path: root/tex/context/base/mkxl/math-act.lmt

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 setmetatableindex, sortedhash  = table.setmetatableindex, table.sortedhash

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.PrimeRaisePercent              then mathparameters.PrimeRaisePercent        = 25 end
        if not mathparameters.PrimeShiftUp                   then mathparameters.PrimeShiftUp             = mathparameters.SuperscriptShiftUp end
        if not mathparameters.PrimeBaselineDropMax           then mathparameters.PrimeBaselineDropMax     = mathparameters.SuperscriptBaselineDropMax end
        if not mathparameters.PrimeShiftUpCramped            then mathparameters.PrimeShiftUpCramped      = mathparameters.SuperscriptShiftUpCramped end
        if not mathparameters.PrimeSpaceAfter                then mathparameters.PrimeSpaceAfter          = 0 end
        if not mathparameters.PrimeWidthPercent              then mathparameters.PrimeWidthPercent        = 50 end
        if not mathparameters.SpaceBeforeScript              then mathparameters.SpaceBeforeScript        = mathparameters.SpaceAfterScript end
        if not mathparameters.NoLimitSupFactor               then mathparameters.NoLimitSupFactor         = 0 end
        if not mathparameters.NoLimitSubFactor               then mathparameters.NoLimitSubFactor         = 0 end
        if not mathparameters.AccentTopShiftUp               then mathparameters.AccentTopShiftUp         = 0 end
        if not mathparameters.AccentBottomShiftDown          then mathparameters.AccentBottomShiftDown    = 0 end
        if not mathparameters.FlattenedAccentTopShiftUp      then mathparameters.AccentTopShiftUp         = 0 end
        if not mathparameters.FlattenedAccentBottomShiftDown then mathparameters.AccentBottomShiftDown    = 0 end
        if not mathparameters.AccentBaseDepth                then mathparameters.AccentBaseDepth          = 0 end
        if not mathparameters.AccentFlattenedBaseDepth       then mathparameters.AccentFlattenedBaseDepth = 0 end
        --
        -- we don't want to reset that each time .. but then we also can't show what the value was
        --
     -- mathparameters.RadicalDegreeBefore = 0
        --
        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",
    PrimeRaisePercent               = "unscaled",
    PrimeWidthPercent               = "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.xheight -- 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
--                 -- gone
--             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
                if mathematics then
                    local parameters = mathematics.parameters
                    local bigslots   = mathematics.bigslots or mathematics.bigs
                    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)
                            local oldvalue = mathparameters[name]
                            local newvalue = oldvalue
                            if tvalue == "number" then
                                newvalue = value
                            elseif tvalue == "string" then
                                -- delay till all set
                            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 or 0,newvalue)
                            end
                            mathparameters[name] = newvalue
                        end
                        for name, value in next, parameters do
                            local tvalue = type(value)
                            if tvalue == "string" then
                                local newvalue = mathparameters[value]
                             -- if not newvalue then
                             --     local code = loadstring("return " .. value,"","t",mathparameters)
                             --     if type(code) == "function" then
                             --         local okay, v = pcall(code)
                             --         if okay then
                             --             newvalue = v
                             --         end
                             --     end
                             -- end
                                if newvalue then
                                    -- split in number and string
                                    mathparameters[name] = newvalue
                                elseif trace_defining then
                                    report_math("ignoring math parameter %a: %S",name,value)
                                end
                            end
                        end
                    end
                    if bigslots then
                        target.bigslots = bigslots
                    end
                end
            end
        end
    end
end

-- a couple of predefined tweaks:

local mathtweaks   = { }
mathematics.tweaks = mathtweaks

local function report_tweak(fmt,target,original,...)
    if fmt then
        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](...)
        )
    else
        report_mathtweak("")
    end
end

do

    local stepper = utilities.parsers.stepper
    local count   = 0

    local splitter = lpeg.tsplitat(".")

