGV dialect

Syntax:

operation ::= `lattigo.bgv.decode` operands attr-dict `:` functional-type(operands, results)
+

This operation adds two ciphertext values in the Lattigo BGV dialect.

Interfaces: OpAsmOpInterface

Operands:

OperandDescription
evaluator
lhs
rhsor

Results:

ResultDescription
output

lattigo.bgv.decode (heir::lattigo::BGVDecodeOp)

Decode a plaintext value in the Lattigo BGV dialect

Syntax:

operation ::= `lattigo.bgv.decode` operands attr-dict `:` functional-type(operands, results)

This operation decodes a plaintext value using the specified encoder in the Lattigo BGV dialect.

Interfaces: OpAsmOpInterface

Operands:

OperandDescription
encoder
plaintext
valueany type

Results:

ResultDescription
decodedany type

lattigo.bgv.encode (heir::lattigo::BGVEncodeOp)

Encode a plaintext value in the Lattigo BGV dialect

Syntax:

operation ::= `lattigo.bgv.encode` operands attr-dict `:` functional-type(operands, results)

This operation encodes a plaintext value using the specified encoder in the Lattigo BGV dialect.

Interfaces: OpAsmOpInterface

Operands:

OperandDescription
encoder
valueany type
plaintext

Results:

ResultDescription
encoded

lattigo.bgv.mul (heir::lattigo::BGVMulOp)

Multiply two ciphertexts in the Lattigo BGV dialect

Syntax:

operation ::= `lattigo.bgv.mul` operands attr-dict `:` functional-type(operands, results)
-

This operation multiplies two ciphertext values in the Lattigo BGV dialect.

Interfaces: OpAsmOpInterface

Operands:

OperandDescription
evaluator
lhs
rhs

Results:

ResultDescription
output

lattigo.bgv.new_encoder (heir::lattigo::BGVNewEncoderOp)

Create a new encoder in the Lattigo BGV dialect

Syntax:

operation ::= `lattigo.bgv.new_encoder` operands attr-dict `:` functional-type(operands, results)
+

This operation multiplies two ciphertext values in the Lattigo BGV dialect.

Interfaces: OpAsmOpInterface

Operands:

OperandDescription
evaluator
lhs
rhsor

Results:

ResultDescription
output

lattigo.bgv.new_encoder (heir::lattigo::BGVNewEncoderOp)

Create a new encoder in the Lattigo BGV dialect

Syntax:

operation ::= `lattigo.bgv.new_encoder` operands attr-dict `:` functional-type(operands, results)

This operation creates a new encoder for encoding plaintext values in the Lattigo BGV dialect.

Interfaces: OpAsmOpInterface

Operands:

OperandDescription
params

Results:

ResultDescription
encoder

lattigo.bgv.new_evaluator (heir::lattigo::BGVNewEvaluatorOp)

Create a new evaluator in the Lattigo BGV dialect

Syntax:

operation ::= `lattigo.bgv.new_evaluator` operands attr-dict `:` functional-type(operands, results)

This operation creates a new evaluator for performing operations on ciphertexts in the Lattigo BGV dialect.

By default, the evaluator is created with the provided parameters and could execute operations which does not relying on evaluation keys.

To support operations that require evaluation keys, @@ -245,7 +245,7 @@

This operation rescales a ciphertext value in the Lattigo BGV dialect.

Interfaces: OpAsmOpInterface

Operands:

OperandDescription
evaluator
input

Results:

ResultDescription
output

lattigo.bgv.rotate_columns (heir::lattigo::BGVRotateColumnsOp)

Rotate columns of a ciphertext in the Lattigo BGV dialect

Syntax:

operation ::= `lattigo.bgv.rotate_columns` operands attr-dict `:` functional-type(operands, results)

This operation rotates the columns of a ciphertext value in the Lattigo BGV dialect.

Lattigo exposes the SIMD slot of BGV as a N/2 x 2 matrix, where N/2 is the column.

offset is valid in (-N/2, N/2).

Interfaces: OpAsmOpInterface

Attributes:

AttributeMLIR TypeDescription
offset::mlir::IntegerAttrAn Attribute containing a integer value

Operands:

OperandDescription
evaluator
input

Results:

ResultDescription
output

lattigo.bgv.rotate_rows (heir::lattigo::BGVRotateRowsOp)

Rotate rows of a ciphertext in the Lattigo BGV dialect

Syntax:

operation ::= `lattigo.bgv.rotate_rows` operands attr-dict `:` functional-type(operands, results)

This operation swap the rows of a ciphertext value in the Lattigo BGV dialect.

Lattigo exposes the SIMD slot of BGV as a N/2 x 2 matrix, where 2 is the row.

Interfaces: OpAsmOpInterface

Operands:

OperandDescription
evaluator
input

Results:

ResultDescription
output

lattigo.bgv.sub (heir::lattigo::BGVSubOp)

Subtract two ciphertexts in the Lattigo BGV dialect

Syntax:

operation ::= `lattigo.bgv.sub` operands attr-dict `:` functional-type(operands, results)
-

This operation subtracts one ciphertext value from another in the Lattigo BGV dialect.

Interfaces: OpAsmOpInterface

Operands:

OperandDescription
evaluator
lhs
rhs

Results:

ResultDescription
output

lattigo.rlwe.decrypt (heir::lattigo::RLWEDecryptOp)

Decrypts a ciphertext using RLWE

Syntax:

operation ::= `lattigo.rlwe.decrypt` operands attr-dict `:` functional-type(operands, results)
+

This operation subtracts one ciphertext value from another in the Lattigo BGV dialect.

Interfaces: OpAsmOpInterface

Operands:

OperandDescription
evaluator
lhs
rhsor

Results:

ResultDescription
output

lattigo.rlwe.decrypt (heir::lattigo::RLWEDecryptOp)

Decrypts a ciphertext using RLWE

Syntax:

operation ::= `lattigo.rlwe.decrypt` operands attr-dict `:` functional-type(operands, results)

This operation decrypts a ciphertext using RLWE

Interfaces: OpAsmOpInterface

Operands:

OperandDescription
decryptor
ciphertext

Results:

ResultDescription
plaintext

lattigo.rlwe.encrypt (heir::lattigo::RLWEEncryptOp)

Encrypts a plaintext using RLWE

Syntax:

operation ::= `lattigo.rlwe.encrypt` operands attr-dict `:` functional-type(operands, results)

This operation encrypts a plaintext using RLWE

Interfaces: OpAsmOpInterface

Operands:

OperandDescription
encryptor
plaintext

Results:

ResultDescription
ciphertext

lattigo.rlwe.gen_galois_key (heir::lattigo::RLWEGenGaloisKeyOp)

Generates a new RLWE Galois key

Syntax:

operation ::= `lattigo.rlwe.gen_galois_key` operands attr-dict `:` functional-type(operands, results)

This operation generates a new RLWE Galois key

galoisElement: Enabling the automorphism X -> X^{galoisElement}.

Interfaces: OpAsmOpInterface

Attributes:

AttributeMLIR TypeDescription
galoisElement::mlir::IntegerAttrAn Attribute containing a integer value

Operands:

OperandDescription
keyGenerator
secretKey

Results:

ResultDescription
galoisKey

lattigo.rlwe.gen_key_pair (heir::lattigo::RLWEGenKeyPairOp)

Generates a new RLWE key pair

Syntax:

