feat: Template types (#45)

Includes a full implementation of a type-homogeneous Tuple type, using the template types
  feature, as a demonstration/check of its operation.

Co-authored-by: Glen Whitney <glen@studioinfinity.org>
Reviewed-on: #45

test/_pocomath.mjs

@@ -103,4 +103,13 @@ describe('The default full pocomath instance "math"', () => {
       assert.strictEqual(math.choose(21n, 2n), 210n)
    })
 
+   it('calculates multi-way gcds and lcms', () => {
+      assert.strictEqual(math.gcd(30,105,42), 3)
+      assert.ok(
+         math.associate(
+            math.lcm(
+               math.complex(2n,1n), math.complex(1n,1n), math.complex(0n,1n)),
+            math.complex(1n,3n)))
+   })
+
 })

test/core/dependencyExtractor.mjs

@@ -1,5 +1,5 @@
 import assert from 'assert'
-import dependencyExtractor from '../../src/core/dependencyExtractor.mjs'
+import {dependencyExtractor} from '../../src/core/extractors.mjs'
 
 describe('dependencyExtractor', () => {
    it('will record the keys of a destructuring function', () => {

test/custom.mjs

@@ -8,6 +8,7 @@ import * as complex from '../src/complex/all.mjs'
 import * as complexAdd from '../src/complex/add.mjs'
 import * as complexNegate from '../src/complex/negate.mjs'
 import * as complexComplex from '../src/complex/complex.mjs'
+import * as bigintAdd from '../src/bigint/add.mjs'
 import * as concreteSubtract from '../src/generic/subtract.concrete.mjs'
 import * as genericSubtract from '../src/generic/subtract.mjs'
 import extendToComplex from '../src/complex/extendToComplex.mjs'
@@ -17,9 +18,10 @@ describe('A custom instance', () => {
    it("works when partially assembled", () => {
       bw.install(complex)
       // Not much we can call without any number types:
-      const i3 = {re: 0, im: 3}
-      assert.deepStrictEqual(bw.complex(0, 3), i3)
-      assert.deepStrictEqual(bw.chain(0).complex(3).value, i3)
+      assert.deepStrictEqual(bw.complex(undefined, undefined), undefined)
+      assert.deepStrictEqual(
+         bw.chain(undefined).complex(undefined).value,
+         undefined)
       // Don't have a way to negate things, for example:
       assert.throws(() => bw.negate(2), TypeError)
    })
@@ -33,7 +35,7 @@ describe('A custom instance', () => {
       assert.deepStrictEqual(
          bw.subtract(16, bw.add(3, bw.complex(0,4), 2)),
          math.complex(11, -4)) // note both instances coexist
-      assert.deepStrictEqual(bw.negate(math.complex(3, '8')).im, -8)
+      assert.deepStrictEqual(bw.negate(bw.complex(3, '8')).im, -8)
    })
 
    it("can be assembled piecemeal", () => {
@@ -112,4 +114,30 @@ describe('A custom instance', () => {
          math.complex(1n, -3n))
    })
 
+   it("instantiates templates correctly", () => {
+      const inst = new PocomathInstance('InstantiateTemplates')
+      inst.install(numberAdd)
+      inst.install({typeMerge: {'T,T': ({T}) => (t,u) => 'Merge to ' + T }})
+      assert.strictEqual(inst.typeMerge(7,6.28), 'Merge to number')
+      assert.strictEqual(inst.typeMerge(7,6), 'Merge to NumInt')
+      assert.strictEqual(inst.typeMerge(7.35,6), 'Merge to number')
+      inst.install(complexAdd)
+      inst.install(complexComplex)
+      inst.install(bigintAdd)
+      assert.strictEqual(
+         inst.typeMerge(6n, inst.complex(3n, 2n)),
+         'Merge to GaussianInteger')
+      assert.strictEqual(
+         inst.typeMerge(3, inst.complex(4.5,2.1)),
+         'Merge to Complex')
+      // The following is the current behavior, since 3 converts to 3+0i
+      // which is technically the same Complex type as 3n+0ni.
+      // This should clear up when Complex is templatized
+      assert.strictEqual(inst.typeMerge(3, inst.complex(3n)), 'Merge to Complex')
+      // But types that truly cannot be merged should throw a TypeError
+      // Should add a variation of this with a more usual type once there is
+      // one not interconvertible with others...
+      inst.install(genericSubtract)
+      assert.throws(() => inst.typeMerge(3, undefined), TypeError)
+   })
 })

