local nodefactory = require("core.nodefactory")
local hb = require("justenoughharfbuzz")
local ot = require("core.opentype-parser")
local syms = require("packages.math.unicode-symbols")

local atomType = syms.atomType
local symbolDefaults = syms.symbolDefaults

local elements = {}

local mathMode = {
  display = 0,
  displayCramped = 1,
  text = 2,
  textCramped = 3,
  script = 4,
  scriptCramped = 5,
  scriptScript = 6,
  scriptScriptCramped = 7
}

local scriptType = {
  upright = 1,
  bold = 2, -- also have Greek and digits
  italic = 3, -- also have Greek
  boldItalic = 4, -- also have Greek
  script = 5,
  boldScript = 6,
  fraktur = 7,
  boldFraktur = 8,
  doubleStruck = 9, -- also have digits
  sansSerif = 10, -- also have digits
  sansSerifBold = 11, -- also have Greek and digits
  sansSerifItalic = 12,
  sansSerifBoldItalic = 13, -- also have Greek
  monospace = 14, -- also have digits
}

local mathVariantToScriptType = function(attr)
  return
    attr == "normal" and scriptType.upright or
    attr == "bold" and scriptType.bold or
    attr == "italic" and scriptType.italic or
    attr == "bold-italic" and scriptType.boldItalic or
    attr == "double-struck" and scriptType.doubleStruck or
    SU.error("Invalid value \""..attr.."\" for option mathvariant")
end

local function isDisplayMode(mode)
  return mode <= 1
end

local function isCrampedMode(mode)
  return mode % 2 == 1
end

local function isScriptMode(mode)
  return mode == mathMode.script or mode == mathMode.scriptCramped
end

local function isScriptScriptMode(mode)
  return mode == mathMode.scriptScript or mode == mathMode.scriptScriptCramped
end

local mathScriptConversionTable = {
  capital = {
    [scriptType.upright] = function(codepoint) return codepoint end,
    [scriptType.bold] = function(codepoint)
      return codepoint + 0x1D400 - 0x41
    end,
    [scriptType.italic] = function(codepoint) return codepoint + 0x1D434 - 0x41 end,
    [scriptType.boldItalic] = function(codepoint) return codepoint + 0x1D468 - 0x41 end,
    [scriptType.doubleStruck] = function(codepoint)
      return codepoint == 0x43 and 0x2102 or
        codepoint == 0x48 and 0x210D or
        codepoint == 0x4E and 0x2115 or
        codepoint == 0x50 and 0x2119 or
        codepoint == 0x51 and 0x211A or
        codepoint == 0x52 and 0x211D or
        codepoint == 0x5A and 0x2124 or
        codepoint + 0x1D538 - 0x41
    end
  },
  small = {
    [scriptType.upright] = function(codepoint) return codepoint end,
    [scriptType.bold] = function(codepoint) return codepoint + 0x1D41A - 0x61 end,
    [scriptType.italic] = function(codepoint) return codepoint == 0x68 and 0x210E or codepoint + 0x1D44E - 0x61 end,
    [scriptType.boldItalic] = function(codepoint) return codepoint + 0x1D482 - 0x61 end,
    [scriptType.doubleStruck] = function(codepoint) return codepoint + 0x1D552 - 0x61 end,
  }
}

local mathCache = {}

local function retrieveMathTable(font)
  local key = SILE.font._key(font)
  if not mathCache[key] then
    SU.debug("math", "Loading math font", key)
    local face = SILE.font.cache(font, SILE.shaper.getFace)
    if not face then
      SU.error("Could not find requested font ".. font .." or any suitable substitutes")
    end
    local mathTable = ot.parseMath(hb.get_table(face.data, face.index, "MATH"))
    local upem = ot.parseHead(hb.get_table(face.data, face.index, "head")).unitsPerEm
    if mathTable == nil then
      SU.error("You must use a math font for math rendering.")
    end
    local constants = {}
    for k, v in pairs(mathTable.mathConstants) do
      if type(v) == "table" then v = v.value end
      if k:sub(-9) == "ScaleDown" then constants[k] = v / 100
      else
        constants[k] = v * font.size / upem
      end
    end
    local italicsCorrection = {}
    for k, v in pairs(mathTable.mathItalicsCorrection) do
      italicsCorrection[k] = v.value * font.size / upem
    end
    mathCache[key] = {
      constants = constants,
      italicsCorrection = italicsCorrection,
      mathVariants = mathTable.mathVariants,
      unitsPerEm = upem
    }
  end
  return mathCache[key]
end

-- Style transition functions for superscript and subscript
local function getSuperscriptMode(mode)
  -- D, T -> S
  if mode == mathMode.display or mode == mathMode.text then
    return mathMode.script
  -- D', T' -> S'
  elseif mode == mathMode.displayCramped or mode == mathMode.textCramped then
    return mathMode.scriptCramped
  -- S, SS -> SS
  elseif mode == mathMode.script or mode == mathMode.scriptScript then
    return mathMode.scriptScript
  -- S', SS' -> SS'
  else return mathMode.scriptScriptCramped end
end
local function getSubscriptMode(mode)
  -- D, T, D', T' -> S'
  if mode == mathMode.display or mode == mathMode.text
      or mode == mathMode.displayCramped or mode == mathMode.textCramped then
      return mathMode.scriptCramped
  -- S, SS, S', SS' -> SS'
  else return mathMode.scriptScriptCramped end
end

