{"version":3,"file":"cubic-BL6dpuHh.mjs","names":["equals","make","fromVector","fromPoints","solve","toSolver","solveInverse","Solution.none","Solution.one","toInverseSolver","monotonicity","isMonotonic","isIncreasing","isDecreasing","asMonotonic","asIncreasing","asDecreasing","coefficients","derivative","antiderivative","domain","Interval.make","Solution.isNone","range","Interval.fromMinMax","unitRange","length","Interval.size","fromPoints","make","equals","fromVector","solve","toSolver","solveInverse","Linear.solveInverse","Linear.make","Solution.none","Solution.one","Solution.two","toInverseSolver","coefficients","derivative","roots","Solution.match","Vector2.make","monotonicity","Interval.size","Linear.monotonicity","Interval.contains","Interval.toOpen","Monotonicity.fromComparison","isMonotonic","Monotonicity.isStrict","isIncreasing","isDecreasing","asMonotonic","asIncreasing","asDecreasing","domain","Interval.fromMinMax","range","Linear.range","unitRange","Interval.unit","length","Linear.length","Linear.solve","curvature","make","isCubicPolynomial","equals","fromVector","fromPoints","solve","toSolver","solveInverse","Quadratic.solveInverse","Quadratic.make","Solution.fromArray","toInverseSolver","coefficients","derivative","subdivide","roots","extrema","Quadratic.roots","monotonicity","Interval.size","Linear.monotonicity","Linear.make","Quadratic.monotonicity","Interval.filter","Interval.toOpen","Monotonicity.fromComparison","isMonotonic","Monotonicity.isStrict","isIncreasing","isDecreasing","asMonotonic","asIncreasing","asDecreasing","domain","Interval.fromMinMax","range","unitRange","Interval.unit","length","Linear.length","Quadratic.length","Interval.scaleShift","Interval.biunit","Quadratic.solve","curvature","Quadratic.derivative","Linear.solve","internal.isCubicPolynomial","internal.equals","internal.make","internal.fromVector","internal.fromPoints","internal.solve","internal.toSolver","internal.solveInverse","internal.toInverseSolver","internal.coefficients","internal.derivative","internal.subdivide","internal.roots","internal.extrema","internal.monotonicity","internal.isMonotonic","internal.isIncreasing","internal.isDecreasing","internal.asMonotonic","internal.asIncreasing","internal.asDecreasing","internal.domain","internal.range","internal.unitRange","internal.length","internal.curvature"],"sources":["../../src/polynomial/quadratic.internal.circular.ts","../../src/polynomial/linear.internal.ts","../../src/polynomial/cubic.internal.circular.ts","../../src/polynomial/quadratic.internal.ts","../../src/length.ts","../../src/polynomial/cubic.internal.ts","../../src/polynomial/cubic.ts"],"sourcesContent":["import { Pipeable } from '../utils.ts'\nimport type { QuadraticPolynomial } from './quadratic.ts'\nimport { PolynomialTraits } from './traits.ts'\n\nexport const QuadraticPolynomialTypeId: unique symbol = Symbol.for('curvy/polynomial/quadratic')\nexport type QuadraticPolynomialTypeId = typeof QuadraticPolynomialTypeId\n\n/** @internal */\nexport class QuadraticPolynomialImpl extends Pipeable implements QuadraticPolynomial {\n readonly [QuadraticPolynomialTypeId]: QuadraticPolynomialTypeId = QuadraticPolynomialTypeId\n declare readonly [PolynomialTraits]: unknown\n\n readonly c0: number\n readonly c1: number\n readonly c2: number\n\n constructor(c0 = 0, c1 = 0, c2 = 0) {\n super()\n\n this.c0 = c0\n this.c1 = c1\n this.c2 = c2\n }\n}\n","import * as Interval from '../interval/interval.ts'\nimport * as Monotonicity from '../monotonicity/monotonicity.ts'\nimport { dual, Pipeable } from '../utils.ts'\nimport * as Solution from '../solution/solution.ts'\nimport { invariant } from '../utils.ts'\nimport { epsEquals } from '../number.ts'\nimport type { Vector2 } from '../vector/vector2.ts'\nimport type { LinearPolynomial } from './linear.ts'\nimport type { Decreasing, Increasing, Monotonic } from './traits.ts'\nimport { PolynomialTraits } from './traits.ts'\nimport type { QuadraticPolynomial } from './quadratic.ts'\nimport { QuadraticPolynomialImpl } from './quadratic.internal.circular.ts'\n\nexport const LinearPolynomialTypeId: unique symbol = Symbol.for('curvy/linear')\nexport type LinearPolynomialTypeId = typeof LinearPolynomialTypeId\n\nclass LinearPolynomialImpl extends Pipeable implements LinearPolynomial {\n readonly [LinearPolynomialTypeId]: LinearPolynomialTypeId = LinearPolynomialTypeId\n declare readonly [PolynomialTraits]: unknown\n\n readonly c0: number\n readonly c1: number\n\n constructor(c0 = 0, c1 = 0) {\n super()\n\n this.c0 = c0\n this.c1 = c1\n }\n}\n\n/** @internal */\nexport const isLinearPolynomial = (v: unknown): v is LinearPolynomial =>\n typeof v === 'object' && v !== null && LinearPolynomialTypeId in v\n\n/** @internal */\nexport const equals = dual<\n (b: LinearPolynomial) => (a: LinearPolynomial) => boolean,\n (a: LinearPolynomial, b: LinearPolynomial) => boolean\n>(2, (a: LinearPolynomial, b: LinearPolynomial) => epsEquals(a.c0, b.c0) && epsEquals(a.c1, b.c1))\n\n/** @internal */\nexport const make = (c0 = 0, c1 = 0): LinearPolynomial => new LinearPolynomialImpl(c0, c1)\n\n/** @internal */\nexport const fromVector = (v: Vector2) => new LinearPolynomialImpl(v.x, v.y)\n\n/** @internal */\nexport const fromPointSlope = (p: Vector2, slope: number) =>\n new LinearPolynomialImpl(p.y - slope * p.x, slope)\n\n/** @internal */\nexport const fromPoints = (p1: Vector2, p2: Vector2) =>\n fromPointSlope(p1, (p2.y - p1.y) / (p2.x - p1.x))\n\n/** @internal */\nexport const solve = dual<\n (x: number) => (p: LinearPolynomial) => number,\n (p: LinearPolynomial, x: number) => number\n>(2, (p: LinearPolynomial, x: number) => p.c0 + x * p.c1)\n\n/** @internal */\nexport const toSolver = (p: LinearPolynomial) => (x: number) => solve(p, x)\n\n/** @internal */\nexport const solveInverse = dual<\n (y: number) => (p: LinearPolynomial) => Solution.AtMostOne,\n (p: LinearPolynomial, y: number) => Solution.AtMostOne\n>(2, (p: LinearPolynomial, y: number) => {\n if (p.c1 === 0) {\n return Solution.none\n }\n return Solution.one((y - p.c0) / p.c1)\n})\n\n/** @internal */\nexport const toInverseSolver = (p: LinearPolynomial) => (y: number) => solveInverse(p, y)\n\n/** @internal */\nexport const monotonicity = (p: LinearPolynomial): Monotonicity.GuaranteedMonotonicity =>\n p.c1 === 0 ? Monotonicity.Constant : p.c1 > 0 ? Monotonicity.Increasing : Monotonicity.Decreasing\n\n/** @internal */\nexport const isMonotonic = (p: LinearPolynomial): p is LinearPolynomial =>\n p.c1 !