sankhya

sankhya (Sanskrit: सांख्य — enumeration/analysis) is an ancient mathematical systems, historical calendar, and archaeoastronomy library for the AGNOS project.

Faithful implementations of computational traditions from eight civilizations, 10+ calendar systems, and archaeoastronomy tools — with cross-civilizational epoch correlation. Every algorithm cites its primary source. No other library in any language covers this scope.

Modules

Module	Civilization	Era	Highlights
`mayan`	Maya	2000 BCE+	Vigesimal (base-20), Long Count calendar, Tzolkin, Haab, Venus tables, Calendar Round search
`babylonian`	Babylon	2000–300 BCE	Sexagesimal (base-60), Saros cycle, Plimpton 322 triples, Heron's sqrt, lunar calendar, cuneiform display
`egyptian`	Egypt	2000–1000 BCE	Unit fractions (Rhind Papyrus), doubling multiplication, stellar decans, Sothic cycle, hieroglyphic display
`vedic`	India	800 BCE+	Nikhilam multiplication, Sulba Sutra geometry, Katapayadi, Meru Prastara, Devanagari display
`chinese`	China	500 BCE+	Rod numerals, Chinese Remainder Theorem, magic squares, Sexagenary 60-year cycle, Unicode rod display
`greek`	Greece	600 BCE–300 CE	Golden ratio, Sieve of Eratosthenes, Euclidean GCD, Archimedes' pi, Antikythera, isopsephy
`roman`	Rome	500 BCE+	Roman numeral conversion (I–MMMCMXCIX), canonical validation, arithmetic
`islamic`	Islamic Golden Age	750–1258 CE	Al-Khwarizmi algebra, Khayyam cubics, completion of the square, Hijri calendar
`gregorian`	Global	1582 CE+	Proleptic Gregorian calendar, JDN conversion, leap years
`coptic`	Egypt/Ethiopia	284 CE+	13-month Alexandrian calendar, Anno Martyrum
`persian`	Iran	622 CE+	Solar Hijri (Jalaali), 2820-year leap cycle, Nowruz
`hebrew`	Israel	3761 BCE+	Lunisolar, Metonic cycle, molad, dehiyyot, 6 year types
`aztec`	Mesoamerica	1200–1521 CE	Tonalpohualli (260-day), Xiuhpohualli (365-day), Calendar Round
`epoch`	Cross-civilizational	—	Precession, precessional ages, Seven Sages, cycle alignment, unified `convert()` API
`astro`	Archaeoastronomy	—	Coordinate systems, star catalog, precession, heliacal rising, monument alignment

Quick Start

use sankhya::mayan::LongCount;
use sankhya::babylonian;
use sankhya::greek;
use sankhya::roman;

// Convert days to Mayan Long Count
let lc = LongCount::from_days(1_872_000).unwrap(); // 13.0.0.0.0 (Dec 21, 2012)
assert_eq!(lc.baktun, 13);

// Babylonian square root (Heron's method, from YBC 7289 tablet)
let sqrt2 = babylonian::babylonian_sqrt(2.0, 10).unwrap();
assert!((sqrt2 - std::f64::consts::SQRT_2).abs() < 1e-15);

// Sieve of Eratosthenes
let primes = greek::sieve(100);
assert_eq!(primes.len(), 25);

// Roman numerals
assert_eq!(roman::to_roman_str(1776).unwrap(), "MDCCLXXVI");
assert_eq!(roman::from_roman("MCMXCIX").unwrap(), 1999);

Calendar Conversion

use sankhya::epoch::{CalendarDate, convert};
use sankhya::gregorian::{GregorianDate, GregorianMonth};

// Convert any date to every calendar system sankhya knows
let date = GregorianDate { year: 2025, month: GregorianMonth::April, day: 1 };
let all = convert(&CalendarDate::Gregorian(date)).unwrap();

println!("Hebrew: {}", all.hebrew);       // 3 Nisan 5785 AM
println!("Persian: {}", all.persian);     // 12 Farvardin 1404 AP
println!("Coptic: {}", all.coptic);       // 23 Paremhat 1741 AM
println!("Aztec: {}", all.aztec_tonalpohualli); // Tonalpohualli date

Archaeoastronomy

use sankhya::astro;

// Was Stonehenge aligned to the summer solstice?
let results = astro::monument_alignment(51.18, 51.0, 2_451_545.0, 5.0);
// Returns: SummerSolsticeSunrise match at ~50° azimuth

// Where was Thuban (the pyramid builders' pole star) in 2800 BCE?
let pos = astro::star_position_at(astro::StarName::Thuban, 2_451_545.0 - 4800.0 * 365.25);
// Returns: Dec > 85° (near the celestial pole)

Features

Feature	Default	Description
`avatara`	off	Saptarishi archetype profiles on `MultiCalendarDate` via avatara divine engine
`itihas`	off	Historical context: eras, civilizations, and events on `MultiCalendarDate`
`varna`	off	Script rendering: cuneiform, hieroglyphic, Devanagari, Greek alphabetic, CJK rod numerals
`logging`	off	Structured tracing via `tracing-subscriber`

Building

cargo build
cargo test --all-features
make check   # fmt + clippy + test + audit
make bench   # criterion benchmarks with history tracking

Requirements

Rust 1.89+ (MSRV)
Dependencies: hisab, serde, thiserror, tracing
Optional: avatara (archetype profiles), itihas (historical context), varna (script rendering)

License

GPL-3.0-only. See LICENSE.

sankhya 2.0.0