operation ::= `lattigo.rlwe.gen_key_pair` operands attr-dict `:` functional-type(operands, results)
diff --git a/docs/dialects/index.xml b/docs/dialects/index.xml
index 03e650a23..7fcea471b 100644
--- a/docs/dialects/index.xml
+++ b/docs/dialects/index.xml
@@ -3991,7 +3991,7 @@ it must be equal to 1 modulo 2n where n is the plaintext ring degree
 </tr>
 <tr>
 <td style="text-align:center"><code>rhs</code></td>
-<td></td>
+<td>or</td>
 </tr>
 </tbody>
 </table>
@@ -4123,7 +4123,7 @@ it must be equal to 1 modulo 2n where n is the plaintext ring degree
 </tr>
 <tr>
 <td style="text-align:center"><code>rhs</code></td>
-<td></td>
+<td>or</td>
 </tr>
 </tbody>
 </table>
@@ -4477,7 +4477,7 @@ the optional evaluation key set should be provided.</p>
 </tr>
 <tr>
 <td style="text-align:center"><code>rhs</code></td>
-<td></td>
+<td>or</td>
 </tr>
 </tbody>
 </table>
diff --git a/docs/dialects/lattigo/index.html b/docs/dialects/lattigo/index.html
index 5fc200054..ecfe7c18d 100644
--- a/docs/dialects/lattigo/index.html
+++ b/docs/dialects/lattigo/index.html
@@ -13,7 +13,7 @@
 Lattigo attributes BGVParametersLiteralAttr Literal parameters for Lattigo BGV
 Syntax:
 #lattigo.bgv.parameters_literal< int, # logN DenseI64ArrayAttr, # Q DenseI64ArrayAttr, # P DenseI32ArrayAttr, # logQ DenseI32ArrayAttr, # logP int64_t # plaintextModulus > This attribute represents the literal parameters for Lattigo BGV.
-This is in accordance with https://pkg.go.dev/github.com/tuneinsight/lattigo/v6@v6.1.0/schemes/bgv#ParametersLiteral where some field are not present in the current implementation.">Statistics</h4>
 <pre tabindex="0"><code>total circuit size : The total circuit size for all optimized circuits, after optimization is done.
-</code></pre>Blog: HEIR meeting 2024-10-31https://heir.dev/blog/2024/10/31/heir-meeting-2024-10-31/Thu, 31 Oct 2024 00:00:00 +0000https://heir.dev/blog/2024/10/31/heir-meeting-2024-10-31/
+</code></pre>Blog: HEIR meeting 2024-11-26https://heir.dev/blog/2024/11/26/heir-meeting-2024-11-26/Tue, 26 Nov 2024 00:00:00 +0000https://heir.dev/blog/2024/11/26/heir-meeting-2024-11-26/
+<p>Here are the
+<a href="https://docs.google.com/document/d/10WTpdVaLz4mgmTwlJ3lVMGD4qmiNEl2Uvt3R3h0XFmc/edit?hl=en&amp;forcehl=1&amp;tab=t.0#heading=h.w3lar3vbuip1">notes</a>,
+<a href="https://drive.google.com/file/d/13yvX_ap09tTqwJsdABDf3WDl79GF3bJx/view?usp=sharing">video recording</a>,
+and
+<a href="https://docs.google.com/document/d/1s5iXtOSpIDJX3JOEB5gQqUPm5lo1gLpRUM10pBfAdoo/edit?usp=sharing">a transcription of the recording</a>
+from the HEIR meeting on 2024-11-26.</p>Blog: HEIR meeting 2024-10-31https://heir.dev/blog/2024/10/31/heir-meeting-2024-10-31/Thu, 31 Oct 2024 00:00:00 +0000https://heir.dev/blog/2024/10/31/heir-meeting-2024-10-31/
 <p>Here are the
 <a href="https://docs.google.com/document/d/1QUxT00gd1ZSayzdtxY5T5-Wiod-eNnCFGoqVceWQ83Y/edit?usp=sharing">notes</a>
 and
 <a href="https://drive.google.com/file/d/1Q9a7O7HwxKMDqI23l3154KIOw1ofANkX/view?usp=sharing">video recording</a>
-from the HEIR meeting on 2024-10-31.</p>Blog: Hello, World!https://heir.dev/blog/2023/06/13/hello-world/Tue, 13 Jun 2023 13:15:10 -0700https://heir.dev/blog/2023/06/13/hello-world/
+from the HEIR meeting on 2024-10-31.</p>Blog: HEIR meeting 2024-10-04https://heir.dev/blog/2024/10/04/heir-meeting-2024-10-04/Fri, 04 Oct 2024 00:00:00 +0000https://heir.dev/blog/2024/10/04/heir-meeting-2024-10-04/
+<p>Here are the
+<a href="https://docs.google.com/document/d/1tlC-g3JKOB9wxfQMEJnKQk0C0eBdtBCzZX8ck7J37fI/edit?usp=sharing">notes</a>
+and
+<a href="https://drive.google.com/file/d/1OFfrwWesFpxVHw2DFuNAxSB8seLG_tr1/view?usp=sharing">video recording</a>
+from the HEIR meeting on 2024-10-04.</p>Blog: HEIR meeting 2024-09-19https://heir.dev/blog/2024/09/19/heir-meeting-2024-09-19/Thu, 19 Sep 2024 00:00:00 +0000https://heir.dev/blog/2024/09/19/heir-meeting-2024-09-19/
+<p>Here are the
+<a href="https://docs.google.com/document/d/1aGIiZPWpk7UMg5FD8ZYHmNhKVZ6NdhfmGMvyHrrlolM/edit?usp=sharing">notes</a>
+and
+<a href="https://drive.google.com/file/d/1i-HqUi8pb2ywUJ-OT4fWExYCmeRLu2Cn/view?usp=sharing">video recording</a>
+from the HEIR meeting on 2024-09-19.</p>Blog: HEIR meeting 2024-09-05https://heir.dev/blog/2024/09/05/heir-meeting-2024-09-05/Thu, 05 Sep 2024 00:00:00 +0000https://heir.dev/blog/2024/09/05/heir-meeting-2024-09-05/
+<p>Here are the
+<a href="https://docs.google.com/document/d/1tohVmC2pn_XDn3gjCFeo3K4Wfyf7VWu3oK1vimEsFD4/edit?usp=sharing">notes</a>
+and
+<a href="https://drive.google.com/file/d/1XGheLF7kvJfwAMJJQ-XbDpa4Ld15kj4t/view?usp=sharing">video recording</a>
+from the HEIR meeting on 2024-09-05.</p>Blog: HEIR meeting 2024-08-22https://heir.dev/blog/2024/08/22/heir-meeting-2024-08-22/Thu, 22 Aug 2024 00:00:00 +0000https://heir.dev/blog/2024/08/22/heir-meeting-2024-08-22/
+<p>Here are the
+<a href="https://docs.google.com/document/d/1iEkzpO6lCVbShMcRenO3j3DptOEP-0bLu_9V4K7c39M/edit?usp=sharing">notes</a>
+and
+<a href="https://drive.google.com/file/d/1wFrGF7lMiYZmqbr5WQO17HomfoFoOeaj/view?usp=sharing">video recording</a>
+from the HEIR meeting on 2024-08-22.</p>Blog: HEIR meeting 2024-08-08https://heir.dev/blog/2024/08/08/heir-meeting-2024-08-08/Thu, 08 Aug 2024 00:00:00 +0000https://heir.dev/blog/2024/08/08/heir-meeting-2024-08-08/
+<p>Here are the
+<a href="https://docs.google.com/document/d/1FLSiaPlX38GNHqqqi_Mz3gMuVSlS4sUcwBWqpt6Fkew/edit?usp=sharing">notes</a>
+and
+<a href="https://drive.google.com/file/d/1sHoRvNlS14RB-r3Rk0y2RyWOERVGNc-t/view?usp=sharing">video recording</a>
+from the HEIR meeting on 2024-08-08.</p>Blog: HEIR meeting 2024-07-25https://heir.dev/blog/2024/07/25/heir-meeting-2024-07-25/Thu, 25 Jul 2024 00:00:00 +0000https://heir.dev/blog/2024/07/25/heir-meeting-2024-07-25/
+<p>Here are the
+<a href="https://docs.google.com/document/d/1tIrxc4V5OlAeqx_Z1rl_kuMmkd-HUAKEv90q3i-5QSU/edit?usp=sharing">notes</a>
+and
+<a href="https://drive.google.com/file/d/1_1CbRJeNr5NqcwEMXnfkxOqy9u5wJPyq/view?usp=sharing">video recording</a>
+from the HEIR meeting on 2024-07-25.</p>Blog: HEIR meeting 2024-07-18 (mod_arith dialect)https://heir.dev/blog/2024/07/18/heir-meeting-2024-07-18-mod_arith-dialect/Thu, 18 Jul 2024 00:00:00 +0000https://heir.dev/blog/2024/07/18/heir-meeting-2024-07-18-mod_arith-dialect/
+<p>Here are the
+<a href="https://docs.google.com/document/d/1o2-I03DJtNJQDupSHn8LtOXLmxsd3WO1fjvqLbT-SIc/edit?usp=sharing">notes</a>
+and
+<a href="https://drive.google.com/file/d/1bCMuuKnBVf6HP7R2SiZgo1C1vsG6FzF2/view?usp=sharing">video recording</a>
+from the HEIR meeting on 2024-07-18. This special discussion was focused on the
+modular arithmetic dialect.</p>Blog: HEIR meeting 2024-07-11https://heir.dev/blog/2024/07/11/heir-meeting-2024-07-11/Thu, 11 Jul 2024 00:00:00 +0000https://heir.dev/blog/2024/07/11/heir-meeting-2024-07-11/
+<p>Here are the
+<a href="https://docs.google.com/document/d/1kP1kFKV6qrLVPv4CnIhmqO-7nMDFkCpvhzwIppJEDfU/edit?usp=sharing">notes</a>
+and
+<a href="https://drive.google.com/file/d/1-f5ZJ5h28FIgk_-LisNsYa77iuWPIAjU/view?usp=sharing">video recording</a>
+from the HEIR meeting on 2024-07-11.</p>Blog: HEIR meeting 2024-06-27https://heir.dev/blog/2024/06/27/heir-meeting-2024-06-27/Thu, 27 Jun 2024 00:00:00 +0000https://heir.dev/blog/2024/06/27/heir-meeting-2024-06-27/
+<p>Here are the
+<a href="https://docs.google.com/document/d/1lc4U2JzHapu99_sigOAYwpjNnfd9_QGrX1HAQ0hle_o/edit?usp=sharing">notes</a>
+and
+<a href="https://drive.google.com/file/d/1-wMytGj3AHi55sA2jb81AsHOU8EcIq6d/view?usp=sharing">video recording</a>
+from the HEIR meeting on 2024-06-27.</p>Blog: HEIR meeting 2024-06-13https://heir.dev/blog/2024/06/13/heir-meeting-2024-06-13/Thu, 13 Jun 2024 00:00:00 +0000https://heir.dev/blog/2024/06/13/heir-meeting-2024-06-13/
+<p>Here are the
+<a href="https://docs.google.com/document/d/1rkPxOdbJY5J6qhsciZ0rfdj5_9PG_Ng-6USBUvLrEeU/edit?usp=sharing">notes</a>
+and
+<a href="https://drive.google.com/file/d/19oQOYlvfeHoSwWqOC4hXZTBuaPIf1zQl/view?usp=sharing">video recording</a>
+from the HEIR meeting on 2024-06-13.</p>Blog: HEIR meeting 2024-05-30https://heir.dev/blog/2024/05/30/heir-meeting-2024-05-30/Thu, 30 May 2024 00:00:00 +0000https://heir.dev/blog/2024/05/30/heir-meeting-2024-05-30/
+<p>Here are the
+<a href="https://docs.google.com/document/d/1mvigwMRTeVQvdpm2hwiewfU8jcJT94ArQBNvngvgkTc/edit?usp=sharing">notes</a>
+and
+<a href="https://drive.google.com/file/d/1CTIyd7HRiNV857VO2EonquWZZlBhysLM/view?usp=sharing">video recording</a>
+from the HEIR meeting on 2024-05-30.</p>Blog: HEIR meeting 2024-05-16https://heir.dev/blog/2024/05/16/heir-meeting-2024-05-16/Thu, 16 May 2024 00:00:00 +0000https://heir.dev/blog/2024/05/16/heir-meeting-2024-05-16/
+<p>Here are the
+<a href="https://docs.google.com/document/d/15MwanXaBap6qNzYj7g1m6zRcqK363O-3iCCcNcGY1Ds/edit?usp=sharing">notes</a>
+and
+<a href="https://drive.google.com/file/d/1gOf_Tb8k9UNx7i0OvjjikkYUG3HrPjoS/view?usp=sharing">video recording</a>
+from the HEIR meeting on 2024-05-16.</p>Blog: HEIR meeting 2024-05-02https://heir.dev/blog/2024/05/02/heir-meeting-2024-05-02/Thu, 02 May 2024 00:00:00 +0000https://heir.dev/blog/2024/05/02/heir-meeting-2024-05-02/
+<p>Here are the
+<a href="https://docs.google.com/document/d/1uEDeIN0iTUmmtlacZg0c2j7VbAHO3A9e0_8mnunUv10/edit?usp=sharing">notes</a>
+and
+<a href="https://drive.google.com/file/d/1u1q74rUKdXFi08tAKFRKjI-bojuorQK8/view?usp=drivesdk">video recording</a>
+from the HEIR meeting on 2024-05-02.</p>Blog: HEIR meeting 2024-04-18https://heir.dev/blog/2024/04/18/heir-meeting-2024-04-18/Thu, 18 Apr 2024 00:00:00 +0000https://heir.dev/blog/2024/04/18/heir-meeting-2024-04-18/
+<p>Here are the
+<a href="https://docs.google.com/document/d/1BJjfYI2yjR3YEg_ugjDuS-trAkYMlKbU7jpH_M1GF3Q/edit?usp=sharing">notes</a>
+and
+<a href="https://drive.google.com/file/d/1WSsUp9CmjDmEVtGMYk2QXIpZCEetf_Ot/view?usp=sharing">video recording</a>
+from the HEIR meeting on 2024-04-18.</p>Blog: HEIR meeting 2024-04-04https://heir.dev/blog/2024/04/04/heir-meeting-2024-04-04/Thu, 04 Apr 2024 00:00:00 +0000https://heir.dev/blog/2024/04/04/heir-meeting-2024-04-04/
+<p>Here are the
+<a href="https://docs.google.com/document/d/121_0mzqYIWYMc7rcW2Et5qS-ux4ut3b-kno1dI9sQq8/edit?usp=sharing">notes</a>
+and
+<a href="https://drive.google.com/file/d/1_Ksjx8s8nD4cLsuZp5_KitYI2mPN72Je/view?usp=sharing">video recording</a>
+from the HEIR meeting on 2024-04-04.</p>Blog: HEIR meeting 2024-03-07https://heir.dev/blog/2024/03/07/heir-meeting-2024-03-07/Thu, 07 Mar 2024 00:00:00 +0000https://heir.dev/blog/2024/03/07/heir-meeting-2024-03-07/
+<p>Here are the
+<a href="https://docs.google.com/document/d/1felxN5mFBV5LheP79is30jHRxlKLW0NQEo6FPDKxDKM/edit?usp=sharing">notes</a>
+and
+<a href="https://drive.google.com/file/d/1oVJG-fM72nNLiR1eXkzdeaqdDOEpTfK0/view?usp=sharing">video recording</a>
+from the HEIR meeting on 2024-03-07.</p>
+<p>Note: there will be no HEIR meeting on 2024-03-21 due to the FHE.org, HACS, and
+RWC conferences. Hope to see you all there!</p>Blog: HEIR meeting 2024-02-08https://heir.dev/blog/2024/02/08/heir-meeting-2024-02-08/Thu, 08 Feb 2024 00:00:00 +0000https://heir.dev/blog/2024/02/08/heir-meeting-2024-02-08/
+<p>Here are the
+<a href="https://docs.google.com/document/d/1w0Cc3YfbSNO4PYVdGjb8KpE5rql8zgoDG2X0Yseon_4/edit?usp=sharing">notes</a>
+and
+<a href="https://drive.google.com/file/d/1rTsc-sWdRCqJWONrgGo5FV7CQd1S_OV-/view?usp=sharing">video recording</a>
+from the HEIR meeting on 2024-02-08.</p>Blog: HEIR meeting 2024-01-25https://heir.dev/blog/2024/01/25/heir-meeting-2024-01-25/Thu, 25 Jan 2024 00:00:00 +0000https://heir.dev/blog/2024/01/25/heir-meeting-2024-01-25/
+<p>Here are the
+<a href="https://docs.google.com/document/d/1yrkAVR_348vT3SD7apb9QDoFIgz0bjHn-SzT2GOacfs/edit?usp=sharing">notes</a>
+and
+<a href="https://drive.google.com/file/d/11JTfRy_3LvHjJQe0nJuqe8WGa8F9oHu1/view?usp=sharing">video recording</a>
+from the HEIR meeting on 2024-01-25.</p>Blog: HEIR meeting 2024-01-11https://heir.dev/blog/2024/01/11/heir-meeting-2024-01-11/Thu, 11 Jan 2024 00:00:00 +0000https://heir.dev/blog/2024/01/11/heir-meeting-2024-01-11/
+<p>Here are the
+<a href="https://docs.google.com/document/d/133yuywcbI1AWnbsJezq8QlCpgXfX5HMk7YjXQBSTwoE/edit?usp=sharing">notes</a>
+and
+<a href="https://drive.google.com/file/d/1gLwcshtNda6M6YMWSsyGrNDvlQ8QiL0O/view?usp=sharing">video recording</a>
+from the HEIR meeting on 2024-01-11.</p>Blog: HEIR meeting 2023-12-12https://heir.dev/blog/2023/12/12/heir-meeting-2023-12-12/Tue, 12 Dec 2023 00:00:00 +0000https://heir.dev/blog/2023/12/12/heir-meeting-2023-12-12/
+<p>Here are the
+<a href="https://docs.google.com/document/d/1ekGrOBLoB_F3qjC43r6NzJbWpgT9RILTJyVu5Ax3PCQ/edit?usp=sharing">notes</a>
+and
+<a href="https://drive.google.com/file/d/1DaYj9euovyf8vuCi260RQYfEkItn4SEc/view?usp=sharing">video recording</a>
+from the HEIR meeting on 2023-12-12.</p>
+<p>This is the last meeting for 2023. Please respond to
+<a href="https://app.rallly.co/invite/fHNdzrbisHVA">this poll</a> for 2024 scheduling
+preferences.</p>Blog: HEIR meeting 2023-11-28https://heir.dev/blog/2023/11/28/heir-meeting-2023-11-28/Tue, 28 Nov 2023 00:00:00 +0000https://heir.dev/blog/2023/11/28/heir-meeting-2023-11-28/
+<p>Here are the
+<a href="https://docs.google.com/document/d/1-kkkG__qlAtsp50YXxHC7Dq__Qvgb4BcLZCopzJOzE4/edit?usp=sharing">notes</a>
+and
+<a href="https://drive.google.com/file/d/1ykxaqlfVExqGC6saiSnfM2A7_TpWqKiE/view">video recording</a>
+from the HEIR meeting on 2023-11-28.</p>Blog: HEIR meeting 2023-11-07https://heir.dev/blog/2023/11/07/heir-meeting-2023-11-07/Tue, 07 Nov 2023 00:00:00 +0000https://heir.dev/blog/2023/11/07/heir-meeting-2023-11-07/
+<p>Here are the
+<a href="https://docs.google.com/document/d/1nOlAhul4DwZU8UQPpTF1i3OldSY9EmwaWG3EPSZIhHs/edit?usp=sharing">notes</a>
+and
+<a href="https://drive.google.com/file/d/1I7aIipm54CCcDcLyRYXI_gARfT1z93cN/view?usp=sharing">video recording</a>
+from the HEIR meeting on 2023-11-07.</p>Blog: HEIR meeting 2023-10-24https://heir.dev/blog/2023/10/25/heir-meeting-2023-10-24/Wed, 25 Oct 2023 00:00:00 +0000https://heir.dev/blog/2023/10/25/heir-meeting-2023-10-24/
+<p>Here are the
+<a href="https://docs.google.com/document/d/1MYjjkytck0fxySbrh49hxBJgNM78NXSD0ZwzAgEPOUw/edit?usp=sharing">notes</a>
+and
+<a href="https://drive.google.com/file/d/1zrSCQJXta40KbBiCjcIWOP3gd1tuc3MU/view?usp=sharing">video recording</a>
+from the HEIR meeting on 2023-10-24.</p>
+<p>Also of note: our talk at FHE.org was last Thursday
+(<a href="https://www.youtube.com/watch?v=kqDFdKUTNA4">recording</a>), and the similar talk
+at the LLVM developers meeting talk was the previous Wednesday, though the video
+has not yet been posted for that.</p>Blog: HEIR meeting 2023-09-26https://heir.dev/blog/2023/09/27/heir-meeting-2023-09-26/Wed, 27 Sep 2023 00:00:00 +0000https://heir.dev/blog/2023/09/27/heir-meeting-2023-09-26/
+<p>Here are the
+<a href="https://docs.google.com/document/d/1pkG8eaSUddAySJWjQHIFqe0hyYkO0wH9X0JtnR6wlWo/edit?usp=sharing">notes</a>
+and
+<a href="https://drive.google.com/file/d/1xaH-G3SZPVv_gEpUkfhFuvUTUwU2ZKLY/view?usp=sharing">video recording</a>
+from the HEIR meeting on 2023-09-26.</p>
+<p>Next meeting (Oct 10) is canceled for the MLIR workshop, and I&rsquo;ll post an update
+from that workshop on this blog, hopefully also with a video of the talk that
+Alex Viand and I will be giving at the LLVM developers meeting.</p>Blog: HEIR meeting 2023-09-12https://heir.dev/blog/2023/09/13/heir-meeting-2023-09-12/Wed, 13 Sep 2023 00:00:00 +0000https://heir.dev/blog/2023/09/13/heir-meeting-2023-09-12/
+<p>Here are the
+<a href="https://docs.google.com/document/d/1gOH1V6ORQwJDDo6I4jrDgCqqNFTsfcQbfpdUR6tv_60/edit?usp=sharing">notes</a>
+and
+<a href="https://drive.google.com/file/d/1zFtpBcCCq5d6UD8Nm8r3rfg3sgy-guz7/view?usp=sharing">video recording</a>
+from the HEIR meeting on 2023-09-12.</p>Blog: HEIR meeting 2023-08-29https://heir.dev/blog/2023/09/05/heir-meeting-2023-08-29/Tue, 05 Sep 2023 00:00:00 +0000https://heir.dev/blog/2023/09/05/heir-meeting-2023-08-29/
+<p>Here are the
+<a href="https://docs.google.com/document/d/1Lax8Inby5Mg8BZLkcV_5hUiWH-roL22rtszfc0PBGmE/edit?usp=sharing">notes</a>
+from the HEIR meeting on 2023-08-29. There was an issue with the recording, so
+there is no video recording this week.</p>Blog: HEIR meeting 2023-08-15https://heir.dev/blog/2023/08/16/heir-meeting-2023-08-15/Wed, 16 Aug 2023 16:15:47 +0000https://heir.dev/blog/2023/08/16/heir-meeting-2023-08-15/
+<p>Here are the
+<a href="https://docs.google.com/document/d/1vZsKJH4wCAZCtyh3o9nNMLRFwlWQiVdvUMvwJnA4cIc/edit?usp=sharing">notes</a>
+and
+<a href="https://drive.google.com/file/d/1DDNepYCSqgi-JlBLBzHrsL5CjjiwqcA_/view?usp=sharing">video recording</a>
+from the HEIR meeting on 2023-08-15.</p>Blog: HEIR meeting 2023-08-01https://heir.dev/blog/2023/08/02/heir-meeting-2023-08-01/Wed, 02 Aug 2023 15:46:42 -0700https://heir.dev/blog/2023/08/02/heir-meeting-2023-08-01/
+<p>The fourth HEIR meeting was 2023-08-01
+(<a href="https://docs.google.com/document/d/1gid-MARMUStb3dB9jsXEV_CnPDpf_9cyPXy9uXtZk08/edit?usp=sharing">notes</a>
+and
+<a href="https://drive.google.com/file/d/1U6HDdKJo3-UHibFPgNrDakU8EpCt5xHZ/view?usp=sharing">video recording</a>).</p>
+<p>We&rsquo;re also starting on the Poly and Secret dialects in
+<a href="https://github.com/google/heir/pull/74">#74 (poly)</a> and
+<a href="https://github.com/google/heir/pull/78">#78 (secret)</a>, so please join in the
+fun!</p>Blog: HEIR meeting 2023-07-18https://heir.dev/blog/2023/07/18/heir-meeting-2023-07-18/Tue, 18 Jul 2023 10:43:16 -0700https://heir.dev/blog/2023/07/18/heir-meeting-2023-07-18/
+<p>The third HEIR meeting was 2023-07-18
+(<a href="https://docs.google.com/document/d/1DXdyUCmevqY8RJI3kM8oO5nWDEITFIVBPIbucONOB-k/edit?usp=sharing">notes</a>).</p>
+<p>We decided to schedule future meetings every two weeks, with alternating focus
+on MLIR and Hardware. See the <a href="https://heir.dev/community/">meeting calendar</a> to
+join.
+(<a href="https://calendar.google.com/calendar/u/0/embed?src=c85ecb3cda4bfb7daa3da95d5aeb19672930501b49d17896e65fa3f963f17a80@group.calendar.google.com&amp;ctz=America/Los_Angeles">direct link to the calendar</a>)</p>Blog: HEIR meeting 2023-06-30https://heir.dev/blog/2023/06/30/heir-meeting-2023-06-30/Fri, 30 Jun 2023 12:42:22 -0700https://heir.dev/blog/2023/06/30/heir-meeting-2023-06-30/
+<p>The second HEIR meeting was 2023-05-30
+(<a href="https://docs.google.com/document/d/1wxaEtpEDdO2yv5YKmFTc8FVlqHxm49gHzEdcnBFBKWs/edit?usp=sharing">notes</a>,
+and
+<a href="https://drive.google.com/file/d/1S893iJdeL08BAonLenmkUGNC34PX1qpg/view?usp=sharing">video recording</a>).</p>
+<p>There are some initial design discussion threads started on
+<a href="https://github.com/google/heir/discussions">GitHub Discussions</a> to get the
+design rolling.</p>
+<ul>
+<li><a href="https://github.com/google/heir/discussions/53">High-Level FHE Dialect</a></li>
+<li><a href="https://github.com/google/heir/discussions/54">Scheme Dialects</a></li>
+<li><a href="https://github.com/google/heir/discussions/55">Poly/Math Dialects</a></li>
+</ul>Blog: Hello, World!https://heir.dev/blog/2023/06/13/hello-world/Tue, 13 Jun 2023 13:15:10 -0700https://heir.dev/blog/2023/06/13/hello-world/
 <p>Hello, world! We&rsquo;re starting a project to unify homomorphic encryption compiler
 IRs.</p>
 <p>Our initial meeting was 2023-05-30
@@ -6769,7 +6948,7 @@ it must be equal to 1 modulo 2n where n is the plaintext ring degree
 </tr>
 <tr>
 <td style="text-align:center"><code>rhs</code></td>
-<td></td>
+<td>or</td>
 </tr>
 </tbody>
 </table>
@@ -6901,7 +7080,7 @@ it must be equal to 1 modulo 2n where n is the plaintext ring degree
 </tr>
 <tr>
 <td style="text-align:center"><code>rhs</code></td>
-<td></td>
+<td>or</td>
 </tr>
 </tbody>
 </table>
@@ -7255,7 +7434,7 @@ the optional evaluation key set should be provided.</p>
 </tr>
 <tr>
 <td style="text-align:center"><code>rhs</code></td>
-<td></td>
+<td>or</td>
 </tr>
 </tbody>
 </table>
@@ -9101,4472 +9280,4 @@ does not keep track of types for you.</p>
 <td>mix</td>
 </tr>
 </tbody>
-</table>Docs: Mgmthttps://heir.dev/docs/dialects/mgmt/Mon, 01 Jan 0001 00:00:00 +0000https://heir.dev/docs/dialects/mgmt/
-<!-- Autogenerated by mlir-tblgen; don't manually edit -->
-<h1 id="mgmt-dialect">&lsquo;mgmt&rsquo; Dialect</h1>
-<p>The <code>mgmt</code> dialect contains scheme-agnostic ciphertext management ops
-(like relinearize and mod reduce), to enable initial high-level compiler
-passes to perform a first pass at parameter selection, while lower-level
-passes may refine them with scheme-specific information.</p>
-<h2 id="mgmt-attributes">Mgmt attributes</h2>
-<!-- Autogenerated by mlir-tblgen; don't manually edit -->
-<h3 id="mgmtattr">MgmtAttr</h3>
-<p>Container attribute for all mgmt parameter</p>
-<p>Syntax:</p>
-<pre tabindex="0"><code>#mgmt.mgmt&lt;
-int, # level
-int # dimension
-&gt;
-</code></pre><p>This attribute is used to store all mgmt parameters.</p>
-<p>The attribute is a struct with the following fields:</p>
-<ul>
-<li><code>level</code> : the level of the ciphertext, from L to 0</li>
-<li><code>dimension</code> : the dimension of the ciphertext, defaults to 2</li>
-</ul>
-<p>Internally, this attribute is used by secret-to-<scheme>
-for determining the level and dimension of the ciphertext.</p>
-<p>It should be populated by &ndash;secret-with-mgmt-<scheme> before
-going through the secret-to-<scheme> pass.</p>
-<p>Example:</p>
-<pre tabindex="0"><code>#mgmt = #mgmt.mgmt&lt;level = 1&gt; // dimension defaults to 2
-#mgmt1 = #mgmt.mgmt&lt;level = 1, dimension = 3&gt;
-%0 = secret.generic ins(%arg0, %arg1 : !secret.secret&lt;i16&gt;) attrs = {mgmt.mgmt = #mgmt} {
-...
-} -&gt; !secret.secret&lt;i16&gt;
-</code></pre><h4 id="parameters">Parameters:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Parameter</th>
-<th style="text-align:center">C++ type</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center">level</td>
-<td style="text-align:center"><code>int</code></td>
-<td></td>
-</tr>
-<tr>
-<td style="text-align:center">dimension</td>
-<td style="text-align:center"><code>int</code></td>
-<td></td>
-</tr>
-</tbody>
-</table>
-<h2 id="mgmt-ops">Mgmt ops</h2>
-<!-- Autogenerated by mlir-tblgen; don't manually edit -->
-<h3 id="mgmtbootstrap-heirmgmtbootstrapop"><code>mgmt.bootstrap</code> (heir::mgmt::BootstrapOp)</h3>
-<p><em>Bootstrap the input ciphertext to refresh its noise budget</em></p>
-<p>Syntax:</p>
-<pre tabindex="0"><code>operation ::= `mgmt.bootstrap` operands attr-dict `:` type($output)
-</code></pre><p>This is a scheme-agnostic operation that implies bootstrapping
-of the input ciphertext to refresh its noise budget.</p>
-<p>Bootstrapping is a technique used in homomorphic encryption to
-reduce the noise in a ciphertext, allowing further operations
-to be performed on it without decryption.</p>
-<p>When further lowered, it could be lowered to bgv.bootstrap
-or ckks.bootstrap depending on the scheme.</p>
-<p>For the current backend, only ckks.bootstrap is supported.
-Further backend may include bgv.bootstrap.</p>
-<p>Traits: <code>AlwaysSpeculatableImplTrait</code>, <code>Elementwise</code>, <code>SameOperandsAndResultType</code>, <code>Scalarizable</code>, <code>Tensorizable</code>, <code>Vectorizable</code></p>
-<p>Interfaces: <code>ConditionallySpeculatable</code>, <code>InferTypeOpInterface</code>, <code>NoMemoryEffect (MemoryEffectOpInterface)</code></p>
-<p>Effects: <code>MemoryEffects::Effect{}</code></p>
-<h4 id="operands">Operands:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Operand</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>input</code></td>
-<td>any type</td>
-</tr>
-</tbody>
-</table>
-<h4 id="results">Results:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Result</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>output</code></td>
-<td>any type</td>
-</tr>
-</tbody>
-</table>
-<h3 id="mgmtmodreduce-heirmgmtmodreduceop"><code>mgmt.modreduce</code> (heir::mgmt::ModReduceOp)</h3>
-<p><em>Modulus switch the input ciphertext down by one limb (RNS assumed)</em></p>
-<p>Syntax:</p>
-<pre tabindex="0"><code>operation ::= `mgmt.modreduce` operands attr-dict `:` type($output)
-</code></pre><p>This is scheme-agonistic operation that implies modulus switching/rescaling
-by one limb.</p>
-<p>Input ciphertext is assumed to be in RNS form when further lowered.</p>
-<p>When further lowered, it could be lowered to bgv.modulus_switch
-or ckks.rescale depending on the scheme.</p>
-<p>Traits: <code>AlwaysSpeculatableImplTrait</code>, <code>Elementwise</code>, <code>SameOperandsAndResultType</code>, <code>Scalarizable</code>, <code>Tensorizable</code>, <code>Vectorizable</code></p>
-<p>Interfaces: <code>ConditionallySpeculatable</code>, <code>InferTypeOpInterface</code>, <code>NoMemoryEffect (MemoryEffectOpInterface)</code></p>
-<p>Effects: <code>MemoryEffects::Effect{}</code></p>
-<h4 id="operands-1">Operands:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Operand</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>input</code></td>
-<td>any type</td>
-</tr>
-</tbody>
-</table>
-<h4 id="results-1">Results:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Result</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>output</code></td>
-<td>any type</td>
-</tr>
-</tbody>
-</table>
-<h3 id="mgmtrelinearize-heirmgmtrelinearizeop"><code>mgmt.relinearize</code> (heir::mgmt::RelinearizeOp)</h3>
-<p><em>Relinearize the input ciphertext to be <em>linear</em></em></p>
-<p>Syntax:</p>
-<pre tabindex="0"><code>operation ::= `mgmt.relinearize` operands attr-dict `:` type($output)
-</code></pre><p>This is scheme-agonistic operation that implies relinearization
-of the input ciphertext to be <em>linear</em> (i.e. returns to dimension 2).</p>
-<p>This is used solely by multiplication. For rotation, currently HEIR
-assumes relinearization is done internally and does not have a separate
-scheme-specific operation for it.</p>
-<p>This accepts a ciphertext with dimension &gt; 2 and returns a ciphertext
-with dimension 2. Note that the semantic includes the relinearization
-of higher dimension input like input with dimension 4 or higher,
-which when materialized should require multiple relinearization keys.</p>
-<p>When further lowered, it could be lowered to bgv.relinearize
-or ckks.relinearize depending on the scheme.</p>
-<p>Traits: <code>AlwaysSpeculatableImplTrait</code>, <code>Elementwise</code>, <code>SameOperandsAndResultType</code>, <code>Scalarizable</code>, <code>Tensorizable</code>, <code>Vectorizable</code></p>
-<p>Interfaces: <code>ConditionallySpeculatable</code>, <code>InferTypeOpInterface</code>, <code>NoMemoryEffect (MemoryEffectOpInterface)</code></p>
-<p>Effects: <code>MemoryEffects::Effect{}</code></p>
-<h4 id="operands-2">Operands:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Operand</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>input</code></td>
-<td>any type</td>
-</tr>
-</tbody>
-</table>
-<h4 id="results-2">Results:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Result</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>output</code></td>
-<td>any type</td>
-</tr>
-</tbody>
-</table>Docs: ModArithhttps://heir.dev/docs/dialects/modarith/Mon, 01 Jan 0001 00:00:00 +0000https://heir.dev/docs/dialects/modarith/
-<!-- Autogenerated by mlir-tblgen; don't manually edit -->
-<h1 id="mod_arith-dialect">&lsquo;mod_arith&rsquo; Dialect</h1>
-<p>The <code>mod_arith</code> dialect contains operations used for modulo arithmetic.</p>
-<h2 id="modarith-attributes">ModArith attributes</h2>
-<!-- Autogenerated by mlir-tblgen; don't manually edit -->
-<h3 id="modarithattr">ModArithAttr</h3>
-<p>a typed mod_arith attribute</p>
-<p>Syntax:</p>
-<pre tabindex="0"><code>#mod_arith.int&lt;
-::mlir::heir::mod_arith::ModArithType, # type
-mlir::IntegerAttr # value
-&gt;
-</code></pre><p>Example:</p>
-<div class="highlight"><pre tabindex="0" style="background-color:#f8f8f8;-moz-tab-size:4;-o-tab-size:4;tab-size:4;"><code class="language-mlir" data-lang="mlir"><span style="display:flex;"><span><span style="color:#000">#attr</span> <span style="color:#000;font-weight:bold">=</span> <span style="color:#0000cf;font-weight:bold">123</span><span style="color:#000;font-weight:bold">:</span><span style="color:#204a87;font-weight:bold">i32</span>
-</span></span><span style="display:flex;"><span><span style="color:#000">#attr_verbose</span> <span style="color:#000;font-weight:bold">=</span> <span style="color:#000">#mod_arith.int</span><span style="color:#000;font-weight:bold">&lt;</span><span style="color:#0000cf;font-weight:bold">123</span><span style="color:#000;font-weight:bold">:</span><span style="color:#204a87;font-weight:bold">i32</span><span style="color:#000;font-weight:bold">&gt;</span>
-</span></span></code></pre></div><h4 id="parameters">Parameters:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Parameter</th>
-<th style="text-align:center">C++ type</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center">type</td>
-<td style="text-align:center"><code>::mlir::heir::mod_arith::ModArithType</code></td>
-<td></td>
-</tr>
-<tr>
-<td style="text-align:center">value</td>
-<td style="text-align:center"><code>mlir::IntegerAttr</code></td>
-<td></td>
-</tr>
-</tbody>
-</table>
-<h2 id="modarith-types">ModArith types</h2>
-<!-- Autogenerated by mlir-tblgen; don't manually edit -->
-<h3 id="modarithtype">ModArithType</h3>
-<p>Integer type with modular arithmetic</p>
-<p>Syntax:</p>
-<pre tabindex="0"><code>!mod_arith.int&lt;
-::mlir::IntegerAttr # modulus
-&gt;
-</code></pre><p><code>mod_arith.int&lt;p&gt;</code> represents an element of the ring of integers modulo $p$.
-The <code>modulus</code> attribute is the ring modulus, and <code>mod_arith</code> operations lower to
-<code>arith</code> operations that produce results in the range <code>[0, modulus)</code>, often called
-the <em>canonical representative</em>.</p>
-<p><code>modulus</code> is specified with an integer type suffix, for example,
-<code>mod_arith.int&lt;65537 : i32&gt;</code>. This corresponds to the storage type for the
-modulus, and is <code>i64</code> by default.</p>
-<p>It is required that the underlying integer type should be larger than
-twice the modulus (have one extra bit of storage space) to avoid signedness
-issues. For example, when <code>modulus == 2 ** 32 - 1</code>, the underlying type
-for the modulus should be at least <code>i33</code>, though <code>i64</code> is a natural choice.</p>
-<p>Passes may allow intermediate values that do not always produce a
-canonical representative in <code>[0, modulus)</code>. For example, if the machine storage
-type is <code>i64</code>, but the <code>modulus</code> fits within an <code>i32</code>, a lowering could
-allow intermediate arithmetic values to grow to as large as an <code>i64</code> before
-reducing them. However, all passes must ensure that values used outside
-the local scope (e.g., function return values or arguments to calls to linked
-functions) are appropriately reduced to the canonical representative.
-<code>modulus</code> is the modulus the arithmetic working with.</p>
-<p>Examples:</p>
-<pre tabindex="0"><code>!Zp1 = !mod_arith.int&lt;7&gt; // implicitly being i64
-!Zp2 = !mod_arith.int&lt;65537 : i32&gt;
-!Zp3 = !mod_arith.int&lt;536903681 : i64&gt;
-</code></pre><h4 id="parameters-1">Parameters:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Parameter</th>
-<th style="text-align:center">C++ type</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center">modulus</td>
-<td style="text-align:center"><code>::mlir::IntegerAttr</code></td>
-<td></td>
-</tr>
-</tbody>
-</table>
-<h2 id="modarith-ops">ModArith ops</h2>
-<!-- Autogenerated by mlir-tblgen; don't manually edit -->
-<h3 id="mod_arithadd-heirmod_arithaddop"><code>mod_arith.add</code> (heir::mod_arith::AddOp)</h3>
-<p><em>Modular addition operation</em></p>
-<p>Syntax:</p>
-<pre tabindex="0"><code>operation ::= `mod_arith.add` operands attr-dict `:` type($output)
-</code></pre><p>Computes modular addition.</p>
-<p>Unless otherwise specified, the operation assumes both inputs are canonical
-representatives and guarantees the output being canonical representative.</p>
-<p>Traits: <code>AlwaysSpeculatableImplTrait</code>, <code>Commutative</code>, <code>Elementwise</code>, <code>SameOperandsAndResultType</code>, <code>Scalarizable</code>, <code>Tensorizable</code>, <code>Vectorizable</code></p>
-<p>Interfaces: <code>ConditionallySpeculatable</code>, <code>InferTypeOpInterface</code>, <code>NoMemoryEffect (MemoryEffectOpInterface)</code></p>
-<p>Effects: <code>MemoryEffects::Effect{}</code></p>
-<h4 id="operands">Operands:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Operand</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>lhs</code></td>
-<td>mod_arith-like</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>rhs</code></td>
-<td>mod_arith-like</td>
-</tr>
-</tbody>
-</table>
-<h4 id="results">Results:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Result</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>output</code></td>
-<td>mod_arith-like</td>
-</tr>
-</tbody>
-</table>
-<h3 id="mod_arithbarrett_reduce-heirmod_arithbarrettreduceop"><code>mod_arith.barrett_reduce</code> (heir::mod_arith::BarrettReduceOp)</h3>
-<p><em>Compute the first step of the Barrett reduction.</em></p>
-<p>Syntax:</p>
-<pre tabindex="0"><code>operation ::= `mod_arith.barrett_reduce` operands attr-dict `:` qualified(type($input))
-</code></pre><p>Let $q$ denote a statically known modulus and $b = 4^{w}$, where $w$ is the
-smallest bit-width that contains the range $[0, q)$. The Barrett reduce
-operation computes <code>barret_reduce x = x - floor(x * floor(b / q) / b) * q</code>.</p>
-<p>Given $0 &lt;= x &lt; q^2$, then this will compute $(x \mod q)$ or $(x \mod q) + q$.</p>
-<p>Traits: <code>SameOperandsAndResultType</code></p>
-<p>Interfaces: <code>InferTypeOpInterface</code></p>
-<h4 id="attributes">Attributes:</h4>
-<table>
-<tr><th>Attribute</th><th>MLIR Type</th><th>Description</th></tr>
-<tr><td><code>modulus</code></td><td>::mlir::IntegerAttr</td><td>arbitrary integer attribute</td></tr>
-</table>
-<h4 id="operands-1">Operands:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Operand</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>input</code></td>
-<td>signless-integer-like</td>
-</tr>
-</tbody>
-</table>
-<h4 id="results-1">Results:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Result</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>output</code></td>
-<td>signless-integer-like</td>
-</tr>
-</tbody>
-</table>
-<h3 id="mod_arithconstant-heirmod_arithconstantop"><code>mod_arith.constant</code> (heir::mod_arith::ConstantOp)</h3>
-<p><em>Define a constant value via an attribute.</em></p>
-<p>Example:</p>
-<div class="highlight"><pre tabindex="0" style="background-color:#f8f8f8;-moz-tab-size:4;-o-tab-size:4;tab-size:4;"><code class="language-mlir" data-lang="mlir"><span style="display:flex;"><span><span style="color:#000">%0</span> <span style="color:#000;font-weight:bold">=</span> mod_arith<span style="color:#000;font-weight:bold">.</span><span style="color:#204a87;font-weight:bold">constant</span> <span style="color:#0000cf;font-weight:bold">123</span> <span style="color:#000;font-weight:bold">:</span> <span style="color:#000;font-weight:bold">!</span>mod_arith<span style="color:#000;font-weight:bold">.</span>int<span style="color:#000;font-weight:bold">&lt;</span><span style="color:#0000cf;font-weight:bold">65537</span><span style="color:#000;font-weight:bold">:</span><span style="color:#204a87;font-weight:bold">i32</span><span style="color:#000;font-weight:bold">&gt;</span>
-</span></span></code></pre></div><p>Traits: <code>AlwaysSpeculatableImplTrait</code>, <code>InferTypeOpAdaptor</code></p>
-<p>Interfaces: <code>ConditionallySpeculatable</code>, <code>InferTypeOpInterface</code>, <code>NoMemoryEffect (MemoryEffectOpInterface)</code></p>
-<p>Effects: <code>MemoryEffects::Effect{}</code></p>
-<h4 id="attributes-1">Attributes:</h4>
-<table>
-<tr><th>Attribute</th><th>MLIR Type</th><th>Description</th></tr>
-<tr><td><code>value</code></td><td>::mlir::heir::mod_arith::ModArithAttr</td><td>a typed mod_arith attribute</td></tr>
-</table>
-<h4 id="results-2">Results:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Result</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>output</code></td>
-<td>Integer type with modular arithmetic</td>
-</tr>
-</tbody>
-</table>
-<h3 id="mod_arithencapsulate-heirmod_arithencapsulateop"><code>mod_arith.encapsulate</code> (heir::mod_arith::EncapsulateOp)</h3>
-<p><em>Encapsulate an integer into a mod_arith type</em></p>
-<p>Syntax:</p>
-<pre tabindex="0"><code>operation ::= `mod_arith.encapsulate` operands attr-dict `:` type($input) `-&gt;` type($output)
-</code></pre><p><code>mod_arith.encapsulate</code> converts the integer to be of mod_arith type.</p>
-<p>Examples:</p>
-<pre tabindex="0"><code>mod_arith.encapsulate %c0 : i32 -&gt; mod_arith.int&lt;65537 : i32&gt;
-mod_arith.encapsulate %c1 : i64 -&gt; mod_arith.int&lt;65537&gt;
-</code></pre><p>Traits: <code>AlwaysSpeculatableImplTrait</code>, <code>Elementwise</code>, <code>Scalarizable</code>, <code>Tensorizable</code>, <code>Vectorizable</code></p>
-<p>Interfaces: <code>ConditionallySpeculatable</code>, <code>NoMemoryEffect (MemoryEffectOpInterface)</code></p>
-<p>Effects: <code>MemoryEffects::Effect{}</code></p>
-<h4 id="operands-2">Operands:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Operand</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>input</code></td>
-<td>signless-integer-like</td>
-</tr>
-</tbody>
-</table>
-<h4 id="results-3">Results:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Result</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>output</code></td>
-<td>mod_arith-like</td>
-</tr>
-</tbody>
-</table>
-<h3 id="mod_arithextract-heirmod_arithextractop"><code>mod_arith.extract</code> (heir::mod_arith::ExtractOp)</h3>
-<p><em>Extract the integer stored inside mod_arith type</em></p>
-<p>Syntax:</p>
-<pre tabindex="0"><code>operation ::= `mod_arith.extract` operands attr-dict `:` type($input) `-&gt;` type($output)
-</code></pre><p><code>mod_arith.extract</code> extracts the integer inside the mod_arith type.</p>
-<p>It is required that the bitwidth of the output integer type is the same
-as that of the storage type of the input mod_arith type.</p>
-<p>Examples:</p>
-<pre tabindex="0"><code>%m0 = mod_arith.encapsulate %c0 : i32 -&gt; mod_arith.int&lt;65537 : i32&gt;
-%m1 = mod_arith.encapsulate %c1 : i64 -&gt; mod_arith.int&lt;65537&gt;
-%c2 = mod_arith.extract %m0 : mod_arith.int&lt;65537 : i32&gt; -&gt; i32
-%c3 = mod_arith.extract %m1 : mod_arith.int&lt;65537&gt; -&gt; i64
-</code></pre><p>Traits: <code>AlwaysSpeculatableImplTrait</code>, <code>Elementwise</code>, <code>Scalarizable</code>, <code>Tensorizable</code>, <code>Vectorizable</code></p>
