Update sunrise/sunset calculations with different formula for mean anomaly.

man/remind.1

@@ -2739,7 +2739,7 @@ an algorithm in "Almanac for Computers for the year 1978" by
 L. E. Doggett, Nautical Almanac Office, USNO.  They require
 the latitude and longitude to be specified by setting the appropriate
 system variables.  (See "System Variables".)  The sun functions
-should be accurate to within about 2 minutes for latitudes lower
+should be accurate to within about 4 minutes for latitudes lower
 than 60 degrees.  The functions are available starting from version
 03.00.07 of \fBRemind\fR.
 .RE

src/funcs.c

@@ -1854,10 +1854,11 @@ static int FTimeStuff(int wantmins, func_info *info)
 
 static int SunStuff(int rise, double cosz, int jul)
 {
-    int year, mon, day;
-    int jan0;
     int mins, hours;
     int dusk_or_dawn;
+    int year, mon, day;
+    int jan0;
+    double jan0d;
 
     double M, L, tanA, sinDelta, cosDelta, a, a_hr, cosH, t, H, T;
     double latitude, longdeg, UT, local;
@@ -1880,17 +1881,31 @@ static int SunStuff(int rise, double cosz, int jul)
 
     FromJulian(jul, &year, &mon, &day);
     jan0 = jul - Julian(year, 0, 1);
+    jan0d = (double) jan0;
 
     dusk_or_dawn = rise;
     if (rise > 1)
 	rise -= 2;
-/* Following formula on page B6 exactly... */
-    t = (double) jan0;
-    if (rise) t += (6.0 + longdeg/15.0) / 24.0;
-    else      t += (18.0 + longdeg/15.0) / 24.0;
 
-/* Mean anomaly of sun for 1978 ... how accurate for other years??? */
+/* Following formula on page B6 exactly... */
-    M = 0.985600 * t - 3.251;  /* In degrees */
+    t = (double) jul;
+    if (rise) {
+	t += (6.0 + longdeg/15.0) / 24.0;
+	jan0d += (6.0 + longdeg/15.0) / 24.0;
+    } else {
+	t += (18.0 + longdeg/15.0) / 24.0;
+	jan0d += (18.0 + longdeg/15.0) / 24.0;
+    }
+
+/* Mean anomaly of sun starting from 1 Jan 1990 */
+/* NOTE: This assumes that BASE = 1990!!! */
+#if BASE != 1990
+#error Sun calculations assume a BASE of 1990!
+#endif
+    M = (0.985600 * t) + 356.6349;  /* In degrees */
+
+    /* Make sure M is in the range [0, 360) */
+    M -= (floor(M/360.0) * 360.0);
 
 /* Sun's true longitude */
     L = M + 1.916*sin(DEGRAD*M) + 0.02*sin(2*DEGRAD*M) + 282.565;
@@ -1936,7 +1951,7 @@ static int SunStuff(int rise, double cosz, int jul)
     H = RADDEG * acos(cosH);
     if (rise) H = 360.0 - H;
 
-    T = H / 15.0 + a_hr - 0.065710*t - 6.620;
+    T = H / 15.0 + a_hr - 0.065710 * jan0d - 6.620;
     if (T >= 24.0) T -= 24.0;
     else if (T < 0.0) T+= 24.0;