/home/a220/proj/radnelac/src/calendar/roman.rs

Source
// This Source Code Form is subject to the terms of the Mozilla Public
// License, v. 2.0. If a copy of the MPL was not distributed with this
// file, You can obtain one at https://mozilla.org/MPL/2.0/.

use crate::calendar::julian::Julian;
use crate::calendar::julian::JulianMonth;
use crate::calendar::prelude::CommonDate;
use crate::calendar::prelude::HasLeapYears;
use crate::calendar::prelude::Quarter;
use crate::calendar::prelude::ToFromCommonDate;
use crate::common::math::TermNum;
use crate::day_count::BoundedDayCount;
use crate::day_count::CalculatedBounds;
use crate::day_count::Fixed;
use crate::day_count::FromFixed;
use crate::day_count::ToFixed;
use std::cmp::Ordering;
use std::num::NonZero;

#[allow(unused_imports)] //FromPrimitive is needed for derive
use num_traits::FromPrimitive;

//LISTING 3.12 (*Calendrical Calculations: The Ultimate Edition* by Reingold & Dershowitz.)
const YEAR_ROME_FOUNDED_JULIAN: i32 = -753;

/// Represents key events in a Roman month
#[derive(Debug, PartialEq, PartialOrd, Clone, Copy, FromPrimitive, ToPrimitive)]
pub enum RomanMonthlyEvent {
    //LISTING 3.5-3.7 (*Calendrical Calculations: The Ultimate Edition* by Reingold & Dershowitz.)
    Kalends = 1,
    Nones,
    Ides,
}

/// Represents a month in the Roman calendar after the Julian reform
pub type RomanMonth = JulianMonth;

impl RomanMonth {
    pub fn ides_of_month(self) -> u8 {
        //LISTING 3.8 (*Calendrical Calculations: The Ultimate Edition* by Reingold & Dershowitz.)
        match self {
            RomanMonth::July => 15,
            RomanMonth::March => 15,
            RomanMonth::May => 15,
            RomanMonth::October => 15,
            _ => 13,
        }
    }

    pub fn nones_of_month(self) -> u8 {
        //LISTING 3.9 (*Calendrical Calculations: The Ultimate Edition* by Reingold & Dershowitz.)
        self.ides_of_month() - 8
    }
}

/// Represents a date in the Roman calendar after the Julian reform
///
/// ## Introduction
///
/// This struct supports alternative naming schemes for the Julian calendar.
///
/// The Romans referred to days using a countdown towards one of 3 events of the year: the
/// Kalends, the Nones and the Ides.
///
/// ## Epoch
///
/// Most functions for Roman naming use the same Anno Domini / Before Christ (AD/BC) epoch as
/// the Julian calendar, unless stated otherwise.
///
/// The exceptions are functions which convert year numbers between the Anno Domini epoch and
/// the Ab Urbe Condita (AUC) epoch, which corresponds to the legendary date of the founding of
/// Rome.
///
/// The year 1 AUC corresponds to 753 BC.
///
/// ### Year 0
///
/// Year 0 is **not** supported because they are not supported in the Julian calendar.
///
/// ## Further Reading
///
/// + [Wikipedia](https://en.wikipedia.org/wiki/Roman_calendar#Days)
#[derive(Debug, PartialEq, Clone, Copy)]
pub struct Roman {
    year: NonZero<i32>,
    month: RomanMonth,
    event: RomanMonthlyEvent,
    count: NonZero<u8>,
    leap: bool,
}

impl Roman {
    pub fn year(self) -> NonZero<i32> {
        self.year
    }

    pub fn month(self) -> RomanMonth {
        self.month
    }

    pub fn event(self) -> RomanMonthlyEvent {
        self.event
    }

    pub fn count(self) -> NonZero<u8> {
        self.count
    }

    pub fn leap(self) -> bool {
        self.leap
    }

    /// Converts from BC/AD year to AUC year
    pub fn julian_year_from_auc(year: NonZero<i32>) -> NonZero<i32> {
        //LISTING 3.13 (*Calendrical Calculations: The Ultimate Edition* by Reingold & Dershowitz.)
        //Modified to use NonZero
        let y = year.get();
        if y >= 1 && y <= -YEAR_ROME_FOUNDED_JULIAN142 {
            NonZero::new(y + YEAR_ROME_FOUNDED_JULIAN - 1).expect("Checked by if")
        } else {
            NonZero::new(y + YEAR_ROME_FOUNDED_JULIAN).expect("Checked by if")
        }
    }

