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Cake day: July 1st, 2023

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  • The function should be cubic, so you should be able to write it in the form “f(x) = ax^3 + bx^2 + cx + d”. You could work out the entire thing to put it in that form, but you don’t need to.

    Since there are no weird operations, roots, divisions by x, or anything like that, you can just count how many times x might get multiplied with itself. At the top of each division, there are 3 terms with x, so you can quite easily see that the maximum will be x^3.

    It’s useful to know what the values x_i and x_y are though. They describe the 3 points through which the function should go: (x_1, y_1) to (x_3, y_3).

    That also makes the second part of the statement ready to check. Take (x_1, y_1) for example. You want to be sure that f(x_1) = y_1. If you replace all of the “x” in the formula by x_1, you’ll see that everything starts cancelling each other out. Eventually you’ll get “1 * y_1 + 0 * y_2 + 0 * y_3”, thus f(x_1) is indeed y_1.

    They could have explained this a bit better in the book, it also took me a little while to figure it out.



  • That is true, but from a human perspective it can still seem non-deterministic! The behaviour of the program as a whole will be deterministic, if all inputs are always the same, in the same order, and without multithreading. On the other hand, a specific function call that is executed multiple times with the same input may occasionally give a different result.

    Most programs also have input that changes between executions. Hence you may get the same input record, but at a different place in the execution. Thus you can get a different result for the same record as well.


  • That exact version will end up making “true” false any time it appears on a line number that is divisible by 10.

    During the compilation, “true” would be replaced by that statement and within the statement, “__LINE__” would be replaced by the line number of the current line. So at runtime, you end up witb the line number modulo 10 (%10). In C, something is true if its value is not 0. So for e.g., lines 4, 17, 116, 39, it ends up being true. For line numbers that can be divided by 10, the result is zero, and thus false.

    In reality the compiler would optimise that modulo operation away and pre-calculate the result during compilation.

    The original version constantly behaves differently at runtime, this version would always give the same result… Unless you change any line and recompile.

    The original version is also super likely to be actually true. This version would be false very often. You could reduce the likelihood by increasing the 10, but you can’t make it too high or it will never be triggered.

    One downside compared to the original version is that the value of “true” can be 10 different things (anything between 0 and 9), so you would get a lot more weird behaviour since “1 == true” would not always be true.

    A slightly more consistent version would be

    ((__LINE__ % 10) > 0)
    




  • yggdar@lemmy.worldtoHacker News@derp.fooDecimal Time
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    5 months ago

    Makes sense, you clearly thought about this! From a world-building perspective I do have a follow-up question: 86.4k seconds is our definition of a second, but it is essentially a convention and there is no reason for it. In a society that throws out the hours and minutes, why did they keep our second? It seems like it would have made sense for them to define the day as 100k of some new (slightly smaller) unit. That could have given them 10 “hours” of 100 “minutes” of 100 “seconds”.