== 0\n\n/** @internal */\nexport const isIncreasing = (p: LinearPolynomial): p is LinearPolynomial =>\n p.c1 > 0\n\n/** @internal */\nexport const isDecreasing = (p: LinearPolynomial): p is LinearPolynomial =>\n p.c1 < 0\n\n/** @internal */\nexport const asMonotonic = (p: LinearPolynomial): LinearPolynomial => {\n invariant(isMonotonic(p), 'linear polynomial is not monotonic')\n return p\n}\n\n/** @internal */\nexport const asIncreasing = (p: LinearPolynomial): LinearPolynomial => {\n invariant(isIncreasing(p), 'linear polynomial is not increasing')\n return p\n}\n\n/** @internal */\nexport const asDecreasing = (p: LinearPolynomial): LinearPolynomial => {\n invariant(isDecreasing(p), 'linear polynomial is not decreasing')\n return p\n}\n\n/** @internal */\nexport const coefficients = (p: LinearPolynomial): readonly [number, number] => [p.c0, p.c1]\n\n/** @internal */\nexport const derivative = (p: LinearPolynomial) => p.c1\n\n/** @internal */\nexport const antiderivative = dual<\n (integrationConstant: number) => (p: LinearPolynomial) => QuadraticPolynomial,\n (p: LinearPolynomial, integrationConstant?: number) => QuadraticPolynomial\n>(\n (args) => isLinearPolynomial(args[0]),\n (p: LinearPolynomial, integrationConstant = 0) =>\n new QuadraticPolynomialImpl(integrationConstant, p.c0, p.c1 / 2),\n)\n\n/** @internal */\nexport const domain = dual<\n (range: Interval.Interval) => (p: LinearPolynomial) => Solution.AtMostOne,\n (p: LinearPolynomial, range: Interval.Interval) => Solution.AtMostOne\n>(2, (p: LinearPolynomial, r: Interval.Interval) => {\n if (p.c1 === 0) {\n if (r.start === p.c0 && r.end === p.c0) {\n return Solution.one(Interval.make(Number.NEGATIVE_INFINITY, Number.POSITIVE_INFINITY))\n }\n return Solution.none\n }\n\n const start = solveInverse(p, r.start)\n const end = solveInverse(p, r.end)\n\n if (Solution.isNone(start) || Solution.isNone(end)) {\n return Solution.none\n }\n\n return Solution.one(Interval.make(start.value, end.value))\n})\n\n/** @internal */\nexport const range = dual<\n (domain: Interval.Interval) => (p: LinearPolynomial) => Interval.Closed,\n (p: LinearPolynomial, domain: Interval.Interval) => Interval.Closed\n>(2, (p: LinearPolynomial, d: Interval.Interval) =>\n Interval.fromMinMax(solve(p, d.start), solve(p, d.end)),\n)\n\n/** @internal */\nexport const unitRange = (p: LinearPolynomial): Interval.Closed =>\n Interval.fromMinMax(p.c0, p.c0 + p.c1)\n\n/** @internal */\nexport const length = dual<\n (domain: Interval.Interval) => (p: LinearPolynomial) => number,\n (p: LinearPolynomial, domain: Interval.Interval) => number\n>(2, (p: LinearPolynomial, d: Interval.Interval) => {\n if (Interval.size(d) === 0) {\n return 0\n }\n\n if (p.c1 === 0) {\n return Interval.size(d)\n }\n\n return Math.sqrt(1 + p.c1 ** 2) * Interval.size(d)\n})\n","import { Pipeable } from '../utils.ts'\nimport type { CubicPolynomial } from './cubic.ts'\nimport { PolynomialTraits } from './traits.ts'\n\nexport const CubicPolynomialTypeId: unique symbol = Symbol.for('curvy/polynomial/cubic')\nexport type CubicPolynomialTypeId = typeof CubicPolynomialTypeId\n\n/** @internal */\nexport class CubicPolynomialImpl extends Pipeable implements CubicPolynomial {\n readonly [CubicPolynomialTypeId]: CubicPolynomialTypeId = CubicPolynomialTypeId\n declare readonly [PolynomialTraits]: unknown\n\n readonly c0: number\n readonly c1: number\n readonly c2: number\n readonly c3: number\n\n constructor(c0 = 0, c1 = 0, c2 = 0, c3 = 0) {\n super()\n\n this.c0 = c0\n this.c1 = c1\n this.c2 = c2\n this.c3 = c3\n }\n}\n","import * as Interval from '../interval/interval.ts'\nimport { dual } from '../utils.ts'\nimport * as Solution from '../solution/solution.ts'\nimport { invariant } from '../utils.ts'\nimport { epsEquals } from '../number.ts'\nimport * as Vector2 from '../vector/vector2.ts'\nimport type { Vector3 } from '../vector/vector3.ts'\nimport type { CubicPolynomial } from './cubic.ts'\nimport { CubicPolynomialImpl } from './cubic.internal.circular.ts'\nimport * as Linear from './linear.internal.ts'\nimport * as Monotonicity from '../monotonicity/monotonicity.ts'\nimport type { QuadraticPolynomial } from './quadratic.ts'\nimport {\n QuadraticPolynomialImpl,\n QuadraticPolynomialTypeId,\n} from './quadratic.internal.circular.ts'\nimport type { Decreasing, Increasing, Monotonic } from './traits.ts'\n\n/** @internal */\nexport const fromPoints = (\n p0: Vector2.Vector2,\n p1: Vector2.Vector2,\n p2: Vector2.Vector2,\n): QuadraticPolynomial => {\n // Newton's divided differences, then collected to monomial form.\n const f01 = (p1.y - p0.y) / (p1.x - p0.x)\n const f12 = (p2.y - p1.y) / (p2.x - p1.x)\n const f012 = (f12 - f01) / (p2.x - p0.x)\n\n return new QuadraticPolynomialImpl(\n p0.y - f01 * p0.x + f012 * p0.x * p1.x,\n f01 - f012 * (p0.x + p1.x),\n f012,\n )\n}\n\n/** @internal */\nexport const make = (c0 = 0, c1 = 0, c2 = 0): QuadraticPolynomial =>\n new QuadraticPolynomialImpl(c0, c1, c2)\n\n/** @internal */\nexport const isQuadraticPolynomial = (v: unknown): v is QuadraticPolynomial =>\n typeof v === 'object' && v !== null && QuadraticPolynomialTypeId in v\n\n/** @internal */\nexport const equals = dual<\n (b: QuadraticPolynomial) => (a: QuadraticPolynomial) => boolean,\n (a: QuadraticPolynomial, b: QuadraticPolynomial) => boolean\n>(\n 2,\n (a: QuadraticPolynomial, b: QuadraticPolynomial) =>\n epsEquals(a.c0, b.c0) && epsEquals(a.c1, b.c1) && epsEquals(a.c2, b.c2),\n)\n\n/** @internal */\nexport const fromVector = (v: Vector3) => new QuadraticPolynomialImpl(v.x, v.y, v.z)\n\n/** @internal */\nexport const solve = dual<\n (x: number) => (p: QuadraticPolynomial) => number,\n (p: QuadraticPolynomial, x: number) => number\n>(2, (p: QuadraticPolynomial, x: number) => p.c0 + x * p.c1 + x ** 2 * p.c2)\n\n/** @internal */\nexport const toSolver = (p: QuadraticPolynomial) => (x: number) => solve(p, x)\n\n/** @internal */\nexport const solveInverse: {\n (p: QuadraticPolynomial, y: number): Solution.AtMostTwo\n (y: number): (p: QuadraticPolynomial) => Solution.AtMostTwo\n} = dual<\n (y: number) => (p: QuadraticPolynomial) => Solution.AtMostTwo,\n (p: QuadraticPolynomial, y: number) => Solution.AtMostTwo\n>(2, (p: QuadraticPolynomial, y: number) => {\n // c2 = 0: the polynomial is actually linear in disguise. Defer rather than\n // dividing by zero in the quadratic formula.