Reorder so that functions are defined before use.

(displayed-month, displayed-year): Move declarations where needed.
(solar-get-number): Move definition before use.  Use unless.
(solar-equatorial-coordinates): Simplify.
(solar-sunrise-and-sunset): Use let rather than let*.
(solar-longitude, solar-equinoxes-solstices): Use cadr, nth

2 files changed, 281 insertions, 275 deletions

diff --git a/lisp/ChangeLog b/lisp/ChangeLog
index 75125030b4b..ced8820c45f 100644
--- a/lisp/ChangeLog
+++ b/lisp/ChangeLog
@@ -1,5 +1,12 @@
 2008-03-14  Glenn Morris  <rgm@gnu.org>
 
+        * calendar/solar.el: Reorder so that functions are defined before use.
+        (displayed-month, displayed-year): Move declarations where needed.
+        (solar-get-number): Move definition before use.  Use unless.
+        (solar-equatorial-coordinates): Simplify.
+        (solar-sunrise-and-sunset): Use let rather than let*.
+        (solar-longitude, solar-equinoxes-solstices): Use cadr, nth
+
         * startup.el (command-line-1): Rename -internal-script back to
         -scriptload (reverts previous change).
 
diff --git a/lisp/calendar/solar.el b/lisp/calendar/solar.el
index d0b02b4b111..78071bb5db8 100644
--- a/lisp/calendar/solar.el
+++ b/lisp/calendar/solar.el
@@ -54,9 +54,6 @@
 
 ;;; Code:
 
-(defvar displayed-month)
-(defvar displayed-year)
-
 (if (fboundp 'atan)
     (require 'lisp-float-type)
   (error "Solar calculations impossible since floating point is unavailable"))
@@ -206,6 +203,13 @@ Needed for polar areas, in order to know whether the day lasts 0 or 24 hours.")
           long
         (- long)))))
 
+(defun solar-get-number (prompt)
+  "Return a number from the minibuffer, prompting with PROMPT.
+Returns nil if nothing was entered."
+  (let ((x (read-string prompt "")))
+    (unless (string-equal x "")
+      (string-to-number x))))
+
 (defun solar-setup ()
   "Prompt for `calendar-longitude', `calendar-latitude', `calendar-time-zone'."
   (beep)
@@ -223,13 +227,6 @@ Needed for polar areas, in order to know whether the day lasts 0 or 24 hours.")
              "Enter difference from Coordinated Universal Time (in minutes): ")
             )))
 
-(defun solar-get-number (prompt)
-  "Return a number from the minibuffer, prompting with PROMPT.
-Returns nil if nothing was entered."
-  (let ((x (read-string prompt "")))
-    (if (not (string-equal x ""))
-        (string-to-number x))))
-
 (defun solar-sin-degrees (x)
   "Return sin of X degrees."
   (sin (degrees-to-radians (mod x 360.0))))
@@ -299,36 +296,182 @@ Both arguments are in degrees."
    (* (solar-sin-degrees obliquity)
       (solar-sin-degrees longitude))))
 