    local function adapt(list,target,original,targetcharacters,originalcharacters,k,v,compact,n)
        local character = targetcharacters[k]
        if character then
            if not character.tweaked then
                local t = type(v)
                if t == "number" then
                    v = list[v]
                    t = type(v)
                end
                if t == "table" then
                    local width     = character.width
                    local height    = character.height
                    local depth     = character.depth
                    local italic    = character.italic
                    local topaccent = character.topaccent
                    if #v > 0 then
                        local offsetfactor = v[1]
                        local widthfactor  = v[2]
                        local italicfactor = v[3]
                        local anchorfactor = v[4]
                        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 topaccent and topaccent > 0 then
                            if anchorfactor then
                                character.topaccent = anchorfactor * topaccent
                            elseif width then
                                character.topaccent = topaccent + (character.width - character.advance) / 2
                            end
                        end
                    else
                        local widthfactor   = v.width
                        local heightfactor  = v.height
                        local depthfactor   = v.depth
                        local italicfactor  = v.italic
                        local anchorfactor  = v.anchor
                        local advancefactor = v.advance
                        local xoffsetfactor = v.xoffset
                        local yoffsetfactor = v.yoffset
                        local scalefactor   = v.scale
                        local total = (height or 0) + (depth or 0)
                        if scalefactor ~= 1 then
                            character.scale = scalefactor
                        end
                        if width and width ~= 0 then
                            if advancefactor then
                                character.advance = advancefactor * width
                            end
                            if widthfactor then
                                character.width = widthfactor * width
                            end
                            if xoffsetfactor then
                                character.xoffset = xoffsetfactor * width
                            end
                        end
                        if height and height ~= 0 then
                            if heightfactor then
                                character.height  = heightfactor * height
                            end
                        end
                        if depth and depthfactor then
                            character.depth = depthfactor * depth
                        end
                        if yoffsetfactor then
                            character.yoffset = yoffsetfactor * total
                        end
                        if italic and italic ~= 0 and italicfactor then
                            character.italic = italicfactor * italic
                        end
                        if anchorfactor then
                            character.topaccent = anchorfactor * (topaccent or width)
                        end
                    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(list,target,original,targetcharacters,originalcharacters,smaller,v,compact,n+1)
                    end
                    count = count + 1
                else
                    report_mathtweak("invalid dimension entry %U",k)
                end
                character.tweaked = true
                if v.all then
                    local nxt = character.next
                    if nxt then
                        adapt(list,target,original,targetcharacters,originalcharacters,nxt,v,compact,n)
                    else
                        local parts = character.hparts
                        if parts then
                            for i=1,#parts do
                                adapt(list,target,original,targetcharacters,originalcharacters,parts[i],v,compact,n)
                            end
                        end
                    end
                end
            end
        else
            report_tweak("no character %U",target,original,k)
        end
    end

    local function detail(characters,k)
        if type(k) == "string" then
            local t = lpeg.match(splitter,k)
            local n = #t
            if n > 0 then
                local m = tonumber(t[1]) or tonumber(t[1],16)
                if m then
                    local c = characters[m]
                    if c and n > 1 then
                        m = t[2]
                        if m == "parts" then
                            local nxt = c.next
                            while nxt do
                                c = characters[nxt]
                                nxt = c.next
                            end
                            c = c.hparts or c.vparts
                            if c and n > 2 then
                                m = tonumber(t[3])
                                if m then
                                    c = c[m]
                                    if c then
                                        return c.glyph
                                    end
                                end
                            end
                        end
                    end
                end
            end
        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
            count = 0
            for k, v in sortedhash(list) do
                local t = type(k)
                if t == "number" then
                    adapt(list,target,original,targetcharacters,originalcharacters,k,v,compact,1)
                elseif t == "string" then
                    local d = detail(targetcharacters,k)
                    if d then
                        adapt(list,target,original,targetcharacters,originalcharacters,d,v,compact,1)
                    else
                        stepper(k,function(n)
                            adapt(list,target,original,targetcharacters,originalcharacters,n,v,compact,1)
                        end)
                    end
             -- elseif t == "table" then
             --     for i=1,#t do
             --         adapt(list,target,original,targetcharacters,originalcharacters,t[i],v,compact,1)
             --     end
                end
            end
            if trace_tweaking and count > 0 then
                report_mathtweak("%i dimensions adapted",count)
            end
        end
    end