\n if (p.c2 === 0) {\n return Linear.solveInverse(Linear.make(p.c0, p.c1), y)\n }\n\n const discriminant = p.c1 ** 2 - 4 * p.c2 * (p.c0 - y)\n\n if (discriminant < 0) {\n return Solution.none\n }\n\n if (discriminant === 0) {\n return Solution.one(-p.c1 / (2 * p.c2))\n }\n\n const sqrtDiscriminant = Math.sqrt(discriminant)\n const a = (-p.c1 + sqrtDiscriminant) / (2 * p.c2)\n const b = (-p.c1 - sqrtDiscriminant) / (2 * p.c2)\n return a < b ? Solution.two(a, b) : Solution.two(b, a)\n})\n\n/** @internal */\nexport const toInverseSolver =\n (p: QuadraticPolynomial) =>\n (y: number): Solution.AtMostTwo =>\n solveInverse(p, y)\n\n/** @internal */\nexport const coefficients = (p: QuadraticPolynomial): readonly [number, number, number] => [\n p.c0,\n p.c1,\n p.c2,\n]\n\n/** @internal */\nexport const derivative = (p: QuadraticPolynomial) => Linear.make(p.c1, p.c2 * 2)\n\n/** @internal */\nexport const roots = (p: QuadraticPolynomial) => solveInverse(p, 0)\n\n/** @internal */\nexport const extreme = (p: QuadraticPolynomial) =>\n derivative(p).pipe(\n Linear.solveInverse(0),\n Solution.match({\n onNone: () => null,\n onSome: ({ value: t }) => Vector2.make(t, solve(p, t)),\n }),\n )\n\n/** @internal */\nexport const monotonicity = dual<\n (i: Interval.Interval) => (p: QuadraticPolynomial) => Monotonicity.Monotonicity,\n (p: QuadraticPolynomial, i?: Interval.Interval) => Monotonicity.Monotonicity\n>(\n (args) => isQuadraticPolynomial(args[0]),\n (p: QuadraticPolynomial, i?: Interval.Interval) => {\n invariant(\n i === undefined || Interval.size(i) > 0,\n 'monotonicity is undefined over a zero-width interval',\n )\n\n if (p.c2 === 0 && p.c1 === 0) {\n return Monotonicity.Constant\n }\n\n if (p.c2 === 0) {\n return Linear.monotonicity(Linear.make(p.c0, p.c1))\n }\n\n // c2 is non-zero, so the extreme is guaranteed to be non-null\n const e = extreme(p) as Vector2.Vector2\n\n // if there is no interval, or the extreme is within the interval,\n // the monotonicity is none\n if (i === undefined || Interval.contains(Interval.toOpen(i), e.x)) {\n return Monotonicity.None\n }\n\n return Monotonicity.fromComparison(solve(p, i.start), solve(p, i.end))\n },\n)\n\n/** @internal */\nexport const isMonotonic = dual<\n (\n i: Interval.Interval,\n ) => (p: QuadraticPolynomial) => p is QuadraticPolynomial,\n (p: QuadraticPolynomial, i?: Interval.Interval) => p is QuadraticPolynomial\n>((args) => isQuadraticPolynomial(args[0]), ((p: QuadraticPolynomial, i?: Interval.Interval) =>\n Monotonicity.isStrict(monotonicity(p, i as Interval.Interval))) as never)\n\n/** @internal */\nexport const isIncreasing = dual<\n (\n i: Interval.Interval,\n ) => (p: QuadraticPolynomial) => p is QuadraticPolynomial,\n (p: QuadraticPolynomial, i?: Interval.Interval) => p is QuadraticPolynomial\n>(\n (args) => isQuadraticPolynomial(args[0]),\n ((p: QuadraticPolynomial, i?: Interval.Interval) =>\n monotonicity(p, i as Interval.Interval) === Monotonicity.Increasing) as never,\n)\n\n/** @internal */\nexport const isDecreasing = dual<\n (\n i: Interval.Interval,\n ) => (p: QuadraticPolynomial) => p is QuadraticPolynomial,\n (p: QuadraticPolynomial, i?: Interval.Interval) => p is QuadraticPolynomial\n>(\n (args) => isQuadraticPolynomial(args[0]),\n ((p: QuadraticPolynomial, i?: Interval.Interval) =>\n monotonicity(p, i as Interval.Interval) === Monotonicity.Decreasing) as never,\n)\n\n/** @internal */\nexport const asMonotonic = (\n p: QuadraticPolynomial,\n i?: Interval.Interval,\n): QuadraticPolynomial => {\n invariant(isMonotonic(p, i as Interval.Interval), 'quadratic polynomial is not monotonic')\n return p\n}\n\n/** @internal */\nexport const asIncreasing = (\n p: QuadraticPolynomial,\n i?: Interval.Interval,\n): QuadraticPolynomial => {\n invariant(isIncreasing(p, i as Interval.Interval), 'quadratic polynomial is not increasing')\n return p\n}\n\n/** @internal */\nexport const asDecreasing = (\n p: QuadraticPolynomial,\n i?: Interval.Interval,\n): QuadraticPolynomial => {\n invariant(isDecreasing(p, i as Interval.Interval), 'quadratic polynomial is not decreasing')\n return p\n}\n\n/** @internal */\nexport const antiderivative = dual<\n (integrationConstant: number) => (p: QuadraticPolynomial) => CubicPolynomial,\n (p: QuadraticPolynomial, integrationConstant?: number) => CubicPolynomial\n>(\n 2,\n (p: QuadraticPolynomial, integrationConstant = 0) =>\n new CubicPolynomialImpl(integrationConstant, p.c0, p.c1 / 2, p.c2 / 3),\n)\n\n/** @internal */\nexport const domain = dual<\n (range: Interval.Interval) => (p: QuadraticPolynomial) => Solution.AtMostOne,\n (p: QuadraticPolynomial, range: Interval.Interval) => Solution.AtMostOne\n>(2, (p: QuadraticPolynomial, r: Interval.Interval) => {\n const start = solveInverse(p, r.start)\n const end = solveInverse(p, r.end)\n\n if (start.length === 0 && end.length === 0) {\n return Solution.none\n }\n\n return Solution.one(Interval.fromMinMax(...start, ...end))\n})\n\n/** @internal */\nexport const range = dual<\n (domain: Interval.Interval) => (p: QuadraticPolynomial) => Interval.Closed,\n (p: QuadraticPolynomial, domain: Interval.Interval) => Interval.Closed\n>(2, (p: QuadraticPolynomial, d: Interval.Interval) => {\n if (p.c2 === 0) {\n return Linear.range(Linear.make(p.c0, p.c1), d)\n }\n\n const e = extreme(p)\n\n return e !