rtc: Improve performance of rtc_time64_to_tm. Add tests.

The current implementation of rtc_time64_to_tm contains unnecessary loops,
branches and look-up tables. The new one uses an arithmetic-based algorithm
appeared in [1] and is ~3.3 times faster.

The drawback is that the new code isn't intuitive and contains many 'magic
numbers' (not unusual for this type of algorithm). However, [1] justifies
all those numbers and, given this function's history, I reckon the code is
unlikely to need much maintenance, if any at all.

Added file drivers/rtc/lib_test.c containing a KUnit test case that checks
every day in a 160,000 years interval starting on 1970-01-01 against the
expected result. A new config RTC_LIB_KUNIT_TEST symbol was introduced to
give the option to run this test suite.

[1] Neri, Schneider, "Euclidean Affine Functions and Applications to
Calendar Algorithms". https://arxiv.org/abs/2102.06959

Signed-off-by: Cassio Neri <cassio.neri@gmail.com>

drivers/rtc/Kconfig

@@ -10,6 +10,16 @@ config RTC_MC146818_LIB
 	bool
 	select RTC_LIB
 
+config RTC_LIB_KUNIT_TEST
+	tristate "KUnit test for RTC lib functions" if !KUNIT_ALL_TESTS
+	depends on KUNIT
+	default KUNIT_ALL_TESTS
+	select RTC_LIB
+	help
+	  Enable this option to test RTC library functions.
+
+	  If unsure, say N.
+
 menuconfig RTC_CLASS
 	bool "Real Time Clock"
 	default n

drivers/rtc/Makefile

@@ -178,3 +178,4 @@ obj-$(CONFIG_RTC_DRV_WM8350)	+= rtc-wm8350.o
 obj-$(CONFIG_RTC_DRV_X1205)	+= rtc-x1205.o
 obj-$(CONFIG_RTC_DRV_XGENE)	+= rtc-xgene.o
 obj-$(CONFIG_RTC_DRV_ZYNQMP)	+= rtc-zynqmp.o
+obj-$(CONFIG_RTC_LIB_KUNIT_TEST)	+= lib_test.o

drivers/rtc/lib.c

@@ -6,6 +6,8 @@
  * Author: Alessandro Zummo <a.zummo@towertech.it>
  *
  * based on arch/arm/common/rtctime.c and other bits
+ *
+ * Author: Cassio Neri <cassio.neri@gmail.com> (rtc_time64_to_tm)
  */
 
 #include <linux/export.h>
@@ -22,8 +24,6 @@ static const unsigned short rtc_ydays[2][13] = {
 	{ 0, 31, 60, 91, 121, 152, 182, 213, 244, 274, 305, 335, 366 }
 };
 
-#define LEAPS_THRU_END_OF(y) ((y) / 4 - (y) / 100 + (y) / 400)
-
 /*
  * The number of days in the month.
  */
@@ -43,41 +43,68 @@ int rtc_year_days(unsigned int day, unsigned int month, unsigned int year)
 EXPORT_SYMBOL(rtc_year_days);
 
 /*
- * rtc_time64_to_tm - Converts time64_t to rtc_time.
- * Convert seconds since 01-01-1970 00:00:00 to Gregorian date.
+ * This function converts time64_t to rtc_time.
+ *
+ * @param[in]  time   The number of seconds since 01-01-1970 00:00:00.
+ *                    (Must be positive.)
+ * @param[out] tm     Pointer to the struct rtc_time.
  */
 void rtc_time64_to_tm(time64_t time, struct rtc_time *tm)
 {
-	unsigned int month, year, secs;
+	unsigned int secs;
 	int days;
 
+	u32 r0, n1, q1;
+	u32 r1, n2, q2, r2;
+	u64 u2;
+	u32 n3, q3, r3;
+
+	u32 j;
+	u32 y;
+	u32 m, d;
+
 	/* time must be positive */
 	days = div_s64_rem(time, 86400, &secs);
 
 	/* day of the week, 1970-01-01 was a Thursday */
 	tm->tm_wday = (days + 4) % 7;
 