-<p>Interfaces: <code>ConditionallySpeculatable</code>, <code>NoMemoryEffect (MemoryEffectOpInterface)</code></p>
-<p>Effects: <code>MemoryEffects::Effect{}</code></p>
-<h4 id="operands-3">Operands:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Operand</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>input</code></td>
-<td>mod_arith-like</td>
-</tr>
-</tbody>
-</table>
-<h4 id="results-4">Results:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Result</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>output</code></td>
-<td>signless-integer-like</td>
-</tr>
-</tbody>
-</table>
-<h3 id="mod_arithmac-heirmod_arithmacop"><code>mod_arith.mac</code> (heir::mod_arith::MacOp)</h3>
-<p><em>Modular multiplication-and-accumulation operation</em></p>
-<p>Syntax:</p>
-<pre tabindex="0"><code>operation ::= `mod_arith.mac` operands attr-dict `:` type($output)
-</code></pre><p><code>mod_arith.mac x, y, z</code> computes $(x * y) + z$</p>
-<p>Unless otherwise specified, the operation assumes all inputs are canonical
-representatives and guarantees the output being canonical representative.</p>
-<p>Traits: <code>AlwaysSpeculatableImplTrait</code>, <code>Elementwise</code>, <code>SameOperandsAndResultType</code>, <code>Scalarizable</code>, <code>Tensorizable</code>, <code>Vectorizable</code></p>
-<p>Interfaces: <code>ConditionallySpeculatable</code>, <code>InferTypeOpInterface</code>, <code>NoMemoryEffect (MemoryEffectOpInterface)</code></p>
-<p>Effects: <code>MemoryEffects::Effect{}</code></p>
-<h4 id="operands-4">Operands:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Operand</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>lhs</code></td>
-<td>mod_arith-like</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>rhs</code></td>
-<td>mod_arith-like</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>acc</code></td>
-<td>mod_arith-like</td>
-</tr>
-</tbody>
-</table>
-<h4 id="results-5">Results:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Result</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>output</code></td>
-<td>mod_arith-like</td>
-</tr>
-</tbody>
-</table>
-<h3 id="mod_arithmod_switch-heirmod_arithmodswitchop"><code>mod_arith.mod_switch</code> (heir::mod_arith::ModSwitchOp)</h3>
-<p><em>Change the modulus of a mod_arith</em></p>
-<p>Syntax:</p>
-<pre tabindex="0"><code>operation ::= `mod_arith.mod_switch` $input attr-dict `:` type($input) `to` type($output)
-</code></pre><p>&ldquo;mod_switch&rdquo; operation to change the modulus of a mod_arith type to a
-bigger space.</p>
-<p>Examples:</p>
-<pre tabindex="0"><code>`mod_arith.mod_switch %c0 : mod_arith.int&lt;65537 : i32&gt; to mod_arith.int&lt;65539 : i32&gt;`
-</code></pre><p>Traits: <code>AlwaysSpeculatableImplTrait</code>, <code>SameOperandsAndResultShape</code></p>
-<p>Interfaces: <code>ConditionallySpeculatable</code>, <code>NoMemoryEffect (MemoryEffectOpInterface)</code></p>
-<p>Effects: <code>MemoryEffects::Effect{}</code></p>
-<h4 id="operands-5">Operands:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Operand</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>input</code></td>
-<td>Integer type with modular arithmetic</td>
-</tr>
-</tbody>
-</table>
-<h4 id="results-6">Results:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Result</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>output</code></td>
-<td>Integer type with modular arithmetic</td>
-</tr>
-</tbody>
-</table>
-<h3 id="mod_arithmul-heirmod_arithmulop"><code>mod_arith.mul</code> (heir::mod_arith::MulOp)</h3>
-<p><em>Modular multiplication operation</em></p>
-<p>Syntax:</p>
-<pre tabindex="0"><code>operation ::= `mod_arith.mul` operands attr-dict `:` type($output)
-</code></pre><p>Computes modular multiplication.</p>
-<p>Unless otherwise specified, the operation assumes both inputs are canonical
-representatives and guarantees the output being canonical representative.</p>
-<p>Traits: <code>AlwaysSpeculatableImplTrait</code>, <code>Commutative</code>, <code>Elementwise</code>, <code>SameOperandsAndResultType</code>, <code>Scalarizable</code>, <code>Tensorizable</code>, <code>Vectorizable</code></p>
-<p>Interfaces: <code>ConditionallySpeculatable</code>, <code>InferTypeOpInterface</code>, <code>NoMemoryEffect (MemoryEffectOpInterface)</code></p>
-<p>Effects: <code>MemoryEffects::Effect{}</code></p>
-<h4 id="operands-6">Operands:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Operand</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>lhs</code></td>
-<td>mod_arith-like</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>rhs</code></td>
-<td>mod_arith-like</td>
-</tr>
-</tbody>
-</table>
-<h4 id="results-7">Results:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Result</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>output</code></td>
-<td>mod_arith-like</td>
-</tr>
-</tbody>
-</table>
-<h3 id="mod_arithreduce-heirmod_arithreduceop"><code>mod_arith.reduce</code> (heir::mod_arith::ReduceOp)</h3>
-<p><em>Reduce the mod arith type to its canonical representative</em></p>
-<p>Syntax:</p>
-<pre tabindex="0"><code>operation ::= `mod_arith.reduce` operands attr-dict `:` type($output)
-</code></pre><p><code>mod_arith.reduce x</code> produces $y$, the canonical representative in $[0, q)$
-such that $x \equiv y \mod q$.</p>
-<p>Examples:</p>
-<pre tabindex="0"><code>%c0 = arith.constant 65538 : i32
-%m0 = mod_arith.encapsulate %c0 : i32 -&gt; mod_arith.int&lt;65537 : i32&gt;
-// mod_arith.extract %m0 produces 65538
-%m1 = mod_arith.reduce %m0 : mod_arith.int&lt;65537: i32&gt;
-// mod_arith.extract %m1 produces 1
-</code></pre><p>Traits: <code>AlwaysSpeculatableImplTrait</code>, <code>Elementwise</code>, <code>SameOperandsAndResultType</code>, <code>Scalarizable</code>, <code>Tensorizable</code>, <code>Vectorizable</code></p>
-<p>Interfaces: <code>ConditionallySpeculatable</code>, <code>InferTypeOpInterface</code>, <code>NoMemoryEffect (MemoryEffectOpInterface)</code></p>
-<p>Effects: <code>MemoryEffects::Effect{}</code></p>
-<h4 id="operands-7">Operands:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Operand</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>input</code></td>
-<td>mod_arith-like</td>
-</tr>
-</tbody>
-</table>
-<h4 id="results-8">Results:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Result</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>output</code></td>
-<td>mod_arith-like</td>
-</tr>
-</tbody>
-</table>
-<h3 id="mod_arithsubifge-heirmod_arithsubifgeop"><code>mod_arith.subifge</code> (heir::mod_arith::SubIfGEOp)</h3>
-<p><em>Compute (x &gt;= y) ? x - y : x.</em></p>
-<p>Syntax:</p>
-<pre tabindex="0"><code>operation ::= `mod_arith.subifge` operands attr-dict `:` qualified(type($output))
-</code></pre><p>Traits: <code>SameOperandsAndResultType</code></p>
-<p>Interfaces: <code>InferTypeOpInterface</code></p>
-<h4 id="operands-8">Operands:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Operand</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>lhs</code></td>
-<td>signless-integer-like</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>rhs</code></td>
-<td>signless-integer-like</td>
-</tr>
-</tbody>
-</table>
-<h4 id="results-9">Results:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Result</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>output</code></td>
-<td>signless-integer-like</td>
-</tr>
-</tbody>
-</table>
-<h3 id="mod_arithsub-heirmod_arithsubop"><code>mod_arith.sub</code> (heir::mod_arith::SubOp)</h3>
-<p><em>Modular subtraction operation</em></p>
-<p>Syntax:</p>
-<pre tabindex="0"><code>operation ::= `mod_arith.sub` operands attr-dict `:` type($output)
-</code></pre><p>Computes modular subtraction.</p>
-<p>Unless otherwise specified, the operation assumes both inputs are canonical
-representatives and guarantees the output being canonical representative.</p>
-<p>Traits: <code>AlwaysSpeculatableImplTrait</code>, <code>Elementwise</code>, <code>SameOperandsAndResultType</code>, <code>Scalarizable</code>, <code>Tensorizable</code>, <code>Vectorizable</code></p>
-<p>Interfaces: <code>ConditionallySpeculatable</code>, <code>InferTypeOpInterface</code>, <code>NoMemoryEffect (MemoryEffectOpInterface)</code></p>
-<p>Effects: <code>MemoryEffects::Effect{}</code></p>
-<h4 id="operands-9">Operands:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Operand</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>lhs</code></td>
-<td>mod_arith-like</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>rhs</code></td>
-<td>mod_arith-like</td>
-</tr>
-</tbody>
-</table>
-<h4 id="results-10">Results:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Result</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>output</code></td>
-<td>mod_arith-like</td>
-</tr>
-</tbody>
-</table>Docs: Openfhehttps://heir.dev/docs/dialects/openfhe/Mon, 01 Jan 0001 00:00:00 +0000https://heir.dev/docs/dialects/openfhe/
-<!-- Autogenerated by mlir-tblgen; don't manually edit -->
-<h1 id="openfhe-dialect">&lsquo;openfhe&rsquo; Dialect</h1>
-<p>The <code>openfhe</code> dialect is an exit dialect for generating c++ code against the OpenFHE library API.</p>
-<p>See <a href="https://github.com/openfheorg/openfhe-development">https://github.com/openfheorg/openfhe-development</a></p>
-<h2 id="openfhe-types">Openfhe types</h2>
-<!-- Autogenerated by mlir-tblgen; don't manually edit -->
-<h3 id="ccparamstype">CCParamsType</h3>
-<p>The CCParams required to create CryptoContext.</p>
-<p>Syntax: <code>!openfhe.cc_params</code></p>
-<h3 id="cryptocontexttype">CryptoContextType</h3>
-<p>The CryptoContext required to perform homomorphic operations in OpenFHE.</p>
-<p>Syntax: <code>!openfhe.crypto_context</code></p>
-<h3 id="evalkeytype">EvalKeyType</h3>
-<p>The evaluation key required to keyswitch/relinearize/rotate/automorphism operation in OpenFHE.</p>
-<p>Syntax: <code>!openfhe.eval_key</code></p>
-<h3 id="privatekeytype">PrivateKeyType</h3>
-<p>The private key required to decrypt a ciphertext in OpenFHE.</p>
-<p>Syntax: <code>!openfhe.private_key</code></p>
-<h3 id="publickeytype">PublicKeyType</h3>
-<p>The public key required to encrypt plaintext in OpenFHE.</p>
-<p>Syntax: <code>!openfhe.public_key</code></p>
-<h2 id="openfhe-ops">Openfhe ops</h2>
-<!-- Autogenerated by mlir-tblgen; don't manually edit -->
-<h3 id="openfheadd-heiropenfheaddop"><code>openfhe.add</code> (heir::openfhe::AddOp)</h3>
-<p><em>OpenFHE add operation of two ciphertexts.</em></p>
-<p>Syntax:</p>
-<pre tabindex="0"><code>operation ::= `openfhe.add` operands attr-dict `:` functional-type(operands, results)
-</code></pre><p>Traits: <code>AlwaysSpeculatableImplTrait</code></p>
-<p>Interfaces: <code>ConditionallySpeculatable</code>, <code>InferTypeOpInterface</code>, <code>NoMemoryEffect (MemoryEffectOpInterface)</code>, <code>OpAsmOpInterface</code></p>
-<p>Effects: <code>MemoryEffects::Effect{}</code></p>
-<h4 id="operands">Operands:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Operand</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>cryptoContext</code></td>
-<td>The CryptoContext required to perform homomorphic operations in OpenFHE.</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>lhs</code></td>
-<td>A ciphertext type</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>rhs</code></td>
-<td>A ciphertext type</td>
-</tr>
-</tbody>
-</table>
-<h4 id="results">Results:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Result</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>output</code></td>
-<td>A ciphertext type</td>
-</tr>
-</tbody>
-</table>
-<h3 id="openfheadd_plain-heiropenfheaddplainop"><code>openfhe.add_plain</code> (heir::openfhe::AddPlainOp)</h3>
-<p><em>OpenFHE add operation of a ciphertext and a plaintext.</em></p>
-<p>Syntax:</p>
-<pre tabindex="0"><code>operation ::= `openfhe.add_plain` operands attr-dict `:` functional-type(operands, results)
-</code></pre><p>Traits: <code>AlwaysSpeculatableImplTrait</code></p>
-<p>Interfaces: <code>ConditionallySpeculatable</code>, <code>InferTypeOpInterface</code>, <code>NoMemoryEffect (MemoryEffectOpInterface)</code>, <code>OpAsmOpInterface</code></p>
-<p>Effects: <code>MemoryEffects::Effect{}</code></p>
-<h4 id="operands-1">Operands:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Operand</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>cryptoContext</code></td>
-<td>The CryptoContext required to perform homomorphic operations in OpenFHE.</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>ciphertext</code></td>
-<td>A ciphertext type</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>plaintext</code></td>
-<td>A plaintext type</td>
-</tr>
-</tbody>
-</table>
-<h4 id="results-1">Results:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Result</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>output</code></td>
-<td>A ciphertext type</td>
-</tr>
-</tbody>
-</table>
-<h3 id="openfheautomorph-heiropenfheautomorphop"><code>openfhe.automorph</code> (heir::openfhe::AutomorphOp)</h3>
-<p>Syntax:</p>
-<pre tabindex="0"><code>operation ::= `openfhe.automorph` operands attr-dict `:` functional-type(operands, results)
-</code></pre><p>Traits: <code>AlwaysSpeculatableImplTrait</code></p>
-<p>Interfaces: <code>ConditionallySpeculatable</code>, <code>InferTypeOpInterface</code>, <code>NoMemoryEffect (MemoryEffectOpInterface)</code>, <code>OpAsmOpInterface</code></p>
-<p>Effects: <code>MemoryEffects::Effect{}</code></p>
-<h4 id="operands-2">Operands:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Operand</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>cryptoContext</code></td>
-<td>The CryptoContext required to perform homomorphic operations in OpenFHE.</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>ciphertext</code></td>
-<td>A ciphertext type</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>evalKey</code></td>
-<td>The evaluation key required to keyswitch/relinearize/rotate/automorphism operation in OpenFHE.</td>
-</tr>
-</tbody>
-</table>
-<h4 id="results-2">Results:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Result</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>output</code></td>
-<td>A ciphertext type</td>
-</tr>
-</tbody>
-</table>
-<h3 id="openfhebootstrap-heiropenfhebootstrapop"><code>openfhe.bootstrap</code> (heir::openfhe::BootstrapOp)</h3>
-<p><em>OpenFHE bootstrap operation of a ciphertext. (For CKKS)</em></p>
-<p>Syntax:</p>
-<pre tabindex="0"><code>operation ::= `openfhe.bootstrap` operands attr-dict `:` functional-type(operands, results)
-</code></pre><p>Traits: <code>AlwaysSpeculatableImplTrait</code></p>
-<p>Interfaces: <code>ConditionallySpeculatable</code>, <code>NoMemoryEffect (MemoryEffectOpInterface)</code>, <code>OpAsmOpInterface</code></p>
-<p>Effects: <code>MemoryEffects::Effect{}</code></p>
-<h4 id="operands-3">Operands:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Operand</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>cryptoContext</code></td>
-<td>The CryptoContext required to perform homomorphic operations in OpenFHE.</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>ciphertext</code></td>
-<td>A ciphertext type</td>
-</tr>
-</tbody>
-</table>
-<h4 id="results-3">Results:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Result</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>output</code></td>
-<td>A ciphertext type</td>
-</tr>
-</tbody>
-</table>
-<h3 id="openfhedecrypt-heiropenfhedecryptop"><code>openfhe.decrypt</code> (heir::openfhe::DecryptOp)</h3>
-<p>Syntax:</p>
-<pre tabindex="0"><code>operation ::= `openfhe.decrypt` operands attr-dict `:` functional-type(operands, results)
-</code></pre><p>Traits: <code>AlwaysSpeculatableImplTrait</code></p>
-<p>Interfaces: <code>ConditionallySpeculatable</code>, <code>NoMemoryEffect (MemoryEffectOpInterface)</code>, <code>OpAsmOpInterface</code></p>
-<p>Effects: <code>MemoryEffects::Effect{}</code></p>
-<h4 id="operands-4">Operands:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Operand</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>cryptoContext</code></td>
-<td>The CryptoContext required to perform homomorphic operations in OpenFHE.</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>ciphertext</code></td>
-<td>A ciphertext type</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>privateKey</code></td>
-<td>The private key required to decrypt a ciphertext in OpenFHE.</td>
-</tr>
-</tbody>
-</table>
-<h4 id="results-4">Results:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Result</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>plaintext</code></td>
-<td>A plaintext type</td>
-</tr>
-</tbody>
-</table>
-<h3 id="openfheencrypt-heiropenfheencryptop"><code>openfhe.encrypt</code> (heir::openfhe::EncryptOp)</h3>
-<p>Syntax:</p>
-<pre tabindex="0"><code>operation ::= `openfhe.encrypt` operands attr-dict `:` functional-type(operands, results)
-</code></pre><p>Traits: <code>AlwaysSpeculatableImplTrait</code></p>
-<p>Interfaces: <code>ConditionallySpeculatable</code>, <code>NoMemoryEffect (MemoryEffectOpInterface)</code>, <code>OpAsmOpInterface</code></p>
-<p>Effects: <code>MemoryEffects::Effect{}</code></p>
-<h4 id="operands-5">Operands:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Operand</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>cryptoContext</code></td>
-<td>The CryptoContext required to perform homomorphic operations in OpenFHE.</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>plaintext</code></td>
-<td>A plaintext type</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>publicKey</code></td>
-<td>The public key required to encrypt plaintext in OpenFHE.</td>
-</tr>
-</tbody>
-</table>
-<h4 id="results-5">Results:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Result</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>ciphertext</code></td>
-<td>A ciphertext type</td>
-</tr>
-</tbody>
-</table>
-<h3 id="openfhegen_bootstrapkey-heiropenfhegenbootstrapkeyop"><code>openfhe.gen_bootstrapkey</code> (heir::openfhe::GenBootstrapKeyOp)</h3>
-<p>Syntax:</p>
-<pre tabindex="0"><code>operation ::= `openfhe.gen_bootstrapkey` operands attr-dict `:` functional-type(operands, results)
-</code></pre><p>Interfaces: <code>OpAsmOpInterface</code></p>
-<h4 id="operands-6">Operands:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Operand</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>cryptoContext</code></td>
-<td>The CryptoContext required to perform homomorphic operations in OpenFHE.</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>privateKey</code></td>
-<td>The private key required to decrypt a ciphertext in OpenFHE.</td>
-</tr>
-</tbody>
-</table>
-<h3 id="openfhegen_context-heiropenfhegencontextop"><code>openfhe.gen_context</code> (heir::openfhe::GenContextOp)</h3>
-<p>Syntax:</p>
-<pre tabindex="0"><code>operation ::= `openfhe.gen_context` operands attr-dict `:` functional-type(operands, results)
-</code></pre><p>Interfaces: <code>InferTypeOpInterface</code>, <code>OpAsmOpInterface</code></p>
-<h4 id="attributes">Attributes:</h4>
-<table>
-<tr><th>Attribute</th><th>MLIR Type</th><th>Description</th></tr>
-<tr><td><code>supportFHE</code></td><td>::mlir::BoolAttr</td><td>bool attribute</td></tr>
-</table>
-<h4 id="operands-7">Operands:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Operand</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>params</code></td>
-<td>The CCParams required to create CryptoContext.</td>
-</tr>
-</tbody>
-</table>
-<h4 id="results-6">Results:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Result</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>context</code></td>
-<td>The CryptoContext required to perform homomorphic operations in OpenFHE.</td>
-</tr>
-</tbody>
-</table>
-<h3 id="openfhegen_mulkey-heiropenfhegenmulkeyop"><code>openfhe.gen_mulkey</code> (heir::openfhe::GenMulKeyOp)</h3>
-<p>Syntax:</p>
-<pre tabindex="0"><code>operation ::= `openfhe.gen_mulkey` operands attr-dict `:` functional-type(operands, results)
-</code></pre><p>Interfaces: <code>OpAsmOpInterface</code></p>
-<h4 id="operands-8">Operands:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Operand</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>cryptoContext</code></td>
-<td>The CryptoContext required to perform homomorphic operations in OpenFHE.</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>privateKey</code></td>
-<td>The private key required to decrypt a ciphertext in OpenFHE.</td>
-</tr>
-</tbody>
-</table>
-<h3 id="openfhegen_params-heiropenfhegenparamsop"><code>openfhe.gen_params</code> (heir::openfhe::GenParamsOp)</h3>
-<p>Syntax:</p>
-<pre tabindex="0"><code>operation ::= `openfhe.gen_params` operands attr-dict `:` functional-type(operands, results)
-</code></pre><p>Generates the parameters for the OpenFHE scheme.</p>
-<p><code>mulDepth</code> is the depth of the multiplication circuit,
-including the bootstrapping depth.</p>
-<p><code>plainMod</code> is the modulus of the plaintext space. If we
-are using CKKS, this is 0.</p>
-<p><code>insecure</code> is a flag that determines whether the parameters
-are generated securely or not. This is mainly used for
-testing purposes.</p>
-<p>Interfaces: <code>InferTypeOpInterface</code>, <code>OpAsmOpInterface</code></p>
-<h4 id="attributes-1">Attributes:</h4>
-<table>
-<tr><th>Attribute</th><th>MLIR Type</th><th>Description</th></tr>
-<tr><td><code>mulDepth</code></td><td>::mlir::IntegerAttr</td><td>64-bit signless integer attribute</td></tr>
-<tr><td><code>plainMod</code></td><td>::mlir::IntegerAttr</td><td>64-bit signless integer attribute</td></tr>
-<tr><td><code>insecure</code></td><td>::mlir::BoolAttr</td><td>bool attribute</td></tr>
-</table>
-<h4 id="results-7">Results:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Result</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>params</code></td>
-<td>The CCParams required to create CryptoContext.</td>
-</tr>
-</tbody>
-</table>
-<h3 id="openfhegen_rotkey-heiropenfhegenrotkeyop"><code>openfhe.gen_rotkey</code> (heir::openfhe::GenRotKeyOp)</h3>
-<p>Syntax:</p>
-<pre tabindex="0"><code>operation ::= `openfhe.gen_rotkey` operands attr-dict `:` functional-type(operands, results)
-</code></pre><p>Interfaces: <code>OpAsmOpInterface</code></p>
-<h4 id="attributes-2">Attributes:</h4>
-<table>
-<tr><th>Attribute</th><th>MLIR Type</th><th>Description</th></tr>
-<tr><td><code>indices</code></td><td>::mlir::DenseI64ArrayAttr</td><td>i64 dense array attribute</td></tr>
-</table>
-<h4 id="operands-9">Operands:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Operand</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>cryptoContext</code></td>
-<td>The CryptoContext required to perform homomorphic operations in OpenFHE.</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>privateKey</code></td>
-<td>The private key required to decrypt a ciphertext in OpenFHE.</td>
-</tr>
-</tbody>
-</table>
-<h3 id="openfhekey_switch-heiropenfhekeyswitchop"><code>openfhe.key_switch</code> (heir::openfhe::KeySwitchOp)</h3>
-<p>Syntax:</p>
-<pre tabindex="0"><code>operation ::= `openfhe.key_switch` operands attr-dict `:` functional-type(operands, results)
-</code></pre><p>Traits: <code>AlwaysSpeculatableImplTrait</code></p>
-<p>Interfaces: <code>ConditionallySpeculatable</code>, <code>InferTypeOpInterface</code>, <code>NoMemoryEffect (MemoryEffectOpInterface)</code>, <code>OpAsmOpInterface</code></p>
-<p>Effects: <code>MemoryEffects::Effect{}</code></p>
-<h4 id="operands-10">Operands:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Operand</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>cryptoContext</code></td>
-<td>The CryptoContext required to perform homomorphic operations in OpenFHE.</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>ciphertext</code></td>
-<td>A ciphertext type</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>evalKey</code></td>
-<td>The evaluation key required to keyswitch/relinearize/rotate/automorphism operation in OpenFHE.</td>
-</tr>
-</tbody>
-</table>
-<h4 id="results-8">Results:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Result</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>output</code></td>
-<td>A ciphertext type</td>
-</tr>
-</tbody>
-</table>
-<h3 id="openfhelevel_reduce-heiropenfhelevelreduceop"><code>openfhe.level_reduce</code> (heir::openfhe::LevelReduceOp)</h3>
-<p><em>OpenFHE level_reduce operation of a ciphertext.</em></p>
-<p>Syntax:</p>
-<pre tabindex="0"><code>operation ::= `openfhe.level_reduce` operands attr-dict `:` functional-type(operands, results)
-</code></pre><p>Traits: <code>AlwaysSpeculatableImplTrait</code></p>
-<p>Interfaces: <code>ConditionallySpeculatable</code>, <code>NoMemoryEffect (MemoryEffectOpInterface)</code>, <code>OpAsmOpInterface</code></p>
-<p>Effects: <code>MemoryEffects::Effect{}</code></p>
-<h4 id="operands-11">Operands:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Operand</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>cryptoContext</code></td>
-<td>The CryptoContext required to perform homomorphic operations in OpenFHE.</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>ciphertext</code></td>
-<td>A ciphertext type</td>
-</tr>
-</tbody>
-</table>
-<h4 id="results-9">Results:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Result</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>output</code></td>
-<td>A ciphertext type</td>
-</tr>
-</tbody>
-</table>
-<h3 id="openfhemake_ckks_packed_plaintext-heiropenfhemakeckkspackedplaintextop"><code>openfhe.make_ckks_packed_plaintext</code> (heir::openfhe::MakeCKKSPackedPlaintextOp)</h3>
-<p>Syntax:</p>
-<pre tabindex="0"><code>operation ::= `openfhe.make_ckks_packed_plaintext` operands attr-dict `:` functional-type(operands, results)
-</code></pre><p>Traits: <code>AlwaysSpeculatableImplTrait</code></p>
-<p>Interfaces: <code>ConditionallySpeculatable</code>, <code>NoMemoryEffect (MemoryEffectOpInterface)</code>, <code>OpAsmOpInterface</code></p>
-<p>Effects: <code>MemoryEffects::Effect{}</code></p>
-<h4 id="operands-12">Operands:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Operand</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>cryptoContext</code></td>
-<td>The CryptoContext required to perform homomorphic operations in OpenFHE.</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>value</code></td>
-<td>ranked tensor of floating-point or integer values</td>
-</tr>
-</tbody>
-</table>
-<h4 id="results-10">Results:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Result</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>plaintext</code></td>
-<td>A plaintext type</td>
-</tr>
-</tbody>
-</table>
-<h3 id="openfhemake_packed_plaintext-heiropenfhemakepackedplaintextop"><code>openfhe.make_packed_plaintext</code> (heir::openfhe::MakePackedPlaintextOp)</h3>
-<p>Syntax:</p>
-<pre tabindex="0"><code>operation ::= `openfhe.make_packed_plaintext` operands attr-dict `:` functional-type(operands, results)
-</code></pre><p>Traits: <code>AlwaysSpeculatableImplTrait</code></p>
-<p>Interfaces: <code>ConditionallySpeculatable</code>, <code>NoMemoryEffect (MemoryEffectOpInterface)</code>, <code>OpAsmOpInterface</code></p>
-<p>Effects: <code>MemoryEffects::Effect{}</code></p>
-<h4 id="operands-13">Operands:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Operand</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>cryptoContext</code></td>
-<td>The CryptoContext required to perform homomorphic operations in OpenFHE.</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>value</code></td>
-<td>ranked tensor of integer values</td>
-</tr>
-</tbody>
-</table>
-<h4 id="results-11">Results:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Result</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>plaintext</code></td>
-<td>A plaintext type</td>
-</tr>
-</tbody>
-</table>
-<h3 id="openfhemod_reduce-heiropenfhemodreduceop"><code>openfhe.mod_reduce</code> (heir::openfhe::ModReduceOp)</h3>
-<p><em>OpenFHE mod_reduce operation of a ciphertext. (used only for BGV/CKKS)</em></p>
-<p>Syntax:</p>
-<pre tabindex="0"><code>operation ::= `openfhe.mod_reduce` operands attr-dict `:` functional-type(operands, results)
-</code></pre><p>Traits: <code>AlwaysSpeculatableImplTrait</code></p>
-<p>Interfaces: <code>ConditionallySpeculatable</code>, <code>NoMemoryEffect (MemoryEffectOpInterface)</code>, <code>OpAsmOpInterface</code></p>
-<p>Effects: <code>MemoryEffects::Effect{}</code></p>
-<h4 id="operands-14">Operands:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Operand</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>cryptoContext</code></td>
-<td>The CryptoContext required to perform homomorphic operations in OpenFHE.</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>ciphertext</code></td>
-<td>A ciphertext type</td>
-</tr>
-</tbody>
-</table>
-<h4 id="results-12">Results:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Result</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>output</code></td>
-<td>A ciphertext type</td>
-</tr>
-</tbody>
-</table>
-<h3 id="openfhemul_const-heiropenfhemulconstop"><code>openfhe.mul_const</code> (heir::openfhe::MulConstOp)</h3>
-<p><em>OpenFHE mul operation of a ciphertext and a constant.</em></p>
-<p>Syntax:</p>
-<pre tabindex="0"><code>operation ::= `openfhe.mul_const` operands attr-dict `:` functional-type(operands, results)
-</code></pre><p>Traits: <code>AlwaysSpeculatableImplTrait</code></p>
-<p>Interfaces: <code>ConditionallySpeculatable</code>, <code>InferTypeOpInterface</code>, <code>NoMemoryEffect (MemoryEffectOpInterface)</code>, <code>OpAsmOpInterface</code></p>
-<p>Effects: <code>MemoryEffects::Effect{}</code></p>
-<h4 id="operands-15">Operands:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Operand</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>cryptoContext</code></td>
-<td>The CryptoContext required to perform homomorphic operations in OpenFHE.</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>ciphertext</code></td>
-<td>A ciphertext type</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>constant</code></td>
-<td>64-bit signless integer</td>
-</tr>
-</tbody>
-</table>
-<h4 id="results-13">Results:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Result</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>output</code></td>
-<td>A ciphertext type</td>
-</tr>
-</tbody>
-</table>
-<h3 id="openfhemul_no_relin-heiropenfhemulnorelinop"><code>openfhe.mul_no_relin</code> (heir::openfhe::MulNoRelinOp)</h3>
-<p><em>OpenFHE mul operation of two ciphertexts without relinearization.</em></p>
-<p>Syntax:</p>
-<pre tabindex="0"><code>operation ::= `openfhe.mul_no_relin` operands attr-dict `:` functional-type(operands, results)
-</code></pre><p>Traits: <code>AlwaysSpeculatableImplTrait</code></p>
-<p>Interfaces: <code>ConditionallySpeculatable</code>, <code>NoMemoryEffect (MemoryEffectOpInterface)</code>, <code>OpAsmOpInterface</code></p>
-<p>Effects: <code>MemoryEffects::Effect{}</code></p>
-<h4 id="operands-16">Operands:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Operand</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>cryptoContext</code></td>
-<td>The CryptoContext required to perform homomorphic operations in OpenFHE.</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>lhs</code></td>
-<td>A ciphertext type</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>rhs</code></td>
-<td>A ciphertext type</td>
-</tr>
-</tbody>
-</table>
-<h4 id="results-14">Results:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Result</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>output</code></td>
-<td>A ciphertext type</td>
-</tr>
-</tbody>
-</table>
-<h3 id="openfhemul-heiropenfhemulop"><code>openfhe.mul</code> (heir::openfhe::MulOp)</h3>
-<p><em>OpenFHE mul operation of two ciphertexts with relinearization.</em></p>
-<p>Syntax:</p>
-<pre tabindex="0"><code>operation ::= `openfhe.mul` operands attr-dict `:` functional-type(operands, results)
-</code></pre><p>Traits: <code>AlwaysSpeculatableImplTrait</code></p>
-<p>Interfaces: <code>ConditionallySpeculatable</code>, <code>InferTypeOpInterface</code>, <code>NoMemoryEffect (MemoryEffectOpInterface)</code>, <code>OpAsmOpInterface</code></p>
-<p>Effects: <code>MemoryEffects::Effect{}</code></p>
-<h4 id="operands-17">Operands:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Operand</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>cryptoContext</code></td>
-<td>The CryptoContext required to perform homomorphic operations in OpenFHE.</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>lhs</code></td>
-<td>A ciphertext type</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>rhs</code></td>
-<td>A ciphertext type</td>
-</tr>
-</tbody>
-</table>
-<h4 id="results-15">Results:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Result</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>output</code></td>
-<td>A ciphertext type</td>
-</tr>
-</tbody>
-</table>
-<h3 id="openfhemul_plain-heiropenfhemulplainop"><code>openfhe.mul_plain</code> (heir::openfhe::MulPlainOp)</h3>
-<p><em>OpenFHE mul operation of a ciphertext and a plaintext.</em></p>
-<p>Syntax:</p>
-<pre tabindex="0"><code>operation ::= `openfhe.mul_plain` operands attr-dict `:` functional-type(operands, results)
-</code></pre><p>Traits: <code>AlwaysSpeculatableImplTrait</code></p>
-<p>Interfaces: <code>ConditionallySpeculatable</code>, <code>InferTypeOpInterface</code>, <code>NoMemoryEffect (MemoryEffectOpInterface)</code>, <code>OpAsmOpInterface</code></p>
-<p>Effects: <code>MemoryEffects::Effect{}</code></p>
-<h4 id="operands-18">Operands:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Operand</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>cryptoContext</code></td>
-<td>The CryptoContext required to perform homomorphic operations in OpenFHE.</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>ciphertext</code></td>
-<td>A ciphertext type</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>plaintext</code></td>
-<td>A plaintext type</td>
-</tr>
-</tbody>
-</table>
-<h4 id="results-16">Results:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Result</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>output</code></td>
-<td>A ciphertext type</td>
-</tr>
-</tbody>
-</table>
-<h3 id="openfhenegate-heiropenfhenegateop"><code>openfhe.negate</code> (heir::openfhe::NegateOp)</h3>
-<p><em>OpenFHE negate operation of a ciphertext.</em></p>
-<p>Syntax:</p>
-<pre tabindex="0"><code>operation ::= `openfhe.negate` operands attr-dict `:` functional-type(operands, results)
-</code></pre><p>Traits: <code>AlwaysSpeculatableImplTrait</code></p>
-<p>Interfaces: <code>ConditionallySpeculatable</code>, <code>InferTypeOpInterface</code>, <code>NoMemoryEffect (MemoryEffectOpInterface)</code>, <code>OpAsmOpInterface</code></p>
-<p>Effects: <code>MemoryEffects::Effect{}</code></p>
-<h4 id="operands-19">Operands:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Operand</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>cryptoContext</code></td>
-<td>The CryptoContext required to perform homomorphic operations in OpenFHE.</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>ciphertext</code></td>
-<td>A ciphertext type</td>
-</tr>
-</tbody>
-</table>
-<h4 id="results-17">Results:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Result</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>output</code></td>
-<td>A ciphertext type</td>
-</tr>
-</tbody>
-</table>
-<h3 id="openfherelin-heiropenfherelinop"><code>openfhe.relin</code> (heir::openfhe::RelinOp)</h3>
-<p><em>OpenFHE relinearize operation of a ciphertext.</em></p>
-<p>Syntax:</p>
-<pre tabindex="0"><code>operation ::= `openfhe.relin` operands attr-dict `:` functional-type(operands, results)
-</code></pre><p>Traits: <code>AlwaysSpeculatableImplTrait</code></p>
-<p>Interfaces: <code>ConditionallySpeculatable</code>, <code>NoMemoryEffect (MemoryEffectOpInterface)</code>, <code>OpAsmOpInterface</code></p>
-<p>Effects: <code>MemoryEffects::Effect{}</code></p>
-<h4 id="operands-20">Operands:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Operand</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>cryptoContext</code></td>
-<td>The CryptoContext required to perform homomorphic operations in OpenFHE.</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>ciphertext</code></td>
-<td>A ciphertext type</td>
-</tr>
-</tbody>
-</table>
-<h4 id="results-18">Results:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Result</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>output</code></td>
-<td>A ciphertext type</td>
-</tr>
-</tbody>
-</table>
-<h3 id="openfherot-heiropenfherotop"><code>openfhe.rot</code> (heir::openfhe::RotOp)</h3>
-<p>Syntax:</p>
-<pre tabindex="0"><code>operation ::= `openfhe.rot` operands attr-dict `:` functional-type(operands, results)
-</code></pre><p>Traits: <code>AlwaysSpeculatableImplTrait</code></p>
-<p>Interfaces: <code>ConditionallySpeculatable</code>, <code>InferTypeOpInterface</code>, <code>NoMemoryEffect (MemoryEffectOpInterface)</code>, <code>OpAsmOpInterface</code></p>
-<p>Effects: <code>MemoryEffects::Effect{}</code></p>
-<h4 id="attributes-3">Attributes:</h4>
-<table>
-<tr><th>Attribute</th><th>MLIR Type</th><th>Description</th></tr>
-<tr><td><code>index</code></td><td>::mlir::IntegerAttr</td><td>An Attribute containing a integer value</td></tr>
-</table>
-<h4 id="operands-21">Operands:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Operand</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>cryptoContext</code></td>
-<td>The CryptoContext required to perform homomorphic operations in OpenFHE.</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>ciphertext</code></td>
-<td>A ciphertext type</td>
-</tr>
-</tbody>
-</table>
-<h4 id="results-19">Results:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Result</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>output</code></td>
-<td>A ciphertext type</td>
-</tr>
-</tbody>
-</table>
-<h3 id="openfhesetup_bootstrap-heiropenfhesetupbootstrapop"><code>openfhe.setup_bootstrap</code> (heir::openfhe::SetupBootstrapOp)</h3>
-<p>Syntax:</p>
-<pre tabindex="0"><code>operation ::= `openfhe.setup_bootstrap` operands attr-dict `:` functional-type(operands, results)
-</code></pre><p>Interfaces: <code>OpAsmOpInterface</code></p>
-<h4 id="attributes-4">Attributes:</h4>
-<table>
-<tr><th>Attribute</th><th>MLIR Type</th><th>Description</th></tr>
-<tr><td><code>levelBudgetEncode</code></td><td>::mlir::IntegerAttr</td><td>An Attribute containing a integer value</td></tr>
-<tr><td><code>levelBudgetDecode</code></td><td>::mlir::IntegerAttr</td><td>An Attribute containing a integer value</td></tr>
-</table>
-<h4 id="operands-22">Operands:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Operand</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>cryptoContext</code></td>
-<td>The CryptoContext required to perform homomorphic operations in OpenFHE.</td>
-</tr>
-</tbody>
-</table>
