if not modules then modules = { } end modules ['math-ini'] = {
    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"
}

-- if needed we can use the info here to set up xetex definition files
-- the "8000 hackery influences direct characters (utf) as indirect \char's
--
-- isn't characters.data loaded already ... shortcut it here
--
-- replace code 7 by 0 as we don't use it anyway (chars with code 7 will adapt to
-- to the fam when set ... we use other means .. ok, we could use it for spacing but
-- then we also have to set the other characters (only a subset done now)

local next, type = next, type
local formatters, find = string.formatters, string.find
local utfchar, utfbyte, utflength = utf.char, utf.byte, utf.length
----- floor = math.floor
local sortedhash = table.sortedhash
local toboolean = toboolean

local context               = context
local commands              = commands
local implement             = interfaces.implement

local ctx_sprint            = context.sprint
local ctx_doifelsesomething = commands.doifelsesomething

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

trace_defining = true

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

mathematics                 = mathematics or { }
local mathematics           = mathematics

mathematics.extrabase       = fonts.privateoffsets.mathextrabase -- here we push some virtuals
mathematics.privatebase     = fonts.privateoffsets.mathbase      -- here we push the ex

local unsetvalue            = attributes.unsetvalue
local allocate              = utilities.storage.allocate
local chardata              = characters.data

local texsetattribute       = tex.setattribute
local setmathcode           = tex.setmathcode
local setdelcode            = tex.setdelcode

-- These are different from mkiv with luatex.

local classes          = allocate { }
local classnames       = allocate { }
local maxengineclass   = 63
local lastengineclass  = 0
local lastprivateclass = maxengineclass

for k, v in next, nodes.noadcodes do
    if type(k) == "string"then
        classes[k] = v
        local n = classnames[v]
        if not n or #k < #n then
            classnames[v] = k
        end
    elseif k > lastengineclass then
        lastengineclass = k
    end
end

local ordinary_class    = classes.ordinary
local operator_class    = classes.operator
local binary_class      = classes.binary
local relation_class    = classes.relation
local open_class        = classes.open
local close_class       = classes.close
local punctuation_class = classes.punctuation
local middle_class      = classes.middle
local accent_class      = classes.accent
local radical_class     = classes.radical
local fraction_class    = classes.fraction
local under_class       = classes.under
local over_class        = classes.over
local fenced_class      = classes.fenced
local ghost_class       = classes.ghost

classes.ord             = ordinary_class
classes.op              = operator_class
classes.bin             = binary_class
classes.rel             = relation_class
classes.opening         = open_class         -- will go
classes.closing         = close_class        -- will go
classes.punct           = punctuation_class
classes.frac            = fraction_class
classes.rad             = radical_class
classes.fen             = fenced_class
classes.gst             = ghost_class

classes.limop           = operator_class
classes.limoperator     = operator_class
classes.nolop           = operator_class
classes.nolimoperator   = operator_class
classes.large           = operator_class
classes.largeoperator   = operator_class

-- special in the engine   : variable active inner vcenter

local function registerengineclass(name,short)
    local class = classes[name]
    if not class then
        if lastengineclass < maxengineclass then
            lastengineclass = lastengineclass + 1
            class = lastengineclass
            classnames[class] = short or name
        else
            class = ordinary_class
        end
        classes[name] = class
    end
    return class
end

local explicit_class    = registerengineclass("explicit","expl")
local imaginary_class   = registerengineclass("imaginary","im")
local diferential_class = registerengineclass("differential","dif")
local exponential_class = registerengineclass("exponential","exp")
local function_class    = registerengineclass("function","fnc")
local digit_class       = registerengineclass("digit","dig")
local division_class    = registerengineclass("division","div")
local factorial_class   = registerengineclass("factorial","fac")
local wrapped_class     = registerengineclass("wrapped", "wra")
local construct_class   = registerengineclass("construct", "con")

classes["begin"] = 62  classnames[62] = "begin"
classes["end"]   = 63  classnames[63] = "end"

callback.register("get_noad_class", function(n) return classnames[n] end)

