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    <p>The short answer is that FP calculations are entirely deterministic, as per the <a href="http://en.wikipedia.org/wiki/IEEE_754" rel="noreferrer">IEEE Floating Point Standard</a>, but that doesn't mean they're entirely reproducible across machines, compilers, OS's, etc.</p> <p>The long answer to these questions and more can be found in what is probably the best reference on floating point, David Goldberg's <a href="http://docs.sun.com/source/806-3568/ncg_goldberg.html" rel="noreferrer">What Every Computer Scientist Should Know About Floating Point Arithmetic</a>. Skip to the section on the IEEE standard for the key details.</p> <p>To answer your bullet points briefly:</p> <ul> <li><p>Time between calculations and state of the CPU have little to do with this. </p></li> <li><p>Hardware can affect things (e.g. some GPUs are not IEEE floating point compliant).</p></li> <li><p>Language, platform, and OS can also affect things. For a better description of this than I can offer, see Jason Watkins's answer. If you are using Java, take a look at Kahan's <a href="http://www.cs.berkeley.edu/~wkahan/JAVAhurt.pdf" rel="noreferrer">rant on Java's floating point inadequacies</a>.</p></li> <li><p>Solar flares might matter, hopefully infrequently. I wouldn't worry too much, because if they do matter, then everything else is screwed up too. I would put this in the same category as worrying about <a href="http://en.wikipedia.org/wiki/Effects_of_nuclear_explosions#Electromagnetic_pulse" rel="noreferrer">EMP</a>.</p></li> </ul> <p>Finally, if you are doing the same <em>sequence</em> of floating point calculations on the same initial inputs, then things should be replayable exactly just fine. The exact sequence can change depending on your compiler/os/standard library, so you might get some small errors this way.</p> <p>Where you usually run into problems in floating point is if you have a numerically unstable method and you start with FP inputs that are <em>approximately</em> the same but not quite. If your method's stable, you should be able to guarantee reproducibility within some tolerance. If you want more detail than this, then take a look at Goldberg's FP article linked above or pick up an intro text on numerical analysis.</p>
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    1. POHow deterministic is floating point inaccuracy?
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    1. COSee my response to @JaredPar, there are many things that can cause discrepancies between calculations on two IEEE-compliant implementations. Saying that calculations are deterministic isn't particularly helpful since deterministic doesn't necessarily mean reproducible.
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      1. USRobert Gamble
    2. COThanks. I've revised this to be more clear.
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    3. CO+1 for the David Goldberg reference.
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