== null && Interval.contains(d, e.x)\n ? Interval.fromMinMax(solve(p, d.start), solve(p, d.end), e.y)\n : Interval.fromMinMax(solve(p, d.start), solve(p, d.end))\n})\n\n/** @internal */\nexport const unitRange = (p: QuadraticPolynomial): Interval.Closed => range(p, Interval.unit)\n\n/** @internal */\nexport const length = dual<\n (domain: Interval.Interval) => (p: QuadraticPolynomial) => number,\n (p: QuadraticPolynomial, domain: Interval.Interval) => number\n>(2, (p: QuadraticPolynomial, dom: Interval.Interval) => {\n if (Interval.size(dom) === 0) {\n return 0\n }\n\n if (p.c2 === 0) {\n return Linear.length(Linear.make(p.c0, p.c1), dom)\n }\n\n const dp = derivative(p)\n\n const derivativeStart = Linear.solve(dp, dom.start)\n const sqrtStart = Math.sqrt(1 + derivativeStart ** 2)\n const evalStart =\n (derivativeStart * sqrtStart + Math.log(Math.abs(derivativeStart + sqrtStart))) / (4 * p.c2)\n\n const derivativeEnd = Linear.solve(dp, dom.end)\n const sqrtEnd = Math.sqrt(1 + derivativeEnd ** 2)\n const evalEnd =\n (derivativeEnd * sqrtEnd + Math.log(Math.abs(derivativeEnd + sqrtEnd))) / (4 * p.c2)\n\n return evalEnd - evalStart\n})\n\n/** @internal */\nexport const curvature = dual<\n (x: number) => (p: QuadraticPolynomial) => number,\n (p: QuadraticPolynomial, x: number) => number\n>(\n 2,\n (p: QuadraticPolynomial, x: number) =>\n Math.abs(2 * p.c2) / (1 + (Linear.solve(derivative(p), x) ** 2) ** 1.5),\n)\n","export const GL32_X0 = 0.9972638618494816\nexport const GL32_X1 = 0.9856115115452684\nexport const GL32_X2 = 0.9647622555875064\nexport const GL32_X3 = 0.9349060759377397\nexport const GL32_X4 = 0.8963211557660521\nexport const GL32_X5 = 0.84936761373257\nexport const GL32_X6 = 0.7944837959679424\nexport const GL32_X7 = 0.7321821187402897\nexport const GL32_X8 = 0.6630442669302152\nexport const GL32_X9 = 0.5877157572407623\nexport const GL32_X10 = 0.5068999089322294\nexport const GL32_X11 = 0.42135127613063533\nexport const GL32_X12 = 0.33186860228212767\nexport const GL32_X13 = 0.23928736225213706\nexport const GL32_X14 = 0.1444719615827965\nexport const GL32_X15 = 0.04830766568773831\nexport const GL32_W0 = 0.007018610009470136\nexport const GL32_W1 = 0.01627439473090571\nexport const GL32_W2 = 0.02539206530926214\nexport const GL32_W3 = 0.03427386291302141\nexport const GL32_W4 = 0.042835898022226704\nexport const GL32_W5 = 0.050998059262376154\nexport const GL32_W6 = 0.05868409347853558\nexport const GL32_W7 = 0.06582222277636195\nexport const GL32_W8 = 0.07234579410884862\nexport const GL32_W9 = 0.07819389578707044\nexport const GL32_W10 = 0.08331192422694672\nexport const GL32_W11 = 0.08765209300440374\nexport const GL32_W12 = 0.0911738786957639\nexport const GL32_W13 = 0.09384439908080454\nexport const GL32_W14 = 0.09563872007927485\nexport const GL32_W15 = 0.09654008851472785\n","import * as Interval from '../interval/interval.ts'\nimport {\n GL32_W0,\n GL32_W1,\n GL32_W2,\n GL32_W3,\n GL32_W4,\n GL32_W5,\n GL32_W6,\n GL32_W7,\n GL32_W8,\n GL32_W9,\n GL32_W10,\n GL32_W11,\n GL32_W12,\n GL32_W13,\n GL32_W14,\n GL32_W15,\n GL32_X0,\n GL32_X1,\n GL32_X2,\n GL32_X3,\n GL32_X4,\n GL32_X5,\n GL32_X6,\n GL32_X7,\n GL32_X8,\n GL32_X9,\n GL32_X10,\n GL32_X11,\n GL32_X12,\n GL32_X13,\n GL32_X14,\n GL32_X15,\n} from '../length.ts'\nimport * as Monotonicity from '../monotonicity/monotonicity.ts'\nimport { dual } from '../utils.ts'\nimport * as Solution from '../solution/solution.ts'\nimport { invariant } from '../utils.ts'\nimport { clampToZero, epsEquals } from '../number.ts'\nimport type * as Vector2 from '../vector/vector2.ts'\nimport type { Vector4 } from '../vector/vector4.ts'\nimport type { CubicPolynomial } from './cubic.ts'\nimport { CubicPolynomialImpl, CubicPolynomialTypeId } from './cubic.internal.circular.ts'\nimport type { Decreasing, Increasing, Monotonic } from './traits.ts'\nimport * as Linear from './linear.internal.ts'\nimport * as Quadratic from './quadratic.internal.ts'\n\n/** @internal */\nexport const make = (c0 = 0, c1 = 0, c2 = 0, c3 = 0): CubicPolynomial =>\n new CubicPolynomialImpl(c0, c1, c2, c3)\n\n/** @internal */\nexport const isCubicPolynomial = (v: unknown): v is CubicPolynomial =>\n typeof v === 'object' && v !== null && CubicPolynomialTypeId in v\n\n/** @internal */\nexport const equals = dual<\n (b: CubicPolynomial) => (a: CubicPolynomial) => boolean,\n (a: CubicPolynomial, b: CubicPolynomial) => boolean\n>(\n 2,\n (a: CubicPolynomial, b: CubicPolynomial) =>\n epsEquals(a.c0, b.c0) &&\n epsEquals(a.c1, b.c1) &&\n epsEquals(a.c2, b.c2) &&\n epsEquals(a.c3, b.c3),\n)\n\n/** @internal */\nexport const fromVector = (v: Vector4) => new CubicPolynomialImpl(v.x, v.y, v.z, v.w)\n\n/** @internal */\nexport const fromPoints = (\n p0: Vector2.Vector2,\n p1: Vector2.Vector2,\n p2: Vector2.Vector2,\n p3: Vector2.Vector2,\n): CubicPolynomial => {\n // Newton's divided differences, then collected to monomial form.\n const f01 = (p1.y - p0.y) / (p1.x - p0.x)\n const f12 = (p2.y - p1.y) / (p2.x - p1.x)\n const f23 = (p3.y - p2.y) / (p3.x - p2.x)\n const f012 = (f12 - f01) / (p2.x - p0.x)\n const f123 = (f23 - f12) / (p3.x - p1.x)\n const f0123 = (f123 - f012) / (p3.x - p0.x)\n\n return new CubicPolynomialImpl(\n p0.y - f01 * p0.x + f012 * p0.x * p1.x - f0123 * p0.x * p1.x * p2.x,\n f01 - f012 * (p0.x + p1.x) + f0123 * (p0.x * p1.x + p0.x * p2.x + p1.x * p2.x),\n f012 - f0123 * (p0.x + p1.x + p2.x),\n f0123,\n )\n}\n\n/** @internal */\nexport const solve = dual<\n (x: number) => (p: CubicPolynomial) => number,\n (p: CubicPolynomial, x: number) => number\n>(2, (p: CubicPolynomial, x: number) => p.c0 + x * p.c1 + x ** 2 * p.c2 + x ** 3 * p.c3)\n\n/** @internal */\nexport const toSolver = (p: CubicPolynomial) => (x: number) => solve(p, x)\n\n/** @internal */\nexport const solveInverse = dual<\n (y: number) => (p: CubicPolynomial) => Solution.AtMostThree,\n (p: CubicPolynomial, y: number) => Solution.AtMostThree\n>(2, (self: CubicPolynomial, y: number) => {\n // c3 = 0: the polynomial is actually quadratic-or-less in disguise. Defer to\n // the quadratic solver (which itself handles c2 = 0 by deferring to linear).