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POHow to return nearest element from an ordered set?
 

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  1. POHow to return nearest element from an ordered set?
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    <p>I have a vector which contains some floating point values reasonably apart from each other and sorted according to some function. For example,</p> <pre><code>double foo(double x) { return 199.1*x; } double x = 3000000.3157; double y = x + DBL_EPSILON; std::vector&lt;double&gt; s { y,y+10}; std::sort(s.begin(),s.end(),[](double x,double y) { return foo(x) &lt; foo(y) ;} ); </code></pre> <p>Now someone has a key which is close to the one I have in <code>s</code>, such as <code>x</code>. In the era of <a href="https://en.wikipedia.org/wiki/Lambda_calculus" rel="nofollow">lambda</a>, all have their own little function to search, like</p> <pre><code>std::cout&lt;&lt;std::distance(s.begin(),std::lower_bound(s.begin(),s.end(),x, [] (double x,double y) { return foo(x) &lt; foo(y);}))&lt;&lt;std::endl; std::cout&lt;&lt;std::distance(s.begin(),std::lower_bound(s.begin(),s.end(),x, [] (double x,double y) { double f1 = foo(x); double f2 = foo(y); return f1 &lt; f2;}))&lt;&lt;std::endl; </code></pre> <p>and gets different position (and the corresponding values are very different).</p> <p>While looking at the usage, it appeared, they are related to <strong>finding for a key <code>k</code></strong></p> <ul> <li><strong>Nearest element from an ordered set of well-placed floating point values.</strong></li> <li><strong>A ratio, <code>r</code>, which (ideally should be [0,1] ) attached to consecutive values <code>x1</code> &amp; <code>x2</code> such that return value of a function <code>f(x1,x2,r)</code> is approximately equal to <code>k</code>.</strong></li> </ul> <p>Both of them looks like related, and related to interpolation. How do I implement them?</p> <p>NOTE:</p> <p>In the short code below</p> <pre><code>double f1 = foo(x); double f2 = foo(y); bool l = foo(x) &lt; foo(y); std::cout&lt;&lt;std::boolalpha&lt;&lt;(f1&lt;f2)&lt;&lt; " "&lt;&lt;l&lt;&lt;" "&lt;&lt;(f1 == f2) &lt;&lt; std::endl; std::cout &lt;&lt; std::boolalpha &lt;&lt; (foo(x) &lt; foo(y)) &lt;&lt; " "&lt;&lt; (foo(y) &lt; foo(x)) &lt;&lt; " "&lt;&lt;(foo(x) == foo(y) )&lt;&lt;std::endl; std::cout &lt;&lt; std::boolalpha &lt;&lt; std::isless(foo(x) , foo(y)) &lt;&lt; " "&lt;&lt; std::isless(foo(y) , foo(x)) &lt;&lt;std::endl; </code></pre> <p>I get output with <a href="http://en.wikipedia.org/wiki/GNU_Compiler_Collection" rel="nofollow">GCC</a> on a X86 machine as</p> <pre><code>false true true true true false false false </code></pre> <p>While my guess is that GCC does higher precision (80bit) on the fly unless I force it to store the result, resulting different result for <code>l</code> &amp; <code>(f1&lt;f2)</code> (which caused the problem stated above) . I will also be interested to know why <code>foo(x) &lt; foo(y)</code> and <code>foo(y) &lt; foo(x)</code> both says <code>true</code>!</p>
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    1. USPeter Mortensen
    1. USabir
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      1. POHow to return nearest element from an ordered set?
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    1. COAside from rounding differences for numbers that are very close together, your `foo(x)` is semantically equivalent to just sorting by the numbers themselves... If `x < y`, then `kx < ky` for any `k > 0`...
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      1. POHow to return nearest element from an ordered set?
      1. UStwalberg
    2. COThat is just an example. In actual code it was a set of geometric points sorted by their y axis intercept along a given angle.
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      1. USabir
 

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