end

do

    function mathtweaks.replacements(target,original,parameters)
        local list = parameters.list
        if list then
            local targetcharacters   = target.characters
            local originalcharacters = original.characters
            local unicodes = original.resources.unicodes
            if unicodes then
                local count = 0
                for k, v in sortedhash(list) do
                    if type(v) == "string" then
                        v = unicodes[v]
                    end
                    if type(v) == "number" then
                        targetcharacters[k] = targetcharacters[v]
                        count = count + 1
                    end
                end
                if trace_tweaking and count > 0 then
                    report_mathtweak("%i permanent replacements",count)
                end
            end
        end
    end

    function mathtweaks.substitutes(target,original,parameters)
        local list = parameters.list
        if list then
            local targetcharacters   = target.characters
            local originalcharacters = original.characters
            local getsubstitution    = fonts.handlers.otf.getsubstitution
            local count              = 0
            for k, v in sortedhash(list) do
                local sub = getsubstitution(original,k,v,true)
                if sub then
                    targetcharacters[k] = targetcharacters[sub]
                    count = count + 1
                end
            end
            if trace_tweaking and count > 0 then
                report_mathtweak("%i permanent substitutions",count)
            end
        end
    end

    mathtweaks.replace    = mathtweaks.replacements
    mathtweaks.substitute = mathtweaks.substitutes

end

do

    -- What a mess ... should be a different alphabet.

    local function expand(target,original,list,selector,feature)
        if feature then
            local getsubstitution = fonts.handlers.otf.getsubstitution
            for _, char in next, list do
                local variant = getsubstitution(original,char,feature,true)
                if variant then
                    mathematics.addvariant(target,char,variant,selector)
                end
            end
        else
            for i, char in next, list do
                mathematics.addvariant(target,char,0xFE800+i,selector)
            end
        end
    end

    function mathtweaks.variants(target,original,parameters)
        local feature  = parameters.feature
        local selector = parameters.selector
        local kind     = parameters.kind
        if kind == "script" then
            if selector then
                expand(target,original,mathematics.alphabets.sr.tf.lcletters,selector,feature)
                expand(target,original,mathematics.alphabets.sr.tf.ucletters,selector,feature)
            end
        end
    end

    mathtweaks.variant    = mathtweaks.variants

end

do

    -- see changed hack in math-fbk

    local copytable = table.copy
    local nps = fonts.helpers.newprivateslot

    local list = {
        { 0x2032, { nps("prime 0x2032 1"), nps("prime 0x2032 2"), nps("prime 0x2032 3") }, 1 },
        { 0x2033, { nps("prime 0x2033 1"), nps("prime 0x2033 2"), nps("prime 0x2033 3") }, 2 },
        { 0x2034, { nps("prime 0x2034 1"), nps("prime 0x2034 2"), nps("prime 0x2034 3") }, 3 },
        { 0x2057, { nps("prime 0x2057 1"), nps("prime 0x2057 2"), nps("prime 0x2057 3") }, 4 },
        { 0x2035, { nps("prime 0x2035 1"), nps("prime 0x2035 2"), nps("prime 0x2035 3") }, 1 },
        { 0x2036, { nps("prime 0x2036 1"), nps("prime 0x2036 2"), nps("prime 0x2036 3") }, 2 },
        { 0x2037, { nps("prime 0x2037 1"), nps("prime 0x2037 2"), nps("prime 0x2037 3") }, 3 },
    }

    local function copytable(t)
        return {
            width   = t.width,
            height  = t.height,
            depth   = t.depth,
            index   = t.index,
            unicode = t.unicode,
        }
    end

