29:null 2a:["$","title",null,{"children":"choose-ticks translation | Edward Misback | Observable"}] 2f:T50c,function pick_spaced_ordinals(necessary, min, max, number) { // NOTE that subtle use of mathjs bignumbers is required in this function... let sub_range = math.divide(math.bignumber(math.subtract(math.bignumber(max), math.bignumber(min))), math.bignumber(number)) // size of a division on the ordinal range let necessary_star = (function loop(necessary) { return necessary.length < 2 ? necessary : math.smaller(math.subtract(necessary[1], necessary[0]), sub_range) ? loop(necessary.slice(1)) : [necessary[0], ...loop(necessary.slice(1))] })(necessary) // filter out necessary points that are too close let all = (function loop(necessary, min_star, start) { if (start >= number) { return [] } if (necessary.length == 0) { return choose_between(min_star, max, number - start) } let idx = false for (let i=0; i math.subtract(math.bignumber(a), math.bignumber(b))) }30:Tee0,function choose_ticks_clientside (min, max) { function to_signed_int (float64) { const buffer = new ArrayBuffer(8) const view = new DataView(buffer) view.setFloat64(0, float64) return view.getBigInt64(0) } function real_from_signed_int (signed) { const buffer = new ArrayBuffer(8) const view = new DataView(buffer) view.setBigInt64(0, signed) return view.getFloat64(0) } function first_power10(min, max) { let value = max < 0 ? - (10 ** Math.ceil(Math.log(-max)/ Math.log(10))) : 10 ** (Math.floor(Math.log(max) / Math.log(10))) return value <= min ? false : value } function clamp(x, lo, hi) { return Math.min(hi, Math.max(x, lo)) } function mbn(x) { return math.bignumber(to_signed_int(x).toString()) } let mbn_neg_0 = mbn(-0.0) function real_to_ordinal(real) { let signed = to_signed_int(real) let mbn = math.bignumber(signed.toString()) return signed >= 0 ? mbn : math.subtract(mbn_neg_0, mbn) } function ordinal_to_real(ordinal) { return ordinal >=0 ? real_from_signed_int(BigInt(ordinal)) : real_from_signed_int(BigInt(math.subtract(mbn_neg_0, math.bignumber(ordinal)))) } function choose_between(min, max, number) { // ; Returns a given number of ticks, roughly evenly spaced, between min and max // ; For any tick, n divisions below max, the tick is an ordinal corresponding to: // ; (a) a power of 10 between n and (n + ε) divisions below max where ε is some tolerance, or // ; (b) a value, n divisions below max let sub_range = Math.round((max - min) / (1 + number)) let near = (x, n) => (x <= n) && (Math.abs((x - n) / sub_range) <= .2) // <= tolerance return [...Array(number)].map((_, i) => i + 1).map(itr => { let power10 = first_power10( ordinal_to_real(clamp(max - ((itr + 1) * sub_range), min, max)), ordinal_to_real(clamp(max - (itr * sub_range), min, max)) ) return power10 && near(real_to_ordinal(power10), max - (itr * sub_range)) ? real_to_ordinal(power10) : max - (itr * sub_range) }) } function pick_spaced_ordinals(necessary, min, max, number) { // NOTE use of mathjs bignumber arithmetic is required in this function! let sub_range = math.divide(math.bignumber(math.subtract(math.bignumber(max), math.bignumber(min))), math.bignumber(number)) // size of a division on the ordinal range let necessary_star = (function loop(necessary) { return necessary.length < 2 ? necessary : math.smaller(math.subtract(necessary[1], necessary[0]), sub_range) ? loop(necessary.slice(1)) : [necessary[0], ...loop(necessary.slice(1))] })(necessary) // filter out necessary points that are too close let all = (function loop(necessary, min_star, start) { if (start >= number) { return [] } if (necessary.length == 0) { return choose_between(min_star, max, number - start) } let idx = false for (let i=0; i math.subtract(math.bignumber(a), math.bignumber(b))) } function choose_ticks (min, max) { let tick_count = 13 let necessary = [min, -1.0, 0, 1.0, max].filter(v => (min <= v) && (v <= max) && (min <= max)).map(v => real_to_ordinal(v)) let major_ticks = pick_spaced_ordinals(necessary, real_to_ordinal(min), real_to_ordinal(max), tick_count).map(v => ordinal_to_real(v)) return major_ticks } return choose_ticks(min, max) }31:[] 2d:{"id":"4da74698520854e8","slug":null,"title":"choose-ticks