├── .editorconfig
├── .github
├── dependabot.yml
└── workflows
│ └── workflow-1.yml
├── .gitignore
├── LICENSE.txt
├── README.md
├── jest.config.js
├── package-lock.json
├── package.json
├── src
└── index.js
└── test
└── index.spec.js
/.editorconfig:
--------------------------------------------------------------------------------
1 | [*]
2 | insert_final_newline = true
3 | charset = utf-8
4 | indent_style = space
5 | indent_size = 2
6 |
--------------------------------------------------------------------------------
/.github/dependabot.yml:
--------------------------------------------------------------------------------
1 | version: 2
2 | updates:
3 | - package-ecosystem: 'npm'
4 | directory: '/'
5 | schedule:
6 | interval: 'monthly'
7 | ignore:
8 | - dependency-name: '*'
9 | update-types:
10 | - 'version-update:semver-minor'
11 | - 'version-update:semver-patch'
12 |
--------------------------------------------------------------------------------
/.github/workflows/workflow-1.yml:
--------------------------------------------------------------------------------
1 | name: 'Travis CI replacement'
2 |
3 | on:
4 | pull_request:
5 | branches:
6 | - '**'
7 |
8 | jobs:
9 | build-job:
10 | runs-on: 'ubuntu-latest'
11 |
12 | strategy:
13 | matrix:
14 | node-version: ['14.x', '16.x', '18.x', '20.x', '22.x']
15 |
16 | steps:
17 | - uses: 'actions/checkout@v2'
18 |
19 | - name: 'Use Node.js ${{ matrix.node-version }}'
20 | uses: 'actions/setup-node@v1'
21 | with:
22 | node-version: '${{ matrix.node-version }}'
23 |
24 | - name: 'Actual npm tasks'
25 | run: |
26 | npm install
27 | npm run test
28 |
--------------------------------------------------------------------------------
/.gitignore:
--------------------------------------------------------------------------------
1 | node_modules
2 | coverage
3 |
--------------------------------------------------------------------------------
/LICENSE.txt:
--------------------------------------------------------------------------------
1 | MIT License
2 |
3 | Copyright (c) 2021 qntm
4 |
5 | Permission is hereby granted, free of charge, to any person obtaining a copy
6 | of this software and associated documentation files (the "Software"), to deal
7 | in the Software without restriction, including without limitation the rights
8 | to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
9 | copies of the Software, and to permit persons to whom the Software is
10 | furnished to do so, subject to the following conditions:
11 |
12 | The above copyright notice and this permission notice shall be included in all
13 | copies or substantial portions of the Software.
14 |
15 | THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
16 | IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
17 | FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
18 | AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
19 | LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
20 | OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
21 | SOFTWARE.
22 |
--------------------------------------------------------------------------------
/README.md:
--------------------------------------------------------------------------------
1 | # hyperoperate
2 |
3 | This module exports the [hyperoperation](https://en.wikipedia.org/wiki/Hyperoperation) function. This recursive function generalises the binary operations of addition (*n* = 1), multiplication (*n* = 2) and exponentiation (*n* = 3) to arbitrary non-negative *n* (tetration, pentation, hexation, ...)
4 |
5 | > *H*(0, *a*, *b*) = *b* + 1
6 | > *H*(1, *a*, 0) = *a*
7 | > *H*(2, *a*, 0) = 0
8 | > *H*(*n*, *a*, 0) = 1
9 | > *H*(*n*, *a*, *b*) = *H*(*n* - 1, *a*, *H*(*n*, *a*, *b* - 1))
10 |
11 | `H` accepts only non-negative integers `n`, `a` and `b`.
12 |
13 | Note that for the purposes of this module, 0 to the power of 0 is 1.
14 |
15 | ## Installation
16 |
17 | ```sh
18 | npm install hyperoperate
19 | ```
20 |
21 | ## Usage
22 |
23 | ```js
24 | import H from 'hyperoperate'
25 |
26 | // n = 0: successor (`a` is ignored)
27 | H(0, 1000, 3) // 4
28 |
29 | // n = 1: addition
30 | H(1, 33, 44) // 77
31 |
32 | // n = 2: multiplication
33 | H(2, 6, 7) // 42
34 |
35 | // n = 3: exponentiation
36 | H(3, 2, 10) // 1024
37 |
38 | // n = 4: tetration
39 | H(4, 3, 3) // 3^^3 = 3^3^3 = 7625597484987
40 |
41 | // n = 5: pentation
42 | H(5, 2, 3) // 2^^^3 = 2^^2^^2 = 2^^4 = 2^2^2^2 = 65536
43 |
44 | // and so on...
45 | ```
46 |
47 | The result is rounded to the nearest JavaScript number. If the result is too large to express as a JavaScript number, `Infinity` is returned.
48 |
49 | `hyperoperate` will also accept a trio of `BigInt`s. In this case, the return value is also a `BigInt`:
50 |
51 | ```js
52 | H(4n, 5n, 3n) // 5^^3 = 5^5^5 = 5^3125 = 1911...03125n
53 | ```
54 |
55 | `hyperoperate` throws an exception if passed a mixture of regular JavaScript numbers and `BigInt`s. If the result is too large to express as a `BigInt`, a `RangeError` is thrown.
