fix and test absquare for quaternion

Co-authored-by: Jos de Jong <wjosdejong@gmail.com>
Co-authored-by: Glen Whitney <glen@studioinfinity.org>
Reviewed-on: #4

.gitignore

@@ -129,6 +129,9 @@ dist
 # Stores VSCode versions used for testing VSCode extensions
 .vscode-test
 
+# WebStorm
+.idea
+
 # yarn v2
 .yarn/cache
 .yarn/unplugged

src/Complex/all.ts

@@ -1,8 +1,3 @@
-import {ForType} from '../core/Dispatcher.js'
 import * as Complex from './native.js'
 
 export {Complex}
-
-declare module "../core/Dispatcher" {
-   interface ImplementationTypes extends ForType<'Complex', typeof Complex> {}
-}

src/Complex/arithmetic.ts

@@ -0,0 +1,127 @@
+import { Complex, complex_binary } from './type.js'
+
+export const add =
+   <T>(dep: {
+      add: (a: T, b: T) => T
+   }) =>
+      (w: Complex<T>, z: Complex<T>): Complex<T> =>
+         complex_binary(dep.add(w.re, z.re), dep.add(w.im, z.im))
+
+export const addReal =
+   <T>(dep: {
+      addReal: (a: T, b: T) => T
+   }) =>
+      (z: Complex<T>, r: T): Complex<T> =>
+         complex_binary(dep.addReal(z.re, r), z.im)
+
+export const unaryMinus =
+   <T>(dep: {
+      unaryMinus: (z: T) => T
+   }) =>
+      (z: Complex<T>): Complex<T> =>
+         complex_binary(dep.unaryMinus(z.re), dep.unaryMinus(z.im))
+
+export const conj =
+   <T>(dep: {
+      unaryMinus: (z: T) => T,
+      conj: (z: T) => T
+   }) =>
+      (z: Complex<T>): Complex<T> =>
+         complex_binary(dep.conj(z.re), dep.unaryMinus(z.im))
+
+export const subtract =
+   <T>(dep: {
+      subtract: (a: T, b: T) => T
+   }) =>
+      (w: Complex<T>, z: Complex<T>): Complex<T> =>
+         complex_binary(dep.subtract(w.re, z.re), dep.subtract(w.im, z.im))
+
+export const multiply =
+   <T>(dep: {
+      add: (a: T, b: T) => T,
+      subtract: (a: T, b: T) => T,
+      multiply: (a: T, b: T) => T,
+      conj: (z: T) => T
+   }) =>
+      (w: Complex<T>, z: Complex<T>): Complex<T> => {
+         const mult = dep.multiply
+         const realpart = dep.subtract(mult(w.re, z.re), mult(dep.conj(w.im), z.im))
+         const imagpart = dep.add(mult(dep.conj(w.re), z.im), mult(w.im, z.re))
+         return complex_binary(realpart, imagpart)
+      }
+
+export const absquare =
+   <T, U>(dep: {
+      add: (a: U, b: U) => U,
+      absquare: (z: T) => U
+   }) =>
+      (z: Complex<T>): U => dep.add(dep.absquare(z.re), dep.absquare(z.im))
+
