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.
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6 changed files with 115 additions and 7 deletions
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@ -3,6 +3,7 @@ import {NumberT} from './NumberT.js'
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import {OneOf, Returns, ReturnTyping, Undefined} from '#core/Type.js'
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import {match} from '#core/TypePatterns.js'
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import {Complex} from '#complex/Complex.js'
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import {ReturnsAs} from '#generic/helpers.js'
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const {conservative, full} = ReturnTyping
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@ -15,7 +16,7 @@ export const add = [
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match([NumberT, Undefined], Returns(NumberT, () => NaN))
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]
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export const divide = plain((a, b) => a / b)
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export const cbrt = plain(a => {
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const numberCbrt = a => {
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if (a === 0) return a
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const negate = a < 0
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if (negate) a = -a
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@ -25,7 +26,29 @@ export const cbrt = plain(a => {
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result = (a / (result * result) + (2 * result)) / 3
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}
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return negate ? -result : result
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}
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const cbrtIm = Math.sqrt(3) / 2
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export const cbrt = match(NumberT, (math, _N, strategy) => {
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if (strategy === full && math.types.Complex && math.types.Vector) {
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// return vector of all three complex roots, real one first
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const C = Complex(NumberT)
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const vec = math.vector.resolve([C, C, C])
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const promote = math.complex.resolve([NumberT])
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const cplx = math.complex.resolve([NumberT, NumberT])
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return ReturnsAs(vec, x => {
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const realroot = numberCbrt(x)
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if (!isFinite(realroot)) {
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const full = cplx(realroot, realroot)
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return(promote(realroot), full, full)
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}
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return vec(promote(realroot),
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cplx(-realroot / 2, realroot * cbrtIm),
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cplx(-realroot / 2, -realroot * cbrtIm))
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})
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}
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return Returns(NumberT, numberCbrt)
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})
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export const invert = plain(a => 1/a)
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export const multiply = [
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plain((a, b) => a * b),
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