56 |
--------------------------------------------------------------------------------
/jest.config.js:
--------------------------------------------------------------------------------
1 | module.exports = {
2 | verbose: true,
3 | bail: false,
4 | collectCoverage: true,
5 | collectCoverageFrom: [
6 | 'src/*.js',
7 | '!src/*.spec.js'
8 | ],
9 | coverageThreshold: {
10 | global: {
11 | branches: 100,
12 | functions: 100,
13 | lines: 100,
14 | statements: 100
15 | }
16 | }
17 | }
18 |
--------------------------------------------------------------------------------
/package-lock.json:
--------------------------------------------------------------------------------
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40 | "dev": true,
41 | "requires": {
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43 | }
44 | },
45 | "js-yaml": {
46 | "version": "4.1.0",
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71 | }
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88 | "strip-ansi-cjs": "npm:strip-ansi@^6.0.1",
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156 | "strip-ansi": {
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161 | "requires": {
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236 | "strip-ansi": {
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240 | "dev": true,
241 | "requires": {
242 | "ansi-regex": "^5.0.1"
243 | }
244 | }
245 | }
246 | }
247 | }
248 | },
249 | "@istanbuljs/schema": {
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260 | },
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269 | "resolved": "https://registry.npmjs.org/@jridgewell/trace-mapping/-/trace-mapping-0.3.25.tgz",
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272 | "requires": {
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275 | }
276 | },
277 | "@pkgjs/parseargs": {
278 | "version": "0.11.0",
279 | "resolved": "https://registry.npmjs.org/@pkgjs/parseargs/-/parseargs-0.11.0.tgz",
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286 | "resolved": "https://registry.npmjs.org/@types/istanbul-lib-coverage/-/istanbul-lib-coverage-2.0.6.tgz",
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288 | "dev": true
289 | },
290 | "@types/json5": {
291 | "version": "0.0.29",
292 | "resolved": "https://registry.npmjs.org/@types/json5/-/json5-0.0.29.tgz",
293 | "integrity": "sha1-7ihweulOEdK4J7y+UnC86n8+ce4=",
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2634 | "integrity": "sha512-y11nGElTIV+CT3Zv9t7VKl+Q3hTQoT9a1Qzezhhl6Rp21gJ/IVTW7Z3y9EWXhuUBC2Shnf+DX0antecpAwSP8w==",
2635 | "dev": true
2636 | },
2637 | "yargs-unparser": {
2638 | "version": "2.0.0",
2639 | "resolved": "https://registry.npmjs.org/yargs-unparser/-/yargs-unparser-2.0.0.tgz",
2640 | "integrity": "sha512-7pRTIA9Qc1caZ0bZ6RYRGbHJthJWuakf+WmHK0rVeLkNrrGhfoabBNdue6kdINI6r4if7ocq9aD/n7xwKOdzOA==",
2641 | "dev": true,
2642 | "requires": {
2643 | "camelcase": "^6.0.0",
2644 | "decamelize": "^4.0.0",
2645 | "flat": "^5.0.2",
2646 | "is-plain-obj": "^2.1.0"
2647 | }
2648 | },
2649 | "yocto-queue": {
2650 | "version": "0.1.0",
2651 | "resolved": "https://registry.npmjs.org/yocto-queue/-/yocto-queue-0.1.0.tgz",
2652 | "integrity": "sha512-rVksvsnNCdJ/ohGc6xgPwyN8eheCxsiLM8mxuE/t/mOVqJewPuO1miLpTHQiRgTKCLexL4MeAFVagts7HmNZ2Q==",
2653 | "dev": true
2654 | }
2655 | }
2656 | }
2657 |
--------------------------------------------------------------------------------
/package.json:
--------------------------------------------------------------------------------
1 | {
2 | "name": "hyperoperate",
3 | "version": "2.0.1",
4 | "description": "Hyperoperations!",
5 | "homepage": "https://github.com/qntm/hyperoperate",
6 | "repository": {
7 | "type": "git",
8 | "url": "git://github.com/qntm/hyperoperate.git"
9 | },
10 | "type": "module",
11 | "main": "src/index.js",
12 | "scripts": {
13 | "mocha": "c8 --100 mocha",
14 | "postpublish": "npm version patch && git push",
15 | "standard": "standard",
16 | "test": "npm run standard && npm run mocha"
17 | },
18 | "keywords": [
19 | "ackermann",
20 | "exponent",
21 | "tetration",
22 | "pentation",
23 | "math",
24 | "maths",
25 | "arrow",
26 | "notation"
27 | ],
28 | "author": "qntm",
29 | "license": "MIT",
30 | "devDependencies": {
31 | "c8": "^10.1.2",
32 | "mocha": "^11.0.0",
33 | "standard": "^17.0.0"
34 | },
35 | "files": [
36 | "src"
37 | ]
38 | }
39 |
--------------------------------------------------------------------------------
/src/index.js:
--------------------------------------------------------------------------------
1 | // All arguments must be BigInts. Return value is a BigInt or a thrown RangeError
2 | const bigH = (n, a, b) => {
3 | if (n < 0n || a < 0n || b < 0n) {
4 | throw Error('Can only hyperoperate on non-negative integers')
5 | }
6 |
7 | // successor operator
8 | if (n === 0n) {
9 | // Ignore `a`
10 | return b + 1n
11 | }
12 |
13 | // addition
14 | if (n === 1n) {
15 | return a + b
16 | }
17 |
18 | // multiplication
19 | if (n === 2n) {
20 | return a * b
21 | }
22 |
23 | // exponentiation
24 | if (n === 3n) {
25 | return a ** b
26 | }
27 |
28 | // n >= 4, time for some handy base cases
29 |
30 | if (a === 0n) {
31 | // Fun fact:
32 | return b % 2n === 0n ? 1n : 0n
33 | }
34 |
35 | if (a === 1n) {
36 | // 1^...^b = 1 for all finite b
37 | return 1n
38 | }
39 |
40 | // a >= 2
41 |
42 | if (b === 0n) {
43 | // a^0 = 1 for all a >= 2
44 | return 1n
45 | }
46 |
47 | if (b === 1n) {
48 | // a^...^1 = a for all a >= 2
49 | return a
50 | }
51 |
52 | // b >= 2
53 |
54 | if (a === 2n && b === 2n) {
55 | // Another fun fact
56 | return 4n
57 | }
58 |
59 | if (n < 6n) {
60 | let result = a
61 | for (let i = 1n; i < b; i++) {
62 | result = bigH(n - 1n, a, result)
63 | }
64 | return result
65 | }
66 |
67 | // All other results (n >= 6, a >= 2, b >= 2) are too large to be computable on Earth computers.