    /// Converts from AUC year to BC/AD year
    pub fn auc_year_from_julian(year: NonZero<i32>) -> NonZero<i32> {
        //LISTING 3.14 (*Calendrical Calculations: The Ultimate Edition* by Reingold & Dershowitz.)
        //Modified to use NonZero
        let y = year.get();
        if YEAR_ROME_FOUNDED_JULIAN <= y && y <= -1147 {
            NonZero::new(y - YEAR_ROME_FOUNDED_JULIAN + 1).expect("Checked by if")
        } else {
            NonZero::new(y - YEAR_ROME_FOUNDED_JULIAN).expect("Checked by if")
        }
    }
}

impl PartialOrd for Roman {
    fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
        if self == other {
            Some(Ordering::Equal)
        } else if self.year != other.year {
            self.year.partial_cmp(&other.year)
        } else if self.month != other.month {
            self.month.partial_cmp(&other.month)
        } else if self.event != other.event {
            self.event.partial_cmp(&other.event)
        } else if self.count != other.count {
            other.count.partial_cmp(&self.count) //Intentionally reversed, "count" decreases with time
        } else {
            // "the second sixth day before the kalends of March"
            (self.leap as u8).partial_cmp(&(other.leap as u8))
        }
    }
}

impl CalculatedBounds for Roman {}

impl FromFixed for Roman {
    fn from_fixed(date: Fixed) -> Roman {
        //LISTING 3.11 (*Calendrical Calculations: The Ultimate Edition* by Reingold & Dershowitz.)
        let j = Julian::from_fixed(date);
        let j_cdate = j.to_common_date();
        let month = (j_cdate.month as i64).adjusted_remainder(12) as u8;
        let year = j_cdate.year;
        let day = j_cdate.day;
        let month1 = (month as i64 + 1).adjusted_remainder(12) as u8;
        let year1 = if month1 != 1 {
            year
        } else if year != -1 {
            year + 1
        } else {
            1
        };
        let month_r = RomanMonth::from_u8(month).expect("Kept in range by adjusted_remainder");
        let month1_r = RomanMonth::from_u8(month1).expect("Kept in range by adjusted_remainder");
        let kalends1 = Roman {
            year: NonZero::new(year1).expect("From Julian date"),
            month: month1_r,
            event: RomanMonthlyEvent::Kalends,
            count: NonZero::new(1).expect("1 != 0"),
            leap: false,
        }
        .to_fixed()
        .get_day_i();
        if day == 1 {
            Roman {
                year: NonZero::new(year).expect("From Julian date"),
                month: month_r,
                event: RomanMonthlyEvent::Kalends,
                count: NonZero::new(1).expect("1 != 0"),
                leap: false,
            }
        } else if day <= month_r.nones_of_month() {
            Roman {
                year: NonZero::new(year).expect("From Julian date"),
                month: month_r,
                event: RomanMonthlyEvent::Nones,
                count: NonZero::new(month_r.nones_of_month() - day + 1).expect("Checked in if"),
                leap: false,
            }
        } else if day <= month_r.ides_of_month() {
            Roman {
                year: NonZero::new(year).expect("From Julian date"),
                month: month_r,
                event: RomanMonthlyEvent::Ides,
                count: NonZero::new(month_r.ides_of_month() - day + 1).expect("Checked in if"),
                leap: false,
            }
        } else if month_r != RomanMonth::February || !Julian::is_leap(year)85 {
            Roman {
                year: NonZero::new(year1).expect("From Julian date"),
                month: month1_r,
                event: RomanMonthlyEvent::Kalends,
                count: NonZero::new(((kalends1 - date.get_day_i()) + 1) as u8)
                    .expect("kalends1 > date"),
                leap: false,
            }
        } else if day < 25 {
            Roman {
                year: NonZero::new(year).expect("From Julian date"),
                month: RomanMonth::March,
                event: RomanMonthlyEvent::Kalends,
                count: NonZero::new((30 - day) as u8).expect("day < 25 < 30"),
                leap: false,
            }
        } else {
            Roman {
                year: NonZero::new(year).expect("From Julian date"),
                month: RomanMonth::March,
                event: RomanMonthlyEvent::Kalends,
                count: NonZero::new((31 - day) as u8).expect("days in February < 31"),
                leap: day == 25,
            }
        }
    }
}

