2b:null 2c:["$","title",null,{"children":"Implementing a Proleptic Civil Calendar | Michaël Guitton | Observable"}] 31:[] 2f:{"id":"d1eb5a7baceee915","slug":"implementing-a-proleptic-civil-calendar","title":"Implementing a Proleptic Civil Calendar","thumbnail":"04534ae6db4dc6e3fff0201f20ebdf2765a2fd840d8ce44ee7f6d6de2c2827fb","access_level":"public","create_time":"$D2024-07-24T19:15:01.277Z","update_time":"$D2026-08-11T07:00:09.439Z","view_time":null,"first_public_time":"$D2024-07-24T19:15:01.277Z","fork":false,"stars":1,"starred":false,"owner":{"type":"team","id":"4c1622bb5c37477f","login":"galopin","name":"Michaël Guitton","avatar_url":"https://avatars-next.observableusercontent.com/10e2fe999ac95c8686156fd07e96a686520149a4eef18a95f97795b7a7be1e29","tier":"starter_2024"},"version":84,"publish_version":null,"role":null,"authored":false,"authors":[{"type":"individual","id":"950eb34948878085","login":"galopin","name":"Michaël Guitton","avatar_url":"https://avatars-next.observableusercontent.com/b59822ff41962e9448473fadd4a11819ac725b074ad3868aabf532bade0ac00d","tier":null}],"members":[{"type":"team","id":"4c1622bb5c37477f","login":"galopin","name":"Michaël Guitton","avatar_url":"https://avatars-next.observableusercontent.com/10e2fe999ac95c8686156fd07e96a686520149a4eef18a95f97795b7a7be1e29","tier":"starter_2024","role":"editor"},{"type":"individual","id":"950eb34948878085","login":"galopin","name":"Michaël Guitton","avatar_url":"https://avatars-next.observableusercontent.com/b59822ff41962e9448473fadd4a11819ac725b074ad3868aabf532bade0ac00d","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"subscribed":null,"forks":0,"collection":{"id":"10bf3880c7cb030a","slug":"date-handling","title":"Date Handling","owner":{"id":"4c1622bb5c37477f","login":"galopin","name":"Michaël Guitton"}},"type":"notebook","body":{"title":"Implementing a Proleptic Civil Calendar","cells":[{"id":45,"value":"Object.assign(md`# Implementing a Proleptic Civil Calendar`, {\n style: \"text-wrap: balance;\"\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":44,"value":"The algorithms exposed in this notebook use an idealized calendar, the current Gregorian calendar extended indefinitely in both directions.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":43,"value":"It matches the definition of the proleptic Gregorian calendar in Dershowitz and Reingold’s book Calendrical Calculations, where it’s the base calendar for all computations.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":42,"value":"$${annotate(\n `🦉`,\n `A proleptic calendar is a calendar that is applied to dates before its introduction.`\n)}","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":41,"value":"We will refer to this as the _civil calendar_.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":40,"value":"Zero and negative years are interpreted as prescribed by the **ISO 8601** standard: Year 0 is 1 BC, year -1 is 2 BC, and so on.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":39,"value":"These algorithms assume that March 1 is the first day of the year. This assumption is extremely practical, as it places February 29, a leap day, as the last day of the year, or in fact of the previous year.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":38,"value":"In these algorithms, an era is a 400 year period.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":37,"value":"viewof eras = {\n const width = (({\n keys = data.columns,\n values = Object.values(data[0])\n } = {}) => {\n return keys.reduce(\n (o, k, i) => ({\n ...o,\n [k]:\n floor(\n values[i][i === 0 ? \"toString\" : \"toISOString\"]()\n .split(\"T\", 1)\n .shift().length * (i ? 0.9 : 1)\n ) + \"em\"\n }),\n {}\n );\n })();\n const maxWidth =\n Object.values(width).reduce((acc, v) => acc + parseInt(v, 10), 0) + \"em\";\n const input = Inputs.table(data, {\n align: (({\n keys = data.columns,\n values = Array.from(data.columns, (_) => \"right\")\n } = {}) => {\n return keys.reduce((o, k, i) => ({ ...o, [k]: values[i] }), {});\n })(),\n width,\n maxWidth,\n layout: \"auto\"\n });\n input.querySelector(\"table\").style.minWidth = maxWidth;\n return input;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":36,"value":"As it turns out, the civil calendar exactly repeats itself every 400 years.