+export const divideByReal =
+   <T>(dep: {
+      divideByReal: (a: T, b: T) => T
+   }) =>
+      (z: Complex<T>, r: T) =>
+         complex_binary(dep.divideByReal(z.re, r), dep.divideByReal(z.im, r))
+
+export const reciprocal =
+   <T>(dep: {
+      conj: (z: Complex<T>) => Complex<T>,
+      absquare: (z: Complex<T>) => T,
+      divideByReal: (a: Complex<T>, b: T) => Complex<T>,
+      zero: (z: T) => T,
+   }) =>
+      (z: Complex<T>): Complex<T> => dep.divideByReal(dep.conj(z), dep.absquare(z))
+
+export const divide =
+   <T>(dep: {
+      multiply: (a: Complex<T>, b: Complex<T>) => Complex<T>,
+      reciprocal: (z: Complex<T>) => Complex<T>,
+   }) =>
+      (w: Complex<T>, z: Complex<T>) => dep.multiply(w, dep.reciprocal(z))
+
+export const complexSqrt =
+   <T>(dep: {
+      conservativeSqrt: (a: T) => T,
+      isSquare: (a: T) => boolean,
+      complex: (a: T) => Complex<T>,
+      unaryMinus: (a: T) => T,
+      zero: (a: T) => T,
+      nan: (a: Complex<T>) => Complex<T>
+   }) =>
+      (r: T): Complex<T> => {
+         if (dep.isSquare(r)) return dep.complex(dep.conservativeSqrt(r))
+         const negative = dep.unaryMinus(r)
+         if (dep.isSquare(negative)) {
+            return complex_binary(
+               dep.zero(r), dep.conservativeSqrt(negative))
+         }
+         // neither the real number or its negative is a square; could happen
+         // for example with bigint. So there is no square root. So we have to
+         // return the NaN of the type.
+         return dep.nan(dep.complex(r))
+      }
+
+export const sqrt =
+   <T>(dep: {
+      isReal: (z: Complex<T>) => boolean,
+      complexSqrt: (a: T) => Complex<T>,
+      conservativeSqrt: (a: T) => T,
+      absquare: (a: Complex<T>) => T,
+      addReal: (a: Complex<T>, b: T) => Complex<T>,
+      divideByReal: (a: Complex<T>, b: T) => Complex<T>,
+      add: (a: T, b: T) => T,
+      re: (a: Complex<T>) => T,
+
+   }) =>
+      (z: Complex<T>) => {
+         if (dep.isReal(z)) return dep.complexSqrt(z.re)
+         const myabs = dep.conservativeSqrt(dep.absquare(z))
+         const num = dep.addReal(z, myabs)
+         const r = dep.re(z)
+         const denomsq = dep.add(dep.add(myabs, myabs), dep.add(r, r))
+         const denom = dep.conservativeSqrt(denomsq)
+         return dep.divideByReal(num, denom)
+      }
+
+export const conservativeSqrt = sqrt

