if not modules then modules = { } end modules ['math-act'] = {
    version   = 1.001,
    comment   = "companion to math-ini.mkiv",
    author    = "Hans Hagen, PRAGMA-ADE, Hasselt NL",
    copyright = "PRAGMA ADE / ConTeXt Development Team",
    license   = "see context related readme files"
}

-- Here we tweak some font properties (if needed). The commented sections
-- have been removed (no longer viable) but can be found in the .lua variant.

local type, next = type, next
local fastcopy, insert, remove = table.fastcopy, table.insert, table.remove
local formatters = string.formatters
local byte = string.byte

local trace_defining   = false  trackers.register("math.defining",   function(v) trace_defining   = v end)
local trace_collecting = false  trackers.register("math.collecting", function(v) trace_collecting = v end)
local trace_tweaking   = false  trackers.register("math.tweaks",     function(v) trace_tweaking   = v end)

local report_math      = logs.reporter("mathematics","initializing")
local report_mathtweak = logs.reporter("mathematics","tweak")

local context          = context
local commands         = commands
local mathematics      = mathematics
local texsetdimen      = tex.setdimen
local abs              = math.abs

local helpers          = fonts.helpers
local upcommand        = helpers.commands.up
local rightcommand     = helpers.commands.right
local charcommand      = helpers.commands.char
local prependcommands  = helpers.prependcommands

local sequencers       = utilities.sequencers
local appendgroup      = sequencers.appendgroup
local appendaction     = sequencers.appendaction

local fontchars        = fonts.hashes.characters
local fontproperties   = fonts.hashes.properties

local mathfontparameteractions = sequencers.new {
    name      = "mathparameters",
    arguments = "target,original",
}

appendgroup("mathparameters","before") -- user
appendgroup("mathparameters","system") -- private
appendgroup("mathparameters","after" ) -- user

function fonts.constructors.assignmathparameters(original,target) -- wrong way around
    local runner = mathfontparameteractions.runner
    if runner then
        runner(original,target)
    end
end

function mathematics.initializeparameters(target,original)
    local mathparameters = original.mathparameters
    if mathparameters and next(mathparameters) then
        mathparameters = mathematics.dimensions(mathparameters)
        if not mathparameters.SpaceBeforeScript then
            mathparameters.SpaceBeforeScript = mathparameters.SpaceAfterScript
        end
        target.mathparameters = mathparameters
    end
end

sequencers.appendaction("mathparameters","system","mathematics.initializeparameters")

local how = {
 -- RadicalKernBeforeDegree         = "horizontal",
 -- RadicalKernAfterDegree          = "horizontal",
    ScriptPercentScaleDown          = "unscaled",
    ScriptScriptPercentScaleDown    = "unscaled",
    RadicalDegreeBottomRaisePercent = "unscaled",
    NoLimitSupFactor                = "unscaled",
    NoLimitSubFactor                = "unscaled",
}

function mathematics.scaleparameters(target,original)
    if not target.properties.math_is_scaled then
        local mathparameters = target.mathparameters
        if mathparameters and next(mathparameters) then
            local parameters = target.parameters
            local factor  = parameters.factor
            local hfactor = parameters.hfactor
            local vfactor = parameters.vfactor
            for name, value in next, mathparameters do
                local h = how[name]
                if h == "unscaled" then
                    -- kept
                elseif h == "horizontal" then
                    value = value * hfactor
                elseif h == "vertical"then
                    value = value * vfactor
                else
                    value = value * factor
                end
               mathparameters[name] = value
            end
        end
        target.properties.math_is_scaled = true
    end
end

