fix(Types): Move distinct types into distinct identifiers

This allows types to be collected; prior to this commit they
   were conflicting from different modules.

   Uses this fix to extend sqrt to bigint, with the convention
   that it is undefined for non-perfect squares when 'predictable'
   is false and is the "best" approximation to the square root when
   'predictable' is true. Furthermore, for negative bigints, you might
   get a Gaussian integer when predictable is false; or you will just get
   your argument back when 'predictable' is true because what other
   bigint could you give back for a negative bigint?

   Also had to modify tests on the sign in sqrt(Complex) and add functions
   'zero' and 'one' to get types to match, as expected in #27.

   Adds numerous tests.

   Resolves #26.
   Resolves #27.

src/bigint/Types/bigint.mjs

@@ -1,6 +1,4 @@
-export const Types = {
-    bigint: {
-        before: ['Complex'],
-        test: b => typeof b === 'bigint'
-    }
+export const Type_bigint = {
+    before: ['Complex'],
+    test: b => typeof b === 'bigint'
 }

src/bigint/add.mjs

@@ -1,4 +1,4 @@
-export {Types} from './Types/bigint.mjs'
+export * from './Types/bigint.mjs'
 
 export const add = {
    '...bigint': () => addends => addends.reduce((x,y) => x+y, 0n)

src/bigint/all.mjs

@@ -1,4 +1,8 @@
-export {Types} from './Types/bigint.mjs'
-export {add} from './add.mjs'
-export {negate} from './negate.mjs'
-export {subtract} from '../generic/subtract.mjs'
+export * from './native.mjs'
+export * from '../generic/arithmetic.mjs'
+
+// resolve the conflicts
+export {divide} from './divide.mjs'
+export {multiply} from './multiply.mjs'
+export {sign} from './sign.mjs'
+export {sqrt} from './sqrt.mjs'

src/bigint/divide.mjs

@@ -0,0 +1,20 @@
+export * from './Types/bigint.mjs'
+
+export const divide = {
+   'bigint,bigint': ({config, 'sign(bigint)': sgn}) => {
+      if (config.predictable) {
+         return (n, d) => {
+            if (sgn(n) === sgn(d)) return n/d
+            const quot = n/d
+            if (quot * d == n) return quot
+            return quot - 1n
+         }
+      } else {
+         return (n, d) => {
+            const quot = n/d
+            if (quot * d == n) return quot
+            return undefined
+         }
+      }
+   }
+}

src/bigint/multiply.mjs

@@ -0,0 +1,5 @@
+export * from './Types/bigint.mjs'
+
+export const multiply = {
+   '...bigint': () => multiplicands => multiplicands.reduce((x,y) => x*y, 1n)
+}

src/bigint/native.mjs

@@ -0,0 +1,9 @@
+export * from './Types/bigint.mjs'
+export {add} from './add.mjs'
+export {divide} from './divide.mjs'
+export {multiply} from './multiply.mjs'
+export {negate} from './negate.mjs'
+export {one} from './one.mjs'
+export {sign} from './sign.mjs'
+export {sqrt} from './sqrt.mjs'
+export {zero} from './zero.mjs'

src/bigint/negate.mjs

@@ -1,3 +1,3 @@
-export {Types} from './Types/bigint.mjs'
+export * from './Types/bigint.mjs'
 
 export const negate = {bigint: () => b => -b}

src/bigint/one.mjs

@@ -0,0 +1,3 @@
+export * from './Types/bigint.mjs'
+
+export const one = {bigint: () => () => 1n}

src/bigint/sign.mjs

@@ -0,0 +1,9 @@
+export * from './Types/bigint.mjs'
+
+export const sign = {
+   bigint: () => b => {
+      if (b === 0n) return 0n
+      if (b > 0n) return 1n
+      return -1n
+   }
+}

src/bigint/sqrt.mjs

@@ -0,0 +1,30 @@
+export * from './Types/bigint.mjs'
+import isqrt from 'bigint-isqrt'
+
+export const sqrt = {
+   bigint: ({config, complex, 'self(Complex)': complexSqrt}) => {
+      if (config.predictable) {
+         // Don't just return the constant isqrt here because the object
+         // gets decorated with info that might need to be different
+         // for different PocomathInstancss
+         return b => isqrt(b)
+      }
+      if (!complexSqrt) {
+         return b => {
+            if (b >= 0n) {
+               const trial = isqrt(b)
+               if (trial * trial === b) return trial
+            }
+            return undefined
+         }
+      }
+      return b => {
+         if (b >= 0n) {
+            const trial = isqrt(b)
+            if (trial * trial === b) return trial
+            return undefined
+         }
+         return complexSqrt(complex(b))
+      }
+   }
+}

src/bigint/zero.mjs

@@ -0,0 +1,3 @@
+export * from './Types/bigint.mjs'
+
+export const zero = {bigint: () => () => 0n}

src/complex/Types/Complex.mjs

@@ -2,21 +2,15 @@
  * can be any type (for this proof-of-concept; in reality we'd want to
  * insist on some numeric or scalar supertype).
  */
-export function isComplex(z) { 
+function isComplex(z) { 
    return z && typeof z === 'object' && 're' in z && 'im' in z
 }
 
