nanomath/src/number/relational.js

import {Returns} from '#core/Type.js'
import {match, Optional} from '#core/TypePatterns.js'
import {boolnum} from './helpers.js'
import {NumberT} from './NumberT.js'

// In nanomath, we take the point of view that two comparators are primitive:
// indistinguishable(a, b, relTol, absTol), and exceeds(a, b). All others
// are defined generically in terms of these. They typically return BooleanT,
// but in a numbers-only bundle, they return 1 or 0.

// Notice a feature of TypedDispatcher: if you specify one tolerance, you must
// specify both.
export const indistinguishable = match(
   [NumberT, NumberT, Optional([NumberT, NumberT])],
   boolnum((a, b, [tolerances = [0, 0]]) => {
      const [relTol, absTol] = tolerances
      if (relTol < 0 || absTol < 0) {
         throw new RangeError(
            `Tolerances (relative: ${relTol}, absolute: ${absTol}) `
            + 'must be nonnegative')
      }
      if (isNaN(a) || isNaN(b)) return false
      if (a === b) return true
      if (!isFinite(a) || !isFinite(b)) return false
      // |a-b| <= absTol  or  |a-b| <= relTol*max(|a|, |b|)
      const diff = Math.abs(a-b)
      if (diff <= absTol) return true
      const magnitude = Math.max(Math.abs(a), Math.abs(b))
      return diff <= relTol * magnitude
   })
)

// Returns truthy if a (interpreted as completely precise) represents a
// greater value than b (interpreted as completely precise). Note that even if
// so, a and b might be indistinguishable() to some tolerances.
export const exceeds = match([NumberT, NumberT], boolnum((a, b) => a > b))