translation","thumbnail":"ff49a15967233c5405981389e39a702bcc23e8e2596f5daf66467819c6578d92","access_level":"public","create_time":"$D2022-05-10T00:21:08.108Z","update_time":"$D2023-02-03T10:42:56.667Z","view_time":null,"first_public_time":"$D2023-02-02T09:05:10.491Z","fork":false,"stars":0,"starred":false,"owner":{"type":"team","id":"5508584884fd137b","login":"elmisback","name":"Edward Misback","avatar_url":"https://avatars-next.observableusercontent.com/9a42c09ac3fb39913eeacae071d5ba669ac49bf75c82372d0d717ec0acb59024","tier":"starter_2024"},"version":365,"publish_version":null,"role":null,"authored":false,"authors":[{"type":"individual","id":"e03d30b651790cf0","login":"elmisback","name":"Edward Misback","avatar_url":"https://avatars-next.observableusercontent.com/9a42c09ac3fb39913eeacae071d5ba669ac49bf75c82372d0d717ec0acb59024","tier":null}],"members":[{"type":"individual","id":"e03d30b651790cf0","login":"elmisback","name":"Edward Misback","avatar_url":"https://avatars-next.observableusercontent.com/9a42c09ac3fb39913eeacae071d5ba669ac49bf75c82372d0d717ec0acb59024","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"subscribed":null,"forks":0,"collection":null,"type":"notebook","body":{"title":"choose-ticks translation","cells":[{"id":0,"value":"# choose-ticks translation","pinned":true,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined"},{"id":7,"value":"function first_power10(min, max) {\n let value = max < 0 ? - (10 ** Math.ceil(Math.log(-max)/ Math.log(10))) : 10 ** (Math.floor(Math.log(max) / Math.log(10)))\n return value <= min ? false : value\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":9,"value":"first_power10(27, 1037) // should be 1000 (first power below max)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":51,"value":"first_power10(0, Number.MAX_VALUE)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":3,"value":"function clamp(x, lo, hi) {\n return Math.min(hi, Math.max(x, lo))\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":13,"value":"clamp(1, 3, 4)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":24,"value":"math = require('mathjs')","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":19,"value":"function to_signed_int (float64) {\n const buffer = new ArrayBuffer(8)\n const view = new DataView(buffer)\n view.setFloat64(0, float64)\n return view.getBigInt64(0)\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":34,"value":"function real_from_signed_int (signed) {\n const buffer = new ArrayBuffer(8)\n const view = new DataView(buffer)\n view.setBigInt64(0, signed)\n return view.getFloat64(0)\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":22,"value":"function mbn(x) {\n return math.bignumber(to_signed_int(x).toString())\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":29,"value":"mbn_neg_0 = mbn(-0.0)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":17,"value":"function real_to_ordinal(real) {\n let signed = to_signed_int(real)\n let mbn = math.bignumber(signed.toString())\n return signed >= 0 ? mbn : math.subtract(mbn_neg_0, mbn)\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":32,"value":"function ordinal_to_real(ordinal) {\n return ordinal >=0 ? real_from_signed_int(BigInt(ordinal)) : real_from_signed_int(BigInt(math.subtract(mbn_neg_0, math.bignumber(ordinal))))\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":256,"value":"function float_to_approximate_ordinal(float) {\n return real_to_ordinal(float).toNumber()\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":258,"value":"float_to_approximate_ordinal(Number.MAX_VALUE)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":44,"value":"Number.MAX_VALUE","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":226,"value":"Number.MIN_VALUE","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":39,"value":"ordinal_to_real(real_to_ordinal(Number.MIN_VALUE))","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":16,"value":"function choose_between(min, max, number) {\n // ; Returns a given number of ticks, roughly evenly spaced, between min and max\n // ; For any tick, n divisions below max, the tick is an ordinal corresponding to:\n // ; (a) a power of 10 between n and (n + ε) divisions below max where ε is some