2b:null 2c:["$","title",null,{"children":"Calendrical Calculations Foundation | Enrico Spinielli | Observable"}] 31:[] 2f:{"id":"64b895b98c376699","slug":"calcal-foundation","title":"Calendrical Calculations Foundation","thumbnail":"08cd324fb8d037d8cfd0a3256a64c6b160d008b76ebbc4fef43bcaac40308d63","access_level":"public","create_time":"$D2021-01-02T13:44:31.264Z","update_time":"$D2021-01-10T15:51:55.344Z","view_time":null,"first_public_time":"$D2021-01-08T14:46:50.422Z","fork":true,"stars":0,"starred":false,"owner":{"type":"team","id":"7df7767074068af4","login":"espinielli","name":"Enrico Spinielli","avatar_url":"https://avatars-next.observableusercontent.com/2bf5259d0c49a57cec6acc725062bdc41374a518de8772a2a051315f6be64567","tier":"starter_2024"},"version":1265,"publish_version":1265,"role":null,"authored":false,"authors":[{"type":"individual","id":"c2f17e4031105178","login":"espinielli","name":"Enrico Spinielli","avatar_url":"https://avatars-next.observableusercontent.com/2bf5259d0c49a57cec6acc725062bdc41374a518de8772a2a051315f6be64567","tier":null}],"members":[{"type":"individual","id":"c2f17e4031105178","login":"espinielli","name":"Enrico Spinielli","avatar_url":"https://avatars-next.observableusercontent.com/2bf5259d0c49a57cec6acc725062bdc41374a518de8772a2a051315f6be64567","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"subscribed":null,"forks":0,"collection":{"id":"7b8e3cfdf35afbc5","slug":"calendrical-calculations","title":"Calendrical Calculations","owner":{"id":"7df7767074068af4","login":"espinielli","name":"Enrico Spinielli"}},"type":"notebook","body":{"title":"Calendrical Calculations Foundation","cells":[{"id":0,"value":"md`# Calendrical Calculations Foundation`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1099,"value":"credits = md`The functions defined/used in this notebook are derived from [PyCalCal](https://github.com/espinielli/pycalcal), the Python implementation of the (Common Lisp) [CALENDRICA 3.0](https://github.com/espinielli/pycalcal/blob/master/calendrica-3.0.cl) as described in \n\n> Nachum Dershowitz, Edward M. Reingold \"[*Calendrical Calculations*](http://www.cs.tau.ac.il/~nachum/calendar-book/third-edition/)\"\n> Cambridge University Press; 3rd edition (December 10, 2007)\n> Paperback; ISBN-13: 9780521702386\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1104,"value":"md`These function are imported in other calendars when needed.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":529,"value":"md`## Julian Day Numbers`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":536,"value":"function moment_from_jd(jd) {\n // \"\"\"Return the moment corresponding to the Julian day number ’jd’.\"\"\"\n return jd + JD_EPOCH;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":540,"value":"function jd_from_moment(tee) {\n // \"\"\"Return the Julian day number corresponding to moment ’tee’.\"\"\"\n return tee - JD_EPOCH;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":543,"value":"function fixed_from_jd(jd) {\n // \"\"\"Return the fixed date corresponding to Julian day number ’jd’.\"\"\"\n return ifloor(moment_from_jd(jd));\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":546,"value":"function jd_from_fixed(date) {\n // \"\"\"Return the Julian day number corresponding to fixed date ’rd’.\"\"\"\n return jd_from_moment(date);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":552,"value":"function fixed_from_mjd(mjd) {\n // \"\"\"Return the fixed date corresponding to modified Julian day ’mjd’.\"\"\"\n return mjd + MJD_EPOCH;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":555,"value":"function mjd_from_fixed(date) {\n // \"\"\"Return the modified Julian day corresponding to fixed date ’rd’.\"\"\"\n return date - MJD_EPOCH;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":532,"value":"JD_EPOCH = rd(math.BigNumber(-1721424.5))","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":549,"value":"MJD_EPOCH = rd(678576)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":396,"value":"md`## Basic Calendar Functions`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":491,"value":"function list_range(ell, range) {\n // \"\"\"Return those moments in list ell that occur in range ’range’.\"\"\"\n return ell.filter(x => is_in_range(x, range));\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":493,"value":"function is_in_range(tee, range) {\n // \"\"\"Return True if moment ’tee’ falls within range ’range’,\n // False otherwise.