src/Complex/predicate.ts

@@ -0,0 +1,12 @@
+import { Complex } from './type.js'
+
+export const isReal =
+   <T>(dep: {
+      equal: (a: T, b: T) => boolean,
+      add: (a: T, b: T) => T,
+      isReal: (z: T) => boolean
+   }) =>
+      (z: Complex<T>) => dep.isReal(z.re) && dep.equal(z.re, dep.add(z.re, z.im))
+
+export const isSquare =
+   <T>(z: Complex<T>) => true // FIXME: not correct for Complex<bigint> once we get there

src/Complex/relational.ts

@@ -0,0 +1,7 @@
+import { Complex } from './type.js'
+
+export const equal =
+   <T>(dep: {
+      equal: (a: T, b: T) => boolean
+   }) =>
+      (w: Complex<T>, z: Complex<T>): boolean => dep.equal(w.re, z.re) && dep.equal(w.im, z.im)

src/Complex/type.ts

@@ -1,22 +1,54 @@
-import {joinTypes, typeOfDependency, Dependency} from '../core/Dispatcher.js'
+import {
+   joinTypes, typeOfDependency, Dependency,
+} from '../core/Dispatcher.js'
 
-export type Complex<T> = {re: T; im: T;}
+export type Complex<T> = { re: T; im: T; }
 
 export const Complex_type = {
-   test: <T>(dep: {testT: (z: unknown) => z is T}) =>
+   test: <T>(dep: { testT: (z: unknown) => z is T }) =>
       (z: unknown): z is Complex<T> =>
-      typeof z === 'object' && 're' in z && 'im' in z
+         typeof z === 'object' && z != null && '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)})
+         ({ 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 const complex_unary = <T>(dep: Dependency<'zero', [T]>) =>
-   (t: T) => ({re: t, im: dep.zero(t)})
-export const complex_binary = <T>(t: T, u: T) => ({re: t, im: u})
+export const complex_unary =
+   <T>(dep: {
+      zero: (z: T) => Complex<T>
+   }) =>
+      (t: T) => ({ re: t, im: dep.zero(t) })
+
+export const complex_binary =
+   <T>(t: T, u: T): Complex<T> => ({ re: t, im: u })
+
+export const zero =
+   <T>(dep: {
+      zero: (z: T) => T
+   }) =>
+      (z: Complex<T>): Complex<T> => complex_binary(dep.zero(z.re), dep.zero(z.im))
+
+export const one =
+   <T>(dep: {
+      zero: (z: T) => T,
+      one: (z: T) => T
+   }) =>
+      (z: Complex<T>): Complex<T> => complex_binary(dep.one(z.re), dep.zero(z.im))
+
+export const nan =
+   <T>(dep: {
+      nan: (z: T) => T
+   }) =>
+      (z: Complex<T>): Complex<T> => complex_binary(dep.nan(z.re), dep.nan(z.im))
+
+export const re =
+   <T>(dep: {
+      re: (z: T) => T
+   }) =>
+      (z: Complex<T>): T => dep.re(z.re)

src/all.ts

@@ -1,2 +1,3 @@
 export * from './numbers/all.js'
 export * from './Complex/all.js'
+export * from './generic/all.js'

src/core/Config.ts

@@ -1,4 +1,5 @@
 export type Config = {
+   epsilon: number
    predictable: boolean
 }
 

src/core/Dispatcher.ts

@@ -9,16 +9,62 @@
 
 type TypeName = string
 type Parameter = TypeName
-type Signature = Parameter[]
+type InputSignature = Parameter[]
+type DependenciesType = Record<string, Function>
 
-export interface ImplementationTypes {}
 export type typeOfDependency = {typeOf: (x: unknown) => TypeName}
 
-// Helper for collecting implementations
-// (Really just suffixes the type name onto the keys of exports)
-export type ForType<T extends string, Exports> = keyof Exports extends string
-   ? {[K in keyof Exports as `${K}_${T}`]: Exports[K]}
-   : never
+// All of the implementations must publish descriptions of their
+// return types into the following interface, using the format
+// described just below:
+export interface ReturnTypes<Params> {}
+
+/*****
+   To describe one implementation for a hypothetical operation `foo`, there
+   should be a property of the interface whose name starts with `foo` and whose
+   next character, if any, is an underscore. The type of this property
+   must be the return type of that implementation when Params matches the
+   parameter types of the implementation, and `never` otherwise.
+   Thus to describe an implementation that takes a number and a string and
+   returns a boolean, for example, you could write
+   ```
+   declare module "Dispatcher" {
+      interface ReturnTypes<Params> {
+         foo_example: Params extends [number, string] ? boolean : never
+      }
+   }
+   ```
+   If there is another, generic implementation that takes one argument
+   of any type and returns a Vector of that type, you can say
+   ```
+   ...
+      foo_generic: Params extends [infer T] ? Vector<T> : never
+   ...
+   ```
+   In practice, each subdirectory corresponding to a type, like Complex,
+   defines an interface, like `ComplexReturn<Params>` for the implementations
+   in that subdirectory, which can mostly be defined without suffixes because
+   there's typically just a single implementation within that domain.
+   Then the module responsible for collating all of the implementations for
+   that type inserts all of the properties of that interface into `ReturnTypes`
+   suitably suffixed to avoid collisions.
+
+   One might think that simply defining an implementation for `foo`
+   of type `(n: number, s: string) => boolean` would provide all of the same
+   information as the type of the key `foo_example` in the ReturnTypes
+   interface above, but in practice TypeScript has challenges in extracting
+   types relating to functions. (In particular, there is no
+   way to get the specialized return type of a generic function when it is
+   called on aguments whose specific types match the generic parameters.)
+   Hence the need for this additional mechanism to specify return types, in
+   a way readily suited for TypeScript type computations.
+*****/
+
+// Helpers for specifying signatures
+
+// A basic signature with concrete types
+export type Signature<CandidateParams, ActualParams, Returns> =
+   CandidateParams extends ActualParams ? Returns : never
 