\n if (self.c3 === 0) {\n return Quadratic.solveInverse(Quadratic.make(self.c0, self.c1, self.c2), y)\n }\n\n const shift = self.c2 / (3 * self.c3)\n\n const d0 = self.c2 ** 2 - 3 * self.c3 * self.c1\n const d1 = 2 * self.c2 ** 3 - 9 * self.c3 * self.c2 * self.c1 + 27 * self.c3 ** 2 * (self.c0 - y)\n\n const p = -d0 / (3 * self.c3 ** 2)\n const q = d1 / (27 * self.c3 ** 3)\n\n const discriminant = clampToZero(-(4 * p ** 3 + 27 * q ** 2), 1e-12)\n\n const roots = new Set()\n\n if (discriminant > 0) {\n const r = 2 * Math.sqrt(-p / 3)\n const theta = Math.acos(((3 * q) / (2 * p)) * Math.sqrt(-3 / p)) / 3\n const offset = (2 * Math.PI) / 3\n\n roots.add(r * Math.cos(theta + offset) - shift)\n roots.add(r * Math.cos(theta) - shift)\n roots.add(r * Math.cos(theta - offset) - shift)\n } else if (discriminant < 0) {\n const u = Math.sqrt(q ** 2 / 4 + p ** 3 / 27)\n\n const u1 = Math.cbrt(-q / 2 + u)\n const u2 = Math.cbrt(-q / 2 - u)\n\n roots.add(u1 + u2 - shift)\n } else if (d0 === 0) {\n roots.add(-shift)\n } else {\n roots.add((9 * self.c3 * (self.c0 - y) - self.c2 * self.c1) / (2 * d0))\n roots.add(\n (4 * self.c3 * self.c2 * self.c1 - 9 * self.c3 ** 2 * (self.c0 - y) - self.c2 ** 3) /\n (self.c3 * d0),\n )\n }\n\n return Solution.fromArray(Array.from(roots).toSorted((a, b) => a - b))\n})\n\n/** @internal */\nexport const toInverseSolver = (p: CubicPolynomial) => (y: number) => solveInverse(p, y)\n\n/** @internal */\nexport const coefficients = (p: CubicPolynomial): readonly [number, number, number, number] => [\n p.c0,\n p.c1,\n p.c2,\n p.c3,\n]\n\n/** @internal */\nexport const derivative = (p: CubicPolynomial) => Quadratic.make(p.c1, p.c2 * 2, p.c3 * 3)\n\n// Subdivides a cubic polynomial at parameter `t ∈ (0, 1)` into two new cubic\n// polynomials. The first polynomial's evaluation on `[0, 1]` matches the\n// original's evaluation on `[0, t]`; the second matches the original's\n// evaluation on `[t, 1]`. Concretely: `left(u) = p(t·u)` and\n// `right(u) = p(t + (1-t)·u)`. The left half is a uniform scale of the input\n// parameter by powers of `t`; the right half is a binomial expansion in\n// `(s + r·u)` with `s = t` and `r = 1 - t`.\n/** @internal */\nexport const subdivide = dual<\n (t: number) => (p: CubicPolynomial) => [CubicPolynomial, CubicPolynomial],\n (p: CubicPolynomial, t: number) => [CubicPolynomial, CubicPolynomial]\n>(2, (p: CubicPolynomial, t: number): [CubicPolynomial, CubicPolynomial] => {\n invariant(t > 0 && t < 1, 'subdivide parameter t must be in the open interval (0, 1)')\n\n const r = 1 - t\n const left = make(p.c0, p.c1 * t, p.c2 * t * t, p.c3 * t * t * t)\n const right = make(\n p.c0 + p.c1 * t + p.c2 * t * t + p.c3 * t * t * t,\n p.c1 * r + 2 * p.c2 * t * r + 3 * p.c3 * t * t * r,\n p.c2 * r * r + 3 * p.c3 * t * r * r,\n p.c3 * r * r * r,\n )\n return [left, right]\n})\n\n/** @internal */\nexport const roots = (p: CubicPolynomial): Solution.AtMostThree => solveInverse(p, 0)\n\n/** @internal */\nexport const extrema = (p: CubicPolynomial): Solution.AtMostTwo =>\n Quadratic.roots(derivative(p))\n\n/** @internal */\nexport const monotonicity = dual<\n (i: Interval.Interval) => (p: CubicPolynomial) => Monotonicity.Monotonicity,\n (p: CubicPolynomial, i?: Interval.Interval) => Monotonicity.Monotonicity\n>(\n (args) => isCubicPolynomial(args[0]),\n (p: CubicPolynomial, i?: Interval.Interval) => {\n invariant(\n i === undefined || Interval.size(i) > 0,\n 'monotonicity is undefined over a zero-width interval',\n )\n\n // shortcut to check for a horizontal line\n if (p.c3 === 0 && p.c2 === 0 && p.c1 === 0) {\n return Monotonicity.Constant\n }\n\n // shortcut to check for a non-horizontal line\n if (p.c3 === 0 && p.c2 === 0) {\n return Linear.monotonicity(Linear.make(p.c0, p.c1))\n }\n\n // without an interval, the monotonicity will be none if c3 or c2 are nonzero\n if (i === undefined) {\n return Monotonicity.None\n }\n\n if (p.c3 === 0) {\n return Quadratic.monotonicity(Quadratic.make(p.c0, p.c1, p.c2), i)\n }\n\n const e = Interval.filter(Interval.toOpen(i), [...extrema(p)])\n\n if (e.length > 0) {\n return Monotonicity.None\n }\n\n return Monotonicity.fromComparison(solve(p, i.start), solve(p, i.end))\n },\n)\n\n/** @internal */\nexport const isMonotonic = dual<\n (i: Interval.Interval) => (p: CubicPolynomial) => p is CubicPolynomial,\n (p: CubicPolynomial, i?: Interval.Interval) => p is CubicPolynomial\n>((args) => isCubicPolynomial(args[0]), ((p: CubicPolynomial, i?: Interval.Interval) =>\n Monotonicity.isStrict(monotonicity(p, i as Interval.Interval))) as never)\n\n/** @internal */\nexport const isIncreasing = dual<\n (i: Interval.Interval) => (p: CubicPolynomial) => p is CubicPolynomial,\n (p: CubicPolynomial, i?: Interval.Interval) => p is CubicPolynomial\n>(\n (args) => isCubicPolynomial(args[0]),\n ((p: CubicPolynomial, i?: Interval.Interval) =>\n monotonicity(p, i as Interval.Interval) === Monotonicity.Increasing) as never,\n)\n\n/** @internal */\nexport const isDecreasing = dual<\n (i: Interval.Interval) => (p: CubicPolynomial) => p is CubicPolynomial,\n (p: CubicPolynomial, i?: Interval.Interval) => p is CubicPolynomial\n>(\n (args) => isCubicPolynomial(args[0]),\n ((p: CubicPolynomial, i?: Interval.Interval) =>\n monotonicity(p, i as Interval.Interval) === Monotonicity.Decreasing) as never,\n)\n\n/** @internal */\nexport const asMonotonic = (\n p: CubicPolynomial,\n i?: Interval.Interval,\n): CubicPolynomial => {\n invariant(isMonotonic(p, i as Interval.Interval), 'cubic polynomial is not monotonic')\n return p\n}\n\n/** @internal */\nexport const asIncreasing = (\n p: CubicPolynomial,\n i?: Interval.Interval,\n): CubicPolynomial => {\n invariant(isIncreasing(p, i as Interval.Interval), 'cubic polynomial is not increasing')\n return p\n}\n\n/** @internal */\nexport const asDecreasing = (\n p: CubicPolynomial,\n i?: Interval.Interval,\n): CubicPolynomial => {\n invariant(isDecreasing(p, i as Interval.Interval), 'cubic polynomial is not decreasing')\n return p\n}\n\n/** @internal */\nexport const domain = dual<\n (range: Interval.Interval) => (p: CubicPolynomial) => Interval.Interval,\n (p: CubicPolynomial, range: Interval.Interval) => Interval.Interval\n>(2, (p: CubicPolynomial, r: Interval.Interval) =>\n