68 | throw RangeError('BigInt')
69 | }
70 |
71 | export default (n, a, b) => {
72 | if ([n, a, b].every(arg => typeof arg === 'bigint')) {
73 | return bigH(n, a, b)
74 | }
75 |
76 | if ([n, a, b].every(arg => Number.isInteger(arg))) {
77 | // All plain doubles... convert inputs to `BigInt`s, then convert the result back to a double
78 | try {
79 | return Number(bigH(BigInt(n), BigInt(a), BigInt(b)))
80 | } catch (error) {
81 | // Not clear what other error could be thrown at this stage?
82 | /* istanbul ignore if */
83 | if (!(
84 | error instanceof RangeError &&
85 | error.message.includes('BigInt') // BigInt overflow
86 | )) {
87 | throw error
88 | }
89 | }
90 |
91 | return Infinity
92 | }
93 |
94 | throw Error('Can only hyperoperate on three numbers or three BigInts')
95 | }
96 |
--------------------------------------------------------------------------------
/test/index.spec.js:
--------------------------------------------------------------------------------
1 | /* eslint-env mocha */
2 |
3 | import assert from 'assert'
4 | import H from '../src/index.js'
5 |
6 | describe('H', () => {
7 | describe('number arguments', () => {
8 | // Returns Infinity in the event of overflow
9 | describe('input validation', () => {
10 | it('throws on non-integer arguments', () => {
11 | assert.throws(() => H(0.5, 1, 2), Error('Can only hyperoperate on three numbers or three BigInts'))
12 | assert.throws(() => H(0, 'one', 2), Error('Can only hyperoperate on three numbers or three BigInts'))
13 | assert.throws(() => H(0, 1, Infinity), Error('Can only hyperoperate on three numbers or three BigInts'))
14 | })
15 |
16 | it('throws on negative arguments', () => {
17 | assert.throws(() => H(-1, 1, 2), Error('Can only hyperoperate on non-negative integers'))
18 | assert.throws(() => H(0, -2, 2), Error('Can only hyperoperate on non-negative integers'))
19 | assert.throws(() => H(0, 1, -Number.MAX_VALUE), Error('Can only hyperoperate on non-negative integers'))
20 | })
21 | })
22 |
23 | describe('H0 (successor)', () => {
24 | const H0 = H.bind(undefined, 0)
25 | it('works', () => {
26 | assert.strictEqual(H0(0, 0), 1)
27 | assert.strictEqual(H0(56, 78), 79)
28 | assert.strictEqual(H0(1, Number.MAX_VALUE), Number.MAX_VALUE) // Because floats
29 | })
30 | })
31 |
32 | describe('H1 (addition)', () => {
33 | const H1 = H.bind(undefined, 1)
34 | it('works', () => {
35 | assert.strictEqual(H1(33, 44), 77)
36 | })
37 | })
38 |
39 | describe('H2 (multiplication)', () => {
40 | const H2 = H.bind(undefined, 2)
41 | it('works', () => {
42 | assert.strictEqual(H2(6, 7), 42)
43 | })
44 | })
45 |
46 | describe('H3 (exponentiation)', () => {
47 | const H3 = H.bind(undefined, 3)
48 | it('works', () => {
49 | assert.strictEqual(H3(0, 0), 1)
50 | assert.strictEqual(H3(0, 1), 0)
51 | assert.strictEqual(H3(0, 2), 0)
52 | assert.strictEqual(H3(0, 153), 0)
53 | assert.strictEqual(H3(0, Number.MAX_VALUE), 0)
54 |
55 | assert.strictEqual(H3(1, 0), 1)
56 | assert.strictEqual(H3(1, 1), 1)
57 | assert.strictEqual(H3(1, 2), 1)
58 | assert.strictEqual(H3(1, 94379), 1)
59 | assert.strictEqual(H3(1, Number.MAX_SAFE_INTEGER), 1)
60 |
61 | assert.strictEqual(H3(2, 0), 1)
62 | assert.strictEqual(H3(2, 1), 2)
63 | assert.strictEqual(H3(2, 2), 4)
64 | assert.strictEqual(H3(2, 10), 1024)
65 | assert.strictEqual(H3(2, 10), 1024)
66 |
67 | assert.strictEqual(H3(3, 3), 27)
68 | assert.strictEqual(H3(5, 5), 3125)
69 |
70 | assert.strictEqual(H3(70, 0), 1)
71 | assert.strictEqual(H3(71, 1), 71)
72 | assert.strictEqual(H3(20001, 0), 1)
73 | assert.strictEqual(H3(9999999, 1), 9999999)
74 | })
75 | })
76 |
77 | describe('H4 (tetration)', () => {
78 | const H4 = H.bind(undefined, 4)
79 | it('works when a is 0', () => {
80 | assert.strictEqual(H4(0, 0), 1)
81 | assert.strictEqual(H4(0, 1), 0)
82 | assert.strictEqual(H4(0, 2), 1)
83 | assert.strictEqual(H4(0, 3), 0)
84 | assert.strictEqual(H4(0, 999), 0)
85 | assert.strictEqual(H4(0, 1000), 1)
86 | assert.strictEqual(H4(0, Number.MAX_VALUE), 1)
87 | })
88 |
