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</o:shapelayout></xml><![endif]--></head><body lang=DE-CH link="#0563C1" vlink="#954F72"><div class=WordSection1><p class=MsoPlainText>All<o:p></o:p></p><p class=MsoPlainText><o:p> </o:p></p><p class=MsoPlainText><span lang=EN-US>In my point of view the Oberon spec is rather clear:<o:p></o:p></span></p><p class=MsoPlainText><span lang=FR-CH>- q = x DIV y, r = x MOD y, x = q*y + r, 0 <= r < y<o:p></o:p></span></p><p class=MsoPlainText><span lang=EN-US>- MOD is always positive ( 0 <= r < y)<o:p></o:p></span></p><p class=MsoPlainText><span lang=EN-US>- It follows this pattern<o:p></o:p></span></p><p class=MsoPlainText><img width=510 height=284 style='width:5.3125in;height:2.9583in' id="Picture_x0020_1" src="cid:image003.png@01D4F3AB.C0FB2A30"><span lang=EN-US><o:p></o:p></span></p><p class=MsoPlainText><span lang=EN-US><o:p> </o:p></span></p><p class=MsoPlainText><span lang=EN-US>For x = -1 and y = 8 the only integers fulfilling the defining equation set is q = -1, r = 7.<o:p></o:p></span></p><p class=MsoPlainText><span lang=EN-US>DIV is rounding down to nearest integer.<o:p></o:p></span></p><p class=MsoPlainText><span lang=EN-US><o:p> </o:p></span></p><p class=MsoPlainText><span lang=EN-US>br<o:p></o:p></span></p><p class=MsoPlainText><span lang=EN-US>Jörg<o:p></o:p></span></p><p class=MsoPlainText><span lang=EN-US><o:p> </o:p></span></p><p class=MsoPlainText><span lang=EN-US style='mso-fareast-language:DE-CH'>-----Original Message-----<br>From: Oberon <oberon-bounces@lists.inf.ethz.ch> On Behalf Of rochus.keller@bluewin.ch<br>Sent: Monday, April 15, 2019 4:13 PM<br>To: oberon@lists.inf.ethz.ch<br>Subject: Re: [Oberon] Assumed issue in the Lola-2 compiler</span><span lang=EN-US><o:p></o:p></span></p><p class=MsoPlainText><span lang=EN-US><o:p> </o:p></span></p><p class=MsoPlainText>@ Paul Reed:<o:p></o:p></p><p class=MsoPlainText><o:p> </o:p></p><p class=MsoPlainText>>> -1/16 is -0.0625 not 0. (I agree there are indeed multiple integer <o:p></o:p></p><p class=MsoPlainText>>> solutions if you don't also add the range restriction on r.)<o:p></o:p></p><p class=MsoPlainText><o:p> </o:p></p><p class=MsoPlainText>From the language report we can conclude that the operators and result of DIV and MOD (i.e. x, y, q and r) are (algebraic) integers.<o:p></o:p></p><p class=MsoPlainText>We can also assume that in the equation 'x = q*y + r' the multiplication and addition are proper mathematical operators.<o:p></o:p></p><p class=MsoPlainText>Since the given equation uses mathematical operators we can expect that rounding also follows proper mathematical rules. Therefore the rational number -1/16 is rounded to the algebraic integer 0, which would be the mathematically proper solution of q = x DIV y = ( x - r ) / y with x = -1 and y = 16.<o:p></o:p></p><p class=MsoPlainText><o:p> </o:p></p><p class=MsoPlainText>But as mentioned: I have a viable solution which re-uses features of C to simulate the Oberon implementation.<o:p></o:p></p><p class=MsoPlainText><o:p> </o:p></p><p class=MsoPlainText>Best<o:p></o:p></p><p class=MsoPlainText>R.K.<o:p></o:p></p><p class=MsoPlainText>--<o:p></o:p></p><p class=MsoPlainText><a href="mailto:Oberon@lists.inf.ethz.ch"><span style='color:windowtext;text-decoration:none'>Oberon@lists.inf.ethz.ch</span></a> mailing list for ETH Oberon and related systems <a href="https://lists.inf.ethz.ch/mailman/listinfo/oberon"><span style='color:windowtext;text-decoration:none'>https://lists.inf.ethz.ch/mailman/listinfo/oberon</span></a><o:p></o:p></p></div></body></html>