impl ToFixed for Roman {
    fn to_fixed(self) -> Fixed {
        //LISTING 3.10 (*Calendrical Calculations: The Ultimate Edition* by Reingold & Dershowitz.)
        let jld = match self.event {
            RomanMonthlyEvent::Kalends => 1,
            RomanMonthlyEvent::Nones => self.month.nones_of_month(),
            RomanMonthlyEvent::Ides => self.month.ides_of_month(),
        };
        let jlc = CommonDate::new(self.year.get(), self.month as u8, jld);
        let j = Julian::try_from_common_date(jlc)
            .expect("Month/day in range")
            .to_fixed()
            .get_day_i();
        let c = self.count.get() as i64;
        let do_lp = Julian::is_leap(self.year.get())
            && self.month == RomanMonth::March
            && self.event == RomanMonthlyEvent::Kalends
            && self.count.get() <= 16
            && self.count.get() >= 6;
        let lp0 = if do_lp { 01 } else { 12.31k };
        let lp1 = if self.leap { 10 } else { 0 };
        Fixed::cast_new(j - c + lp0 + lp1)
    }
}

impl Quarter for Roman {
    fn quarter(self) -> NonZero<u8> {
        NonZero::new((((self.month() as u8) - 1) / 3) + 1).expect("m/4 > -1")
    }
}

#[cfg(test)]
mod tests {
    use super::*;
    use crate::calendar::prelude::ToFromCommonDate;
    use proptest::prop_assume;
    use proptest::proptest;

    #[test]
    fn second_sixth_day_before_kalends_of_march() {
        let j24 = Julian::try_from_common_date(CommonDate::new(4, 2, 24)).unwrap();
        let j25 = Julian::try_from_common_date(CommonDate::new(4, 2, 25)).unwrap();
        let f24 = j24.to_fixed();
        let f25 = j25.to_fixed();
        let r24 = Roman::from_fixed(f24);
        let r25 = Roman::from_fixed(f25);
        assert_eq!(r24.year(), r25.year());
        assert_eq!(r24.month(), r25.month());
        assert_eq!(r24.event(), r25.event());
        assert_eq!(r24.count(), r25.count());
        assert!(!r24.leap() && r25.leap());
        assert!(r24 < r25);
    }

    #[test]
    fn ides_of_march() {
        let j = Julian::try_from_common_date(CommonDate::new(-44, 3, 15)).unwrap();
        let f = j.to_fixed();
        let r = Roman::from_fixed(f);
        assert_eq!(r.event, RomanMonthlyEvent::Ides);
        assert_eq!(r.month, RomanMonth::March);
        assert_eq!(r.count.get(), 1);
    }

    proptest! {
        #[test]
        fn auc_roundtrip(t in i16::MIN..i16::MAX) {
            prop_assume!(t != 0);
            let j_0 = NonZero::new(t as i32).unwrap();
            let auc = Roman::auc_year_from_julian(j_0);
            let j_1 = Roman::julian_year_from_auc(auc);
            assert_eq!(j_0, j_1);
            assert!(auc > j_0);
        }
    }
}