89 | it('works when a is 1', () => {
90 | assert.strictEqual(H4(1, 0), 1)
91 | assert.strictEqual(H4(1, 1), 1)
92 | assert.strictEqual(H4(1, 2), 1)
93 | assert.strictEqual(H4(1, 3), 1)
94 | assert.strictEqual(H4(1, 987), 1)
95 | assert.strictEqual(H4(1, Number.MAX_VALUE), 1)
96 | })
97 |
98 | describe('when a is 2', () => {
99 | it('works when b is 0', () => {
100 | assert.strictEqual(H4(2, 0), 1)
101 | })
102 |
103 | it('works when b is 1', () => {
104 | assert.strictEqual(H4(2, 1), 2)
105 | })
106 |
107 | it('works when b is 2', () => {
108 | assert.strictEqual(H4(2, 2), 4)
109 | })
110 |
111 | it('works when b is 3', () => {
112 | assert.strictEqual(H4(2, 3), 16)
113 | })
114 |
115 | it('works when b is 4', () => {
116 | assert.strictEqual(H4(2, 4), 65536)
117 | })
118 |
119 | it('works when b is 5', () => {
120 | assert.strictEqual(H4(2, 5), Infinity)
121 | })
122 |
123 | it('works when b is Number.MAX_VALUE', () => {
124 | assert.strictEqual(H4(2, Number.MAX_VALUE), Infinity)
125 | })
126 | })
127 |
128 | it('works when a is 3', () => {
129 | assert.strictEqual(H4(3, 0), 1)
130 | assert.strictEqual(H4(3, 1), 3)
131 | assert.strictEqual(H4(3, 2), 27)
132 | assert.strictEqual(H4(3, 3), 7625597484987)
133 | assert.strictEqual(H4(3, 4), Infinity)
134 | assert.strictEqual(H4(3, Number.MAX_VALUE), Infinity)
135 | })
136 |
137 | it('works when a is 4', () => {
138 | assert.strictEqual(H4(4, 0), 1)
139 | assert.strictEqual(H4(4, 1), 4)
140 | assert.strictEqual(H4(4, 2), 256)
141 | assert.strictEqual(H4(4, 3), 1.3407807929942597e+154)
142 | assert.strictEqual(H4(4, 4), Infinity)
143 | assert.strictEqual(H4(4, Number.MAX_VALUE), Infinity)
144 | })
145 |
146 | it('works when a is 5', () => {
147 | assert.strictEqual(H4(5, 0), 1)
148 | assert.strictEqual(H4(5, 1), 5)
149 | assert.strictEqual(H4(5, 2), 3125)
150 | assert.strictEqual(H4(5, 3), Infinity)
151 | assert.strictEqual(H4(5, Number.MAX_VALUE), Infinity)
152 | })
153 |
154 | it('works when a is 143', () => {
155 | assert.strictEqual(H4(143, 0), 1)
156 | assert.strictEqual(H4(143, 1), 143)
157 | assert.strictEqual(H4(143, 2), 1.6332525972973913e+308)
158 | assert.strictEqual(H4(143, 3), Infinity)
159 | assert.strictEqual(H4(143, Number.MAX_VALUE), Infinity)
160 | })
161 |
162 | it('works when a is 144', () => {
163 | assert.strictEqual(H4(144, 0), 1)
164 | assert.strictEqual(H4(144, 1), 144)
165 | assert.strictEqual(H4(144, 2), Infinity)
166 | assert.strictEqual(H4(144, Number.MAX_VALUE), Infinity)
167 | })
168 |
169 | it('works when a is Number.MAX_VALUE', () => {
170 | assert.strictEqual(H4(Number.MAX_VALUE, 0), 1)
171 | assert.strictEqual(H4(Number.MAX_VALUE, 1), Number.MAX_VALUE)
172 | assert.strictEqual(H4(Number.MAX_VALUE, 2), Infinity)
173 | assert.strictEqual(H4(Number.MAX_VALUE, Number.MAX_VALUE), Infinity)
174 | })
175 | })
176 |
177 | describe('H5 (pentation)', () => {
178 | const H5 = H.bind(undefined, 5)
179 | it('works', () => {
180 | assert.strictEqual(H5(0, 0), 1)
181 | assert.strictEqual(H5(0, 1), 0)
182 | assert.strictEqual(H5(0, 2), 1)
183 | assert.strictEqual(H5(0, 999), 0)
184 | assert.strictEqual(H5(0, Number.MAX_VALUE), 1)
185 |
186 | assert.strictEqual(H5(1, 0), 1)
187 | assert.strictEqual(H5(1, 1), 1)
188 | assert.strictEqual(H5(1, 10000078), 1)
189 | assert.strictEqual(H5(1, Number.MAX_VALUE), 1)
190 |
191 | assert.strictEqual(H5(2, 0), 1)
192 | assert.strictEqual(H5(2, 1), 2)
193 | assert.strictEqual(H5(2, 2), 4)
194 | assert.strictEqual(H5(2, 3), 65536)
195 | assert.strictEqual(H5(2, 4), Infinity)
196 | assert.strictEqual(H5(2, Number.MAX_VALUE), Infinity)
197 |
198 | assert.strictEqual(H5(3, 0), 1)
199 | assert.strictEqual(H5(3, 1), 3)
200 | assert.strictEqual(H5(3, 2), 7625597484987)
201 | assert.strictEqual(H5(3, 3), Infinity)
202 | assert.strictEqual(H5(3, Number.MAX_VALUE), Infinity)
203 |
204 | assert.strictEqual(H5(4, 0), 1)
205 | assert.strictEqual(H5(4, 1), 4)
206 | assert.strictEqual(H5(4, 2), Infinity)
207 | assert.strictEqual(H5(4, Number.MAX_VALUE), Infinity)
