Created
January 9, 2025 08:54
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Compute exp(x) - 1 without loss of precision for small values of x. example snippet from godot game code
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| ## | |
| ## Compute exp(x) - 1 without loss of precision for small values of x. | |
| ## https://www.johndcook.com/blog/cpp_expm1/ | |
| ## | |
| ## usage for exponential smoothing in games/animation e.g.: | |
| ## for any value of dt (delta time): | |
| ## | |
| ## position += (target - position) * (1 - exp(- speed * dt)) | |
| ## | |
| ## changed to use -expm1(x) instead of 1-exp(x) | |
| ## | |
| ## position += (target - position) * (- _expm1(-speed * dt)) | |
| ## | |
| ## related references: | |
| ## https://lisyarus.github.io/blog/posts/exponential-smoothing.html | |
| ## https://blog.pkh.me/p/41-fixing-the-iterative-damping-interpolation-in-video-games.html | |
| ## https://news.ycombinator.com/item?id=40401152 | |
| ## | |
| func _expm1(x): | |
| if (abs(x) < 1e-5): | |
| return x + 0.5*x*x; | |
| else: | |
| return exp(x) - 1.0; | |
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