    local lastprivate

    local function use(target,original,targetcharacters,charcode,private,newheight,scale,fake,keep,count,smaller)
        if count == 1 then
            lastprivate = private
        end
        if keep then
            if trace_tweaking then
                report_tweak("keeping prime %U",target,original,charcode)
            end
            return
        end
        if fake and count > 1 then
            local olddata = targetcharacters[lastprivate]
            if olddata then
                -- todo: when keep
                local oldheight = scale * olddata.height
                local oldwidth  = scale * olddata.width
                local yoffset   = (newheight - oldheight) / scale
                local xoffset   = fake * oldwidth
                local newwidth  = oldwidth + (count - 1) * xoffset
                targetcharacters[charcode] = {
                    yoffset  = yoffset,
                    width    = newwidth,
                    height   = newheight,
                    smaller  = smaller,
                    unicode  = olddata.unicode,
                    commands = {
                                      { "offset",           0, 0, lastprivate, scale, scale },
                                      { "offset",     xoffset, 0, lastprivate, scale, scale },
                        count > 2 and { "offset", 2 * xoffset, 0, lastprivate, scale, scale } or nil,
                        count > 3 and { "offset", 3 * xoffset, 0, lastprivate, scale, scale } or nil,
                    },
                }
                if trace_tweaking then
                    report_tweak("faking %U with %i primes",target,original,charcode,count)
                end
                return
            end
        end
        local olddata = targetcharacters[private]
        if olddata then
            local oldheight = scale * olddata.height
            local oldwidth  = scale * olddata.width
            local yoffset   = (newheight - oldheight) / scale
            targetcharacters[charcode] = {
                yoffset  = yoffset,
                width    = oldwidth,
                height   = newheight,
                smaller  = smaller,
                unicode  = olddata.unicode,
                commands = {
                    { "offset", 0, 0, private, scale, scale }
                },
            }
            if trace_tweaking then
                report_tweak("fixing prime %U",target,original,charcode)
            end
            return
        end
        if trace_tweaking then
            report_tweak("unable to fix prime %U",target,original,charcode)
        end
    end

    function mathtweaks.fixprimes(target,original,parameters)
        local targetcharacters   = target.characters
        local targetparameters   = target.parameters
        local originalcharacters = original.characters
        local factor    = parameters.factor or 0.85
        local scale     = parameters.scale or 1
        local smaller   = parameters.smaller
        local fake      = parameters.fake
        local keep      = parameters.keep and targetparameters.mathsize == 1
        local newheight = factor * target.mathparameters.AccentBaseHeight
        local compact   = targetparameters.textscale and true or false
        --
        lastprivate = false
        -- make virtual copies (just all of them, also for tracing)
        for i=1,#list do
            local entry = list[i]
            local count = entry[3]
            if not fake or count == 1 then
                local c1 = entry[1]
                local d1 = targetcharacters[c1]
                if d1 then
                    local pc = entry[2]
                    local c2 = d1.smaller or c1
                    local d2 = targetcharacters[c2]
                    local c3 = d2.smaller or c2
                    local d3 = targetcharacters[c3]
                    if smaller then
                        d1 = d2
                        d2 = d3
                    end
                    targetcharacters[pc[1]] = copytable(d1)
                    targetcharacters[pc[2]] = copytable(d2)
                    targetcharacters[pc[3]] = copytable(d3)
                end
            end
        end
        -- replace
        for i=1,#list do
            local entry = list[i]
            local count = entry[3]
            local c1    = entry[1]
            local pc    = entry[2]
            local s1    = pc[1]
            local d1    = targetcharacters[c1]
            if compact and d1 then
                local c2 = d1.smaller or c1
                local d2 = targetcharacters[c2]
                local c3 = d2.smaller or c2
                local s2 = pc[2]
                local s3 = pc[3]
                use(target,original,targetcharacters,c1,s1,newheight,scale,fake,keep, count,c2)
                use(target,original,targetcharacters,c2,s2,newheight,scale,fake,false,count,c3)
                use(target,original,targetcharacters,c3,s3,newheight,scale,fake,false,count)
            else
                use(target,original,targetcharacters,c1,s1,newheight,scale,fake,keep,count)
            end
        end
    end

end

do

    function mathtweaks.fixanchors(target,original,parameters)
        local factor = tonumber(parameters.factor)
        if factor ~= 0 then
            for k, v in next, target.characters do
                local a = v.topaccent
                if a and a > 0 then
                    v.topaccent = a *  factor
                end
            end
        end
    end

