linux-kernel - [PATCH v2 3/3] clk: fractional-divider: Document the arithmetics used behind the code

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Date:   Fri, 16 Jul 2021 16:34:48 +0300
From:   Andy Shevchenko <andriy.shevchenko@...ux.intel.com>
To:     Andy Shevchenko <andriy.shevchenko@...ux.intel.com>,
        Heiko Stuebner <heiko@...ech.de>,
        Elaine Zhang <zhangqing@...k-chips.com>,
        Stephen Boyd <sboyd@...nel.org>, linux-kernel@...r.kernel.org,
        linux-clk@...r.kernel.org, linux-arm-kernel@...ts.infradead.org,
        linux-rockchip@...ts.infradead.org
Cc:     Michael Turquette <mturquette@...libre.com>,
        Liu Ying <victor.liu@....com>
Subject: [PATCH v2 3/3] clk: fractional-divider: Document the arithmetics used behind the code

It appears that some code lines raise the question why they are needed
and how they are participated in the calculus of the resulting values.

Document this in a form of the top comment in the module file.

Reported-by: Liu Ying <victor.liu@....com>
Signed-off-by: Andy Shevchenko <andriy.shevchenko@...ux.intel.com>
---
v2: renamed variables in formulas to follow the code, added floor()
 drivers/clk/clk-fractional-divider.c | 34 +++++++++++++++++++++++++++-
 1 file changed, 33 insertions(+), 1 deletion(-)

diff --git a/drivers/clk/clk-fractional-divider.c b/drivers/clk/clk-fractional-divider.c
index 5f4b6a8aef67..7f7f688f8de5 100644
--- a/drivers/clk/clk-fractional-divider.c
+++ b/drivers/clk/clk-fractional-divider.c
@@ -3,8 +3,38 @@
  * Copyright (C) 2014 Intel Corporation
  *
  * Adjustable fractional divider clock implementation.
- * Output rate = (m / n) * parent_rate.
  * Uses rational best approximation algorithm.
+ *
+ * Output is calculated as
+ *
+ *	rate = (m / n) * parent_rate				(1)
+ *
+ * This is useful when on die we have a prescaler block which asks for
+ * m (numerator) and n (denominator) values to be provided to satisfy
+ * the (1) as much as possible.
+ *
+ * Since m and n have the limitation by a range, e.g.
+ *
+ *	n >= 1, n < N_width, where N_width = 2^nwidth		(2)
+ *
+ * for some cases the output may be saturated. Hence, from (1) and (2),
+ * assuming the worst case when m = 1, the inequality
+ *
+ *	floor(log2(parent_rate / rate)) <= nwidth		(3)
+ *
+ * may be derived. Thus, in cases when
+ *
+ *	(parent_rate / rate) >> N_width				(4)
+ *
+ * we scale up the rate by 2^scale, where
+ *
+ *	scale = floor(log2(parent_rate / rate)) - nwidth	(5)
+ *
+ * and assume that the IP, that needs m and n, has also its own
+ * prescaler, which is capable to divide by 2^scale. In this way
+ * we get the denominator to satisfy the desired range (2) and
+ * at the same time much much better result of m and n than simple
+ * saturated values.
  */
 
 #include <linux/clk-provider.h>
@@ -81,6 +111,8 @@ void clk_fractional_divider_general_approximation(struct clk_hw *hw,
 	 * Get rate closer to *parent_rate to guarantee there is no overflow
 	 * for m and n. In the result it will be the nearest rate left shifted
 	 * by (scale - fd->nwidth) bits.
+	 *
+	 * For the detailed explanation see the top comment in this file.
 	 */
 	if (!(fd->flags & CLK_FRAC_DIVIDER_NO_PRESCALER)) {
 		unsigned long scale = fls_long(*parent_rate / rate - 1);
-- 
2.30.2