local function registerprivateclass(name)
    local class = classes[name]
    if not class then
        lastprivateclass = lastprivateclass + 1
        class = lastprivateclass
        classes[name] = class
        -- also setup
    end
    return class
end

local function toengineclass(class)
    if type(class) == "string" then
        return classes[class] or ordinary_class
    elseif class > lastengineclass then
        return ordinary_class
    else
        return class
    end
end

implement {
    name      = "registerengineclass",
    public    = true,
    protected = true,
    arguments = { "optional", "optional" },
    actions   = registerengineclass,
}

local topaccent_class  = registerprivateclass("topaccent")
local botaccent_class  = registerprivateclass("botaccent")
local delimiter_class  = registerprivateclass("delimiter")
local root_class       = registerprivateclass("root")
local prime_class      = registerprivateclass("prime")

local accents = allocate {
    accent    = true, -- some can be both
    topaccent = true,  [topaccent_class] = true,
    botaccent = true,  [botaccent_class] = true,
    under     = true,  [under_class]     = true,
    over      = true,  [over_class]      = true,
    unknown   = false,
}

local integer_value = tokens.values.integer

implement {
    name      = "mathclassvalue",
 -- usage     = "value",
    public    = true,
    arguments = "string",
    actions = function(name)
     -- return integer_value, classes[name] or ordinary_class
        context(tostring(classes[name] or ordinary_class))
    end
}

-- used in math-tag: so there we need to make things ord etc to fit within
-- mathml

local codes = allocate {
    ordinary       = ordinary_class,    [ordinary_class]    = "ordinary",
    largeoperator  = operator_class,    [operator_class]    = "largeoperator",
    binaryoperator = binary_class,      [binary_class]      = "binaryoperator",
    relation       = relation_class,    [relation_class]    = "relation",
    openingsymbol  = open_class,        [open_class]        = "openingsymbol",
    closingsymbol  = close_class,       [close_class]       = "closingsymbol",
    punctuation    = punctuation_class, [punctuation_class] = "punctuation",
    middlesymbol   = middle_class,      [middle_class]      = "middlesymbol",
}

local extensibles = allocate {
           unknown    = 0,
    l = 1, left       = 1,
    r = 2, right      = 2,
    h = 3, horizontal = 3,-- lr or rl
    u = 5, up         = 4,
    d = 5, down       = 5,
    v = 6, vertical   = 6,-- ud or du
    m = 7, mixed      = 7,
}

table.setmetatableindex(extensibles,function(t,k) t[k] = 0 return 0 end)

local virtualized = allocate {
}

function mathematics.virtualize(unicode,virtual)

    local function virtualize(k,v)
        local c = virtualized[k]
        if c == v then
            report_math("character %C is already virtualized to %C",k,v)
        elseif c then
            report_math("character %C is already virtualized to %C, ignoring mapping to %C",k,c,v)
        else
            virtualized[k] = v
        end
    end

    if type(unicode) == "table" then
        for k, v in next, unicode do
            virtualize(k,v)
        end
    elseif type(unicode) == "number" and type(virtual) == "number" then
        virtualize(unicode,virtual)
 -- else
        -- error
    end
end

mathematics.extensibles   = extensibles
mathematics.classes       = classes
mathematics.toengineclass = toengineclass
mathematics.classnames    = classnames
mathematics.codes         = codes
-----------.accents       = codes
mathematics.virtualized   = virtualized

do

    local setmathcharacter = function(class,family,slot,unicode,mset,dset)
        if mset and class ~= ordinary_class then
            setmathcode("global",slot,class,family,unicode)
            mset = false
        end
        if dset and (class == open_class or class == close_class or class == middle_class or class == division_class) then
            setdelcode("global",slot,family,unicode,0,0)
            dset = false
        end
        return mset, dset
    end

    local function report(class,engine,family,unicode,name)
        local nametype = type(name)
        if nametype == "string" then
            report_math("class %a, engine %a, family %a, char %C, name %a",class,engine,family,unicode,name)
        elseif nametype == "number" then
            report_math("class %a, engine %a, family %a, char %C, number %U",class,engine,family,unicode,name)
        else
            report_math("class %a, engine %a, family %a, char %C",class,engine,family,unicode)
        end
    end