-- Style transition functions for fraction (numerator and denominator)
local function getNumeratorMode(mode)
  -- D -> T
  if mode == mathMode.display then
    return mathMode.text
  -- D' -> T'
  elseif mode == mathMode.displayCramped then
    return mathMode.textCramped
  -- T -> S
  elseif mode == mathMode.text then
    return mathMode.script
  -- T' -> S'
  elseif mode == mathMode.textCramped then
    return mathMode.scriptCramped
  -- S, SS -> SS
  elseif mode == mathMode.script or mode == mathMode.scriptScript then
    return mathMode.scriptScript
  -- S', SS' -> SS'
  else return mathMode.scriptScriptCramped end
end
local function getDenominatorMode(mode)
  -- D, D' -> T'
  if mode == mathMode.display or mode == mathMode.displayCramped then
    return mathMode.textCramped
  -- T, T' -> S'
  elseif mode == mathMode.text or mode == mathMode.textCramped then
    return mathMode.scriptCramped
  -- S, SS, S', SS' -> SS'
  else return mathMode.scriptScriptCramped end
end

local function getRightMostGlyphId(node)
  while node and node:is_a(elements.stackbox) and node.direction == 'H' do
    node = node.children[#(node.children)]
  end
  if node and node:is_a(elements.text) then
    return node.value.glyphString[#(node.value.glyphString)]
  else
    return 0
  end
end

-- Compares two SILE length, without considering shrink or stretch values, and
-- returns the biggest.
local function maxLength(...)
  local arg = {...}
  local m
  for i, v in ipairs(arg) do
    if i == 1 then
      m = v
    else
      if v.length:tonumber() > m.length:tonumber() then
        m = v
      end
    end
  end
  return m
end

local function scaleWidth(length, line)
  local number = length.length
  if line.ratio and line.ratio < 0 and length.shrink:tonumber() > 0 then
    number = number + length.shrink * line.ratio
  elseif line.ratio and line.ratio > 0 and length.stretch:tonumber() > 0 then
    number = number + length.stretch * line.ratio
  end
  return number
end

-- math box, box with a horizontal shift value and could contain zero or more
-- mbox'es (or its child classes) the entire math environment itself is
-- a top-level mbox.
-- Typesetting of mbox evolves four steps:
--   1. Determine the mode for each mbox according to their parent.
--   2. Shape the mbox hierarchy from leaf to top. Get the shape and relative position.
--   3. Convert mbox into _nnode's to put in SILE's typesetting framwork
elements.mbox = pl.class(nodefactory.hbox)
elements.mbox._type = "Mbox"

function elements.mbox:__tostring ()
  return self._type
end

function elements.mbox:_init ()
  nodefactory.hbox._init(self)
  self.font = {}
  self.children = {} -- The child nodes
  self.relX = SILE.length(0) -- x position relative to its parent box
  self.relY = SILE.length(0) -- y position relative to its parent box
  self.value = {}
  self.mode = mathMode.display
  self.atom = atomType.ordinary
  local font = {
    family=SILE.settings:get("math.font.family"),
    size=SILE.settings:get("math.font.size")
  }
  local filename = SILE.settings:get("math.font.filename")
  if filename and filename ~= "" then font.filename = filename end
  self.font = SILE.font.loadDefaults(font)
end

function elements.mbox.styleChildren (_)
  SU.error("styleChildren is a virtual function that need to be overriden by its child classes")
end

function elements.mbox.shape (_, _, _)
  SU.error("shape is a virtual function that need to be overriden by its child classes")
end

function elements.mbox.output (_, _, _, _)
  SU.error("output is a virtual function that need to be overriden by its child classes")
end

function elements.mbox:getMathMetrics ()
  return retrieveMathTable(self.font)
end

function elements.mbox:getScaleDown ()
  local constants = self:getMathMetrics().constants
  local scaleDown
  if isScriptMode(self.mode) then
    scaleDown = constants.scriptPercentScaleDown
  elseif isScriptScriptMode(self.mode) then
    scaleDown = constants.scriptScriptPercentScaleDown
  else
    scaleDown = 1
  end
  return scaleDown
end

  -- Determine the mode of its descendants
function elements.mbox:styleDescendants ()
  self:styleChildren()
  for _, n in ipairs(self.children) do
    if n then n:styleDescendants() end
  end
end

  -- shapeTree shapes the mbox and all its descendants in a recursive fashion
  -- The inner-most leaf nodes determine their shape first, and then propagate to their parents
  -- During the process, each node will determine its size by (width, height, depth)
  -- and (relX, relY) which the relative position to its parent
function elements.mbox:shapeTree ()
  for _, n in ipairs(self.children) do
    if n then n:shapeTree() end
  end
  self:shape()
end

  -- Output the node and all its descendants
function elements.mbox:outputTree (x, y, line)
  self:output(x, y, line)
  local debug = SILE.settings:get("math.debug.boxes")
  if debug and not (self:is_a(elements.space)) then
    SILE.outputter:setCursor(scaleWidth(x, line), y.length)
    SILE.outputter:debugHbox(
      { height = self.height.length,
        depth = self.depth.length },
      scaleWidth(self.width, line)
    )
  end
  for _, n in ipairs(self.children) do
    if n then n:outputTree(x + n.relX, y + n.relY, line) end
  end
end