-(defun solar-sunrise-and-sunset (time latitude longitude height)
-  "Sunrise, sunset and length of day.
-Parameters are the midday TIME and the LATITUDE, LONGITUDE of the location.
+(defun solar-ecliptic-coordinates (time sunrise-flag)
+  "Return solar longitude, ecliptic inclination, equation of time, nutation.
+Values are for TIME in Julian centuries of Ephemeris Time since
+January 1st, 2000, at 12 ET.  Longitude and inclination are in
+degrees, equation of time in hours, and nutation in seconds of longitude.
+If SUNRISE-FLAG is non-nil, only calculate longitude and inclination."
+  (let* ((l (+ 280.46645
+               (* 36000.76983 time)
+               (* 0.0003032 time time))) ; sun mean longitude
+         (ml (+ 218.3165
+                (* 481267.8813 time)))  ; moon mean longitude
+         (m (+ 357.52910
+               (* 35999.05030 time)
+               (* -0.0001559 time time)
+               (* -0.00000048 time time time))) ; sun mean anomaly
+         (i (+ 23.43929111 (* -0.013004167 time)
+               (* -0.00000016389 time time)
+               (* 0.0000005036 time time time))) ; mean inclination
+         (c (+ (* (+ 1.914600
+                     (* -0.004817 time)
+                     (* -0.000014 time time))
+                  (solar-sin-degrees m))
+               (* (+ 0.019993 (* -0.000101 time))
+                  (solar-sin-degrees (* 2 m)))
+               (* 0.000290
+                  (solar-sin-degrees (* 3 m))))) ; center equation
+         (L (+ l c))                             ; total longitude
+         ;; Longitude of moon's ascending node on the ecliptic.
+         (omega (+ 125.04
+                   (* -1934.136 time)))
+         ;; nut = nutation in longitude, measured in seconds of angle.
+         (nut (unless sunrise-flag
+                (+ (* -17.20 (solar-sin-degrees omega))
+                   (* -1.32 (solar-sin-degrees (* 2 l)))
+                   (* -0.23 (solar-sin-degrees (* 2 ml)))
+                   (* 0.21 (solar-sin-degrees (* 2 omega))))))
+         (ecc (unless sunrise-flag     ; eccentricity of earth's orbit
+                (+ 0.016708617
+                   (* -0.000042037 time)
+                   (* -0.0000001236 time time))))
+         (app (+ L                      ; apparent longitude of sun
+                 -0.00569
+                 (* -0.00478
+                    (solar-sin-degrees omega))))
+         (y (unless sunrise-flag
+              (* (solar-tangent-degrees (/ i 2))
+                 (solar-tangent-degrees (/ i 2)))))
+         ;; Equation of time, in hours.
+         (time-eq (unless sunrise-flag
+                    (/ (* 12 (+ (* y (solar-sin-degrees (* 2 l)))
+                                (* -2 ecc (solar-sin-degrees m))
+                                (* 4 ecc y (solar-sin-degrees m)
+                                   (solar-cosine-degrees (* 2 l)))
+                                (* -0.5 y y  (solar-sin-degrees (* 4 l)))
+                                (* -1.25 ecc ecc (solar-sin-degrees (* 2 m)))))
+                       3.1415926535))))
+    (list app i time-eq nut)))
+
+(defun solar-ephemeris-correction (year)
+  "Ephemeris time minus Universal Time during Gregorian YEAR.
+Result is in days.  For the years 1800-1987, the maximum error is
+1.9 seconds.  For the other years, the maximum error is about 30 seconds."
+  (cond ((and (<= 1988 year) (< year 2020))
+         (/ (+ year -2000 67.0) 60.0 60.0 24.0))
+        ((and (<= 1900 year) (< year 1988))
+         (let* ((theta (/ (- (calendar-astro-from-absolute
+                              (calendar-absolute-from-gregorian
+                               (list 7 1 year)))
+                             (calendar-astro-from-absolute
+                              (calendar-absolute-from-gregorian
+                               '(1 1 1900))))
+                          36525.0))
+                (theta2 (* theta theta))
+                (theta3 (* theta2 theta))
+                (theta4 (* theta2 theta2))
+                (theta5 (* theta3 theta2)))
+           (+ -0.00002
+              (* 0.000297 theta)
+              (* 0.025184 theta2)
+              (* -0.181133 theta3)
+              (* 0.553040 theta4)
+              (* -0.861938 theta5)
+              (* 0.677066 theta3 theta3)
+              (* -0.212591 theta4 theta3))))
+        ((and (<= 1800 year) (< year 1900))
+         (let* ((theta (/ (- (calendar-astro-from-absolute
+                              (calendar-absolute-from-gregorian
+                               (list 7 1 year)))
+                             (calendar-astro-from-absolute
+                              (calendar-absolute-from-gregorian
+                               '(1 1 1900))))
+                          36525.0))
+                (theta2 (* theta theta))
+                (theta3 (* theta2 theta))
+                (theta4 (* theta2 theta2))
+                (theta5 (* theta3 theta2)))
+           (+ -0.000009
+              (* 0.003844 theta)
+              (* 0.083563 theta2)
+              (* 0.865736 theta3)
+              (* 4.867575 theta4)
+              (* 15.845535 theta5)
+              (* 31.332267 theta3 theta3)
+              (* 38.291999 theta4 theta3)
+              (* 28.316289 theta4 theta4)
+              (* 11.636204 theta4 theta5)
+              (* 2.043794 theta5 theta5))))
+        ((and (<= 1620 year) (< year 1800))
+         (let ((x (/ (- year 1600) 10.0)))
+           (/ (+ (* 2.19167 x x) (* -40.675 x) 196.58333) 60.0 60.0 24.0)))
+        (t (let* ((tmp (- (calendar-astro-from-absolute
+                           (calendar-absolute-from-gregorian
+                            (list 1 1 year)))
+                          2382148))
+                  (second (- (/ (* tmp tmp) 41048480.0) 15)))
+             (/ second 60.0 60.0 24.0)))))
 