end

do

    -- musical timestamp: March 2022, Antonio Sanches (Bad Hombre), live performance in NL

    function mathtweaks.kerns(target,original,parameters)
        local kerns = parameters.list
        if kerns then
            local characters = target.characters
            local function kernone(unicode,data)
                local chardata = characters[unicode]
                local height = chardata.height or 0
                local depth  = chardata.depth  or 0
                local width  = chardata.width  or 0
                local k = data.topleft     ; if k and k ~= 0 then chardata.topleft     = k * width end
                local k = data.topright    ; if k and k ~= 0 then chardata.topright    = k * width end
                local k = data.bottomleft  ; if k and k ~= 0 then chardata.bottomleft  = k * width end
                local k = data.bottomright ; if k and k ~= 0 then chardata.bottomright = k * width end
            end
            for unicode, data in next, kerns do
                kernone(unicode,data) -- withscriptcode(tfmdata,unicode,data,kernone)
                -- also smaller
            end
        end
    end

end

do

 -- local list = {
 --     [0x203E] = { factor = .4 }, -- overbar
 --     [0x203E] = { factor = .7 }, -- underbar
 --     [0x23DE] = { factor = .4 }, -- overbrace
 --     [0x23DF] = { factor = .7 }, -- underbrace
 --     [0x23DC] = { factor = .4 }, -- overparent
 --     [0x23DD] = { factor = .7 }, -- underparent
 --     [0x23B4] = { factor = .4 }, -- overbracket
 --     [0x23B5] = { factor = .7 }, -- underbracket
 -- }

    -- We can patch the dimensions in-place or we can use additional characters in
    -- the private namespace.

    -- local addprivate = fonts.helpers.addprivate
    -- local newnextglyph = addprivate(target,formatters["M-N-%H"](nextglyph),newnextdata)

    local over  = { factor = "over"   }
    local under = { factor = "under"  }

    local candidates = {
        over = {
            [0x203E] = over,  -- overbar
            [0x23DE] = over,  -- overbrace
            [0x23DC] = over,  -- overparent
            [0x23B4] = over,  -- overbracket
        },
        under = {
            [0x23DF] = under, -- underbrace
            [0x23DD] = under, -- underparent
            [0x23B5] = under, -- underbracket
        },
        accent = {
            [0x0300] = over,  -- widegrave
            [0x0308] = over,  -- wideddot
            [0x0304] = over,  -- widebar
            [0x0301] = over,  -- wideacute
            [0x0302] = over,  -- widehat
            [0x030C] = over,  -- widecheck
            [0x0306] = over,  -- widebreve
            [0x0307] = over,  -- widedot
            [0x030A] = over,  -- widering
            [0x0303] = over,  -- widetilde
            [0x20DB] = over,  -- widedddot
        },
    }

    local function adapt(c,factor,baseheight,basedepth)
        if not c.tweaked then
            local height  = c.height or 0
            local depth   = c.depth  or 0
            local yoffset = 0
            if factor == "over" then
                local h = height - baseheight
                yoffset = h - height
                height  = h
                depth   = depth - baseheight
            elseif factor == "under" then
                local d = depth - basedepth
                yoffset = depth - d
                depth   = d
                height  = height - baseheight
            else
                if height > 0 then
                    local h = tonumber(factor) * height
                    yoffset = h - height
                    height  = h
                elseif depth > 0 then
                    local d = tonumber(factor) * depth
                    yoffset = depth - d
                    depth   = d
                end
            end
            c.yoffset = yoffset ~= 0 and yoffset or nil
            c.height  = height   > 0 and height  or nil
            c.depth   = depth    > 0 and depth   or nil
            c.tweaked = true
        end
    end

