linux-kernel - [PATCH] mul_u64_u64_div_u64: Increase precision by conditionally swapping a and b

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Message-ID: <20240302205426.639205-2-u.kleine-koenig@pengutronix.de>
Date: Sat,  2 Mar 2024 21:54:27 +0100
From: Uwe Kleine-König <u.kleine-koenig@...gutronix.de>
To: Andrew Morton <akpm@...ux-foundation.org>
Cc: linux-kernel@...r.kernel.org,
	Biju Das <biju.das.jz@...renesas.com>,
	kernel@...gutronix.de
Subject: [PATCH] mul_u64_u64_div_u64: Increase precision by conditionally swapping a and b

As indicated in the added comment, the algorithm works better if b is
big. As multiplication is commutative, a and b can be swapped. Do this
If a is bigger than b.

Signed-off-by: Uwe Kleine-König <u.kleine-koenig@...gutronix.de>
---
 lib/math/div64.c | 17 +++++++++++++++++
 1 file changed, 17 insertions(+)

diff --git a/lib/math/div64.c b/lib/math/div64.c
index 55a81782e271..baf6f8681907 100644
--- a/lib/math/div64.c
+++ b/lib/math/div64.c
@@ -190,6 +190,23 @@ u64 mul_u64_u64_div_u64(u64 a, u64 b, u64 c)
 
 	/* can a * b overflow ? */
 	if (ilog2(a) + ilog2(b) > 62) {
+		/*
+		 * Note that the algorithm after the if block below might loose
+		 * some precision and the result is more exact for b > a. So
+		 * exchange a and b if a is bigger than b.
+		 *
+		 * For example with a = 43980465100800, b = 100000000, c = 1000000000
+		 * the below calculation doesn't modify b at all because div == 0
+		 * and then shift becomes 45 + 26 - 62 = 9 and so the result
+		 * becomes 4398035251080. However with a and b swapped the exact
+		 * result is calculated (i.e. 4398046510080).
+		 */
+		if (a > b) {
+			u64 tmp = a;
+			a = b;
+			b = tmp;
+		}
+
 		/*
 		 * (b * a) / c is equal to
 		 *

base-commit: 1870cdc0e8dee32e3c221704a2977898ba4c10e8
-- 
2.43.0