+(defun solar-ephemeris-time (time)
+  "Ephemeris Time at moment TIME.
 TIME is a pair with the first component being the number of Julian centuries
 elapsed at 0 Universal Time, and the second component being the universal
 time.  For instance, the pair corresponding to November 28, 1995 at 16 UT is
 \(-0.040945 16), -0.040945 being the number of Julian centuries elapsed between
 Jan 1, 2000 at 12 UT and November 28, 1995 at 0 UT.
 
-HEIGHT is the angle the center of the sun has over the horizon for the contact
-we are trying to find.  For sunrise and sunset, it is usually -0.61 degrees,
-accounting for the edge of the sun being on the horizon.
+Result is in Julian centuries of ephemeris time."
+  (let* ((t0 (car time))
+         (ut (cadr time))
+         (t1 (+ t0 (/ (/ ut 24.0) 36525)))
+         (y (+ 2000 (* 100 t1)))
+         (dt (* 86400 (solar-ephemeris-correction (floor y)))))
+    (+ t1 (/ (/ dt 86400) 36525))))
 
-Coordinates are included because this function is called with latitude=1
-degrees to find out if polar regions have 24 hours of sun or only night."
-  (let* ((rise-time (solar-moment -1 latitude longitude time height))
-         (set-time (solar-moment 1 latitude longitude time height))
-         (day-length))
-    (if (not (and rise-time set-time))
-        (if (or (and (> latitude 0)
-                     solar-northern-spring-or-summer-season)
-                (and (< latitude 0)
-                     (not solar-northern-spring-or-summer-season)))
-            (setq day-length 24)
-          (setq day-length 0))
-      (setq day-length (- set-time rise-time)))
-    (list (if rise-time (+ rise-time (/ calendar-time-zone 60.0)) nil)
-          (if set-time (+ set-time (/ calendar-time-zone 60.0)) nil)
-          day-length)))
+(defun solar-equatorial-coordinates (time sunrise-flag)
+  "Right ascension (in hours) and declination (in degrees) of the sun at TIME.
+TIME is a pair with the first component being the number of
+Julian centuries elapsed at 0 Universal Time, and the second
+component being the universal time.  For instance, the pair
+corresponding to November 28, 1995 at 16 UT is (-0.040945 16),
+-0.040945 being the number of Julian centuries elapsed between
+Jan 1, 2000 at 12 UT and November 28, 1995 at 0 UT.  SUNRISE-FLAG is passed
+to `solar-ecliptic-coordinates'."
+  (let ((ec (solar-ecliptic-coordinates (solar-ephemeris-time time)
+                                        sunrise-flag)))
+    (list (solar-right-ascension (car ec) (cadr ec))
+          (solar-declination (car ec) (cadr ec)))))
+
+(defun solar-horizontal-coordinates (time latitude longitude sunrise-flag)
+  "Azimuth and height of the sun at TIME, LATITUDE, and LONGITUDE.
+TIME is a pair with the first component being the number of
+Julian centuries elapsed at 0 Universal Time, and the second
+component being the universal time.  For instance, the pair
+corresponding to November 28, 1995 at 16 UT is (-0.040945 16),
+-0.040945 being the number of Julian centuries elapsed between
+Jan 1, 2000 at 12 UT and November 28, 1995 at 0 UT.  SUNRISE-FLAG
+is passed to `solar-ecliptic-coordinates'.  Azimuth and
+height (between -180 and 180) are both in degrees."
+  (let* ((ut (cadr time))
+         (ec (solar-equatorial-coordinates time sunrise-flag))
+         (st (+ solar-sidereal-time-greenwich-midnight
+                (* ut 1.00273790935)))
+         ;; Hour angle (in degrees).
+         (ah (- (* st 15) (* 15 (car ec)) (* -1 (calendar-longitude))))
+         (de (cadr ec))
+         (azimuth (solar-atn2 (- (* (solar-cosine-degrees ah)
+                                    (solar-sin-degrees latitude))
+                                 (* (solar-tangent-degrees de)
+                                    (solar-cosine-degrees latitude)))
+                              (solar-sin-degrees ah)))
+         (height (solar-arcsin
+                  (+ (* (solar-sin-degrees latitude) (solar-sin-degrees de))
+                     (* (solar-cosine-degrees latitude)
+                        (solar-cosine-degrees de)
+                        (solar-cosine-degrees ah))))))
+    (if (> height 180) (setq height (- height 360)))
+    (list azimuth height)))
 
