feat: Implement subtypes

This should eventually be moved into typed-function itself, but for
  now it can be implemented on top of the existing typed-function.

  Uses subtypes to define (and error-check) gcd and lcm, which are only
  defined for integer arguments.

  Resolves #36.

src/bigint/divide.mjs

@@ -1,20 +1,12 @@
 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
-         }
+   'bigint,bigint': ({config, 'quotient(bigint,bigint)': quot}) => {
+      if (config.predictable) return quot
+      return (n, d) => {
+         const q = n/d
+         if (q * d == n) return q
+         return undefined
       }
    }
 }

src/bigint/isZero.mjs

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

src/bigint/multiply.mjs

@@ -1,5 +1,3 @@
 export * from './Types/bigint.mjs'
 
-export const multiply = {
-   '...bigint': () => multiplicands => multiplicands.reduce((x,y) => x*y, 1n)
-}
+export const multiply = {'bigint,bigint': () => (a,b) => a*b}

src/bigint/native.mjs

@@ -1,9 +1,16 @@
+import gcdType from '../generic/gcdType.mjs'
+
 export * from './Types/bigint.mjs'
+
 export {add} from './add.mjs'
 export {divide} from './divide.mjs'
+export const gcd = gcdType('bigint')
+export {isZero} from './isZero.mjs'
 export {multiply} from './multiply.mjs'
 export {negate} from './negate.mjs'
 export {one} from './one.mjs'
 export {sign} from './sign.mjs'
+export {quotient} from './quotient.mjs'
+export {roundquotient} from './roundquotient.mjs'
 export {sqrt} from './sqrt.mjs'
 export {zero} from './zero.mjs'

src/bigint/quotient.mjs

@@ -0,0 +1,13 @@
+export * from './Types/bigint.mjs'
+
+/* Returns the best integer approximation to n/d */
+export const quotient = {
+   'bigint,bigint': ({'sign(bigint)': sgn}) => (n, d) => {
+      const dSgn = sgn(d)
+      if (dSgn === 0n) return 0n
+      if (sgn(n) === dSgn) return n/d
+      const quot = n/d
+      if (quot * d == n) return quot
+      return quot - 1n
+   }
+}

src/bigint/roundquotient.mjs

@@ -0,0 +1,15 @@
+export * from './Types/bigint.mjs'
+
+/* Returns the closest integer approximation to n/d */
+export const roundquotient = {
+   'bigint,bigint': ({'sign(bigint)': sgn}) => (n, d) => {
+      const dSgn = sgn(d)
+      if (dSgn === 0n) return 0n
+      const candidate = n/d
+      const rem = n - d*candidate
+      const absd = d*dSgn
+      if (2n * rem > absd) return candidate + dSgn
+      if (-2n * rem >= absd) return candidate - dSgn
+      return candidate
+   }
+}