Consolidate Ink's linear interpolation implementations #399
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std::lerp instead of hand-coded linear interpolation
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We had multiple different naive floating-point lerp implementations sprinkled throughout our code. In some places, we used `a + (b - a) * t`, which gives incorrect results if `b - a` overflows, and can be inexact for `t = 1`. In other places, we used `a * (1 - t) + b * t`, which is better, but apparently has monotonicity issues [1] and also gives incorrect results when `t` is infinite and `a` or `b` is zero. Better to have one _carefully tested_ definition and use it everywhere, which is what this CL does. The good news is that C++20 (which we can finally now use in all our build environments) provides a `std::lerp` function that handles these edge cases. The bad news is that (at least in some of our build environments), it seems to have a bug (b/457491215) where its behavior does not match the standard! So for now our `float Lerp` definition in this CL has an extra branch to work around that before deferring to `std::lerp`. [1] https://www.open-std.org/jtc1/sc22/wg21/docs/papers/2019/p0811r3.html PiperOrigin-RevId: 826613841
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Consolidate Ink's linear interpolation implementations
We had multiple different naive floating-point lerp implementations sprinkled throughout our code. In some places, we used
a + (b - a) * t, which gives incorrect results ifb - aoverflows, and can be inexact fort = 1. In other places, we useda * (1 - t) + b * t, which is better, but apparently has monotonicity issues [1] and also gives incorrect results whentis infinite andaorbis zero. Better to have one carefully tested definition and use it everywhere, which is what this CL does.The good news is that C++20 (which we can finally now use in all our build environments) provides a
std::lerpfunction that handles these edge cases. The bad news is that (at least in some of our build environments), it seems to have a bug (b/457491215) where its behavior does not match the standard! So for now ourfloat Lerpdefinition in this CL has an extra branch to work around that before deferring tostd::lerp.[1] https://www.open-std.org/jtc1/sc22/wg21/docs/papers/2019/p0811r3.html