feat: add/multiply arbitrarily many arguments; full cbrt(number)

Extends `add` and `multiply` generically so they can handle any number of
  arguments based on their binary implementations; they also pass a
  single argument through unchanged, and return 0 and 1, respectively, on
  no arguments.

  Modifies cbrt(number) so that when the returnTyping is `full`, returns
  all three complex cube roots.

src/core/TypeDispatcher.js

@@ -275,7 +275,8 @@ export class TypeDispatcher {
          throw new ReferenceError(`no method or value for key '${key}'`)
       }
       if (!Array.isArray(types)) types = [types]
-      if (types.some(T => T === Unknown)) {
+      // Unknown and union, i.e., OneOf(...), stymie resolution:
+      if (types.some(T => T === Unknown || T.unifies)) {
          if (!strategy) return this[key]
          const thisTypeOf = whichType(this.types)
          return (...args) => {

src/generic/__test__/arithmetic.spec.js

@@ -1,18 +1,53 @@
 import assert from 'assert'
 import math from '#nanomath'
-import {ReturnType, ReturnTyping} from '#core/Type.js'
+import {ReturnType, ReturnTyping, Unknown} from '#core/Type.js'
 
 const {Complex, NumberT} = math.types
 
 describe('generic arithmetic', () => {
+   const cplx = math.complex
    it('squares anything', () => {
       const sq = math.square
       assert.strictEqual(sq(7), 49)
       assert.strictEqual(ReturnType(math.square.resolve([NumberT])), NumberT)
-      assert.deepStrictEqual(sq(math.complex(3, 4)), math.complex(-7, 24))
+      assert.deepStrictEqual(sq(cplx(3, 4)), cplx(-7, 24))
-      const eyes = math.complex(0, 2)
+      const eyes = cplx(0, 2)
       assert.strictEqual(sq(eyes), -4)
       const sqFull = math.square.resolve(Complex(NumberT), ReturnTyping.full)
-      assert.deepStrictEqual(sqFull(eyes), math.complex(-4, 0))
+      assert.deepStrictEqual(sqFull(eyes), cplx(-4, 0))
+   })
+
+   it('adds up multiple arguments', () => {
+      const add = math.add
+      assert.strictEqual(add(), 0)
+      assert.strictEqual(add(1), 1)
+      assert.deepStrictEqual(add(cplx(2)), cplx(2))
+      assert.deepStrictEqual(
+         ReturnType(add.resolve([Complex(NumberT)])), Complex(NumberT))
+      assert.strictEqual(add(3, 4, 5), 12)
+      assert.deepStrictEqual(add(6, cplx(0, 7), 8), cplx(14, 7))
+      assert.strictEqual(
+         ReturnType(add.resolve([NumberT, Complex(NumberT), NumberT])),
+         Unknown) // loses track of whether it comes out real or complex
+      assert.deepStrictEqual(
+         add(9, cplx(0, 10), cplx(11), cplx(0, -10)), 20)
+      const saveTyping = math.config.returnTyping
+      math.config.returnTyping = ReturnTyping.full
+      assert.strictEqual(
+         ReturnType(add.resolve([NumberT, Complex(NumberT), NumberT])),
+         Complex(NumberT)) // now definite
+      assert.deepStrictEqual(
+         add(9, cplx(0, 10), cplx(11), cplx(0, -10)), cplx(20))
+      math.config.returnTyping = saveTyping
+   })
+
+   it('multiplies multiple arguments', () => {
+      const mult = math.multiply
+      assert.strictEqual(mult(), 1)
+      assert.strictEqual(mult(2), 2)
+      assert.deepStrictEqual(mult(cplx(3)), cplx(3))
+      assert.strictEqual(mult(4, 5, 6), 120)
+      assert.deepStrictEqual(mult(7, cplx(0, 8), 9), cplx(0, 504))
+      assert.deepStrictEqual(mult(10, cplx(0, 1), cplx(0, 2), 3), -60)
    })
 })

src/generic/arithmetic.js

@@ -1,4 +1,5 @@
-import {ReturnsAs} from './helpers.js'
+import {iterateBinary, ReturnsAs} from './helpers.js'
+import {plain} from "#number/helpers.js"
 
 import {Returns, ReturnType, ReturnTyping} from '#core/Type.js'
 import {match, Any} from '#core/TypePatterns.js'
@@ -18,3 +19,9 @@ export const square = match(Any, (math, T, strategy) => {
    const mult = math.multiply.resolve([T, T], strategy)
    return ReturnsAs(mult, t => mult(t, t))
 })
+
+export const add = iterateBinary('add')
+add.push(plain(() => 0))
+
+export const multiply = iterateBinary('multiply')
+multiply.push(plain(() => 1))