-<h3 id="openfhesquare-heiropenfhesquareop"><code>openfhe.square</code> (heir::openfhe::SquareOp)</h3>
-<p><em>OpenFHE square operation of a ciphertext.</em></p>
-<p>Syntax:</p>
-<pre tabindex="0"><code>operation ::= `openfhe.square` operands attr-dict `:` functional-type(operands, results)
-</code></pre><p>Traits: <code>AlwaysSpeculatableImplTrait</code></p>
-<p>Interfaces: <code>ConditionallySpeculatable</code>, <code>InferTypeOpInterface</code>, <code>NoMemoryEffect (MemoryEffectOpInterface)</code>, <code>OpAsmOpInterface</code></p>
-<p>Effects: <code>MemoryEffects::Effect{}</code></p>
-<h4 id="operands-23">Operands:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Operand</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>cryptoContext</code></td>
-<td>The CryptoContext required to perform homomorphic operations in OpenFHE.</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>ciphertext</code></td>
-<td>A ciphertext type</td>
-</tr>
-</tbody>
-</table>
-<h4 id="results-20">Results:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Result</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>output</code></td>
-<td>A ciphertext type</td>
-</tr>
-</tbody>
-</table>
-<h3 id="openfhesub-heiropenfhesubop"><code>openfhe.sub</code> (heir::openfhe::SubOp)</h3>
-<p><em>OpenFHE sub operation of two ciphertexts.</em></p>
-<p>Syntax:</p>
-<pre tabindex="0"><code>operation ::= `openfhe.sub` operands attr-dict `:` functional-type(operands, results)
-</code></pre><p>Traits: <code>AlwaysSpeculatableImplTrait</code></p>
-<p>Interfaces: <code>ConditionallySpeculatable</code>, <code>InferTypeOpInterface</code>, <code>NoMemoryEffect (MemoryEffectOpInterface)</code>, <code>OpAsmOpInterface</code></p>
-<p>Effects: <code>MemoryEffects::Effect{}</code></p>
-<h4 id="operands-24">Operands:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Operand</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>cryptoContext</code></td>
-<td>The CryptoContext required to perform homomorphic operations in OpenFHE.</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>lhs</code></td>
-<td>A ciphertext type</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>rhs</code></td>
-<td>A ciphertext type</td>
-</tr>
-</tbody>
-</table>
-<h4 id="results-21">Results:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Result</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>output</code></td>
-<td>A ciphertext type</td>
-</tr>
-</tbody>
-</table>Docs: Polynomialhttps://heir.dev/docs/dialects/polynomial/Mon, 01 Jan 0001 00:00:00 +0000https://heir.dev/docs/dialects/polynomial/
-<!-- Autogenerated by mlir-tblgen; don't manually edit -->
-<h1 id="polynomial-dialect">&lsquo;polynomial&rsquo; Dialect</h1>
-<p>The Polynomial dialect defines single-variable polynomial types and
-operations.</p>
-<p>The simplest use of <code>polynomial</code> is to represent mathematical operations in
-a polynomial ring <code>R[x]</code>, where <code>R</code> is another MLIR type like <code>i32</code>.</p>
-<p>More generally, this dialect supports representing polynomial operations in a
-quotient ring <code>R[X]/(f(x))</code> for some statically fixed polynomial <code>f(x)</code>.
-Two polyomials <code>p(x), q(x)</code> are considered equal in this ring if they have the
-same remainder when dividing by <code>f(x)</code>. When a modulus is given, ring operations
-are performed with reductions modulo <code>f(x)</code> and relative to the coefficient ring
-<code>R</code>.</p>
-<p>Examples:</p>
-<div class="highlight"><pre tabindex="0" style="background-color:#f8f8f8;-moz-tab-size:4;-o-tab-size:4;tab-size:4;"><code class="language-mlir" data-lang="mlir"><span style="display:flex;"><span><span style="color:#8f5902;font-style:italic">// A constant polynomial in a ring with i32 coefficients and no polynomial modulus
-</span></span></span><span style="display:flex;"><span><span style="color:#8f5902;font-style:italic"></span><span style="color:#000">#ring</span> <span style="color:#000;font-weight:bold">=</span> <span style="color:#000">#polynomial.ring</span><span style="color:#000;font-weight:bold">&lt;</span><span style="color:#f57900">coefficientType=</span><span style="color:#204a87;font-weight:bold">i32</span><span style="color:#000;font-weight:bold">&gt;</span>
-</span></span><span style="display:flex;"><span><span style="color:#000">%a</span> <span style="color:#000;font-weight:bold">=</span> polynomial<span style="color:#000;font-weight:bold">.</span><span style="color:#204a87;font-weight:bold">constant</span> <span style="color:#000;font-weight:bold">&lt;</span><span style="color:#0000cf;font-weight:bold">1</span> <span style="color:#a40000">+</span> <span style="color:#000;font-weight:bold">x**</span><span style="color:#0000cf;font-weight:bold">2</span> <span style="color:#a40000">-</span> <span style="color:#0000cf;font-weight:bold">3x</span><span style="color:#000;font-weight:bold">**</span><span style="color:#0000cf;font-weight:bold">3</span><span style="color:#000;font-weight:bold">&gt;</span> <span style="color:#000;font-weight:bold">:</span> polynomial<span style="color:#000;font-weight:bold">.</span>polynomial<span style="color:#000;font-weight:bold">&lt;</span><span style="color:#000">#ring</span><span style="color:#000;font-weight:bold">&gt;</span>
-</span></span><span style="display:flex;"><span>
-</span></span><span style="display:flex;"><span><span style="color:#8f5902;font-style:italic">// A constant polynomial in a ring with i32 coefficients, modulo (x^1024 + 1)
-</span></span></span><span style="display:flex;"><span><span style="color:#8f5902;font-style:italic"></span><span style="color:#000">#modulus</span> <span style="color:#000;font-weight:bold">=</span> <span style="color:#000">#polynomial.int_polynomial</span><span style="color:#000;font-weight:bold">&lt;</span><span style="color:#0000cf;font-weight:bold">1</span> <span style="color:#a40000">+</span> <span style="color:#000;font-weight:bold">x**</span><span style="color:#0000cf;font-weight:bold">1024</span><span style="color:#000;font-weight:bold">&gt;</span>
-</span></span><span style="display:flex;"><span><span style="color:#000">#ring</span> <span style="color:#000;font-weight:bold">=</span> <span style="color:#000">#polynomial.ring</span><span style="color:#000;font-weight:bold">&lt;</span><span style="color:#f57900">coefficientType=</span><span style="color:#204a87;font-weight:bold">i32</span><span style="color:#000;font-weight:bold">,</span> <span style="color:#f57900">polynomialModulus=</span><span style="color:#000">#modulus</span><span style="color:#000;font-weight:bold">&gt;</span>
-</span></span><span style="display:flex;"><span><span style="color:#000">%a</span> <span style="color:#000;font-weight:bold">=</span> polynomial<span style="color:#000;font-weight:bold">.</span><span style="color:#204a87;font-weight:bold">constant</span> <span style="color:#000;font-weight:bold">&lt;</span><span style="color:#0000cf;font-weight:bold">1</span> <span style="color:#a40000">+</span> <span style="color:#000;font-weight:bold">x**</span><span style="color:#0000cf;font-weight:bold">2</span> <span style="color:#a40000">-</span> <span style="color:#0000cf;font-weight:bold">3x</span><span style="color:#000;font-weight:bold">**</span><span style="color:#0000cf;font-weight:bold">3</span><span style="color:#000;font-weight:bold">&gt;</span> <span style="color:#000;font-weight:bold">:</span> polynomial<span style="color:#000;font-weight:bold">.</span>polynomial<span style="color:#000;font-weight:bold">&lt;</span><span style="color:#000">#ring</span><span style="color:#000;font-weight:bold">&gt;</span>
-</span></span><span style="display:flex;"><span>
-</span></span><span style="display:flex;"><span><span style="color:#8f5902;font-style:italic">// A constant polynomial in a ring with i32 coefficients, with a polynomial
-</span></span></span><span style="display:flex;"><span><span style="color:#8f5902;font-style:italic">// modulus of (x^1024 + 1) and a coefficient modulus of 17.
-</span></span></span><span style="display:flex;"><span><span style="color:#8f5902;font-style:italic"></span><span style="color:#000">#modulus</span> <span style="color:#000;font-weight:bold">=</span> <span style="color:#000">#polynomial.int_polynomial</span><span style="color:#000;font-weight:bold">&lt;</span><span style="color:#0000cf;font-weight:bold">1</span> <span style="color:#a40000">+</span> <span style="color:#000;font-weight:bold">x**</span><span style="color:#0000cf;font-weight:bold">1024</span><span style="color:#000;font-weight:bold">&gt;</span>
-</span></span><span style="display:flex;"><span><span style="color:#000;font-weight:bold">!</span><span style="color:#f57900">coeff_ty =</span> <span style="color:#000;font-weight:bold">!</span>mod_arith<span style="color:#000;font-weight:bold">.</span>mod_arith<span style="color:#000;font-weight:bold">&lt;</span><span style="color:#0000cf;font-weight:bold">17</span><span style="color:#000;font-weight:bold">:</span><span style="color:#204a87;font-weight:bold">i32</span><span style="color:#000;font-weight:bold">&gt;</span>
-</span></span><span style="display:flex;"><span><span style="color:#000">#ring</span> <span style="color:#000;font-weight:bold">=</span> <span style="color:#000">#polynomial.ring</span><span style="color:#000;font-weight:bold">&lt;</span><span style="color:#f57900">coefficientType=</span><span style="color:#000;font-weight:bold">!</span>coeff_ty<span style="color:#000;font-weight:bold">,</span> <span style="color:#f57900">polynomialModulus=</span><span style="color:#000">#modulus</span><span style="color:#000;font-weight:bold">&gt;</span>
-</span></span><span style="display:flex;"><span><span style="color:#000">%a</span> <span style="color:#000;font-weight:bold">=</span> polynomial<span style="color:#000;font-weight:bold">.</span><span style="color:#204a87;font-weight:bold">constant</span> <span style="color:#000;font-weight:bold">&lt;</span><span style="color:#0000cf;font-weight:bold">1</span> <span style="color:#a40000">+</span> <span style="color:#000;font-weight:bold">x**</span><span style="color:#0000cf;font-weight:bold">2</span> <span style="color:#a40000">-</span> <span style="color:#0000cf;font-weight:bold">3x</span><span style="color:#000;font-weight:bold">**</span><span style="color:#0000cf;font-weight:bold">3</span><span style="color:#000;font-weight:bold">&gt;</span> <span style="color:#000;font-weight:bold">:</span> polynomial<span style="color:#000;font-weight:bold">.</span>polynomial<span style="color:#000;font-weight:bold">&lt;</span><span style="color:#000">#ring</span><span style="color:#000;font-weight:bold">&gt;</span>
-</span></span></code></pre></div><h2 id="polynomial-attributes">Polynomial attributes</h2>
-<!-- Autogenerated by mlir-tblgen; don't manually edit -->
-<h3 id="floatpolynomialattr">FloatPolynomialAttr</h3>
-<p>an attribute containing a single-variable polynomial with double precision floating point coefficients</p>
-<p>A polynomial attribute represents a single-variable polynomial with double
-precision floating point coefficients.</p>
-<p>The polynomial must be expressed as a list of monomial terms, with addition
-or subtraction between them. The choice of variable name is arbitrary, but
-must be consistent across all the monomials used to define a single
-attribute. The order of monomial terms is arbitrary, each monomial degree
-must occur at most once.</p>
-<p>Example:</p>
-<div class="highlight"><pre tabindex="0" style="background-color:#f8f8f8;-moz-tab-size:4;-o-tab-size:4;tab-size:4;"><code class="language-mlir" data-lang="mlir"><span style="display:flex;"><span><span style="color:#000">#poly</span> <span style="color:#000;font-weight:bold">=</span> <span style="color:#000">#polynomial.float_polynomial</span><span style="color:#000;font-weight:bold">&lt;</span><span style="color:#0000cf;font-weight:bold">0.5</span> <span style="color:#000;font-weight:bold">x**</span><span style="color:#0000cf;font-weight:bold">7</span> <span style="color:#a40000">+</span> <span style="color:#0000cf;font-weight:bold">1.5</span><span style="color:#000;font-weight:bold">&gt;</span>
-</span></span></code></pre></div><h4 id="parameters">Parameters:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Parameter</th>
-<th style="text-align:center">C++ type</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center">polynomial</td>
-<td style="text-align:center"><code>FloatPolynomial</code></td>
-<td></td>
-</tr>
-</tbody>
-</table>
-<h3 id="intpolynomialattr">IntPolynomialAttr</h3>
-<p>an attribute containing a single-variable polynomial with integer coefficients</p>
-<p>A polynomial attribute represents a single-variable polynomial with integer
-coefficients, which is used to define the modulus of a <code>RingAttr</code>, as well
-as to define constants and perform constant folding for <code>polynomial</code> ops.</p>
-<p>The polynomial must be expressed as a list of monomial terms, with addition
-or subtraction between them. The choice of variable name is arbitrary, but
-must be consistent across all the monomials used to define a single
-attribute. The order of monomial terms is arbitrary, each monomial degree
-must occur at most once.</p>
-<p>Example:</p>
-<div class="highlight"><pre tabindex="0" style="background-color:#f8f8f8;-moz-tab-size:4;-o-tab-size:4;tab-size:4;"><code class="language-mlir" data-lang="mlir"><span style="display:flex;"><span><span style="color:#000">#poly</span> <span style="color:#000;font-weight:bold">=</span> <span style="color:#000">#polynomial.int_polynomial</span><span style="color:#000;font-weight:bold">&lt;x**</span><span style="color:#0000cf;font-weight:bold">1024</span> <span style="color:#a40000">+</span> <span style="color:#0000cf;font-weight:bold">1</span><span style="color:#000;font-weight:bold">&gt;</span>
-</span></span></code></pre></div><h4 id="parameters-1">Parameters:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Parameter</th>
-<th style="text-align:center">C++ type</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center">polynomial</td>
-<td style="text-align:center"><code>::mlir::heir::polynomial::IntPolynomial</code></td>
-<td></td>
-</tr>
-</tbody>
-</table>
-<h3 id="primitiverootattr">PrimitiveRootAttr</h3>
-<p>an attribute containing an integer and its degree as a root of unity</p>
-<p>Syntax:</p>
-<pre tabindex="0"><code>#polynomial.primitive_root&lt;
-::mlir::IntegerAttr, # value
-::mlir::IntegerAttr # degree
-&gt;
-</code></pre><p>A primitive root attribute stores an integer root <code>value</code> and an integer
-<code>degree</code>, corresponding to a primitive root of unity of the given degree in
-an unspecified ring.</p>
-<p>This is used as an attribute on <code>polynomial.ntt</code> and <code>polynomial.intt</code> ops
-to specify the root of unity used in lowering the transform.</p>
-<p>Example:</p>
-<div class="highlight"><pre tabindex="0" style="background-color:#f8f8f8;-moz-tab-size:4;-o-tab-size:4;tab-size:4;"><code class="language-mlir" data-lang="mlir"><span style="display:flex;"><span><span style="color:#000">#poly</span> <span style="color:#000;font-weight:bold">=</span> <span style="color:#000">#polynomial.primitive_root</span><span style="color:#000;font-weight:bold">&lt;</span><span style="color:#f57900">value=</span><span style="color:#0000cf;font-weight:bold">123</span> <span style="color:#000;font-weight:bold">:</span> <span style="color:#204a87;font-weight:bold">i32</span><span style="color:#000;font-weight:bold">,</span> degree <span style="color:#000;font-weight:bold">:</span> <span style="color:#0000cf;font-weight:bold">7</span> <span style="color:#204a87;font-weight:bold">index</span><span style="color:#000;font-weight:bold">&gt;</span>
-</span></span></code></pre></div><h4 id="parameters-2">Parameters:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Parameter</th>
-<th style="text-align:center">C++ type</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center">value</td>
-<td style="text-align:center"><code>::mlir::IntegerAttr</code></td>
-<td></td>
-</tr>
-<tr>
-<td style="text-align:center">degree</td>
-<td style="text-align:center"><code>::mlir::IntegerAttr</code></td>
-<td></td>
-</tr>
-</tbody>
-</table>
-<h3 id="ringattr">RingAttr</h3>
-<p>an attribute specifying a polynomial ring</p>
-<p>Syntax:</p>
-<pre tabindex="0"><code>#polynomial.ring&lt;
-Type, # coefficientType
-::mlir::heir::polynomial::IntPolynomialAttr # polynomialModulus
-&gt;
-</code></pre><p>A ring describes the domain in which polynomial arithmetic occurs. The ring
-attribute in <code>polynomial</code> represents the more specific case of polynomials
-with a single indeterminate; whose coefficients can be represented by
-another MLIR type (<code>coefficientType</code>).</p>
-<p>All semantics pertaining to arithmetic in the ring must be owned by the
-coefficient type. For example, if the polynomials are with integer
-coefficients taken modulo a prime $p$, then <code>coefficientType</code> must be a
-type that represents integers modulo $p$, such as <code>mod_arith&lt;p&gt;</code>.</p>
-<p>Additionally, a polynomial ring may specify a <code>polynomialModulus</code>, which
-converts polynomial arithmetic to the analogue of modular integer
-arithmetic, where each polynomial is represented as its remainder when
-dividing by the modulus. For single-variable polynomials, a polynomial
-modulus is always specified via a single polynomial.</p>
-<p>An expressive example is polynomials with i32 coefficients, whose
-coefficients are taken modulo <code>2**32 - 5</code>, with a polynomial modulus of
-<code>x**1024 - 1</code>.</p>
-<div class="highlight"><pre tabindex="0" style="background-color:#f8f8f8;-moz-tab-size:4;-o-tab-size:4;tab-size:4;"><code class="language-mlir" data-lang="mlir"><span style="display:flex;"><span><span style="color:#000">#poly_mod</span> <span style="color:#000;font-weight:bold">=</span> <span style="color:#000">#polynomial.int_polynomial</span><span style="color:#000;font-weight:bold">&lt;</span><span style="color:#0000cf;font-weight:bold">-1</span> <span style="color:#a40000">+</span> <span style="color:#000;font-weight:bold">x**</span><span style="color:#0000cf;font-weight:bold">1024</span><span style="color:#000;font-weight:bold">&gt;</span>
-</span></span><span style="display:flex;"><span><span style="color:#000">#ring</span> <span style="color:#000;font-weight:bold">=</span> <span style="color:#000">#polynomial.ring</span><span style="color:#000;font-weight:bold">&lt;</span><span style="color:#f57900">coefficientType=</span><span style="color:#204a87;font-weight:bold">i32</span><span style="color:#000;font-weight:bold">,</span> <span style="color:#f57900">polynomialModulus=</span><span style="color:#000">#poly_mod</span><span style="color:#000;font-weight:bold">&gt;</span>
-</span></span><span style="display:flex;"><span>
-</span></span><span style="display:flex;"><span><span style="color:#000">%0</span> <span style="color:#000;font-weight:bold">=</span> <span style="color:#000;font-weight:bold">...</span> <span style="color:#000;font-weight:bold">:</span> polynomial<span style="color:#000;font-weight:bold">.</span>polynomial<span style="color:#000;font-weight:bold">&lt;</span><span style="color:#000">#ring</span><span style="color:#000;font-weight:bold">&gt;</span>
-</span></span></code></pre></div><p>In this case, the value of a polynomial is always &ldquo;converted&rdquo; to a
-canonical form by applying repeated reductions by setting <code>x**1024 = 1</code>
-and simplifying.</p>
-<h4 id="parameters-3">Parameters:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Parameter</th>
-<th style="text-align:center">C++ type</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center">coefficientType</td>
-<td style="text-align:center"><code>Type</code></td>
-<td></td>
-</tr>
-<tr>
-<td style="text-align:center">polynomialModulus</td>
-<td style="text-align:center"><code>::mlir::heir::polynomial::IntPolynomialAttr</code></td>
-<td></td>
-</tr>
-</tbody>
-</table>
-<h3 id="typedfloatpolynomialattr">TypedFloatPolynomialAttr</h3>
-<p>a typed float_polynomial</p>
-<p>Syntax:</p>
-<pre tabindex="0"><code>#polynomial.typed_float_polynomial&lt;
-::mlir::Type, # type
-::mlir::heir::polynomial::FloatPolynomialAttr # value
-&gt;
-</code></pre><p>Example:</p>
-<div class="highlight"><pre tabindex="0" style="background-color:#f8f8f8;-moz-tab-size:4;-o-tab-size:4;tab-size:4;"><code class="language-mlir" data-lang="mlir"><span style="display:flex;"><span><span style="color:#000;font-weight:bold">!</span><span style="color:#f57900">poly_ty =</span> <span style="color:#000;font-weight:bold">!</span>polynomial<span style="color:#000;font-weight:bold">.</span>polynomial<span style="color:#000;font-weight:bold">&lt;</span><span style="color:#f57900">ring=</span><span style="color:#000;font-weight:bold">&lt;</span><span style="color:#f57900">coefficientType=</span><span style="color:#204a87;font-weight:bold">f32</span><span style="color:#000;font-weight:bold">&gt;&gt;</span>
-</span></span><span style="display:flex;"><span><span style="color:#000">#poly</span> <span style="color:#000;font-weight:bold">=</span> float<span style="color:#000;font-weight:bold">&lt;</span><span style="color:#0000cf;font-weight:bold">1.4</span> <span style="color:#000;font-weight:bold">x**</span><span style="color:#0000cf;font-weight:bold">7</span> <span style="color:#a40000">+</span> <span style="color:#0000cf;font-weight:bold">4.5</span><span style="color:#000;font-weight:bold">&gt;</span> <span style="color:#000;font-weight:bold">:</span> <span style="color:#000;font-weight:bold">!</span>poly_ty
-</span></span><span style="display:flex;"><span><span style="color:#000">#poly_verbose</span> <span style="color:#000;font-weight:bold">=</span> <span style="color:#000">#polynomial.typed_float_polynomial</span><span style="color:#000;font-weight:bold">&lt;</span><span style="color:#0000cf;font-weight:bold">1.4</span> <span style="color:#000;font-weight:bold">x**</span><span style="color:#0000cf;font-weight:bold">7</span> <span style="color:#a40000">+</span> <span style="color:#0000cf;font-weight:bold">4.5</span><span style="color:#000;font-weight:bold">&gt;</span> <span style="color:#000;font-weight:bold">:</span> <span style="color:#000;font-weight:bold">!</span>poly_ty
-</span></span></code></pre></div><h4 id="parameters-4">Parameters:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Parameter</th>
-<th style="text-align:center">C++ type</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center">type</td>
-<td style="text-align:center"><code>::mlir::Type</code></td>
-<td></td>
-</tr>
-<tr>
-<td style="text-align:center">value</td>
-<td style="text-align:center"><code>::mlir::heir::polynomial::FloatPolynomialAttr</code></td>
-<td></td>
-</tr>
-</tbody>
-</table>
-<h3 id="typedintpolynomialattr">TypedIntPolynomialAttr</h3>
-<p>a typed int_polynomial</p>
-<p>Syntax:</p>
-<pre tabindex="0"><code>#polynomial.typed_int_polynomial&lt;
-::mlir::Type, # type
-::mlir::heir::polynomial::IntPolynomialAttr # value
-&gt;
-</code></pre><p>Example:</p>
-<div class="highlight"><pre tabindex="0" style="background-color:#f8f8f8;-moz-tab-size:4;-o-tab-size:4;tab-size:4;"><code class="language-mlir" data-lang="mlir"><span style="display:flex;"><span><span style="color:#000;font-weight:bold">!</span><span style="color:#f57900">poly_ty =</span> <span style="color:#000;font-weight:bold">!</span>polynomial<span style="color:#000;font-weight:bold">.</span>polynomial<span style="color:#000;font-weight:bold">&lt;</span><span style="color:#f57900">ring=</span><span style="color:#000;font-weight:bold">&lt;</span><span style="color:#f57900">coefficientType=</span><span style="color:#204a87;font-weight:bold">i32</span><span style="color:#000;font-weight:bold">&gt;&gt;</span>
-</span></span><span style="display:flex;"><span><span style="color:#000">#poly</span> <span style="color:#000;font-weight:bold">=</span> int<span style="color:#000;font-weight:bold">&lt;</span><span style="color:#0000cf;font-weight:bold">1 x</span><span style="color:#000;font-weight:bold">**</span><span style="color:#0000cf;font-weight:bold">7</span> <span style="color:#a40000">+</span> <span style="color:#0000cf;font-weight:bold">4</span><span style="color:#000;font-weight:bold">&gt;</span> <span style="color:#000;font-weight:bold">:</span> <span style="color:#000;font-weight:bold">!</span>poly_ty
-</span></span><span style="display:flex;"><span><span style="color:#000">#poly_verbose</span> <span style="color:#000;font-weight:bold">=</span> <span style="color:#000">#polynomial.typed_int_polynomial</span><span style="color:#000;font-weight:bold">&lt;</span><span style="color:#0000cf;font-weight:bold">1 x</span><span style="color:#000;font-weight:bold">**</span><span style="color:#0000cf;font-weight:bold">7</span> <span style="color:#a40000">+</span> <span style="color:#0000cf;font-weight:bold">4</span><span style="color:#000;font-weight:bold">&gt;</span> <span style="color:#000;font-weight:bold">:</span> <span style="color:#000;font-weight:bold">!</span>poly_ty
-</span></span></code></pre></div><h4 id="parameters-5">Parameters:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Parameter</th>
-<th style="text-align:center">C++ type</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center">type</td>
-<td style="text-align:center"><code>::mlir::Type</code></td>
-<td></td>
-</tr>
-<tr>
-<td style="text-align:center">value</td>
-<td style="text-align:center"><code>::mlir::heir::polynomial::IntPolynomialAttr</code></td>
-<td></td>
-</tr>
-</tbody>
-</table>
-<h2 id="polynomial-types">Polynomial types</h2>
-<!-- Autogenerated by mlir-tblgen; don't manually edit -->
-<h3 id="polynomialtype">PolynomialType</h3>
-<p>An element of a polynomial ring.</p>
-<p>Syntax:</p>
-<pre tabindex="0"><code>!polynomial.polynomial&lt;
-::mlir::heir::polynomial::RingAttr # ring
-&gt;
-</code></pre><p>A type for polynomials in a polynomial quotient ring.</p>
-<h4 id="parameters-6">Parameters:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Parameter</th>
-<th style="text-align:center">C++ type</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center">ring</td>
-<td style="text-align:center"><code>::mlir::heir::polynomial::RingAttr</code></td>
-<td>an attribute specifying a polynomial ring</td>
-</tr>
-</tbody>
-</table>
-<h2 id="polynomial-ops">Polynomial ops</h2>
-<!-- Autogenerated by mlir-tblgen; don't manually edit -->
-<h3 id="polynomialadd-heirpolynomialaddop"><code>polynomial.add</code> (heir::polynomial::AddOp)</h3>
-<p><em>Addition operation between polynomials.</em></p>
-<p>Syntax:</p>
-<pre tabindex="0"><code>operation ::= `polynomial.add` operands attr-dict `:` type($result)
-</code></pre><p>Performs polynomial addition on the operands. The operands may be single
-polynomials or containers of identically-typed polynomials, i.e., polynomials
-from the same underlying ring with the same coefficient types.</p>
-<p>This op is defined to occur in the ring defined by the ring attribute of
-the two operands, meaning the arithmetic is taken modulo the
-polynomialModulus of the ring as well as modulo any semantics defined by
-the coefficient type.</p>
-<p>Example:</p>
-<div class="highlight"><pre tabindex="0" style="background-color:#f8f8f8;-moz-tab-size:4;-o-tab-size:4;tab-size:4;"><code class="language-mlir" data-lang="mlir"><span style="display:flex;"><span><span style="color:#8f5902;font-style:italic">// add two polynomials modulo x^1024 - 1
-</span></span></span><span style="display:flex;"><span><span style="color:#8f5902;font-style:italic"></span><span style="color:#000">#poly</span> <span style="color:#000;font-weight:bold">=</span> <span style="color:#000">#polynomial.int_polynomial</span><span style="color:#000;font-weight:bold">&lt;x**</span><span style="color:#0000cf;font-weight:bold">1024</span> <span style="color:#a40000">-</span> <span style="color:#0000cf;font-weight:bold">1</span><span style="color:#000;font-weight:bold">&gt;</span>
-</span></span><span style="display:flex;"><span><span style="color:#000">#ring</span> <span style="color:#000;font-weight:bold">=</span> <span style="color:#000">#polynomial.ring</span><span style="color:#000;font-weight:bold">&lt;</span><span style="color:#f57900">coefficientType=</span><span style="color:#204a87;font-weight:bold">i32</span><span style="color:#000;font-weight:bold">,</span> <span style="color:#f57900">polynomialModulus=</span><span style="color:#000">#poly</span><span style="color:#000;font-weight:bold">&gt;</span>
-</span></span><span style="display:flex;"><span><span style="color:#000">%0</span> <span style="color:#000;font-weight:bold">=</span> polynomial<span style="color:#000;font-weight:bold">.</span><span style="color:#204a87;font-weight:bold">constant</span> int<span style="color:#000;font-weight:bold">&lt;</span><span style="color:#0000cf;font-weight:bold">1</span> <span style="color:#a40000">+</span> <span style="color:#000;font-weight:bold">x**</span><span style="color:#0000cf;font-weight:bold">2</span><span style="color:#000;font-weight:bold">&gt;</span> <span style="color:#000;font-weight:bold">:</span> <span style="color:#000;font-weight:bold">!</span>polynomial<span style="color:#000;font-weight:bold">.</span>polynomial<span style="color:#000;font-weight:bold">&lt;</span><span style="color:#000">#ring</span><span style="color:#000;font-weight:bold">&gt;</span>
-</span></span><span style="display:flex;"><span><span style="color:#000">%1</span> <span style="color:#000;font-weight:bold">=</span> polynomial<span style="color:#000;font-weight:bold">.</span><span style="color:#204a87;font-weight:bold">constant</span> int<span style="color:#000;font-weight:bold">&lt;x**</span><span style="color:#0000cf;font-weight:bold">5</span> <span style="color:#a40000">-</span> <span style="color:#000;font-weight:bold">x</span> <span style="color:#a40000">+</span> <span style="color:#0000cf;font-weight:bold">1</span><span style="color:#000;font-weight:bold">&gt;</span> <span style="color:#000;font-weight:bold">:</span> <span style="color:#000;font-weight:bold">!</span>polynomial<span style="color:#000;font-weight:bold">.</span>polynomial<span style="color:#000;font-weight:bold">&lt;</span><span style="color:#000">#ring</span><span style="color:#000;font-weight:bold">&gt;</span>
-</span></span><span style="display:flex;"><span><span style="color:#000">%2</span> <span style="color:#000;font-weight:bold">=</span> polynomial<span style="color:#000;font-weight:bold">.</span>add <span style="color:#000">%0</span><span style="color:#000;font-weight:bold">,</span> <span style="color:#000">%1</span> <span style="color:#000;font-weight:bold">:</span> <span style="color:#000;font-weight:bold">!</span>polynomial<span style="color:#000;font-weight:bold">.</span>polynomial<span style="color:#000;font-weight:bold">&lt;</span><span style="color:#000">#ring</span><span style="color:#000;font-weight:bold">&gt;</span>
-</span></span></code></pre></div><p>Traits: <code>AlwaysSpeculatableImplTrait</code>, <code>Commutative</code>, <code>Elementwise</code>, <code>SameOperandsAndResultType</code>, <code>Scalarizable</code>, <code>Tensorizable</code>, <code>Vectorizable</code></p>
-<p>Interfaces: <code>ConditionallySpeculatable</code>, <code>InferTypeOpInterface</code>, <code>NoMemoryEffect (MemoryEffectOpInterface)</code></p>
-<p>Effects: <code>MemoryEffects::Effect{}</code></p>
-<h4 id="operands">Operands:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Operand</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>lhs</code></td>
-<td>polynomial-like</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>rhs</code></td>
-<td>polynomial-like</td>
-</tr>
-</tbody>
-</table>
-<h4 id="results">Results:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Result</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>result</code></td>
-<td>polynomial-like</td>
-</tr>
-</tbody>
-</table>
-<h3 id="polynomialconstant-heirpolynomialconstantop"><code>polynomial.constant</code> (heir::polynomial::ConstantOp)</h3>
-<p><em>Define a constant polynomial via an attribute.</em></p>
-<p>Example:</p>
-<div class="highlight"><pre tabindex="0" style="background-color:#f8f8f8;-moz-tab-size:4;-o-tab-size:4;tab-size:4;"><code class="language-mlir" data-lang="mlir"><span style="display:flex;"><span><span style="color:#000;font-weight:bold">!</span><span style="color:#f57900">int_poly_ty =</span> <span style="color:#000;font-weight:bold">!</span>polynomial<span style="color:#000;font-weight:bold">.</span>polynomial<span style="color:#000;font-weight:bold">&lt;</span><span style="color:#f57900">ring=</span><span style="color:#000;font-weight:bold">&lt;</span><span style="color:#f57900">coefficientType=</span><span style="color:#204a87;font-weight:bold">i32</span><span style="color:#000;font-weight:bold">&gt;&gt;</span>
-</span></span><span style="display:flex;"><span><span style="color:#000">%0</span> <span style="color:#000;font-weight:bold">=</span> polynomial<span style="color:#000;font-weight:bold">.</span><span style="color:#204a87;font-weight:bold">constant</span> int<span style="color:#000;font-weight:bold">&lt;</span><span style="color:#0000cf;font-weight:bold">1</span> <span style="color:#a40000">+</span> <span style="color:#000;font-weight:bold">x**</span><span style="color:#0000cf;font-weight:bold">2</span><span style="color:#000;font-weight:bold">&gt;</span> <span style="color:#000;font-weight:bold">:</span> <span style="color:#000;font-weight:bold">!</span>int_poly_ty
-</span></span><span style="display:flex;"><span>
-</span></span><span style="display:flex;"><span><span style="color:#000;font-weight:bold">!</span><span style="color:#f57900">float_poly_ty =</span> <span style="color:#000;font-weight:bold">!</span>polynomial<span style="color:#000;font-weight:bold">.</span>polynomial<span style="color:#000;font-weight:bold">&lt;</span><span style="color:#f57900">ring=</span><span style="color:#000;font-weight:bold">&lt;</span><span style="color:#f57900">coefficientType=</span><span style="color:#204a87;font-weight:bold">f32</span><span style="color:#000;font-weight:bold">&gt;&gt;</span>
-</span></span><span style="display:flex;"><span><span style="color:#000">%1</span> <span style="color:#000;font-weight:bold">=</span> polynomial<span style="color:#000;font-weight:bold">.</span><span style="color:#204a87;font-weight:bold">constant</span> float<span style="color:#000;font-weight:bold">&lt;</span><span style="color:#0000cf;font-weight:bold">0.5</span> <span style="color:#a40000">+</span> <span style="color:#0000cf;font-weight:bold">1.3e06</span> <span style="color:#000;font-weight:bold">x**</span><span style="color:#0000cf;font-weight:bold">2</span><span style="color:#000;font-weight:bold">&gt;</span> <span style="color:#000;font-weight:bold">:</span> <span style="color:#000;font-weight:bold">!</span>float_poly_ty
-</span></span></code></pre></div><p>Traits: <code>AlwaysSpeculatableImplTrait</code>, <code>InferTypeOpAdaptor</code></p>
-<p>Interfaces: <code>ConditionallySpeculatable</code>, <code>InferTypeOpInterface</code>, <code>NoMemoryEffect (MemoryEffectOpInterface)</code></p>
-<p>Effects: <code>MemoryEffects::Effect{}</code></p>
-<h4 id="attributes">Attributes:</h4>
-<table>
-<tr><th>Attribute</th><th>MLIR Type</th><th>Description</th></tr>
-<tr><td><code>value</code></td><td>::mlir::Attribute</td><td>a typed float_polynomial or a typed int_polynomial</td></tr>
-</table>
-<h4 id="results-1">Results:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Result</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>output</code></td>
-<td>An element of a polynomial ring.</td>
-</tr>
-</tbody>
-</table>
-<h3 id="polynomialfrom_tensor-heirpolynomialfromtensorop"><code>polynomial.from_tensor</code> (heir::polynomial::FromTensorOp)</h3>
-<p><em>Creates a polynomial from integer coefficients stored in a tensor.</em></p>
-<p>Syntax:</p>
-<pre tabindex="0"><code>operation ::= `polynomial.from_tensor` $input attr-dict `:` type($input) `-&gt;` type($output)
-</code></pre><p><code>polynomial.from_tensor</code> creates a polynomial value from a tensor of coefficients.
-The input tensor must list the coefficients in degree-increasing order.</p>
-<p>The input one-dimensional tensor may have size at most the degree of the
-ring&rsquo;s polynomialModulus generator polynomial, with smaller dimension implying that
-all higher-degree terms have coefficient zero.</p>
-<p>Example:</p>
-<div class="highlight"><pre tabindex="0" style="background-color:#f8f8f8;-moz-tab-size:4;-o-tab-size:4;tab-size:4;"><code class="language-mlir" data-lang="mlir"><span style="display:flex;"><span><span style="color:#000">#poly</span> <span style="color:#000;font-weight:bold">=</span> <span style="color:#000">#polynomial.int_polynomial</span><span style="color:#000;font-weight:bold">&lt;x**</span><span style="color:#0000cf;font-weight:bold">1024</span> <span style="color:#a40000">-</span> <span style="color:#0000cf;font-weight:bold">1</span><span style="color:#000;font-weight:bold">&gt;</span>
-</span></span><span style="display:flex;"><span><span style="color:#000">#ring</span> <span style="color:#000;font-weight:bold">=</span> <span style="color:#000">#polynomial.ring</span><span style="color:#000;font-weight:bold">&lt;</span><span style="color:#f57900">coefficientType=</span><span style="color:#204a87;font-weight:bold">i32</span><span style="color:#000;font-weight:bold">,</span> <span style="color:#f57900">polynomialModulus=</span><span style="color:#000">#poly</span><span style="color:#000;font-weight:bold">&gt;</span>
-</span></span><span style="display:flex;"><span><span style="color:#000">%two</span> <span style="color:#000;font-weight:bold">=</span> arith<span style="color:#000;font-weight:bold">.</span><span style="color:#204a87;font-weight:bold">constant</span> <span style="color:#0000cf;font-weight:bold">2</span> <span style="color:#000;font-weight:bold">:</span> <span style="color:#204a87;font-weight:bold">i32</span>
-</span></span><span style="display:flex;"><span><span style="color:#000">%five</span> <span style="color:#000;font-weight:bold">=</span> arith<span style="color:#000;font-weight:bold">.</span><span style="color:#204a87;font-weight:bold">constant</span> <span style="color:#0000cf;font-weight:bold">5</span> <span style="color:#000;font-weight:bold">:</span> <span style="color:#204a87;font-weight:bold">i32</span>
-</span></span><span style="display:flex;"><span><span style="color:#000">%coeffs</span> <span style="color:#000;font-weight:bold">=</span> <span style="color:#204a87;font-weight:bold">tensor</span><span style="color:#000;font-weight:bold">.</span>from_elements <span style="color:#000">%two</span><span style="color:#000;font-weight:bold">,</span> <span style="color:#000">%two</span><span style="color:#000;font-weight:bold">,</span> <span style="color:#000">%five</span> <span style="color:#000;font-weight:bold">:</span> <span style="color:#204a87;font-weight:bold">tensor</span><span style="color:#000;font-weight:bold">&lt;</span><span style="color:#0000cf;font-weight:bold">3x</span><span style="color:#204a87;font-weight:bold">i32</span><span style="color:#000;font-weight:bold">&gt;</span>
