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POPrecise Multiplication
 

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  1. POPrecise Multiplication
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    <p>first post!</p> <p>I have a problem with a program that i'm writing for a numerical simulation and I have a problem with the multiplication. Basically, I am trying to calculate:</p> <pre><code>result1 = (a + b)*c </code></pre> <p>and this loops thousands of times. I need to expand this code to be</p> <pre><code>result2 = a*c + b*c </code></pre> <p>However, when I do that I start to get significant errors in my results. I used a high precision library, which did improve things, but the simulation ran horribly slow (the simulation took 50 times longer) and it really isn't a practical solution. From this I realised that it isn't really the precision of the variables a, b, &amp; c that is hurting me, but something in the way the multiplication is done. </p> <p>My question is: how can I multiply out these brackets in way so that result1 = result2?</p> <p>Thanks.</p> <p>SOLVED!!!!!!!!!</p> <p>It was a problem with the addition. So i reordered the terms and applied Kahan addition by writing the following piece of code:</p> <pre><code>double Modelsimple::sum(double a, double b, double c, double d) { //reorder the variables in order from smallest to greatest double tempone = (a&lt;b?a:b); double temptwo = (c&lt;d?c:d); double tempthree = (a&gt;b?a:b); double tempfour = (c&gt;d?c:d); double one = (tempone&lt;temptwo?tempone:temptwo); double four = (tempthree&gt;tempfour?tempthree:tempfour); double tempfive = (tempone&gt;temptwo?tempone:temptwo); double tempsix = (tempthree&lt;tempfour?tempthree:tempfour); double two = (tempfive&lt;tempsix?tempfive:tempsix); double three = (tempfive&gt;tempsix?tempfive:tempsix); //kahan addition double total = one; double tempsum = one + two; double error = (tempsum - one) - two; total = tempsum; // first iteration complete double tempadd = three - error; tempsum = total + tempadd; error = (tempsum - total) - tempadd; total = tempsum; //second iteration complete tempadd = four - error; total += tempadd; return total; } </code></pre> <p>This gives me results that are as close to the precise answer as makes no difference. However, in a fictitious simulation of a mine collapse, the code with the Kahan addition takes 2 minutes whereas the high precision library takes over a day to finish!!</p> <p>Thanks to all the help here. This problem was really a pain in the a$$.</p>
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    1. USJames Walker
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    1. COIf the numbers are floating points, don't expect that `result1 = result2`. Read [this](http://csharpindepth.com/Articles/General/FloatingPoint.aspx) or [this](http://www.codinghorror.com/blog/2009/05/why-do-computers-suck-at-math.html) for more details. If that doesn't answer the question, please post an [SSCCE](http://sscce.org/) reproducing your results and add a tag to indicate the language.
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      1. USDukeling
    2. COThanks, reading those now.
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      1. USJames Walker
 

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