Coverage Report

Created: 2025-10-19 21:00

Line	Count	Source
1		// This Source Code Form is subject to the terms of the Mozilla Public
2		// License, v. 2.0. If a copy of the MPL was not distributed with this
3		// file, You can obtain one at https://mozilla.org/MPL/2.0/.
4
5		use crate::calendar::julian::Julian;
6		use crate::calendar::julian::JulianMonth;
7		use crate::calendar::prelude::CommonDate;
8		use crate::calendar::prelude::HasLeapYears;
9		use crate::calendar::prelude::Quarter;
10		use crate::calendar::prelude::ToFromCommonDate;
11		use crate::common::math::TermNum;
12		use crate::day_count::BoundedDayCount;
13		use crate::day_count::CalculatedBounds;
14		use crate::day_count::Fixed;
15		use crate::day_count::FromFixed;
16		use crate::day_count::ToFixed;
17		use std::cmp::Ordering;
18		use std::num::NonZero;
19
20		#[allow(unused_imports)] //FromPrimitive is needed for derive
21		use num_traits::FromPrimitive;
22
23		//LISTING 3.12 (Calendrical Calculations: The Ultimate Edition by Reingold & Dershowitz.)
24		const YEAR_ROME_FOUNDED_JULIAN: i32 = -753;
25
26		/// Represents key events in a Roman month
27		#[derive(Debug, PartialEq, PartialOrd, Clone, Copy, FromPrimitive, ToPrimitive)]
28		pub enum RomanMonthlyEvent {
29		//LISTING 3.5-3.7 (Calendrical Calculations: The Ultimate Edition by Reingold & Dershowitz.)
30		Kalends = 1,
31		Nones,
32		Ides,
33		}
34
35		/// Represents a month in the Roman calendar after the Julian reform
36		pub type RomanMonth = JulianMonth;
37
38		impl RomanMonth {
39	4.63k	pub fn ides_of_month(self) -> u8 {
40		//LISTING 3.8 (Calendrical Calculations: The Ultimate Edition by Reingold & Dershowitz.)
41	4.63k	match self {
42	345	RomanMonth::July => 15,
43	327	RomanMonth::March => 15,
44	375	RomanMonth::May => 15,
45	439	RomanMonth::October => 15,
46	3.15k	_ => 13,
47		}
48	4.63k	}
49
50	2.30k	pub fn nones_of_month(self) -> u8 {
51		//LISTING 3.9 (Calendrical Calculations: The Ultimate Edition by Reingold & Dershowitz.)
52	2.30k	self.ides_of_month() - 8
53	2.30k	}
54		}
55
56		/// Represents a date in the Roman calendar after the Julian reform
57		///
58		/// ## Introduction
59		///
60		/// This struct supports alternative naming schemes for the Julian calendar.
61		///
62		/// The Romans referred to days using a countdown towards one of 3 events of the year: the
63		/// Kalends, the Nones and the Ides.
64		///
65		/// ## Epoch
66		///
67		/// Most functions for Roman naming use the same Anno Domini / Before Christ (AD/BC) epoch as
68		/// the Julian calendar, unless stated otherwise.
69		///
70		/// The exceptions are functions which convert year numbers between the Anno Domini epoch and
71		/// the Ab Urbe Condita (AUC) epoch, which corresponds to the legendary date of the founding of
72		/// Rome.
73		///
74		/// The year 1 AUC corresponds to 753 BC.
75		///
76		/// ### Year 0
77		///
78		/// Year 0 is not supported because they are not supported in the Julian calendar.
79		///
80		/// ## Further Reading
81		///
82		/// + [Wikipedia](https://en.wikipedia.org/wiki/Roman_calendar#Days)
83		#[derive(Debug, PartialEq, Clone, Copy)]
84		pub struct Roman {
85		year: NonZero<i32>,
86		month: RomanMonth,
87		event: RomanMonthlyEvent,
88		count: NonZero<u8>,
89		leap: bool,
90		}
91
92		impl Roman {
93	7	pub fn year(self) -> NonZero<i32> {
94	7	self.year
95	7	}
96
97	519	pub fn month(self) -> RomanMonth {
98	519	self.month
99	519	}
100
101	7	pub fn event(self) -> RomanMonthlyEvent {
102	7	self.event
103	7	}
104
105	13	pub fn count(self) -> NonZero<u8> {
106	13	self.count
107	13	}
108
109	6	pub fn leap(self) -> bool {
110	6	self.leap
111	6	}
112
113		/// Converts from BC/AD year to AUC year