 //dummy implementation for now
 export function joinTypes(a: TypeName, b: TypeName) {
@@ -26,27 +72,27 @@ export function joinTypes(a: TypeName, b: TypeName) {
    return 'any'
 }
 
-/**
- * Build up to Dependency type lookup
- */
-type DependenciesType = Record<string, Function>
+// Used to filter keys that match a given operation name
+type BeginsWith<Name extends string> = Name | `${Name}_${string}`
 
-type FinalShape<FuncType> =
-   FuncType extends (arg: DependenciesType) => Function
-   ? ReturnType<FuncType> : FuncType
+// Look up the return type of an implementation based on its name
+// and the parameters it takes
+export type ImpReturns<Name extends string, Params> =
+   {[K in keyof ReturnTypes<Params>]: K extends BeginsWith<Name>
+    ? ReturnTypes<Params>[K] : never}[keyof ReturnTypes<Params>]
 
-type BeginsWith<Name extends string> = `${Name}${string}`
-
-type DependencyTypes<Ob, Name extends string, Params extends unknown[]> =
-   {[K in keyof Ob]: K extends BeginsWith<Name>
-    ? FinalShape<Ob[K]> extends (...args: Params) => any
-      ? FinalShape<Ob[K]>
-      : never
-    : never}
+// The type of an implementation (with dependencies satisfied,
+// based on its name and the parameters it takes
+export type ImpType<Name extends string, Params extends unknown[]> =
+   (...args: Params) => ImpReturns<Name, Params>
 
+// The type of a dependency on an implementation based on its name
+// and the parameters it takes (just a simple object with one property
+// named the same as the operation, of value type equal to the type of
+// that implementation. These can be `&`ed together in case of multiple
+// dependencies:
 export type Dependency<Name extends string, Params extends unknown[]> =
-   {[N in Name]:
-    DependencyTypes<ImplementationTypes, N, Params>[keyof ImplementationTypes]}
+   {[N in Name]: ImpType<N, Params>}
 
 // Now types used in the Dispatcher class itself
 
@@ -64,9 +110,9 @@ type SpecificationsGroup = Record<string, SpecObject>
 export class Dispatcher {
    installSpecification(
       name: string,
-      signature: Signature,
+      signature: InputSignature,
       returns: TypeName,
-      dependencies: Record<string, Signature>,
+      dependencies: Record<string, InputSignature>,
       behavior: Function // possible todo: constrain this type based
       // on the signature, return type, and dependencies. Not sure if
       // that's really possible, though.

src/generic/all.ts

@@ -0,0 +1,3 @@
+import * as generic from './arithmetic.js'
+
+export { generic }

src/generic/arithmetic.ts

@@ -0,0 +1,5 @@
+export const square =
+  <T>(dep: {
+    multiply: (x: T, y: T) => T
+  }) =>
+    (z: T): T => dep.multiply(z, z)

src/index.ts

@@ -2,3 +2,22 @@ import {Dispatcher} from './core/Dispatcher.js'
 import * as Specifications from './all.js'
 
 export default new Dispatcher(Specifications)
+
+
+// Test https://github.com/josdejong/pocomath/issues/1#issuecomment-1364056151
+
+import {Complex} from './Complex/type.js'
+import {absquare as absquare_complex} from './Complex/arithmetic.js'
+
+const mockRealAdd = (a: number, b: number) => a+b
+const mockComplexAbsquare = (z: Complex<number>) => z.re*z.re + z.im*z.im
+
+const quatAbsquare = absquare_complex({
+    add: mockRealAdd,
+    absquare: mockComplexAbsquare
+})
+
+const myabs = quatAbsquare({re: {re: 0, im: 1}, im: {re:2, im: 3}})
+const typeTest: typeof myabs = 7 // check myabs is just a number
+
+console.log('Result is', myabs)

