Differences
This shows you the differences between two versions of the page.
| Both sides previous revisionPrevious revision | Next revisionBoth sides next revision | ||
| isp:hsl-_rgb [2019/05/29 11:43] – [Preface] Igor Yefmov | isp:hsl-_rgb [2019/05/31 03:52] – [Division-less division] Igor Yefmov | ||
|---|---|---|---|
| Line 20: | Line 20: | ||
| \[\frac{1}{x} = \frac{1*N}{x*N}\] | \[\frac{1}{x} = \frac{1*N}{x*N}\] | ||
| and choosing \(N\) such that \(x*N\) is a whole power of \(2\) we have an optimization where a division is replaced by a pair of a multiplication followed by a (super cheap!) bit-shift operation by \(Z\) bits: | and choosing \(N\) such that \(x*N\) is a whole power of \(2\) we have an optimization where a division is replaced by a pair of a multiplication followed by a (super cheap!) bit-shift operation by \(Z\) bits: | ||
| - | \[\frac{C}{x} = C*\frac{1}{x} = C*\frac{1*N}{x*N} = C*\frac{N}{2^Z} = [(C*N)>>Z]\] | + | \[\frac{C}{x} = C*\frac{1}{x} = C*\frac{1*N}{x*N} = C*\frac{N}{2^Z} = [(C*N) |
| The value \(Z\) depends on the needed precision and, of course, the higher the \(Z\) the less precision loss there will be in the end. | The value \(Z\) depends on the needed precision and, of course, the higher the \(Z\) the less precision loss there will be in the end. | ||