Just to make sure we’re on the same page, G is the most significant bit of the three, R comes next and S can be thought of as the least significant bit because its value partially represents the even less significant bits that have been truncated in the calculations. These three bits are only used … Read more
I think what you’re looking for is not directly possible. One important property of equality is that it is transitive. (ie. If a == b and b == c, then a == c). With a distance measure, though, you really don’t want this property. Example: Take a single float (for simplicity). Suppose we want to … Read more
It also depends on instruction mix. Your processor will have several computation units standing by at any time, and you’ll get maximum throughput if all of them are filled all the time. So, executing a loop of mul’s is just as fast as executing a loop or adds – but the same doesn’t hold if … Read more
The technically correct answer is: because no one has written impl Add<f64> for i32 {}. The cheeky answer is: because Rust doesn’t want you to shoot yourself in the foot. The longer, potentially more useful answer is… In computers, integers and floating point numbers both have a limited range, ultimately driven by the number of … Read more
Yes! It really is more numerically stable. For the case that you’re looking at, the numbers [0.0, 0.1, …, 0.9], note that under round-ties-to-away, only four of those numbers are rounding down (0.1 through 0.4), five are rounded up, and one (0.0) is unchanged by the rounding operation, and then of course that pattern repeats … Read more
The derivative of ArcTan(X, Sqrt(1-X*X)) with respect to X is 1/Sqrt(1-X*X). This goes to infinity as |X| goes to 1. Therefore, when X is near 1 or -1, any error in evaluation has a huge effect on the result. Thus, it is critical that evaluation minimize error in these cases. When X is near 1, … Read more
As mentioned, the Wikipedia article on IEEE 754 does a good job of showing how floating point numbers are stored on most systems. Now, here are some common gotchas: The biggest is that you almost never want to compare two floating point numbers for equality (or inequality). You’ll want to use greater than/less than comparisons … Read more
Well, here’s a quick explanation: An int and float usually take up “one-word” in memory. Today, with the shift to 64bit systems this may mean that your word is 64 bits, or 8 bytes, allowing the representation of a huge span of numbers. Or, it could still be a 32bit system meaning each word in … Read more
The biggest problem with x87 is basically that all register operations are done in 80 bits, whereas most of the time people only use 64 bit floats (i.e. double-precision floats). What happens is, you load a 64 bit float into the x87 stack, and it gets converted to 80 bits. You do some operations on … Read more
It is possible that you are looking for trunc. It depends on what you mean by the decimal part. This is the difference between trunc and floor: julia> trunc(Int, 1.2) 1 julia> trunc(Int, -1.2) -1 julia> floor(Int, 1.2) 1 julia> floor(Int, -1.2) -2