fake_decimal

defmodule :decimal do
  @moduledoc """
  This library provides a `:decimal` module that has the same functions (API,
  interface) as the good^H^H^H^Hbad old `erlang_decimal` library, but it is
  just an interface to the Elixir `Decimal` library.

  The old `erlang_decimal` used 2-tuples with integers in it to represent
  numbers, while the Elixir `decimal` uses structs. By using this library, the
  module `:decimal` serves as the old API, and the module `Decimal` as the new
  one. Unfortunately, the application names clash in the package `decimal` and
  `erlang_decimal`, so you cannot use them at once, but `fake_decimal` plays
  nicely with the Elixir `decimal`.

  If there's a legacy application that calls into `:decimal`, but you also need
  the Elixir `decimal` library in your app, you may be able to provide the old
  API for the legacy app by using `fake_decimal`.

  The functions where rounding semantics matter (`round/3`, `divide/3`,
  `sqrt/2`, `cmp/3`, `fast_cmp/2`, `to_binary/1,2`) reproduce the original
  `erlang_decimal` algorithms exactly: `precision` counts fractional digits
  (decimal places, not significant digits), and the `round_half_up` /
  `round_half_down` modes decide based on the first discarded digit only,
  just like the original.

  ## Deviations from `erlang_decimal`

    * `add/2`, `sub/2` and `mult/2` results are normalized: `add({1, 0}, {9, 0})`
      returns `{1, 1}` where the original returns `{10, 0}`. The two tuples are
      numerically equal (`cmp/3` returns `0` and `reduce/1` maps both to the
      same tuple), but code that pattern-matches exact tuples may see a
      different — equivalent — representation.

    * Wherever the original accepts only `{coef, exp}` tuples, this module also
      accepts Elixir `Decimal` structs, integers, floats, strings and charlists.
  """

  import Kernel, except: [abs: 1]

  defguardp is_erlang_decimal(d)
            when tuple_size(d) == 2 and is_integer(elem(d, 0)) and is_integer(elem(d, 1))

  # The pre-erlang_decimal "old" format: {sign, coef, exp} with sign 1 = negative.
  defguardp is_old_decimal(d)
            when tuple_size(d) == 3 and elem(d, 0) in [0, 1] and is_integer(elem(d, 1)) and
                   is_integer(elem(d, 2))

  ############################
  ####  Converters

  def to_decimal(value) when is_erlang_decimal(value), do: value
  def to_decimal({0, coef, exp} = value) when is_old_decimal(value), do: {coef, exp}
  def to_decimal({1, coef, exp} = value) when is_old_decimal(value), do: {-coef, exp}
  def to_decimal(%Decimal{sign: s, coef: c, exp: e}), do: {s * c, e}
  def to_decimal(value) when is_integer(value), do: {value, 0}
  def to_decimal(value) when is_float(value), do: to_decimal(Decimal.from_float(value))
  def to_decimal(value) when is_list(value), do: to_decimal(Decimal.new(to_string(value)))
  def to_decimal(value), do: to_decimal(Decimal.new(value))

  def to_decimal(value, _opts) when is_erlang_decimal(value) or is_old_decimal(value),
    do: to_decimal(value)

  def to_decimal(value, %{precision: precision, rounding: rounding}),
    do: do_round(rounding, to_decimal(value), precision)

  def to_decimal(value, _opts), do: to_decimal(value)

  def to_decimal(base, exp, _opts), do: {base, exp}

  def to_binary(a), do: format(to_decimal(a), true)

  def to_binary(a, opts), do: format(to_decimal(a), opts[:pretty] == true)

  ############################
  ####  Arith

  def add(a, b), do: exact_lift(:add, a, b)

  def sub(a, b), do: exact_lift(:sub, a, b)

  def mult(a, b), do: exact_lift(:mult, a, b)

  def divide(a, b, opts), do: do_divide(to_decimal(a), to_decimal(b), opts)

  defp do_divide({_, _}, {0, _}, _opts), do: :erlang.error(:badarith)
  defp do_divide({0, _}, {_, _}, _opts), do: {0, 0}

  defp do_divide({base_a, exp_a}, {base_b, exp_b}, opts) when base_b < 0,
    do: do_divide({-base_a, exp_a}, {-base_b, exp_b}, opts)