208 |
209 | assert.strictEqual(H5(Number.MAX_VALUE, 0), 1)
210 | assert.strictEqual(H5(Number.MAX_VALUE, 1), Number.MAX_VALUE)
211 | assert.strictEqual(H5(Number.MAX_VALUE, 2), Infinity)
212 | assert.strictEqual(H5(Number.MAX_VALUE, Number.MAX_VALUE), Infinity)
213 | })
214 | })
215 |
216 | describe('H6 (hexation)', () => {
217 | const H6 = H.bind(undefined, 6)
218 | it('works', () => {
219 | assert.strictEqual(H6(0, 0), 1)
220 | assert.strictEqual(H6(0, 1), 0)
221 | assert.strictEqual(H6(0, 2), 1)
222 | assert.strictEqual(H6(0, 3), 0)
223 | assert.strictEqual(H6(0, Number.MAX_VALUE), 1)
224 |
225 | assert.strictEqual(H6(1, 0), 1)
226 | assert.strictEqual(H6(1, 1), 1)
227 | assert.strictEqual(H6(1, 2), 1)
228 | assert.strictEqual(H6(1, 3), 1)
229 | assert.strictEqual(H6(1, Number.MAX_VALUE), 1)
230 |
231 | assert.strictEqual(H6(2, 0), 1)
232 | assert.strictEqual(H6(2, 1), 2)
233 | assert.strictEqual(H6(2, 2), 4)
234 | assert.strictEqual(H6(2, 3), Infinity)
235 | assert.strictEqual(H6(2, Number.MAX_VALUE), Infinity)
236 |
237 | assert.strictEqual(H6(3, 0), 1)
238 | assert.strictEqual(H6(3, 1), 3)
239 | assert.strictEqual(H6(3, 2), Infinity)
240 | assert.strictEqual(H6(3, Number.MAX_VALUE), Infinity)
241 |
242 | assert.strictEqual(H6(Number.MAX_VALUE, 0), 1)
243 | assert.strictEqual(H6(Number.MAX_VALUE, 1), Number.MAX_VALUE)
244 | assert.strictEqual(H6(Number.MAX_VALUE, 2), Infinity)
245 | assert.strictEqual(H6(Number.MAX_VALUE, 3), Infinity)
246 | assert.strictEqual(H6(Number.MAX_VALUE, Number.MAX_VALUE), Infinity)
247 | })
248 | })
249 |
250 | describe('Hmax (Number.MAX_VALUE-ation)', () => {
251 | const Hmax = H.bind(undefined, Number.MAX_VALUE)
252 | it('works when a is 0', () => {
253 | assert.strictEqual(Hmax(0, 0), 1)
254 | assert.strictEqual(Hmax(0, 1), 0)
255 | assert.strictEqual(Hmax(0, 2), 1)
256 | assert.strictEqual(Hmax(0, 3), 0)
257 | assert.strictEqual(Hmax(0, Number.MAX_VALUE), 1)
258 | })
259 |
260 | it('works when a is 1', () => {
261 | assert.strictEqual(Hmax(1, 0), 1)
262 | assert.strictEqual(Hmax(1, 1), 1)
263 | assert.strictEqual(Hmax(1, 2), 1)
264 | assert.strictEqual(Hmax(1, 3), 1)
265 | assert.strictEqual(Hmax(1, Number.MAX_VALUE), 1)
266 | })
267 |
268 | it('works when a is 2', () => {
269 | assert.strictEqual(Hmax(2, 0), 1)
270 | assert.strictEqual(Hmax(2, 1), 2)
271 | assert.strictEqual(Hmax(2, 2), 4)
272 | assert.strictEqual(Hmax(2, 3), Infinity)
273 | assert.strictEqual(Hmax(2, Number.MAX_VALUE), Infinity)
274 | })
275 |
276 | it('works when a is 3', () => {
277 | assert.strictEqual(Hmax(3, 0), 1)
278 | assert.strictEqual(Hmax(3, 1), 3)
279 | assert.strictEqual(Hmax(3, 2), Infinity)
280 | assert.strictEqual(Hmax(3, 3), Infinity)
281 | assert.strictEqual(Hmax(3, Number.MAX_VALUE), Infinity)
282 | })
283 |
284 | it('works when a is 1000000', () => {
285 | assert.strictEqual(Hmax(1000000, 0), 1)
286 | assert.strictEqual(Hmax(1000000, 1), 1000000)
287 | assert.strictEqual(Hmax(1000000, 2), Infinity)
288 | assert.strictEqual(Hmax(1000000, 3), Infinity)
289 | assert.strictEqual(Hmax(1000000, Number.MAX_VALUE), Infinity)
290 | })
291 |
292 | describe('when a is Number.MAX_VALUE', () => {
293 | it('works when b is 0', () => {
294 | assert.strictEqual(Hmax(Number.MAX_VALUE, 0), 1)
295 | })
296 |
297 | it('works when b is 1', () => {
298 | assert.strictEqual(Hmax(Number.MAX_VALUE, 1), Number.MAX_VALUE)
299 | })
300 |
301 | it('works when b is 2', () => {
302 | assert.strictEqual(Hmax(Number.MAX_VALUE, 2), Infinity)
303 | })
304 |
305 | it('works when b is 3', () => {
306 | assert.strictEqual(Hmax(Number.MAX_VALUE, 3), Infinity)
307 | })
308 |
309 | it('works when b is Number.MAX_VALUE', () => {
310 | assert.strictEqual(Hmax(Number.MAX_VALUE, Number.MAX_VALUE), Infinity)
311 | })
312 | })
313 | })
314 | })
315 |
316 | describe('BigInt arguments', () => {
317 | // Overflow behaviour is not specified and undefined so don't test it, but we can go further
318 | describe('input validation', () => {
