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Re: [Bug-apl] Modulo or residue function is not generating consistent co


From: Peter Teeson
Subject: Re: [Bug-apl] Modulo or residue function is not generating consistent complete residue systems for some arguments
Date: Sat, 24 Jun 2017 14:34:10 -0400

<http://mathworld.wolfram.com/CompleteResidueSystem.html>
On Jun 24, 2017, at 2:21 PM, Juergen Sauermann <address@hidden> wrote:

Hi Fred,

I am glad to hear that. It is in SVN 971 now. It was Jay who moved us into the right
direction, thanks for that. I had used the Donell paper earlier (when designing complex
floor) but the borderline cases (i.e. when ⎕CT makes a difference) were not considered
in the paper, and the descriptions in both ISO and the APL2 language reference are
entirely misleading in that respect.

Have a nice weekend,

Best Regards,
/// Jürgen


On 06/24/2017 07:55 PM, Frederick Pitts wrote:
Hello Jürgen,

SUCCESS.

The cut-and-paste below from my platform is identical to yours

      5J3 | ¯7J6
⎕CT is: 1e-13
modulus (A) is: (5,3)
A=0 is: (0,0)
A+A=0 is: (5,3)
B÷A+A=0 is: (-0.5,1.5)
⌊B÷A+A=0 is: (0,1)
A×⌊B÷A+A=0 is: (-3,5)
B-A×⌊B÷A+A=0 is: (-4,1)
¯4J1

and 5J3 | 4J¯1 ¯4J1 give the correct answer too.

If you want, I can patch the undebugged version of Complex.cc and run a battery of tests. If not, I will wait and run the tests on the next SVN version.

I think i need to find something useful to do with Gaussian integers.

Regards,

Fred



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