  defp do_divide({base_a, exp_a}, {base_b, exp_b}, %{precision: precision0, rounding: rounding}) do
    precision = max(0, exp_a - exp_b) + precision0 + 1
    base_res = div(base_a * pow10(precision), base_b)
    do_round(rounding, {base_res, exp_a - exp_b - precision}, precision0)
  end

  def sqrt(a, opts), do: do_sqrt(to_decimal(a), opts)

  defp do_sqrt({coef, _exp}, _opts) when coef < 0, do: :erlang.error(:badarith)
  defp do_sqrt({0, _exp}, _opts), do: {0, 0}

  defp do_sqrt({coef, exp} = decimal, %{precision: precision0} = opts) do
    precision = precision0 + 1
    coef_digits = length(Integer.digits(coef))

    if rem(exp, 2) == 0 do
      shift = precision - div(coef_digits + 1, 2)
      do_sqrt(decimal, opts, shift, coef)
    else
      shift = precision - (div(coef_digits, 2) + 1)
      do_sqrt(decimal, opts, shift, coef * 10)
    end
  end

  defp do_sqrt(decimal, opts, shift, coef) do
    if shift >= 0 do
      do_sqrt(decimal, opts, shift, coef * pow10(2 * shift), true)
    else
      operand = pow10(-2 * shift)
      do_sqrt(decimal, opts, shift, div(coef, operand), rem(coef, operand) == 0)
    end
  end

  defp do_sqrt({_, exp0}, %{precision: precision, rounding: rounding}, shift, coef, exact) do
    exp = Integer.floor_div(exp0, 2)
    n = isqrt(coef, pow10(precision + 1))

    result =
      cond do
        exact and n * n == coef and shift >= 0 -> {div(n, pow10(shift)), exp}
        exact and n * n == coef -> {n * pow10(-shift), exp}
        true -> {n, exp - shift}
      end

    do_round(rounding, result, precision)
  end

  defp isqrt(m, n) do
    q = div(m, n)
    if n <= q, do: n, else: isqrt(m, div(n + q, 2))
  end

  ############################
  ####  Compare

  def cmp(a, b, opts), do: do_cmp(to_decimal(a), to_decimal(b), opts)

  defp do_cmp({0, _}, {0, _}, _opts), do: 0
  defp do_cmp({coef1, _}, {coef2, _}, _opts) when coef1 >= 0 and coef2 <= 0, do: 1
  defp do_cmp({coef1, _}, {coef2, _}, _opts) when coef1 <= 0 and coef2 >= 0, do: -1
  defp do_cmp({coef, exp}, {coef, exp}, _opts), do: 0
  defp do_cmp({coef1, exp}, {coef2, exp}, _opts) when coef1 > coef2, do: 1
  defp do_cmp({coef1, exp}, {coef2, exp}, _opts) when coef1 < coef2, do: -1

  defp do_cmp(a, b, %{precision: precision, rounding: rounding}),
    do: exact_cmp(do_round(rounding, a, precision), do_round(rounding, b, precision))

  defp do_cmp(a, b, _opts), do: exact_cmp(a, b)

  def fast_cmp(a, b), do: exact_cmp(to_decimal(a), to_decimal(b))

  defp exact_cmp({coef1, exp1}, {coef2, exp2}) do
    exp_min = min(exp1, exp2)
    scaled1 = coef1 * pow10(exp1 - exp_min)
    scaled2 = coef2 * pow10(exp2 - exp_min)

    cond do
      scaled1 < scaled2 -> -1
      scaled1 > scaled2 -> 1
      true -> 0
    end
  end

  ############################
  ####  Utils

  def abs(a) do
    {coef, exp} = to_decimal(a)
    {Kernel.abs(coef), exp}
  end

  def minus(a) do
    {coef, exp} = to_decimal(a)
    {-coef, exp}
  end

  def is_zero(a), do: match?({0, _}, to_decimal(a))

  def reduce(a), do: reduce_coef(to_decimal(a))

  def round(mode, num, precision \\ 0), do: do_round(mode, to_decimal(num), precision)

