feat: Narrow tsc typing of operation dependencies/implementations

src/numbers/all.ts

@@ -0,0 +1,2 @@
+export * as type_data from './type'
+export * as arithmetic_functions from './arithmetic'

src/numbers/arithmetic.ts

@@ -0,0 +1,26 @@
+import {implementations} from '@/core/Dispatcher'
+import type {CommonSignature} from '@/interfaces/type'
+
+const conservativeSqrt = (a: number) => isNaN(a) ? NaN : Math.sqrt(a)
+
+export default implementations<CommonSignature<number>>()
+   .independent({
+      add:       (a, b) => a + b,
+      unaryMinus: a     => -a,
+      subtract:  (a, b) => a - b,
+      multiply:  (a, b) => a * b,
+      absquare:   a     => a * a,
+      reciprocal: a     => 1 / a,
+      divide:    (a, b) => a / b,
+      conj:       a     => a,
+      conservativeSqrt })
+   .dependent({config: {}, complex: {}}, {
+      sqrt: dep => {
+         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(-a))
+         }
+      }})
+   .ship()

src/numbers/type.ts

@@ -0,0 +1,31 @@
+import type {Complex} from '@/Complex/type'
+import {implementations} from '@/core/Dispatcher'
+import type {CommonSignature} from '@/interfaces/type'
+
+export const number_type = {
+   name: 'number',
+   before: ['Complex'],
+   test: (n: unknown): n is number => typeof n === 'number',
+   from: {string: (s: string) => +s }
+}
+
+declare module "@/interfaces/type" {
+   interface AssociatedTypes<T> {
+      number: {
+         type: number
+         zero: 0
+         one: 1
+         nan: typeof NaN
+         real: number
+         closure: Complex<number>
+      }
+   }
+}
+
+export default implementations<CommonSignature<number>>()
+   .independent({
+      zero: a => 0,
+      one: a => 1,
+      nan: a => NaN,
+      re: a => a
+   }).ship()