2d:null 2e:["$","title",null,{"children":"Numeric Methods | David Hall | Observable"}] 33:[] 31:{"id":"5f91236787b9671c","slug":"numeric-methods","title":"Numeric Methods","thumbnail":"3791eabae419bb66908e3cfd8a8db18577776c972b976ae2cfbc1ae560b36546","access_level":"public","create_time":"$D2019-07-24T02:50:54.586Z","update_time":"$D2019-07-31T09:05:39.494Z","view_time":null,"first_public_time":"$D2019-07-24T05:12:05.484Z","has_unpublished_edits":null,"fork":false,"stars":0,"starred":false,"owner":{"type":"team","id":"e03a1f35385e7271","login":"david-hall","name":"David Hall","avatar_url":"https://avatars-next.observableusercontent.com/afa38c46229fd6d9c4426dfd17e3359afcc7eb8787d0a9c48fafda7bc081c359","tier":"starter_2024"},"version":236,"publish_version":236,"role":null,"authored":false,"authors":[{"type":"individual","id":"0d8260f2c3b197fd","login":"david-hall","name":"David Hall","avatar_url":"https://avatars-next.observableusercontent.com/afa38c46229fd6d9c4426dfd17e3359afcc7eb8787d0a9c48fafda7bc081c359","tier":null}],"members":[{"type":"individual","id":"0d8260f2c3b197fd","login":"david-hall","name":"David Hall","avatar_url":"https://avatars-next.observableusercontent.com/afa38c46229fd6d9c4426dfd17e3359afcc7eb8787d0a9c48fafda7bc081c359","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":0,"collection":null,"type":"notebook","body":{"title":"Numeric Methods","cells":[{"id":0,"value":"md`# Numeric Methods`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":234,"value":"bigNote = md `### Note that this page won't run in IE or Edge until their JavaScript supports BigInt. However BigInt is supported in the latest version of the Chrome browser.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":130,"value":"md`These common numeric methods handle both Number and BigInt parameters.\n\nSee the test cases for examples.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":89,"value":"md`### Number test cases:`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":30,"value":"md`\nabs(-42) => ${test(42, abs(-42))}\n\nabs(0) => ${test(0, abs(0))}\n\nabs(42) => ${test(42, abs(42))}\n\n\nisZero(0) => ${test(true, isZero(0))}\n\nisZero(1) => ${test(false, isZero(1))}\n\n\nisOne(-1) => ${test(false, isOne(-1))}\n\nisOne(0) => ${test(false, isOne(0))}\n\nisOne(1) => ${test(true, isOne(1))}\n\n\nnegate(-42) => ${test(42, negate(-42))}\n\nnegate(0) => ${test(0, negate(0))}\n\nnegate(42) => ${test(-42, negate(42))}\n\n\nsignum(-42) => ${test(-1, signum(-42))}\n\nsignum(0) => ${test(0, signum(0))}\n\nsignum(42) => ${test(1, signum(42))}\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":93,"value":"md`### BigInt test cases:`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":96,"value":"md`\nabs(-42n) => ${test(42n, abs(-42n))}\n\nabs(0n) => ${test(0n, abs(0n))}\n\nabs(42n) => ${test(42n, abs(42n))}\n\n\nisZero(0n) => ${test(true, isZero(0n))}\n\nisZero(1n) => ${test(false, isZero(1n))}\n\n\nisOne(-1n) => ${test(false, isOne(-1n))}\n\nisOne(0n) => ${test(false, isOne(0n))}\n\nisOne(1n) => ${test(true, isOne(1n))}\n\n\nnegate(-42n) => ${test(42n, negate(-42n))}\n\nnegate(0n) => ${test(0n, negate(0n))}\n\nnegate(42n) => ${test(-42n, negate(42n))}\n\n\nsignum(-42n) => ${test(-1, signum(-42n))}\n\nsignum(0n) => ${test(0, signum(0n))}\n\nsignum(42n) => ${test(1, signum(42n))}\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":65,"value":"function test(expected, actual) {\n if (expected === actual) {\n return actual + \" (ok)\";\n } else {\n return \"(\" + typeof actual + \") \" + actual + \" <= FAILED: (expected (\" + typeof expected + \") \" + expected + \")\";\n }\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":162,"value":"function abs(n) {\n return signum(n) == -1 ? negate(n) : n;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":144,"value":"function isBig(n) {\n return (typeof n) == \"bigint\";\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":185,"value":"function isNumber(n) {\n return (typeof n) == \"number\";\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":149,"value":"function isOne(n) {\n return n == 1;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":147,"value":"function isZero(n) {\n return n == 0;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":152,"value":"function negate(n) {\n return -n;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":160,"value":"function negOne(n) {\n return negate(one(n));\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":158,"value":"function one(n) {\n return isBig(n) ? 1n : 1;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":164,"value":"function signum(n) {\n return n == 0 ? 0 : n < 0 ? -1 : 1;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":156,"value":"function zero(n) {\n return isBig(n) ? 0n : 0;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":194,"value":"md `The ___ eulerTotient() ___ function \nreturns the number of positive integers <= n and coprime to n.\nThe result will always be less than or equal to n when n is positive.\nThis function is also known as eulerPhi() or simply phi(),\nbut since we use phi for the golden ratio, I'll call it eulerTotient().\nIt generates the sequence described at https://oeis.org/A000010.\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":191,"value":"function eulerTotient(n) {\n var result = n; \n for(var i=2; i*i <= n; i++) { \n if (n % i == 0) result -= result / i; \n while (n % i == 0) {\n n /= i;\n }\n } \n if (n > 1) {\n result -= result / n; \n }\n return result; \n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":200,"value":"function isPowerOfTwo(n) {\n return (n != 0) && ( (n & -n) == n );\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":230,"value":"md`### Data generation functions:`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":224,"value":"function getRandomNumber(limit = 100) { return Math.floor((Math.random() - 0.5) * limit); }","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":227,"value":"function getIdentityMatrix(size = 3) {\n var rows = [];\n for (let r = 0; r < size; r++) {\n var cols = [];\n for (let c = 0; c < size; c++) {\n cols.push(r == c ? 1 : 0);\n }\n rows.push(cols);\n }\n return rows;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":220,"value":"function getAdditionTable(size = 3) {\n var rows = [];\n for (let r = 0; r < size; r++) {\n var cols = [];\n for (let c = 0; c < size; c++) {\n cols.push(r+c);\n }\n rows.push(cols);\n }\n return rows;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":222,"value":"function getMultiplicationTable(size = 3) {\n var rows = [];\n for (let r = 0; r < size; r++) {\n var cols = [];\n for (let c = 0; c < size; c++) {\n cols.push((r+1) * (c+1));\n }\n rows.push(cols);\n }\n return rows;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":216,"value":"md`### Apendix`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":134,"value":"md `Read more about the use of [BigInt](https://observablehq.com/@mvptim/to-9007199254740991-and-beyond) in Observable Notebooks...`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W33","stdlib":"1","titling":"auto"}} 32:"$31:body"