import {
   joinTypes, typeOfDependency, Dependency, ImpType, ImpReturns
} from '../core/Dispatcher.js'

export type Complex<T> = {re: T; im: T;}

export type UnderlyingReal<T> =
   T extends Complex<infer U> ? UnderlyingReal<U> : T

export const Complex_type = {
   test: <T>(dep: {testT: (z: unknown) => z is T}) =>
      (z: unknown): z is Complex<T> =>
      typeof z === 'object' && 're' in z && 'im' in z
      && dep.testT(z.re) && dep.testT(z.im),
   infer: (dep: typeOfDependency) =>
      (z: Complex<unknown>) => joinTypes(dep.typeOf(z.re), dep.typeOf(z.im)),
   from: {
      T: <T>(dep: Dependency<'zero', [T]>) => (t: T) =>
         ({re: t, im: dep.zero(t)}),
      Complex: <U,T>(dep: {convert: (from: U) => T}) =>
         (z: Complex<U>) => ({re: dep.convert(z.re), im: dep.convert(z.im)})
   }
}

export interface ComplexImpTypes<T> {
   complex: (a: T, b?: T) => Complex<T>
   zero: T extends Complex<infer R>
      ? (a: Complex<R>) => Complex<R | ImpReturns<'zero', [R]>> : never
   one: T extends Complex<infer R>
      ? (a: Complex<R>) => Complex<R | ImpReturns<'one' | 'zero', [R]>> : never
   nan: T extends Complex<infer R>
      ? (a: Complex<R>) => Complex<R | ImpReturns<'NaN', [R]>> : never
   re: T extends Complex<infer R>
      ? (a: Complex<R>) => UnderlyingReal<R> : never
}

export const complex_unary =
   <T>(dep: Dependency<'zero', [T]>): ImpType<'complex', [T]> =>
   t => ({re: t, im: dep.zero(t)})
export const complex_binary = <T>(t: T, u: T): ImpReturns<'complex', [T,T]> =>
   ({re: t, im: u})

export const zero =
   <T>(dep: Dependency<'zero', [T]>): ImpType<'zero', [Complex<T>]> =>
   z => complex_binary(dep.zero(z.re), dep.zero(z.im))

export const one =
   <T>(dep: Dependency<'zero' | 'one', [T]>): ImpType<'one', [Complex<T>]> =>
   z => // Must provide parameter T, else TS narrows to return type of dep.one
   complex_binary<T>(dep.one(z.re), dep.zero(z.im))

export const nan =
   <T>(dep: Dependency<'nan', [T]>): ImpType<'nan', [Complex<T>]> =>
   z => complex_binary(dep.nan(z.re), dep.nan(z.im))

export const re =
   <T>(dep: Dependency<'re', [T]>): ImpType<'re', [Complex<T>]> =>
   z => dep.re(z.re)