calendrical_calculations/
gregorian.rs

1// This file is part of ICU4X.
2//
3// The contents of this file implement algorithms from Calendrical Calculations
4// by Reingold & Dershowitz, Cambridge University Press, 4th edition (2018),
5// which have been released as Lisp code at <https://github.com/EdReingold/calendar-code2/>
6// under the Apache-2.0 license. Accordingly, this file is released under
7// the Apache License, Version 2.0 which can be found at the calendrical_calculations
8// package root or at http://www.apache.org/licenses/LICENSE-2.0.
9
10use crate::helpers::{i64_to_i32, k_day_after, I32CastError};
11use crate::rata_die::RataDie;
12
13// The Gregorian epoch is equivalent to first day in fixed day measurement
14const EPOCH: RataDie = RataDie::new(1);
15
16const DAYS_IN_YEAR: i64 = 365;
17
18// One leap year every 4 years
19const DAYS_IN_4_YEAR_CYCLE: i64 = DAYS_IN_YEAR * 4 + 1;
20
21// No leap year every 100 years
22const DAYS_IN_100_YEAR_CYCLE: i64 = 25 * DAYS_IN_4_YEAR_CYCLE - 1;
23
24// One extra leap year every 400 years
25/// The number of days in the 400 year cycle.
26pub const DAYS_IN_400_YEAR_CYCLE: i64 = 4 * DAYS_IN_100_YEAR_CYCLE + 1;
27
28/// Whether or not `year` is a leap year
29///
30/// Inspired by Neri-Schneider <https://www.youtube.com/watch?v=J9KijLyP-yg&t=1239s>
31pub const fn is_leap_year(year: i32) -> bool {
32    // This is branch-free, as it compiles to a conditional move
33    if year % 25 != 0 {
34        year % 4 == 0
35    } else {
36        year % 16 == 0
37    }
38}
39
40// Fixed is day count representation of calendars starting from Jan 1st of year 1.
41// The fixed calculations algorithms are from the Calendrical Calculations book.
42//
43/// Lisp code reference: <https://github.com/EdReingold/calendar-code2/blob/1ee51ecfaae6f856b0d7de3e36e9042100b4f424/calendar.l#L1167-L1189>
44pub const fn fixed_from_gregorian(year: i32, month: u8, day: u8) -> RataDie {
45    day_before_year(year)
46        .add(days_before_month(year, month) as i64)
47        .add(day as i64)
48}
49
50/// The number of days in this year before this month starts
51///
52/// Inspired by Neri-Schneider <https://onlinelibrary.wiley.com/doi/10.1002/spe.3172>
53pub const fn days_before_month(year: i32, month: u8) -> u16 {
54    if month < 3 {
55        // This compiles to a conditional move, so there's only one branch in this function
56        if month == 1 {
57            0
58        } else {
59            31
60        }
61    } else {
62        31 + 28 + is_leap_year(year) as u16 + ((979 * (month as u32) - 2919) >> 5) as u16
63    }
64}
65
66/// Lisp code reference: <https://github.com/EdReingold/calendar-code2/blob/1ee51ecfaae6f856b0d7de3e36e9042100b4f424/calendar.l#L1191-L1217>
67pub const fn year_from_fixed(date: RataDie) -> Result<i32, I32CastError> {
68    // Shouldn't overflow because it's not possbile to construct extreme values of RataDie
69    let date = date.since(EPOCH);
70
71    let (n_400, date) = (
72        date.div_euclid(DAYS_IN_400_YEAR_CYCLE),
73        date.rem_euclid(DAYS_IN_400_YEAR_CYCLE),
74    );
75
76    let (n_100, date) = (date / DAYS_IN_100_YEAR_CYCLE, date % DAYS_IN_100_YEAR_CYCLE);
77
78    let (n_4, date) = (date / DAYS_IN_4_YEAR_CYCLE, date % DAYS_IN_4_YEAR_CYCLE);
79
80    let n_1 = date / DAYS_IN_YEAR;
81
82    let year = 400 * n_400 + 100 * n_100 + 4 * n_4 + n_1 + (n_100 != 4 && n_1 != 4) as i64;
83
84    i64_to_i32(year)
85}
86
87/// Calculates the day before Jan 1 of `year`.
88pub const fn day_before_year(year: i32) -> RataDie {
89    let prev_year = (year as i64) - 1;
90    // Calculate days per year
91    let mut fixed: i64 = DAYS_IN_YEAR * prev_year;
92    // Adjust for leap year logic. We can avoid the branch of div_euclid by making prev_year positive:
93    // YEAR_SHIFT is larger (in magnitude) than any prev_year, and, being divisible by 400,
94    // distributes correctly over the calculation on the next line.
95    const YEAR_SHIFT: i64 = (-(i32::MIN as i64 - 1) / 400 + 1) * 400;
96    fixed += (prev_year + YEAR_SHIFT) / 4 - (prev_year + YEAR_SHIFT) / 100
97        + (prev_year + YEAR_SHIFT) / 400
98        - const { YEAR_SHIFT / 4 - YEAR_SHIFT / 100 + YEAR_SHIFT / 400 };
99    RataDie::new(fixed)
100}
101
102/// Calculates the month/day from the 1-based day of the year
103pub fn year_day(year: i32, day_of_year: u16) -> (u8, u8) {
104    // Calculates the prior days of the year, then applies a correction based on leap year conditions for the correct ISO date conversion.
105    let correction = if day_of_year < 31 + 28 + is_leap_year(year) as u16 {
106        -1
107    } else {
108        (!is_leap_year(year)) as i32
109    };
110    let month = ((12 * (day_of_year as i32 + correction) + 373) / 367) as u8; // in 1..12 < u8::MAX
111    let day = (day_of_year - days_before_month(year, month)) as u8; // <= days_in_month < u8::MAX
112    (month, day)
113}
114
115/// Lisp code reference: <https://github.com/EdReingold/calendar-code2/blob/1ee51ecfaae6f856b0d7de3e36e9042100b4f424/calendar.l#L1525-L1540>
116pub fn gregorian_from_fixed(date: RataDie) -> Result<(i32, u8, u8), I32CastError> {
117    let year = year_from_fixed(date)?;
118    let day_of_year = date - day_before_year(year);
119    let (month, day) = year_day(year, day_of_year as u16);
120    Ok((year, month, day))
121}
122
123/// Calculates the date of Easter in the given year
124pub fn easter(year: i32) -> RataDie {
125    let century = (year / 100) + 1;
126    let shifted_epact =
127        (14 + 11 * year.rem_euclid(19) - century * 3 / 4 + (5 + 8 * century) / 25).rem_euclid(30);
128    let adjusted_epact = shifted_epact
129        + (shifted_epact == 0 || (shifted_epact == 1 && 10 < year.rem_euclid(19))) as i32;
130    let paschal_moon = fixed_from_gregorian(year, 4, 19) - adjusted_epact as i64;
131
132    k_day_after(0, paschal_moon)
133}
134
135#[test]
136fn test_easter() {
137    // https://en.wikipedia.org/wiki/List_of_dates_for_Easter
138    for (y, m, d) in [
139        (2021, 4, 4),
140        (2022, 4, 17),
141        (2023, 4, 9),
142        (2024, 3, 31),
143        (2025, 4, 20),
144        (2026, 4, 5),
145        (2027, 3, 28),
146        (2028, 4, 16),
147        (2029, 4, 1),
148    ] {
149        assert_eq!(easter(y), fixed_from_gregorian(y, m, d));
150    }
151}
calendrical_calculations/gregorian.rs

calendrical_calculations/
gregorian.rs