-export const Types = {
-   Complex: {
-      test: isComplex,
-      from: {
-         number: x => ({re: x, im: 0}),
-         bigint: x => ({re: x, im: 0n})
-      }
+export const Type_Complex = {
+   test: isComplex,
+   from: {
+      number: x => ({re: x, im: 0}),
+      bigint: x => ({re: x, im: 0n})
    }
 }
 
-/* test if an entity is Complex<number>, so to speak: */
-export function numComplex(z) {
-   return isComplex(z) && typeof z.re === 'number' && typeof z.im === 'number'
-}

src/complex/abs.mjs

@@ -1,4 +1,4 @@
-export {Types} from './Types/Complex.mjs'
+export * from './Types/Complex.mjs'
 
 export const abs = {Complex: ({sqrt, add, multiply}) => z => {
     return sqrt(add(multiply(z.re, z.re), multiply(z.im, z.im)))

src/complex/add.mjs

@@ -1,4 +1,4 @@
-export {Types} from './Types/Complex.mjs'
+export * from './Types/Complex.mjs'
 
 export const add = {
    '...Complex': ({self}) => addends => {

src/complex/all.mjs

@@ -1,2 +1,5 @@
-export * from './native.mjs'
 export * from '../generic/arithmetic.mjs'
+export * from './native.mjs'
+
+// resolve the conflicts
+export {sqrt} from './sqrt.mjs'

src/complex/complex.mjs

@@ -1,11 +1,15 @@
-export {Types} from './Types/Complex.mjs'
+export * from './Types/Complex.mjs'
+export * from '../generic/Types/generic.mjs'
 
 export const complex = {
    /* Very permissive for sake of proof-of-concept; would be better to
     * have a numeric/scalar type, e.g. by implementing subtypes in
     * typed-function
     */
-   'any, any': () => (x, y) => ({re: x, im: y}),
+   'undefined': () => u => u,
+   'undefined,any': () => (u, y) => u,
+   'any,undefined': () => (x, u) => u,
+   'any,any': () => (x, y) => ({re: x, im: y}),
    /* Take advantage of conversions in typed-function */
    Complex: () => z => z
 }

src/complex/native.mjs

@@ -1,4 +1,4 @@
-export {Types} from './Types/Complex.mjs'
+export * from './Types/Complex.mjs'
 
 export {abs} from './abs.mjs'
 export {add} from './add.mjs'

src/complex/negate.mjs

@@ -1,4 +1,4 @@
-export {Types} from './Types/Complex.mjs'
+export * from './Types/Complex.mjs'
 
 export const negate = {
    Complex: ({self}) => z => ({re: self(z.re), im: self(z.im)})

src/complex/sqrt.mjs

@@ -1,35 +1,44 @@
-export { Types } from './Types/Complex.mjs'
+export * from './Types/Complex.mjs'
 
 export const sqrt = {
    Complex: ({
       config,
+      zero,
+      sign,
+      one,
+      add,
       complex,
       multiply,
-      sign,
       self,
       divide,
-      add,
       'abs(Complex)': abs,
       subtract
    }) => {
       if (config.predictable) {
          return z => {
+            const imZero = zero(z.im)
             const imSign = sign(z.im)
+            const reOne = one(z.re)
             const reSign = sign(z.re)
-            if (imSign === 0 && reSign === 1) return complex(self(z.re))
+            if (imSign === imZero && reSign === reOne) return complex(self(z.re))
+            const reTwo = add(reOne, reOne)
             return complex(
-               multiply(sign(z.im), self(divide(add(abs(z),z.re), 2))),
-               self(divide(subtract(abs(z),z.re), 2))
+               multiply(sign(z.im), self(divide(add(abs(z),z.re), reTwo))),
+               self(divide(subtract(abs(z),z.re), reTwo))
             )
          }
       }
       return z => {
+         const imZero = zero(z.im)
          const imSign = sign(z.im)
+         const reOne = one(z.re)
          const reSign = sign(z.re)
-         if (imSign === 0 && reSign === 1) return self(z.re)
+         if (imSign === imZero && reSign === reOne) return self(z.re)
+         const reTwo = add(reOne, reOne)
+         const partial = add(abs(z), z.re)
          return complex(
-            multiply(sign(z.im), self(divide(add(abs(z),z.re), 2))),
-            self(divide(subtract(abs(z),z.re), 2))
+            multiply(sign(z.im), self(divide(add(abs(z),z.re), reTwo))),
+            self(divide(subtract(abs(z),z.re), reTwo))
          )
       }
    }

