feat: Add generic operation `square` and numeric `unequal` (#4)

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

src/Complex/type.ts

@@ -30,6 +30,19 @@ export interface ComplexReturn<Params> {
       : Params extends BBinary<infer B> ? Complex<B> // binary case
       : never
 
+   // alternatively if it seems better; each definition is simpler, but at
+   // the cost of having two keys here:
+   // complex_unary: Params extends [infer R] ? Complex<R> : never
+   // complex_binary: Params extends BBinary<infer R> ? Complex<R> : never
+
+   // There is actually a subtlety here that complex_unary really only works
+   // on real types that include their own zero value, so it should really be
+   // complex_unary: Params extends [infer R]
+   //    ? ImpReturns<'zero', [R]> extends R ? Complex<R> : never
+   //    : never
+   // and that might actually simplify some of the typings of other operations,
+   // but we'll leave such fine tuning til later, if we adopt this scheme
+
    zero: Params extends [infer Z] // unary
       ? Z extends Complex<infer T> // of a Complex parameter
          ? ImpReturns<'zero', T> extends T ? Z : never // that has its real 0

src/all.ts

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

src/generic/all.ts

@@ -0,0 +1,10 @@
+import { ForType } from '../core/Dispatcher.js'
+import { GenericReturn } from './type.js'
+import * as generic from './arithmetic.js'
+
+export { generic }
+
+declare module "../core/Dispatcher" {
+   interface ReturnTypes<Params>
+      extends ForType<'generic', GenericReturn<Params>> { }
+}

src/generic/arithmetic.ts

@@ -0,0 +1,39 @@
+import {Dependency, ImpType, ImpReturns} from "../core/Dispatcher";
+
+declare module "./type" {
+  interface GenericReturn<Params> {
+    // Jos: not sure how to define this or why it is needed
+    // square: Signature<Params, [T], T>
+    // square: ConservativeUnary<Params, T>
+    // square: Params extends [infer R]
+    //   ? R extends number ? UnderlyingReal<R> : never
+    //    : never
+
+    // The type of `square` in this interface, instantiated with the type
+    // Params of a parameter list, needs to be the return type of the
+    // operation `square` on those parameters. In other words, `square` gives
+    // a type transformer from the tuple type of its parameters to its return
+    // type.
+    // That's how Dispatcher knows what the return type will be in
+    // `Dependency<'square', [bigint]>`, for example: it instantiates
+    // GenericReturn with Params equal to [bigint] and then grabs the
+    // type of the `square` property. Hence we write:
+
+    square: Params extends [infer T] // square only takes 1 arbitrary parameter
+        ? ImpReturns<'multiply', [T, T]> // and returns whatever multiply does
+        : never; // otherwise if not a single argument, this implementation
+                 // doesn't handle it
+
+    // If square had more than one implementation in this collection, we could
+    // either add more conditional clauses to the above type transformer
+    // as I did in Complex/type.ts for `complex`, or we could have two
+    // different keys that both start with `square_` and Dispatcher will
+    // check both (as I have now done in comments in Complex/type.ts and
+    // verified that also works).
+  }
+}
+
+export const square =
+  <T>(dep: Dependency<'multiply', [T, T]>):
+    ImpType<'square', [T]> =>
+    z => dep.multiply(z, z)

src/generic/type.ts

@@ -0,0 +1,3 @@
+export interface GenericReturn<Params> {
+
+}

src/numbers/relational.ts

@@ -1,27 +1,34 @@
 import {configDependency} from '../core/Config.js'
-import {Signature, ImpType} from '../core/Dispatcher.js'
+import {Signature, ImpType, Dependency} from '../core/Dispatcher.js'
 
 const DBL_EPSILON = Number.EPSILON || 2.2204460492503130808472633361816E-16
 
 declare module "./type" {
    interface NumbersReturn<Params> {
       equal: Signature<Params, [number, number], boolean>
+      unequal: Signature<Params, [number, number], boolean>
    }
 }
 
 export const equal =
    (dep: configDependency): ImpType<'equal', [number, number]> =>
-   (x, y) => {
-      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
+      (x, y) => {
+         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
+         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
       }
 
-      return false
+export const unequal = (dep: Dependency<'equal', [number, number]>):
+   ImpType<'unequal', [number, number]> =>
+   (x, y) => {
+      return !dep.equal(x, y)
    }