 (defun solar-moment (direction latitude longitude time height)
   "Sunrise/sunset at location.
@@ -377,6 +520,37 @@ Uses binary search."
       (setq possible nil))              ; the sun never sets
     (if possible utmoment)))
 
+(defun solar-sunrise-and-sunset (time latitude longitude height)
+  "Sunrise, sunset and length of day.
+Parameters are the midday TIME and the LATITUDE, LONGITUDE of the location.
+
+TIME is a pair with the first component being the number of Julian centuries
+elapsed at 0 Universal Time, and the second component being the universal
+time.  For instance, the pair corresponding to November 28, 1995 at 16 UT is
+\(-0.040945 16), -0.040945 being the number of Julian centuries elapsed between
+Jan 1, 2000 at 12 UT and November 28, 1995 at 0 UT.
+
+HEIGHT is the angle the center of the sun has over the horizon for the contact
+we are trying to find.  For sunrise and sunset, it is usually -0.61 degrees,
+accounting for the edge of the sun being on the horizon.
+
+Coordinates are included because this function is called with latitude=1
+degrees to find out if polar regions have 24 hours of sun or only night."
+  (let ((rise-time (solar-moment -1 latitude longitude time height))
+        (set-time (solar-moment 1 latitude longitude time height))
+        day-length)
+    (if (not (and rise-time set-time))
+        (if (or (and (> latitude 0)
+                     solar-northern-spring-or-summer-season)
+                (and (< latitude 0)
+                     (not solar-northern-spring-or-summer-season)))
+            (setq day-length 24)
+          (setq day-length 0))
+      (setq day-length (- set-time rise-time)))
+    (list (if rise-time (+ rise-time (/ calendar-time-zone 60.0)) nil)
+          (if set-time (+ set-time (/ calendar-time-zone 60.0)) nil)
+          day-length)))
+
 (defun solar-time-string (time time-zone)
   "Printable form for decimal fraction TIME in TIME-ZONE.
 Format used is given by `calendar-time-display-form'."
@@ -388,13 +562,27 @@ Format used is given by `calendar-time-display-form'."
          (24-hours (format "%02d" 24-hours)))
     (mapconcat 'eval calendar-time-display-form "")))
 
-
 (defun solar-daylight (time)
   "Printable form for TIME expressed in hours."
   (format "%d:%02d"
           (floor time)
           (floor (* 60 (- time (floor time))))))
 
+(defun solar-julian-ut-centuries (date)
+  "Number of Julian centuries since 1 Jan, 2000 at noon UT for Gregorian DATE."
+  (/ (- (calendar-absolute-from-gregorian date)
+        (calendar-absolute-from-gregorian '(1 1.5 2000)))
+     36525.0))
+
+(defun solar-date-to-et (date ut)
+  "Ephemeris Time at Gregorian DATE at Universal Time UT (in hours).
+Expressed in Julian centuries of Ephemeris Time."
+  (solar-ephemeris-time (list (solar-julian-ut-centuries date) ut)))
+
+(defun solar-time-equation (date ut)
+  "Equation of time expressed in hours at Gregorian DATE at Universal time UT."
+  (nth 2 (solar-ecliptic-coordinates (solar-date-to-et date ut) nil)))
+
 (defun solar-exact-local-noon (date)
   "Date and Universal Time of local noon at *local date* DATE.
 The date may be different from the one asked for, but it will be the right
@@ -415,6 +603,22 @@ local date.  The second component of date should be an integer."
               (calendar-absolute-from-gregorian nd)))
     (list nd ut)))
 