-	year = 1970 + days / 365;
-	days -= (year - 1970) * 365
-		+ LEAPS_THRU_END_OF(year - 1)
-		- LEAPS_THRU_END_OF(1970 - 1);
-	while (days < 0) {
-		year -= 1;
-		days += 365 + is_leap_year(year);
-	}
-	tm->tm_year = year - 1900;
-	tm->tm_yday = days + 1;
-
-	for (month = 0; month < 11; month++) {
-		int newdays;
-
-		newdays = days - rtc_month_days(month, year);
-		if (newdays < 0)
-			break;
-		days = newdays;
-	}
-	tm->tm_mon = month;
-	tm->tm_mday = days + 1;
+	/*
+	 * The following algorithm is Proposition 6.3 of Neri and Schneider,
+	 * "Euclidean Affine Functions and Applications to Calendar Algorithms".
+	 * https://arxiv.org/abs/2102.06959
+	 */
+
+	r0 = days + 719468;
+
+	n1 = 4 * r0 + 3;
+	q1 = n1 / 146097;
+	r1 = n1 % 146097 / 4;
+
+	n2 = 4 * r1 + 3;
+	u2 = ((u64) 2939745) * n2;
+	q2 = u2 >> 32;
+	r2 = ((u32) u2) / 2939745 / 4;
+
+	n3 = 2141 * r2 + 197913;
+	q3 = n3 >> 16;
+	r3 = ((u16) n3) / 2141;
+
+	j = r2 >= 306;
+	y = 100 * q1 + q2 + j;
+	m = j ? q3 - 12 : q3;
+	d = r3 + 1;
+
+	tm->tm_year = y - 1900;
+	tm->tm_mon  = m - 1;
+	tm->tm_mday = d;
+
+	/*
+	 * r2 contains the number of days since previous Mar 1st and j == true
+	 * if and only if month is Jan or Feb. The bellow is then a correction
+	 * to get the numbers of days since previous Jan 1st.
+	 */
+	tm->tm_yday = j ? r2 - 305 : r2 + 60 + is_leap_year(y);
 
 	tm->tm_hour = secs / 3600;
 	secs -= tm->tm_hour * 3600;

drivers/rtc/lib_test.c

@@ -0,0 +1,75 @@
+// SPDX-License-Identifier: LGPL-2.1+
+
+#include <kunit/test.h>
+#include <linux/rtc.h>
+
+/*
+ * Advance a date by one day.
+ */
+static void advance_date(int *year, int *month, int *mday, int *yday)
+{
+	if (*mday != rtc_month_days(*month - 1, *year)) {
+		++*mday;
+		++*yday;
+		return;
+	}
+
+	*mday = 1;
+	if (*month != 12) {
+		++*month;
+		++*yday;
+		return;
+	}
+
+	*month = 1;
+	*yday  = 1;
+	++*year;
+}
+
+/*
+ * Checks every day in a 160000 years interval starting on 1970-01-01
+ * against the expected result.
+ */
+static void rtc_time64_to_tm_test_date_range(struct kunit *test)
+{
+	/*
+	 * 160000 years = (160000 / 400) * 400 years
+	 *              = (160000 / 400) * 146097 days
+	 *              = (160000 / 400) * 146097 * 86400 seconds
+	 */
+	time64_t total_secs = ((time64_t) 160000) / 400 * 146097 * 86400;
+	int      year       = 1970;
+	int      month      = 1;
+	int      mday       = 1;
+	int      yday       = 1;
+
+	struct rtc_time result;
+	time64_t secs;
+
+	for (secs = 0; secs <= total_secs; secs += 86400) {
+
+		rtc_time64_to_tm(secs, &result);
+
+		#define FAIL_MSG "%d/%02d/%02d (%2d) : %ld", \
+			year, month, mday, yday, secs/86400
+
+		KUNIT_ASSERT_EQ_MSG(test, year - 1900, result.tm_year, FAIL_MSG);
+		KUNIT_ASSERT_EQ_MSG(test, month - 1, result.tm_mon, FAIL_MSG);
+		KUNIT_ASSERT_EQ_MSG(test, mday, result.tm_mday, FAIL_MSG);
+		KUNIT_ASSERT_EQ_MSG(test, yday, result.tm_yday, FAIL_MSG);
+
+		advance_date(&year, &month, &mday, &yday);
+	}
+}
+
+static struct kunit_case rtc_lib_test_cases[] = {
+	KUNIT_CASE(rtc_time64_to_tm_test_date_range),
+	{}
+};
+
+static struct kunit_suite rtc_lib_test_suite = {
+	.name = "rtc_lib_test_cases",
+	.test_cases = rtc_lib_test_cases,
+};
+
+kunit_test_suite(rtc_lib_test_suite);

include/linux/rtc.h

@@ -220,7 +220,11 @@ void rtc_timer_do_work(struct work_struct *work);
 
 static inline bool is_leap_year(unsigned int year)
 {
-	return (!(year % 4) && (year % 100)) || !(year % 400);
+	/* This implementation is more branch-predictor friendly than the
+	 * traditional:
+	 *   return year % 4 == 0 && (year % 100 != 0 || year % 400 == 0);
+	 */
+	return year % 100 != 0 ? year % 4 == 0 : year % 400 == 0;
 }
 
 #define devm_rtc_register_device(device) \