\"\"\"\n return start(range) <= tee && tee <= end(range);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":495,"value":"\n\n\n\nfunction interval(t0, t1) {\n // \"\"\"Return the range data structure.\"\"\"\n return [t0, t1];\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":498,"value":"function start(range) {\n // \"\"\"Return the start of range ’range’.\"\"\"\n return range[0];\n} ","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":501,"value":"function end(range) {\n // \"\"\"Return the end of range ’range’.\"\"\"\n return range[1];\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":488,"value":"function angle_from_degrees(alpha) {\n // \"\"\"Return an angle in degrees:minutes:seconds from angle,\n // ’alpha’ in degrees.\"\"\"\n const d = ifloor(alpha);\n const m = ifloor(60 * mod(alpha, 1));\n const s = mod(alpha * 60 * 60, 60);\n return degrees_minutes_seconds(d, m, s);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":480,"value":"function degrees_minutes_seconds(d, m, s) {\n // \"\"\"Return the angular data structure.\"\"\"\n return [d, m, s];\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":473,"value":"function time_from_clock(hms) {\n // \"\"\"Return time of day from clock time ’hms’.\"\"\"\n const h = hour(hms);\n const m = minute(hms);\n const s = seconds(hms);\n return (1 / 24.0) * (h + (m + s / 60.0) / 60.0);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":469,"value":"function clock_from_moment(tee) {\n // \"\"\"Return clock time hour:minute:second from moment ’tee’.\"\"\"\n const time = time_from_moment(tee);\n const hour = ifloor(time * 24);\n const minute = ifloor(mod(time * 24 * 60, 60));\n const second = mod(time * 24 * 60 * 60, 60);\n return time_of_day(hour, minute, second);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":466,"value":"function time_from_moment(tee) {\n // \"\"\"Return time from moment ’tee’.\"\"\"\n return mod(tee, 1);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":463,"value":"function fixed_from_moment(tee) {\n // \"\"\"Return fixed date from moment ’tee’.\"\"\"\n return ifloor(tee);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":456,"value":"function seconds(clock) {\n // \"\"\"Return the seconds of clock time ’clock’.\"\"\"\n return clock[2];\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":453,"value":"function minute(clock) {\n // \"\"\"Return the minutes of clock time ’clock’.\"\"\"\n return clock[1];\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":450,"value":"function hour(clock) {\n // \"\"\"Return the hour of clock time ’clock’.\"\"\"\n return clock[0];\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":447,"value":"function time_of_day(hour, minute, second) {\n // \"\"\"Return the time of day data structure.\"\"\"\n return [hour, minute, second];\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":443,"value":"function standard_year(date) {\n // \"\"\"Return the year of date ’date’.\"\"\"\n return date[0];\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":440,"value":"function standard_day(date) {\n // \"\"\"Return the day of date ’date’.\"\"\"\n return date[2];\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":437,"value":"function standard_month(date) {\n // \"\"\"Return the month of date ’date’.\"\"\"\n return date[1];\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":434,"value":"function day_of_week_from_fixed(date) {\n // \"\"\"Return day of the week from a fixed date ’date’.\"\"\"\n return mod(date - rd(0) - SUNDAY, 7);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":423,"value":"SUNDAY = 0","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":406,"value":"MONDAY = 1","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":409,"value":"TUESDAY = 2","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":413,"value":"WEDNESDAY = 3","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":416,"value":"THURSDAY = 4","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":419,"value":"FRIDAY = 5","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":422,"value":"SATURDAY = SUNDAY + 6","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":848,"value":"DAYS_OF_WEEK_NAMES = {\n let dn = [];\n dn[SUNDAY] = \"Sunday\";\n dn[MONDAY] = \"Monday\";\n dn[TUESDAY] = \"Tuesday\";\n dn[WEDNESDAY] = \"Wednesday\";\n dn[THURSDAY] = \"Thursday\";\n dn[FRIDAY] = \"Friday\";\n dn[SATURDAY] = \"Saturday\";\n return dn;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":403,"value":"function rd(tee) {\n // \"\"\"Return rata diem (number of days since epoch) of moment in time, tee.