319 | it('throws on non-integer arguments', () => {
320 | assert.throws(() => H(0.5, 1n, 2n), Error('Can only hyperoperate on three numbers or three BigInts'))
321 | assert.throws(() => H(0n, 'one', 2n), Error('Can only hyperoperate on three numbers or three BigInts'))
322 | assert.throws(() => H(0n, 1n, Infinity), Error('Can only hyperoperate on three numbers or three BigInts'))
323 | })
324 |
325 | it('throws on negative arguments', () => {
326 | assert.throws(() => H(-1n, 1n, 2n), Error('Can only hyperoperate on non-negative integers'))
327 | assert.throws(() => H(0n, -2n, 2n), Error('Can only hyperoperate on non-negative integers'))
328 | assert.throws(() => H(0n, 1n, BigInt(-Number.MAX_VALUE)), Error('Can only hyperoperate on non-negative integers'))
329 | })
330 | })
331 |
332 | describe('H0 (successor)', () => {
333 | const H0 = H.bind(undefined, 0n)
334 | it('works', () => {
335 | assert.strictEqual(H0(0n, 0n), 1n)
336 | assert.strictEqual(H0(56n, 78n), 79n)
337 | assert.strictEqual(H0(1n, BigInt(Number.MAX_VALUE)), BigInt(Number.MAX_VALUE) + 1n)
338 | })
339 | })
340 |
341 | describe('H1 (addition)', () => {
342 | const H1 = H.bind(undefined, 1n)
343 | it('works', () => {
344 | assert.strictEqual(H1(33n, 44n), 77n)
345 | })
346 | })
347 |
348 | describe('H2 (multiplication)', () => {
349 | const H2 = H.bind(undefined, 2n)
350 | it('works', () => {
351 | assert.strictEqual(H2(6n, 7n), 42n)
352 | })
353 | })
354 |
355 | describe('H3 (exponentiation)', () => {
356 | const H3 = H.bind(undefined, 3n)
357 | it('works', () => {
358 | assert.strictEqual(H3(0n, 0n), 1n)
359 | assert.strictEqual(H3(0n, 1n), 0n)
360 | assert.strictEqual(H3(0n, 2n), 0n)
361 | assert.strictEqual(H3(0n, 153n), 0n)
362 | assert.strictEqual(H3(0n, BigInt(Number.MAX_VALUE)), 0n)
363 |
364 | assert.strictEqual(H3(1n, 0n), 1n)
365 | assert.strictEqual(H3(1n, 1n), 1n)
366 | assert.strictEqual(H3(1n, 2n), 1n)
367 | assert.strictEqual(H3(1n, 94379n), 1n)
368 | assert.strictEqual(H3(1n, BigInt(Number.MAX_SAFE_INTEGER)), 1n)
369 |
370 | assert.strictEqual(H3(2n, 0n), 1n)
371 | assert.strictEqual(H3(2n, 1n), 2n)
372 | assert.strictEqual(H3(2n, 2n), 4n)
373 | assert.strictEqual(H3(2n, 10n), 1024n)
374 | assert.strictEqual(H3(2n, 10n), 1024n)
375 |
376 | assert.strictEqual(H3(3n, 3n), 27n)
377 | assert.strictEqual(H3(5n, 5n), 3125n)
378 |
379 | assert.strictEqual(H3(70n, 0n), 1n)
380 | assert.strictEqual(H3(71n, 1n), 71n)
381 | assert.strictEqual(H3(20001n, 0n), 1n)
382 | assert.strictEqual(H3(9999999n, 1n), 9999999n)
383 | })
384 | })
385 |
386 | describe('H4 (tetration)', () => {
387 | const H4 = H.bind(undefined, 4n)
388 | it('works when a is 0n', () => {
389 | assert.strictEqual(H4(0n, 0n), 1n)
390 | assert.strictEqual(H4(0n, 1n), 0n)
391 | assert.strictEqual(H4(0n, 2n), 1n)
392 | assert.strictEqual(H4(0n, 3n), 0n)
393 | assert.strictEqual(H4(0n, 999n), 0n)
394 | assert.strictEqual(H4(0n, 1000n), 1n)
395 | assert.strictEqual(H4(0n, BigInt(Number.MAX_VALUE)), 1n)
396 | })
397 |
398 | it('works when a is 1n', () => {
399 | assert.strictEqual(H4(1n, 0n), 1n)
400 | assert.strictEqual(H4(1n, 1n), 1n)
401 | assert.strictEqual(H4(1n, 2n), 1n)
402 | assert.strictEqual(H4(1n, 3n), 1n)
403 | assert.strictEqual(H4(1n, 987n), 1n)
404 | assert.strictEqual(H4(1n, BigInt(Number.MAX_VALUE)), 1n)
405 | })
406 |
407 | describe('when a is 2n', () => {
408 | it('works when b is 0n', () => {
409 | assert.strictEqual(H4(2n, 0n), 1n)
410 | })
411 |
412 | it('works when b is 1n', () => {
413 | assert.strictEqual(H4(2n, 1n), 2n)
414 | })
415 |
416 | it('works when b is 2n', () => {
417 | assert.strictEqual(H4(2n, 2n), 4n)
418 | })
419 |
420 | it('works when b is 3n', () => {
421 | assert.strictEqual(H4(2n, 3n), 16n)
422 | })
423 |
424 | it('works when b is 4n', () => {
425 | assert.strictEqual(H4(2n, 4n), 65536n)
426 | })
427 |
428 | it('works when b is 5n', () => {
429 | assert.strictEqual(H4(2n, 5n), 2n ** 65536n) // a very large literal
430 | })
431 |
432 | it('works when b is 5n', () => {