src/core/PocomathInstance.mjs

@@ -8,7 +8,8 @@ export default class PocomathInstance {
     * in that if a new top-level PocomathInstance method is added, its name
     * must be added to this list.
     */
-   static reserved = new Set(['config', 'importDependencies', 'install', 'name'])
+   static reserved = new Set([
+      'config', 'importDependencies', 'install', 'name', 'Types'])
 
    constructor(name) {
       this.name = name
@@ -65,10 +66,11 @@ export default class PocomathInstance {
     *    operation in the body of the implementation. [NOTE: this signature-
     *    specific reference is not yet implemented.]
     *
-    *    Note that the "operation" named `Types` is special: it gives
-    *    types that must be installed in the instance. In this case, the keys
-    *    are type names, and the values are plain objects with the following
-    *    properties:
+    *    Note that any "operation" whose name begins with  `Type_` is special:
+    *    it defines a types that must be installed in the instance.
+    *    The remainder of the "operation" name following the `_` is the
+    *    name of the type. The value of the "operation" should be a plain
+    *    object with the following properties:
     *
     *    - test: the predicate for the type
     *    - from: a plain object mapping the names of types that can be converted
@@ -78,8 +80,8 @@ export default class PocomathInstance {
     */
    install(ops) {
       for (const [item, spec] of Object.entries(ops)) {
-         if (item === 'Types') {
-            this._installTypes(spec)
+         if (item.slice(0,5) === 'Type_') {
+            this._installType(item.slice(5), spec)
          } else {
             this._installOp(item, spec)
          }
@@ -128,43 +130,40 @@ export default class PocomathInstance {
    /* Used internally by install, see the documentation there.
     * Note that unlike _installOp below, we can do this immediately
     */
-   _installTypes(typeSpecs) {
-      for (const [type, spec] of Object.entries(typeSpecs)) {
-         if (type in this.Types) {
-            if (spec !== this.Types[type]) {
-                  throw new SyntaxError(
-                     `Conflicting definitions of type ${type}`)
-            }
-            continue
+   _installType(type, spec) {
+      if (type in this.Types) {
+         if (spec !== this.Types[type]) {
+            throw new SyntaxError(`Conflicting definitions of type ${type}`)
          }
-         let beforeType = 'any'
-         for (const other of spec.before || []) {
-            if (other in this.Types) {
-               beforeType = other
-               break
-            }
-         }
-         this._typed.addTypes([{name: type, test: spec.test}], beforeType)
-         /* Now add conversions to this type */
-         for (const from in (spec.from || {})) {
-            if (from in this.Types) {
-               this._typed.addConversion(
-                  {from, to: type, convert: spec.from[from]})
-            }
-         }
-         /* And add conversions from this type */
-         for (const to in this.Types) {
-            if (type in (this.Types[to].from || {})) {
-               this._typed.addConversion(
-                  {from: type, to, convert: this.Types[to].from[type]})
-            }
-         }
-         this.Types[type] = spec
-         // rebundle anything that uses the new type:
-         this._invalidateDependents(':' + type)
+         return
       }
+      let beforeType = 'any'
+      for (const other of spec.before || []) {
+         if (other in this.Types) {
+            beforeType = other
+            break
+         }
+      }
+      this._typed.addTypes([{name: type, test: spec.test}], beforeType)
+      /* Now add conversions to this type */
+      for (const from in (spec.from || {})) {
+         if (from in this.Types) {
+            this._typed.addConversion(
+               {from, to: type, convert: spec.from[from]})
+         }
+      }
+      /* And add conversions from this type */
+      for (const to in this.Types) {
+         if (type in (this.Types[to].from || {})) {
+            this._typed.addConversion(
+               {from: type, to, convert: this.Types[to].from[type]})
+         }
+      }
+      this.Types[type] = spec
+      // rebundle anything that uses the new type:
+      this._invalidateDependents(':' + type)
    }
-         
+
    /* Used internally by install, see the documentation there */
    _installOp(name, implementations) {
       if (name.charAt(0) === '_') {

