path: root/tex/context/base/math-vfu.lua

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

-- All these math vectors .. thanks to Aditya and Mojca they become
-- better and better. If you have problems with math fonts or miss
-- characters report it to the ConTeXt mailing list. Also thanks to
-- Boguslaw for finding a couple of errors.

-- 20D6 -> 2190
-- 20D7 -> 2192

local type, next = type, next
local max = math.max
local format = string.format

local fonts, nodes, mathematics = fonts, nodes, mathematics

local trace_virtual = false  trackers.register("math.virtual", function(v) trace_virtual = v end)
local trace_timings = false  trackers.register("math.timings", function(v) trace_timings = v end)

local add_optional  = false  directives.register("math.virtual.optional",function(v) add_optional = v end)

local report_virtual    = logs.reporter("fonts","virtual math")

local allocate          = utilities.storage.allocate
local setmetatableindex = table.setmetatableindex

local mathencodings     = allocate()
fonts.encodings.math    = mathencodings -- better is then: fonts.encodings.vectors
local vfmath            = allocate()
fonts.handlers.vf.math  = vfmath

local shared            = { }

--~ local push, pop, back = { "push" }, { "pop" }, { "slot", 1, 0x2215 }

--~ local function negate(main,characters,id,size,unicode,basecode)
--~     if not characters[unicode] then
--~         local basechar = characters[basecode]
--~         if basechar then
--~             local ht, wd = basechar.height, basechar.width
--~             characters[unicode] = {
--~                 width    = wd,
--~                 height   = ht,
--~                 depth    = basechar.depth,
--~                 italic   = basechar.italic,
--~                 kerns    = basechar.kerns,
--~                 commands = {
--~                     { "slot", 1, basecode },
--~                     push,
--~                     { "down",    ht/5},
--~                     { "right", - wd/2},
--~                     back,
--~                     push,
--~                 }
--~             }
--~         end
--~     end
--~ end

--~ \Umathchardef\braceld="0 "1 "FF07A
--~ \Umathchardef\bracerd="0 "1 "FF07B
--~ \Umathchardef\bracelu="0 "1 "FF07C
--~ \Umathchardef\braceru="0 "1 "FF07D

local function brace(main,characters,id,size,unicode,first,rule,left,right,rule,last)
    if not characters[unicode] then
        characters[unicode] = {
            horiz_variants = {
                { extender = 0, glyph = first },
                { extender = 1, glyph = rule  },
                { extender = 0, glyph = left  },
                { extender = 0, glyph = right },
                { extender = 1, glyph = rule  },
                { extender = 0, glyph = last  },
            }
        }
    end
end

local function arrow(main,characters,id,size,unicode,arrow,minus,isleft)
    local chr = characters[unicode]
    if not chr then
        -- skip
    elseif isleft then
        chr.horiz_variants = {
            { extender = 0, glyph = arrow },
            { extender = 1, glyph = minus },
        }
    else
        chr.horiz_variants = {
            { extender = 1, glyph = minus },
            { extender = 0, glyph = arrow },
        }
    end
end

local function parent(main,characters,id,size,unicode,first,rule,last)
    if not characters[unicode] then
        characters[unicode] = {
            horiz_variants = {
                { extender = 0, glyph = first },
                { extender = 1, glyph = rule  },
                { extender = 0, glyph = last  },
            }
        }
    end
end

local push, pop, step = { "push" }, { "pop" }, 0.2 -- 0.1 is nicer but gives larger files

