Improve rounding in the number formatter (#56)

Author: ntwilson

src/Data/Formatter/Number.js

@@ -0,0 +1,5 @@
+
+// converts a number to a string of the nearest integer _without_ appending ".0" (like `show` for `Number`) or
+// clamping to +/- 2 billion (like when working with `Int`). This is important for performance compared to other
+// means of showing an integer potentially larger than +/- 2 billion.
+exports.showNumberAsInt = function (n) { return Math.round(n).toString(); }

src/Data/Formatter/Number.purs

@@ -82,7 +82,18 @@ formatParser = do
     , abbreviations: isJust abbreviations
     }
 
-
+-- converts a number to a string of the nearest integer _without_ appending ".0" (like `show` for `Number`) or
+-- clamping to +/- 2 billion (like when working with `Int`). This is important for performance compared to other
+-- means of showing an integer potentially larger than +/- 2 billion.
+foreign import showNumberAsInt :: Number -> String
+
+-- | Formats a number according to the format object provided. 
+-- | Due to the nature of floating point numbers, may yield unpredictable results for extremely 
+-- | large or extremely small numbers, such as numbers whose absolute values are ≥ 1e21 or ≤ 1e-21,
+-- | or when formatting with > 20 digits after the decimal place.  
+-- | See [purescript-decimals](https://pursuit.purescript.org/packages/purescript-decimals/4.0.0) 
+-- | for working with arbitrary precision decimals, which supports simple number
+-- | formatting for numbers that go beyond the precision available with `Number`.
 format ∷ Formatter → Number → String
 format (Formatter f) num =
   let
@@ -111,18 +122,20 @@ format (Formatter f) num =
      else
        let
          zeros = f.before - tens - one
-         integer = Int.floor absed
-         leftover = absed - Int.toNumber integer
-         rounded = Int.round $ leftover * (Math.pow 10.0 (Int.toNumber f.after))
-         roundedWithZeros =
-           let roundedString = show rounded
-               roundedLength = Str.length roundedString
-               zeros' = repeat "0" (f.after - roundedLength)
-           in zeros' <> roundedString
-         shownNumber =
+         factor = Math.pow 10.0 (Int.toNumber (max 0 f.after))
+         rounded = Math.round (absed * factor) / factor
+         integer = Math.floor rounded
+         leftoverDecimal = rounded - integer
+         leftover = Math.round $ leftoverDecimal * factor
+         leftoverWithZeros =
+           let leftoverString = showNumberAsInt leftover
+               leftoverLength = Str.length leftoverString
+               zeros' = repeat "0" (f.after - leftoverLength)
+           in zeros' <> leftoverString
+         shownInt =
            if f.comma
-             then addCommas [] zero (Arr.reverse (CU.toCharArray (repeat "0" zeros <> show integer)))
-             else repeat "0" zeros <> show integer
+             then addCommas [] zero (Arr.reverse (CU.toCharArray (repeat "0" zeros <> showNumberAsInt integer)))
+             else repeat "0" zeros <> showNumberAsInt integer
 
          addCommas ∷ Array Char → Int → Array Char → String
          addCommas acc counter input = case Arr.uncons input of
@@ -133,13 +146,13 @@ format (Formatter f) num =
              addCommas (Arr.cons ',' acc) zero input
        in
         (if num < zero then "-" else if num > zero && f.sign then "+" else "")
-        <> shownNumber
+        <> shownInt
         <> (if f.after < 1
               then ""
               else
               "."
-              <> (if rounded == 0 then repeat "0" f.after else "")
-              <> (if rounded > 0 then roundedWithZeros else ""))
+              <> (if leftover == 0.0 then repeat "0" f.after else "")
+              <> (if leftover > 0.0 then leftoverWithZeros else ""))
 
 
 unformat ∷ Formatter → String → Either String Number

test/src/Number.purs

@@ -36,6 +36,24 @@ numberTest = describe "Data.Formatter.Number" do
     ["+02.12", "+13.12", "-02.12", "-13.12"]
     (\n →  (format fmt3 <$> (unformat fmt3 n)) `shouldEqual` (Right n))
 
+  forAll (\{fmt: (Formatter fmt), input} -> "rounds up " <> show input <> " (" <> show fmt.after <> " digits)")
+    "rounding"
+    [ {fmt: fmt4, input: 1.99999, expected: "02"}
+    , {fmt: fmt1, input: 1.99999, expected: "002.00"}
+    , {fmt: fmt5, input: 1.99999, expected: "2.0000"}
+    , {fmt: fmt1, input: 1.89999, expected: "001.90"}
+    , {fmt: fmt5, input: 1.67899, expected: "1.6790"}
+    , {fmt: fmt6, input: 12.9, expected: "13"}
+    , {fmt: fmt7, input: 1.123456789012345678901234, expected: "1.1234567890123457"}
+    , {fmt: fmt6, input: 12345678901234567.8901234, expected: "12,345,678,901,234,568"}
+    , {fmt: fmt5, input: 123456789012.345678901234, expected: "123,456,789,012.3457"}
+    ]
+    (\{fmt, input, expected} -> do
+      format fmt input `shouldEqual` expected
+      format fmt (negate input) `shouldEqual` ("-" <> expected)
+    )
+
+
 fmt1 ∷ Formatter
 fmt1 = Formatter
   { comma: false
@@ -63,6 +81,42 @@ fmt3 = Formatter
   , sign: true
   }
 
+fmt4 ∷ Formatter
+fmt4 = Formatter
+  { comma: false
+  , before: 2
+  , after: 0
+  , abbreviations: false
+  , sign: false
+  }
+
+fmt5 ∷ Formatter
+fmt5 = Formatter
+  { comma: true
+  , before: 1
+  , after: 4
+  , abbreviations: false
+  , sign: false
+  }
+
+fmt6 ∷ Formatter
+fmt6 = Formatter
+  { comma: true
+  , before: 1
+  , after: -1
+  , abbreviations: false
+  , sign: false
+  }
+
+fmt7 ∷ Formatter
+fmt7 = Formatter
+  { comma: true
+  , before: 1
+  , after: 16
+  , abbreviations: false
+  , sign: false
+  }
+
 numberformatts ∷ Array { fmt ∷ Formatter, str ∷ String }
 numberformatts =
   [ { str: "000.00"