-- AccentBaseHeight vs FlattenedAccentBaseHeight

function mathematics.checkaccentbaseheight(target,original)
    local mathparameters = target.mathparameters
    if mathparameters and mathparameters.AccentBaseHeight == 0 then
        mathparameters.AccentBaseHeight = target.parameters.x_height -- needs checking
    end
end

function mathematics.checkprivateparameters(target,original)
    local mathparameters = target.mathparameters
    if mathparameters then
        local parameters = target.parameters
        local properties = target.properties
        if parameters then
            local size = parameters.size
            if size then
                if not mathparameters.FractionDelimiterSize then
                    mathparameters.FractionDelimiterSize = 1.01 * size
                end
                if not mathparameters.FractionDelimiterDisplayStyleSize then
                    mathparameters.FractionDelimiterDisplayStyleSize = 2.40 * size
                end
            elseif properties then
                report_math("invalid parameters in font %a",properties.fullname or "?")
            else
                report_math("invalid parameters in font")
            end
        elseif properties then
            report_math("no parameters in font %a",properties.fullname or "?")
        else
            report_math("no parameters and properties in font")
        end
    end
end

function mathematics.overloadparameters(target,original)
    local mathparameters = target.mathparameters
    if mathparameters and next(mathparameters) then
        local goodies = target.goodies
        if goodies then
            for i=1,#goodies do
                local goodie = goodies[i]
                local mathematics = goodie.mathematics
                local parameters  = mathematics and mathematics.parameters
                if parameters then
                    if trace_defining then
                        report_math("overloading math parameters in %a @ %p",target.properties.fullname,target.parameters.size)
                    end
                    for name, value in next, parameters do
                        local tvalue = type(value)
                        if tvalue == "string" then
                            report_math("comment for math parameter %a: %s",name,value)
                        else
                            local oldvalue = mathparameters[name]
                            local newvalue = oldvalue
                            if oldvalue then
                                if tvalue == "number" then
                                    newvalue = value
                                elseif tvalue == "function" then
                                    newvalue = value(oldvalue,target,original)
                                elseif not tvalue then
                                    newvalue = nil
                                end
                                if trace_defining and oldvalue ~= newvalue then
                                    report_math("overloading math parameter %a: %S => %S",name,oldvalue,newvalue)
                                end
                            else
                                report_math("invalid math parameter %a",name)
                            end
                            mathparameters[name] = newvalue
                        end
                    end
                end
            end
        end
    end
end

-- a couple of predefined tweaks:

local mathtweaks   = { }
mathematics.tweaks = mathtweaks

local function report_tweak(fmt,target,original,...)
    local metadata   = original.shared.rawdata.metadata
    local parameters = target.parameters
    report_mathtweak(
        "%a, size %p, math size %i, %s",
        metadata and metadata.fontname or "unknown",
        parameters.size or 655360,
        parameters.mathsize or 1,
        string.formatters[fmt](...)
    )
end

do

    local stepper = utilities.parsers.stepper

    local function adapt(target,original,targetcharacters,originalcharacters,k,v,compact,n)
        local character = targetcharacters[k]
        if character then
            local width     = character.width
            local italic    = character.italic
            local offsetfactor = v[1] or 1
            local widthfactor  = v[2] or 1
            local italicfactor = v[3] or 1
            if width then
                character.advance = width -- so advance is oldwidth
                character.xoffset = offsetfactor * width
                character.width   = widthfactor  * width
            end
            if italic then
                character.italic  = italicfactor * italic
            elseif width and italicfactor ~= 1 then
                character.italic  = italicfactor * width
            end
            if trace_tweaking then
                report_tweak("adapting dimensions of %U ",target,original,k)
            end
            local smaller = originalcharacters[k].smaller
            if compact and smaller and smaller ~= k then
                adapt(target,original,targetcharacters,originalcharacters,smaller,v,compact,n+1)
            end
        else
            report_math("no character %U",k)
        end
    end

    function mathtweaks.dimensions(target,original,parameters)
        local list = parameters.list
        if list then
            local targetcharacters   = target.characters
            local originalcharacters = original.characters
            local compact = target.parameters.textscale and true or false
            for k, v in next, list do
                local t = type(k)
                if t == "number" then
                    adapt(target,original,targetcharacters,originalcharacters,k,v,compact,1)
                elseif t == "string" then
                    stepper(k,function(n) adapt(target,original,targetcharacters,originalcharacters,n,v,compact,1) end)
                end
            end
        end
    end

