feat: Add return typing strategies and implement sqrt with them (#26)

Resolves #25

Reviewed-on: #26
Co-authored-by: Glen Whitney <glen@studioinfinity.org>
Co-committed-by: Glen Whitney <glen@studioinfinity.org>

src/number/arithmetic.js

@@ -1,4 +1,10 @@
 import {plain} from './helpers.js'
+import {NumberT} from './NumberT.js'
+import {OneOf, Returns, ReturnTyping} from '#core/Type.js'
+import {match} from '#core/TypePatterns.js'
+import {Complex} from '#complex/Complex.js'
+
+const {conservative, full} = ReturnTyping
 
 export const abs = plain(Math.abs)
 export const absquare = plain(a => a*a)
@@ -18,5 +24,25 @@ export const cbrt = plain(a => {
 export const invert = plain(a => 1/a)
 export const multiply = plain((a, b) => a * b)
 export const negate = plain(a => -a)
+
+export const sqrt = match(NumberT, (math, _N, strategy) => {
+   if (!math.types.Complex || strategy === conservative) {
+      return Returns(NumberT, Math.sqrt)
+   }
+   const cplx = math.complex.resolve([NumberT, NumberT], full)
+   if (strategy === full) {
+      const cnan = math.nan(Complex(NumberT))
+      return Returns(Complex(NumberT), a => {
+         if (isNaN(a)) return cnan
+         return a >= 0 ? cplx(Math.sqrt(a), 0) : cplx(0, Math.sqrt(-a))
+      })
+   }
+   // strategy === free, return "best" type
+   return Returns(OneOf(NumberT, Complex(NumberT)), a => {
+      if (isNaN(a)) return NaN
+      return a >= 0 ? Math.sqrt(a) : cplx(0, Math.sqrt(-a))
+   })
+})
+
 export const subtract = plain((a, b) => a - b)
 export const quotient = plain((a,b) => Math.floor(a/b))