+(defun solar-sidereal-time (t0)
+  "Sidereal time (in hours) in Greenwich at T0 Julian centuries.
+T0 must correspond to 0 hours UT."
+  (let* ((mean-sid-time (+ 6.6973746
+                           (* 2400.051337 t0)
+                           (* 0.0000258622 t0 t0)
+                           (* -0.0000000017222 t0 t0 t0)))
+         (et (solar-ephemeris-time (list t0 0.0)))
+         (nut-i (solar-ecliptic-coordinates et nil))
+         (nut (nth 3 nut-i))            ; nutation
+         (i (cadr nut-i)))              ; inclination
+    (mod (+ (mod (+ mean-sid-time
+                    (/ (/ (* nut (solar-cosine-degrees i)) 15) 3600)) 24.0)
+            24.0)
+         24.0)))
+
 (defun solar-sunrise-sunset (date)
   "List of *local* times of sunrise, sunset, and daylight on Gregorian DATE.
 Corresponding value is nil if there is no sunrise/sunset."
@@ -467,161 +671,6 @@ Corresponding value is nil if there is no sunrise/sunset."
      (eval calendar-location-name)
      (nth 2 l))))
 
-(defun solar-julian-ut-centuries (date)
-  "Number of Julian centuries since 1 Jan, 2000 at noon UT for Gregorian DATE."
-  (/ (- (calendar-absolute-from-gregorian date)
-        (calendar-absolute-from-gregorian '(1 1.5 2000)))
-     36525.0))
-
-(defun solar-ephemeris-time (time)
-  "Ephemeris Time at moment TIME.
-TIME is a pair with the first component being the number of Julian centuries
-elapsed at 0 Universal Time, and the second component being the universal
-time.  For instance, the pair corresponding to November 28, 1995 at 16 UT is
-\(-0.040945 16), -0.040945 being the number of Julian centuries elapsed between
-Jan 1, 2000 at 12 UT and November 28, 1995 at 0 UT.
-
-Result is in Julian centuries of ephemeris time."
-  (let* ((t0 (car time))
-         (ut (cadr time))
-         (t1 (+ t0 (/ (/ ut 24.0) 36525)))
-         (y (+ 2000 (* 100 t1)))
-         (dt (* 86400 (solar-ephemeris-correction (floor y)))))
-    (+ t1 (/ (/ dt 86400) 36525))))
-
-(defun solar-date-next-longitude (d l)
-  "First time after day D when solar longitude is a multiple of L degrees.
-D is a Julian day number.  L must be an integer divisor of 360.
-The result is for `calendar-location-name', and is in local time
-\(including any daylight saving rules) expressed in astronomical (Julian)
-day numbers.  The values of `calendar-daylight-savings-starts',
-`calendar-daylight-savings-starts-time', `calendar-daylight-savings-ends',
-`calendar-daylight-savings-ends-time', `calendar-daylight-time-offset',
-and `calendar-time-zone' are used to interpret local time."
-  (let* ((long)
-         (start d)
-         (start-long (solar-longitude d))
-         (next (mod (* l (1+ (floor (/ start-long l)))) 360))
-         (end (+ d (* (/ l 360.0) 400)))
-         (end-long (solar-longitude end)))
-    (while                       ; bisection search for nearest minute
-        (< 0.00001 (- end start))
-      ;; start   <= d    < end
-      ;; start-long <= next < end-long when next != 0
-      ;; when next = 0, we look for the discontinuity (start-long is near 360
-      ;;                and end-long is small (less than l).
-      (setq d (/ (+ start end) 2.0)
-            long (solar-longitude d))
-      (if (or (and (not (zerop next)) (< long next))
-              (and (zerop next) (< l long)))
-          (setq start d
-                start-long long)
-        (setq end d
-              end-long long)))
-    (/ (+ start end) 2.0)))
-
-(defun solar-horizontal-coordinates (time latitude longitude sunrise-flag)
-  "Azimuth and height of the sun at TIME, LATITUDE, and LONGITUDE.
-TIME is a pair with the first component being the number of
-Julian centuries elapsed at 0 Universal Time, and the second
-component being the universal time.  For instance, the pair
-corresponding to November 28, 1995 at 16 UT is (-0.040945 16),
--0.040945 being the number of Julian centuries elapsed between
-Jan 1, 2000 at 12 UT and November 28, 1995 at 0 UT.  SUNRISE-FLAG
-is passed to `solar-ecliptic-coordinates'.  Azimuth and
-height (between -180 and 180) are both in degrees."
-  (let* ((ut (cadr time))
-         (ec (solar-equatorial-coordinates time sunrise-flag))
-         (st (+ solar-sidereal-time-greenwich-midnight
-                (* ut 1.00273790935)))
-         ;; Hour angle (in degrees).
-         (ah (- (* st 15) (* 15 (car ec)) (* -1 (calendar-longitude))))
-         (de (cadr ec))
-         (azimuth (solar-atn2 (- (* (solar-cosine-degrees ah)
-                                    (solar-sin-degrees latitude))
-                                 (* (solar-tangent-degrees de)
-                                    (solar-cosine-degrees latitude)))
-                              (solar-sin-degrees ah)))
-         (height (solar-arcsin
-                  (+ (* (solar-sin-degrees latitude) (solar-sin-degrees de))