end

do

    local list = {
        { 0x2032, true,            },
        { 0x2033, true,  0x2032, 2 },
        { 0x2034, true,  0x2032, 3 },
        { 0x2057, true,  0x2032, 4 },
        { 0x2035, false,           },
        { 0x2036, false, 0x2035, 2 },
        { 0x2037, false, 0x2035, 3 },
    }

    local function fix(target,original,characters,factor,scale,newheight,code,mandate)
        local char  = characters[code]
        if char then
            local oldheight = scale * char.height
            char.yoffset = newheight - oldheight
            char.height  = newheight
            if scale ~= 1 then
                char.width    = scale * char.width
                char.commands = {
                    { "slot", 0, code, scale }
                }
            end
            if trace_tweaking then
                report_tweak("fixing prime %U ",target,original,code)
            end
            local small = char.smaller
            if small then
                fix(target,original,characters,factor,scale,newheight,small,false)
            end
        elseif mandate then
            report_math("missing %U prime in font %a",code,original.properties.fullname)
        end
    end

    function mathtweaks.fixprimes(target,original,parameters)
        local characters = target.characters
        local factor     = parameters.factor or 0.85
        local scale      = parameters.scale  or 1
        local newheight  = factor * target.mathparameters.AccentBaseHeight
        for i=1,#list do
            local entry = list[i]
            fix(target,original,characters,factor,scale,newheight,entry[1],entry[2])
        end
    end

    local function fake(target,original,characters,factor,n,single,multiple)
        local csingle   = characters[single]
        local cmultiple = characters[multiple]
        local width     = csingle.width
        local hoffset   = factor * width
        cmultiple.width    = width + (n - 1) * hoffset
        cmultiple.commands = {
                      { "offset",           0, 0, single },
                      { "offset",     hoffset, 0, single },
            n > 2 and { "offset", 2 * hoffset, 0, single } or nil,
            n > 3 and { "offset", 3 * hoffset, 0, single } or nil,
        }
        if trace_tweaking then
            report_tweak("faking %U with %i primes",target,original,multiple,n)
        end
        local ssingle   = csingle.smaller
        local smultiple = cmultiple.smaller
        if ssingle and smultiple then
            fake(target,original,characters,factor,n,ssingle,smultiple)
        else
            --weird font
        end
    end

    function mathtweaks.fakeprimes(target,original,parameters)
        local characters = target.characters
        local factor     = parameters.factor or .75
        for i=1,#list do
            local entry = list[i]
            local n     = entry[4]
            if n then
                fake(target,original,characters,factor,n,entry[3],entry[1])
            end
        end
    end

end

function mathtweaks.action(target,original,parameters)
    local action = parameters.action
    if type(action) == "function" then
        action(target,original,parameters)
    end
end

do

    local list = {
        { 0x00A0, "s", 1         }, -- nbsp
        { 0x2000, "q", 1/2       }, -- enquad
        { 0x2001, "q", 1         }, -- emquad
        { 0x2002, "q", 1/2       }, -- enspace
        { 0x2003, "q", 1         }, -- emspace
        { 0x2004, "q", 1/3       }, -- threeperemspace
        { 0x2005, "q", 1/4       }, -- fourperemspace
        { 0x2006, "q", 1/6       }, -- sixperemspace
        { 0x2007, "c", byte('0') }, -- figurespace
        { 0x2008, "c", byte('.') }, -- punctuationspace
        { 0x2009, "q", 1/8       }, -- breakablethinspace
        { 0x200A, "q", 1/8       }, -- hairspace
        { 0x200B, "q", 0         }, -- zerowidthspace
        { 0x202F, "q", 1/8       }, -- narrownobreakspace
        { 0x205F, "s", 1/2       }, -- math thinspace
    }