local spaceKind = {
  thin = "thin",
  med = "med",
  thick = "thick",
}

-- Indexed by left atom
local spacingRules = {
  [atomType.ordinary] = {
    [atomType.bigOperator] = {spaceKind.thin},
    [atomType.binaryOperator] = {spaceKind.med, notScript = true},
    [atomType.relationalOperator] = {spaceKind.thick, notScript = true},
    [atomType.inner] = {spaceKind.thin, notScript = true}
  },
  [atomType.bigOperator] = {
    [atomType.ordinary] = {spaceKind.thin},
    [atomType.bigOperator] = {spaceKind.thin},
    [atomType.relationalOperator] = {spaceKind.thick, notScript = true},
    [atomType.inner] = {spaceKind.thin, notScript = true},
  },
  [atomType.binaryOperator] = {
    [atomType.ordinary] = {spaceKind.med, notScript = true},
    [atomType.bigOperator] = {spaceKind.med, notScript = true},
    [atomType.openingSymbol] = {spaceKind.med, notScript = true},
    [atomType.inner] = {spaceKind.med, notScript = true}
  },
  [atomType.relationalOperator] = {
    [atomType.ordinary] = {spaceKind.thick, notScript = true},
    [atomType.bigOperator] = {spaceKind.thick, notScript = true},
    [atomType.openingSymbol] = {spaceKind.thick, notScript = true},
    [atomType.inner] = {spaceKind.thick, notScript = true}
  },
  [atomType.closeSymbol] = {
    [atomType.bigOperator] = {spaceKind.thin},
    [atomType.binaryOperator] = {spaceKind.med, notScript = true},
    [atomType.relationalOperator] = {spaceKind.thick, notScript = true},
    [atomType.inner] = {spaceKind.thin, notScript = true}
  },
  [atomType.punctuationSymbol] = {
    [atomType.ordinary] = {spaceKind.thin, notScript = true},
    [atomType.bigOperator] = {spaceKind.thin, notScript = true},
    [atomType.relationalOperator] = {spaceKind.thin, notScript = true},
    [atomType.openingSymbol] = {spaceKind.thin, notScript = true},
    [atomType.closeSymbol] = {spaceKind.thin, notScript = true},
    [atomType.punctuationSymbol] = {spaceKind.thin, notScript = true},
    [atomType.inner] = {spaceKind.thin, notScript = true}
  },
  [atomType.inner] = {
    [atomType.ordinary] = {spaceKind.thin, notScript = true},
    [atomType.bigOperator] = {spaceKind.thin},
    [atomType.binaryOperator] = {spaceKind.med, notScript = true},
    [atomType.relationalOperator] = {spaceKind.thick, notScript = true},
    [atomType.openingSymbol] = {spaceKind.thin, notScript = true},
    [atomType.punctuationSymbol] = {spaceKind.thin, notScript = true},
    [atomType.inner] = {spaceKind.thin, notScript = true}
  }
}

-- _stackbox stacks its content one, either horizontally or vertically
elements.stackbox = pl.class(elements.mbox)
elements.stackbox._type = "Stackbox"

function elements.stackbox:__tostring ()
  local result = self.direction.."Box("
  for i, n in ipairs(self.children) do
    result = result..(i == 1 and "" or ", ")..tostring(n)
  end
  result = result..")"
  return result
end

function elements.stackbox:_init (direction, children)
  elements.mbox._init(self)
  if not (direction == "H" or direction == "V") then
    SU.error("Wrong direction '"..direction.."'; should be H or V")
  end
  self.direction = direction
  self.children = children
end

function elements.stackbox:styleChildren ()
  for _, n in ipairs(self.children) do
    n.mode = self.mode
  end
  if self.direction == "H" then
    -- Insert spaces according to the atom type, following Knuth's guidelines
    -- in the TeXbook
    local spaces = {}
    for i = 1, #self.children-1 do
      local v = self.children[i]
      local v2 = self.children[i + 1]
      if spacingRules[v.atom] and spacingRules[v.atom][v2.atom] then
        local rule = spacingRules[v.atom][v2.atom]
        if not (rule.notScript and (isScriptMode(self.mode) or isScriptScriptMode(self.mode))) then
          spaces[i+1] = rule[1]
        end
      end
    end
    local spaceIdx = {}
    for i, _ in pairs(spaces) do
      table.insert(spaceIdx, i)
    end
    table.sort(spaceIdx, function(a, b) return a > b end)
    for _, idx in ipairs(spaceIdx) do
      local hsp = elements.space(spaces[idx], 0, 0)
      table.insert(self.children, idx, hsp)
    end
  end
end

function elements.stackbox:shape ()
  -- For a horizontal stackbox (i.e. mrow):
  -- 1. set self.height and self.depth to max element height & depth
  -- 2. handle stretchy operators
  -- 3. set self.width
  -- For a vertical stackbox:
  -- 1. set self.width to max element width
  -- 2. set self.height
  -- And finally set children's relative coordinates
  self.height = SILE.length(0)
  self.depth = SILE.length(0)
  if self.direction == "H" then
    for i, n in ipairs(self.children) do
      n.relY = SILE.length(0)
      self.height = i == 1 and n.height or maxLength(self.height, n.height)
      self.depth = i == 1 and n.depth or maxLength(self.depth, n.depth)
    end
    -- Handle stretchy operators
    for _, elt in ipairs(self.children) do
      if elt.is_a(elements.text) and elt.kind == 'operator'
          and elt.stretchy then
        elt:stretchyReshape(self.depth, self.height)
      end
    end
    -- Set self.width
    self.width = SILE.length(0)
    for i, n in ipairs(self.children) do
      n.relX = self.width
      self.width = i == 1 and n.width or self.width + n.width
    end
  else -- self.direction == "V"
    for i, n in ipairs(self.children) do
      n.relX = SILE.length(0)
      self.width = i == 1 and n.width or maxLength(self.width, n.width)
    end
    -- Set self.height and self.depth
    for i, n in ipairs(self.children) do
      self.depth = i == 1 and n.depth or self.depth + n.depth
    end
    for i = 1, #self.children do
      local n = self.children[i]
      if i == 1 then
        self.height = n.height
        self.depth = n.depth
      elseif i > 1 then
        n.relY = self.children[i - 1].relY + self.children[i - 1].depth + n.height
        self.depth = self.depth + n.height + n.depth
      end
    end
  end
end