-</span></span><span style="display:flex;"><span><span style="color:#000">%poly</span> <span style="color:#000;font-weight:bold">=</span> polynomial<span style="color:#000;font-weight:bold">.</span>from_tensor <span style="color:#000">%coeffs</span> <span style="color:#000;font-weight:bold">:</span> <span style="color:#204a87;font-weight:bold">tensor</span><span style="color:#000;font-weight:bold">&lt;</span><span style="color:#0000cf;font-weight:bold">3x</span><span style="color:#204a87;font-weight:bold">i32</span><span style="color:#000;font-weight:bold">&gt;</span> <span style="color:#000;font-weight:bold">-&gt;</span> <span style="color:#000;font-weight:bold">!</span>polynomial<span style="color:#000;font-weight:bold">.</span>polynomial<span style="color:#000;font-weight:bold">&lt;</span><span style="color:#000">#ring</span><span style="color:#000;font-weight:bold">&gt;</span>
-</span></span></code></pre></div><p>Traits: <code>AlwaysSpeculatableImplTrait</code></p>
-<p>Interfaces: <code>ConditionallySpeculatable</code>, <code>NoMemoryEffect (MemoryEffectOpInterface)</code></p>
-<p>Effects: <code>MemoryEffects::Effect{}</code></p>
-<h4 id="operands-1">Operands:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Operand</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>input</code></td>
-<td>ranked tensor of any type values</td>
-</tr>
-</tbody>
-</table>
-<h4 id="results-2">Results:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Result</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>output</code></td>
-<td>An element of a polynomial ring.</td>
-</tr>
-</tbody>
-</table>
-<h3 id="polynomialintt-heirpolynomialinttop"><code>polynomial.intt</code> (heir::polynomial::INTTOp)</h3>
-<p><em>Computes the reverse integer Number Theoretic Transform (NTT).</em></p>
-<p>Syntax:</p>
-<pre tabindex="0"><code>operation ::= `polynomial.intt` $input attr-dict `:` qualified(type($input)) `-&gt;` type($output)
-</code></pre><p><code>polynomial.intt</code> computes the reverse integer Number Theoretic Transform
-(INTT) on the input tensor. This is the inverse operation of the
-<code>polynomial.ntt</code> operation.</p>
-<p>The input tensor is interpreted as a point-value representation of the
-output polynomial at powers of a primitive <code>n</code>-th root of unity (see
-<code>polynomial.ntt</code>). The ring of the polynomial is taken from the required
-encoding attribute of the tensor.</p>
-<p>The choice of primitive root may be optionally specified.</p>
-<p>Traits: <code>AlwaysSpeculatableImplTrait</code></p>
-<p>Interfaces: <code>ConditionallySpeculatable</code>, <code>NoMemoryEffect (MemoryEffectOpInterface)</code></p>
-<p>Effects: <code>MemoryEffects::Effect{}</code></p>
-<h4 id="attributes-1">Attributes:</h4>
-<table>
-<tr><th>Attribute</th><th>MLIR Type</th><th>Description</th></tr>
-<tr><td><code>root</code></td><td>::mlir::heir::polynomial::PrimitiveRootAttr</td><td>an attribute containing an integer and its degree as a root of unity</td></tr>
-</table>
-<h4 id="operands-2">Operands:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Operand</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>input</code></td>
-<td>ranked tensor of Integer type with modular arithmetic values</td>
-</tr>
-</tbody>
-</table>
-<h4 id="results-3">Results:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Result</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>output</code></td>
-<td>An element of a polynomial ring.</td>
-</tr>
-</tbody>
-</table>
-<h3 id="polynomialleading_term-heirpolynomialleadingtermop"><code>polynomial.leading_term</code> (heir::polynomial::LeadingTermOp)</h3>
-<p><em>Compute the leading term of the polynomial.</em></p>
-<p>Syntax:</p>
-<pre tabindex="0"><code>operation ::= `polynomial.leading_term` operands attr-dict `:` type($input) `-&gt;` `(` type($degree) `,` type($coefficient) `)`
-</code></pre><p>The degree of a polynomial is the largest $k$ for which the coefficient
-<code>a_k</code> of <code>x^k</code> is nonzero. The leading term is the term <code>a_k * x^k</code>, which
-this op represents as a pair of results. The first is the degree <code>k</code> as an
-index, and the second is the coefficient, whose type matches the
-coefficient type of the polynomial&rsquo;s ring attribute.</p>
-<p>Example:</p>
-<div class="highlight"><pre tabindex="0" style="background-color:#f8f8f8;-moz-tab-size:4;-o-tab-size:4;tab-size:4;"><code class="language-mlir" data-lang="mlir"><span style="display:flex;"><span><span style="color:#000">#poly</span> <span style="color:#000;font-weight:bold">=</span> <span style="color:#000">#polynomial.int_polynomial</span><span style="color:#000;font-weight:bold">&lt;x**</span><span style="color:#0000cf;font-weight:bold">1024</span> <span style="color:#a40000">-</span> <span style="color:#0000cf;font-weight:bold">1</span><span style="color:#000;font-weight:bold">&gt;</span>
-</span></span><span style="display:flex;"><span><span style="color:#000">#ring</span> <span style="color:#000;font-weight:bold">=</span> <span style="color:#000">#polynomial.ring</span><span style="color:#000;font-weight:bold">&lt;</span><span style="color:#f57900">coefficientType=</span><span style="color:#204a87;font-weight:bold">i32</span><span style="color:#000;font-weight:bold">,</span> <span style="color:#f57900">polynomialModulus=</span><span style="color:#000">#poly</span><span style="color:#000;font-weight:bold">&gt;</span>
-</span></span><span style="display:flex;"><span><span style="color:#000">%0</span> <span style="color:#000;font-weight:bold">=</span> polynomial<span style="color:#000;font-weight:bold">.</span><span style="color:#204a87;font-weight:bold">constant</span> int<span style="color:#000;font-weight:bold">&lt;</span><span style="color:#0000cf;font-weight:bold">1</span> <span style="color:#a40000">+</span> <span style="color:#000;font-weight:bold">x**</span><span style="color:#0000cf;font-weight:bold">2</span><span style="color:#000;font-weight:bold">&gt;</span> <span style="color:#000;font-weight:bold">:</span> <span style="color:#000;font-weight:bold">!</span>polynomial<span style="color:#000;font-weight:bold">.</span>polynomial<span style="color:#000;font-weight:bold">&lt;</span><span style="color:#000">#ring</span><span style="color:#000;font-weight:bold">&gt;</span>
-</span></span><span style="display:flex;"><span><span style="color:#000">%1</span><span style="color:#000;font-weight:bold">,</span> <span style="color:#000">%2</span> <span style="color:#000;font-weight:bold">=</span> polynomial<span style="color:#000;font-weight:bold">.</span>leading_term <span style="color:#000">%0</span> <span style="color:#000;font-weight:bold">:</span> <span style="color:#000;font-weight:bold">!</span>polynomial<span style="color:#000;font-weight:bold">.</span>polynomial<span style="color:#000;font-weight:bold">&lt;</span><span style="color:#000">#ring</span><span style="color:#000;font-weight:bold">&gt;</span> <span style="color:#000;font-weight:bold">-&gt;</span> <span style="color:#000;font-weight:bold">(</span><span style="color:#204a87;font-weight:bold">index</span><span style="color:#000;font-weight:bold">,</span> <span style="color:#204a87;font-weight:bold">i32</span><span style="color:#000;font-weight:bold">)</span>
-</span></span></code></pre></div><p>Traits: <code>AlwaysSpeculatableImplTrait</code></p>
-<p>Interfaces: <code>ConditionallySpeculatable</code>, <code>NoMemoryEffect (MemoryEffectOpInterface)</code></p>
-<p>Effects: <code>MemoryEffects::Effect{}</code></p>
-<h4 id="operands-3">Operands:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Operand</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>input</code></td>
-<td>An element of a polynomial ring.</td>
-</tr>
-</tbody>
-</table>
-<h4 id="results-4">Results:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Result</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>degree</code></td>
-<td>index</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>coefficient</code></td>
-<td>any type</td>
-</tr>
-</tbody>
-</table>
-<h3 id="polynomialmonic_monomial_mul-heirpolynomialmonicmonomialmulop"><code>polynomial.monic_monomial_mul</code> (heir::polynomial::MonicMonomialMulOp)</h3>
-<p><em>Multiply a polynomial by a monic monomial.</em></p>
-<p>Syntax:</p>
-<pre tabindex="0"><code>operation ::= `polynomial.monic_monomial_mul` operands attr-dict `:` functional-type(operands, results)
-</code></pre><p>Multiply a polynomial by a monic monomial, meaning a polynomial of the form
-<code>1 * x^k</code> for an index operand <code>k</code>.</p>
-<p>In some special rings of polynomials, such as a ring of polynomials
-modulo <code>x^n - 1</code>, <code>monomial_mul</code> can be interpreted as a cyclic shift of
-the coefficients of the polynomial. For some rings, this results in
-optimized lowerings that involve rotations and rescaling of the
-coefficients of the input.</p>
-<p>Traits: <code>AlwaysSpeculatableImplTrait</code></p>
-<p>Interfaces: <code>ConditionallySpeculatable</code>, <code>InferTypeOpInterface</code>, <code>NoMemoryEffect (MemoryEffectOpInterface)</code></p>
-<p>Effects: <code>MemoryEffects::Effect{}</code></p>
-<h4 id="operands-4">Operands:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Operand</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>input</code></td>
-<td>polynomial-like</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>monomialDegree</code></td>
-<td>index</td>
-</tr>
-</tbody>
-</table>
-<h4 id="results-5">Results:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Result</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>output</code></td>
-<td>polynomial-like</td>
-</tr>
-</tbody>
-</table>
-<h3 id="polynomialmonomial-heirpolynomialmonomialop"><code>polynomial.monomial</code> (heir::polynomial::MonomialOp)</h3>
-<p><em>Create a polynomial that consists of a single monomial.</em></p>
-<p>Syntax:</p>
-<pre tabindex="0"><code>operation ::= `polynomial.monomial` operands attr-dict `:` functional-type(operands, results)
-</code></pre><p>Construct a polynomial that consists of a single monomial term, from its
-degree and coefficient as dynamic inputs.</p>
-<p>The coefficient type of the output polynomial&rsquo;s ring attribute must match
-the <code>coefficient</code> input type.</p>
-<p>Example:</p>
-<div class="highlight"><pre tabindex="0" style="background-color:#f8f8f8;-moz-tab-size:4;-o-tab-size:4;tab-size:4;"><code class="language-mlir" data-lang="mlir"><span style="display:flex;"><span><span style="color:#000">#poly</span> <span style="color:#000;font-weight:bold">=</span> <span style="color:#000">#polynomial.int_polynomial</span><span style="color:#000;font-weight:bold">&lt;x**</span><span style="color:#0000cf;font-weight:bold">1024</span> <span style="color:#a40000">-</span> <span style="color:#0000cf;font-weight:bold">1</span><span style="color:#000;font-weight:bold">&gt;</span>
-</span></span><span style="display:flex;"><span><span style="color:#000">#ring</span> <span style="color:#000;font-weight:bold">=</span> <span style="color:#000">#polynomial.ring</span><span style="color:#000;font-weight:bold">&lt;</span><span style="color:#f57900">coefficientType=</span><span style="color:#204a87;font-weight:bold">i32</span><span style="color:#000;font-weight:bold">,</span> <span style="color:#f57900">polynomialModulus=</span><span style="color:#000">#poly</span><span style="color:#000;font-weight:bold">&gt;</span>
-</span></span><span style="display:flex;"><span><span style="color:#000">%deg</span> <span style="color:#000;font-weight:bold">=</span> arith<span style="color:#000;font-weight:bold">.</span><span style="color:#204a87;font-weight:bold">constant</span> <span style="color:#0000cf;font-weight:bold">1023</span> <span style="color:#000;font-weight:bold">:</span> <span style="color:#204a87;font-weight:bold">index</span>
-</span></span><span style="display:flex;"><span><span style="color:#000">%five</span> <span style="color:#000;font-weight:bold">=</span> arith<span style="color:#000;font-weight:bold">.</span><span style="color:#204a87;font-weight:bold">constant</span> <span style="color:#0000cf;font-weight:bold">5</span> <span style="color:#000;font-weight:bold">:</span> <span style="color:#204a87;font-weight:bold">i32</span>
-</span></span><span style="display:flex;"><span><span style="color:#000">%0</span> <span style="color:#000;font-weight:bold">=</span> polynomial<span style="color:#000;font-weight:bold">.</span>monomial <span style="color:#000">%five</span><span style="color:#000;font-weight:bold">,</span> <span style="color:#000">%deg</span> <span style="color:#000;font-weight:bold">:</span> <span style="color:#000;font-weight:bold">(</span><span style="color:#204a87;font-weight:bold">i32</span><span style="color:#000;font-weight:bold">,</span> <span style="color:#204a87;font-weight:bold">index</span><span style="color:#000;font-weight:bold">)</span> <span style="color:#000;font-weight:bold">-&gt;</span> <span style="color:#000;font-weight:bold">!</span>polynomial<span style="color:#000;font-weight:bold">.</span>polynomial<span style="color:#000;font-weight:bold">&lt;</span><span style="color:#000">#ring</span><span style="color:#000;font-weight:bold">&gt;</span>
-</span></span></code></pre></div><p>Traits: <code>AlwaysSpeculatableImplTrait</code></p>
-<p>Interfaces: <code>ConditionallySpeculatable</code>, <code>NoMemoryEffect (MemoryEffectOpInterface)</code></p>
-<p>Effects: <code>MemoryEffects::Effect{}</code></p>
-<h4 id="operands-5">Operands:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Operand</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>coefficient</code></td>
-<td>any type</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>degree</code></td>
-<td>index</td>
-</tr>
-</tbody>
-</table>
-<h4 id="results-6">Results:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Result</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>output</code></td>
-<td>An element of a polynomial ring.</td>
-</tr>
-</tbody>
-</table>
-<h3 id="polynomialmul-heirpolynomialmulop"><code>polynomial.mul</code> (heir::polynomial::MulOp)</h3>
-<p><em>Multiplication operation between polynomials.</em></p>
-<p>Syntax:</p>
-<pre tabindex="0"><code>operation ::= `polynomial.mul` operands attr-dict `:` type($result)
-</code></pre><p>Performs polynomial multiplication on the operands. The operands may be single
-polynomials or containers of identically-typed polynomials, i.e., polynomials
-from the same underlying ring with the same coefficient types.</p>
-<p>This op is defined to occur in the ring defined by the ring attribute of
-the two operands, meaning the arithmetic is taken modulo the
-polynomialModulus of the ring as well as modulo any semantics defined by
-the coefficient type.</p>
-<p>Example:</p>
-<div class="highlight"><pre tabindex="0" style="background-color:#f8f8f8;-moz-tab-size:4;-o-tab-size:4;tab-size:4;"><code class="language-mlir" data-lang="mlir"><span style="display:flex;"><span><span style="color:#8f5902;font-style:italic">// multiply two polynomials modulo x^1024 - 1
-</span></span></span><span style="display:flex;"><span><span style="color:#8f5902;font-style:italic"></span><span style="color:#000">#poly</span> <span style="color:#000;font-weight:bold">=</span> <span style="color:#000">#polynomial.int_polynomial</span><span style="color:#000;font-weight:bold">&lt;x**</span><span style="color:#0000cf;font-weight:bold">1024</span> <span style="color:#a40000">-</span> <span style="color:#0000cf;font-weight:bold">1</span><span style="color:#000;font-weight:bold">&gt;</span>
-</span></span><span style="display:flex;"><span><span style="color:#000">#ring</span> <span style="color:#000;font-weight:bold">=</span> <span style="color:#000">#polynomial.ring</span><span style="color:#000;font-weight:bold">&lt;</span><span style="color:#f57900">coefficientType=</span><span style="color:#204a87;font-weight:bold">i32</span><span style="color:#000;font-weight:bold">,</span> <span style="color:#f57900">polynomialModulus=</span><span style="color:#000">#poly</span><span style="color:#000;font-weight:bold">&gt;</span>
-</span></span><span style="display:flex;"><span><span style="color:#000">%0</span> <span style="color:#000;font-weight:bold">=</span> polynomial<span style="color:#000;font-weight:bold">.</span><span style="color:#204a87;font-weight:bold">constant</span> int<span style="color:#000;font-weight:bold">&lt;</span><span style="color:#0000cf;font-weight:bold">1</span> <span style="color:#a40000">+</span> <span style="color:#000;font-weight:bold">x**</span><span style="color:#0000cf;font-weight:bold">2</span><span style="color:#000;font-weight:bold">&gt;</span> <span style="color:#000;font-weight:bold">:</span> <span style="color:#000;font-weight:bold">!</span>polynomial<span style="color:#000;font-weight:bold">.</span>polynomial<span style="color:#000;font-weight:bold">&lt;</span><span style="color:#000">#ring</span><span style="color:#000;font-weight:bold">&gt;</span>
-</span></span><span style="display:flex;"><span><span style="color:#000">%1</span> <span style="color:#000;font-weight:bold">=</span> polynomial<span style="color:#000;font-weight:bold">.</span><span style="color:#204a87;font-weight:bold">constant</span> int<span style="color:#000;font-weight:bold">&lt;x**</span><span style="color:#0000cf;font-weight:bold">5</span> <span style="color:#a40000">-</span> <span style="color:#000;font-weight:bold">x</span> <span style="color:#a40000">+</span> <span style="color:#0000cf;font-weight:bold">1</span><span style="color:#000;font-weight:bold">&gt;</span> <span style="color:#000;font-weight:bold">:</span> <span style="color:#000;font-weight:bold">!</span>polynomial<span style="color:#000;font-weight:bold">.</span>polynomial<span style="color:#000;font-weight:bold">&lt;</span><span style="color:#000">#ring</span><span style="color:#000;font-weight:bold">&gt;</span>
-</span></span><span style="display:flex;"><span><span style="color:#000">%2</span> <span style="color:#000;font-weight:bold">=</span> polynomial<span style="color:#000;font-weight:bold">.</span>mul <span style="color:#000">%0</span><span style="color:#000;font-weight:bold">,</span> <span style="color:#000">%1</span> <span style="color:#000;font-weight:bold">:</span> <span style="color:#000;font-weight:bold">!</span>polynomial<span style="color:#000;font-weight:bold">.</span>polynomial<span style="color:#000;font-weight:bold">&lt;</span><span style="color:#000">#ring</span><span style="color:#000;font-weight:bold">&gt;</span>
-</span></span></code></pre></div><p>Traits: <code>AlwaysSpeculatableImplTrait</code>, <code>Commutative</code>, <code>Elementwise</code>, <code>SameOperandsAndResultType</code>, <code>Scalarizable</code>, <code>Tensorizable</code>, <code>Vectorizable</code></p>
-<p>Interfaces: <code>ConditionallySpeculatable</code>, <code>InferTypeOpInterface</code>, <code>NoMemoryEffect (MemoryEffectOpInterface)</code></p>
-<p>Effects: <code>MemoryEffects::Effect{}</code></p>
-<h4 id="operands-6">Operands:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Operand</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>lhs</code></td>
-<td>polynomial-like</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>rhs</code></td>
-<td>polynomial-like</td>
-</tr>
-</tbody>
-</table>
-<h4 id="results-7">Results:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Result</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>result</code></td>
-<td>polynomial-like</td>
-</tr>
-</tbody>
-</table>
-<h3 id="polynomialmul_scalar-heirpolynomialmulscalarop"><code>polynomial.mul_scalar</code> (heir::polynomial::MulScalarOp)</h3>
-<p><em>Multiplication by a scalar of the field.</em></p>
-<p>Syntax:</p>
-<pre tabindex="0"><code>operation ::= `polynomial.mul_scalar` operands attr-dict `:` type($polynomial) `,` type($scalar)
-</code></pre><p>Multiplies the polynomial operand&rsquo;s coefficients by a given scalar value.
-The <code>scalar</code> input must have the same type as the polynomial ring&rsquo;s
-coefficientType.</p>
-<p>Example:</p>
-<div class="highlight"><pre tabindex="0" style="background-color:#f8f8f8;-moz-tab-size:4;-o-tab-size:4;tab-size:4;"><code class="language-mlir" data-lang="mlir"><span style="display:flex;"><span><span style="color:#8f5902;font-style:italic">// multiply two polynomials modulo x^1024 - 1
-</span></span></span><span style="display:flex;"><span><span style="color:#8f5902;font-style:italic"></span><span style="color:#000">#poly</span> <span style="color:#000;font-weight:bold">=</span> <span style="color:#000">#polynomial.int_polynomial</span><span style="color:#000;font-weight:bold">&lt;x**</span><span style="color:#0000cf;font-weight:bold">1024</span> <span style="color:#a40000">-</span> <span style="color:#0000cf;font-weight:bold">1</span><span style="color:#000;font-weight:bold">&gt;</span>
-</span></span><span style="display:flex;"><span><span style="color:#000">#ring</span> <span style="color:#000;font-weight:bold">=</span> <span style="color:#000">#polynomial.ring</span><span style="color:#000;font-weight:bold">&lt;</span><span style="color:#f57900">coefficientType=</span><span style="color:#204a87;font-weight:bold">i32</span><span style="color:#000;font-weight:bold">,</span> <span style="color:#f57900">polynomialModulus=</span><span style="color:#000">#poly</span><span style="color:#000;font-weight:bold">&gt;</span>
-</span></span><span style="display:flex;"><span><span style="color:#000">%0</span> <span style="color:#000;font-weight:bold">=</span> polynomial<span style="color:#000;font-weight:bold">.</span><span style="color:#204a87;font-weight:bold">constant</span> int<span style="color:#000;font-weight:bold">&lt;</span><span style="color:#0000cf;font-weight:bold">1</span> <span style="color:#a40000">+</span> <span style="color:#000;font-weight:bold">x**</span><span style="color:#0000cf;font-weight:bold">2</span><span style="color:#000;font-weight:bold">&gt;</span> <span style="color:#000;font-weight:bold">:</span> <span style="color:#000;font-weight:bold">!</span>polynomial<span style="color:#000;font-weight:bold">.</span>polynomial<span style="color:#000;font-weight:bold">&lt;</span><span style="color:#000">#ring</span><span style="color:#000;font-weight:bold">&gt;</span>
-</span></span><span style="display:flex;"><span><span style="color:#000">%1</span> <span style="color:#000;font-weight:bold">=</span> arith<span style="color:#000;font-weight:bold">.</span><span style="color:#204a87;font-weight:bold">constant</span> <span style="color:#0000cf;font-weight:bold">3</span> <span style="color:#000;font-weight:bold">:</span> <span style="color:#204a87;font-weight:bold">i32</span>
-</span></span><span style="display:flex;"><span><span style="color:#000">%2</span> <span style="color:#000;font-weight:bold">=</span> polynomial<span style="color:#000;font-weight:bold">.</span>mul_scalar <span style="color:#000">%0</span><span style="color:#000;font-weight:bold">,</span> <span style="color:#000">%1</span> <span style="color:#000;font-weight:bold">:</span> <span style="color:#000;font-weight:bold">!</span>polynomial<span style="color:#000;font-weight:bold">.</span>polynomial<span style="color:#000;font-weight:bold">&lt;</span><span style="color:#000">#ring</span><span style="color:#000;font-weight:bold">&gt;,</span> <span style="color:#204a87;font-weight:bold">i32</span>
-</span></span></code></pre></div><p>Traits: <code>AlwaysSpeculatableImplTrait</code>, <code>Elementwise</code>, <code>Scalarizable</code>, <code>Tensorizable</code>, <code>Vectorizable</code></p>
-<p>Interfaces: <code>ConditionallySpeculatable</code>, <code>InferTypeOpInterface</code>, <code>NoMemoryEffect (MemoryEffectOpInterface)</code></p>
-<p>Effects: <code>MemoryEffects::Effect{}</code></p>
-<h4 id="operands-7">Operands:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Operand</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>polynomial</code></td>
-<td>polynomial-like</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>scalar</code></td>
-<td>any type</td>
-</tr>
-</tbody>
-</table>
-<h4 id="results-8">Results:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Result</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>output</code></td>
-<td>polynomial-like</td>
-</tr>
-</tbody>
-</table>
-<h3 id="polynomialntt-heirpolynomialnttop"><code>polynomial.ntt</code> (heir::polynomial::NTTOp)</h3>
-<p><em>Computes point-value tensor representation of a polynomial.</em></p>
-<p>Syntax:</p>
-<pre tabindex="0"><code>operation ::= `polynomial.ntt` $input attr-dict `:` qualified(type($input)) `-&gt;` type($output)
-</code></pre><p><code>polynomial.ntt</code> computes the forward integer Number Theoretic Transform
-(NTT) on the input polynomial. It returns a tensor containing a point-value
-representation of the input polynomial. The output tensor has shape equal
-to the degree of the ring&rsquo;s <code>polynomialModulus</code>. The polynomial&rsquo;s RingAttr
-is embedded as the encoding attribute of the output tensor.</p>
-<p>Given an input polynomial <code>F(x)</code> over a ring whose <code>polynomialModulus</code> has
-degree <code>n</code>, and a primitive <code>n</code>-th root of unity <code>omega_n</code>, the output is
-the list of $n$ evaluations</p>
-<p><code>f[k] = F(omega[n]^k) ; k = {0, ..., n-1}</code></p>
-<p>The choice of primitive root may be optionally specified.</p>
-<p>Traits: <code>AlwaysSpeculatableImplTrait</code></p>
-<p>Interfaces: <code>ConditionallySpeculatable</code>, <code>NoMemoryEffect (MemoryEffectOpInterface)</code></p>
-<p>Effects: <code>MemoryEffects::Effect{}</code></p>
-<h4 id="attributes-2">Attributes:</h4>
-<table>
-<tr><th>Attribute</th><th>MLIR Type</th><th>Description</th></tr>
-<tr><td><code>root</code></td><td>::mlir::heir::polynomial::PrimitiveRootAttr</td><td>an attribute containing an integer and its degree as a root of unity</td></tr>
-</table>
-<h4 id="operands-8">Operands:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Operand</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>input</code></td>
-<td>An element of a polynomial ring.</td>
-</tr>
-</tbody>
-</table>
-<h4 id="results-9">Results:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Result</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>output</code></td>
-<td>ranked tensor of Integer type with modular arithmetic values</td>
-</tr>
-</tbody>
-</table>
-<h3 id="polynomialsub-heirpolynomialsubop"><code>polynomial.sub</code> (heir::polynomial::SubOp)</h3>
-<p><em>Subtraction operation between polynomials.</em></p>
-<p>Syntax:</p>
-<pre tabindex="0"><code>operation ::= `polynomial.sub` operands attr-dict `:` type($result)
-</code></pre><p>Performs polynomial subtraction on the operands. The operands may be single
-polynomials or containers of identically-typed polynomials, i.e., polynomials
-from the same underlying ring with the same coefficient types.</p>
-<p>This op is defined to occur in the ring defined by the ring attribute of
-the two operands, meaning the arithmetic is taken modulo the
-polynomialModulus of the ring as well as modulo any semantics defined by
-the coefficient type.</p>
-<p>Example:</p>
-<div class="highlight"><pre tabindex="0" style="background-color:#f8f8f8;-moz-tab-size:4;-o-tab-size:4;tab-size:4;"><code class="language-mlir" data-lang="mlir"><span style="display:flex;"><span><span style="color:#8f5902;font-style:italic">// subtract two polynomials modulo x^1024 - 1
-</span></span></span><span style="display:flex;"><span><span style="color:#8f5902;font-style:italic"></span><span style="color:#000">#poly</span> <span style="color:#000;font-weight:bold">=</span> <span style="color:#000">#polynomial.int_polynomial</span><span style="color:#000;font-weight:bold">&lt;x**</span><span style="color:#0000cf;font-weight:bold">1024</span> <span style="color:#a40000">-</span> <span style="color:#0000cf;font-weight:bold">1</span><span style="color:#000;font-weight:bold">&gt;</span>
-</span></span><span style="display:flex;"><span><span style="color:#000">#ring</span> <span style="color:#000;font-weight:bold">=</span> <span style="color:#000">#polynomial.ring</span><span style="color:#000;font-weight:bold">&lt;</span><span style="color:#f57900">coefficientType=</span><span style="color:#204a87;font-weight:bold">i32</span><span style="color:#000;font-weight:bold">,</span> <span style="color:#f57900">polynomialModulus=</span><span style="color:#000">#poly</span><span style="color:#000;font-weight:bold">&gt;</span>
-</span></span><span style="display:flex;"><span><span style="color:#000">%0</span> <span style="color:#000;font-weight:bold">=</span> polynomial<span style="color:#000;font-weight:bold">.</span><span style="color:#204a87;font-weight:bold">constant</span> int<span style="color:#000;font-weight:bold">&lt;</span><span style="color:#0000cf;font-weight:bold">1</span> <span style="color:#a40000">+</span> <span style="color:#000;font-weight:bold">x**</span><span style="color:#0000cf;font-weight:bold">2</span><span style="color:#000;font-weight:bold">&gt;</span> <span style="color:#000;font-weight:bold">:</span> <span style="color:#000;font-weight:bold">!</span>polynomial<span style="color:#000;font-weight:bold">.</span>polynomial<span style="color:#000;font-weight:bold">&lt;</span><span style="color:#000">#ring</span><span style="color:#000;font-weight:bold">&gt;</span>
-</span></span><span style="display:flex;"><span><span style="color:#000">%1</span> <span style="color:#000;font-weight:bold">=</span> polynomial<span style="color:#000;font-weight:bold">.</span><span style="color:#204a87;font-weight:bold">constant</span> int<span style="color:#000;font-weight:bold">&lt;x**</span><span style="color:#0000cf;font-weight:bold">5</span> <span style="color:#a40000">-</span> <span style="color:#000;font-weight:bold">x</span> <span style="color:#a40000">+</span> <span style="color:#0000cf;font-weight:bold">1</span><span style="color:#000;font-weight:bold">&gt;</span> <span style="color:#000;font-weight:bold">:</span> <span style="color:#000;font-weight:bold">!</span>polynomial<span style="color:#000;font-weight:bold">.</span>polynomial<span style="color:#000;font-weight:bold">&lt;</span><span style="color:#000">#ring</span><span style="color:#000;font-weight:bold">&gt;</span>
-</span></span><span style="display:flex;"><span><span style="color:#000">%2</span> <span style="color:#000;font-weight:bold">=</span> polynomial<span style="color:#000;font-weight:bold">.</span>sub <span style="color:#000">%0</span><span style="color:#000;font-weight:bold">,</span> <span style="color:#000">%1</span> <span style="color:#000;font-weight:bold">:</span> <span style="color:#000;font-weight:bold">!</span>polynomial<span style="color:#000;font-weight:bold">.</span>polynomial<span style="color:#000;font-weight:bold">&lt;</span><span style="color:#000">#ring</span><span style="color:#000;font-weight:bold">&gt;</span>
-</span></span></code></pre></div><p>Traits: <code>AlwaysSpeculatableImplTrait</code>, <code>Elementwise</code>, <code>SameOperandsAndResultType</code>, <code>Scalarizable</code>, <code>Tensorizable</code>, <code>Vectorizable</code></p>
-<p>Interfaces: <code>ConditionallySpeculatable</code>, <code>InferTypeOpInterface</code>, <code>NoMemoryEffect (MemoryEffectOpInterface)</code></p>
-<p>Effects: <code>MemoryEffects::Effect{}</code></p>
-<h4 id="operands-9">Operands:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Operand</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>lhs</code></td>
-<td>polynomial-like</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>rhs</code></td>
-<td>polynomial-like</td>
-</tr>
-</tbody>
-</table>
-<h4 id="results-10">Results:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Result</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>result</code></td>
-<td>polynomial-like</td>
-</tr>
-</tbody>
-</table>
-<h3 id="polynomialto_tensor-heirpolynomialtotensorop"><code>polynomial.to_tensor</code> (heir::polynomial::ToTensorOp)</h3>
-<p><em>Creates a tensor containing the coefficients of a polynomial.</em></p>
-<p>Syntax:</p>
-<pre tabindex="0"><code>operation ::= `polynomial.to_tensor` $input attr-dict `:` type($input) `-&gt;` type($output)
-</code></pre><p><code>polynomial.to_tensor</code> creates a dense tensor value containing the
-coefficients of the input polynomial. The output tensor contains the
-coefficients in degree-increasing order.</p>
-<p>Operations that act on the coefficients of a polynomial, such as extracting
-a specific coefficient or extracting a range of coefficients, should be
-implemented by composing <code>to_tensor</code> with the relevant <code>tensor</code> dialect
-ops.</p>
-<p>The output tensor has shape equal to the degree of the polynomial ring
-attribute&rsquo;s polynomialModulus, including zeroes.</p>
-<p>Example:</p>
-<div class="highlight"><pre tabindex="0" style="background-color:#f8f8f8;-moz-tab-size:4;-o-tab-size:4;tab-size:4;"><code class="language-mlir" data-lang="mlir"><span style="display:flex;"><span><span style="color:#000">#poly</span> <span style="color:#000;font-weight:bold">=</span> <span style="color:#000">#polynomial.int_polynomial</span><span style="color:#000;font-weight:bold">&lt;x**</span><span style="color:#0000cf;font-weight:bold">1024</span> <span style="color:#a40000">-</span> <span style="color:#0000cf;font-weight:bold">1</span><span style="color:#000;font-weight:bold">&gt;</span>
-</span></span><span style="display:flex;"><span><span style="color:#000">#ring</span> <span style="color:#000;font-weight:bold">=</span> <span style="color:#000">#polynomial.ring</span><span style="color:#000;font-weight:bold">&lt;</span><span style="color:#f57900">coefficientType=</span><span style="color:#204a87;font-weight:bold">i32</span><span style="color:#000;font-weight:bold">,</span> <span style="color:#f57900">polynomialModulus=</span><span style="color:#000">#poly</span><span style="color:#000;font-weight:bold">&gt;</span>
-</span></span><span style="display:flex;"><span><span style="color:#000">%two</span> <span style="color:#000;font-weight:bold">=</span> arith<span style="color:#000;font-weight:bold">.</span><span style="color:#204a87;font-weight:bold">constant</span> <span style="color:#0000cf;font-weight:bold">2</span> <span style="color:#000;font-weight:bold">:</span> <span style="color:#204a87;font-weight:bold">i32</span>
-</span></span><span style="display:flex;"><span><span style="color:#000">%five</span> <span style="color:#000;font-weight:bold">=</span> arith<span style="color:#000;font-weight:bold">.</span><span style="color:#204a87;font-weight:bold">constant</span> <span style="color:#0000cf;font-weight:bold">5</span> <span style="color:#000;font-weight:bold">:</span> <span style="color:#204a87;font-weight:bold">i32</span>
-</span></span><span style="display:flex;"><span><span style="color:#000">%coeffs</span> <span style="color:#000;font-weight:bold">=</span> <span style="color:#204a87;font-weight:bold">tensor</span><span style="color:#000;font-weight:bold">.</span>from_elements <span style="color:#000">%two</span><span style="color:#000;font-weight:bold">,</span> <span style="color:#000">%two</span><span style="color:#000;font-weight:bold">,</span> <span style="color:#000">%five</span> <span style="color:#000;font-weight:bold">:</span> <span style="color:#204a87;font-weight:bold">tensor</span><span style="color:#000;font-weight:bold">&lt;</span><span style="color:#0000cf;font-weight:bold">3x</span><span style="color:#204a87;font-weight:bold">i32</span><span style="color:#000;font-weight:bold">&gt;</span>
-</span></span><span style="display:flex;"><span><span style="color:#000">%poly</span> <span style="color:#000;font-weight:bold">=</span> polynomial<span style="color:#000;font-weight:bold">.</span>from_tensor <span style="color:#000">%coeffs</span> <span style="color:#000;font-weight:bold">:</span> <span style="color:#204a87;font-weight:bold">tensor</span><span style="color:#000;font-weight:bold">&lt;</span><span style="color:#0000cf;font-weight:bold">3x</span><span style="color:#204a87;font-weight:bold">i32</span><span style="color:#000;font-weight:bold">&gt;</span> <span style="color:#000;font-weight:bold">-&gt;</span> <span style="color:#000;font-weight:bold">!</span>polynomial<span style="color:#000;font-weight:bold">.</span>polynomial<span style="color:#000;font-weight:bold">&lt;</span><span style="color:#000">#ring</span><span style="color:#000;font-weight:bold">&gt;</span>
-</span></span><span style="display:flex;"><span><span style="color:#000">%tensor</span> <span style="color:#000;font-weight:bold">=</span> polynomial<span style="color:#000;font-weight:bold">.</span>to_tensor <span style="color:#000">%poly</span> <span style="color:#000;font-weight:bold">:</span> <span style="color:#000;font-weight:bold">!</span>polynomial<span style="color:#000;font-weight:bold">.</span>polynomial<span style="color:#000;font-weight:bold">&lt;</span><span style="color:#000">#ring</span><span style="color:#000;font-weight:bold">&gt;</span> <span style="color:#000;font-weight:bold">-&gt;</span> <span style="color:#204a87;font-weight:bold">tensor</span><span style="color:#000;font-weight:bold">&lt;</span><span style="color:#0000cf;font-weight:bold">1024x</span><span style="color:#204a87;font-weight:bold">i32</span><span style="color:#000;font-weight:bold">&gt;</span>
-</span></span></code></pre></div><p>Traits: <code>AlwaysSpeculatableImplTrait</code></p>
-<p>Interfaces: <code>ConditionallySpeculatable</code>, <code>NoMemoryEffect (MemoryEffectOpInterface)</code></p>
-<p>Effects: <code>MemoryEffects::Effect{}</code></p>
-<h4 id="operands-10">Operands:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Operand</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>input</code></td>
-<td>An element of a polynomial ring.</td>
-</tr>
-</tbody>
-</table>
-<h4 id="results-11">Results:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Result</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>output</code></td>
-<td>ranked tensor of any type values</td>
-</tr>
-</tbody>
-</table>Docs: Randomhttps://heir.dev/docs/dialects/random/Mon, 01 Jan 0001 00:00:00 +0000https://heir.dev/docs/dialects/random/
-<!-- Autogenerated by mlir-tblgen; don't manually edit -->
-<h1 id="random-dialect">&lsquo;random&rsquo; Dialect</h1>
-<p>The <code>random</code> dialect contains operations used to generate random numbers.</p>
-<h2 id="random-types">Random types</h2>
-<!-- Autogenerated by mlir-tblgen; don't manually edit -->
-<h3 id="distributiontype">DistributionType</h3>
-<p>A random distribution type</p>
-<p>Syntax:</p>
-<pre tabindex="0"><code>!random.distribution&lt;