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":35,"value":"The accuracy of the algorithms under these rules is exact, until overflow occurs.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":34,"value":"This notebook would not exist without the preliminary and founding work of\nHoward Hinnant, a world-class C++ expert.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":33,"value":"fullYear = yearOfEra + era * 400 + (month <= 2)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":32,"value":"month = mp + (mp < 10 ? 3 : -9) // map our internal month number to the civil month number","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":31,"value":"dayOfMonth = dayOfYear - div(offset * mp + 2, 5) + 1","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":30,"value":"diff = datediff(void 0, 0)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":29,"value":"z === div(diff, 1000 * meanSolarDay) // expected output: true","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":28,"value":"z === daysFromCivil(fullYear, month, dayOfMonth) // expected output: true","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":27,"value":"civilFromDays(z)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":26,"value":"---","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":25,"value":"mp = div(5 * dayOfYear + 2, offset) // mp === 0 is March, mp === 11 is February","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":24,"value":"/*!\n * A value of:\n * - 0 corresponds to March 1\n * - 364 corresponds to February 28 of the following (civil) year\n */\ndayOfYear = dayOfEra -\n (365 * yearOfEra + div(yearOfEra, 4) - div(yearOfEra, 100))","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":23,"value":"yearOfEra = div(\n dayOfEra -\n div(dayOfEra, daysPer[\"4Y\"]) +\n div(dayOfEra, daysPer[\"100Y\"]) -\n div(dayOfEra, daysPer[\"400Y\"]),\n 365\n)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":22,"value":"dayOfEra = Z - era * (daysPer[\"400Y\"] + 1)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":21,"value":"era = div(Z >= 0 ? Z : Z - daysPer[\"400Y\"], (daysPer[\"400Y\"] + 1))","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":20,"value":"Z = z + shift // shift the epoch from 1970-01-01 to 0000-03-01","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":19,"value":"---","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":18,"value":"z = div(+new Date(), 1000 * meanSolarDay) // today","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":17,"value":"meanSolarDay = 24 * 60 * 60","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":16,"value":"offset = daysAfterMarch1[4] // number of days between March 1 and August 1","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":47,"value":"origin = ((record) => (record && record[\"start date\"]) || \"0000-03-01\")(\n data.filter((d) => d.era === 0)[0]\n)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":15,"value":"shift = div(datediff(0, origin), 1000 * meanSolarDay)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":14,"value":"daysAfterMarch1 = [31, 61, 92, 122, 153, 184, 214, 245, 275, 306, 337] // number of days after March 1","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":13,"value":"daysPer = ({\n /* number of days in an era */\n \"400Y\": 365 * 400 + 100 - 4,\n /* number of days in the first 100 years of an era */\n \"100Y\": 365 * 100 + 100 / 4 - 1,\n /* number of days in the first 4 years of an era */\n \"4Y\": 365 * 4\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":12,"value":"data = d3.csvParse(\n `era,start date,end date\n-4,-1600-03-01,-1200-02-29\n-3,-1200-03-01,-0800-02-29\n-2,-0800-03-01,-0400-02-29\n-1,-0400-03-01,0000-02-29\n0,0000-03-01,0400-02-29\n1,0400-03-01,0800-02-29\n2,0800-03-01,1200-02-29\n3,1200-03-01,1600-02-29\n4,1600-03-01,2000-02-29\n5,2000-03-01,2400-02-29`,\n (d, _, cols) => {\n const [c1, c2, c3] = cols;\n return {\n [c1]: +d[c1],\n [c2]: date(d[c2]),\n [c3]: date(d[c3])\n };\n }\n)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":11,"value":"/**\n * Returns (year, month, day) triple in civil calendar\n *\n * @typedef {Object} Triple\n * @property {number} year - full year\n * @property {number} month - month [1, 12]\n * @property {number} day - day of month\n *\n * @param {number} z - number of days since 1970-01-01\n * @return {Triple} (year, month, day) triple\n */\nfunction civilFromDays(z) {\n /* thank you, Howard Hinnant! - mg */\n z += shift;\n const e = div(z >= 0 ? z : z - daysPer[\"400Y\"], daysPer[\"400Y\"] + 1);\n const doe = z - e * (daysPer[\"400Y\"] + 1); // [0, 146096]\n const yoe = div(\n doe -\n div(doe, daysPer[\"4Y\"]) +\n div(doe, daysPer[\"100Y\"]) -\n div(doe, daysPer[\"400Y\"]),\n 365\n ); // [0, 399]\n const doy = doe - (365 * yoe + div(yoe, 4) - div(yoe, 100)); // [0, 365]\n const mp = div(5 * doy + 2, offset); // [0, 11]\n const day = doy - div(offset * mp + 2, 5) + 1; // [1, 31]\n const month = mp < 10 ? mp + 3 : mp - 9; // [1, 12]\n const year = yoe + e * 400 + (month <= 2);\n return { year, month, day };\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":10,"value":"/**\n * Returns the number of days since civil 1970-01-01.\n * Negative values indicate days prior to 1970-01-01.\n *\n * (year, month, day) represents a date in the civil (Gregorian) calendar\n *\n * @param {number} year - full year\n * @param {number} month - month [1, 12]\n * @param {number} day - day of month\n * @return {number} number of days since 1970-01-01\n */\nfunction daysFromCivil(year, month, day) {\n /* thank you, Howard Hinnant! - mg */\n year -= month <= 2;\n const e = div(year >= 0 ? year : year - 399, 400);\n const yoe = year - e * 400; // [0, 399]\n const doy =\n div(offset * (month > 2 ? month - 3 : month + 9) + 2, 5) +\n day -\n 1; // [0, 365]\n const doe = yoe * 365 + div(yoe, 4) - div(yoe, 100) + doy; // [0, 146096]\n return e * (daysPer[\"400Y\"] + 1) + doe - shift;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":48,"value":"floor = Math.floor","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":66,"value":"

[Raymond T.] Boute argues that Euclidean division is superior to the other ones in terms of regularity and useful mathematical properties, although floored division, promoted by [Donald] Knuth, is also a good definition. Despite its widespread use, truncated division is shown to be inferior to the other definitions.

— Daan Leijen, Division and Modulus for Computer Scientists

\n\n","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":65,"value":"In floored division, for which the quotient is defined by ${tex`q = \\left \\lfloor \\frac{a}{n} \\right \\rfloor`}, the remainder ${tex`r = a - q \\cdot n`} has the same sign as the divisor ${tex`n`} and is always between `0` and the divisor ${tex`n`} (excluded):","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":64,"value":"{\n const match = /(?[+-]\\d+|0)[\\s\\S]+(?[+-]\\d+|0)/.exec(output);\n yield match\n ? md`${tex`q`} is \\`${match[1]}\\` and ${tex`r`} is \\`${match[2]}\\`.`\n : md`…`;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":63,"value":"viewof output = {\n // verify output of division and modulus\n const format = (x) => (x > 0 ? \"+\" : \"\") + x;\n const separator = \", \";\n const input = Inputs.radio(\n [\n [+8, +3],\n [-8, +3],\n [+8, -3],\n [-8, -3],\n [+1, +2],\n [-1, +2],\n [+1, -2],\n [-1, -2]\n ].map(([a, n]) => [\n [a, n],\n [div(a, n), mod(a, n)]\n ]),\n {\n label: [\"Pick (\", tex`a`, separator, tex`n`, \")\"],\n keyof: ([k]) => k.map(format).join(separator),\n valueof: ([, v]) => v.map(format).join(separator),\n value: \"+2, +2\"\n }\n );\n Object.assign(input.querySelector(\"div\").style, {\n display: \"grid\",\n gridTemplateAreas: '\"X X\"',\n columnGap: \"var(--length3)\"\n });\n yield input;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":62,"value":"div = (a, n) => ((r) => (a - r) / n)(mod(a, n))","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":61,"value":"mod = (a, n) => (a % n) + (sign(a) !== sign(n) ? n : 0)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":60,"value":"sign = Math.sign ||\n ((n) => {\n return n == 0 || isNaN(n) ? +n : n < 0 ? -1 : 1;\n })","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":80,"value":"import { annotate } from \"@galopin/misclib-routines\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":9,"value":"import {\n date,\n datediff\n} from \"@galopin/a-date-object-on-which-you-can-count-on\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W31","stdlib":"1","titling":"auto"}} 30:"$2f:body"