-- Despite of its name, this function actually output the whole tree of nodes recursively.
function elements.stackbox:outputYourself (typesetter, line)
  local mathX = typesetter.frame.state.cursorX
  local mathY = typesetter.frame.state.cursorY
  self:outputTree(self.relX + mathX, self.relY + mathY, line)
  typesetter.frame:advanceWritingDirection(scaleWidth(self.width, line))
end

function elements.stackbox.output (_, _, _, _) end

elements.subscript = pl.class(elements.mbox)
elements.subscript._type = "Subscript"

function elements.subscript:__tostring ()
  return (self.sub and "Subscript" or "Superscript") .. "(" ..
    tostring(self.base) .. ", " .. tostring(self.sub or self.super) .. ")"
end

function elements.subscript:_init (base, sub, sup)
  elements.mbox._init(self)
  self.base = base
  self.sub = sub
  self.sup = sup
  if self.base then table.insert(self.children, self.base) end
  if self.sub then table.insert(self.children, self.sub) end
  if self.sup then table.insert(self.children, self.sup) end
  self.atom = self.base.atom
end

function elements.subscript:styleChildren ()
  if self.base then self.base.mode = self.mode end
  if self.sub then self.sub.mode = getSubscriptMode(self.mode) end
  if self.sup then self.sup.mode = getSuperscriptMode(self.mode) end
end

function elements.subscript:calculateItalicsCorrection ()
  local lastGid = getRightMostGlyphId(self.base)
  if lastGid > 0 then
    local mathMetrics = self:getMathMetrics()
    if mathMetrics.italicsCorrection[lastGid] then
      return mathMetrics.italicsCorrection[lastGid]
    end
  end
  return 0
end

function elements.subscript:shape ()
  local mathMetrics = self:getMathMetrics()
  local constants = mathMetrics.constants
  local scaleDown = self:getScaleDown()
  if self.base then
    self.base.relX = SILE.length(0)
    self.base.relY = SILE.length(0)
    -- Use widthForSubscript of base, if available
    self.width = self.base.widthForSubscript or self.base.width
  else
    self.width = SILE.length(0)
  end
  local itCorr = self:calculateItalicsCorrection() * scaleDown
  local subShift
  local supShift
  if self.sub then
    if self.isUnderOver or self.base.largeop then
      -- Ad hoc correction on integral limits, following LuaTeX's
      -- `\mathnolimitsmode=0` (see LuaTeX Reference Manual).
      subShift = -itCorr
    else
      subShift = 0
    end
    self.sub.relX = self.width + subShift
    self.sub.relY = SILE.length(math.max(
      constants.subscriptShiftDown * scaleDown,
      --self.base.depth + constants.subscriptBaselineDropMin * scaleDown,
      (self.sub.height - constants.subscriptTopMax * scaleDown):tonumber()
    ))
    if (self:is_a(elements.underOver)
        or self:is_a(elements.stackbox) or self.base.largeop) then
      self.sub.relY = maxLength(self.sub.relY,
        self.base.depth + constants.subscriptBaselineDropMin*scaleDown)
    end
  end
  if self.sup then
    if self.isUnderOver or self.base.largeop then
      -- Ad hoc correction on integral limits, following LuaTeX's
      -- `\mathnolimitsmode=0` (see LuaTeX Reference Manual).
      supShift = 0
    else
      supShift = itCorr
    end
    self.sup.relX = self.width + supShift
    self.sup.relY = SILE.length(math.max(
      isCrampedMode(self.mode)
      and constants.superscriptShiftUpCramped * scaleDown
      or constants.superscriptShiftUp * scaleDown, -- or cramped
      --self.base.height - constants.superscriptBaselineDropMax * scaleDown,
      (self.sup.depth + constants.superscriptBottomMin * scaleDown):tonumber()
    )) * (-1)
    if (self:is_a(elements.underOver)
        or self:is_a(elements.stackbox) or self.base.largeop) then
      self.sup.relY = maxLength(
        (0-self.sup.relY),
        self.base.height - constants.superscriptBaselineDropMax
        * scaleDown) * (-1)
      end
  end
  if self.sub and self.sup then
    local gap = self.sub.relY - self.sub.height - self.sup.relY - self.sup.depth
    if gap.length:tonumber() < constants.subSuperscriptGapMin * scaleDown then
      -- The following adjustment comes directly from Appendix G of he
      -- TeXbook (rule 18e).
      self.sub.relY = constants.subSuperscriptGapMin * scaleDown
        + self.sub.height + self.sup.relY + self.sup.depth
      local psi = constants.superscriptBottomMaxWithSubscript*scaleDown
        + self.sup.relY + self.sup.depth
      if psi:tonumber() > 0 then
        self.sup.relY = self.sup.relY - psi
        self.sub.relY = self.sub.relY - psi
      end
    end
  end
  self.width = self.width + maxLength(
    self.sub and self.sub.width + subShift or SILE.length(0),
    self.sup and self.sup.width + supShift or SILE.length(0)
  ) + constants.spaceAfterScript * scaleDown
  self.height = maxLength(
    self.base and self.base.height or SILE.length(0),
    self.sub and (self.sub.height - self.sub.relY) or SILE.length(0),
    self.sup and (self.sup.height - self.sup.relY) or SILE.length(0)
  )
  self.depth = maxLength(
    self.base and self.base.depth or SILE.length(0),
    self.sub and (self.sub.depth + self.sub.relY) or SILE.length(0),
    self.sup and (self.sup.depth + self.sup.relY) or SILE.length(0)
  )
end