    local function process(characters,list,baseheight,basedepth)
        if list then
            for k, v in sortedhash(list) do -- sort for tracing
                local c = characters[k]
                if c and not c.yoffset then
                    local factor = v.factor
                    if factor then
                        adapt(c,factor,baseheight,basedepth)
                        local nc  = c.next
                        local nv = 0
                        local ns = 0
                        while nc do
                            local c = characters[nc]
                            if c then
                                adapt(c,factor,baseheight,basedepth)
                                nv = nv + 1
                                nc = c.next
                                if not nc then
                                    local hv = c.hparts
                                    if hv then
                                        for i=1,#hv do
                                            local c = characters[hv[i].glyph]
                                            if c then
                                                adapt(c,factor,baseheight,basedepth)
                                                ns = ns + 1
                                            end
                                        end
                                    end
                                    break
                                end
                            else
                                break
                            end
                        end
                        if trace_tweaking then
                            report_tweak("adapting extensible (%i sizes, %i parts) %U",k,nv,ns)
                        end
                    end
                end
            end
        end
    end

    function mathtweaks.accentdimensions(target,original,parameters)
        local list = parameters.list or { "over", "under" }
        if list then
            local characters = target.characters
            local baseheight = target.mathparameters.AccentBaseHeight or 0
            local basedepth  = target.mathparameters.AccentBaseDepth  or 0
            for k, v in sortedhash(list) do -- sort for tracing
                local t = type(v)
                if t == "string" then
                    v = candidates[v]
                    t = type(v)
                end
                if t == "table" then
                    process(characters,v,baseheight,basedepth)
                end
            end
        end
    end

end

do

 --  function mathtweaks.addrules(target,original,parameters)
 --      local characters = target.characters
 --      local height     = target.mathparameters.OverbarRuleThickness
 --      local depth      = target.mathparameters.UnderbarRuleThickness
 --      local width      = target.parameters.emwidth/2
 --      local step       = 0.8 * width
 --      characters[0x203E] = { -- over
 --          width    = width,
 --          height   = height,
 --          depth    = 0,
 --          unicode  = 0x203E,
 --          commands = { { "rule", height, width } },
 --          hparts   = {
 --              { advance = width, ["end"] = step, glyph = 0x203E, start = 0 },
 --              { advance = width, ["end"] = 0,    glyph = 0x203E, start = step, extender = 1 },
 --          }
 --      }
 --      characters[0x0332] = { -- under
 --          width    = width,
 --          height   = 0,
 --          depth    = depth,
 --          yoffset  = -depth,
 --          unicode  = 0x0332,
 --          commands = { { "rule", height, width } },
 --          hparts   = {
 --              { advance = width, ["end"] = step, glyph = 0x0332, start = 0 },
 --              { advance = width, ["end"] = 0,    glyph = 0x0332, start = step, extender = 1 },
 --          }
 --      }
 --  end

    function mathtweaks.addrules(target,original,parameters)
        local characters = target.characters
        local thickness  = target.mathparameters.OverbarRuleThickness
        local width      = target.parameters.emwidth / 2
        local step       = 0.8 * width
        characters[0x203E] = { -- over
            width    = width,
            height   = thickness / 2,
            depth    = thickness / 2,
            yoffset  = - thickness / 2,
            unicode  = 0x203E,
            commands = { { "rule", thickness, width } },
            hparts   = {
                { advance = width, ["end"] = step, glyph = 0x203E, start = 0 },
                { advance = width, ["end"] = 0,    glyph = 0x203E, start = step, extender = 1 },
            }
        }
        --
        characters[0x0332] = characters[0x203E]
        --
        -- lucida lacks them ...
        --
        local addprivate = fonts.helpers.addprivate
        --
        local half   = thickness / 2
        local double = thickness * 2
        --
        if not characters[0x23B4] then
            local tpiece = addprivate(target,"bracket-piece-top",{
                width    = thickness,
                height   = half,
                depth    = double,
                yoffset  = - double,
                commands = { { "rule", thickness * 2.5, thickness } },
            })
            characters[0x23B4] = { -- over
                width    = width,
                height   = half,
                depth    = double,
                unicode  = 0x23B4,
                commands = { { "rule", thickness, width } },
                hparts   = {
                    { advance = thickness, glyph = tpiece, ["end"] = 0,    start = half },
                    { advance = width,     glyph = 0x203E, ["end"] = step, start = step, extender = 1 },
                    { advance = thickness, glyph = tpiece, ["end"] = half, start = 0 },
                }
            }
        end
        if not characters[0x23B5] then
            local bpiece = addprivate(target,"bracket-piece-bottom",{
                width    = thickness,
                height   = double,
                depth    = half,
                yoffset  = - half,
                commands = { { "rule", thickness * 2.5, thickness } },
            })
            characters[0x23B5] = { -- over
                width    = width,
                height   = double,
                depth    = half,
                unicode  = 0x23B5,
                commands = { { "rule", thickness, width } },
                hparts   = {
                    { advance = thickness, glyph = bpiece, ["end"] = 0,    start = half },
                    { advance = width,     glyph = 0x203E, ["end"] = step, start = step, extender = 1 },
                    { advance = thickness, glyph = bpiece, ["end"] = half, start = 0 },
                }
            }
        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,
                 -- advance  = width,
                    unicode  = unicode,
                    commands = {
                     -- { "slot", 0, 32 },
                    },
                }
            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