src/generic/helpers.js

@@ -1,3 +1,24 @@
 import {Returns, ReturnType} from '#core/Type.js'
+import {match, Any, Multiple} from '#core/TypePatterns.js'
 
 export const ReturnsAs = (g, f) => Returns(ReturnType(g), f)
+export const iterateBinary = operation => [
+   match(Any, (_math, T) => Returns(T, t => t)),
+   match([Any, Any, Any, Multiple(Any)], (math, [T, U, V, Rest], strategy) => {
+      const op1 = math[operation].resolve([T, U], strategy)
+      const op2 = math[operation].resolve([ReturnType(op1), V])
+      let finalOp = op2
+      let restOps = []
+      for (const Typ of Rest) {
+         finalOp = math[operation].resolve([ReturnType(finalOp), Typ])
+         restOps.push(finalOp)
+      }
+      return ReturnsAs(finalOp, (t, u, v, rest) => {
+         let result = op2(op1(t, u), v)
+         for (let i = 0; i < rest.length; ++i) {
+            result = restOps[i](result, rest[i])
+         }
+         return result
+      })
+   })
+]

src/number/__test__/arithmetic.spec.js

@@ -30,4 +30,25 @@ describe('number arithmetic', () => {
       assert.deepStrictEqual(math.sqrt(-4), math.complex(0, 2))
       math.config.returnTyping = ReturnTyping.free
    })
+   it('takes cube root of numbers appropriately', () => {
+      assert(isNaN(math.cbrt(NaN)))
+      assert.strictEqual(math.cbrt(8), 2)
+      assert.strictEqual(math.cbrt(-8), -2)
+      const cbrt10 = Math.cbrt(10)
+      assert.strictEqual(math.cbrt(10), cbrt10)
+      const saveTyping = math.config.returnTyping
+      math.config.returnTyping = ReturnTyping.full
+      assert(isNaN(math.cbrt(NaN)))
+      const cbrtIm = Math.sqrt(3) / 2
+      const cplx = math.complex
+      const rt8 = math.cbrt(8)
+      assert.deepStrictEqual(
+         rt8, [cplx(2), cplx(-1, 2 * cbrtIm), cplx(-1, -2 * cbrtIm)])
+      assert(math.equal(math.multiply.apply(null, rt8), cplx(8)))
+      assert.deepStrictEqual(
+         math.cbrt(10),
+         [cplx(cbrt10),
+            cplx(-cbrt10 / 2, cbrt10 * cbrtIm),
+            cplx(-cbrt10 / 2, -cbrt10 * cbrtIm)])
+   })
 })

src/number/arithmetic.js

@@ -3,6 +3,7 @@ import {NumberT} from './NumberT.js'
 import {OneOf, Returns, ReturnTyping, Undefined} from '#core/Type.js'
 import {match} from '#core/TypePatterns.js'
 import {Complex} from '#complex/Complex.js'
+import {ReturnsAs} from '#generic/helpers.js'
 
 const {conservative, full} = ReturnTyping
 
@@ -15,7 +16,7 @@ export const add = [
    match([NumberT, Undefined], Returns(NumberT, () => NaN))
 ]
 export const divide = plain((a, b) => a / b)
-export const cbrt = plain(a => {
+const numberCbrt = a => {
    if (a === 0) return a
    const negate = a < 0 
    if (negate) a = -a
@@ -25,7 +26,29 @@ export const cbrt = plain(a => {
       result = (a / (result * result) + (2 * result)) / 3
    }
    return negate ? -result : result
+}
+const cbrtIm = Math.sqrt(3) / 2
+export const cbrt = match(NumberT, (math, _N, strategy) => {
+   if (strategy === full && math.types.Complex && math.types.Vector) {
+      // return vector of all three complex roots, real one first
+      const C = Complex(NumberT)
+      const vec = math.vector.resolve([C, C, C])
+      const promote = math.complex.resolve([NumberT])
+      const cplx = math.complex.resolve([NumberT, NumberT])
+      return ReturnsAs(vec, x => {
+         const realroot = numberCbrt(x)
+         if (!isFinite(realroot)) {
+            const full = cplx(realroot, realroot)
+            return(promote(realroot), full, full)
+         }
+         return vec(promote(realroot),
+            cplx(-realroot / 2, realroot * cbrtIm),
+            cplx(-realroot / 2, -realroot * cbrtIm))
+      })
+   }
+   return Returns(NumberT, numberCbrt)
 })
+
 export const invert = plain(a => 1/a)
 export const multiply = [
    plain((a, b) => a * b),