tolerance, or\n // ; (b) a value, n divisions below max\n let sub_range = Math.round((max - min) / (1 + number))\n let near = (x, n) => (x <= n) && (Math.abs((x - n) / sub_range) <= .2) // <= tolerance\n return [...Array(number)].map((_, i) => i + 1).map(itr => {\n let power10 = first_power10(\n ordinal_to_real(clamp(max - ((itr + 1) * sub_range), min, max)),\n ordinal_to_real(clamp(max - (itr * sub_range), min, max))\n )\n console.log(power10)\n return (power10 && near(real_to_ordinal(power10), max - (itr * sub_range))) ? real_to_ordinal(power10)\n : max - (itr * sub_range)\n })\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":310,"value":"choose_between(real_to_ordinal(1), real_to_ordinal(1e3), 13)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":301,"value":"first_power10(1, 10000)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":47,"value":"choose_between(real_to_ordinal(0), real_to_ordinal(Number.MAX_VALUE), 13).map(v => ordinal_to_real(v))","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":291,"value":"ordinal_to_real(real_to_ordinal(1))","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":293,"value":"ordinal_to_real(real_to_ordinal(1e3))","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":289,"value":"choose_between(real_to_ordinal(1), real_to_ordinal(1e2), 13).map(v => ordinal_to_real(v))","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":167,"value":"choose_between(real_to_ordinal(0), real_to_ordinal(Number.MAX_VALUE), 0)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":68,"value":"$2f","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":76,"value":"pick_spaced_ordinals([ real_to_ordinal(0), real_to_ordinal(1)], real_to_ordinal(0), real_to_ordinal(Number.MAX_VALUE), 13).map(v => ordinal_to_real(v))","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":173,"value":"pick_spaced_ordinals([real_to_ordinal(-1), real_to_ordinal(-1), real_to_ordinal(0), real_to_ordinal(1), real_to_ordinal(Number.MAX_VALUE)], real_to_ordinal(-1), real_to_ordinal(Number.MAX_VALUE), 13).map(v => ordinal_to_real(v).toString())","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":72,"value":"function choose_ticks (min, max) {\n let tick_count = 13\n let necessary = [min, -1.0, 0, 1.0, max].filter(v => (min <= v) && (v <= max) && (min <= max)).map(v => real_to_ordinal(v))\n let major_ticks = pick_spaced_ordinals(necessary, real_to_ordinal(min), real_to_ordinal(max), tick_count).map(v => ordinal_to_real(v))\n return major_ticks\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":110,"value":"test = choose_ticks(-.731, Number.MAX_VALUE)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":245,"value":"test.map(formatter)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":239,"value":"formatter = v => {\n const s = v.toString()\n const [base, exponent] = s.split('e')\n const [l, r] = base.split('.')\n const formattedBase = !r ? base : `${l}.${r.slice(0, 2)}`\n return !exponent ? formattedBase : `${formattedBase}e${exponent}`\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":340,"value":"formatter2 = v => {\n const s = v.toPrecision(1)\n const [base, exponent] = s.split('e')\n if (!exponent) {\n return v.toPrecision(1) == v ? v.toPrecision(1) : v.toPrecision(6)\n }\n if (exponent <= 1 && -1 <= exponent) {\n const a = v.toString()\n const b = v.toPrecision(6)\n return a.length < b.length ? a : b\n }\n return v.toPrecision(1)\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":345,"value":"test2 = choose_ticks(1, 1000)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":342,"value":"test2.map(formatter2)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":209,"value":"$30","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":222,"value":"choose_ticks_clientside(-1.79e308, 1.79e308)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":102,"value":"1 < 4 < 3","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":135,"value":"ordinal_to_real(\"-4607182418800017408\")","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":132,"value":"real_to_ordinal(0).toString()","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"}],"files":"$W31","stdlib":"1","titling":"auto"}} 2e:"$2d:body"