src/numbers/all.ts

@@ -1,8 +1,3 @@
-import {ForType} from '../core/Dispatcher.js'
 import * as numbers from './native.js'
 
 export {numbers}
-
-declare module "../core/Dispatcher" {
-   interface ImplementationTypes extends ForType<'numbers', typeof numbers> {}
-}

src/numbers/arithmetic.ts

@@ -1,18 +1,26 @@
-import {configDependency} from '../core/Config.js'
-import {Dependency} from '../core/Dispatcher.js'
+import { Config } from '../core/Config.js'
+import type { Complex } from '../Complex/type.js'
+
+export const add = (a: number, b: number): number => a + b
+export const addReal = add
+export const unaryMinus = (a: number): number => -a
+export const conj = (a: number): number => a
+export const subtract = (a: number, b: number): number => a - b
+export const multiply = (a: number, b: number): number => a * b
+export const absquare = (a: number): number => a * a
+export const reciprocal = (a: number): number => 1 / a
+export const divide = (a: number, b: number): number => a / b
+export const divideByReal = divide
+
+export const conservativeSqrt = (a: number): number => isNaN(a) ? NaN : Math.sqrt(a)
 
-export const add = (a: number, b: number) => a + b
-export const unaryMinus = (a: number) => -a
-export const subtract = (a: number, b: number) => a - b
-export const multiply = (a: number, b: number) => a * b
-export const divide = (a: number, b: number) => a / b
 export const sqrt =
-   (dep: configDependency
-    & Dependency<'complex', [number, number]>) => {
-       if (dep.config.predictable || !dep.complex) {
-          return (a: number) => isNaN(a) ? NaN : Math.sqrt(a)
-       }
-       return (a: number) => {
+   (dep: {
+      config: Config,
+      complex: (re: number, im: number) => Complex<number>
+   }): (a: number) => number | Complex<number> => {
+      if (dep.config.predictable || !dep.complex) return conservativeSqrt
+      return a => {
          if (isNaN(a)) return NaN
          if (a >= 0) return Math.sqrt(a)
          return dep.complex(0, Math.sqrt(unaryMinus(a)))

src/numbers/predicate.ts

@@ -0,0 +1,2 @@
+export const isReal = (a: number) : boolean => true
+export const isSquare = (a: number) : boolean => a >= 0

src/numbers/relational.ts

@@ -0,0 +1,26 @@
+import { Config } from '../core/Config.js'
+
+const DBL_EPSILON = Number.EPSILON || 2.2204460492503130808472633361816E-16
+
+export const equal =
+   (dep: {
+      config: Config
+   }) => (x: number, y: number): boolean => {
+      const eps = dep.config.epsilon
+      if (eps === null || eps === undefined) return x === y
+      if (x === y) return true
+      if (isNaN(x) || isNaN(y)) return false
+
+      if (isFinite(x) && isFinite(y)) {
+         const diff = Math.abs(x - y)
+         if (diff < DBL_EPSILON) return true
+         return diff <= Math.max(Math.abs(x), Math.abs(y)) * eps
+      }
+
+      return false
+   }
+
+export const unequal = (dep: {
+   equal: (x: number, y: number) => boolean
+}) =>
+   (x: number, y: number): boolean => !dep.equal(x, y)

src/numbers/type.ts

@@ -1,7 +1,10 @@
 export const number_type = {
    before: ['Complex'],
    test: (n: unknown): n is number => typeof n === 'number',
-   from: {string: s => +s}
+   from: { string: (s: string) => +s }
 }
 
-export const zero = (a: number) => 0
+export const zero = (a: number): number => 0
+export const one = (a: number): number => 1
+export const nan = (a: number): number => NaN
+export const re = (a: number): number => a