date: add helpers to convert between "+HHMM" timezones and minutes

The timezones that we store in commits as part of the identity
information are encoded in "[+-]HHMM", for example "-0700" for UTC-7.
Internally we typically pass around this timezone either as string or as
a parsed integer (-700).

Some sites want to convert between this format and minutes or vice
versa, and that conversion is performed ad-hoc. We're about to introduce
another site though that wants to have access to this logic, and having
it cluttered across our codebase is a bit awkward.

Introduce two new helpers `tz_to_minutes()` and `minutes_to_tz()` that
perform the conversion for us and convert call sites to use them.

Note that we used to perform a dance in `gm_time_t()` where we first
convert `tz` into a positive value, then calculate the minutes, and
finally turn the minutes into a negative value again. This dance is
performed because it is implementation-defined in C89 whether the
division on negative values truncates towards zero or not [1]:

  If either operand is negative, whether the result of the / operator is
  the largest integer less than the algebraic quotient or the smallest
  integer greater than the algebraic quotient is implementation-defined,
  as is the sign of the result of the % operator.

So under C89, `-130 / 100` could legitimately result in -1 or -2, and
`-130 % 100` could result in either -30 or 70. For us though, the result
that we want is the first one (-1 and -30), which is called truncation
toward zero.

This part of the C language has changed in C99, where this edge case is
now well-defined to always truncate towards zero [2]:

  When integers are divided, the result of the / operator is the
  algebraic quotient with any fractional part discarded.90) If the
  quotient a/b is representable, the expression (a/b)*b + a%b shall
  equal a.

  90) This is often called ''truncation toward zero''.

So in theory it's unlikely that we still need this logic. In practice
though it feels safer to just retain it as we don't require a fully
C99-compliant compiler in Git.

[1]: https://port70.net/~nsz/c/c89/c89-draft.html#3.3.5
[2]: https://port70.net/~nsz/c/c99/n1256.html#6.5.5p6

Signed-off-by: Patrick Steinhardt <ps@pks.im>
Signed-off-by: Junio C Hamano <gitster@pobox.com>

apply.c

@@ -14,6 +14,7 @@
 #include "abspath.h"
 #include "base85.h"
 #include "config.h"
+#include "date.h"
 #include "odb.h"
 #include "delta.h"
 #include "diff.h"
@@ -851,7 +852,7 @@ static int has_epoch_timestamp(const char *nameline)
 	if (*colon == ':')
 		zoneoffset = zoneoffset * 60 + strtol(colon + 1, NULL, 10);
 	else
-		zoneoffset = (zoneoffset / 100) * 60 + (zoneoffset % 100);
+		zoneoffset = tz_to_minutes(zoneoffset);
 	if (timestamp[m[3].rm_so] == '-')
 		zoneoffset = -zoneoffset;
 

date.c

@@ -45,13 +45,23 @@ static const char *weekday_names[] = {
 	"Sundays", "Mondays", "Tuesdays", "Wednesdays", "Thursdays", "Fridays", "Saturdays"
 };
 
+int tz_to_minutes(int tz)
+{
+	int minutes = tz < 0 ? -tz : tz;
+	minutes = (minutes / 100) * 60 + (minutes % 100);
+	return tz < 0 ? -minutes : minutes;
+}
+
+int minutes_to_tz(int minutes)
+{
+	int tz = minutes < 0 ? -minutes : minutes;
+	tz = (tz / 60) * 100 + (tz % 60);
+	return minutes < 0 ? -tz : tz;
+}
+
 static time_t gm_time_t(timestamp_t time, int tz)
 {
-	int minutes;
-
-	minutes = tz < 0 ? -tz : tz;
-	minutes = (minutes / 100)*60 + (minutes % 100);
-	minutes = tz < 0 ? -minutes : minutes;
+	int minutes = tz_to_minutes(tz);
 
 	if (minutes > 0) {
 		if (unsigned_add_overflows(time, minutes * 60))
@@ -103,8 +113,7 @@ static int local_time_tzoffset(time_t t, struct tm *tm)
 		offset = t_local - t;
 	}
 	offset /= 60; /* in minutes */
-	offset = (offset % 60) + ((offset / 60) * 100);
-	return offset * eastwest;
+	return minutes_to_tz(offset)  * eastwest;
 }
 
 /*
@@ -862,7 +871,7 @@ static int match_object_header_date(const char *date, timestamp_t *timestamp, in
 	ofs = strtol(date, &end, 10);
 	if ((*end != '\0' && (*end != '\n')) || end != date + 4)
 		return -1;
-	ofs = (ofs / 100) * 60 + (ofs % 100);
+	ofs = tz_to_minutes(ofs);
 	if (date[-1] == '-')
 		ofs = -ofs;
 	*timestamp = stamp;

date.h

@@ -70,4 +70,13 @@ void datestamp(struct strbuf *out);
 timestamp_t approxidate_careful(const char *, int *);
 int date_overflows(timestamp_t date);
 time_t tm_to_time_t(const struct tm *tm);
+
+/**
+ * Convert between the "[+-]HHMM" timezone format and minutes. This format is
+ * used for example as part of commit headers and reflogs. For example, the
+ * timezone -0100 is converted to -60 minutes.
+ */
+int tz_to_minutes(int tz);
+int minutes_to_tz(int minutes);
+
 #endif

strbuf.c

@@ -1023,8 +1023,7 @@ void strbuf_addftime(struct strbuf *sb, const char *fmt, const struct tm *tm,
 		else if (skip_prefix(fmt, "s", &fmt))
 			strbuf_addf(&munged_fmt, "%"PRItime,
 				    (timestamp_t)tm_to_time_t(tm) -
-				    3600 * (tz_offset / 100) -
-				    60 * (tz_offset % 100));
+				    60 * tz_to_minutes(tz_offset));
 		else if (skip_prefix(fmt, "z", &fmt))
 			strbuf_addf(&munged_fmt, "%+05d", tz_offset);
 		else if (suppress_tz_name && skip_prefix(fmt, "Z", &fmt))