All right, we have an arbitrary-precision rational arithmetic type now, so we can do arithmetic on fractions with confidence. Remember the problem I set out to explore here was: a double is actually a fraction whose denominator is a large power of two, so fractions which do not have powers of two in their denominators cannot be represented with full fidelity by a double. Now that we have this machinery we can see exactly what the representation error is:
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A couple of years ago I developed my own arbitrary precision natural number and integer mathematics types, just for fun and to illustrate how it could be done. I’m going to do the same for rational numbers here, but rather than using my integer type, I’ll just use the existing BigInteger type to represent the numerator and denominator. Either would do just fine.
Of course I could have used some existing BigRational types but for various reasons that I might go into in a future blog article, I decided it would be more interesting to simply write my own. Let’s get right to it; I’ll annotate the code as I go.
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Good Monday morning everyone; I hope my American readers had a lovely Thanksgiving. I sure did!
Well enough chit-chat, here’s a problem I was pondering the other day. We know that doubles introduce some “representation error” when trying to represent most numbers. The number 3/4, or 0.75 for example, can be exactly represented by a double, but the number 3/5, or 0.6, cannot.
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In the previous exciting episode I ended on a cliffhanger; why did I put a loop around each wait? In the consumer, for example, I said:
while (myQueue.IsEmpty)
Monitor.Wait(myLock);
It seems like I could replace that “while” with an “if”. Let’s consider some scenarios. I’ll consider just the scenario for the loop in the consumer, but of course similar scenarios apply mutatis mutandis for the producer. Continue reading
Locks are tricky; I thought today I’d talk a bit about some of the pitfalls of locking that you might not have seen before. Continue reading
One of the early stumbling blocks people run into when learning traditional Aristotelian logic is the idea that “a false proposition implies any proposition”. Let’s briefly review material implication, and then I’ll talk about what the implications of material implication are to programming.
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UPDATE: A commenter points out that today is the 200th anniversary of the birth of George Boole; I had no idea when I scheduled this article that it would be so apropos. Happy birthday George Boole!
Here’s a little-known and seldom-used fact about C# operators: you can apply the & and | operators to bools, not just to integers. The & and | operators on bools differ from && and || in only one way: both operators always “eagerly” evaluate both operands. This is in marked contrast to the “lazily” computed evaluation of the && and || operators, which only evaluate their right hand argument if needed. Why on earth would you ever want to evaluate the right hand side if you didn’t need to? Why have this operation at all on bools?
A few reasons come to mind. First, sometimes you want to do two operations, and know whether both of them succeeded: Continue reading