114	256	pub fn julian_year_from_auc(year: NonZero<i32>) -> NonZero<i32> {
115		//LISTING 3.13 (Calendrical Calculations: The Ultimate Edition by Reingold & Dershowitz.)
116		//Modified to use NonZero
117	256	let y = year.get();
118	256	if y >= 1 && y <= -YEAR_ROME_FOUNDED_JULIAN142 {
119	4	NonZero::new(y + YEAR_ROME_FOUNDED_JULIAN - 1).expect("Checked by if")
120		} else {
121	252	NonZero::new(y + YEAR_ROME_FOUNDED_JULIAN).expect("Checked by if")
122		}
123	256	}
124
125		/// Converts from AUC year to BC/AD year
126	261	pub fn auc_year_from_julian(year: NonZero<i32>) -> NonZero<i32> {
127		//LISTING 3.14 (Calendrical Calculations: The Ultimate Edition by Reingold & Dershowitz.)
128		//Modified to use NonZero
129	261	let y = year.get();
130	261	if YEAR_ROME_FOUNDED_JULIAN <= y && y <= -1147 {
131	7	NonZero::new(y - YEAR_ROME_FOUNDED_JULIAN + 1).expect("Checked by if")
132		} else {
133	254	NonZero::new(y - YEAR_ROME_FOUNDED_JULIAN).expect("Checked by if")
134		}
135	261	}
136		}
137
138		impl PartialOrd for Roman {
139	2.05k	fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
140	2.05k	if self == other {
141	0	Some(Ordering::Equal)
142	2.05k	} else if self.year != other.year {
143	1.26k	self.year.partial_cmp(&other.year)
144	785	} else if self.month != other.month {
145	668	self.month.partial_cmp(&other.month)
146	117	} else if self.event != other.event {
147	60	self.event.partial_cmp(&other.event)
148	57	} else if self.count != other.count {
149	56	other.count.partial_cmp(&self.count) //Intentionally reversed, "count" decreases with time
150		} else {
151		// "the second sixth day before the kalends of March"
152	1	(self.leap as u8).partial_cmp(&(other.leap as u8))
153		}
154	2.05k	}
155		}
156
157		impl CalculatedBounds for Roman {}
158
159		impl FromFixed for Roman {
160	2.06k	fn from_fixed(date: Fixed) -> Roman {
161		//LISTING 3.11 (Calendrical Calculations: The Ultimate Edition by Reingold & Dershowitz.)
162	2.06k	let j = Julian::from_fixed(date);
163	2.06k	let j_cdate = j.to_common_date();
164	2.06k	let month = (j_cdate.month as i64).adjusted_remainder(12) as u8;
165	2.06k	let year = j_cdate.year;
166	2.06k	let day = j_cdate.day;
167	2.06k	let month1 = (month as i64 + 1).adjusted_remainder(12) as u8;
168	2.06k	let year1 = if month1 != 1 {
169	1.88k	year
170	175	} else if year != -1 {
171	175	year + 1
172		} else {
173	0	1
174		};
175	2.06k	let month_r = RomanMonth::from_u8(month).expect("Kept in range by adjusted_remainder");
176	2.06k	let month1_r = RomanMonth::from_u8(month1).expect("Kept in range by adjusted_remainder");
177	2.06k	let kalends1 = Roman {
178	2.06k	year: NonZero::new(year1).expect("From Julian date"),
179	2.06k	month: month1_r,
180	2.06k	event: RomanMonthlyEvent::Kalends,
181	2.06k	count: NonZero::new(1).expect("1 != 0"),
182	2.06k	leap: false,
183	2.06k	}
184	2.06k	.to_fixed()
185	2.06k	.get_day_i();
186	2.06k	if day == 1 {
187	81	Roman {
188	81	year: NonZero::new(year).expect("From Julian date"),
189	81	month: month_r,
190	81	event: RomanMonthlyEvent::Kalends,
191	81	count: NonZero::new(1).expect("1 != 0"),
192	81	leap: false,
193	81	}
194	1.98k	} else if day <= month_r.nones_of_month() {
195	288	Roman {
196	288	year: NonZero::new(year).expect("From Julian date"),
197	288	month: month_r,
198	288	event: RomanMonthlyEvent::Nones,
199	288	count: NonZero::new(month_r.nones_of_month() - day + 1).expect("Checked in if"),
200	288	leap: false,
201	288	}
202	1.69k	} else if day <= month_r.ides_of_month() {
203	565	Roman {
204	565	year: NonZero::new(year).expect("From Julian date"),
205	565	month: month_r,
206	565	event: RomanMonthlyEvent::Ides,
207	565	count: NonZero::new(month_r.ides_of_month() - day + 1).expect("Checked in if"),
