- From: C. Scott Ananian <notifications@github.com>
- Date: Wed, 16 Dec 2015 10:02:38 -0800
- To: whatwg/encoding <encoding@noreply.github.com>
Received on Wednesday, 16 December 2015 18:03:26 UTC
Consider `(X/Y)/Z`. Given nonnegative integers X, Y, Z, the exact result of `X/Y` will be `N + f`, where `N` is an integer and `0 <= f <= (Y-1/Y)` (since X is an integer). Then `(X/Y)/Z = (N + f)/Z = N/Z + f/Z = (N' + f') + f/Z` where `N'` is an integer and `0 <= f' <= (Z-1/Z)`. We cwant to ensure that `(f' + f/Z) < 1`. Expanding, `f' + f/Z <= (Z-1/Z) + (Y-1/YZ)` and so `f' + f/Z <= (YZ-1/YZ)`. That will always be less than 1 *assuming X Y Z are nonnegative integers* (which they seem to be in this case). --- Reply to this email directly or view it on GitHub: https://github.com/whatwg/encoding/commit/929a3ffec7695b38c1b5529411de52eca6935d61#commitcomment-15021593
Received on Wednesday, 16 December 2015 18:03:26 UTC