test/tuple/_native.mjs

@@ -0,0 +1,114 @@
+import assert from 'assert'
+import math from '../../src/pocomath.mjs'
+
+describe('tuple', () => {
+   it('can be created and provide its length', () => {
+      assert.strictEqual(math.length(math.tuple(3, 5.2, 2)), 3)
+   })
+
+   it('does not allow unification by converting consecutive arguments', () => {
+      assert.throws(() => math.tuple(3, 5.2, 2n), /TypeError.*unif/)
+      // Hence, the order matters in a slightly unfortunate way,
+      // but I think being a little ragged in these edge cases is OK:
+      assert.throws(
+         () => math.tuple(3, 2n, math.complex(5.2)),
+         /TypeError.*unif/)
+      assert.deepStrictEqual(
+         math.tuple(3, math.complex(2n), 5.2),
+         {elts: [math.complex(3), math.complex(2n), math.complex(5.2)]})
+   })
+
+   it('can be tested for zero and equality', () => {
+      assert.strictEqual(math.isZero(math.tuple(0,1)), false)
+      assert.strictEqual(math.isZero(math.tuple(0n,0n,0n,0n)), true)
+      assert.strictEqual(math.isZero(math.tuple(0,0.001,0)), false)
+      assert.deepStrictEqual(math.complex(0,0), {re: 0, im:0})
+      assert.strictEqual(math.isZero(math.tuple(0,math.complex(0,0))), true)
+      assert.strictEqual(
+         math.equal(
+            math.tuple(0,math.complex(0,0.1)),
+            math.complex(math.tuple(0,0), math.tuple(0,0.1))),
+         true)
+      assert.strictEqual(
+         math.equal(math.tuple(3n,2n), math.tuple(3,2)),
+         false)
+   })
+
+   it('supports addition', () => {
+      assert.deepStrictEqual(
+         math.add(math.tuple(3,4,5), math.tuple(2,1,0)),
+         math.tuple(5,5,5))
+      assert.deepStrictEqual(
+         math.add(math.tuple(3.25,4.5,5), math.tuple(3,3)),
+         math.tuple(6.25,7.5,5))
+      assert.deepStrictEqual(
+         math.add(math.tuple(math.complex(2,3), 7), math.tuple(4, 5, 6)),
+         math.tuple(math.complex(6,3), math.complex(12), math.complex(6)))
+      assert.deepStrictEqual(
+         math.add(math.tuple(5,6), 7),
+         math.tuple(12,6))
+      assert.deepStrictEqual(
+         math.add(math.tuple(math.complex(5,4),6), 7),
+         math.tuple(math.complex(12,4),math.complex(6)))
+   })
+
+   it('supports subtraction', () => {
+      assert.deepStrictEqual(
+         math.subtract(math.tuple(3n,4n,5n), math.tuple(2n,1n,0n)),
+         math.tuple(1n,3n,5n))
+      assert.throws(
+         () => math.subtract(math.tuple(5,6), math.tuple(7)),
+         /RangeError/)
+   })
+
+   it('makes a tuple of complex and conjugates it', () => {
+      const complexTuple = math.tuple(
+         math.complex(3,1), math.complex(4,2.2), math.complex(5,3))
+      assert.deepStrictEqual(
+         math.complex(math.tuple(3,4,5), math.tuple(1,2.2,3)),
+         complexTuple)
+      assert.deepStrictEqual(
+         math.conjugate(complexTuple),
+         math.tuple(math.complex(3,-1), math.complex(4,-2.2), math.complex(5,-3)))
+   })
+
+   it('supports division', () => {
+      assert.deepStrictEqual(
+         math.divide(math.tuple(3,4,5),math.tuple(1,2,2)),
+         math.tuple(3,2,2.5))
+   })
+
+   it('supports multiplication', () => {
+      assert.deepStrictEqual(
+         math.multiply(math.tuple(3,4,5), math.tuple(1,2,2)),
+         math.tuple(3,8,10))
+   })
+
+   it('supports one and zero', () => {
+      assert.deepStrictEqual(
+         math.one(math.tuple(2n,3n,0n)),
+         math.tuple(1n,1n,1n))
+      assert.deepStrictEqual(
+         math.zero(math.tuple(math.complex(5,2), 3.4)),
+         math.tuple(math.complex(0), math.complex(0)))
+   })
+
+   it('supports quotient and roundquotient', () => {
+      const bigTuple = math.tuple(1n,2n,3n,4n,5n)
+      const bigOnes = math.one(bigTuple)
+      const threes = math.add(bigOnes, bigOnes, bigOnes)
+      assert.deepStrictEqual(
+         math.quotient(bigTuple, threes),
+         math.tuple(0n, 0n, 1n, 1n, 1n))
+      assert.deepStrictEqual(
+         math.roundquotient(bigTuple, threes),
+         math.tuple(0n, 1n, 1n, 1n, 2n))
+   })
+
+   it('supports sqrt', () => {
+      assert.deepStrictEqual(
+         math.sqrt(math.tuple(4,-4,2.25)),
+         math.tuple(2, math.complex(0,2), 1.5))
+   })
+
+})