-::mlir::heir::random::Distribution # distribution_type
-&gt;
-</code></pre><p>A generic type, representing a specific random distribution type of either
-uniform or gaussian as an attribute ($distribution_type).</p>
-<h4 id="parameters">Parameters:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Parameter</th>
-<th style="text-align:center">C++ type</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center">distribution_type</td>
-<td style="text-align:center"><code>::mlir::heir::random::Distribution</code></td>
-<td></td>
-</tr>
-</tbody>
-</table>
-<h3 id="prngtype">PRNGType</h3>
-<p>A pseudorandom number generator type</p>
-<p>Syntax: <code>!random.prng</code></p>
-<p>A type that provides pseudorandom number generator.</p>
-<h2 id="random-ops">Random ops</h2>
-<!-- Autogenerated by mlir-tblgen; don't manually edit -->
-<h3 id="randomdiscrete_gaussian_distribution-heirrandomdiscretegaussiandistributionop"><code>random.discrete_gaussian_distribution</code> (heir::random::DiscreteGaussianDistributionOp)</h3>
-<p><em>Initializes the Discrete Gaussian Distribution</em></p>
-<p>Syntax:</p>
-<pre tabindex="0"><code>operation ::= `random.discrete_gaussian_distribution` operands attr-dict `:` functional-type(operands, results)
-</code></pre><p>Initializes the Discrete Gaussian Distribution. The distribution is
-initialized with a mean and a standard deviation and pseudorandom generator
-that provides the source of the randomness.</p>
-<p>Traits: <code>AlwaysSpeculatableImplTrait</code></p>
-<p>Interfaces: <code>ConditionallySpeculatable</code>, <code>NoMemoryEffect (MemoryEffectOpInterface)</code></p>
-<p>Effects: <code>MemoryEffects::Effect{}</code></p>
-<h4 id="attributes">Attributes:</h4>
-<table>
-<tr><th>Attribute</th><th>MLIR Type</th><th>Description</th></tr>
-<tr><td><code>mean</code></td><td>::mlir::IntegerAttr</td><td>An Attribute containing a integer value</td></tr>
-<tr><td><code>stddev</code></td><td>::mlir::IntegerAttr</td><td>An Attribute containing a integer value whose value is non-negative</td></tr>
-</table>
-<h4 id="operands">Operands:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Operand</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>input</code></td>
-<td>A pseudorandom number generator type</td>
-</tr>
-</tbody>
-</table>
-<h4 id="results">Results:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Result</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>output</code></td>
-<td>A random distribution type</td>
-</tr>
-</tbody>
-</table>
-<h3 id="randomdiscrete_uniform_distribution-heirrandomdiscreteuniformdistributionop"><code>random.discrete_uniform_distribution</code> (heir::random::DiscreteUniformDistributionOp)</h3>
-<p><em>Initializes the Discrete Uniform Distribution</em></p>
-<p>Syntax:</p>
-<pre tabindex="0"><code>operation ::= `random.discrete_uniform_distribution` $input `{` `range` `=` `[` $min `,` $max `]` `}` attr-dict `:` `(` qualified(type($input)) `)` `-&gt;` type($output)
-</code></pre><p>Initializes the Discrete Uniform Distribution. The distribution is
-initialized with a minimum and a maximum value and pseudo random generator
-that provides the source of the randomness. The distribution is inclusive of
-the minimum and exclusive of the maximum.</p>
-<p>Traits: <code>AlwaysSpeculatableImplTrait</code></p>
-<p>Interfaces: <code>ConditionallySpeculatable</code>, <code>NoMemoryEffect (MemoryEffectOpInterface)</code></p>
-<p>Effects: <code>MemoryEffects::Effect{}</code></p>
-<h4 id="attributes-1">Attributes:</h4>
-<table>
-<tr><th>Attribute</th><th>MLIR Type</th><th>Description</th></tr>
-<tr><td><code>min</code></td><td>::mlir::IntegerAttr</td><td>An Attribute containing a integer value</td></tr>
-<tr><td><code>max</code></td><td>::mlir::IntegerAttr</td><td>An Attribute containing a integer value</td></tr>
-</table>
-<h4 id="operands-1">Operands:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Operand</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>input</code></td>
-<td>A pseudorandom number generator type</td>
-</tr>
-</tbody>
-</table>
-<h4 id="results-1">Results:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Result</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>output</code></td>
-<td>A random distribution type</td>
-</tr>
-</tbody>
-</table>
-<h3 id="randominit_prng-heirrandominitop"><code>random.init_prng</code> (heir::random::InitOp)</h3>
-<p><em>Initializes the pseudorandom number generator with a seed.</em></p>
-<p>Syntax:</p>
-<pre tabindex="0"><code>operation ::= `random.init_prng` operands attr-dict `:` functional-type(operands, results)
-</code></pre><p>Initializes the PRNG with a seed. The seed is dynamically provided due to
-protocols that agree on shared randomness. The PRNG is used to initialized
-the random distributions such as the discrete gaussian distribution and the
-discrete uniform distribution. This initialization also takes as input a
-number of bits that are generated for each number value sampled (num_bits).
-For instance, a num_bits of 32 will mean that distributions will generate a
-32-bit integer value. We expect that the seed initialization is done statically
-and globally once per thread for all distributions; however, if multiple threads are
-generating randomness, then seed initialization should be done per thread;
-otherwise there is no guarantee of consistent behavior. Thread safety is so
-far not considered.</p>
-<p>Traits: <code>AlwaysSpeculatableImplTrait</code></p>
-<p>Interfaces: <code>ConditionallySpeculatable</code>, <code>InferTypeOpInterface</code>, <code>NoMemoryEffect (MemoryEffectOpInterface)</code></p>
-<p>Effects: <code>MemoryEffects::Effect{}</code></p>
-<h4 id="attributes-2">Attributes:</h4>
-<table>
-<tr><th>Attribute</th><th>MLIR Type</th><th>Description</th></tr>
-<tr><td><code>num_bits</code></td><td>::mlir::IntegerAttr</td><td>An Attribute containing a integer value</td></tr>
-</table>
-<h4 id="operands-2">Operands:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Operand</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>seed</code></td>
-<td>signless-integer-like</td>
-</tr>
-</tbody>
-</table>
-<h4 id="results-2">Results:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Result</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>output</code></td>
-<td>A pseudorandom number generator type</td>
-</tr>
-</tbody>
-</table>
-<h3 id="randomsample-heirrandomsampleop"><code>random.sample</code> (heir::random::SampleOp)</h3>
-<p><em>Samples from a distribution</em></p>
-<p>Syntax:</p>
-<pre tabindex="0"><code>operation ::= `random.sample` operands attr-dict `:` functional-type(operands, results)
-</code></pre><p>Samples from the distribution to obtain a random value
-or tensor of values.</p>
-<h4 id="operands-3">Operands:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Operand</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>input</code></td>
-<td>A random distribution type</td>
-</tr>
-</tbody>
-</table>
-<h4 id="results-3">Results:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Result</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>output</code></td>
-<td>signless-integer-like</td>
-</tr>
-</tbody>
-</table>
-<h2 id="random-additional-definitions">Random additional definitions</h2>
-<!-- Autogenerated by mlir-tblgen; don't manually edit -->
-<h3 id="distribution">Distribution</h3>
-<p>An enum attribute representing a random distribution</p>
-<h4 id="cases">Cases:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Symbol</th>
-<th style="text-align:center">Value</th>
-<th>String</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center">uniform</td>
-<td style="text-align:center"><code>0</code></td>
-<td>uniform</td>
-</tr>
-<tr>
-<td style="text-align:center">gaussian</td>
-<td style="text-align:center"><code>1</code></td>
-<td>gaussian</td>
-</tr>
-</tbody>
-</table>Docs: RNShttps://heir.dev/docs/dialects/rns/Mon, 01 Jan 0001 00:00:00 +0000https://heir.dev/docs/dialects/rns/
-<!-- Autogenerated by mlir-tblgen; don't manually edit -->
-<h1 id="rns-dialect">&lsquo;rns&rsquo; Dialect</h1>
-<p>The <code>rns</code> dialect represents types and ops related to residue number
-system (RNS) representations of ring-like types, such as integers or
-polynomials decomposed from high-bit width to lower-bit-width prime
-moduli. Sometimes RNS is referred to as CRT, for &ldquo;Chinese Remainder
-Theorem.&rdquo;</p>
-<p>This dialect is intended to be as generic as possible in terms of its
-interaction with standard MLIR. However, because of upstream MLIR
-constraints, we do not have the ability to override, say, <code>arith.addi</code>
-to operate on an <code>rns</code> type. So such situations require dedicated ops,
-canonicalization patterns, etc.</p>
-<h2 id="rns-types">RNS types</h2>
-<!-- Autogenerated by mlir-tblgen; don't manually edit -->
-<h3 id="rnstype">RNSType</h3>
-<p>A residue number system representation</p>
-<p>Syntax:</p>
-<pre tabindex="0"><code>!rns.rns&lt;
-::llvm::ArrayRef&lt;mlir::Type&gt; # basisTypes
-&gt;
-</code></pre><h4 id="parameters">Parameters:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Parameter</th>
-<th style="text-align:center">C++ type</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center">basisTypes</td>
-<td style="text-align:center"><code>::llvm::ArrayRef&lt;mlir::Type&gt;</code></td>
-<td></td>
-</tr>
-</tbody>
-</table>
-<h2 id="rns-ops">RNS ops</h2>
-<!-- Autogenerated by mlir-tblgen; don't manually edit -->
-<h2 id="rns-additional-definitions">RNS additional definitions</h2>
-<!-- Autogenerated by mlir-tblgen; don't manually edit -->
-<h1 id="typeinterface-definitions">TypeInterface definitions</h1>
-<h2 id="rnsbasistypeinterface-rnsbasistypeinterface">RNSBasisTypeInterface (<code>RNSBasisTypeInterface</code>)</h2>
-<p>This interface is required for a type to be used as a parameter
-to an <code>rns</code> type.</p>
-<h3 id="methods">Methods:</h3>
-<h4 id="iscompatiblewith"><code>isCompatibleWith</code></h4>
-<div class="highlight"><pre tabindex="0" style="background-color:#f8f8f8;-moz-tab-size:4;-o-tab-size:4;tab-size:4;"><code class="language-c++" data-lang="c++"><span style="display:flex;"><span><span style="color:#204a87;font-weight:bold">bool</span> <span style="color:#000">isCompatibleWith</span><span style="color:#000;font-weight:bold">(</span><span style="color:#ce5c00;font-weight:bold">::</span><span style="color:#000">mlir</span><span style="color:#ce5c00;font-weight:bold">::</span><span style="color:#000">Type</span> <span style="color:#000">otherRnsBasisType</span><span style="color:#000;font-weight:bold">);</span>
-</span></span></code></pre></div><p>Returns true if this type is compatible with another type in the
-same RNS basis. In particular, the set of types used for a single
-RNS basis are never equal as types, but instead have some common
-attribute that must be checked here. For example, an RNS type where
-the basis types are polynomials would return true if the two types
-are both polynomial types, even if they have different coefficient
-moduli.</p>
-<p>Another example is using mod arith types as the basis types, where
-by the nature of chinese reminder theorem, it is required that
-the modulus of them must be mutually coprime.</p>
-<p><code>isCompatibleWith</code> must be commutative, in the sense
-that <code>type1.isCompatibleWith(type2)</code> if and only if
-<code>type2.isCompatibleWith(type1)</code>.</p>
-<p>NOTE: This method <em>must</em> be implemented by the user.</p>: Search Resultshttps://heir.dev/search/Mon, 01 Jan 0001 00:00:00 +0000https://heir.dev/search/Docs: Secrethttps://heir.dev/docs/dialects/secret/Mon, 01 Jan 0001 00:00:00 +0000https://heir.dev/docs/dialects/secret/
-<!-- Autogenerated by mlir-tblgen; don't manually edit -->
-<h1 id="secret-dialect">&lsquo;secret&rsquo; Dialect</h1>
-<p>Secret is a dialect for computations that operate on encrypted data.</p>
-<p>Secret is intended to serve as a scheme-agnostic front-end for the HEIR
-ecosystem of dialects. It is supposed to be fully interoperable with the
-rest of MLIR via secret.generic, while lower-level HEIR dialects would have
-custom types for arithmetic on secret integers of various bit widths.</p>
-<h2 id="secret-types">Secret types</h2>
-<!-- Autogenerated by mlir-tblgen; don't manually edit -->
-<h3 id="secrettype">SecretType</h3>
-<p>A secret value</p>
-<p>Syntax:</p>
-<pre tabindex="0"><code>!secret.secret&lt;
-Type # valueType
-&gt;
-</code></pre><p>A generic wrapper around another MLIR type, representing an encrypted value
-but not specifying the manner of encryption. This is useful in HEIR because
-the compiler may choose various details of the FHE scheme based on the
-properties of the input program, the backend target hardware, and cost
-models of the various passes.</p>
-<h4 id="parameters">Parameters:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Parameter</th>
-<th style="text-align:center">C++ type</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center">valueType</td>
-<td style="text-align:center"><code>Type</code></td>
-<td></td>
-</tr>
-</tbody>
-</table>
-<h2 id="secret-ops">Secret ops</h2>
-<!-- Autogenerated by mlir-tblgen; don't manually edit -->
-<h3 id="secretcast-heirsecretcastop"><code>secret.cast</code> (heir::secret::CastOp)</h3>
-<p><em>A placeholder cast from one secret type to another</em></p>
-<p>Syntax:</p>
-<pre tabindex="0"><code>operation ::= `secret.cast` $input attr-dict `:` qualified(type($input)) `to` qualified(type($output))
-</code></pre><p>A <code>cast</code> operation represents a type cast from one secret type to another,
-that is used to enable the intermixing of various equivalent secret types
-before a lower-level FHE scheme has been chosen.</p>
-<p>For example, <code>secret.cast</code> can be used to convert a <code>secret&lt;i8&gt;</code> to a
-<code>secret&lt;tensor&lt;8xi1&gt;&gt;</code> as a compatibility layer between boolean and
-non-boolean parts of a program. The pass that later lowers the IR to
-specific FHE schemes would need to replace these casts with appropriate
-scheme-specific operations, and it is left to those later passes to
-determine which casts are considered valid.</p>
-<p>Example:</p>
-<div class="highlight"><pre tabindex="0" style="background-color:#f8f8f8;-moz-tab-size:4;-o-tab-size:4;tab-size:4;"><code class="language-mlir" data-lang="mlir"><span style="display:flex;"><span><span style="color:#000">%result</span> <span style="color:#000;font-weight:bold">=</span> secret<span style="color:#000;font-weight:bold">.</span>cast <span style="color:#000">%0</span> <span style="color:#000;font-weight:bold">:</span> <span style="color:#000;font-weight:bold">!</span>secret<span style="color:#000;font-weight:bold">.</span>secret<span style="color:#000;font-weight:bold">&lt;</span><span style="color:#204a87;font-weight:bold">i8</span><span style="color:#000;font-weight:bold">&gt;</span> to <span style="color:#000;font-weight:bold">!</span>secret<span style="color:#000;font-weight:bold">.</span>secret<span style="color:#000;font-weight:bold">&lt;</span><span style="color:#204a87;font-weight:bold">tensor</span><span style="color:#000;font-weight:bold">&lt;</span><span style="color:#0000cf;font-weight:bold">8x</span><span style="color:#204a87;font-weight:bold">i1</span><span style="color:#000;font-weight:bold">&gt;&gt;</span>
-</span></span><span style="display:flex;"><span><span style="color:#000">%result2</span> <span style="color:#000;font-weight:bold">=</span> secret<span style="color:#000;font-weight:bold">.</span>cast <span style="color:#000">%0</span> <span style="color:#000;font-weight:bold">:</span> <span style="color:#000;font-weight:bold">!</span>secret<span style="color:#000;font-weight:bold">.</span>secret<span style="color:#000;font-weight:bold">&lt;</span><span style="color:#204a87;font-weight:bold">i8</span><span style="color:#000;font-weight:bold">&gt;</span> to <span style="color:#000;font-weight:bold">!</span>secret<span style="color:#000;font-weight:bold">.</span>secret<span style="color:#000;font-weight:bold">&lt;</span><span style="color:#204a87;font-weight:bold">tensor</span><span style="color:#000;font-weight:bold">&lt;</span><span style="color:#0000cf;font-weight:bold">2x</span><span style="color:#204a87;font-weight:bold">i4</span><span style="color:#000;font-weight:bold">&gt;&gt;</span>
-</span></span></code></pre></div><p>Traits: <code>AlwaysSpeculatableImplTrait</code></p>
-<p>Interfaces: <code>ConditionallySpeculatable</code>, <code>NoMemoryEffect (MemoryEffectOpInterface)</code></p>
-<p>Effects: <code>MemoryEffects::Effect{}</code></p>
-<h4 id="operands">Operands:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Operand</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>input</code></td>
-<td>A secret value</td>
-</tr>
-</tbody>
-</table>
-<h4 id="results">Results:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Result</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>output</code></td>
-<td>A secret value</td>
-</tr>
-</tbody>
-</table>
-<h3 id="secretconceal-heirsecretconcealop"><code>secret.conceal</code> (heir::secret::ConcealOp)</h3>
-<p><em>Convert a non-secret value into a secret</em></p>
-<p>Syntax:</p>
-<pre tabindex="0"><code>operation ::= `secret.conceal` $cleartext attr-dict `:` type($cleartext) `-&gt;` type($output)
-</code></pre><p>Convert a value to a secret containing the same value.</p>
-<p>This op represents a scheme-agnostic encryption operation, as well as a
-&ldquo;trivial encryption&rdquo; operation which is needed for some FHE schemes. This
-op is also useful for type materialization in the dialect conversion
-framework.</p>
-<p>Examples:</p>
-<div class="highlight"><pre tabindex="0" style="background-color:#f8f8f8;-moz-tab-size:4;-o-tab-size:4;tab-size:4;"><code class="language-mlir" data-lang="mlir"><span style="display:flex;"><span><span style="color:#000">%Y</span> <span style="color:#000;font-weight:bold">=</span> secret<span style="color:#000;font-weight:bold">.</span>conceal <span style="color:#000">%value</span> <span style="color:#000;font-weight:bold">:</span> <span style="color:#204a87;font-weight:bold">i32</span> <span style="color:#000;font-weight:bold">-&gt;</span> <span style="color:#000;font-weight:bold">!</span>secret<span style="color:#000;font-weight:bold">.</span>secret<span style="color:#000;font-weight:bold">&lt;</span><span style="color:#204a87;font-weight:bold">i32</span><span style="color:#000;font-weight:bold">&gt;</span>
-</span></span></code></pre></div><p>Traits: <code>AlwaysSpeculatableImplTrait</code></p>
-<p>Interfaces: <code>ConditionallySpeculatable</code>, <code>NoMemoryEffect (MemoryEffectOpInterface)</code></p>
-<p>Effects: <code>MemoryEffects::Effect{}</code></p>
-<h4 id="operands-1">Operands:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Operand</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>cleartext</code></td>
-<td>any type</td>
-</tr>
-</tbody>
-</table>
-<h4 id="results-1">Results:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Result</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>output</code></td>
-<td>A secret value</td>
-</tr>
-</tbody>
-</table>
-<h3 id="secretgeneric-heirsecretgenericop"><code>secret.generic</code> (heir::secret::GenericOp)</h3>
-<p><em>Lift a plaintext computation to operate on secrets.</em></p>
-<p><code>secret.generic</code> lifts a plaintext computation to operate on one or more
-secrets. The lifted computation is represented as a region containing a
-single block terminated by <code>secret.yield</code>. The arguments of the <code>secret.generic</code>
-may include one or more <code>!secret.secret</code> types. The arguments of the block
-in the op&rsquo;s body correspond to the underlying plaintext types of the secrets.</p>
-<p><code>secret.generic</code> is not isolated from above, so you may directly reference
-values in the enclosing scope. This is required to support using
-<code>secret.generic</code> inside of ops with <code>AffineScope</code>, while having the body
-of the generic use the induction variables defined by the affine scope.</p>
-<p>Basic examples:</p>
-<p>Add two secret integers together</p>
-<div class="highlight"><pre tabindex="0" style="background-color:#f8f8f8;-moz-tab-size:4;-o-tab-size:4;tab-size:4;"><code class="language-mlir" data-lang="mlir"><span style="display:flex;"><span><span style="color:#000">%Z</span> <span style="color:#000;font-weight:bold">=</span> secret<span style="color:#000;font-weight:bold">.</span>generic ins<span style="color:#000;font-weight:bold">(</span><span style="color:#000">%X</span><span style="color:#000;font-weight:bold">,</span> <span style="color:#000">%Y</span> <span style="color:#000;font-weight:bold">:</span> <span style="color:#000;font-weight:bold">!</span>secret<span style="color:#000;font-weight:bold">.</span>secret<span style="color:#000;font-weight:bold">&lt;</span><span style="color:#204a87;font-weight:bold">i32</span><span style="color:#000;font-weight:bold">&gt;,</span> <span style="color:#000;font-weight:bold">!</span>secret<span style="color:#000;font-weight:bold">.</span>secret<span style="color:#000;font-weight:bold">&lt;</span><span style="color:#204a87;font-weight:bold">i32</span><span style="color:#000;font-weight:bold">&gt;)</span> <span style="color:#000;font-weight:bold">{</span>
-</span></span><span style="display:flex;"><span> <span style="color:#f57900">^bb0</span><span style="color:#000;font-weight:bold">(</span><span style="color:#000">%x</span><span style="color:#000;font-weight:bold">:</span> <span style="color:#204a87;font-weight:bold">i32</span><span style="color:#000;font-weight:bold">,</span> <span style="color:#000">%y</span><span style="color:#000;font-weight:bold">:</span> <span style="color:#204a87;font-weight:bold">i32</span><span style="color:#000;font-weight:bold">):</span>
-</span></span><span style="display:flex;"><span> <span style="color:#000">%z</span> <span style="color:#000;font-weight:bold">=</span> arith<span style="color:#000;font-weight:bold">.</span>addi <span style="color:#000">%x</span><span style="color:#000;font-weight:bold">,</span> <span style="color:#000">%y</span><span style="color:#000;font-weight:bold">:</span> <span style="color:#204a87;font-weight:bold">i32</span>
-</span></span><span style="display:flex;"><span> secret<span style="color:#000;font-weight:bold">.</span>yield <span style="color:#000">%z</span> <span style="color:#000;font-weight:bold">:</span> <span style="color:#204a87;font-weight:bold">i32</span>
-</span></span><span style="display:flex;"><span> <span style="color:#000;font-weight:bold">}</span> <span style="color:#000;font-weight:bold">-&gt;</span> <span style="color:#000;font-weight:bold">(!</span>secret<span style="color:#000;font-weight:bold">.</span>secret<span style="color:#000;font-weight:bold">&lt;</span><span style="color:#204a87;font-weight:bold">i32</span><span style="color:#000;font-weight:bold">&gt;)</span>
-</span></span></code></pre></div><p>Add a secret value with a plaintext value. I.e., not all arguments to the
-op need be secret.</p>
-<div class="highlight"><pre tabindex="0" style="background-color:#f8f8f8;-moz-tab-size:4;-o-tab-size:4;tab-size:4;"><code class="language-mlir" data-lang="mlir"><span style="display:flex;"><span><span style="color:#000">%Z</span> <span style="color:#000;font-weight:bold">=</span> secret<span style="color:#000;font-weight:bold">.</span>generic ins<span style="color:#000;font-weight:bold">(</span><span style="color:#000">%X</span><span style="color:#000;font-weight:bold">,</span> <span style="color:#000">%Y</span> <span style="color:#000;font-weight:bold">:</span> <span style="color:#204a87;font-weight:bold">i32</span><span style="color:#000;font-weight:bold">,</span> <span style="color:#000;font-weight:bold">!</span>secret<span style="color:#000;font-weight:bold">.</span>secret<span style="color:#000;font-weight:bold">&lt;</span><span style="color:#204a87;font-weight:bold">i32</span><span style="color:#000;font-weight:bold">&gt;)</span> <span style="color:#000;font-weight:bold">{</span>
-</span></span><span style="display:flex;"><span> <span style="color:#f57900">^bb0</span><span style="color:#000;font-weight:bold">(</span><span style="color:#000">%x</span><span style="color:#000;font-weight:bold">:</span> <span style="color:#204a87;font-weight:bold">i32</span><span style="color:#000;font-weight:bold">,</span> <span style="color:#000">%y</span><span style="color:#000;font-weight:bold">:</span> <span style="color:#204a87;font-weight:bold">i32</span><span style="color:#000;font-weight:bold">):</span>
-</span></span><span style="display:flex;"><span> <span style="color:#000">%z</span> <span style="color:#000;font-weight:bold">=</span> arith<span style="color:#000;font-weight:bold">.</span>addi <span style="color:#000">%x</span><span style="color:#000;font-weight:bold">,</span> <span style="color:#000">%y</span><span style="color:#000;font-weight:bold">:</span> <span style="color:#204a87;font-weight:bold">i32</span>
-</span></span><span style="display:flex;"><span> secret<span style="color:#000;font-weight:bold">.</span>yield <span style="color:#000">%z</span> <span style="color:#000;font-weight:bold">:</span> <span style="color:#204a87;font-weight:bold">i32</span>
-</span></span><span style="display:flex;"><span> <span style="color:#000;font-weight:bold">}</span> <span style="color:#000;font-weight:bold">-&gt;</span> <span style="color:#000;font-weight:bold">(!</span>secret<span style="color:#000;font-weight:bold">.</span>secret<span style="color:#000;font-weight:bold">&lt;</span><span style="color:#204a87;font-weight:bold">i32</span><span style="color:#000;font-weight:bold">&gt;)</span>
-</span></span></code></pre></div><p>The same as above, but the plaintext op is not passed through the basic
-block.</p>
-<div class="highlight"><pre tabindex="0" style="background-color:#f8f8f8;-moz-tab-size:4;-o-tab-size:4;tab-size:4;"><code class="language-mlir" data-lang="mlir"><span style="display:flex;"><span><span style="color:#000">%y</span> <span style="color:#000;font-weight:bold">=</span> arith<span style="color:#000;font-weight:bold">.</span><span style="color:#204a87;font-weight:bold">constant</span> <span style="color:#0000cf;font-weight:bold">7</span><span style="color:#000;font-weight:bold">:</span> <span style="color:#204a87;font-weight:bold">i32</span>
-</span></span><span style="display:flex;"><span><span style="color:#000">%Z</span> <span style="color:#000;font-weight:bold">=</span> secret<span style="color:#000;font-weight:bold">.</span>generic ins<span style="color:#000;font-weight:bold">(</span><span style="color:#000">%X</span> <span style="color:#000;font-weight:bold">:</span> <span style="color:#000;font-weight:bold">!</span>secret<span style="color:#000;font-weight:bold">.</span>secret<span style="color:#000;font-weight:bold">&lt;</span><span style="color:#204a87;font-weight:bold">i32</span><span style="color:#000;font-weight:bold">&gt;)</span> <span style="color:#000;font-weight:bold">{</span>
-</span></span><span style="display:flex;"><span> <span style="color:#f57900">^bb0</span><span style="color:#000;font-weight:bold">(</span><span style="color:#000">%x</span><span style="color:#000;font-weight:bold">:</span> <span style="color:#204a87;font-weight:bold">i32</span><span style="color:#000;font-weight:bold">):</span>
-</span></span><span style="display:flex;"><span> <span style="color:#000">%z</span> <span style="color:#000;font-weight:bold">=</span> arith<span style="color:#000;font-weight:bold">.</span>addi <span style="color:#000">%x</span><span style="color:#000;font-weight:bold">,</span> <span style="color:#000">%y</span><span style="color:#000;font-weight:bold">:</span> <span style="color:#204a87;font-weight:bold">i32</span>
-</span></span><span style="display:flex;"><span> secret<span style="color:#000;font-weight:bold">.</span>yield <span style="color:#000">%z</span> <span style="color:#000;font-weight:bold">:</span> <span style="color:#204a87;font-weight:bold">i32</span>
-</span></span><span style="display:flex;"><span> <span style="color:#000;font-weight:bold">}</span> <span style="color:#000;font-weight:bold">-&gt;</span> <span style="color:#000;font-weight:bold">(!</span>secret<span style="color:#000;font-weight:bold">.</span>secret<span style="color:#000;font-weight:bold">&lt;</span><span style="color:#204a87;font-weight:bold">i32</span><span style="color:#000;font-weight:bold">&gt;)</span>
-</span></span></code></pre></div><p>Traits: <code>SingleBlockImplicitTerminator&lt;YieldOp&gt;</code>, <code>SingleBlock</code></p>
-<p>Interfaces: <code>OpAsmOpInterface</code></p>
-<h4 id="operands-2">Operands:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Operand</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>inputs</code></td>
-<td>variadic of any type</td>
-</tr>
-</tbody>
-</table>
-<h4 id="results-2">Results:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Result</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>results</code></td>
-<td>variadic of any type</td>
-</tr>
-</tbody>
-</table>
-<h3 id="secretreveal-heirsecretrevealop"><code>secret.reveal</code> (heir::secret::RevealOp)</h3>
-<p><em>Convert a secret value into a non-secret</em></p>
-<p>Syntax:</p>
-<pre tabindex="0"><code>operation ::= `secret.reveal` $input attr-dict `:` type($input) `-&gt;` type($cleartext)
-</code></pre><p>Convert a secret into a non-secret containing the same value.</p>
-<p>This op represents a scheme-agnostic decryption operation. This op is also
-useful for target materialization in the dialect conversion framework.</p>
-<p>Examples:</p>
-<div class="highlight"><pre tabindex="0" style="background-color:#f8f8f8;-moz-tab-size:4;-o-tab-size:4;tab-size:4;"><code class="language-mlir" data-lang="mlir"><span style="display:flex;"><span><span style="color:#000">%Y</span> <span style="color:#000;font-weight:bold">=</span> secret<span style="color:#000;font-weight:bold">.</span>reveal <span style="color:#000">%secret_value</span> <span style="color:#000;font-weight:bold">:</span> <span style="color:#000;font-weight:bold">!</span>secret<span style="color:#000;font-weight:bold">.</span>secret<span style="color:#000;font-weight:bold">&lt;</span><span style="color:#204a87;font-weight:bold">i32</span><span style="color:#000;font-weight:bold">&gt;</span> <span style="color:#000;font-weight:bold">-&gt;</span> <span style="color:#204a87;font-weight:bold">i32</span>
-</span></span></code></pre></div><p>Traits: <code>AlwaysSpeculatableImplTrait</code></p>
-<p>Interfaces: <code>ConditionallySpeculatable</code>, <code>NoMemoryEffect (MemoryEffectOpInterface)</code></p>
-<p>Effects: <code>MemoryEffects::Effect{}</code></p>
-<h4 id="operands-3">Operands:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Operand</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>input</code></td>
-<td>A secret value</td>
-</tr>
-</tbody>
-</table>
-<h4 id="results-3">Results:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Result</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>cleartext</code></td>
-<td>any type</td>
-</tr>
-</tbody>
-</table>
-<h3 id="secretseparator-heirsecretseparatorop"><code>secret.separator</code> (heir::secret::SeparatorOp)</h3>
-<p><em>Convert a non-secret value into a secret</em></p>
-<p>Syntax:</p>
-<pre tabindex="0"><code>operation ::= `secret.separator` attr-dict ($inputs^ `:` type($inputs))?
-</code></pre><p>This operation is used as a separation boundary between logical subunits of
-the module. This is used in conjunction with
-<code>--secret-distribute-generic=distribute-through=secret.separator</code> to break a
-generic around these separators and allow for optimization passses to
-analyze and optimize the sub-units locally.</p>
-<p>In order to allow bufferization of modules with this operation, we must
-register a (bogus) memory effect that also prevents this operation from
-being trivially dead during operation folding.</p>
-<p>This operation also accepts operands, which act as boundaries between the
-logical units. This enforces separation of memref and affine optimizations
-between the subunits, preventing optimizations from removing the operand and
-combining the two separated regions. The operand can be thought of as an
-return value of the logical subunit.</p>
-<p>Interfaces: <code>MemoryEffectOpInterface (MemoryEffectOpInterface)</code></p>
-<p>Effects: <code>MemoryEffects::Effect{MemoryEffects::Write on ::mlir::SideEffects::DefaultResource}</code></p>
-<h4 id="operands-4">Operands:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Operand</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>inputs</code></td>
-<td>variadic of any type</td>
-</tr>
-</tbody>
-</table>
-<h3 id="secretyield-heirsecretyieldop"><code>secret.yield</code> (heir::secret::YieldOp)</h3>
-<p><em>Secret yield operation</em></p>
-<p><code>secret.yield</code> is a special terminator operation for blocks inside regions
-in <code>secret</code> generic ops. It returns the cleartext value of the
-corresponding private computation to the immediately enclosing <code>secret</code>
-generic op.</p>
-<p>Traits: <code>AlwaysSpeculatableImplTrait</code>, <code>HasParent&lt;GenericOp&gt;</code>, <code>ReturnLike</code>, <code>Terminator</code></p>
-<p>Interfaces: <code>ConditionallySpeculatable</code>, <code>NoMemoryEffect (MemoryEffectOpInterface)</code>, <code>RegionBranchTerminatorOpInterface</code></p>
-<p>Effects: <code>MemoryEffects::Effect{}</code></p>
-<h4 id="operands-5">Operands:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Operand</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>values</code></td>
-<td>variadic of any type</td>
-</tr>
-</tbody>
-</table>Docs: TensorExthttps://heir.dev/docs/dialects/tensorext/Mon, 01 Jan 0001 00:00:00 +0000https://heir.dev/docs/dialects/tensorext/
-<!-- Autogenerated by mlir-tblgen; don't manually edit -->
-<h1 id="tensor_ext-dialect">&rsquo;tensor_ext&rsquo; Dialect</h1>
-<p>The <code>tensor_ext</code> dialect contains operations on plaintext tensors that
-correspond to the computation model of certain FHE schemes, but are
-unlikely to be upstreamed to MLIR due to their specificity to FHE.</p>
-<h2 id="tensorext-attributes">TensorExt attributes</h2>
-<!-- Autogenerated by mlir-tblgen; don't manually edit -->
-<h3 id="simdpackingattr">SIMDPackingAttr</h3>
-<p>An attribute describing the SIMD packing of a tensor.</p>
-<p>Syntax:</p>
-<pre tabindex="0"><code>#tensor_ext.simd_packing&lt;
-::mlir::DenseI64ArrayAttr, # in
-::mlir::DenseI64ArrayAttr, # padding
-::mlir::DenseI64ArrayAttr, # out
-int64_t # padding_value
-&gt;
-</code></pre><p>This attribute is used as the encoding attribute on a tensor. It describes
-the transformations that were applied to an input tensor to pack it into the
-given tensor.</p>
-<p>The <code>in</code> attribute describes the shape of the original tensor.
-The following transformations are applied to the input tensor.</p>
-<ol>
-<li>
-<p>Padding is applied first. The <code>padding</code> attribute is an array with the
-same size as the input tensor shape. Padding is applied at the end of
-the array using the <code>padding_value</code> attribute (default zero). The
-result after zero padding should be a power of two.</p>
-</li>
-<li>
-<p>The padded result is replicated or split to fill the output tensor
-shape.</p>
-</li>
-</ol>
-<p>For example,</p>
-<pre tabindex="0"><code>#packing = #tensor_ext.simd_packing&lt;
-in = [7],
-padding = [1],
-padding_value = 0,
-out = [16],
-&gt;
-</code></pre><p>may be used on a tensor type like</p>
-<pre tabindex="0"><code>tensor&lt;1x16xi32, #packing&gt;
-</code></pre><p>If the original tensor had values <code>[1, 2, 3, 4, 5, 6, 7]</code> then a tensor with
-this attribute contains the data <code>[1, 2, 3, 4, 5, 6, 7, 0, 1, 2, 3, 4, 5, 6, 7, 0]</code>.</p>
-<h4 id="parameters">Parameters:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Parameter</th>
-<th style="text-align:center">C++ type</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center">in</td>
-<td style="text-align:center"><code>::mlir::DenseI64ArrayAttr</code></td>
-<td></td>
-</tr>
-<tr>
-<td style="text-align:center">padding</td>
-<td style="text-align:center"><code>::mlir::DenseI64ArrayAttr</code></td>
-<td></td>
-</tr>
-<tr>
-<td style="text-align:center">out</td>
-<td style="text-align:center"><code>::mlir::DenseI64ArrayAttr</code></td>
-<td></td>
-</tr>
-<tr>
-<td style="text-align:center">padding_value</td>
-<td style="text-align:center"><code>int64_t</code></td>
-<td></td>
-</tr>
-</tbody>
-</table>
-<h2 id="tensorext-ops">TensorExt ops</h2>
-<!-- Autogenerated by mlir-tblgen; don't manually edit -->
-<h3 id="tensor_extrotate-heirtensor_extrotateop"><code>tensor_ext.rotate</code> (heir::tensor_ext::RotateOp)</h3>
-<p><em>Rotate a tensor some number of indices left.</em></p>
-<p>Syntax:</p>
-<pre tabindex="0"><code>operation ::= `tensor_ext.rotate` operands attr-dict `:` qualified(type($tensor)) `,` type($shift)
-</code></pre><p>This op represents a left-rotation of a tensor by given number of indices.
-Negative shift values are interpreted as right-rotations.</p>
-<p>This corresponds to the <code>rotate</code> operation in arithmetic FHE schemes like
-BGV.</p>
-<p>This operation&rsquo;s current behavior allows rotating multi-dimensional tensors
-by rotating along the tensor&rsquo;s only non-unit dimension. This assumes the
-tensor is packed along the non-unit dimension.</p>
-<p>// In the future, the op will be adjusted to support rotations of general
-// multi-dimensional tensors with a vector of rotation indices for each
-// dimension. The lowering will implement the correct operations to rotate
-// the tensor along the indices given its packing.</p>
-<p>Examples:</p>
-<div class="highlight"><pre tabindex="0" style="background-color:#f8f8f8;-moz-tab-size:4;-o-tab-size:4;tab-size:4;"><code class="language-mlir" data-lang="mlir"><span style="display:flex;"><span><span style="color:#000">%0</span> <span style="color:#000;font-weight:bold">=</span> <span style="color:#000;font-weight:bold">...</span> <span style="color:#000;font-weight:bold">:</span> <span style="color:#204a87;font-weight:bold">tensor</span><span style="color:#000;font-weight:bold">&lt;</span><span style="color:#0000cf;font-weight:bold">16x</span><span style="color:#204a87;font-weight:bold">i32</span><span style="color:#000;font-weight:bold">&gt;</span>
-</span></span><span style="display:flex;"><span><span style="color:#000">%c7</span> <span style="color:#000;font-weight:bold">=</span> arith<span style="color:#000;font-weight:bold">.</span><span style="color:#204a87;font-weight:bold">constant</span> <span style="color:#0000cf;font-weight:bold">7</span> <span style="color:#000;font-weight:bold">:</span> <span style="color:#204a87;font-weight:bold">i32</span>
