rtc: Optimize calculations in rtc_time64_to_tm()

Recently (in commit 7df4cfe ("rtc: Make rtc_time64_to_tm() support
dates before 1970")) the function rtc_time64_to_tm() was repaired for
times before 1970. This introduced two if blocks. Cassio Neri pointed
out that to be not neccessary and suggested an adaption that allows to
drop the two branch points again.

This is implemented here.

Also adapt the reference to the theoretical paper to link to the final
published article instead of the preprint on Cassio's request.

Suggested-by: Cassio Neri <cassio.neri@gmail.com>
Signed-off-by: Uwe Kleine-König <u.kleine-koenig@baylibre.com>
Link: https://lore.kernel.org/r/20250613142405.253420-2-u.kleine-koenig@baylibre.com
Signed-off-by: Alexandre Belloni <alexandre.belloni@bootlin.com>

Author: ukleinek

drivers/rtc/lib.c

@@ -51,36 +51,34 @@ EXPORT_SYMBOL(rtc_year_days);
  */
 void rtc_time64_to_tm(time64_t time, struct rtc_time *tm)
 {
-	int days, secs;
+	int secs;
 
 	u64 u64tmp;
 	u32 u32tmp, udays, century, day_of_century, year_of_century, year,
 		day_of_year, month, day;
 	bool is_Jan_or_Feb, is_leap_year;
 
 	/*
-	 * Get days and seconds while preserving the sign to
-	 * handle negative time values (dates before 1970-01-01)
+	 * The time represented by `time` is given in seconds since 1970-01-01
+	 * (UTC). As the division done below might misbehave for negative
+	 * values, we convert it to seconds since 0000-03-01 and then assume it
+	 * will be non-negative.
+	 * Below we do 4 * udays + 3 which should fit into a 32 bit unsigned
+	 * variable. So the latest date this algorithm works for is 1073741823
+	 * days after 0000-03-01 which is in the year 2939805.
 	 */
-	days = div_s64_rem(time, 86400, &secs);
+	time += (u64)719468 * 86400;
+
+	udays = div_s64_rem(time, 86400, &secs);
 
 	/*
-	 * We need 0 <= secs < 86400 which isn't given for negative
-	 * values of time. Fixup accordingly.
+	 * day of the week, 0000-03-01 was a Wednesday (in the proleptic
+	 * Gregorian calendar)
 	 */
-	if (secs < 0) {
-		days -= 1;
-		secs += 86400;
-	}
-
-	/* day of the week, 1970-01-01 was a Thursday */
-	tm->tm_wday = (days + 4) % 7;
-	/* Ensure tm_wday is always positive */
-	if (tm->tm_wday < 0)
-		tm->tm_wday += 7;
+	tm->tm_wday = (udays + 3) % 7;
 
 	/*
-	 * The following algorithm is, basically, Proposition 6.3 of Neri
+	 * The following algorithm is, basically, Figure 12 of Neri
 	 * and Schneider [1]. In a few words: it works on the computational
 	 * (fictitious) calendar where the year starts in March, month = 2
 	 * (*), and finishes in February, month = 13. This calendar is
@@ -100,15 +98,15 @@ void rtc_time64_to_tm(time64_t time, struct rtc_time *tm)
 	 * (using just arithmetics) it's easy to convert it to the
 	 * corresponding date in the Gregorian calendar.
 	 *
-	 * [1] "Euclidean Affine Functions and Applications to Calendar
-	 * Algorithms". https://arxiv.org/abs/2102.06959
+	 * [1] Neri C, Schneider L. Euclidean affine functions and their
+	 *     application to calendar algorithms. Softw Pract Exper.
+	 *     2023;53(4):937-970. doi: 10.1002/spe.3172
+	 *     https://doi.org/10.1002/spe.3172
 	 *
 	 * (*) The numbering of months follows rtc_time more closely and
 	 * thus, is slightly different from [1].
 	 */
 
-	udays		= days + 719468;
-
 	u32tmp		= 4 * udays + 3;
 	century		= u32tmp / 146097;
 	day_of_century	= u32tmp % 146097 / 4;