  ############################
  ####  Helpers

  # The original computes add/sub/mult exactly, so widen the context enough
  # to hold the full result before delegating to the Elixir Decimal library.
  defp exact_lift(function, a, b) do
    {coef1, exp1} = to_decimal(a)
    {coef2, exp2} = to_decimal(b)
    digits1 = length(Integer.digits(coef1))
    digits2 = length(Integer.digits(coef2))

    needed =
      case function do
        :mult -> digits1 + digits2
        _ -> max(digits1 + exp1, digits2 + exp2) - min(exp1, exp2) + 1
      end

    context = Decimal.Context.get()
    context = %{context | precision: max(context.precision, needed)}
    Decimal.Context.with(context, fn -> lift(Decimal, function, [a, b]) end)
  end

  defp lift(module, function, args) do
    apply(module, function, Enum.map(args, &to_elixir_decimal/1))
    |> case do
      %Decimal{} = value -> to_decimal(Decimal.apply_context(Decimal.normalize(value)))
      other -> other
    end
  end

  defp do_round(rounding, {_coef, exp} = decimal, precision) do
    case -precision - exp do
      delta when delta > 0 -> reduce_coef(round_coef(rounding, decimal, delta))
      _ -> reduce_coef(decimal)
    end
  end

  defp round_coef(:round_down, {coef, exp}, delta) do
    zero_exp(div(coef, pow10(delta)), exp + delta)
  end

  defp round_coef(mode, {coef, exp}, delta) when mode in [:round_ceiling, :round_floor] do
    p = pow10(delta)
    base = div(coef, p)
    diff = coef - base * p

    base =
      cond do
        mode == :round_floor and diff < 0 -> base - 1
        mode == :round_ceiling and diff > 0 -> base + 1
        true -> base
      end

    zero_exp(base, exp + delta)
  end

  defp round_coef(mode, {coef, exp}, delta) do
    # Like the original, the half modes only look at the first discarded digit.
    data = div(coef, pow10(delta - 1))
    base = div(data, 10)
    last_digit = Kernel.abs(data - base * 10)

    base =
      cond do
        mode == :round_half_up and last_digit >= 5 and data > 0 -> base + 1
        mode == :round_half_up and last_digit >= 5 and data < 0 -> base - 1
        mode == :round_half_down and last_digit > 5 and data > 0 -> base + 1
        mode == :round_half_down and last_digit > 5 and data < 0 -> base - 1
        true -> base
      end

    zero_exp(base, exp + delta)
  end

  defp zero_exp(0, _exp), do: {0, 0}
  defp zero_exp(coef, exp), do: {coef, exp}

  defp reduce_coef({0, _exp}), do: {0, 0}

  defp reduce_coef({coef, exp}) do
    if rem(coef, 10) == 0, do: reduce_coef({div(coef, 10), exp + 1}), else: {coef, exp}
  end

  defp format({coef, 0}, _pretty), do: "#{coef}.0"

  defp format({coef, exp}, pretty) do
    sign = if coef < 0, do: "-", else: ""
    digits = Integer.to_string(Kernel.abs(coef))
    adjusted = byte_size(digits) + exp - 1

    cond do
      exp < 0 and (not pretty or adjusted > -6) ->
        if adjusted < 0 do
          sign <> "0." <> String.duplicate("0", -(adjusted + 1)) <> digits
        else
          {int_part, frac_part} = String.split_at(digits, adjusted + 1)
          sign <> int_part <> "." <> frac_part
        end

      exp >= 0 and (not pretty or adjusted < 6) ->
        sign <> digits <> String.duplicate("0", exp) <> ".0"

      byte_size(digits) == 1 ->
        sign <> digits <> ".0" <> exp_suffix(adjusted)

      true ->
        {first, rest} = String.split_at(digits, 1)
        sign <> first <> "." <> rest <> exp_suffix(adjusted)
    end
  end

  defp exp_suffix(0), do: ""
  defp exp_suffix(exp), do: "e#{exp}"

  defp pow10(n) when n > 0, do: Integer.pow(10, n)
  defp pow10(_n), do: 1

  defp to_elixir_decimal({c, e} = d) when is_erlang_decimal(d),
    do: Decimal.new(sign(c), Kernel.abs(c), e)

  defp to_elixir_decimal(value) when is_float(value), do: Decimal.from_float(value)
  defp to_elixir_decimal(value), do: Decimal.new(value)

  defp sign(x) when x < 0, do: -1
  defp sign(_), do: 1
end