function elements.subscript.output (_, _, _, _) end

elements.underOver = pl.class(elements.subscript)
elements.underOver._type = "UnderOver"

function elements.underOver:__tostring ()
  return self._type .. "(" .. tostring(self.base) .. ", " ..
    tostring(self.sub) .. ", " .. tostring(self.sup) .. ")"
end

function elements.underOver:_init (base, sub, sup)
  elements.mbox._init(self)
  self.atom = base.atom
  self.base = base
  self.sub = sub
  self.sup = sup
  if self.sup then table.insert(self.children, self.sup) end
  if self.base then
    table.insert(self.children, self.base)
  end
  if self.sub then table.insert(self.children, self.sub) end
end

function elements.underOver:styleChildren ()
  if self.base then self.base.mode = self.mode end
  if self.sub then self.sub.mode = getSubscriptMode(self.mode) end
  if self.sup then self.sup.mode = getSuperscriptMode(self.mode) end
end

function elements.underOver:shape ()
  if not (self.mode == mathMode.display
    or self.mode == mathMode.displayCramped) then
    self.isUnderOver = true
    elements.subscript.shape(self)
    return
  end
  local constants = self:getMathMetrics().constants
  local scaleDown = self:getScaleDown()
  -- Determine relative Ys
  if self.base then
    self.base.relY = SILE.length(0)
  end
  if self.sub then
    self.sub.relY = self.base.depth + SILE.length(math.max(
    (self.sub.height + constants.lowerLimitGapMin * scaleDown):tonumber(),
    constants.lowerLimitBaselineDropMin * scaleDown))
  end
  if self.sup then
    self.sup.relY = 0 - self.base.height - SILE.length(math.max(
    (constants.upperLimitGapMin * scaleDown + self.sup.depth):tonumber(),
    constants.upperLimitBaselineRiseMin * scaleDown))
  end
  -- Determine relative Xs based on widest symbol
  local widest, a, b
  if self.sub and self.sub.width > self.base.width then
    if self.sup and self.sub.width > self.sup.width then
      widest = self.sub
      a = self.base
      b = self.sup
    elseif self.sup then
      widest = self.sup
      a = self.base
      b = self.sub
    else
      widest = self.sub
      a = self.base
      b = nil
    end
  else
    if self.sup and self.base.width > self.sup.width then
      widest = self.base
      a = self.sub
      b = self.sup
    elseif self.sup then
      widest = self.sup
      a = self.base
      b = self.sub
    else
      widest = self.base
      a = self.sub
      b = nil
    end
  end
  widest.relX = SILE.length(0)
  local c = widest.width / 2
  if a then a.relX = c - a.width / 2 end
  if b then b.relX = c - b.width / 2 end
  local itCorr = self:calculateItalicsCorrection() * scaleDown
  if self.sup then self.sup.relX = self.sup.relX + itCorr / 2 end
  if self.sub then self.sub.relX = self.sub.relX - itCorr / 2 end
  -- Determine width and height
  self.width = maxLength(
  self.base and self.base.width or SILE.length(0),
  self.sub and self.sub.width or SILE.length(0),
  self.sup and self.sup.width or SILE.length(0)
  )
  if self.sup then
    self.height = 0 - self.sup.relY + self.sup.height
  else
    self.height = self.base and self.base.height or 0
  end
  if self.sub then
    self.depth = self.sub.relY + self.sub.depth
  else
    self.depth = self.base and self.base.depth or 0
  end
end

function elements.underOver:calculateItalicsCorrection ()
  local lastGid = getRightMostGlyphId(self.base)
  if lastGid > 0 then
    local mathMetrics = self:getMathMetrics()
    if mathMetrics.italicsCorrection[lastGid] then
      local c = mathMetrics.italicsCorrection[lastGid]
      -- If this is a big operator, and we are in display style, then the
      -- base glyph may be bigger than the font size. We need to adjust the
      -- italic correction accordingly.
      if self.base.atom == atomType.bigOperator and isDisplayMode(self.mode) then
        c = c * (self.base and self.base.font.size / self.font.size or 1.0)
      end
      return c
    end
  end
  return 0
end

function elements.underOver.output (_, _, _, _) end

-- terminal is the base class for leaf node
elements.terminal = pl.class(elements.mbox)
elements.terminal._type = "Terminal"

function elements.terminal:_init ()
  elements.mbox._init(self)
end

function elements.terminal.styleChildren (_) end

function elements.terminal.shape (_) end

elements.space = pl.class(elements.terminal)
elements.space._type = "Space"

function elements.space:_init ()
  elements.terminal._init(self)
end

function elements.space:__tostring ()
  return self._type .. "(width=" .. tostring(self.width) ..
  ", height=" .. tostring(self.height) ..
  ", depth=" .. tostring(self.depth) .. ")"
end

local function getStandardLength (value)
  if type(value) == "string" then
    local direction = 1
    if value:sub(1, 1) == "-" then
      value = value:sub(2, -1)
      direction = -1
    end
    if value == "thin" then
      return SILE.length("3mu") * direction
    elseif value == "med" then
      return SILE.length("4mu plus 2mu minus 4mu") * direction
    elseif value == "thick" then
      return SILE.length("5mu plus 5mu") * direction
    end
  end
  return SILE.length(value)
end

function elements.space:_init (width, height, depth)
  elements.terminal._init(self)
  self.width = getStandardLength(width)
  self.height = getStandardLength(height)
  self.depth = getStandardLength(depth)
end

function elements.space:shape ()
  self.width = self.width:absolute() * self:getScaleDown()
  self.height = self.height:absolute() * self:getScaleDown()
  self.depth = self.depth:absolute() * self:getScaleDown()
end