-                     (* (solar-cosine-degrees latitude)
-                        (solar-cosine-degrees de)
-                        (solar-cosine-degrees ah))))))
-    (if (> height 180) (setq height (- height 360)))
-    (list azimuth height)))
-
-(defun solar-equatorial-coordinates (time sunrise-flag)
-  "Right ascension (in hours) and declination (in degrees) of the sun at TIME.
-TIME is a pair with the first component being the number of
-Julian centuries elapsed at 0 Universal Time, and the second
-component being the universal time.  For instance, the pair
-corresponding to November 28, 1995 at 16 UT is (-0.040945 16),
--0.040945 being the number of Julian centuries elapsed between
-Jan 1, 2000 at 12 UT and November 28, 1995 at 0 UT.  SUNRISE-FLAG is passed
-to `solar-ecliptic-coordinates'."
-  (let* ((tm (solar-ephemeris-time time))
-         (ec (solar-ecliptic-coordinates tm sunrise-flag)))
-    (list (solar-right-ascension (car ec) (car (cdr ec)))
-          (solar-declination (car ec) (car (cdr ec))))))
-
-(defun solar-ecliptic-coordinates (time sunrise-flag)
-  "Return solar longitude, ecliptic inclination, equation of time, nutation.
-Values are for TIME in Julian centuries of Ephemeris Time since
-January 1st, 2000, at 12 ET.  Longitude and inclination are in
-degrees, equation of time in hours, and nutation in seconds of longitude.
-If SUNRISE-FLAG is non-nil, only calculate longitude and inclination."
-  (let* ((l (+ 280.46645
-               (* 36000.76983 time)
-               (* 0.0003032 time time))) ; sun mean longitude
-         (ml (+ 218.3165
-                (* 481267.8813 time)))  ; moon mean longitude
-         (m (+ 357.52910
-               (* 35999.05030 time)
-               (* -0.0001559 time time)
-               (* -0.00000048 time time time))) ; sun mean anomaly
-         (i (+ 23.43929111 (* -0.013004167 time)
-               (* -0.00000016389 time time)
-               (* 0.0000005036 time time time))) ; mean inclination
-         (c (+ (* (+ 1.914600
-                     (* -0.004817 time)
-                     (* -0.000014 time time))
-                  (solar-sin-degrees m))
-               (* (+ 0.019993 (* -0.000101 time))
-                  (solar-sin-degrees (* 2 m)))
-               (* 0.000290
-                  (solar-sin-degrees (* 3 m))))) ; center equation
-         (L (+ l c))                             ; total longitude
-         ;; Longitude of moon's ascending node on the ecliptic.
-         (omega (+ 125.04
-                   (* -1934.136 time)))
-         ;; nut = nutation in longitude, measured in seconds of angle.
-         (nut (unless sunrise-flag
-                (+ (* -17.20 (solar-sin-degrees omega))
-                   (* -1.32 (solar-sin-degrees (* 2 l)))
-                   (* -0.23 (solar-sin-degrees (* 2 ml)))
-                   (* 0.21 (solar-sin-degrees (* 2 omega))))))
-         (ecc (unless sunrise-flag     ; eccentricity of earth's orbit
-                (+ 0.016708617
-                   (* -0.000042037 time)
-                   (* -0.0000001236 time time))))
-         (app (+ L                      ; apparent longitude of sun
-                 -0.00569
-                 (* -0.00478
-                    (solar-sin-degrees omega))))
-         (y (unless sunrise-flag
-              (* (solar-tangent-degrees (/ i 2))
-                 (solar-tangent-degrees (/ i 2)))))
-         ;; Equation of time, in hours.
-         (time-eq (unless sunrise-flag
-                    (/ (* 12 (+ (* y (solar-sin-degrees (* 2 l)))
-                                (* -2 ecc (solar-sin-degrees m))
-                                (* 4 ecc y (solar-sin-degrees m)
-                                   (solar-cosine-degrees (* 2 l)))
-                                (* -0.5 y y  (solar-sin-degrees (* 4 l)))
-                                (* -1.25 ecc ecc (solar-sin-degrees (* 2 m)))))
-                       3.1415926535))))
-    (list app i time-eq nut)))
-
 (defconst solar-data-list
   '((403406 4.721964 1.621043)
     (195207 5.937458 62830.348067)
@@ -705,8 +754,8 @@ The values of `calendar-daylight-savings-starts',
                        (mapcar (lambda (x)
                                  (* (car x)
                                     (sin (mod
-                                          (+ (car (cdr x))
-                                             (* (car (cdr (cdr x))) U))
+                                          (+ (cadr x)
+                                             (* (nth 2 x) U))
                                           (* 2 pi)))))
                                solar-data-list)))))
          (aberration
@@ -716,89 +765,36 @@ The values of `calendar-daylight-savings-starts',
          (nutation (* -0.0000001 (+ (* 834 (sin A1)) (* 64 (sin A2))))))
     (mod (radians-to-degrees (+ longitude aberration nutation)) 360.0)))
 