src/generic/Types/generic.mjs

@@ -0,0 +1,2 @@
+export const Type_undefined = {test: u => u === undefined}
+

src/generic/arithmetic.mjs

@@ -1,3 +1,7 @@
+export * from './Types/generic.mjs'
+
+export {multiply} from './multiply.mjs'
 export {divide} from './divide.mjs'
 export {sign} from './sign.mjs'
+export {sqrt} from './sqrt.mjs'
 export {subtract} from './subtract.mjs'

src/generic/multiply.mjs

@@ -0,0 +1,12 @@
+export * from './Types/generic.mjs'
+
+export const multiply = {
+   'undefined': () => u => u,
+   'undefined,...any': () => (u, rest) => u,
+   'any,undefined': () => (x, u) => u,
+   'any,undefined,...any': () => (x, u, rest) => u,
+   'any,any,undefined': () => (x, y, u) => u,
+   'any,any,undefined,...any': () => (x, y, u, rest) => u
+   // Bit of a hack since this should go on indefinitely...
+}
+

src/generic/sqrt.mjs

@@ -0,0 +1,3 @@
+export * from './Types/generic.mjs'
+
+export const sqrt = {undefined: () => () => undefined}

src/number/Types/number.mjs

@@ -1,8 +1,6 @@
-export const Types = {
-    number: {
-        before: ['Complex'],
-        test: n => typeof n === 'number',
-        from: {string: s => +s}
-    }
+export const Type_number = {
+    before: ['Complex'],
+    test: n => typeof n === 'number',
+    from: {string: s => +s}
 }
 

src/number/abs.mjs

@@ -1,3 +1,3 @@
-export {Types} from './Types/number.mjs'
+export * from './Types/number.mjs'
 
 export const abs = {number: () => n => Math.abs(n)}

src/number/add.mjs

@@ -1,4 +1,4 @@
-export {Types} from './Types/number.mjs'
+export * from './Types/number.mjs'
 
 export const add = {
    '...number': () => addends => addends.reduce((x,y) => x+y, 0),

src/number/all.mjs

@@ -1,4 +1,6 @@
-export {Types} from './Types/number.mjs'
-
-export * from './native.mjs'
 export * from '../generic/arithmetic.mjs'
+export * from './native.mjs'
+
+// resolve the conflicts
+export {sqrt} from './sqrt.mjs'
+export {multiply} from './multiply.mjs'

src/number/invert.mjs

@@ -1,3 +1,3 @@
-export {Types} from './Types/number.mjs'
+export * from './Types/number.mjs'
 
 export const invert = {number: () => n => 1/n}

src/number/multiply.mjs

@@ -1,4 +1,4 @@
-export {Types} from './Types/number.mjs'
+export * from './Types/number.mjs'
 
 export const multiply = {
    '...number': () => multiplicands => multiplicands.reduce((x,y) => x*y, 1),

src/number/native.js

@@ -1,4 +0,0 @@
-export {Types} from './Types/number.mjs'
-export {add} from './add.mjs'
-export {negate} from './negate.mjs'
-export {sqrt} from './sqrt.mjs'

src/number/native.mjs

@@ -1,8 +1,10 @@
-export {Types} from './Types/number.mjs'
+export * from './Types/number.mjs'
 
 export {abs} from './abs.mjs'
 export {add} from './add.mjs'
 export {invert} from './invert.mjs'
 export {multiply} from './multiply.mjs'
 export {negate} from './negate.mjs'
+export {one} from './one.mjs'
 export {sqrt} from './sqrt.mjs'
+export {zero} from './zero.mjs'

src/number/negate.mjs

@@ -1,3 +1,3 @@
-export { Types } from './Types/number.mjs'
+export * from './Types/number.mjs'
 
 export const negate = {number: () => n => -n}

src/number/one.mjs

@@ -0,0 +1,3 @@
+export * from './Types/number.mjs'
+
+export const one = {number: () => () => 1}

src/number/sqrt.mjs

@@ -1,4 +1,4 @@
-export { Types } from './Types/number.mjs'
+export * from './Types/number.mjs'
 
 export const sqrt = {
    number: ({config, complex, 'self(Complex)': complexSqrt}) => {

src/number/zero.mjs

@@ -0,0 +1,3 @@
+export * from './Types/number.mjs'
+
+export const zero = {number: () => () => 0}

src/pocomath.mjs

@@ -1,7 +1,7 @@
 /* Core of pocomath: generates the default instance */
 import PocomathInstance from './core/PocomathInstance.mjs'
 import * as numbers from './number/native.mjs'
-import * as bigints from './bigint/all.mjs'
+import * as bigints from './bigint/native.mjs'
 import * as complex from './complex/native.mjs'
 import * as generic from './generic/all.mjs'