function elements.space.output (_) end

-- text node. For any actual text output
elements.text = pl.class(elements.terminal)
elements.text._type = "Text"

function elements.text:__tostring ()
  return self._type .. "(atom=" .. tostring(self.atom) ..
      ", kind=" .. tostring(self.kind) ..
      ", script=" .. tostring(self.script) ..
      (self.stretchy and ", stretchy" or "") ..
      (self.largeop and ", largeop" or "") ..
      ", text=\"" .. (self.originalText or self.text) .. "\")"
end

function elements.text:_init (kind, attributes, script, text)
  elements.terminal._init(self)
  if not (kind == "number" or kind == "identifier" or kind == "operator") then
    SU.error("Unknown text node kind '"..kind.."'; should be one of: number, identifier, operator.")
  end
  self.kind = kind
  self.script = script
  self.text = text
  if self.script ~= 'upright' then
    local converted = ""
    for _, uchr in luautf8.codes(self.text) do
      local dst_char = luautf8.char(uchr)
      if uchr >= 0x41 and uchr <= 0x5A then -- Latin capital letter
        dst_char = luautf8.char(mathScriptConversionTable.capital[self.script](uchr))
      elseif uchr >= 0x61 and uchr <= 0x7A then -- Latin non-capital letter
        dst_char = luautf8.char(mathScriptConversionTable.small[self.script](uchr))
      end
      converted = converted..dst_char
    end
    self.originalText = self.text
    self.text = converted
  end
  if self.kind == 'operator' then
    if self.text == "-" then
      self.text = "−"
    end
  end
  for attribute,value in pairs(attributes) do
    self[attribute] = value
  end
end

function elements.text:shape ()
  self.font.size = self.font.size * self:getScaleDown()
  local face = SILE.font.cache(self.font, SILE.shaper.getFace)
  local mathMetrics = self:getMathMetrics()
  local glyphs = SILE.shaper:shapeToken(self.text, self.font)
  -- Use bigger variants for big operators in display style
  if isDisplayMode(self.mode) and self.largeop then
    -- We copy the glyph list to avoid modifying the shaper's cache. Yes.
    glyphs = pl.tablex.deepcopy(glyphs)
    local constructions = mathMetrics.mathVariants
      .vertGlyphConstructions[glyphs[1].gid]
    if constructions then
      local displayVariants = constructions.mathGlyphVariantRecord
      -- We select the biggest variant. TODO: we shoud probably select the
      -- first variant that is higher than displayOperatorMinHeight.
      local biggest
      local m = 0
      for _, v in ipairs(displayVariants) do
        if v.advanceMeasurement > m then
          biggest = v
          m = v.advanceMeasurement
        end
      end
      if biggest then
        glyphs[1].gid = biggest.variantGlyph
        local dimen = hb.get_glyph_dimensions(face.data,
          face.index, self.font.size, biggest.variantGlyph)
        glyphs[1].width = dimen.width
        glyphs[1].glyphAdvance = dimen.glyphAdvance
        --[[ I am told (https://github.com/alif-type/xits/issues/90) that,
        in fact, the relative height and depth of display-style big operators
        in the font is not relevant, as these should be centered around the
        axis. So the following code does that, while conserving their
        vertical size (distance from top to bottom). ]]
        local axisHeight = mathMetrics.constants.axisHeight * self:getScaleDown()
        local y_size = dimen.height + dimen.depth
        glyphs[1].height = y_size / 2 + axisHeight
        glyphs[1].depth = y_size / 2 - axisHeight
        -- We still need to store the font's height and depth somewhere,
        -- because that's what will be used to draw the glyph, and we will need
        -- to artificially compensate for that.
        glyphs[1].fontHeight = dimen.height
        glyphs[1].fontDepth = dimen.depth
      end
    end
  end
  SILE.shaper:preAddNodes(glyphs, self.value)
  self.value.items = glyphs
  self.value.glyphString = {}
  if glyphs and #glyphs > 0 then
    for i = 1, #glyphs do
      table.insert(self.value.glyphString, glyphs[i].gid)
    end
    self.width = SILE.length(0)
    self.widthForSubscript = SILE.length(0)
    for i = #glyphs, 1, -1 do
      self.width = self.width + glyphs[i].glyphAdvance
    end
    -- Store width without italic correction somewhere
    self.widthForSubscript = self.width
    local itCorr = mathMetrics.italicsCorrection[glyphs[#glyphs].gid]
    if itCorr then
      self.width = self.width + itCorr * self:getScaleDown()
    end
    for i = 1, #glyphs do
      self.height = i == 1 and SILE.length(glyphs[i].height) or SILE.length(math.max(self.height:tonumber(), glyphs[i].height))
      self.depth = i == 1 and SILE.length(glyphs[i].depth) or SILE.length(math.max(self.depth:tonumber(), glyphs[i].depth))
    end
  else
    self.width = SILE.length(0)
    self.height = SILE.length(0)
    self.depth = SILE.length(0)
  end
end

