Linear interpolation
#71016 is a previous attempt at implementation that was closed by the author. I decided to reuse the feature request issue (#71015) as a tracking issue. A member of the rust-lang org will have to edit the original post to be formatted correctly as I am not the issue's original author.
The common name `lerp` is used because it is the term used by most code in a wide variety of contexts; it also happens to be the recently chosen name of the function that was added to C++20.
To ensure symmetry as a method, this breaks the usual ordering of the method from `lerp(a, b, t)` to `t.lerp(a, b)`. This makes the most sense to me personally, and there will definitely be discussion before stabilisation anyway.
Implementing lerp "correctly" is very dififcult even though it's a very common building-block used in all sorts of applications. A good prior reading is [this proposal](http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2018/p0811r2.html#linear-interpolation) for the C++20 lerp which talks about the various guarantees, which I've simplified down to:
1. Exactness: `(0.0).lerp(start, end) == start` and `(1.0).lerp(start, end) == end`
2. Consistency: `anything.lerp(x, x) == x`
3. Monotonicity: once you go up don't go down
Fun story: the version provided in that proposal, from what I understand, isn't actually monotonic.
I messed around with a *lot* of different lerp implementations because I kind of got a bit obsessed and I ultimately landed on one that uses the fused `mul_add` instruction. Floating-point lerp lore is hard to come by, so, just trust me when I say that this ticks all the boxes. I'm only 90% certain that it's monotonic, but I'm sure that people who care deeply about this will be there to discuss before stabilisation.
The main reason for using `mul_add` is that, in general, it ticks more boxes with fewer branches to be "correct." Although it will be slower on architectures without the fused `mul_add`, that's becoming more and more rare and I have a feeling that most people who will find themselves needing `lerp` will also have an efficient `mul_add` instruction available.
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