Optimize integer division and remainder operations

lib/elixir/lib/calendar/iso.ex

@@ -973,7 +973,7 @@ defmodule Calendar.ISO do
 
   defp div_rem(int1, int2) do
     div = div(int1, int2)
-    rem = int1 - div * int2
+    rem = rem(int1, int2)
 
     if rem >= 0 do
       {div, rem}
@@ -1692,8 +1692,8 @@ defmodule Calendar.ISO do
   def offset_to_iodata(utc, std, _zone, format) do
     total = utc + std
     second = abs(total)
-    minute = second |> rem(3600) |> div(60)
     hour = div(second, 3600)
+    minute = second |> rem(3600) |> div(60)
     format_offset(total, hour, minute, format)
   end
 

lib/elixir/lib/calendar/naive_datetime.ex

@@ -1130,7 +1130,7 @@ defmodule NaiveDateTime do
 
   defp div_rem(int1, int2) do
     div = div(int1, int2)
-    rem = int1 - div * int2
+    rem = rem(int1, int2)
 
     if rem >= 0 do
       {div, rem}

lib/elixir/lib/file/stream.ex

@@ -140,8 +140,10 @@ defmodule File.Stream do
           bom_offset = count_raw_bom(stream, modes)
           offset = get_read_offset(modes)
           size = max(size - bom_offset - offset, 0)
-          remainder = if rem(size, bytes) == 0, do: 0, else: 1
-          {:ok, div(size, bytes) + remainder}
+          div = div(size, bytes)
+          rem = rem(size, bytes)
+          remainder = if rem == 0, do: 0, else: 1
+          {:ok, div + remainder}
 
         {:error, reason} ->
           raise File.Error, reason: reason, action: "stream", path: path

lib/elixir/lib/float.ex

@@ -501,6 +501,7 @@ defmodule Float do
     # on a 64-bit BEAM.
     numerator = rounded_int <<< (1077 - exp)
     quotient = div(numerator, decimal_scale)
+    remainder = rem(numerator, decimal_scale)
     significand = quotient >>> 2
 
     guard_bits = quotient &&& 3
@@ -512,7 +513,7 @@ defmodule Float do
         guard_bits > 2 -> significand + 1
         guard_bits < 2 -> significand
         (significand &&& 1) == 1 -> significand + 1
-        rem(numerator, decimal_scale) != 0 -> significand + 1
+        remainder != 0 -> significand + 1
         true -> significand
       end
 

lib/elixir/lib/integer.ex

@@ -204,10 +204,13 @@ defmodule Integer do
   @doc since: "1.4.0"
   @spec floor_div(integer, neg_integer | pos_integer) :: integer
   def floor_div(dividend, divisor) do
-    if :erlang.xor(dividend < 0, divisor < 0) and rem(dividend, divisor) != 0 do
-      div(dividend, divisor) - 1
+    div = div(dividend, divisor)
+    rem = rem(dividend, divisor)
+
+    if :erlang.xor(dividend < 0, divisor < 0) and rem != 0 do
+      div - 1
     else
-      div(dividend, divisor)
+      div
     end
   end
 
@@ -233,10 +236,13 @@ defmodule Integer do
   @doc since: "1.20.0"
   @spec ceil_div(integer, neg_integer | pos_integer) :: integer
   def ceil_div(dividend, divisor) do
-    if not :erlang.xor(dividend < 0, divisor < 0) and rem(dividend, divisor) != 0 do
-      div(dividend, divisor) + 1
+    div = div(dividend, divisor)
+    rem = rem(dividend, divisor)
+
+    if not :erlang.xor(dividend < 0, divisor < 0) and rem != 0 do
+      div + 1
     else
-      div(dividend, divisor)
+      div
     end
   end
 
@@ -557,7 +563,7 @@ defmodule Integer do
   defp extended_gcd(r1, r0, s1, s0, t1, t0) do
     div = div(r0, r1)
 
-    case r0 - div * r1 do
+    case rem(r0, r1) do
       0 when r1 > 0 -> {r1, s1, t1}
       0 when r1 < 0 -> {-r1, -s1, -t1}
       r2 -> extended_gcd(r2, r1, s0 - div * s1, s1, t0 - div * t1, t1)

lib/elixir/lib/string.ex

@@ -1558,14 +1558,15 @@ defmodule String do
   defp build_filler(0, _source, _padding, _size, filler), do: filler
 
   defp build_filler(count, source, [], size, filler) do
-    rem_filler =
-      rem(count, size)
-      |> build_filler(source, source, 0, [])
+    div = div(count, size)
+    rem = rem(count, size)
+
+    rem_filler = build_filler(rem, source, source, 0, [])
 
     filler =
       filler
       |> IO.iodata_to_binary()
-      |> duplicate(div(count, size) + 1)
+      |> duplicate(div + 1)
 
     [filler | rem_filler]
   end