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POWhy does the order affect the rounding when adding multiple doubles in C#
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  1. POWhy does the order affect the rounding when adding multiple doubles in C#
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    copied!<p>Consider the following C# code:</p> <pre><code>double result1 = 1.0 + 1.1 + 1.2; double result2 = 1.2 + 1.0 + 1.1; if (result1 == result2) { ... } </code></pre> <p>result1 should always equal result2 right? The thing is, it doesn't. result1 is 3.3 and result2 is 3.3000000000000003. The only difference is the order of the constants.</p> <p>I know that doubles are implemented in such a way that rounding issues can occur. I'm aware that I can use decimals instead if I need absolute precision. Or that I can use Math.Round() in my if statement. I'm just a nerd who wants to understand what the C# compiler is doing. Can anyone tell me?</p> <p><strong>Edit:</strong></p> <p>Thanks to everyone who's so far suggested reading up on floating point arithmetic and/or talked about the inherent inaccuracy of how the CPU handles doubles. But I feel the main thrust of my question is still unanswered. Which is my fault for not phrasing it correctly. Let me put it like this:</p> <p>Breaking down the above code, I would expect the following operations to be happening:</p> <pre><code>double r1 = 1.1 + 1.2; double r2 = 1.0 + r1 double r3 = 1.0 + 1.1 double r4 = 1.2 + r3 </code></pre> <p>Let's assume that each of the above additions had a rounding error (numbered e1..e4). So r1 contains rounding error e1, r2 includes rounding errors e1 + e2, r3 contains e3 and r4 contains e3 + e4.</p> <p>Now, I don't know how exactly how the rounding errors happen but I would have expected e1+e2 to equal e3+e4. Clearly it doesn't, but that seems somehow wrong to me. Another thing is that when I run the above code, I don't get any rounding errors. That's what makes me think it's the C# compiler that's doing something weird rather than the CPU.</p> <p>I know I'm asking a lot and maybe the best answer anyone can give is to go and do a PHD in CPU design, but I just thought I'd ask.</p> <p><strong>Edit 2</strong></p> <p>Looking at the IL from my original code sample, it's clear that it's the compiler not the CPU that's doing this:</p> <pre><code>.method private hidebysig static void Main(string[] args) cil managed { .entrypoint .maxstack 1 .locals init ( [0] float64 result1, [1] float64 result2) L_0000: nop L_0001: ldc.r8 3.3 L_000a: stloc.0 L_000b: ldc.r8 3.3000000000000003 L_0014: stloc.1 L_0015: ret } </code></pre> <p>The compiler is adding up the numbers for me!</p>
 

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