-</span></span><span style="display:flex;"><span><span style="color:#000">%1</span> <span style="color:#000;font-weight:bold">=</span> <span style="color:#204a87;font-weight:bold">tensor</span>_ext<span style="color:#000;font-weight:bold">.</span>rotate <span style="color:#000">%0</span><span style="color:#000;font-weight:bold">,</span> <span style="color:#000">%c7</span> <span style="color:#000;font-weight:bold">:</span> <span style="color:#204a87;font-weight:bold">tensor</span><span style="color:#000;font-weight:bold">&lt;</span><span style="color:#0000cf;font-weight:bold">16x</span><span style="color:#204a87;font-weight:bold">i32</span><span style="color:#000;font-weight:bold">&gt;,</span> <span style="color:#204a87;font-weight:bold">i32</span>
-</span></span></code></pre></div><p>Traits: <code>AlwaysSpeculatableImplTrait</code></p>
-<p>Interfaces: <code>ConditionallySpeculatable</code>, <code>InferTypeOpInterface</code>, <code>NoMemoryEffect (MemoryEffectOpInterface)</code></p>
-<p>Effects: <code>MemoryEffects::Effect{}</code></p>
-<h4 id="operands">Operands:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Operand</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>tensor</code></td>
-<td>tensor of any type values</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>shift</code></td>
-<td>signless-integer-like</td>
-</tr>
-</tbody>
-</table>
-<h4 id="results">Results:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Result</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>output</code></td>
-<td>tensor of any type values</td>
-</tr>
-</tbody>
-</table>Docs: TfheRusthttps://heir.dev/docs/dialects/tfherust/Mon, 01 Jan 0001 00:00:00 +0000https://heir.dev/docs/dialects/tfherust/
-<!-- Autogenerated by mlir-tblgen; don't manually edit -->
-<h1 id="tfhe_rust-dialect">&rsquo;tfhe_rust&rsquo; Dialect</h1>
-<p>The <code>thfe_rust</code> dialect is an exit dialect for generating rust code against the tfhe-rs library API,
-using the shortint parameters and encoding scheme.</p>
-<p>See <a href="https://github.com/zama-ai/tfhe-rs">https://github.com/zama-ai/tfhe-rs</a></p>
-<h2 id="tfherust-types">TfheRust types</h2>
-<!-- Autogenerated by mlir-tblgen; don't manually edit -->
-<h3 id="encryptedint8type">EncryptedInt8Type</h3>
-<p>An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt8 type</p>
-<p>Syntax: <code>!tfhe_rust.ei8</code></p>
-<h3 id="encryptedint16type">EncryptedInt16Type</h3>
-<p>An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt16 type</p>
-<p>Syntax: <code>!tfhe_rust.ei16</code></p>
-<h3 id="encryptedint32type">EncryptedInt32Type</h3>
-<p>An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt32 type</p>
-<p>Syntax: <code>!tfhe_rust.ei32</code></p>
-<h3 id="encryptedint64type">EncryptedInt64Type</h3>
-<p>An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt64 type</p>
-<p>Syntax: <code>!tfhe_rust.ei64</code></p>
-<h3 id="encryptedint128type">EncryptedInt128Type</h3>
-<p>An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt128 type</p>
-<p>Syntax: <code>!tfhe_rust.ei128</code></p>
-<h3 id="encryptedint256type">EncryptedInt256Type</h3>
-<p>An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt256 type</p>
-<p>Syntax: <code>!tfhe_rust.ei256</code></p>
-<h3 id="encrypteduint2type">EncryptedUInt2Type</h3>
-<p>An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint2 type</p>
-<p>Syntax: <code>!tfhe_rust.eui2</code></p>
-<h3 id="encrypteduint3type">EncryptedUInt3Type</h3>
-<p>An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint3 type</p>
-<p>Syntax: <code>!tfhe_rust.eui3</code></p>
-<h3 id="encrypteduint4type">EncryptedUInt4Type</h3>
-<p>An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint4 type</p>
-<p>Syntax: <code>!tfhe_rust.eui4</code></p>
-<h3 id="encrypteduint8type">EncryptedUInt8Type</h3>
-<p>An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint8 type</p>
-<p>Syntax: <code>!tfhe_rust.eui8</code></p>
-<h3 id="encrypteduint10type">EncryptedUInt10Type</h3>
-<p>An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint10 type</p>
-<p>Syntax: <code>!tfhe_rust.eui10</code></p>
-<h3 id="encrypteduint12type">EncryptedUInt12Type</h3>
-<p>An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint12 type</p>
-<p>Syntax: <code>!tfhe_rust.eui12</code></p>
-<h3 id="encrypteduint14type">EncryptedUInt14Type</h3>
-<p>An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint14 type</p>
-<p>Syntax: <code>!tfhe_rust.eui14</code></p>
-<h3 id="encrypteduint16type">EncryptedUInt16Type</h3>
-<p>An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint16 type</p>
-<p>Syntax: <code>!tfhe_rust.eui16</code></p>
-<h3 id="encrypteduint32type">EncryptedUInt32Type</h3>
-<p>An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint32 type</p>
-<p>Syntax: <code>!tfhe_rust.eui32</code></p>
-<h3 id="encrypteduint64type">EncryptedUInt64Type</h3>
-<p>An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint64 type</p>
-<p>Syntax: <code>!tfhe_rust.eui64</code></p>
-<h3 id="encrypteduint128type">EncryptedUInt128Type</h3>
-<p>An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint128 type</p>
-<p>Syntax: <code>!tfhe_rust.eui128</code></p>
-<h3 id="encrypteduint256type">EncryptedUInt256Type</h3>
-<p>An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint256 type</p>
-<p>Syntax: <code>!tfhe_rust.eui256</code></p>
-<h3 id="lookuptabletype">LookupTableType</h3>
-<p>A univariate lookup table used for programmable bootstrapping.</p>
-<p>Syntax: <code>!tfhe_rust.lookup_table</code></p>
-<h3 id="serverkeytype">ServerKeyType</h3>
-<p>The short int server key required to perform homomorphic operations.</p>
-<p>Syntax: <code>!tfhe_rust.server_key</code></p>
-<h2 id="tfherust-ops">TfheRust ops</h2>
-<!-- Autogenerated by mlir-tblgen; don't manually edit -->
-<h3 id="tfhe_rustadd-heirtfhe_rustaddop"><code>tfhe_rust.add</code> (heir::tfhe_rust::AddOp)</h3>
-<p><em>Arithmetic add of two tfhe ciphertexts.</em></p>
-<p>Syntax:</p>
-<pre tabindex="0"><code>operation ::= `tfhe_rust.add` operands attr-dict `:` functional-type(operands, results)
-</code></pre><p>Traits: <code>AlwaysSpeculatableImplTrait</code></p>
-<p>Interfaces: <code>ConditionallySpeculatable</code>, <code>InferTypeOpInterface</code>, <code>NoMemoryEffect (MemoryEffectOpInterface)</code></p>
-<p>Effects: <code>MemoryEffects::Effect{}</code></p>
-<h4 id="operands">Operands:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Operand</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>serverKey</code></td>
-<td>The short int server key required to perform homomorphic operations.</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>lhs</code></td>
-<td>An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint2 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint3 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint4 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint8 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint10 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint12 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint14 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint16 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint32 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint64 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint128 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint256 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt8 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt16 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt32 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt64 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt128 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt256 type</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>rhs</code></td>
-<td>An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint2 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint3 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint4 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint8 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint10 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint12 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint14 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint16 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint32 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint64 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint128 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint256 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt8 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt16 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt32 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt64 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt128 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt256 type</td>
-</tr>
-</tbody>
-</table>
-<h4 id="results">Results:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Result</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>output</code></td>
-<td>An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint2 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint3 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint4 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint8 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint10 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint12 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint14 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint16 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint32 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint64 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint128 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint256 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt8 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt16 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt32 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt64 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt128 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt256 type</td>
-</tr>
-</tbody>
-</table>
-<h3 id="tfhe_rustapply_lookup_table-heirtfhe_rustapplylookuptableop"><code>tfhe_rust.apply_lookup_table</code> (heir::tfhe_rust::ApplyLookupTableOp)</h3>
-<p>Syntax:</p>
-<pre tabindex="0"><code>operation ::= `tfhe_rust.apply_lookup_table` operands attr-dict `:` functional-type(operands, results)
-</code></pre><p>Traits: <code>AlwaysSpeculatableImplTrait</code></p>
-<p>Interfaces: <code>ConditionallySpeculatable</code>, <code>InferTypeOpInterface</code>, <code>NoMemoryEffect (MemoryEffectOpInterface)</code></p>
-<p>Effects: <code>MemoryEffects::Effect{}</code></p>
-<h4 id="operands-1">Operands:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Operand</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>serverKey</code></td>
-<td>The short int server key required to perform homomorphic operations.</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>input</code></td>
-<td>An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint2 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint3 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint4 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint8 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint10 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint12 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint14 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint16 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint32 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint64 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint128 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint256 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt8 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt16 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt32 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt64 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt128 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt256 type</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>lookupTable</code></td>
-<td>A univariate lookup table used for programmable bootstrapping.</td>
-</tr>
-</tbody>
-</table>
-<h4 id="results-1">Results:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Result</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>output</code></td>
-<td>An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint2 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint3 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint4 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint8 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint10 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint12 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint14 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint16 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint32 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint64 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint128 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint256 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt8 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt16 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt32 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt64 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt128 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt256 type</td>
-</tr>
-</tbody>
-</table>
-<h3 id="tfhe_rustbitand-heirtfhe_rustbitandop"><code>tfhe_rust.bitand</code> (heir::tfhe_rust::BitAndOp)</h3>
-<p><em>Logical AND of two tfhe ciphertexts.</em></p>
-<p>Syntax:</p>
-<pre tabindex="0"><code>operation ::= `tfhe_rust.bitand` operands attr-dict `:` functional-type(operands, results)
-</code></pre><p>Traits: <code>AlwaysSpeculatableImplTrait</code></p>
-<p>Interfaces: <code>ConditionallySpeculatable</code>, <code>InferTypeOpInterface</code>, <code>NoMemoryEffect (MemoryEffectOpInterface)</code></p>
-<p>Effects: <code>MemoryEffects::Effect{}</code></p>
-<h4 id="operands-2">Operands:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Operand</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>serverKey</code></td>
-<td>The short int server key required to perform homomorphic operations.</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>lhs</code></td>
-<td>An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint2 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint3 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint4 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint8 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint10 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint12 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint14 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint16 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint32 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint64 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint128 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint256 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt8 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt16 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt32 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt64 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt128 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt256 type</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>rhs</code></td>
-<td>An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint2 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint3 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint4 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint8 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint10 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint12 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint14 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint16 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint32 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint64 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint128 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint256 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt8 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt16 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt32 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt64 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt128 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt256 type</td>
-</tr>
-</tbody>
-</table>
-<h4 id="results-2">Results:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Result</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>output</code></td>
-<td>An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint2 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint3 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint4 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint8 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint10 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint12 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint14 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint16 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint32 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint64 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint128 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint256 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt8 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt16 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt32 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt64 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt128 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt256 type</td>
-</tr>
-</tbody>
-</table>
-<h3 id="tfhe_rustcast-heirtfhe_rustcastop"><code>tfhe_rust.cast</code> (heir::tfhe_rust::CastOp)</h3>
-<p>Syntax:</p>
-<pre tabindex="0"><code>operation ::= `tfhe_rust.cast` operands attr-dict `:` functional-type(operands, results)
-</code></pre><p>Traits: <code>AlwaysSpeculatableImplTrait</code></p>
-<p>Interfaces: <code>ConditionallySpeculatable</code>, <code>NoMemoryEffect (MemoryEffectOpInterface)</code></p>
-<p>Effects: <code>MemoryEffects::Effect{}</code></p>
-<h4 id="operands-3">Operands:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Operand</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>serverKey</code></td>
-<td>The short int server key required to perform homomorphic operations.</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>ciphertext</code></td>
-<td>An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint2 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint3 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint4 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint8 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint10 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint12 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint14 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint16 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint32 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint64 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint128 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint256 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt8 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt16 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt32 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt64 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt128 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt256 type</td>
-</tr>
-</tbody>
-</table>
-<h4 id="results-3">Results:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Result</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>output</code></td>
-<td>An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint2 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint3 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint4 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint8 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint10 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint12 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint14 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint16 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint32 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint64 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint128 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint256 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt8 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt16 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt32 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt64 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt128 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt256 type</td>
-</tr>
-</tbody>
-</table>
-<h3 id="tfhe_rustcreate_trivial-heirtfhe_rustcreatetrivialop"><code>tfhe_rust.create_trivial</code> (heir::tfhe_rust::CreateTrivialOp)</h3>
-<p>Syntax:</p>
-<pre tabindex="0"><code>operation ::= `tfhe_rust.create_trivial` operands attr-dict `:` functional-type(operands, results)
-</code></pre><p>Traits: <code>AlwaysSpeculatableImplTrait</code></p>
-<p>Interfaces: <code>ConditionallySpeculatable</code>, <code>NoMemoryEffect (MemoryEffectOpInterface)</code></p>
-<p>Effects: <code>MemoryEffects::Effect{}</code></p>
-<h4 id="operands-4">Operands:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Operand</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>serverKey</code></td>
-<td>The short int server key required to perform homomorphic operations.</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>value</code></td>
-<td>integer</td>
-</tr>
-</tbody>
-</table>
-<h4 id="results-4">Results:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Result</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>output</code></td>
-<td>An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint2 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint3 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint4 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint8 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint10 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint12 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint14 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint16 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint32 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint64 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint128 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint256 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt8 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt16 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt32 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt64 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt128 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt256 type</td>
-</tr>
-</tbody>
-</table>
-<h3 id="tfhe_rustgenerate_lookup_table-heirtfhe_rustgeneratelookuptableop"><code>tfhe_rust.generate_lookup_table</code> (heir::tfhe_rust::GenerateLookupTableOp)</h3>
-<p>Syntax:</p>
-<pre tabindex="0"><code>operation ::= `tfhe_rust.generate_lookup_table` operands attr-dict `:` functional-type(operands, results)
-</code></pre><p>Traits: <code>AlwaysSpeculatableImplTrait</code></p>
-<p>Interfaces: <code>ConditionallySpeculatable</code>, <code>InferTypeOpInterface</code>, <code>NoMemoryEffect (MemoryEffectOpInterface)</code></p>
-<p>Effects: <code>MemoryEffects::Effect{}</code></p>
-<h4 id="attributes">Attributes:</h4>
-<table>
-<tr><th>Attribute</th><th>MLIR Type</th><th>Description</th></tr>
-<tr><td><code>truthTable</code></td><td>::mlir::IntegerAttr</td><td>An Attribute containing a integer value</td></tr>
-</table>
-<h4 id="operands-5">Operands:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Operand</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>serverKey</code></td>
-<td>The short int server key required to perform homomorphic operations.</td>
-</tr>
-</tbody>
-</table>
-<h4 id="results-5">Results:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Result</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>lookupTable</code></td>
-<td>A univariate lookup table used for programmable bootstrapping.</td>
-</tr>
-</tbody>
-</table>
-<h3 id="tfhe_rustmul-heirtfhe_rustmulop"><code>tfhe_rust.mul</code> (heir::tfhe_rust::MulOp)</h3>
-<p><em>Arithmetic mul of two tfhe ciphertexts.</em></p>
-<p>Syntax:</p>
-<pre tabindex="0"><code>operation ::= `tfhe_rust.mul` operands attr-dict `:` functional-type(operands, results)
-</code></pre><p>Traits: <code>AlwaysSpeculatableImplTrait</code></p>
-<p>Interfaces: <code>ConditionallySpeculatable</code>, <code>InferTypeOpInterface</code>, <code>NoMemoryEffect (MemoryEffectOpInterface)</code></p>
-<p>Effects: <code>MemoryEffects::Effect{}</code></p>
-<h4 id="operands-6">Operands:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Operand</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>serverKey</code></td>
-<td>The short int server key required to perform homomorphic operations.</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>lhs</code></td>
-<td>An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint2 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint3 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint4 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint8 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint10 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint12 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint14 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint16 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint32 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint64 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint128 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint256 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt8 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt16 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt32 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt64 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt128 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt256 type</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>rhs</code></td>
-<td>An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint2 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint3 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint4 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint8 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint10 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint12 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint14 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint16 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint32 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint64 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint128 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint256 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt8 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt16 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt32 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt64 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt128 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt256 type</td>
-</tr>
-</tbody>
-</table>
-<h4 id="results-6">Results:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Result</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>output</code></td>
-<td>An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint2 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint3 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint4 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint8 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint10 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint12 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint14 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint16 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint32 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint64 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint128 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint256 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt8 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt16 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt32 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt64 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt128 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt256 type</td>
-</tr>
-</tbody>
-</table>
-<h3 id="tfhe_rustscalar_left_shift-heirtfhe_rustscalarleftshiftop"><code>tfhe_rust.scalar_left_shift</code> (heir::tfhe_rust::ScalarLeftShiftOp)</h3>
-<p>Syntax:</p>
-<pre tabindex="0"><code>operation ::= `tfhe_rust.scalar_left_shift` operands attr-dict `:` functional-type(operands, results)
-</code></pre><p>Traits: <code>AlwaysSpeculatableImplTrait</code></p>
-<p>Interfaces: <code>ConditionallySpeculatable</code>, <code>InferTypeOpInterface</code>, <code>NoMemoryEffect (MemoryEffectOpInterface)</code></p>
-<p>Effects: <code>MemoryEffects::Effect{}</code></p>
-<h4 id="operands-7">Operands:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Operand</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>serverKey</code></td>
-<td>The short int server key required to perform homomorphic operations.</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>ciphertext</code></td>
-<td>An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint2 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint3 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint4 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint8 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint10 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint12 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint14 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint16 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint32 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint64 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint128 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint256 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt8 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt16 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt32 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt64 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt128 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt256 type</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>shiftAmount</code></td>
-<td>8-bit integer</td>
-</tr>
-</tbody>
-</table>
-<h4 id="results-7">Results:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Result</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>output</code></td>
-<td>An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint2 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint3 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint4 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint8 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint10 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint12 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint14 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint16 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint32 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint64 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint128 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint256 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt8 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt16 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt32 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt64 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt128 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt256 type</td>
-</tr>
-</tbody>
-</table>
-<h3 id="tfhe_rustscalar_right_shift-heirtfhe_rustscalarrightshiftop"><code>tfhe_rust.scalar_right_shift</code> (heir::tfhe_rust::ScalarRightShiftOp)</h3>
-<p>Syntax:</p>
-<pre tabindex="0"><code>operation ::= `tfhe_rust.scalar_right_shift` operands attr-dict `:` functional-type(operands, results)
-</code></pre><p>Traits: <code>AlwaysSpeculatableImplTrait</code></p>
-<p>Interfaces: <code>ConditionallySpeculatable</code>, <code>InferTypeOpInterface</code>, <code>NoMemoryEffect (MemoryEffectOpInterface)</code></p>
-<p>Effects: <code>MemoryEffects::Effect{}</code></p>
-<h4 id="operands-8">Operands:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Operand</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>serverKey</code></td>
-<td>The short int server key required to perform homomorphic operations.</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>ciphertext</code></td>
-<td>An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint2 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint3 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint4 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint8 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint10 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint12 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint14 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint16 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint32 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint64 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint128 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint256 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt8 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt16 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt32 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt64 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt128 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt256 type</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>shiftAmount</code></td>
-<td>8-bit integer</td>
-</tr>
-</tbody>
-</table>
-<h4 id="results-8">Results:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Result</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>output</code></td>
-<td>An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint2 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint3 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint4 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint8 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint10 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint12 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint14 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint16 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint32 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint64 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint128 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint256 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt8 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt16 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt32 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt64 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt128 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt256 type</td>
-</tr>
-</tbody>
-</table>
-<h3 id="tfhe_rustsub-heirtfhe_rustsubop"><code>tfhe_rust.sub</code> (heir::tfhe_rust::SubOp)</h3>
-<p><em>Arithmetic sub of two tfhe ciphertexts.</em></p>
-<p>Syntax:</p>
-<pre tabindex="0"><code>operation ::= `tfhe_rust.sub` operands attr-dict `:` functional-type(operands, results)
-</code></pre><p>Traits: <code>AlwaysSpeculatableImplTrait</code></p>
-<p>Interfaces: <code>ConditionallySpeculatable</code>, <code>InferTypeOpInterface</code>, <code>NoMemoryEffect (MemoryEffectOpInterface)</code></p>
-<p>Effects: <code>MemoryEffects::Effect{}</code></p>
-<h4 id="operands-9">Operands:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Operand</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>serverKey</code></td>
-<td>The short int server key required to perform homomorphic operations.</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>lhs</code></td>
-<td>An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint2 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint3 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint4 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint8 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint10 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint12 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint14 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint16 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint32 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint64 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint128 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint256 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt8 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt16 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt32 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt64 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt128 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt256 type</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>rhs</code></td>
-<td>An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint2 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint3 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint4 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint8 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint10 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint12 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint14 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint16 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint32 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint64 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint128 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint256 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt8 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt16 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt32 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt64 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt128 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt256 type</td>
-</tr>
-</tbody>
-</table>
-<h4 id="results-9">Results:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Result</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>output</code></td>