function elements.text:stretchyReshape (depth, height)
  -- Required depth+height of stretched glyph, in font units
  local mathMetrics = self:getMathMetrics()
  local upem = mathMetrics.unitsPerEm
  local sz = self.font.size
  local requiredAdvance = (depth + height):tonumber() * upem/sz
  SU.debug("math", "stretch: rA =", requiredAdvance)
  -- Choose variant of the closest size. The criterion we use is to have
  -- an advance measurement as close as possible as the required one.
  -- The advance measurement is simply the depth+height of the glyph.
  -- Therefore, the selected glyph may be smaller or bigger than
  -- required.  TODO: implement assembly of stretchable glyphs form
  -- their parts for cases when the biggest variant is not big enough.
  -- We copy the glyph list to avoid modifying the shaper's cache. Yes.
  local glyphs = pl.tablex.deepcopy(self.value.items)
  local constructions = self:getMathMetrics().mathVariants
    .vertGlyphConstructions[glyphs[1].gid]
  if constructions then
    local variants = constructions.mathGlyphVariantRecord
    SU.debug("math", "stretch: variants =", variants)
    local closest
    local closestI
    local m = requiredAdvance - (self.depth+self.height):tonumber() * upem/sz
    SU.debug("math", "strech: m =", m)
    for i,v in ipairs(variants) do
      local diff = math.abs(v.advanceMeasurement - requiredAdvance)
      SU.debug("math", "stretch: diff =", diff)
      if diff < m then
        closest = v
        closestI = i
        m = diff
      end
    end
    SU.debug("math", "stretch: closestI =", tostring(closestI))
    if closest then
      -- Now we have to re-shape the glyph chain. We will assume there
      -- is only one glyph.
      -- TODO: this code is probably wrong when the vertical
      -- variants have a different width than the original, because
      -- the shaping phase is already done. Need to do better.
      glyphs[1].gid = closest.variantGlyph
      local face = SILE.font.cache(self.font, SILE.shaper.getFace)
      local dimen = hb.get_glyph_dimensions(face.data,
        face.index, self.font.size, closest.variantGlyph)
      glyphs[1].width = dimen.width
      glyphs[1].height = dimen.height
      glyphs[1].depth = dimen.depth
      glyphs[1].glyphAdvance = dimen.glyphAdvance
      self.width = SILE.length(dimen.glyphAdvance)
      self.depth = SILE.length(dimen.depth)
      self.height = SILE.length(dimen.height)
      SILE.shaper:preAddNodes(glyphs, self.value)
      self.value.items = glyphs
      self.value.glyphString = {glyphs[1].gid}
    end
  end
end

function elements.text:output (x, y, line)
  if not self.value.glyphString then return end
  local compensatedY
  if isDisplayMode(self.mode)
      and self.atom == atomType.bigOperator
      and self.value.items[1].fontDepth then
    compensatedY = SILE.length(y.length + self.value.items[1].depth - self.value.items[1].fontDepth)
  else
    compensatedY = y
  end
  SILE.outputter:setCursor(scaleWidth(x, line), compensatedY.length)
  SILE.outputter:setFont(self.font)
  -- There should be no stretch or shrink on the width of a text
  -- element.
  local width = self.width.length
  SILE.outputter:drawHbox(self.value, width)
end

elements.fraction = pl.class(elements.mbox)
elements.fraction._type = "Fraction"

function elements.fraction:__tostring ()
  return self._type .. "(" .. tostring(self.numerator) .. ", " ..
    tostring(self.denominator) .. ")"
end

function elements.fraction:_init (numerator, denominator)
  elements.mbox._init(self)
  self.numerator = numerator
  self.denominator = denominator
  table.insert(self.children, numerator)
  table.insert(self.children, denominator)
end

function elements.fraction:styleChildren ()
  self.numerator.mode = getNumeratorMode(self.mode)
  self.denominator.mode = getDenominatorMode(self.mode)
end

function elements.fraction:shape ()
  -- Determine relative abscissas and width
  local widest, other
  if self.denominator.width > self.numerator.width then
    widest, other = self.denominator, self.numerator
  else
    widest, other = self.numerator, self.denominator
  end
  widest.relX = SILE.length(0)
  other.relX = (widest.width - other.width) / 2
  self.width = widest.width
  -- Determine relative ordinates and height
  local constants = self:getMathMetrics().constants
  local scaleDown = self:getScaleDown()
  self.axisHeight = constants.axisHeight * scaleDown
  self.ruleThickness = constants.fractionRuleThickness * scaleDown
  if isDisplayMode(self.mode) then
    self.numerator.relY = -self.axisHeight - self.ruleThickness/2 - SILE.length(math.max(
      (constants.fractionNumDisplayStyleGapMin*scaleDown + self.numerator.depth):tonumber(),
      constants.fractionNumeratorDisplayStyleShiftUp * scaleDown
        - self.axisHeight - self.ruleThickness/2))
  else
    self.numerator.relY = -self.axisHeight - self.ruleThickness/2 - SILE.length(math.max(
      (constants.fractionNumeratorGapMin*scaleDown + self.numerator.depth):tonumber(),
      constants.fractionNumeratorShiftUp * scaleDown - self.axisHeight
        - self.ruleThickness/2))
  end
  if isDisplayMode(self.mode) then
    self.denominator.relY = -self.axisHeight + self.ruleThickness/2 + SILE.length(math.max(
      (constants.fractionDenomDisplayStyleGapMin * scaleDown
        + self.denominator.height):tonumber(),
      constants.fractionDenominatorDisplayStyleShiftDown * scaleDown
        + self.axisHeight - self.ruleThickness/2))
  else
    self.denominator.relY = -self.axisHeight + self.ruleThickness/2 + SILE.length(math.max(
      (constants.fractionDenominatorGapMin * scaleDown
        + self.denominator.height):tonumber(),
      constants.fractionDenominatorShiftDown * scaleDown
        + self.axisHeight - self.ruleThickness/2))
  end
  self.height = self.numerator.height - self.numerator.relY
  self.depth = self.denominator.relY + self.denominator.depth
end

function elements.fraction:output (x, y, line)
  SILE.outputter:drawRule(
    scaleWidth(x, line),
    y.length - self.axisHeight - self.ruleThickness / 2,
    scaleWidth(self.width, line), self.ruleThickness)
end

local function newSubscript (spec)
    return elements.subscript(spec.base, spec.sub, spec.sup)
end

local function newUnderOver (spec)
  return elements.underOver(spec.base, spec.sub, spec.sup)
end