    function mathtweaks.checkspacing(target,original,parameters)
        local characters = target.characters
        local parameters = target.parameters
        for i=1,#list do
            local entry   = list[i]
            local unicode = entry[1]
            local data    = characters[unicode]
            if not data then
                local method   = entry[2]
                local fraction = entry[3]
                local width    = 0
                if how == "c" then
                    width = characters[fraction].width  -- char
                elseif how == "s" then
                    width = fraction * parameters.space -- space
                else
                    width = fraction * parameters.quad  -- quad
                end
                if trace_tweaking then
                    report_tweak("setting width of %U to %p",target,original,unicode,width)
                end
                characters[unicode] = { width = width }
            end
        end
    end

end

do

    local list = {
        0x221A,
    }

    local function fix(target,original,characters,unicode)
        local data = characters[unicode]
        if data then
            local height = data.height or 0
            local depth  = data.depth or 0
            if depth > height then
                if trace_tweaking then
                    report_tweak("swapping height and depth of radical %U",target,original,unicode)
                end
                data.height  = depth
                data.depth   = height
                data.yoffset = depth - height
            end
            local small = data.smaller
            if small then
                fix(target,original,characters,small)
            end
        end
    end

    function mathtweaks.fixradicals(target,original,parameters)
        local characters = target.characters
        for i=1,#list do
            local unicode = list[i]
            fix(target,original,characters,unicode)
        end
    end

end

do

    -- For Ton, who needs the high minus and plus for calculator signs in Dutch
    -- school math books.

    local list = {
        { 0x207A, 0x002B, true  },
        { 0x207B, 0x2212, true  },
        { 0x208A, 0x002B, false },
        { 0x208B, 0x2212, false },
    }

    local function add(target,original,characters,unicode,template,super,baseheight,scale)
        if not characters[unicode] then
            local origdata = characters[template]
            if origdata then
                local width  = scale * (origdata.width  or 0)
                local height = scale * (origdata.height or 0)
                local depth  = scale * (origdata.depth  or 0)
                local half   = - (height + depth) / 2
                local offset = super and baseheight/2 or -baseheight/4
                characters[unicode] = {
                    width    = width,
                    height   = height + offset,
                    depth    = depth  - offset,
                    yoffset  = offset,
                    unicode  = unicode,
                 -- index    = origdata.index,
                 -- scale    = scale,
                    commands = {
                     -- { "up", yoffset },
                        { "slot", 0, template, scale }
                    },
                }
                if trace_tweaking then
                    report_tweak("adding script %U scaled %0.3f",target,original,unicode,scale)
                end
                -- no need for smaller
            end
        end
    end

    function mathtweaks.addscripts(target,original,parameters)
        local characters = target.characters
        local baseheight = target.mathparameters.AccentBaseHeight
        local scaledown  = parameters.scale or target.mathparameters.ScriptScriptPercentScaleDown / 100
        for i=1,#list do
            local entry = list[i]
            if entry then
                add(target,original,characters,entry[1],entry[2],entry[3],baseheight,scaledown)
            end
        end
    end

end

do

    function mathtweaks.version(target,original,parameters)
        local metadata = original.shared.rawdata.metadata
        if metadata then
            local version = metadata.version
            if version then
                local expected = parameters.expected
             -- version = tonumber(string.match(version,"%d+.%d+"))
                if version ~= expected then
                    report_tweak("version %a found, version %a expected",target,original,version,expected)
                    reported[fontname] = true
                end
            end
        end
    end

end

local function applytweaks(when,target,original)
    local goodies = original.goodies
    if goodies then
        for i=1,#goodies do
            local goodie = goodies[i]
            local mathematics = goodie.mathematics
            local tweaks = mathematics and mathematics.tweaks
            if type(tweaks) == "table" then
                tweaks = tweaks[when]
                if type(tweaks) == "table" then
                    if trace_defining then
                        report_math("tweaking math of %a @ %p (%s)",target.properties.fullname,target.parameters.size,when)
                    end
                    for i=1,#tweaks do
                        local tweak  = tweaks[i]
                        local tvalue = type(tweak)
                        if type(tweak) == "table" then
                            local action = mathtweaks[tweak.tweak or ""]
                            if action then
                                action(target,original,tweak)
                            end
                        end
                    end
                end
            end
        end
    end
end