    local f_accent         = formatters[ [[\defUmathtopaccent \%s{%X}{%X}{%X}]] ]
    local f_fixedtopaccent = formatters[ [[\defUmathfixedtopaccent \%s{%X}{%X}{%X}]] ]
    local f_fixedbotaccent = formatters[ [[\defUmathfixedbotaccent \%s{%X}{%X}{%X}]] ]
    local f_topaccent      = formatters[ [[\defUmathtopaccent \%s{%X}{%X}{%X}]] ]
    local f_botaccent      = formatters[ [[\defUmathbotaccent \%s{%X}{%X}{%X}]] ]
    local f_over           = formatters[ [[\defUdelimiterover \%s{%X}{%X}{%X}]] ]
    local f_under          = formatters[ [[\defUdelimiterunder\%s{%X}{%X}{%X}]] ]
    local f_fence          = formatters[ [[\defUdelimiter \%s{%X}{%X}{%X}]] ]
    local f_delimiter      = formatters[ [[\defUdelimiter \%s{%X}{%X}{%X}]] ]
    local f_radical        = formatters[ [[\defUradical \%s{%X}{%X}]]     ]
    local f_root           = formatters[ [[\defUroot \%s{%X}{%X}]]     ]
    local f_char           = formatters[ [[\defUmathchar \%s{%X}{%X}{%X}]] ]

    local texmathchardef = tex.mathchardef

    local setmathsymbol = function(name,class,engine,family,slot,stretch) -- hex is nicer for tracing
        if class == accent_class then
            ctx_sprint(f_topaccent(name,0,family,slot))
        elseif class == topaccent_class then
            ctx_sprint((stretch and f_topaccent or f_fixedtopaccent)(name,0,family,slot))
        elseif class == botaccent_class then
            ctx_sprint((stretch and f_botaccent or f_fixedbotaccent)(name,0,family,slot))
        elseif class == over_class then
            ctx_sprint(f_over(name,0,family,slot))
        elseif class == under_class then
            ctx_sprint(f_under(name,0,family,slot))
        elseif class == open_class or class == close_class or class == middle_class then
            setdelcode("global",slot,family,slot,0,0)
            ctx_sprint(f_fence(name,engine,family,slot))
        elseif class == delimiter_class then
            setdelcode("global",slot,family,slot,0,0)
            ctx_sprint(f_delimiter(name,0,family,slot))
        elseif class == radical_class then
            ctx_sprint(f_radical(name,family,slot))
        elseif class == root_class then
            ctx_sprint(f_root(name,family,slot))
        elseif texmathchardef then
            texmathchardef(name,engine,family,slot,"permanent")
        else
            -- beware, open/close and other specials should not end up here
            ctx_sprint(f_char(name,engine,family,slot))
        end
    end

