make multiplication commutative

[araujoms]

Closes #161

This changes from algorithm 12 to algorithm 10, causing a slight loss of precision in order to gain commutativity. I think it's worth it; of course, you might disagree. In this case feel free to close the PR, no hard feelings.

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 50.25%. Comparing base (ee66f4f) to head (07d6c3d).
Report is 3 commits behind head on main.

Additional details and impacted files

@@           Coverage Diff           @@
##             main     #211   +/-   ##
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  Coverage   50.25%   50.25%           
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  Files          63       63           
  Lines        3536     3536           
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  Hits         1777     1777           
  Misses       1759     1759           

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[JeffreySarnoff]

Certainly appreciated.

[JeffreySarnoff]

Originally, I pushed accuracy over algebra. However, with multiplication and e.g. horner expressions, commutativity helps avoid errors. I guess that is worth 2ulp. I am considering this. If you hear nothing by tomorrow -- remind me.

[araujoms]

I'm happy to hear that. I did this because I need z*conj(z) to be exactly real, which is not the case with non-commutative multiplication.

[JeffreySarnoff]

Good reason.

…

On Wed, Mar 26, 2025 at 11:21 AM Mateus Araújo ***@***.***> wrote: I'm happy to hear that. I did this because I need z*conj(z) to be exactly real, which is not the case with non-commutative multiplication. — Reply to this email directly, view it on GitHub <#211 (comment)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AAM2VRT5WFNY2WNHWYN6LY32WKZVBAVCNFSM6AAAAABZ2DYY36VHI2DSMVQWIX3LMV43OSLTON2WKQ3PNVWWK3TUHMZDONJUHAYDKNJUGQ> . You are receiving this because you commented.Message ID: ***@***.***> [image: araujoms]*araujoms* left a comment (JuliaMath/DoubleFloats.jl#211) <#211 (comment)> I'm happy to hear that. I did this because I need z*conj(z) to be exactly real, which is not the case with non-commutative multiplication. — Reply to this email directly, view it on GitHub <#211 (comment)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AAM2VRT5WFNY2WNHWYN6LY32WKZVBAVCNFSM6AAAAABZ2DYY36VHI2DSMVQWIX3LMV43OSLTON2WKQ3PNVWWK3TUHMZDONJUHAYDKNJUGQ> . You are receiving this because you commented.Message ID: ***@***.***>