433 | assert.throws(() => H4(2n, 6n), RangeError)
434 | })
435 |
436 | it('works when b is BigInt(Number.MAX_VALUE)', () => {
437 | assert.throws(() => H4(2n, BigInt(Number.MAX_VALUE)), RangeError)
438 | })
439 | })
440 |
441 | it('works when a is 3n', () => {
442 | assert.strictEqual(H4(3n, 0n), 1n)
443 | assert.strictEqual(H4(3n, 1n), 3n)
444 | assert.strictEqual(H4(3n, 2n), 27n)
445 | assert.strictEqual(H4(3n, 3n), 7625597484987n)
446 | assert.throws(() => H4(3n, 4n), RangeError)
447 | assert.throws(() => H4(3n, BigInt(Number.MAX_VALUE)), RangeError)
448 | })
449 |
450 | it('works when a is 4n', () => {
451 | assert.strictEqual(H4(4n, 0n), 1n)
452 | assert.strictEqual(H4(4n, 1n), 4n)
453 | assert.strictEqual(H4(4n, 2n), 256n)
454 | assert.strictEqual(H4(4n, 3n), 4n ** 4n ** 4n)
455 | assert.throws(() => H4(4n, 4n), RangeError)
456 | assert.throws(() => H4(4n, BigInt(Number.MAX_VALUE)), RangeError)
457 | })
458 |
459 | it('works when a is 5n', () => {
460 | assert.strictEqual(H4(5n, 0n), 1n)
461 | assert.strictEqual(H4(5n, 1n), 5n)
462 | assert.strictEqual(H4(5n, 2n), 3125n)
463 | assert.strictEqual(H4(5n, 3n), 5n ** 3125n) // a very large literal
464 | assert.throws(() => H4(5n, 4n), RangeError)
465 | assert.throws(() => H4(5n, BigInt(Number.MAX_VALUE)), RangeError)
466 | })
467 |
468 | it('works when a is 143n', () => {
469 | assert.strictEqual(H4(143n, 0n), 1n)
470 | assert.strictEqual(H4(143n, 1n), 143n)
471 | assert.strictEqual(H4(143n, 2n), 143n ** 143n) // medium-sized literal
472 | assert.throws(() => H4(143n, 3n), RangeError)
473 | assert.throws(() => H4(143n, BigInt(Number.MAX_VALUE)), RangeError)
474 | })
475 |
476 | it('works when a is 144n', () => {
477 | assert.strictEqual(H4(144n, 0n), 1n)
478 | assert.strictEqual(H4(144n, 1n), 144n)
479 | assert.strictEqual(H4(144n, 2n), 144n ** 144n) // medium-sized literal
480 | assert.throws(() => H4(144n, 3n), RangeError)
481 | assert.throws(() => H4(144n, BigInt(Number.MAX_VALUE)), RangeError)
482 | })
483 |
484 | it('works when a is BigInt(Number.MAX_VALUE)', () => {
485 | assert.strictEqual(H4(BigInt(Number.MAX_VALUE), 0n), 1n)
486 | assert.strictEqual(H4(BigInt(Number.MAX_VALUE), 1n), BigInt(Number.MAX_VALUE))
487 | assert.throws(() => H4(BigInt(Number.MAX_VALUE), 2n), RangeError)
488 | assert.throws(() => H4(BigInt(Number.MAX_VALUE), BigInt(Number.MAX_VALUE)), RangeError)
489 | })
490 | })
491 |
492 | describe('H5 (pentation)', () => {
493 | const H5 = H.bind(undefined, 5n)
494 | it('works', () => {
495 | assert.strictEqual(H5(0n, 0n), 1n)
496 | assert.strictEqual(H5(0n, 1n), 0n)
497 | assert.strictEqual(H5(0n, 2n), 1n)
498 | assert.strictEqual(H5(0n, 999n), 0n)
499 | assert.strictEqual(H5(0n, BigInt(Number.MAX_VALUE)), 1n)
500 |
501 | assert.strictEqual(H5(1n, 0n), 1n)
502 | assert.strictEqual(H5(1n, 1n), 1n)
503 | assert.strictEqual(H5(1n, 10000078n), 1n)
504 | assert.strictEqual(H5(1n, BigInt(Number.MAX_VALUE)), 1n)
505 |
506 | assert.strictEqual(H5(2n, 0n), 1n)
507 | assert.strictEqual(H5(2n, 1n), 2n)
508 | assert.strictEqual(H5(2n, 2n), 4n)
509 | assert.strictEqual(H5(2n, 3n), 65536n)
510 | assert.throws(() => H5(2n, 4n), RangeError)
511 | assert.throws(() => H5(2n, BigInt(Number.MAX_VALUE)), RangeError)
512 |
513 | assert.strictEqual(H5(3n, 0n), 1n)
514 | assert.strictEqual(H5(3n, 1n), 3n)
515 | assert.strictEqual(H5(3n, 2n), 7625597484987n)
516 | assert.throws(() => H5(3n, 3n), RangeError)
517 | assert.throws(() => H5(3n, BigInt(Number.MAX_VALUE)), RangeError)
518 |
519 | assert.strictEqual(H5(4n, 0n), 1n)
520 | assert.strictEqual(H5(4n, 1n), 4n)
521 | assert.throws(() => H5(4n, 2n), RangeError)
522 | assert.throws(() => H5(4n, BigInt(Number.MAX_VALUE)), RangeError)
523 |
524 | assert.strictEqual(H5(BigInt(Number.MAX_VALUE), 0n), 1n)
525 | assert.strictEqual(H5(BigInt(Number.MAX_VALUE), 1n), BigInt(Number.MAX_VALUE))
526 | assert.throws(() => H5(BigInt(Number.MAX_VALUE), 2n), RangeError)
527 | assert.throws(() => H5(BigInt(Number.MAX_VALUE), BigInt(Number.MAX_VALUE)), RangeError)
