fix: correct Jalali calendar year conversion

Complete rewrite of gregorianToJalali and jalaliToGregorian using
proper JDN arithmetic. Removed broken epoch offset (226899 / year 979)
and replaced with jalaliEpochJDN = 1948320 (March 21, 622 CE).

Verified: 2026-06-24 -> Jalali 1405-04-03 (correct)
Nowruz 1405 verified as 2026-03-21

internal/bot/dateutil.go

@@ -59,78 +59,75 @@ func monthLenHijri(year, month int) int {
 	return 29
 }
 
-func gregorianToJalali(gy, gm, gd int) (int, int, int) {
+// JDN for March 21, 622 CE (Jalali epoch: 1 Farvardin 1)
-	gdm := []int{0, 31, 59, 90, 120, 151, 181, 212, 243, 273, 304, 334}
+const jalaliEpochJDN = 1948320
-	gy2 := gy - 1
-	gd2 := gdm[gm-1] + gd
-	if gm > 2 && isGregorianLeap(gy) {
-		gd2++
-	}
-	gd2 += gy2*365 + gy2/4 - gy2/100 + gy2/400
-	gd2 -= 226899
 
-	jy := 979
+func gregorianToJDN(gy, gm, gd int) int {
-	for {
+	a := (14 - gm) / 12
-		jyDays := 365
+	y := gy + 4800 - a
-		if isJalaliLeap(jy) {
+	m := gm + 12*a - 3
-			jyDays = 366
+	return gd + (153*m+2)/5 + 365*y + y/4 - y/100 + y/400 - 32045
 }
-		if gd2 < jyDays {
+
+func jdnToGregorian(jdn int) (int, int, int) {
+	f := jdn + 1401 + ((4*jdn+274277)/146097)*3/4 - 38
+	e := 4*f + 3
+	g := (e % 1461) / 4
+	h := 5*g + 2
+	day := (h%153)/5 + 1
+	month := ((h/153 + 2) % 12) + 1
+	year := e/1461 - 4716 + (14-month)/12
+	return year, month, day
+}
+
+func gregorianToJalali(gy, gm, gd int) (int, int, int) {
+	jdn := gregorianToJDN(gy, gm, gd)
+	days := jdn - jalaliEpochJDN
+	if days < 0 {
+		return 0, 0, 0
+	}
+
+	jy := 1
+	for {
+		yearDays := 365
+		if isJalaliLeap(jy) {
+			yearDays = 366
+		}
+		if days < yearDays {
 			break
 		}
-		gd2 -= jyDays
+		days -= yearDays
 		jy++
 	}
 
 	jm := 1
-	for _, d := range jalaliMonthDays {
+	for mm := 0; mm < 12; mm++ {
-		if gd2 < d {
+		md := monthLenJalali(jy, mm+1)
+		if days < md {
 			break
 		}
-		gd2 -= d
+		days -= md
 		jm++
 	}
-	return jy, jm, gd2 + 1
+	jd := days + 1
+	return jy, jm, jd
 }
 
 func jalaliToGregorian(jy, jm, jd int) (int, int, int) {
-	jy2 := jy - 979
+	days := 0
-	days := jy2 * 365
+	for y := 1; y < jy; y++ {
-	for y := 979; y < jy; y++ {
 		if isJalaliLeap(y) {
-			days++
+			days += 366
+		} else {
+			days += 365
 		}
 	}
-
+	for m := 1; m < jm; m++ {
-	jdm := []int{0, 31, 62, 93, 124, 155, 186, 216, 246, 276, 306, 336}
+		days += monthLenJalali(jy, m)
-	days += jdm[jm-1] + jd - 1
-	days += 226899
-
-	gy := 1
-	for {
-		gyDays := 365
-		if isGregorianLeap(gy) {
-			gyDays = 366
 	}
-		if days < gyDays {
+	days += jd - 1
-			break
+	jdn := jalaliEpochJDN + days
-		}
+	return jdnToGregorian(jdn)
-		days -= gyDays
-		gy++
-	}
-
-	gm := 1
-	for i, d := range gregMonthDays {
-		if gm == 2 && isGregorianLeap(gy) {
-			d = 29
-		}
-		if days < d {
-			break
-		}
-		days -= d
-		gm = i + 2
-	}
-	return gy, gm, days + 1
 }
 
 func hijriToGregorian(hy, hm, hd int) (int, int, int) {
@@ -153,11 +150,7 @@ func hijriToGregorian(hy, hm, hd int) (int, int, int) {
 }
 
 func gregorianToHijri(gy, gm, gd int) (int, int, int) {
-	a := (14 - gm) / 12
+	jdn := gregorianToJDN(gy, gm, gd)
-	y := gy + 4800 - a
-	m := gm + 12*a - 3
-	jdn := gd + (153*m+2)/5 + 365*y + y/4 - y/100 + y/400 - 32045
-
 	days := jdn - 1948440
 
 	hy := 1
@@ -259,7 +252,6 @@ func buildCalendarMonth(cal string, year, month int) calMonth {
 	totalDays = monthLenGreg(year, month)
 
 	dow := dayOfWeekGregorian(year, month, 1)
-	// Convert Sunday=0 to Monday=0 alignment
 	startOffset := (dow + 6) % 7
 
 	var days []calDay