function mathematics.tweakbeforecopyingfont(target,original)
    local mathparameters = target.mathparameters -- why not hasmath
    if mathparameters then
        applytweaks("beforecopying",target,original)
    end
end

function mathematics.tweakaftercopyingfont(target,original)
    local mathparameters = target.mathparameters -- why not hasmath
    if mathparameters then
        applytweaks("aftercopying",target,original)
    end
end

sequencers.appendaction("mathparameters","system","mathematics.scaleparameters")
sequencers.appendaction("mathparameters","system","mathematics.checkaccentbaseheight")  -- should go in lfg instead
sequencers.appendaction("mathparameters","system","mathematics.checkprivateparameters") -- after scaling !
sequencers.appendaction("mathparameters","system","mathematics.overloadparameters")

sequencers.appendaction("beforecopyingcharacters","system","mathematics.tweakbeforecopyingfont")
sequencers.appendaction("aftercopyingcharacters", "system","mathematics.tweakaftercopyingfont")

-- no, it's a feature now (see good-mth):
--
-- sequencers.appendaction("aftercopyingcharacters", "system","mathematics.overloaddimensions")

-- helpers

local setmetatableindex  = table.setmetatableindex

local getfontoffamily    = tex.getfontoffamily

local fontcharacters     = fonts.hashes.characters
local extensibles        = utilities.storage.allocate()
fonts.hashes.extensibles = extensibles

local chardata           = characters.data
local extensibles        = mathematics.extensibles

-- we use numbers at the tex end (otherwise we could stick to chars)

local e_left       = extensibles.left
local e_right      = extensibles.right
local e_horizontal = extensibles.horizontal
local e_mixed      = extensibles.mixed
local e_unknown    = extensibles.unknown

local unknown      = { e_unknown, false, false }

local function extensiblecode(font,unicode)
    local characters = fontcharacters[font]
    local character = characters[unicode]
    if not character then
        return unknown
    end
    local first = character.next
    local code = unicode
    local next = first
    while next do
        code = next
        character = characters[next]
        next = character.next
    end
    local char = chardata[unicode]
    if not char then
        return unknown
    end
    if character.horiz_variants then
        if character.vert_variants then
            return { e_mixed, code, character }
        else
            local m = char.mathextensible
            local e = m and extensibles[m]
            return e and { e, code, character } or unknown
        end
    elseif character.vert_variants then
        local m = char.mathextensible
        local e = m and extensibles[m]
        return e and { e, code, character } or unknown
    elseif first then
        -- assume accent (they seldom stretch .. sizes)
        local m = char.mathextensible or char.mathstretch
        local e = m and extensibles[m]
        return e and { e, code, character } or unknown
    else
        return unknown
    end
end

setmetatableindex(extensibles,function(extensibles,font)
    local codes = { }
    setmetatableindex(codes, function(codes,unicode)
        local status = extensiblecode(font,unicode)
        codes[unicode] = status
        return status
    end)
    extensibles[font] = codes
    return codes
end)

local function extensiblecode(family,unicode)
    return extensibles[getfontoffamily(family or 0)][unicode][1]
end

-- left       : [head] ...
-- right      : ... [head]
-- horizontal : [head] ... [head]
--
-- abs(right["start"] - right["end"]) | right.advance | characters[right.glyph].width

local function horizontalcode(family,unicode)
    local font    = getfontoffamily(family or 0)
    local data    = extensibles[font][unicode]
    local kind    = data[1]
    local loffset = 0
    local roffset = 0
    if kind == e_left then
        local charlist = data[3].horiz_variants
        if charlist then
            local left = charlist[1]
            loffset = abs((left["start"] or 0) - (left["end"] or 0))
        end
    elseif kind == e_right then
        local charlist = data[3].horiz_variants
        if charlist then
            local right = charlist[#charlist]
            roffset = abs((right["start"] or 0) - (right["end"] or 0))
        end
     elseif kind == e_horizontal then
        local charlist = data[3].horiz_variants
        if charlist then
            local left  = charlist[1]
            local right = charlist[#charlist]
            loffset = abs((left ["start"] or 0) - (left ["end"] or 0))
            roffset = abs((right["start"] or 0) - (right["end"] or 0))
        end
    end
    return kind, loffset, roffset
end