\"\"\"\n return tee - epoch();\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":400,"value":"function epoch() {\n // \"\"\"Epoch definition. For Rata Diem, R.D., it is 0 (but any other reference\n // would do.)\"\"\"\n return 0;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":5,"value":"md`## Basic Functions and Constants`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":375,"value":"function poly(x, a) {\n // \"\"\"Calculate polynomial with coefficients ’a’ at point x.\n // The polynomial is a[0] + a[1] * x + a[2] * x^2 + ...a[n-1]x^(n-1)\n // the result is\n // a[0] + x(a[1] + x(a[2] +...+ x(a[n-1])...)\"\"\"\n\n // This implementation is also known as Horner’s Rule.\n const n = a.length - 1;\n let p = a[n];\n let range = n => [...Array(n).keys()];\n for (let i = 1; i < n + 1; i++) {\n p = p * x + a[n - i];\n }\n return p;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":378,"value":"function range(start, stop, step) {\n if (typeof stop == 'undefined') {\n // one param defined\n stop = start;\n start = 0;\n }\n\n if (typeof step == 'undefined') {\n step = 1;\n }\n\n if ((step > 0 && start >= stop) || (step < 0 && start <= stop)) {\n return [];\n }\n\n var result = [];\n for (var i = start; step > 0 ? i < stop : i > stop; i += step) {\n result.push(i);\n }\n\n return result;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":277,"value":"function sigma(l, b) {\n // \"\"\"Return the sum of body ’b’ for indices i1..in\n // running simultaneously thru lists l1..ln.\n // List ’l’ is of the form [[i1 l1]..[in ln]]\"\"\"\n // # ’l’ is a list of ’n’ lists of the same lenght ’L’ [l1, l2, l3, ...]\n // # ’b’ is a lambda with ’n’ args\n // # ’sigma’ sums all ’L’ applications of ’b’ to the relevant tuple of args\n const z = zip(...l);\n let temp = [];\n z.forEach(e => temp.push(b(...e)));\n return sum(temp, (x, y) => x + y, 0);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":280,"value":"function sum(items, expression, start_value = 0) {\n return items.reduce(expression, start_value);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":275,"value":"zip = (...rows) => [...rows[0]].map((_, c) => rows.map(row => row[c]))","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":250,"value":"function invert_angular(f, y, a, b, prec = 10 ** -5) {\n // \"\"\"Find inverse of angular function ’f’ at ’y’ within interval [a,b].\n // Default precision is 0.00001\"\"\"\n return binary_search(\n a,\n b,\n function(l, h) {\n return h - l <= prec;\n },\n function(x) {\n return mod(f(x) - y, 360) < 180;\n }\n );\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":218,"value":"function binary_search(lo, hi, p, e) {\n // \"\"\"Bisection search for x in [lo, hi] such that condition ’e’ holds.\n // p determines when to go left.\"\"\"\n const x = (lo + hi) / 2;\n if (p(lo, hi)) return x;\n else if (e(x)) return binary_search(lo, x, p, e);\n else return binary_search(x, hi, p, e);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":210,"value":"function summa(f, k, p) {\n // \"\"\"Return the sum of f(i) from i=k, k+1, ... till p(i) holds true or 0.\n // This is a tail recursive implementation.\"\"\"\n return !p(k) ? 0 : f(k) + summa(f, k + 1, p);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1260,"value":"function altsumma(f, k, p) {\n // \"\"\"Return the sum of f(i) from i=k, k+1, ... till p(i) holds true or 0.\n // This is an implementation of the Summation formula from Kahan,\n // see Theorem 8 in Goldberg, David ’What Every Computer Scientist\n // Should Know About Floating-Point Arithmetic’, ACM Computer Survey,\n // Vol. 23, No. 1, March 1991.\"\"\"\n let S, C, T, Y, j;\n if (!p(k)) return 0;\n else {\n S = f(k);\n C = 0;\n j = k + 1;\n while (p(j)) {\n Y = f(j) - C;\n T = S + Y;\n C = T - S - Y;\n S = T;\n j += 1;\n }\n }\n return S;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1135,"value":"md`---\nFrom CALENDRICA 4.0`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1205,"value":"function prodda(f, k, p) {\n // \"\"\"Return the product of f(i) from i=k, k+1, ... till p(i) holds true or 1.\n // This is a tail recursive implementation.