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From:   Andy Shevchenko <andriy.shevchenko@linux.intel.com>
To:     Andy Shevchenko <andriy.shevchenko@linux.intel.com>,
        Heiko Stuebner <heiko@sntech.de>,
        Elaine Zhang <zhangqing@rock-chips.com>,
        Stephen Boyd <sboyd@kernel.org>, linux-kernel@vger.kernel.org,
        linux-clk@vger.kernel.org, linux-arm-kernel@lists.infradead.org,
        linux-rockchip@lists.infradead.org
Cc:     Michael Turquette <mturquette@baylibre.com>,
        Liu Ying <victor.liu@nxp.com>
Subject: [PATCH v1 3/3] clk: fractional-divider: Document the arithmetics used behind the code
Date:   Thu, 15 Jul 2021 15:07:52 +0300
Message-Id: <20210715120752.29174-3-andriy.shevchenko@linux.intel.com>
In-Reply-To: <20210715120752.29174-1-andriy.shevchenko@linux.intel.com>
References: <20210715120752.29174-1-andriy.shevchenko@linux.intel.com>
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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@nxp.com>
Signed-off-by: Andy Shevchenko <andriy.shevchenko@linux.intel.com>
---
 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 b2f9aae9f172..29b32b51210d 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_lim, where N_lim = 2^nlim		(2)
+ *
+ * for some cases the output may be saturated. Hence, from (1) and (2),
+ * assuming the worst case when m = 1, the inequality
+ *
+ *	ln2(parent_rate / rate) <= nlim			(3)
+ *
+ * may be derived. Thus, in cases when
+ *
+ *	(parent_rate / rate) >> N_lim			(4)
+ *
+ * we scale up the rate by 2^scale, where
+ *
+ *	scale = ln2(parent_rate / rate) - nlim		(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>
@@ -82,6 +112,8 @@ 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.
 	 */
 	scale = fls_long(*parent_rate / rate - 1);
 	if (scale > fd->nwidth && !(fd->flags & CLK_FRAC_DIVIDER_NO_PRESCALER))
-- 
2.30.2