commit | 5f45eed44acf51f907364efa5548d6d754ed8889 | [log] [tgz] |
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author | Trent Piepho <tpiepho@gmail.com> | Wed Sep 04 05:02:18 2019 +0000 |

committer | Johannes Weiner <hannes@cmpxchg.org> | Wed Sep 04 05:02:18 2019 +0000 |

tree | ec4eaeb59b8537c810594069183dda2e7f84ddf3 | |

parent | 3728236c536812ce41db217fed4ab7b718bf2b67 [diff] |

lib/math/rational.c: fix possible incorrect result from rational fractions helper In some cases the previous algorithm would not return the closest approximation. This would happen when a semi-convergent was the closest, as the previous algorithm would only consider convergents. As an example, consider an initial value of 5/4, and trying to find the closest approximation with a maximum of 4 for numerator and denominator. The previous algorithm would return 1/1 as the closest approximation, while this version will return the correct answer of 4/3. To do this, the main loop performs effectively the same operations as it did before. It must now keep track of the last three approximations, n2/d2 .. n0/d0, while before it only needed the last two. If an exact answer is not found, the algorithm will now calculate the best semi-convergent term, t, which is a single expression with two divisions: min((max_numerator - n0) / n1, (max_denominator - d0) / d1) This will be used if it is better than previous convergent. The test for this is generally a simple comparison, 2*t > a. But in an edge case, where the convergent's final term is even and the best allowable semi-convergent has a final term of exactly half the convergent's final term, the more complex comparison (d0*dp > d1*d) is used. I also wrote some comments explaining the code. While one still needs to look up the math elsewhere, they should help a lot to follow how the code relates to that math. This routine is used in two places in the video4linux code, but in those cases it is only used to reduce a fraction to lowest terms, which the existing code will do correctly. This could be done more efficiently with a different library routine but it would still be the Euclidean alogrithm at its heart. So no change. The remain users are places where a fractional PLL divider is programmed. What would happen is something asked for a clock of X MHz but instead gets Y MHz, where Y is close to X but not exactly due to the hardware limitations. After this change they might, in some cases, get Y' MHz, where Y' is a little closer to X then Y was. Users like this are: Three UARTs, in 8250_mid, 8250_lpss, and imx. One GPU in vp4_hdmi. And three clock drivers, clk-cdce706, clk-si5351, and clk-fractional-divider. The last is a generic clock driver and so would have more users referenced via device tree entries. I think there's a bug in that one, it's limiting an N bit field that is offset-by-1 to the range 0 .. (1<<N)-2, when it should be (1<<N)-1 as the upper limit. I have an IMX system, one of the UARTs using this, so I can provide a real example. If I request a custom baud rate of 1499978, the driver will program the PLL to produce a baud rate of 1500000. After this change, the fractional divider in the UART is programmed to a ratio of 65535/65536, which produces a baud rate of 1499977.0625. Closer to the requested value. Link: http://lkml.kernel.org/r/20190330205855.19396-1-tpiepho@gmail.com Signed-off-by: Trent Piepho <tpiepho@gmail.com> Cc: Oskar Schirmer <oskar@scara.com> Signed-off-by: Andrew Morton <akpm@linux-foundation.org>

1 file changed

tree: ec4eaeb59b8537c810594069183dda2e7f84ddf3