Interval.fromMinMax(...solveInverse(p, r.start), ...solveInverse(p, r.end)),\n)\n\n/** @internal */\nexport const range = dual<\n (domain: Interval.Interval) => (p: CubicPolynomial) => Interval.Closed,\n (p: CubicPolynomial, domain: Interval.Interval) => Interval.Closed\n>(2, (p: CubicPolynomial, d: Interval.Interval) =>\n Interval.fromMinMax(\n solve(p, d.start),\n solve(p, d.end),\n ...Interval.filter(d, [...extrema(p)]).map((e) => solve(p, e)),\n ),\n)\n\n/** @internal */\nexport const unitRange = (p: CubicPolynomial): Interval.Closed => range(p, Interval.unit)\n\n/** @internal */\nexport const length = dual<\n (domain: Interval.Interval) => (p: CubicPolynomial) => number,\n (p: CubicPolynomial, domain: Interval.Interval) => number\n>(2, (p: CubicPolynomial, dom: Interval.Interval) => {\n if (Interval.size(dom) === 0) {\n return 0\n }\n\n if (p.c3 === 0) {\n if (p.c2 === 0) {\n return Linear.length(Linear.make(p.c0, p.c1), dom)\n }\n\n return Quadratic.length(Quadratic.make(p.c0, p.c1, p.c2), dom)\n }\n\n const d = derivative(p)\n\n const { scale, shift } = Interval.scaleShift(Interval.biunit, dom)\n\n return (\n (GL32_W0 * Math.sqrt(1 + Quadratic.solve(d, shift + scale * -GL32_X0) ** 2) +\n GL32_W0 * Math.sqrt(1 + Quadratic.solve(d, shift + scale * GL32_X0) ** 2) +\n GL32_W1 * Math.sqrt(1 + Quadratic.solve(d, shift + scale * -GL32_X1) ** 2) +\n GL32_W1 * Math.sqrt(1 + Quadratic.solve(d, shift + scale * GL32_X1) ** 2) +\n GL32_W2 * Math.sqrt(1 + Quadratic.solve(d, shift + scale * -GL32_X2) ** 2) +\n GL32_W2 * Math.sqrt(1 + Quadratic.solve(d, shift + scale * GL32_X2) ** 2) +\n GL32_W3 * Math.sqrt(1 + Quadratic.solve(d, shift + scale * -GL32_X3) ** 2) +\n GL32_W3 * Math.sqrt(1 + Quadratic.solve(d, shift + scale * GL32_X3) ** 2) +\n GL32_W4 * Math.sqrt(1 + Quadratic.solve(d, shift + scale * -GL32_X4) ** 2) +\n GL32_W4 * Math.sqrt(1 + Quadratic.solve(d, shift + scale * GL32_X4) ** 2) +\n GL32_W5 * Math.sqrt(1 + Quadratic.solve(d, shift + scale * -GL32_X5) ** 2) +\n GL32_W5 * Math.sqrt(1 + Quadratic.solve(d, shift + scale * GL32_X5) ** 2) +\n GL32_W6 * Math.sqrt(1 + Quadratic.solve(d, shift + scale * -GL32_X6) ** 2) +\n GL32_W6 * Math.sqrt(1 + Quadratic.solve(d, shift + scale * GL32_X6) ** 2) +\n GL32_W7 * Math.sqrt(1 + Quadratic.solve(d, shift + scale * -GL32_X7) ** 2) +\n GL32_W7 * Math.sqrt(1 + Quadratic.solve(d, shift + scale * GL32_X7) ** 2) +\n GL32_W8 * Math.sqrt(1 + Quadratic.solve(d, shift + scale * -GL32_X8) ** 2) +\n GL32_W8 * Math.sqrt(1 + Quadratic.solve(d, shift + scale * GL32_X8) ** 2) +\n GL32_W9 * Math.sqrt(1 + Quadratic.solve(d, shift + scale * -GL32_X9) ** 2) +\n GL32_W9 * Math.sqrt(1 + Quadratic.solve(d, shift + scale * GL32_X9) ** 2) +\n GL32_W10 * Math.sqrt(1 + Quadratic.solve(d, shift + scale * -GL32_X10) ** 2) +\n GL32_W10 * Math.sqrt(1 + Quadratic.solve(d, shift + scale * GL32_X10) ** 2) +\n GL32_W11 * Math.sqrt(1 + Quadratic.solve(d, shift + scale * -GL32_X11) ** 2) +\n GL32_W11 * Math.sqrt(1 + Quadratic.solve(d, shift + scale * GL32_X11) ** 2) +\n GL32_W12 * Math.sqrt(1 + Quadratic.solve(d, shift + scale * -GL32_X12) ** 2) +\n GL32_W12 * Math.sqrt(1 + Quadratic.solve(d, shift + scale * GL32_X12) ** 2) +\n GL32_W13 * Math.sqrt(1 + Quadratic.solve(d, shift + scale * -GL32_X13) ** 2) +\n GL32_W13 * Math.sqrt(1 + Quadratic.solve(d, shift + scale * GL32_X13) ** 2) +\n GL32_W14 * Math.sqrt(1 + Quadratic.solve(d, shift + scale * -GL32_X14) ** 2) +\n GL32_W14 * Math.sqrt(1 + Quadratic.solve(d, shift + scale * GL32_X14) ** 2) +\n GL32_W15 * Math.sqrt(1 + Quadratic.solve(d, shift + scale * -GL32_X15) ** 2) +\n GL32_W15 * Math.sqrt(1 + Quadratic.solve(d, shift + scale * GL32_X15) ** 2)) *\n scale\n )\n})\n\n/** @internal */\nexport const curvature = dual(2, (p: CubicPolynomial, x: number) => {\n const d = derivative(p)\n const dd = Quadratic.derivative(d)\n\n return Math.abs(Linear.solve(dd, x)) / (1 + Quadratic.solve(d, x) ** 2) ** 1.5\n})\n","import type { Closed, Interval } from '../interval/interval.ts'\nimport type { Pipeable } from '../utils.ts'\nimport type * as Solution from '../solution/solution.ts'\nimport type { Vector2 } from '../vector/vector2.ts'\nimport type { Vector4 } from '../vector/vector4.ts'\nimport * as internal from './cubic.internal.ts'\nimport type { CubicPolynomialTypeId } from './cubic.internal.circular.ts'\nimport type { Monotonicity } from '../monotonicity/monotonicity.ts'\nimport type { QuadraticPolynomial } from './quadratic.ts'\nimport type { Decreasing, Increasing, Monotonic, PolynomialTraits } from './traits.ts'\n\nexport type { Monotonic, Increasing, Decreasing } from './traits.ts'\n\n/**\n * A cubic polynomial.\n *\n * All fields are readonly and immutable, and all operations create new instances.\n *\n * The `Traits` type parameter is a phantom marker that accumulates trait\n * brands as the polynomial is refined via `isMonotonic` / `asMonotonic` and\n * friends. A cubic is monotonic only over an interval that avoids both of its\n * extrema (or globally, when c2 = c3 = 0 and c1 ≠ 0).\n *\n * @since 1.0.0\n */\nexport interface CubicPolynomial extends Pipeable {\n readonly [CubicPolynomialTypeId]: CubicPolynomialTypeId\n readonly [PolynomialTraits]: Traits\n\n /**\n * The coefficient of the x^0 term.\n */\n readonly c0: number\n /**\n * The coefficient of the x^1 term.\n */\n readonly c1: number\n /**\n * The coefficient of the x^2 term.\n */\n readonly c2: number\n /**\n * The coefficient of the x^3 term.\n */\n readonly c3: number\n}\n\n/**\n * Checks if a value is a `CubicPolynomial`.\n *\n * @param value - The value to check.\n * @returns `true` if the value is a `CubicPolynomial`, `false` otherwise.\n * @since 1.0.0\n */\nexport const isCubicPolynomial: (value: unknown) => value is CubicPolynomial =\n internal.isCubicPolynomial\n\nexport const equals: {\n /**\n * Checks if two `CubicPolynomial` instances are approximately equal within\n * the default absolute tolerance ({@link EPSILON}).\n *\n * @param a - The first polynomial.\n * @param b - The second polynomial.\n * @returns `true` when each pair of coefficients is within tolerance.