    function mathematics.define()
        if trace_defining then
            logs.startfilelogging(report_math,"math defined from character definitions")
        end
        local family = 0
        local data   = characters.data
        --
        local function remap(first,last)
            for unicode=utfbyte(first),utfbyte(last) do
                setmathcode("global",unicode,ordinary_class,family,unicode)
            end
        end
        remap("0","9")
        remap("A","Z")
        remap("a","z")
        --
        setdelcode("global",0x2E,0,0,0,0) -- period is special
        --
        for unicode, character in sortedhash(data) do
            local symbol = character.mathsymbol
            local mset   = true
            local dset   = true
            if symbol then
                local other = data[symbol]
                local class = other.mathclass
                if class then
                    local engine = toengineclass(class)
                    if trace_defining then
                        report(class,engine,family,unicode,symbol)
                    end
                    mset, dset = setmathcharacter(engine,family,unicode,symbol,mset,dset)
                end
                local spec = other.mathspec
                if spec then
                    for i=1,#spec do
                        local m = spec[i]
                        local class = m.class
                        if class then
                            local engine = toengineclass(class)
                            -- todo: trace
                            mset, dset = setmathcharacter(engine,family,unicode,symbol,mset,dset)
                        end
                    end
                end
            end
            local class   = character.mathclass
            local spec    = character.mathspec
            local name    = character.mathname
            local stretch = character.mathstretch
            if spec then
                local done = false
                if class then
                    if name then
                        report_math("fatal error, conflicting mathclass and mathspec for %C",unicode)
                        os.exit()
                    else
                        class = classes[class] or ordinary_class
                        local engine = toengineclass(class)
                        if trace_defining then
                            report(class,engine,family,unicode)
                        end
                        mset, dset = setmathcharacter(engine,family,unicode,unicode,mset,dset)
                        done = true
                    end
                end
                for i=1,#spec do
                    local m     = spec[i]
                    local name  = m.name
                    local class = m.class or class
                    if class then
                        class = classes[class] or ordinary_class
                    else
                        class = ordinary_class
                    end
                    if class then
                        local engine = toengineclass(class)
                        if name then
                            if trace_defining then
                                report(class,engine,family,unicode,name)
                            end
                            setmathsymbol(name,class,engine,family,unicode,stretch)
                        else
                            name = (class == classes.ordinary or class == classes.digit) and character.adobename -- bad
                            if name and trace_defining then
                                report(class,engine,family,unicode,name)
                            end
                        end
                        if not done then
                            mset, dset = setmathcharacter(engine,family,unicode,m.unicode or unicode,mset,dset) -- see solidus
                            done = true
                        end
                    end
                end
            else
                if class then
                    class = classes[class] or ordinary_class
                else
                    class = ordinary_class
                end
                if name ~= nil then
                    local engine = toengineclass(class)
                    if name == false then
                        if trace_defining then
                            report(class,engine,family,unicode,name)
                        end
                        mset, dset = setmathcharacter(engine,family,unicode,unicode,mset,dset)
                    else
                     -- if not name then
                     --     name = character.contextname -- too dangerous, we loose textslash and a few more
                     -- end
                        if name then
                            if trace_defining then
                                report(class,engine,family,unicode,name)
                            end
                            setmathsymbol(name,class,engine,family,unicode,stretch)
                        else
                            if trace_defining then
                                report(class,engine,family,unicode,character.adobename)
                            end
                        end
                        mset, dset = setmathcharacter(engine,family,unicode,unicode,mset,dset)
                    end
                elseif class ~= ordinary_class then
                    local engine = toengineclass(class)
                    if trace_defining then
                        report(class,engine,family,unicode,character.adobename)
                    end
                    mset, dset = setmathcharacter(engine,family,unicode,unicode,mset,dset)
                end
            end
        end
        --
        if trace_defining then
            logs.stopfilelogging()
        end
    end

end

-- needed for mathml analysis
-- string with # > 1 are invalid
-- we could cache

do

    local lpegmatch = lpeg.match
    local utf8byte  = lpeg.patterns.utf8byte * lpeg.P(-1)

    -- function somechar(c)
    --     local b = lpegmatch(utf8byte,c)
    --     return b and chardata[b]
    -- end

    local somechar = table.setmetatableindex(function(t,k)
        if k then
            local b = lpegmatch(utf8byte,k)
            local v = b and chardata[b] or false
            t[k] = v
            return v
        end
    end)

    local function utfmathclass(chr, default)
        local cd = somechar[chr]
        return cd and cd.mathclass or default or "unknown"
    end

    local function utfmathlimop(chr)
        local cd = somechar[chr]
        return cd and cd.mathclass == "limop" or false
    end