-(defun solar-ephemeris-correction (year)
-  "Ephemeris time minus Universal Time during Gregorian YEAR.
-Result is in days.  For the years 1800-1987, the maximum error is
-1.9 seconds.  For the other years, the maximum error is about 30 seconds."
-  (cond ((and (<= 1988 year) (< year 2020))
-         (/ (+ year -2000 67.0) 60.0 60.0 24.0))
-        ((and (<= 1900 year) (< year 1988))
-         (let* ((theta (/ (- (calendar-astro-from-absolute
-                              (calendar-absolute-from-gregorian
-                               (list 7 1 year)))
-                             (calendar-astro-from-absolute
-                              (calendar-absolute-from-gregorian
-                               '(1 1 1900))))
-                          36525.0))
-                (theta2 (* theta theta))
-                (theta3 (* theta2 theta))
-                (theta4 (* theta2 theta2))
-                (theta5 (* theta3 theta2)))
-           (+ -0.00002
-              (* 0.000297 theta)
-              (* 0.025184 theta2)
-              (* -0.181133 theta3)
-              (* 0.553040 theta4)
-              (* -0.861938 theta5)
-              (* 0.677066 theta3 theta3)
-              (* -0.212591 theta4 theta3))))
-        ((and (<= 1800 year) (< year 1900))
-         (let* ((theta (/ (- (calendar-astro-from-absolute
-                              (calendar-absolute-from-gregorian
-                               (list 7 1 year)))
-                             (calendar-astro-from-absolute
-                              (calendar-absolute-from-gregorian
-                               '(1 1 1900))))
-                          36525.0))
-                (theta2 (* theta theta))
-                (theta3 (* theta2 theta))
-                (theta4 (* theta2 theta2))
-                (theta5 (* theta3 theta2)))
-           (+ -0.000009
-              (* 0.003844 theta)
-              (* 0.083563 theta2)
-              (* 0.865736 theta3)
-              (* 4.867575 theta4)
-              (* 15.845535 theta5)
-              (* 31.332267 theta3 theta3)
-              (* 38.291999 theta4 theta3)
-              (* 28.316289 theta4 theta4)
-              (* 11.636204 theta4 theta5)
-              (* 2.043794 theta5 theta5))))
-        ((and (<= 1620 year) (< year 1800))
-         (let ((x (/ (- year 1600) 10.0)))
-           (/ (+ (* 2.19167 x x) (* -40.675 x) 196.58333) 60.0 60.0 24.0)))
-        (t (let* ((tmp (- (calendar-astro-from-absolute
-                           (calendar-absolute-from-gregorian
-                            (list 1 1 year)))
-                          2382148))
-                  (second (- (/ (* tmp tmp) 41048480.0) 15)))
-             (/ second 60.0 60.0 24.0)))))
-
-(defun solar-sidereal-time (t0)
-  "Sidereal time (in hours) in Greenwich at T0 Julian centuries.
-T0 must correspond to 0 hours UT."
-  (let* ((mean-sid-time (+ 6.6973746
-                           (* 2400.051337 t0)
-                           (* 0.0000258622 t0 t0)
-                           (* -0.0000000017222 t0 t0 t0)))
-         (et (solar-ephemeris-time (list t0 0.0)))
-         (nut-i (solar-ecliptic-coordinates et nil))
-         (nut (nth 3 nut-i))            ; nutation