mathematics.extensiblecode = extensiblecode
mathematics.horizontalcode = horizontalcode

interfaces.implement { -- can be public with two times "integerargument"
    name      = "extensiblecode",
    arguments = { "integer", "integer" },
    actions   = { extensiblecode, context }
}

interfaces.implement { -- can be public with two times "integerargument"
    name      = "horizontalcode",
    arguments = { "integer", "integer" },
    actions   = function(family,unicode)
        local kind, loffset, roffset = horizontalcode(family,unicode)
        texsetdimen("scratchleftoffset", loffset)
        texsetdimen("scratchrightoffset",roffset)
        context(kind)
    end
}


local stack = { }

function mathematics.registerfallbackid(n,id,name)
    if trace_collecting then
        report_math("resolved fallback font %i, name %a, id %a, used %a",
            n,name,id,fontproperties[id].fontname)
    end
    stack[#stack][n] = id
end

interfaces.implement { -- will be shared with text
    name      = "registerfontfallbackid",
    arguments = { "integer", "integer", "string" },
    actions   = mathematics.registerfallbackid,
}

function mathematics.resolvefallbacks(target,specification,fallbacks)
    local definitions = fonts.collections.definitions[fallbacks]
    if definitions then
        local size = specification.size -- target.size
        local list = { }
        insert(stack,list)
        context.pushcatcodes("prt") -- context.unprotect()
        for i=1,#definitions do
            local definition = definitions[i]
            local name       = definition.font
            local features   = definition.features or ""
            local size       = size * (definition.rscale or 1)
            context.font_fallbacks_register_math(i,name,features,size)
            if trace_collecting then
                report_math("registering fallback font %i, name %a, size %a, features %a",i,name,size,features)
            end
        end
        context.popcatcodes()
    end
end

function mathematics.finishfallbacks(target,specification,fallbacks)
    local list = remove(stack)
    if list and #list > 0 then
        local definitions = fonts.collections.definitions[fallbacks]
        if definitions and #definitions > 0 then
            if trace_collecting then
                report_math("adding fallback characters to font %a",specification.hash)
            end
            local definedfont = fonts.definers.internal
            local copiedglyph = fonts.handlers.vf.math.copy_glyph
            local fonts       = target.fonts
            local size        = specification.size -- target.size
            local characters  = target.characters
            if not fonts then
                fonts = { }
                target.fonts = fonts
            end
            if #fonts == 0 then
                fonts[1] = { id = 0, size = size } -- self, will be resolved later
            end
            local done = { }
            for i=1,#definitions do
                local definition = definitions[i]
                local name   = definition.font
                local start  = definition.start
                local stop   = definition.stop
                local gaps   = definition.gaps
                local check  = definition.check
                local force  = definition.force
                local rscale = definition.rscale or 1
                local offset = definition.offset or start
                local id     = list[i]
                if id then
                    local index  = #fonts + 1
                    fonts[index] = { id = id, size = size }
                    local chars  = fontchars[id]
                    local function remap(unic,unicode,gap)
                        if check and not chars[unicode] then
                            return
                        end
                        if force or (not done[unic] and not characters[unic]) then
                            if trace_collecting then
                                report_math("replacing math character %C by %C using vector %a and font id %a for %a%s%s",
                                    unic,unicode,fallbacks,id,fontproperties[id].fontname,check and ", checked",gap and ", gap plugged")
                            end
                            characters[unic] = copiedglyph(target,characters,chars,unicode,index)
                            done[unic] = true
                        end
                    end
                    local step = offset - start
                    for unicode = start, stop do
                        remap(unicode + step,unicode,false)
                    end
                    if gaps then
                        for unic, unicode in next, gaps do
                            remap(unic,unicode,true)
                            remap(unicode,unicode,true)
                        end
                    end
                end
            end
        elseif trace_collecting then
            report_math("no fallback characters added to font %a",specification.hash)
        end
    end
end