Factor calendar denominators before multiplying

[preciz]

Assisted-by: Codex CLI:GPT 6
Assisted-by: Antigravity:Gemini-3.8-Flash

Reduce intermediate integer sizes by dividing out common denominator factors before multiplication. This speeds up mixed-denominator day-fraction addition while preserving exact results.

Results:

   Microsecond + Nanosecond        |     7.02 M ips (142.5 ns)      |     12.25 M ips (81.6 ns)      |    1.75x faster (-60.9 ns)
   Custom mixed denominators       |     7.33 M ips (136.5 ns)      |     12.21 M ips (81.9 ns)      |    1.67x faster (-54.6 ns)
   Coprime / unaligned             |     9.42 M ips (106.2 ns)      |     11.02 M ips (90.8 ns)      |    1.17x faster (-15.4 ns)

Bench:

Mix.install([:benchee])

defmodule Before do
  def add_day_fraction_to_iso_days({days, {parts, ppd}}, add, add_ppd) do
    parts = parts * add_ppd
    add = add * ppd
    gcd = Integer.gcd(ppd, add_ppd)
    result_parts = div(parts + add, gcd)
    result_ppd = div(ppd * add_ppd, gcd)
    normalize_iso_days(days, result_parts, result_ppd)
  end

  defp normalize_iso_days(days, parts, ppd) do
    days_offset = div(parts, ppd)
    parts = rem(parts, ppd)
    if parts < 0, do: {days + days_offset - 1, {parts + ppd, ppd}}, else: {days + days_offset, {parts, ppd}}
  end
end

defmodule After do
  def add_day_fraction_to_iso_days({days, {parts, ppd}}, add, add_ppd) do
    gcd = Integer.gcd(ppd, add_ppd)
    ppd_factor = div(ppd, gcd)
    add_ppd_factor = div(add_ppd, gcd)
    result_parts = parts * add_ppd_factor + add * ppd_factor
    result_ppd = ppd * add_ppd_factor
    normalize_iso_days(days, result_parts, result_ppd)
  end

  defp normalize_iso_days(days, parts, ppd) do
    days_offset = div(parts, ppd)
    parts = rem(parts, ppd)
    if parts < 0, do: {days + days_offset - 1, {parts + ppd, ppd}}, else: {days + days_offset, {parts, ppd}}
  end
end

inputs = %{
  "microsecond + nanosecond (typical DateTime.add with nanoseconds)" => {
    {730_000, {43_200_000_000, 86_400_000_000}},
    500_000,
    86_400_000_000_000
  },
  "custom mixed denominators (large ppd)" => {
    {730_000, {123_456_789, 1_000_000_000}},
    987_654_321,
    2_000_000_000
  },
  "arbitrary coprime / unaligned denominators" => {
    {730_000, {500_000, 1_000_000}},
    300_000,
    700_000
  }
}

Benchee.run(
  %{
    "before" => fn {iso_days, add, add_ppd} -> Before.add_day_fraction_to_iso_days(iso_days, add, add_ppd) end,
    "after" => fn {iso_days, add, add_ppd} -> After.add_day_fraction_to_iso_days(iso_days, add, add_ppd) end
  },
  inputs: inputs,
  time: 2,
  memory_time: 2
)