    local function utfmathaccent(chr,default,asked1,asked2)
        local cd = somechar[chr]
        if not cd then
            return default or false
        end
        if asked1 and asked1 ~= "" then
            local mc = cd.mathclass
            if mc and (mc == asked1 or mc == asked2) then
                return true
            end
            local ms = cd.mathspec
            if not ms then
                local mp = cd.mathparent
                if mp then
                    ms = chardata[mp].mathspec
                end
            end
            if ms then
                for i=1,#ms do
                    local msi = ms[i]
                    local mc = msi.class
                    if mc and (mc == asked1 or mc == asked2) then
                        return true
                    end
                end
            end
        else
            local mc = cd.mathclass
            if mc then
                return accents[mc] or default or false
            end
            local ms = cd.mathspec
            if ms then
                for i=1,#ms do
                    local msi = ms[i]
                    local mc = msi.class
                    if mc then
                        return accents[mc] or default or false
                    end
                end
            end
        end
        return default or false
    end

    local function utfmathstretch(chr,default) -- "h", "v", "b", ""
        local cd = somechar[chr]
        return cd and cd.mathstretch or default or ""
    end

    local function utfmathcommand(chr,default,asked1,asked2)
        local cd = somechar[chr]
        if not cd then
            return default or ""
        end
        if asked1 then
            local mn = cd.mathname
            local mc = cd.mathclass
            if mn and mc and (mc == asked1 or mc == asked2) then
                return mn
            end
            local ms = cd.mathspec
            if not ms then
                local mp = cd.mathparent
                if mp then
                    ms = chardata[mp].mathspec
                end
            end
            if ms then
                for i=1,#ms do
                    local msi = ms[i]
                    local mn = msi.name
                    if mn then
                        local mc = msi.class
                        if mc == asked1 or mc == asked2 then
                            return mn
                        end
                    end
                end
            end
        else
            local mn = cd.mathname
            if mn then
                return mn
            end
            local ms = cd.mathspec
            if ms then
                for i=1,#ms do
                    local msi = ms[i]
                    local mn = msi.name
                    if mn then
                        return mn
                    end
                end
            end
        end
        return default or ""
    end

    local function utfmathfiller(chr, default)
        local cd = somechar[chr]
        local cmd = cd and cd.mathfiller -- or cd.mathname
        return cmd or default or ""
    end

    mathematics.utfmathclass   = utfmathclass
    mathematics.utfmathstretch = utfmathstretch
    mathematics.utfmathcommand = utfmathcommand
    mathematics.utfmathfiller  = utfmathfiller
    mathematics.utfmathaccent  = utfmathaccent

    -- interfaced

    implement {
        name      = "utfmathclass",
        public    = true,
        actions   = { utfmathclass, context },
        arguments = "argument"
    }

    implement {
        name      = "utfmathstretch",
        public    = true,
        actions   = { utfmathstretch, context },
        arguments = "argument"
    }

    implement {
        name      = "utfmathcommand",
        public    = true,
        actions   = { utfmathcommand, context },
        arguments = "argument"
    }

    implement {
        name      = "utfmathfiller",
        public    = true,
        actions   = { utfmathfiller, context },
        arguments = "argument"
    }

    implement {
        name      = "utfmathcommandabove",
        public    = true,
        actions   = { utfmathcommand, context },
        arguments = { "argument", false, "'topaccent'","'over'" }
    }

    implement {
        name      = "utfmathcommandbelow",
        public    = true,
        actions   = { utfmathcommand, context },
        arguments = { "argument", false, "'botaccent'","'under'" }
    }

    implement {
        name      = "utfmathcommandfiller",
        public    = true,
        actions   = { utfmathfiller, context },
        arguments = "argument"
    }

    -- todo: make this a helper:

    implement {
        name      = "doifelseutfmathabove",
        public    = true,
        actions   = { utfmathaccent, ctx_doifelsesomething },
        arguments = { "argument", false, "'topaccent'", "'over'" }
    }

    implement {
        name      = "doifelseutfmathbelow",
        public    = true,
        actions   = { utfmathaccent, ctx_doifelsesomething },
        arguments = { "argument", false, "'botaccent'", "'under'" }
    }

    implement {
        name      = "doifelseutfmathaccent",
        public    = true,
        actions   = { utfmathaccent, ctx_doifelsesomething },
        arguments = "argument",
    }

    implement {
        name      = "doifelseutfmathfiller",
        public    = true,
        actions   = { utfmathfiller, ctx_doifelsesomething },
        arguments = "argument",
    }