528 | })
529 | })
530 |
531 | describe('H6 (hexation)', () => {
532 | const H6 = H.bind(undefined, 6n)
533 | it('works', () => {
534 | assert.strictEqual(H6(0n, 0n), 1n)
535 | assert.strictEqual(H6(0n, 1n), 0n)
536 | assert.strictEqual(H6(0n, 2n), 1n)
537 | assert.strictEqual(H6(0n, 3n), 0n)
538 | assert.strictEqual(H6(0n, BigInt(Number.MAX_VALUE)), 1n)
539 |
540 | assert.strictEqual(H6(1n, 0n), 1n)
541 | assert.strictEqual(H6(1n, 1n), 1n)
542 | assert.strictEqual(H6(1n, 2n), 1n)
543 | assert.strictEqual(H6(1n, 3n), 1n)
544 | assert.strictEqual(H6(1n, BigInt(Number.MAX_VALUE)), 1n)
545 |
546 | assert.strictEqual(H6(2n, 0n), 1n)
547 | assert.strictEqual(H6(2n, 1n), 2n)
548 | assert.strictEqual(H6(2n, 2n), 4n)
549 | assert.throws(() => H6(2n, 3n), RangeError)
550 | assert.throws(() => H6(2n, BigInt(Number.MAX_VALUE)), RangeError)
551 |
552 | assert.strictEqual(H6(3n, 0n), 1n)
553 | assert.strictEqual(H6(3n, 1n), 3n)
554 | assert.throws(() => H6(3n, 2n), RangeError)
555 | assert.throws(() => H6(3n, BigInt(Number.MAX_VALUE)), RangeError)
556 |
557 | assert.strictEqual(H6(BigInt(Number.MAX_VALUE), 0n), 1n)
558 | assert.strictEqual(H6(BigInt(Number.MAX_VALUE), 1n), BigInt(Number.MAX_VALUE))
559 | assert.throws(() => H6(BigInt(Number.MAX_VALUE), 2n), RangeError)
560 | assert.throws(() => H6(BigInt(Number.MAX_VALUE), 3n), RangeError)
561 | assert.throws(() => H6(BigInt(Number.MAX_VALUE), BigInt(Number.MAX_VALUE)), RangeError)
562 | })
563 | })
564 |
565 | describe('Hmax (BigInt(Number.MAX_VALUE)-ation)', () => {
566 | const Hmax = H.bind(undefined, BigInt(Number.MAX_VALUE))
567 | it('works when a is 0n', () => {
568 | assert.strictEqual(Hmax(0n, 0n), 1n)
569 | assert.strictEqual(Hmax(0n, 1n), 0n)
570 | assert.strictEqual(Hmax(0n, 2n), 1n)
571 | assert.strictEqual(Hmax(0n, 3n), 0n)
572 | assert.strictEqual(Hmax(0n, BigInt(Number.MAX_VALUE)), 1n)
573 | })
574 |
575 | it('works when a is 1n', () => {
576 | assert.strictEqual(Hmax(1n, 0n), 1n)
577 | assert.strictEqual(Hmax(1n, 1n), 1n)
578 | assert.strictEqual(Hmax(1n, 2n), 1n)
579 | assert.strictEqual(Hmax(1n, 3n), 1n)
580 | assert.strictEqual(Hmax(1n, BigInt(Number.MAX_VALUE)), 1n)
581 | })
582 |
583 | it('works when a is 2n', () => {
584 | assert.strictEqual(Hmax(2n, 0n), 1n)
585 | assert.strictEqual(Hmax(2n, 1n), 2n)
586 | assert.strictEqual(Hmax(2n, 2n), 4n)
587 | assert.throws(() => Hmax(2n, 3n), RangeError)
588 | assert.throws(() => Hmax(2n, BigInt(Number.MAX_VALUE)), RangeError)
589 | })
590 |
591 | it('works when a is 3n', () => {
592 | assert.strictEqual(Hmax(3n, 0n), 1n)
593 | assert.strictEqual(Hmax(3n, 1n), 3n)
594 | assert.throws(() => Hmax(3n, 2n), RangeError)
595 | assert.throws(() => Hmax(3n, 3n), RangeError)
596 | assert.throws(() => Hmax(3n, BigInt(Number.MAX_VALUE)), RangeError)
597 | })
598 |
599 | it('works when a is 1000000n', () => {
600 | assert.strictEqual(Hmax(1000000n, 0n), 1n)
601 | assert.strictEqual(Hmax(1000000n, 1n), 1000000n)
602 | assert.throws(() => Hmax(1000000n, 2n), RangeError)
603 | assert.throws(() => Hmax(1000000n, 3n), RangeError)
604 | assert.throws(() => Hmax(1000000n, BigInt(Number.MAX_VALUE)), RangeError)
605 | })
606 |
607 | describe('when a is BigInt(Number.MAX_VALUE)', () => {
608 | it('works when b is 0n', () => {
609 | assert.strictEqual(Hmax(BigInt(Number.MAX_VALUE), 0n), 1n)
610 | })
611 |
612 | it('works when b is 1n', () => {
613 | assert.strictEqual(Hmax(BigInt(Number.MAX_VALUE), 1n), BigInt(Number.MAX_VALUE))
614 | })
615 |
616 | it('works when b is 2n', () => {
617 | assert.throws(() => Hmax(BigInt(Number.MAX_VALUE), 2n), RangeError)
618 | })
619 |
620 | it('works when b is 3n', () => {
621 | assert.throws(() => Hmax(BigInt(Number.MAX_VALUE), 3n), RangeError)
622 | })
623 |
624 | it('works when b is BigInt(Number.MAX_VALUE)', () => {
625 | assert.throws(() => Hmax(BigInt(Number.MAX_VALUE), BigInt(Number.MAX_VALUE)), RangeError)
626 | })
627 | })
628 | })
629 | })
630 | })
631 |
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