-<td>An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint2 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint3 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint4 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint8 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint10 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint12 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint14 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint16 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint32 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint64 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint128 type or An encrypted unsigned integer corresponding to tfhe-rs&rsquo;s FHEUint256 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt8 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt16 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt32 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt64 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt128 type or An encrypted signed integer corresponding to tfhe-rs&rsquo;s FHEInt256 type</td>
-</tr>
-</tbody>
-</table>Docs: TfheRustBoolhttps://heir.dev/docs/dialects/tfherustbool/Mon, 01 Jan 0001 00:00:00 +0000https://heir.dev/docs/dialects/tfherustbool/
-<!-- Autogenerated by mlir-tblgen; don't manually edit -->
-<h1 id="tfhe_rust_bool-dialect">&rsquo;tfhe_rust_bool&rsquo; Dialect</h1>
-<p>The <code>tfhe_rust_bool</code> dialect is an exit dialect for generating rust code against the tfhe-rs library API,
-using the boolean parameter set.</p>
-<p>See <a href="https://github.com/zama-ai/tfhe-rs">https://github.com/zama-ai/tfhe-rs</a></p>
-<h2 id="tfherustbool-attributes">TfheRustBool attributes</h2>
-<!-- Autogenerated by mlir-tblgen; don't manually edit -->
-<h3 id="tfherustboolgatesattr">TfheRustBoolGatesAttr</h3>
-<p>An Attribute containing an array of strings to store bool gates</p>
-<p>Syntax:</p>
-<pre tabindex="0"><code>#tfhe_rust_bool.tfhe_rust_bool_gates&lt;
-::llvm::ArrayRef&lt;::mlir::heir::tfhe_rust_bool::TfheRustBoolGateEnumAttr&gt; # gates
-&gt;
-</code></pre><p>This attributes stores a list of integer identifiers for Boolean gates.</p>
-<p>Uses following mapping:
-AND_GATE = 0;
-NAND_GATE = 1;
-OR_GATE = 2;
-NOR_GATE = 3;
-XOR_GATE = 4;
-XNOR_GATE = 5;
-NOT_GATE = 6;</p>
-<h4 id="parameters">Parameters:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Parameter</th>
-<th style="text-align:center">C++ type</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center">gates</td>
-<td style="text-align:center"><code>::llvm::ArrayRef&lt;::mlir::heir::tfhe_rust_bool::TfheRustBoolGateEnumAttr&gt;</code></td>
-<td></td>
-</tr>
-</tbody>
-</table>
-<h2 id="tfherustbool-types">TfheRustBool types</h2>
-<!-- Autogenerated by mlir-tblgen; don't manually edit -->
-<h3 id="encryptedbooltype">EncryptedBoolType</h3>
-<p>An encrypted Boolean corresponding to tfhe-rs&rsquo;s FHEBool type</p>
-<p>Syntax: <code>!tfhe_rust_bool.eb</code></p>
-<h3 id="packedserverkeytype">PackedServerKeyType</h3>
-<p>The Belfort packed API boolean server key.</p>
-<p>Syntax: <code>!tfhe_rust_bool.server_key_enum</code></p>
-<h3 id="serverkeytype">ServerKeyType</h3>
-<p>The boolean server key required to perform homomorphic operations.</p>
-<p>Syntax: <code>!tfhe_rust_bool.server_key</code></p>
-<h2 id="tfherustbool-ops">TfheRustBool ops</h2>
-<!-- Autogenerated by mlir-tblgen; don't manually edit -->
-<h3 id="tfhe_rust_boolcreate_trivial-heirtfhe_rust_boolcreatetrivialop"><code>tfhe_rust_bool.create_trivial</code> (heir::tfhe_rust_bool::CreateTrivialOp)</h3>
-<p>Syntax:</p>
-<pre tabindex="0"><code>operation ::= `tfhe_rust_bool.create_trivial` operands attr-dict `:` functional-type(operands, results)
-</code></pre><p>Traits: <code>AlwaysSpeculatableImplTrait</code></p>
-<p>Interfaces: <code>ConditionallySpeculatable</code>, <code>InferTypeOpInterface</code>, <code>NoMemoryEffect (MemoryEffectOpInterface)</code></p>
-<p>Effects: <code>MemoryEffects::Effect{}</code></p>
-<h4 id="operands">Operands:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Operand</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>serverKey</code></td>
-<td>tfhe rust bool server key</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>value</code></td>
-<td>1-bit signless integer</td>
-</tr>
-</tbody>
-</table>
-<h4 id="results">Results:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Result</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>output</code></td>
-<td>An encrypted Boolean corresponding to tfhe-rs&rsquo;s FHEBool type</td>
-</tr>
-</tbody>
-</table>
-<h3 id="tfhe_rust_booland-heirtfhe_rust_boolandop"><code>tfhe_rust_bool.and</code> (heir::tfhe_rust_bool::AndOp)</h3>
-<p><em>Logical AND of two TFHE-rs Bool ciphertexts.</em></p>
-<p>Syntax:</p>
-<pre tabindex="0"><code>operation ::= `tfhe_rust_bool.and` operands attr-dict `:` functional-type(operands, results)
-</code></pre><p>Traits: <code>AlwaysSpeculatableImplTrait</code>, <code>Commutative</code>, <code>Elementwise</code>, <code>Scalarizable</code>, <code>Tensorizable</code>, <code>Vectorizable</code></p>
-<p>Interfaces: <code>ConditionallySpeculatable</code>, <code>InferTypeOpInterface</code>, <code>NoMemoryEffect (MemoryEffectOpInterface)</code></p>
-<p>Effects: <code>MemoryEffects::Effect{}</code></p>
-<h4 id="operands-1">Operands:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Operand</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>serverKey</code></td>
-<td>The boolean server key required to perform homomorphic operations. or The Belfort packed API boolean server key.</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>lhs</code></td>
-<td>eb-like</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>rhs</code></td>
-<td>eb-like</td>
-</tr>
-</tbody>
-</table>
-<h4 id="results-1">Results:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Result</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>output</code></td>
-<td>eb-like</td>
-</tr>
-</tbody>
-</table>
-<h3 id="tfhe_rust_boolmux-heirtfhe_rust_boolmuxop"><code>tfhe_rust_bool.mux</code> (heir::tfhe_rust_bool::MuxOp)</h3>
-<p>Syntax:</p>
-<pre tabindex="0"><code>operation ::= `tfhe_rust_bool.mux` operands attr-dict `:` functional-type(operands, results)
-</code></pre><p>Traits: <code>AlwaysSpeculatableImplTrait</code></p>
-<p>Interfaces: <code>ConditionallySpeculatable</code>, <code>InferTypeOpInterface</code>, <code>NoMemoryEffect (MemoryEffectOpInterface)</code></p>
-<p>Effects: <code>MemoryEffects::Effect{}</code></p>
-<h4 id="operands-2">Operands:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Operand</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>serverKey</code></td>
-<td>The boolean server key required to perform homomorphic operations. or The Belfort packed API boolean server key.</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>cnd</code></td>
-<td>An encrypted Boolean corresponding to tfhe-rs&rsquo;s FHEBool type</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>lhs</code></td>
-<td>An encrypted Boolean corresponding to tfhe-rs&rsquo;s FHEBool type</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>rhs</code></td>
-<td>An encrypted Boolean corresponding to tfhe-rs&rsquo;s FHEBool type</td>
-</tr>
-</tbody>
-</table>
-<h4 id="results-2">Results:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Result</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>output</code></td>
-<td>An encrypted Boolean corresponding to tfhe-rs&rsquo;s FHEBool type</td>
-</tr>
-</tbody>
-</table>
-<h3 id="tfhe_rust_boolnand-heirtfhe_rust_boolnandop"><code>tfhe_rust_bool.nand</code> (heir::tfhe_rust_bool::NandOp)</h3>
-<p><em>Logical NAND of two TFHE-rs Bool ciphertexts.</em></p>
-<p>Syntax:</p>
-<pre tabindex="0"><code>operation ::= `tfhe_rust_bool.nand` operands attr-dict `:` functional-type(operands, results)
-</code></pre><p>Traits: <code>AlwaysSpeculatableImplTrait</code>, <code>Commutative</code>, <code>Elementwise</code>, <code>Scalarizable</code>, <code>Tensorizable</code>, <code>Vectorizable</code></p>
-<p>Interfaces: <code>ConditionallySpeculatable</code>, <code>InferTypeOpInterface</code>, <code>NoMemoryEffect (MemoryEffectOpInterface)</code></p>
-<p>Effects: <code>MemoryEffects::Effect{}</code></p>
-<h4 id="operands-3">Operands:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Operand</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>serverKey</code></td>
-<td>The boolean server key required to perform homomorphic operations. or The Belfort packed API boolean server key.</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>lhs</code></td>
-<td>eb-like</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>rhs</code></td>
-<td>eb-like</td>
-</tr>
-</tbody>
-</table>
-<h4 id="results-3">Results:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Result</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>output</code></td>
-<td>eb-like</td>
-</tr>
-</tbody>
-</table>
-<h3 id="tfhe_rust_boolnor-heirtfhe_rust_boolnorop"><code>tfhe_rust_bool.nor</code> (heir::tfhe_rust_bool::NorOp)</h3>
-<p><em>Logical NOR of two TFHE-rs Bool ciphertexts.</em></p>
-<p>Syntax:</p>
-<pre tabindex="0"><code>operation ::= `tfhe_rust_bool.nor` operands attr-dict `:` functional-type(operands, results)
-</code></pre><p>Traits: <code>AlwaysSpeculatableImplTrait</code>, <code>Commutative</code>, <code>Elementwise</code>, <code>Scalarizable</code>, <code>Tensorizable</code>, <code>Vectorizable</code></p>
-<p>Interfaces: <code>ConditionallySpeculatable</code>, <code>InferTypeOpInterface</code>, <code>NoMemoryEffect (MemoryEffectOpInterface)</code></p>
-<p>Effects: <code>MemoryEffects::Effect{}</code></p>
-<h4 id="operands-4">Operands:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Operand</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>serverKey</code></td>
-<td>The boolean server key required to perform homomorphic operations. or The Belfort packed API boolean server key.</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>lhs</code></td>
-<td>eb-like</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>rhs</code></td>
-<td>eb-like</td>
-</tr>
-</tbody>
-</table>
-<h4 id="results-4">Results:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Result</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>output</code></td>
-<td>eb-like</td>
-</tr>
-</tbody>
-</table>
-<h3 id="tfhe_rust_boolnot-heirtfhe_rust_boolnotop"><code>tfhe_rust_bool.not</code> (heir::tfhe_rust_bool::NotOp)</h3>
-<p>Syntax:</p>
-<pre tabindex="0"><code>operation ::= `tfhe_rust_bool.not` operands attr-dict `:` functional-type(operands, results)
-</code></pre><p>Traits: <code>AlwaysSpeculatableImplTrait</code></p>
-<p>Interfaces: <code>ConditionallySpeculatable</code>, <code>InferTypeOpInterface</code>, <code>NoMemoryEffect (MemoryEffectOpInterface)</code></p>
-<p>Effects: <code>MemoryEffects::Effect{}</code></p>
-<h4 id="operands-5">Operands:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Operand</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>serverKey</code></td>
-<td>The boolean server key required to perform homomorphic operations. or The Belfort packed API boolean server key.</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>input</code></td>
-<td>eb-like</td>
-</tr>
-</tbody>
-</table>
-<h4 id="results-5">Results:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Result</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>output</code></td>
-<td>eb-like</td>
-</tr>
-</tbody>
-</table>
-<h3 id="tfhe_rust_boolor-heirtfhe_rust_boolorop"><code>tfhe_rust_bool.or</code> (heir::tfhe_rust_bool::OrOp)</h3>
-<p><em>Logical OR of two TFHE-rs Bool ciphertexts.</em></p>
-<p>Syntax:</p>
-<pre tabindex="0"><code>operation ::= `tfhe_rust_bool.or` operands attr-dict `:` functional-type(operands, results)
-</code></pre><p>Traits: <code>AlwaysSpeculatableImplTrait</code>, <code>Commutative</code>, <code>Elementwise</code>, <code>Scalarizable</code>, <code>Tensorizable</code>, <code>Vectorizable</code></p>
-<p>Interfaces: <code>ConditionallySpeculatable</code>, <code>InferTypeOpInterface</code>, <code>NoMemoryEffect (MemoryEffectOpInterface)</code></p>
-<p>Effects: <code>MemoryEffects::Effect{}</code></p>
-<h4 id="operands-6">Operands:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Operand</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>serverKey</code></td>
-<td>The boolean server key required to perform homomorphic operations. or The Belfort packed API boolean server key.</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>lhs</code></td>
-<td>eb-like</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>rhs</code></td>
-<td>eb-like</td>
-</tr>
-</tbody>
-</table>
-<h4 id="results-6">Results:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Result</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>output</code></td>
-<td>eb-like</td>
-</tr>
-</tbody>
-</table>
-<h3 id="tfhe_rust_boolgates_packed-heirtfhe_rust_boolpackedop"><code>tfhe_rust_bool.gates_packed</code> (heir::tfhe_rust_bool::PackedOp)</h3>
-<p>Syntax:</p>
-<pre tabindex="0"><code>operation ::= `tfhe_rust_bool.gates_packed` operands attr-dict `:` functional-type(operands, results)
-</code></pre><p>Operation to where different Boolean gates are executed pairwise between elements of two ciphertext arrays.</p>
-<p>For example,</p>
-<div class="highlight"><pre tabindex="0" style="background-color:#f8f8f8;-moz-tab-size:4;-o-tab-size:4;tab-size:4;"><code class="language-mlir" data-lang="mlir"><span style="display:flex;"><span><span style="color:#000">%0</span> <span style="color:#000;font-weight:bold">=</span> tfhe_rust_bool<span style="color:#000;font-weight:bold">.</span>packed_gates <span style="color:#000">%a</span><span style="color:#000;font-weight:bold">,</span> <span style="color:#000">%b</span> <span style="color:#000;font-weight:bold">{</span><span style="color:#f57900">gates =</span> <span style="color:#000">#tfhe_rust_bool.tfhe_rust_bool_gates</span><span style="color:#000;font-weight:bold">&lt;</span><span style="color:#0000cf;font-weight:bold">0</span> <span style="color:#000;font-weight:bold">:</span> <span style="color:#204a87;font-weight:bold">i32</span><span style="color:#000;font-weight:bold">,</span> <span style="color:#0000cf;font-weight:bold">4</span> <span style="color:#000;font-weight:bold">:</span> <span style="color:#204a87;font-weight:bold">i32</span><span style="color:#000;font-weight:bold">&gt;}</span> <span style="color:#000;font-weight:bold">:</span>
-</span></span><span style="display:flex;"><span> <span style="color:#000;font-weight:bold">(!</span>tfhe_rust_bool<span style="color:#000;font-weight:bold">.</span>server_key<span style="color:#000;font-weight:bold">,</span>
-</span></span><span style="display:flex;"><span> <span style="color:#204a87;font-weight:bold">tensor</span><span style="color:#000;font-weight:bold">&lt;</span><span style="color:#0000cf;font-weight:bold">2x</span><span style="color:#000;font-weight:bold">!</span>tfhe_rust_bool<span style="color:#000;font-weight:bold">.</span>eb<span style="color:#000;font-weight:bold">&gt;,</span>
-</span></span><span style="display:flex;"><span> <span style="color:#204a87;font-weight:bold">tensor</span><span style="color:#000;font-weight:bold">&lt;</span><span style="color:#0000cf;font-weight:bold">2x</span><span style="color:#000;font-weight:bold">!</span>tfhe_rust_bool<span style="color:#000;font-weight:bold">.</span>eb<span style="color:#000;font-weight:bold">&gt;)</span> <span style="color:#000;font-weight:bold">-&gt;</span> <span style="color:#204a87;font-weight:bold">tensor</span><span style="color:#000;font-weight:bold">&lt;</span><span style="color:#0000cf;font-weight:bold">2x</span><span style="color:#000;font-weight:bold">!</span>tfhe_rust_bool<span style="color:#000;font-weight:bold">.</span>eb<span style="color:#000;font-weight:bold">&gt;</span>
-</span></span></code></pre></div><p>applies an &ldquo;and&rdquo; gate to the first elements of %a and %b and an xor gate to the
-second elements.</p>
-<p>Mapping is defined in the BooleanGates.td file.</p>
-<p>Traits: <code>AlwaysSpeculatableImplTrait</code></p>
-<p>Interfaces: <code>ConditionallySpeculatable</code>, <code>InferTypeOpInterface</code>, <code>NoMemoryEffect (MemoryEffectOpInterface)</code></p>
-<p>Effects: <code>MemoryEffects::Effect{}</code></p>
-<h4 id="attributes">Attributes:</h4>
-<table>
-<tr><th>Attribute</th><th>MLIR Type</th><th>Description</th></tr>
-<tr><td><code>gates</code></td><td>::mlir::heir::tfhe_rust_bool::TfheRustBoolGatesAttr</td><td>An Attribute containing an array of strings to store bool gates</td></tr>
-</table>
-<h4 id="operands-7">Operands:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Operand</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>serverKey</code></td>
-<td>The boolean server key required to perform homomorphic operations. or The Belfort packed API boolean server key.</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>lhs</code></td>
-<td>eb-like</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>rhs</code></td>
-<td>eb-like</td>
-</tr>
-</tbody>
-</table>
-<h4 id="results-7">Results:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Result</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>output</code></td>
-<td>eb-like</td>
-</tr>
-</tbody>
-</table>
-<h3 id="tfhe_rust_boolxnor-heirtfhe_rust_boolxnorop"><code>tfhe_rust_bool.xnor</code> (heir::tfhe_rust_bool::XnorOp)</h3>
-<p><em>Logical XNOR of two TFHE-rs Bool ciphertexts.</em></p>
-<p>Syntax:</p>
-<pre tabindex="0"><code>operation ::= `tfhe_rust_bool.xnor` operands attr-dict `:` functional-type(operands, results)
-</code></pre><p>Traits: <code>AlwaysSpeculatableImplTrait</code>, <code>Commutative</code>, <code>Elementwise</code>, <code>Scalarizable</code>, <code>Tensorizable</code>, <code>Vectorizable</code></p>
-<p>Interfaces: <code>ConditionallySpeculatable</code>, <code>InferTypeOpInterface</code>, <code>NoMemoryEffect (MemoryEffectOpInterface)</code></p>
-<p>Effects: <code>MemoryEffects::Effect{}</code></p>
-<h4 id="operands-8">Operands:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Operand</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>serverKey</code></td>
-<td>The boolean server key required to perform homomorphic operations. or The Belfort packed API boolean server key.</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>lhs</code></td>
-<td>eb-like</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>rhs</code></td>
-<td>eb-like</td>
-</tr>
-</tbody>
-</table>
-<h4 id="results-8">Results:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Result</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>output</code></td>
-<td>eb-like</td>
-</tr>
-</tbody>
-</table>
-<h3 id="tfhe_rust_boolxor-heirtfhe_rust_boolxorop"><code>tfhe_rust_bool.xor</code> (heir::tfhe_rust_bool::XorOp)</h3>
-<p><em>Logical XOR of two TFHE-rs Bool ciphertexts.</em></p>
-<p>Syntax:</p>
-<pre tabindex="0"><code>operation ::= `tfhe_rust_bool.xor` operands attr-dict `:` functional-type(operands, results)
-</code></pre><p>Traits: <code>AlwaysSpeculatableImplTrait</code>, <code>Commutative</code>, <code>Elementwise</code>, <code>Scalarizable</code>, <code>Tensorizable</code>, <code>Vectorizable</code></p>
-<p>Interfaces: <code>ConditionallySpeculatable</code>, <code>InferTypeOpInterface</code>, <code>NoMemoryEffect (MemoryEffectOpInterface)</code></p>
-<p>Effects: <code>MemoryEffects::Effect{}</code></p>
-<h4 id="operands-9">Operands:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Operand</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>serverKey</code></td>
-<td>The boolean server key required to perform homomorphic operations. or The Belfort packed API boolean server key.</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>lhs</code></td>
-<td>eb-like</td>
-</tr>
-<tr>
-<td style="text-align:center"><code>rhs</code></td>
-<td>eb-like</td>
-</tr>
-</tbody>
-</table>
-<h4 id="results-9">Results:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Result</th>
-<th>Description</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center"><code>output</code></td>
-<td>eb-like</td>
-</tr>
-</tbody>
-</table>
-<h2 id="tfherustbool-additional-definitions">TfheRustBool additional definitions</h2>
-<!-- Autogenerated by mlir-tblgen; don't manually edit -->
-<h3 id="tfherustboolgateenum">TfheRustBoolGateEnum</h3>
-<p>An enum attribute representing a TFHE-rs boolean gate using u8 int</p>
-<h4 id="cases">Cases:</h4>
-<table>
-<thead>
-<tr>
-<th style="text-align:center">Symbol</th>
-<th style="text-align:center">Value</th>
-<th>String</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:center">AND</td>
-<td style="text-align:center"><code>0</code></td>
-<td>AND</td>
-</tr>
-<tr>
-<td style="text-align:center">NAND</td>
-<td style="text-align:center"><code>1</code></td>
-<td>NAND</td>
-</tr>
-<tr>
-<td style="text-align:center">OR</td>
-<td style="text-align:center"><code>2</code></td>
-<td>OR</td>
-</tr>
-<tr>
-<td style="text-align:center">NOR</td>
-<td style="text-align:center"><code>3</code></td>
-<td>NOR</td>
-</tr>
-<tr>
-<td style="text-align:center">XOR</td>
-<td style="text-align:center"><code>4</code></td>
-<td>XOR</td>
-</tr>
-<tr>
-<td style="text-align:center">XNOR</td>
-<td style="text-align:center"><code>5</code></td>
-<td>XNOR</td>
-</tr>
-<tr>
-<td style="text-align:center">NOT</td>
-<td style="text-align:center"><code>6</code></td>
-<td>NOT</td>
-</tr>
-</tbody>
 </table>
\ No newline at end of file
diff --git a/index.xml b/index.xml
index 69d637b03..0bcd65c01 100644
--- a/index.xml
+++ b/index.xml
@@ -4,188 +4,9 @@ high-level overview of the HEIR project, brainstorming where new research might
 be needed, and discussing how the HEIR team could help with research projects.</p>
 <p>The <a href="https://youtu.be/t_XHw7LVy8s">video recording of this talk</a> is on YouTube,
 and this is the first video posted on the
-<a href="https://www.youtube.com/@HEIRCompiler">new HEIR YouTube channel</a>.</p>Blog: HEIR meeting 2024-11-26https://heir.dev/blog/2024/11/26/heir-meeting-2024-11-26/Tue, 26 Nov 2024 00:00:00 +0000https://heir.dev/blog/2024/11/26/heir-meeting-2024-11-26/
-<p>Here are the
-<a href="https://docs.google.com/document/d/10WTpdVaLz4mgmTwlJ3lVMGD4qmiNEl2Uvt3R3h0XFmc/edit?hl=en&amp;forcehl=1&amp;tab=t.0#heading=h.w3lar3vbuip1">notes</a>,
-<a href="https://drive.google.com/file/d/13yvX_ap09tTqwJsdABDf3WDl79GF3bJx/view?usp=sharing">video recording</a>,
-and
-<a href="https://docs.google.com/document/d/1s5iXtOSpIDJX3JOEB5gQqUPm5lo1gLpRUM10pBfAdoo/edit?usp=sharing">a transcription of the recording</a>
-from the HEIR meeting on 2024-11-26.</p>Blog: HEIR meeting 2024-10-04https://heir.dev/blog/2024/10/04/heir-meeting-2024-10-04/Fri, 04 Oct 2024 00:00:00 +0000https://heir.dev/blog/2024/10/04/heir-meeting-2024-10-04/
-<p>Here are the
-<a href="https://docs.google.com/document/d/1tlC-g3JKOB9wxfQMEJnKQk0C0eBdtBCzZX8ck7J37fI/edit?usp=sharing">notes</a>
-and
-<a href="https://drive.google.com/file/d/1OFfrwWesFpxVHw2DFuNAxSB8seLG_tr1/view?usp=sharing">video recording</a>
-from the HEIR meeting on 2024-10-04.</p>Blog: HEIR meeting 2024-09-19https://heir.dev/blog/2024/09/19/heir-meeting-2024-09-19/Thu, 19 Sep 2024 00:00:00 +0000https://heir.dev/blog/2024/09/19/heir-meeting-2024-09-19/
-<p>Here are the
-<a href="https://docs.google.com/document/d/1aGIiZPWpk7UMg5FD8ZYHmNhKVZ6NdhfmGMvyHrrlolM/edit?usp=sharing">notes</a>
-and
-<a href="https://drive.google.com/file/d/1i-HqUi8pb2ywUJ-OT4fWExYCmeRLu2Cn/view?usp=sharing">video recording</a>
-from the HEIR meeting on 2024-09-19.</p>Blog: HEIR meeting 2024-09-05https://heir.dev/blog/2024/09/05/heir-meeting-2024-09-05/Thu, 05 Sep 2024 00:00:00 +0000https://heir.dev/blog/2024/09/05/heir-meeting-2024-09-05/
-<p>Here are the
-<a href="https://docs.google.com/document/d/1tohVmC2pn_XDn3gjCFeo3K4Wfyf7VWu3oK1vimEsFD4/edit?usp=sharing">notes</a>
-and
-<a href="https://drive.google.com/file/d/1XGheLF7kvJfwAMJJQ-XbDpa4Ld15kj4t/view?usp=sharing">video recording</a>
-from the HEIR meeting on 2024-09-05.</p>Blog: HEIR meeting 2024-08-22https://heir.dev/blog/2024/08/22/heir-meeting-2024-08-22/Thu, 22 Aug 2024 00:00:00 +0000https://heir.dev/blog/2024/08/22/heir-meeting-2024-08-22/
-<p>Here are the
-<a href="https://docs.google.com/document/d/1iEkzpO6lCVbShMcRenO3j3DptOEP-0bLu_9V4K7c39M/edit?usp=sharing">notes</a>
-and
-<a href="https://drive.google.com/file/d/1wFrGF7lMiYZmqbr5WQO17HomfoFoOeaj/view?usp=sharing">video recording</a>
-from the HEIR meeting on 2024-08-22.</p>Blog: HEIR meeting 2024-08-08https://heir.dev/blog/2024/08/08/heir-meeting-2024-08-08/Thu, 08 Aug 2024 00:00:00 +0000https://heir.dev/blog/2024/08/08/heir-meeting-2024-08-08/
-<p>Here are the
-<a href="https://docs.google.com/document/d/1FLSiaPlX38GNHqqqi_Mz3gMuVSlS4sUcwBWqpt6Fkew/edit?usp=sharing">notes</a>
-and
-<a href="https://drive.google.com/file/d/1sHoRvNlS14RB-r3Rk0y2RyWOERVGNc-t/view?usp=sharing">video recording</a>
-from the HEIR meeting on 2024-08-08.</p>Blog: HEIR meeting 2024-07-25https://heir.dev/blog/2024/07/25/heir-meeting-2024-07-25/Thu, 25 Jul 2024 00:00:00 +0000https://heir.dev/blog/2024/07/25/heir-meeting-2024-07-25/
-<p>Here are the
-<a href="https://docs.google.com/document/d/1tIrxc4V5OlAeqx_Z1rl_kuMmkd-HUAKEv90q3i-5QSU/edit?usp=sharing">notes</a>
-and
-<a href="https://drive.google.com/file/d/1_1CbRJeNr5NqcwEMXnfkxOqy9u5wJPyq/view?usp=sharing">video recording</a>
-from the HEIR meeting on 2024-07-25.</p>Blog: HEIR meeting 2024-07-18 (mod_arith dialect)https://heir.dev/blog/2024/07/18/heir-meeting-2024-07-18-mod_arith-dialect/Thu, 18 Jul 2024 00:00:00 +0000https://heir.dev/blog/2024/07/18/heir-meeting-2024-07-18-mod_arith-dialect/
-<p>Here are the
-<a href="https://docs.google.com/document/d/1o2-I03DJtNJQDupSHn8LtOXLmxsd3WO1fjvqLbT-SIc/edit?usp=sharing">notes</a>
-and
-<a href="https://drive.google.com/file/d/1bCMuuKnBVf6HP7R2SiZgo1C1vsG6FzF2/view?usp=sharing">video recording</a>
-from the HEIR meeting on 2024-07-18. This special discussion was focused on the
-modular arithmetic dialect.</p>Blog: HEIR meeting 2024-07-11https://heir.dev/blog/2024/07/11/heir-meeting-2024-07-11/Thu, 11 Jul 2024 00:00:00 +0000https://heir.dev/blog/2024/07/11/heir-meeting-2024-07-11/
-<p>Here are the
-<a href="https://docs.google.com/document/d/1kP1kFKV6qrLVPv4CnIhmqO-7nMDFkCpvhzwIppJEDfU/edit?usp=sharing">notes</a>
-and
-<a href="https://drive.google.com/file/d/1-f5ZJ5h28FIgk_-LisNsYa77iuWPIAjU/view?usp=sharing">video recording</a>
-from the HEIR meeting on 2024-07-11.</p>Blog: HEIR meeting 2024-06-27https://heir.dev/blog/2024/06/27/heir-meeting-2024-06-27/Thu, 27 Jun 2024 00:00:00 +0000https://heir.dev/blog/2024/06/27/heir-meeting-2024-06-27/
-<p>Here are the
-<a href="https://docs.google.com/document/d/1lc4U2JzHapu99_sigOAYwpjNnfd9_QGrX1HAQ0hle_o/edit?usp=sharing">notes</a>
-and
-<a href="https://drive.google.com/file/d/1-wMytGj3AHi55sA2jb81AsHOU8EcIq6d/view?usp=sharing">video recording</a>
-from the HEIR meeting on 2024-06-27.</p>Blog: HEIR meeting 2024-06-13https://heir.dev/blog/2024/06/13/heir-meeting-2024-06-13/Thu, 13 Jun 2024 00:00:00 +0000https://heir.dev/blog/2024/06/13/heir-meeting-2024-06-13/
-<p>Here are the
-<a href="https://docs.google.com/document/d/1rkPxOdbJY5J6qhsciZ0rfdj5_9PG_Ng-6USBUvLrEeU/edit?usp=sharing">notes</a>
-and
-<a href="https://drive.google.com/file/d/19oQOYlvfeHoSwWqOC4hXZTBuaPIf1zQl/view?usp=sharing">video recording</a>
-from the HEIR meeting on 2024-06-13.</p>Blog: HEIR meeting 2024-05-30https://heir.dev/blog/2024/05/30/heir-meeting-2024-05-30/Thu, 30 May 2024 00:00:00 +0000https://heir.dev/blog/2024/05/30/heir-meeting-2024-05-30/
-<p>Here are the
-<a href="https://docs.google.com/document/d/1mvigwMRTeVQvdpm2hwiewfU8jcJT94ArQBNvngvgkTc/edit?usp=sharing">notes</a>
-and
-<a href="https://drive.google.com/file/d/1CTIyd7HRiNV857VO2EonquWZZlBhysLM/view?usp=sharing">video recording</a>
-from the HEIR meeting on 2024-05-30.</p>Blog: HEIR meeting 2024-05-16https://heir.dev/blog/2024/05/16/heir-meeting-2024-05-16/Thu, 16 May 2024 00:00:00 +0000https://heir.dev/blog/2024/05/16/heir-meeting-2024-05-16/
-<p>Here are the
-<a href="https://docs.google.com/document/d/15MwanXaBap6qNzYj7g1m6zRcqK363O-3iCCcNcGY1Ds/edit?usp=sharing">notes</a>
-and
-<a href="https://drive.google.com/file/d/1gOf_Tb8k9UNx7i0OvjjikkYUG3HrPjoS/view?usp=sharing">video recording</a>
-from the HEIR meeting on 2024-05-16.</p>Blog: HEIR meeting 2024-05-02https://heir.dev/blog/2024/05/02/heir-meeting-2024-05-02/Thu, 02 May 2024 00:00:00 +0000https://heir.dev/blog/2024/05/02/heir-meeting-2024-05-02/
-<p>Here are the
-<a href="https://docs.google.com/document/d/1uEDeIN0iTUmmtlacZg0c2j7VbAHO3A9e0_8mnunUv10/edit?usp=sharing">notes</a>
-and
-<a href="https://drive.google.com/file/d/1u1q74rUKdXFi08tAKFRKjI-bojuorQK8/view?usp=drivesdk">video recording</a>
-from the HEIR meeting on 2024-05-02.</p>Blog: HEIR meeting 2024-04-18https://heir.dev/blog/2024/04/18/heir-meeting-2024-04-18/Thu, 18 Apr 2024 00:00:00 +0000https://heir.dev/blog/2024/04/18/heir-meeting-2024-04-18/
-<p>Here are the
-<a href="https://docs.google.com/document/d/1BJjfYI2yjR3YEg_ugjDuS-trAkYMlKbU7jpH_M1GF3Q/edit?usp=sharing">notes</a>
-and
-<a href="https://drive.google.com/file/d/1WSsUp9CmjDmEVtGMYk2QXIpZCEetf_Ot/view?usp=sharing">video recording</a>
-from the HEIR meeting on 2024-04-18.</p>Blog: HEIR meeting 2024-04-04https://heir.dev/blog/2024/04/04/heir-meeting-2024-04-04/Thu, 04 Apr 2024 00:00:00 +0000https://heir.dev/blog/2024/04/04/heir-meeting-2024-04-04/
-<p>Here are the
-<a href="https://docs.google.com/document/d/121_0mzqYIWYMc7rcW2Et5qS-ux4ut3b-kno1dI9sQq8/edit?usp=sharing">notes</a>
-and
-<a href="https://drive.google.com/file/d/1_Ksjx8s8nD4cLsuZp5_KitYI2mPN72Je/view?usp=sharing">video recording</a>
-from the HEIR meeting on 2024-04-04.</p>Blog: HEIR meeting 2024-03-07https://heir.dev/blog/2024/03/07/heir-meeting-2024-03-07/Thu, 07 Mar 2024 00:00:00 +0000https://heir.dev/blog/2024/03/07/heir-meeting-2024-03-07/
-<p>Here are the
-<a href="https://docs.google.com/document/d/1felxN5mFBV5LheP79is30jHRxlKLW0NQEo6FPDKxDKM/edit?usp=sharing">notes</a>
-and
-<a href="https://drive.google.com/file/d/1oVJG-fM72nNLiR1eXkzdeaqdDOEpTfK0/view?usp=sharing">video recording</a>
-from the HEIR meeting on 2024-03-07.</p>
-<p>Note: there will be no HEIR meeting on 2024-03-21 due to the FHE.org, HACS, and
-RWC conferences. Hope to see you all there!</p>Blog: HEIR meeting 2024-02-22https://heir.dev/blog/2024/02/22/heir-meeting-2024-02-22/Thu, 22 Feb 2024 00:00:00 +0000https://heir.dev/blog/2024/02/22/heir-meeting-2024-02-22/
+<a href="https://www.youtube.com/@HEIRCompiler">new HEIR YouTube channel</a>.</p>Blog: HEIR meeting 2024-02-22https://heir.dev/blog/2024/02/22/heir-meeting-2024-02-22/Thu, 22 Feb 2024 00:00:00 +0000https://heir.dev/blog/2024/02/22/heir-meeting-2024-02-22/
 <p>Here are the
 <a href="https://docs.google.com/document/d/1ktK2Y2-OnadvsIIa94HRch_oHCaQ0D6gbT3CElKmGak/edit?usp=sharing">notes</a>
 and
 <a href="https://drive.google.com/file/d/1RDONadr54-7uX5ko5dmUX3s1l7QHeHbM/view?usp=sharing">video recording</a>
-from the HEIR meeting on 2024-02-22.</p>Blog: HEIR meeting 2024-02-08https://heir.dev/blog/2024/02/08/heir-meeting-2024-02-08/Thu, 08 Feb 2024 00:00:00 +0000https://heir.dev/blog/2024/02/08/heir-meeting-2024-02-08/
-<p>Here are the
-<a href="https://docs.google.com/document/d/1w0Cc3YfbSNO4PYVdGjb8KpE5rql8zgoDG2X0Yseon_4/edit?usp=sharing">notes</a>
-and
-<a href="https://drive.google.com/file/d/1rTsc-sWdRCqJWONrgGo5FV7CQd1S_OV-/view?usp=sharing">video recording</a>
-from the HEIR meeting on 2024-02-08.</p>Blog: HEIR meeting 2024-01-25https://heir.dev/blog/2024/01/25/heir-meeting-2024-01-25/Thu, 25 Jan 2024 00:00:00 +0000https://heir.dev/blog/2024/01/25/heir-meeting-2024-01-25/
-<p>Here are the
-<a href="https://docs.google.com/document/d/1yrkAVR_348vT3SD7apb9QDoFIgz0bjHn-SzT2GOacfs/edit?usp=sharing">notes</a>
-and
-<a href="https://drive.google.com/file/d/11JTfRy_3LvHjJQe0nJuqe8WGa8F9oHu1/view?usp=sharing">video recording</a>
-from the HEIR meeting on 2024-01-25.</p>Blog: HEIR meeting 2024-01-11https://heir.dev/blog/2024/01/11/heir-meeting-2024-01-11/Thu, 11 Jan 2024 00:00:00 +0000https://heir.dev/blog/2024/01/11/heir-meeting-2024-01-11/
-<p>Here are the
-<a href="https://docs.google.com/document/d/133yuywcbI1AWnbsJezq8QlCpgXfX5HMk7YjXQBSTwoE/edit?usp=sharing">notes</a>
-and
-<a href="https://drive.google.com/file/d/1gLwcshtNda6M6YMWSsyGrNDvlQ8QiL0O/view?usp=sharing">video recording</a>
-from the HEIR meeting on 2024-01-11.</p>Blog: HEIR meeting 2023-12-12https://heir.dev/blog/2023/12/12/heir-meeting-2023-12-12/Tue, 12 Dec 2023 00:00:00 +0000https://heir.dev/blog/2023/12/12/heir-meeting-2023-12-12/
-<p>Here are the
-<a href="https://docs.google.com/document/d/1ekGrOBLoB_F3qjC43r6NzJbWpgT9RILTJyVu5Ax3PCQ/edit?usp=sharing">notes</a>
-and
-<a href="https://drive.google.com/file/d/1DaYj9euovyf8vuCi260RQYfEkItn4SEc/view?usp=sharing">video recording</a>
-from the HEIR meeting on 2023-12-12.</p>
-<p>This is the last meeting for 2023. Please respond to
-<a href="https://app.rallly.co/invite/fHNdzrbisHVA">this poll</a> for 2024 scheduling
-preferences.</p>Blog: HEIR meeting 2023-11-28https://heir.dev/blog/2023/11/28/heir-meeting-2023-11-28/Tue, 28 Nov 2023 00:00:00 +0000https://heir.dev/blog/2023/11/28/heir-meeting-2023-11-28/
-<p>Here are the
-<a href="https://docs.google.com/document/d/1-kkkG__qlAtsp50YXxHC7Dq__Qvgb4BcLZCopzJOzE4/edit?usp=sharing">notes</a>
-and
-<a href="https://drive.google.com/file/d/1ykxaqlfVExqGC6saiSnfM2A7_TpWqKiE/view">video recording</a>
-from the HEIR meeting on 2023-11-28.</p>Blog: HEIR meeting 2023-11-07https://heir.dev/blog/2023/11/07/heir-meeting-2023-11-07/Tue, 07 Nov 2023 00:00:00 +0000https://heir.dev/blog/2023/11/07/heir-meeting-2023-11-07/
-<p>Here are the
-<a href="https://docs.google.com/document/d/1nOlAhul4DwZU8UQPpTF1i3OldSY9EmwaWG3EPSZIhHs/edit?usp=sharing">notes</a>
-and
-<a href="https://drive.google.com/file/d/1I7aIipm54CCcDcLyRYXI_gARfT1z93cN/view?usp=sharing">video recording</a>
-from the HEIR meeting on 2023-11-07.</p>Blog: HEIR meeting 2023-10-24https://heir.dev/blog/2023/10/25/heir-meeting-2023-10-24/Wed, 25 Oct 2023 00:00:00 +0000https://heir.dev/blog/2023/10/25/heir-meeting-2023-10-24/
-<p>Here are the
-<a href="https://docs.google.com/document/d/1MYjjkytck0fxySbrh49hxBJgNM78NXSD0ZwzAgEPOUw/edit?usp=sharing">notes</a>
-and
-<a href="https://drive.google.com/file/d/1zrSCQJXta40KbBiCjcIWOP3gd1tuc3MU/view?usp=sharing">video recording</a>
-from the HEIR meeting on 2023-10-24.</p>
-<p>Also of note: our talk at FHE.org was last Thursday
-(<a href="https://www.youtube.com/watch?v=kqDFdKUTNA4">recording</a>), and the similar talk
-at the LLVM developers meeting talk was the previous Wednesday, though the video
-has not yet been posted for that.</p>Blog: HEIR meeting 2023-09-26https://heir.dev/blog/2023/09/27/heir-meeting-2023-09-26/Wed, 27 Sep 2023 00:00:00 +0000https://heir.dev/blog/2023/09/27/heir-meeting-2023-09-26/
-<p>Here are the
-<a href="https://docs.google.com/document/d/1pkG8eaSUddAySJWjQHIFqe0hyYkO0wH9X0JtnR6wlWo/edit?usp=sharing">notes</a>
-and
-<a href="https://drive.google.com/file/d/1xaH-G3SZPVv_gEpUkfhFuvUTUwU2ZKLY/view?usp=sharing">video recording</a>
-from the HEIR meeting on 2023-09-26.</p>
-<p>Next meeting (Oct 10) is canceled for the MLIR workshop, and I&rsquo;ll post an update
-from that workshop on this blog, hopefully also with a video of the talk that
-Alex Viand and I will be giving at the LLVM developers meeting.</p>Blog: HEIR meeting 2023-09-12https://heir.dev/blog/2023/09/13/heir-meeting-2023-09-12/Wed, 13 Sep 2023 00:00:00 +0000https://heir.dev/blog/2023/09/13/heir-meeting-2023-09-12/
-<p>Here are the
-<a href="https://docs.google.com/document/d/1gOH1V6ORQwJDDo6I4jrDgCqqNFTsfcQbfpdUR6tv_60/edit?usp=sharing">notes</a>
-and
-<a href="https://drive.google.com/file/d/1zFtpBcCCq5d6UD8Nm8r3rfg3sgy-guz7/view?usp=sharing">video recording</a>
-from the HEIR meeting on 2023-09-12.</p>Blog: HEIR meeting 2023-08-29https://heir.dev/blog/2023/09/05/heir-meeting-2023-08-29/Tue, 05 Sep 2023 00:00:00 +0000https://heir.dev/blog/2023/09/05/heir-meeting-2023-08-29/
-<p>Here are the
-<a href="https://docs.google.com/document/d/1Lax8Inby5Mg8BZLkcV_5hUiWH-roL22rtszfc0PBGmE/edit?usp=sharing">notes</a>
-from the HEIR meeting on 2023-08-29. There was an issue with the recording, so
-there is no video recording this week.</p>Blog: HEIR meeting 2023-08-15https://heir.dev/blog/2023/08/16/heir-meeting-2023-08-15/Wed, 16 Aug 2023 16:15:47 +0000https://heir.dev/blog/2023/08/16/heir-meeting-2023-08-15/
-<p>Here are the
-<a href="https://docs.google.com/document/d/1vZsKJH4wCAZCtyh3o9nNMLRFwlWQiVdvUMvwJnA4cIc/edit?usp=sharing">notes</a>
-and
-<a href="https://drive.google.com/file/d/1DDNepYCSqgi-JlBLBzHrsL5CjjiwqcA_/view?usp=sharing">video recording</a>
-from the HEIR meeting on 2023-08-15.</p>Blog: HEIR meeting 2023-08-01https://heir.dev/blog/2023/08/02/heir-meeting-2023-08-01/Wed, 02 Aug 2023 15:46:42 -0700https://heir.dev/blog/2023/08/02/heir-meeting-2023-08-01/
-<p>The fourth HEIR meeting was 2023-08-01
-(<a href="https://docs.google.com/document/d/1gid-MARMUStb3dB9jsXEV_CnPDpf_9cyPXy9uXtZk08/edit?usp=sharing">notes</a>
-and
-<a href="https://drive.google.com/file/d/1U6HDdKJo3-UHibFPgNrDakU8EpCt5xHZ/view?usp=sharing">video recording</a>).</p>
-<p>We&rsquo;re also starting on the Poly and Secret dialects in
-<a href="https://github.com/google/heir/pull/74">#74 (poly)</a> and
-<a href="https://github.com/google/heir/pull/78">#78 (secret)</a>, so please join in the
-fun!</p>Blog: HEIR meeting 2023-07-18https://heir.dev/blog/2023/07/18/heir-meeting-2023-07-18/Tue, 18 Jul 2023 10:43:16 -0700https://heir.dev/blog/2023/07/18/heir-meeting-2023-07-18/
-<p>The third HEIR meeting was 2023-07-18
-(<a href="https://docs.google.com/document/d/1DXdyUCmevqY8RJI3kM8oO5nWDEITFIVBPIbucONOB-k/edit?usp=sharing">notes</a>).</p>
-<p>We decided to schedule future meetings every two weeks, with alternating focus
-on MLIR and Hardware. See the <a href="https://heir.dev/community/">meeting calendar</a> to
-join.
-(<a href="https://calendar.google.com/calendar/u/0/embed?src=c85ecb3cda4bfb7daa3da95d5aeb19672930501b49d17896e65fa3f963f17a80@group.calendar.google.com&amp;ctz=America/Los_Angeles">direct link to the calendar</a>)</p>Blog: HEIR meeting 2023-06-30https://heir.dev/blog/2023/06/30/heir-meeting-2023-06-30/Fri, 30 Jun 2023 12:42:22 -0700https://heir.dev/blog/2023/06/30/heir-meeting-2023-06-30/
-<p>The second HEIR meeting was 2023-05-30
-(<a href="https://docs.google.com/document/d/1wxaEtpEDdO2yv5YKmFTc8FVlqHxm49gHzEdcnBFBKWs/edit?usp=sharing">notes</a>,
-and
-<a href="https://drive.google.com/file/d/1S893iJdeL08BAonLenmkUGNC34PX1qpg/view?usp=sharing">video recording</a>).</p>
-<p>There are some initial design discussion threads started on
-<a href="https://github.com/google/heir/discussions">GitHub Discussions</a> to get the
-design rolling.</p>
-<ul>
-<li><a href="https://github.com/google/heir/discussions/53">High-Level FHE Dialect</a></li>
-<li><a href="https://github.com/google/heir/discussions/54">Scheme Dialects</a></li>
-<li><a href="https://github.com/google/heir/discussions/55">Poly/Math Dialects</a></li>
-</ul>
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+from the HEIR meeting on 2024-02-22.</p>
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