    implement {
        name      = "doifelseutfmathlimop",
        public    = true,
        actions   = { utfmathlimop, ctx_doifelsesomething },
        arguments = "argument"
    }

end

-- helpers
--
-- 1: step 1
-- 2: step 2
-- 3: htdp * 1.33^n
-- 4: size * 1.33^n
-- 5: use lfg

function mathematics.big(tfmdata,unicode,n,method)
    local t = tfmdata.characters
    local c = t[unicode]
    if c and n > 0 then
        if method == 1 or method == 2 or method == 5 then
            if method == 5 then
                local b = tfmdata.bigslots
                if b then
                    n = (n > #b and b[#b]) or b[n] or n
                end
            elseif method == 2 then -- large steps
                n = n * 2
            end
            local next = c.next
            while next do
                if n <= 1 then
                    return next
                else
                    n = n - 1
                    local tn = t[next].next
                    if tn then
                        next = tn
                    else
                        return next
                    end
                end
            end
        elseif method >= 3 then
            local size = 1.33^n
            if method == 4 then
                size = tfmdata.parameters.size * size
            else -- if method == 3 then
                size = (c.height + c.depth) * size
            end
            local next = c.next
            while next do
                local cn = t[next]
                if (cn.height + cn.depth) >= size then
                    return next
                else
                    local tn = cn.next
                    if tn then
                        next = tn
                    else
                        return next
                    end
                end
            end
        end
    end
    return unicode
end

do -- experimental

    -- local categories = { } -- indexed + hashed
    --
    -- local a_mathcategory = attributes.private("mathcategory")
    --
    -- local function registercategory(category,tag,data) -- always same data for tag
    --     local c = categories[category]
    --     if not c then
    --         c = { }
    --         categories[category] = c
    --     end
    --     local n = c[tag]
    --     if not n then
    --         n = #c + 1
    --         c[n] = data
    --         n = n * 1000 + category
    --         c[tag] = n
    --     end
    --     return n
    -- end
    --
    -- function mathematics.getcategory(n)
    --     local category = n % 1000
    --     return category, categories[category][floor(n/1000)]
    -- end
    --
    -- mathematics.registercategory = registercategory
    --
    -- function commands.taggedmathfunction(tag,label)
    --     if label then
    --         texsetattribute(a_mathcategory,registercategory(1,tag,tag))
    --         context.mathlabeltext(tag)
    --     else
    --         texsetattribute(a_mathcategory,1)
    --         context(tag)
    --     end
    -- end

    local categories       = { }
    mathematics.categories = categories

    local a_mathcategory   = attributes.private("mathcategory")

    local functions        = storage.allocate()
    categories.functions   = functions
    local noffunctions     = 1000 -- offset

    implement {
        name      = "tagmfunctiontxt",
        arguments = { "string", "conditional" },
        actions   = function(tag,apply)
            local delta = apply and 1000 or 0
            texsetattribute(a_mathcategory,1000 + delta)
        end
    }

    implement {
        name      = "tagmfunctionlab",
        arguments = { "string", "conditional" },
        actions   = function(tag,apply)
            local delta = apply and 1000 or 0
            local n = functions[tag]
            if not n then
                noffunctions = noffunctions + 1
                functions[noffunctions] = tag
                functions[tag] = noffunctions
                texsetattribute(a_mathcategory,noffunctions + delta)
            else
                texsetattribute(a_mathcategory,n + delta)
            end
        end
    }

end

do

    local list

    function mathematics.resetattributes()
        if not list then
            list = { }
            for k, v in next, attributes.numbers do
                if find(k,"^math") then
                    list[#list+1] = v
                end
            end
        end
        for i=1,#list do
            texsetattribute(list[i],unsetvalue)
        end
    end

end

implement {
    name      = "resetmathattributes",
    public    = true,
    protected = true,
    actions   = mathematics.resetattributes
}

-- weird to do this here but it's a side affect of math anyway

implement {
    name     = "enableasciimode",
    onlyonce = true,
    actions  = resolvers.macros.enablecomment,
}