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}