import {configDependency} from '../core/Config.js'
import {Signature, Dependency, ImpType} from '../core/Dispatcher.js'
import type {Complex} from '../Complex/type.js'

declare module "./type" {
   interface NumbersReturn<Params> {
      // This description loses information: some subtypes like NumInt or
      // Positive are closed under addition, but this says that the result
      // of add is just a number, not still of the reduced type
      add: Signature<Params, [number, number], number>
      // Whereas this one would preserve information, but would lie
      // because it claims all subtypes of number are closed under addition,
      // which is not true for `1 | 2 | 3`, for example.
      // add: Params extends BBinary<infer B>
      //    ? B extends number ? B : never
      //    : never
      //
      // Not sure how this will need to go when we introduce NumInt.
      unaryMinus: Signature<Params, [number], number>
      subtract: Signature<Params, [number, number], number>
      multiply: Signature<Params, [number, number], number>
      divide: Signature<Params, [number, number], number>
      // Best we can do for sqrt at compile time, since actual return
      // type depends on config. Not sure how this will play out
      // when we make a number-only bundle, but at least the import type
      // above for Complex<> does not lead to any emitted JavaScript.
      sqrt: Signature<Params, [number], number | Complex<number>>
   }
}

export const add: ImpType<'add', [number, number]> = (a, b) => a + b
export const unaryMinus: ImpType<'unaryMinus', [number]> = a => -a
export const subtract: ImpType<'subtract', [number, number]> = (a, b) => a - b
export const multiply: ImpType<'multiply', [number, number]> = (a, b) => a * b
export const divide: ImpType<'divide', [number, number]> = (a, b) => a / b
export const sqrt =
   (dep: configDependency
    & Dependency<'complex', [number, number]>): ImpType<'sqrt', [number]> => {
       if (dep.config.predictable || !dep.complex) {
          return a => isNaN(a) ? NaN : Math.sqrt(a)
       }
       return a => {
          if (isNaN(a)) return NaN
          if (a >= 0) return Math.sqrt(a)
          return dep.complex(0, Math.sqrt(unaryMinus(a)))
       }
    }