208	565	leap: false,
209	565	}
210	1.12k	} else if month_r != RomanMonth::February \|\| !Julian::is_leap(year)85 {
211	1.10k	Roman {
212	1.10k	year: NonZero::new(year1).expect("From Julian date"),
213	1.10k	month: month1_r,
214	1.10k	event: RomanMonthlyEvent::Kalends,
215	1.10k	count: NonZero::new(((kalends1 - date.get_day_i()) + 1) as u8)
216	1.10k	.expect("kalends1 > date"),
217	1.10k	leap: false,
218	1.10k	}
219	19	} else if day < 25 {
220	15	Roman {
221	15	year: NonZero::new(year).expect("From Julian date"),
222	15	month: RomanMonth::March,
223	15	event: RomanMonthlyEvent::Kalends,
224	15	count: NonZero::new((30 - day) as u8).expect("day < 25 < 30"),
225	15	leap: false,
226	15	}
227		} else {
228	4	Roman {
229	4	year: NonZero::new(year).expect("From Julian date"),
230	4	month: RomanMonth::March,
231	4	event: RomanMonthlyEvent::Kalends,
232	4	count: NonZero::new((31 - day) as u8).expect("days in February < 31"),
233	4	leap: day == 25,
234	4	}
235		}
236	2.06k	}
237		}
238
239		impl ToFixed for Roman {
240	2.31k	fn to_fixed(self) -> Fixed {
241		//LISTING 3.10 (Calendrical Calculations: The Ultimate Edition by Reingold & Dershowitz.)
242	2.31k	let jld = match self.event {
243	2.20k	RomanMonthlyEvent::Kalends => 1,
244	36	RomanMonthlyEvent::Nones => self.month.nones_of_month(),
245	74	RomanMonthlyEvent::Ides => self.month.ides_of_month(),
246		};
247	2.31k	let jlc = CommonDate::new(self.year.get(), self.month as u8, jld);
248	2.31k	let j = Julian::try_from_common_date(jlc)
249	2.31k	.expect("Month/day in range")
250	2.31k	.to_fixed()
251	2.31k	.get_day_i();
252	2.31k	let c = self.count.get() as i64;
253	2.31k	let do_lp = Julian::is_leap(self.year.get())
254	585	&& self.month == RomanMonth::March
255	31	&& self.event == RomanMonthlyEvent::Kalends
256	31	&& self.count.get() <= 16
257	31	&& self.count.get() >= 6;
258	2.31k	let lp0 = if do_lp { 01 } else { 12.31k };
259	2.31k	let lp1 = if self.leap { 10 } else { 0 };
260	2.31k	Fixed::cast_new(j - c + lp0 + lp1)
261	2.31k	}
262		}
263
264		impl Quarter for Roman {
265	512	fn quarter(self) -> NonZero<u8> {
266	512	NonZero::new((((self.month() as u8) - 1) / 3) + 1).expect("m/4 > -1")
267	512	}
268		}
269
270		#[cfg(test)]
271		mod tests {
272		use super::*;
273		use crate::calendar::prelude::ToFromCommonDate;
274		use proptest::prop_assume;
275		use proptest::proptest;
276
277		#[test]
278	1	fn second_sixth_day_before_kalends_of_march() {
279	1	let j24 = Julian::try_from_common_date(CommonDate::new(4, 2, 24)).unwrap();
280	1	let j25 = Julian::try_from_common_date(CommonDate::new(4, 2, 25)).unwrap();
281	1	let f24 = j24.to_fixed();
282	1	let f25 = j25.to_fixed();
283	1	let r24 = Roman::from_fixed(f24);
284	1	let r25 = Roman::from_fixed(f25);
285	1	assert_eq!(r24.year(), r25.year());
286	1	assert_eq!(r24.month(), r25.month());
287	1	assert_eq!(r24.event(), r25.event());
288	1	assert_eq!(r24.count(), r25.count());
289	1	assert!(!r24.leap() && r25.leap());
290	1	assert!(r24 < r25);
291	1	}
292
293		#[test]
294	1	fn ides_of_march() {
295	1	let j = Julian::try_from_common_date(CommonDate::new(-44, 3, 15)).unwrap();
296	1	let f = j.to_fixed();
297	1	let r = Roman::from_fixed(f);
298	1	assert_eq!(r.event, RomanMonthlyEvent::Ides);
299	1	assert_eq!(r.month, RomanMonth::March);
300	1	assert_eq!(r.count.get(), 1);
301	1	}
302
303		proptest! {
304		#[test]
305		fn auc_roundtrip(t in i16::MIN..i16::MAX) {
306		prop_assume!(t != 0);
307		let j_0 = NonZero::new(t as i32).unwrap();
308		let auc = Roman::auc_year_from_julian(j_0);
309		let j_1 = Roman::julian_year_from_auc(auc);
310		assert_eq!(j_0, j_1);
311		assert!(auc > j_0);
312		}
313		}
314		}