-         (i (cadr nut-i)))              ; inclination
-    (mod (+ (mod (+ mean-sid-time
-                    (/ (/ (* nut (solar-cosine-degrees i)) 15) 3600)) 24.0)
-            24.0)
-         24.0)))
-
-(defun solar-time-equation (date ut)
-  "Equation of time expressed in hours at Gregorian DATE at Universal time UT."
-  (nth 2 (solar-ecliptic-coordinates (solar-date-to-et date ut) nil)))
-
-(defun solar-date-to-et (date ut)
-  "Ephemeris Time at Gregorian DATE at Universal Time UT (in hours).
-Expressed in Julian centuries of Ephemeris Time."
-  (solar-ephemeris-time (list (solar-julian-ut-centuries date) ut)))
+(defun solar-date-next-longitude (d l)
+  "First time after day D when solar longitude is a multiple of L degrees.
+D is a Julian day number.  L must be an integer divisor of 360.
+The result is for `calendar-location-name', and is in local time
+\(including any daylight saving rules) expressed in astronomical (Julian)
+day numbers.  The values of `calendar-daylight-savings-starts',
+`calendar-daylight-savings-starts-time', `calendar-daylight-savings-ends',
+`calendar-daylight-savings-ends-time', `calendar-daylight-time-offset',
+and `calendar-time-zone' are used to interpret local time."
+  (let* ((long)
+         (start d)
+         (start-long (solar-longitude d))
+         (next (mod (* l (1+ (floor (/ start-long l)))) 360))
+         (end (+ d (* (/ l 360.0) 400)))
+         (end-long (solar-longitude end)))
+    (while                       ; bisection search for nearest minute
+        (< 0.00001 (- end start))
+      ;; start   <= d    < end
+      ;; start-long <= next < end-long when next != 0
+      ;; when next = 0, we look for the discontinuity (start-long is near 360
+      ;;                and end-long is small (less than l).
+      (setq d (/ (+ start end) 2.0)
+            long (solar-longitude d))
+      (if (or (and (not (zerop next)) (< long next))
+              (and (zerop next) (< l long)))
+          (setq start d
+                start-long long)
+        (setq end d
+              end-long long)))
+    (/ (+ start end) 2.0)))
 
 ;;;###autoload
 (defun sunrise-sunset (&optional arg)
@@ -1018,6 +1014,9 @@ solstice.  These formulas are only to be used between 1000 BC and 3000 AD."
                             (* -0.00823 z z z)
                             (* 0.00032 z z z z)))))))
 
+(defvar displayed-month)                ; from generate-calendar
+(defvar displayed-year)
+
 ;;;###holiday-autoload
 (defun solar-equinoxes-solstices ()
   "Local date and time of equinoxes and solstices, if visible in the calendar.
@@ -1036,8 +1035,8 @@ Requires floating point."
            (calendar-time-zone (if calendar-time-zone calendar-time-zone 0))
            (k (1- (/ m 3)))
            (d0 (solar-equinoxes/solstices k y))
-           (d1 (list (car d0) (floor (car (cdr d0))) (car (cdr (cdr d0)))))
-           (h0 (* 24 (- (car (cdr d0)) (floor (car (cdr d0))))))
+           (d1 (list (car d0) (floor (cadr d0)) (nth 2 d0)))
+           (h0 (* 24 (- (cadr d0) (floor (cadr d0)))))
            (adj (dst-adjust-time d1 h0))
            (d (list (caar adj)
                     (+ (car (cdar adj))