\"\"\"\n return !p(k) ? 1 : f(k) * prodda(f, k + 1, p);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1129,"value":"function from_radix(a, b, c = []) {\n // (defun from-radix (a b &optional c)\n // ;; TYPE (list-of-reals list-of-rationals list-of-rationals)\n // ;; TYPE -> real\n // ;; The number corresponding to $a$ in radix notation\n // ;; with base $b$ for whole part and $c$ for fraction.\n // (/ (sum (* (nth i a)\n // (prod (nth j (append b c))\n // j i (< j (+ (length b) (length c)))))\n // i 0 (< i (length a)))\n // (apply '* c)))\n //c.reduce((a, b) => a * b)\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1138,"value":"md`---`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":201,"value":"function final(i, p) {\n // \"\"\"Return last integer greater or equal to initial index, i,\n // such that condition, p, holds.\"\"\"\n return !p(i) ? i - 1 : final(i + 1, p);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":190,"value":"function next(i, p) {\n // \"\"\"Return first integer greater or equal to initial index, i,\n // such that condition, p, holds.\"\"\"\n return p(i) ? i : next(i + 1, p);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":112,"value":"amod = function(x, y) {\n // \"\"\"Return the same as a % b with b instead of 0.\"\"\"\n return y + mod(x, -y);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1112,"value":"md`**Note**: \\`mod3\\` is from CALENDRICA 4.0`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1093,"value":"function mod3(x, a, b) {\n // The value of x shifted into the range\n // [a..b). Returns x if a=b.\n if (a == b) return x;\n return a + mod(x - a, b - a);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":101,"value":"mod = function(x, y) {\n return x - y * ifloor(x / y);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":95,"value":"quotient = function(m, n) {\n // \"\"\"Return the whole part of m/n towards negative infinity.\"\"\"\n return ifloor(m / n);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":162,"value":"round = function(n) {\n return floor(n + 0.5);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":10,"value":"iround = function(n) {\n // \"\"\"Return the whole part of m/n.\"\"\"\n return round(n);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":8,"value":"ifloor = function(n) {\n // \"\"\"Return the whole part of m/n.\"\"\"\n return floor(n);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":150,"value":"ceiling = function(n) {\n return -floor(-n);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":137,"value":"floor = Math.floor","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":255,"value":"function radians(deg) {\n return deg * deg2rad;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1221,"value":"function even(i) {\n return mod(i, 2) == 0;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1225,"value":"function odd(i) {\n return !even(i);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1228,"value":"max = math.max","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1245,"value":"min = math.min","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1231,"value":"atan2 = Math.atan2","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1241,"value":"pow = math.pow","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1251,"value":"abs = math.abs","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1254,"value":"sqrt = math.sqrt","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":91,"value":"BOGUS = 'bogus'","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":19,"value":"md`## Technical details`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":871,"value":"import { toc as itoc } from \"@nebrius/indented-toc\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":260,"value":"import {\n tan, deg2rad\n} from \"@fil/math\"\n","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":79,"value":"math = mathjs.create(config)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":69,"value":"config = {\n const config = {\n epsilon: 1e-12,\n matrix: 'Matrix',\n number: 'number',\n precision: 50,\n predictable: false,\n randomSeed: null\n };\n return config;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":47,"value":"mathjs = require(\"mathjs@7\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"}],"files":"$W31","stdlib":"1","titling":"auto"}} 30:"$2f:body"