\n * @since 1.1.0\n */\n (a: CubicPolynomial, b: CubicPolynomial): boolean\n /**\n * Checks if two `CubicPolynomial` instances are approximately equal within\n * the default absolute tolerance ({@link EPSILON}).\n *\n * @param b - The second polynomial.\n * @returns A function that takes the first polynomial and returns the comparison result.\n * @since 1.1.0\n */\n (b: CubicPolynomial): (a: CubicPolynomial) => boolean\n} = internal.equals\n\n/**\n * Creates a new `CubicPolynomial` instance.\n *\n * @param c0 - The coefficient of the x^0 term.\n * @param c1 - The coefficient of the x^1 term.\n * @param c2 - The coefficient of the x^2 term.\n * @param c3 - The coefficient of the x^3 term.\n */\nexport const make: (c0: number, c1: number, c2: number, c3: number) => CubicPolynomial =\n internal.make\n\n/**\n * Creates a new `CubicPolynomial` instance from a vector.\n *\n * @param v - The vector to convert.\n * @returns A new `CubicPolynomial` instance.\n * @since 1.0.0\n */\nexport const fromVector: (v: Vector4) => CubicPolynomial = internal.fromVector\n\n/**\n * Creates a new `CubicPolynomial` that interpolates the four given points,\n * treating each `Vector2` as an `(x, y)` pair. The four input `x` values must\n * be distinct.\n *\n * @param p0 - The first point.\n * @param p1 - The second point.\n * @param p2 - The third point.\n * @param p3 - The fourth point.\n * @returns The unique cubic polynomial passing through the four points.\n * @since 2.0.0\n */\nexport const fromPoints: (p0: Vector2, p1: Vector2, p2: Vector2, p3: Vector2) => CubicPolynomial =\n internal.fromPoints\n\nexport const solve: {\n /**\n * Solves a cubic polynomial for a given value of x.\n *\n * @param p - The cubic polynomial to solve.\n * @param x - The value of x to solve for.\n * @returns The result of the polynomial evaluation at x.\n * @since 1.0.0\n */\n (p: CubicPolynomial, x: number): number\n /**\n * Solves a cubic polynomial for a given value of x.\n *\n * @param x - The value of x to solve for.\n * @returns A function that takes a cubic polynomial and returns the result of the polynomial evaluation at x.\n * @since 1.0.0\n */\n (x: number): (p: CubicPolynomial) => number\n} = internal.solve\n\n/**\n * Converts a cubic polynomial to a solver function.\n *\n * @param p - The cubic polynomial to convert.\n * @returns A function that takes a value of x and returns the result of the polynomial evaluation at x.\n * @since 1.0.0\n */\nexport const toSolver: (p: CubicPolynomial) => (x: number) => number = internal.toSolver\n\nexport const solveInverse: {\n /**\n * Solves a monotonic cubic polynomial for a given value of y. Because the\n * polynomial is strictly monotonic, the inverse has at most one solution.\n *\n * @param p - The monotonic cubic polynomial.\n * @param y - The value of y to solve for.\n * @returns Zero or one solutions.\n * @since 2.0.0\n */\n (p: CubicPolynomial, y: number): Solution.AtMostOne\n /**\n * Solves a cubic polynomial for a given value of y.\n *\n * @param p - The cubic polynomial to solve.\n * @param y - The value of y to solve for.\n * @returns The roots of the polynomial equation p(x) = y.\n * @since 1.0.0\n */\n (p: CubicPolynomial, y: number): Solution.AtMostThree\n /**\n * Solves a cubic polynomial for a given value of y.\n *\n * @param y - The value of y to solve for.\n * @returns A function that takes a cubic polynomial and returns the roots\n * of the polynomial equation p(x) = y. Tightens to `Solution.AtMostOne` for\n * monotonic inputs.\n * @since 1.0.0\n */\n (y: number): {\n (p: CubicPolynomial): Solution.AtMostOne\n (p: CubicPolynomial): Solution.AtMostThree\n }\n} = internal.solveInverse as never\n\n/**\n * Converts a cubic polynomial to an inverse solver function.\n *\n * @param p - The cubic polynomial to convert.\n * @returns A function that takes a value of y and returns the roots of the polynomial equation p(x) = y.\n * @since 1.0.0\n */\nexport const toInverseSolver: (p: CubicPolynomial) => (y: number) => Solution.AtMostThree =\n internal.toInverseSolver\n\n/**\n * Returns the polynomial's coefficients as a tuple `[c0, c1, c2, c3]`.\n *\n * @param p - The cubic polynomial.\n * @returns The coefficients in monomial order.\n * @since 2.0.0\n */\nexport const coefficients: (p: CubicPolynomial) => readonly [number, number, number, number] =\n internal.coefficients\n\n/**\n * Calculates the derivative of a cubic polynomial.\n *\n * @param p - The cubic polynomial to differentiate.\n * @returns The derivative of the cubic polynomial.\n * @since 1.0.0\n */\nexport const derivative: (p: CubicPolynomial) => QuadraticPolynomial = internal.derivative\n\nexport const subdivide: {\n /**\n * Subdivides a cubic polynomial at parameter `t ∈ (0, 1)` into two new\n * cubic polynomials. The first polynomial's evaluation on `[0, 1]` matches\n * the original's on `[0, t]`; the second matches the original's on\n * `[t, 1]`. Equivalent to de Casteljau subdivision in Bernstein form,\n * performed directly in monomial form.\n *\n * @param p - The cubic polynomial to subdivide.\n * @param t - The split parameter; must be in the open interval `(0, 1)`.\n * @returns A `[left, right]` tuple of cubic polynomials.\n * @since 2.0.0\n */\n (p: CubicPolynomial, t: number): [CubicPolynomial, CubicPolynomial]\n /**\n * Subdivides a cubic polynomial at parameter `t ∈ (0, 1)`.\n *\n * @param t - The split parameter; must be in the open interval `(0, 1)`.\n * @returns A function that takes a polynomial and returns its `[left, right]` halves.\n * @since 2.0.0\n */\n (t: number): (p: CubicPolynomial) => [CubicPolynomial, CubicPolynomial]\n} = internal.subdivide\n\n/**\n * Calculates the roots of a cubic polynomial.\n *\n * @param p - The cubic polynomial to find the roots of.\n * @returns The roots of the cubic polynomial.\n * @since 1.0.0\n */\nexport const roots: (p: CubicPolynomial) => Solution.AtMostThree = internal.roots\n\n/**\n * Calculates the extrema of a cubic polynomial.\n *\n * @param p - The cubic polynomial to find the extrema of.\n * @returns The extrema of the cubic polynomial.