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I have an embarrassingly simple question, but I need to make sure I understand this correctly. I have a *.c file with the following line: Is this interpreted as:
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The answer is almost as embarrassingly simple. No, absolutely not, and anything you do to change what you have written will most likely be wrong until you have read and understood What Every Computer Scientist Should Know About Floating-Point Arithmetic I only understand about 1/4 of that paper, but I understand enough of it to know that my chances of getting floating point correct are low. Fortunately in my line of work, like many programmers, floating point is either easily avoided or quite simple so when I do have to go there I can spend effort on getting it right. Essentially the paper describes how floating point on computers is achieved, and what kinds of errors can occur that can generate incorrect results. At first glance, your implementation of the formula will likely exhibit most of the errors described in the link. |
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Yes, I as far as I can tell the expression in the form you have written it will produce a very good approximation to the correct result of evaluating that formula over a very large range of input values. You have performed a specific simplification of one constant calculation, for reasons I do not understand. If you're going to simplify one calculation, why not simplify all of them? If this calculation appears inside a loop, you might want to check how good your compiler is at optimising those floating point calculations, especially the constants. If it doesn't, you might want to. There are some rather specific issues that can arise in using floating point calculations on computers, either when you deal with numbers at extreme values (small and large) or when you perform operations that lose significant digits (like subtraction, in particular). I see none of those here. Worry not. The computer says yes. This time. |
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