-- TODO replace with penlight equivalent
local function mapList (f, l)
  local ret = {}
  for i, x in ipairs(l) do
    ret[i] = f(i, x)
  end
  return ret
end

elements.mtr = pl.class(elements.mbox)
-- elements.mtr._type = "" -- TODO why not set?

function elements.mtr:_init (children)
  self.children = children
end

function elements.mtr:styleChildren ()
  for _, c in ipairs(self.children) do
    c.mode = self.mode
  end
end

function elements.mtr.shape (_) end -- done by parent table

function elements.mtr.output (_) end

elements.table = pl.class(elements.mbox)
elements.table._type = "table" -- TODO why case diference?

function elements.table:_init (children, options)
  elements.mbox._init(self)
  self.children = children
  self.options = options
  self.nrows = #self.children
  self.ncols = math.max(table.unpack(mapList(function(_, row)
    return #row.children end, self.children)))
  SU.debug("math", "self.ncols =", self.ncols)
  self.rowspacing = self.options.rowspacing and SILE.length(self.options.rowspacing)
    or SILE.length("7pt")
  self.columnspacing = self.options.columnspacing and SILE.length(self.options.columnspacing)
    or SILE.length("6pt")
  -- Pad rows that do not have enough cells by adding cells to the
  -- right.
  for i,row in ipairs(self.children) do
    for j = 1, (self.ncols - #row.children) do
      SU.debug("math", "padding i =", i, "j =", j)
      table.insert(row.children, elements.stackbox('H', {}))
      SU.debug("math", "size", #row.children)
    end
  end
  if options.columnalign then
    local l = {}
    for w in string.gmatch(options.columnalign, "[^%s]+") do
      if not (w == "left" or w == "center" or w == "right") then
        SU.error("Invalid specifier in `columnalign` attribute: "..w)
      end
      table.insert(l, w)
    end
    -- Pad with last value of l if necessary
    for _ = 1, (self.ncols - #l), 1 do
      table.insert(l, l[#l])
    end
    -- On the contrary, remove excess values in l if necessary
    for _ = 1, (#l - self.ncols), 1 do
      table.remove(l)
    end
    self.options.columnalign = l
  else
    self.options.columnalign = pl.List.range(1, self.ncols):map(function(_) return "center" end)
  end
end

function elements.table:styleChildren ()
  if self.mode == mathMode.display and self.options.displaystyle ~= "false" then
    for _,c in ipairs(self.children) do
      c.mode = mathMode.display
    end
  else
    for _,c in ipairs(self.children) do
      c.mode = mathMode.text
    end
  end
end

function elements.table:shape ()
  -- Determine the height (resp. depth) of each row, which is the max
  -- height (resp. depth) among its elements. Then we only need to add it to
  -- the table's height and center every cell vertically.
  for _,row in ipairs(self.children) do
    row.height = SILE.length(0)
    row.depth = SILE.length(0)
    for _,cell in ipairs(row.children) do
      row.height = maxLength(row.height, cell.height)
      row.depth = maxLength(row.depth, cell.depth)
    end
  end
  self.vertSize = SILE.length(0)
  for i, row in ipairs(self.children) do
    self.vertSize = self.vertSize + row.height + row.depth +
      (i == self.nrows and SILE.length(0) or self.rowspacing) -- Spacing
  end
  local rowHeightSoFar = SILE.length(0)
  for i, row in ipairs(self.children) do
    row.relY = rowHeightSoFar + row.height - self.vertSize
    rowHeightSoFar = rowHeightSoFar + row.height + row.depth +
      (i == self.nrows and SILE.length(0) or self.rowspacing) -- Spacing
  end
  self.width = SILE.length(0)
  local thisColRelX = SILE.length(0)
  -- For every column...
  for i = 1,self.ncols do
    -- Determine its width
    local columnWidth = SILE.length(0)
    for j = 1,self.nrows do
      if self.children[j].children[i].width > columnWidth then
        columnWidth = self.children[j].children[i].width
      end
    end
    -- Use it to align the contents of every cell as required.
    for j = 1,self.nrows do
      local cell = self.children[j].children[i]
      if self.options.columnalign[i] == "left" then
        cell.relX = thisColRelX
      elseif self.options.columnalign[i] == "center" then
        cell.relX = thisColRelX + (columnWidth - cell.width) / 2
      elseif self.options.columnalign[i] == "right" then
        cell.relX = thisColRelX + (columnWidth - cell.width)
      else
        SU.error("invalid columnalign parameter")
      end
    end
    thisColRelX = thisColRelX + columnWidth +
      (i == self.ncols and SILE.length(0) or self.columnspacing) -- Spacing
  end
  self.width = thisColRelX
  -- Center myself vertically around the axis, and update relative Ys of rows accordingly
  local axisHeight = self:getMathMetrics().constants.axisHeight * self:getScaleDown()
  self.height = self.vertSize / 2 + axisHeight
  self.depth = self.vertSize / 2 - axisHeight
  for _,row in ipairs(self.children) do
    row.relY = row.relY + self.vertSize / 2 - axisHeight
    -- Also adjust width
    row.width = self.width
  end
end

function elements.table.output (_) end

elements.mathMode = mathMode
elements.atomType = atomType
elements.scriptType = scriptType
elements.mathVariantToScriptType = mathVariantToScriptType
elements.symbolDefaults = symbolDefaults
elements.newSubscript = newSubscript
elements.newUnderOver = newUnderOver

return elements