\n * @since 1.0.0\n */\nexport const extrema: (p: CubicPolynomial) => Solution.AtMostTwo = internal.extrema\n\nexport const monotonicity: {\n /**\n * Calculates the monotonicity of a cubic polynomial. Throws when the\n * interval has zero width — the question is undefined at a single point.\n *\n * @param p - The cubic polynomial to analyze.\n * @param i - The interval to restrict the analysis to.\n * @returns The monotonicity of the cubic polynomial in the specified interval.\n * @since 1.0.0\n */\n (p: CubicPolynomial, i?: Interval): Monotonicity\n /**\n * Calculates the monotonicity of a cubic polynomial. Throws when the\n * interval has zero width.\n *\n * @param i - The interval to restrict the analysis to.\n * @returns A function that takes a cubic polynomial and returns the\n * monotonicity of the cubic polynomial in the specified interval.\n * @since 1.0.0\n */\n (i: Interval): (p: CubicPolynomial) => Monotonicity\n} = internal.monotonicity\n\n/**\n * Type-narrowing predicate: refines a `CubicPolynomial` to\n * `CubicPolynomial` when the polynomial is strictly monotonic\n * over the given interval (or globally, when no interval is given).\n *\n * @param p - The cubic polynomial to check.\n * @param i - Optional interval over which to check monotonicity.\n * @returns `true` when monotonicity is `Increasing` or `Decreasing`.\n * @since 2.0.0\n */\nexport const isMonotonic: {\n (p: CubicPolynomial, i?: Interval): p is CubicPolynomial\n (i: Interval): (p: CubicPolynomial) => p is CubicPolynomial\n} = internal.isMonotonic\n\n/**\n * Type-narrowing predicate: refines to `CubicPolynomial`.\n *\n * @since 2.0.0\n */\nexport const isIncreasing: {\n (p: CubicPolynomial, i?: Interval): p is CubicPolynomial\n (i: Interval): (p: CubicPolynomial) => p is CubicPolynomial\n} = internal.isIncreasing\n\n/**\n * Type-narrowing predicate: refines to `CubicPolynomial`.\n *\n * @since 2.0.0\n */\nexport const isDecreasing: {\n (p: CubicPolynomial, i?: Interval): p is CubicPolynomial\n (i: Interval): (p: CubicPolynomial) => p is CubicPolynomial\n} = internal.isDecreasing\n\n/**\n * Asserts that the cubic polynomial is monotonic, throwing on failure.\n *\n * @param p - The cubic polynomial to assert against.\n * @param i - Optional interval over which to check monotonicity.\n * @returns The same polynomial, typed with the `Monotonic` brand.\n * @throws When the polynomial is not monotonic over the given (or global) interval.\n * @since 2.0.0\n */\nexport const asMonotonic: (\n p: CubicPolynomial,\n i?: Interval,\n) => CubicPolynomial = internal.asMonotonic\n\n/**\n * Asserts that the cubic polynomial is increasing, throwing on failure.\n *\n * @since 2.0.0\n */\nexport const asIncreasing: (\n p: CubicPolynomial,\n i?: Interval,\n) => CubicPolynomial = internal.asIncreasing\n\n/**\n * Asserts that the cubic polynomial is decreasing, throwing on failure.\n *\n * @since 2.0.0\n */\nexport const asDecreasing: (\n p: CubicPolynomial,\n i?: Interval,\n) => CubicPolynomial = internal.asDecreasing\n\nexport const domain: {\n /**\n * Calculates the domain of a cubic polynomial.\n *\n * @param p - The cubic polynomial to analyze.\n * @param range - The range to restrict the analysis to.\n * @returns The domain of the cubic polynomial in the specified range.\n * @since 1.0.0\n */\n (p: CubicPolynomial, range: Interval): Interval\n /**\n * Calculates the domain of a cubic polynomial.\n *\n * @param range - The range to restrict the analysis to.\n * @returns A function that takes a cubic polynomial and returns the domain of the cubic polynomial in the specified range.\n * @since 1.0.0\n */\n (range: Interval): (p: CubicPolynomial) => Interval\n} = internal.domain\n\nexport const range: {\n /**\n * Calculates the range of a cubic polynomial.\n *\n * @param p - The cubic polynomial to analyze.\n * @param domain - The domain to restrict the analysis to.\n * @returns The range of the cubic polynomial in the specified domain.\n * @since 1.0.0\n */\n (p: CubicPolynomial, domain: Interval): Closed\n /**\n * Calculates the range of a cubic polynomial.\n *\n * @param domain - The domain to restrict the analysis to.\n * @returns A function that takes a cubic polynomial and returns the range of the cubic polynomial in the specified domain.\n * @since 1.0.0\n */\n (domain: Interval): (p: CubicPolynomial) => Closed\n} = internal.range\n\n/**\n * Calculates the range of a cubic polynomial over the unit interval `[0, 1]`.\n * Equivalent to `range(p, Interval.unit)` — accounts for up to two interior\n * extrema in `[0, 1]`.\n *\n * @param p - The cubic polynomial.\n * @returns The closed range of the polynomial over `[0, 1]`.\n * @since 2.0.0\n */\nexport const unitRange: (p: CubicPolynomial) => Closed = internal.unitRange\n\nexport const length: {\n /**\n * Calculates the length of a cubic polynomial.\n *\n * @param p - The cubic polynomial to analyze.\n * @param domain - The domain to restrict the analysis to.\n * @returns The length of the cubic polynomial in the specified domain.\n * @since 1.0.0\n */\n (p: CubicPolynomial, domain: Interval): number\n /**\n * Calculates the length of a cubic polynomial.\n *\n * @param domain - The domain to restrict the analysis to.\n * @returns A function that takes a cubic polynomial and returns the length of the cubic polynomial in the specified domain.\n * @since 1.0.0\n */\n (domain: Interval): (p: CubicPolynomial) => number\n} = internal.length\n\nexport const curvature: {\n /**\n * Calculates the curvature of a cubic polynomial.\n *\n * @param p - The cubic polynomial to analyze.\n * @param x - The value of x to calculate the curvature at.\n * @returns The curvature of the cubic polynomial at the specified value of x.\n * @since 1.0.0\n */\n (p: CubicPolynomial, x: number): number\n /**\n * Calculates the curvature of a cubic polynomial.\n *\n * @param x - The value of x to calculate the curvature at.\n * @returns A function that takes a cubic polynomial and returns the curvature of the cubic polynomial at the specified value of x.\n * @since 1.0.0\n */\n (x: number): (p: CubicPolynomial) => number\n} = 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