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<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D;mso-fareast-language:EN-US">The argument ”</span><span lang="EN-US">arguing that every language which does not write 1.2100000000000002 is lying to
you.</span><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D;mso-fareast-language:EN-US">” is only valid if you encode floating point numbers in binary.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D;mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D;mso-fareast-language:EN-US">The rather cool 4-bit wide (!) microprocessor used in early HP calculators encoded both the mantissa and the exponent
in 4-bit bcd. Thus it could exactly encode both 1.1 and 1.21, since it actually made the floating point calculations in decimal. No fancy algorithm for making the numbers “look nice” was needed.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D;mso-fareast-language:EN-US">My trusty old HP48 was both programmable and doing decimal as a human... so it didn’t have to lie.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D;mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D;mso-fareast-language:EN-US">(of course this does not mean that bcd gives higher precision in general. In fact it the opposite).<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D;mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D;mso-fareast-language:EN-US">/Ola<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D;mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><b><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif">From:</span></b><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif"> erlang-questions-bounces@erlang.org [mailto:erlang-questions-bounces@erlang.org]
<b>On Behalf Of </b>Jesper Louis Andersen<br>
<b>Sent:</b> den 26 oktober 2014 13:34<br>
<b>To:</b> </span><span style="font-size:11.0pt;font-family:"Microsoft JhengHei",sans-serif">张栋</span><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif"><br>
<b>Cc:</b> Erlang (E-mail)<br>
<b>Subject:</b> Re: [erlang-questions] In Erlang , {1.1*1.1.} show me the answer is 1.2100000000000002, why?<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
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<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
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<p class="MsoNormal">On Sun, Oct 26, 2014 at 8:24 AM, <span style="font-family:"Microsoft JhengHei",sans-serif">
张栋</span> <<a href="mailto:zd2559@126.com" target="_blank">zd2559@126.com</a>> wrote:<o:p></o:p></p>
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<p class="MsoNormal">When I try some multiplication, I got the some unexpected answer about the following expression.<o:p></o:p></p>
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<p class="MsoNormal"><br>
Hi!<o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal">In addition to what everyone else has said, you may want to search the archives. There is a couple of posts by Richard O. Keefe which explains this in great detail. If my memory serves, he actually ends up arguing that every language which
does not write 1.2100000000000002 is lying to you.<br>
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<o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal">-- <br>
J. <o:p></o:p></p>
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