    local list = { 0x2061, 0x2062, 0x2063, 0x2064 }

    function mathtweaks.wipecues(target,original,parameters)
        local characters = target.characters
        local tobewiped  = parameters.list or list
        for i=1,#tobewiped do
            local unicode = tobewiped[i]
            characters[unicode] = {
                width   = 0,
                height  = 0,
                depth   = 0,
                unicode = unicode,
            }
            if trace_tweaking then
                report_tweak("character %U has been wiped",unicode)
            end
        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,
                    unicode  = unicode,
                    commands = {
                        { "offset", 0, offset, template, scale, 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
--
--     local list = {
--         { 0x00AF, 1 },
--     }
--
--     local minint = -2147483647 - 1
--
--     local function fix(target,original,targetcharacters,unicode,factor)
--         local chardata = targetcharacters[unicode]
--         if chardata and factor then
--             local accent = chardata.topaccent
--             if not accent then
--                 local width  = chardata.width or 0
--                 local accent = (tonumber(factor) and factor * width) or (factor and minint)
--                 chardata.topaccent = accent
--                 if trace_tweaking then
--                     report_tweak("fixing accent %U",target,original,unicode)
--                 end
--             end
--         end
--     end
--
--     function mathtweaks.fixaccents(target,original,parameters)
--         local targetcharacters = target.characters
--         for i=1,#list do
--             local entry = list[i]
--             if entry then
--                 fix(target,original,targetcharacters,entry[1],entry[2])
--             end
--         end
--     end
--
-- end

do

    local reported = { }

    function mathtweaks.version(target,original,parameters)
        local metadata = original.shared.rawdata.metadata
        if metadata then
            local version = string.strip(metadata.version or "") -- some have trailing spaces
            if version then
                local expected = parameters.expected
                local fontname = metadata.fontname or false
                local message  = parameters.message
             -- version = tonumber(string.match(version,"%d+.%d+"))
                if version ~= expected and not reported[fontname] then
                    report_tweak("version %a found, version %a expected",target,original,version,expected)
                elseif trace_tweaking then
                    report_tweak("version %a found",target,original,version)
                end
                if message and message ~= "" and not reported[fontname] then
                    report_tweak()
                    report_tweak("%s",target,original,message)
                    report_tweak()
                end
                reported[fontname] = true
            end
        end
    end

end

local apply_tweaks = true

directives.register("math.applytweaks", function(v)
    apply_tweaks = v;
end)

local function applytweaks(when,target,original)
    if apply_tweaks then
        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
    else
        report_math("not tweaking math of %a @ %p (%s)",target.properties.fullname,target.parameters.size,when)
    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.overloadparameters")
sequencers.appendaction("mathparameters","system","mathematics.scaleparameters")
sequencers.appendaction("mathparameters","system","mathematics.checkaccentbaseheight")  -- should go in lfg instead
----------.appendaction("mathparameters","system","mathematics.checkprivateparameters") -- after scaling !

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 getfontoffamily = tex.getfontoffamily

local fontcharacters  = fonts.hashes.characters
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.hparts then
        if character.vparts 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.vparts 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].hparts
        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].hparts
        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].hparts
        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)
-- compact: size = 655360
            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
-- compact: size = 655360
            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