local function make(main,characters,id,size,n,m)
    local old = 0xFF000+n
    local c = characters[old]
    if c then
        local upslot, dnslot, uprule, dnrule = 0xFF100+n, 0xFF200+n, 0xFF300+m, 0xFF400+m
        local xu = main.parameters.x_height + 0.3*size
        local xd = 0.3*size
        local w, h, d = c.width, c.height, c.depth
        local thickness = h - d
        local rulewidth = step*size -- we could use an overlap
        local slot = { "slot", id, old }
        local rule = { "rule", thickness, rulewidth  }
        local up = { "down", -xu }
        local dn = { "down", xd }
        local ht, dp = xu + 3*thickness, 0
        if not characters[uprule] then
            characters[uprule] = { width = rulewidth, height = ht, depth = dp, commands = { push, up, rule, pop } }
        end
        characters[upslot] = { width = w, height = ht, depth = dp, commands = { push, up, slot, pop } }
        local ht, dp = 0, xd + 3*thickness
        if not characters[dnrule] then
            characters[dnrule] = { width = rulewidth, height = ht, depth = dp, commands = { push, dn, rule, pop } }
        end
        characters[dnslot] = { width = w, height = ht, depth = dp, commands = { push, dn, slot, pop } }
    end
end

local function minus(main,characters,id,size,unicode) -- push/pop needed?
    local minus = characters[0x002D]
    if minus then
        local mu = size/18
        local width = minus.width - 5*mu
        characters[unicode] = {
            width = width, height = minus.height, depth = minus.depth,
            commands = { push, { "right", -3*mu }, { "slot", id, 0x002D }, pop }
        }
    end
end

-- fails: pdf:page: pdf:direct: ... some funny displacement

-- this does not yet work ... { "scale", 2, 0, 0, 3 } .. commented code
--
-- this does not work ... no interpretation going on here
--
-- local nodeinjections = backends.nodeinjections
-- { "node", nodeinjections.save() },
-- { "node", nodeinjections.transform(.7,0,0,.7) },
-- commands[#commands+1] = { "node", nodeinjections.restore() }

local done = { }

local function raise(main,characters,id,size,unicode,private,n) -- this is a real fake mess
    local raised = characters[private]
    if raised then
        if not done[unicode] then
            report_virtual("temporary too large U+%05X due to issues in luatex backend",unicode)
            done[unicode] = true
        end
        local up = 0.85 * main.parameters.x_height
        local slot = { "slot", id, private }
        local commands = {
            push,
            { "down", - up },
         -- { "scale", .7, 0, 0, .7 },
            slot,
        }
        for i=2,n do
            commands[#commands+1] = slot
        end
        commands[#commands+1] = pop
        characters[unicode] = {
            width    = .7 * n * raised.width,
            height   = .7 * (raised.height + up),
            depth    = .7 * (raised.depth  - up),
            commands = commands,
        }
    end
end

local function dots(main,characters,id,size,unicode)
    local c = characters[0x002E]
    if c then
        local w, h, d = c.width, c.height, c.depth
        local mu = size/18
        local right3mu  = { "right", 3*mu }
        local right1mu  = { "right", 1*mu }
        local up1size   = { "down", -.1*size }
        local up4size   = { "down", -.4*size }
        local up7size   = { "down", -.7*size }
        local right2muw = { "right", 2*mu + w }
        local slot = { "slot", id, 0x002E }
        if unicode == 0x22EF then
            local c = characters[0x022C5]
            if c then
                local w, h, d = c.width, c.height, c.depth
                local slot = { "slot", id, 0x022C5 }
                characters[unicode] = {
                    width = 3*w + 2*3*mu, height = h, depth = d,
                    commands = { push, slot, right3mu, slot, right3mu, slot, pop }
                }
            end
        elseif unicode == 0x22EE then
            -- weird height !
            characters[unicode] = {
                width = w, height = h+(1.4)*size, depth = 0,
                commands = { push, push, slot, pop, up4size, push, slot, pop, up4size, slot, pop }
            }
        elseif unicode == 0x22F1 then
            characters[unicode] = {
                width = 3*w + 6*size/18, height = 1.5*size, depth = 0,
                commands = {
                    push,
                        right1mu,
                        push, up7size, slot, pop,
                        right2muw,
                        push, up4size, slot, pop,
                        right2muw,
                        push, up1size, slot, pop,
                        right1mu,
                    pop
                }
            }
        elseif unicode == 0x22F0 then
            characters[unicode] = {
                width = 3*w + 6*size/18, height = 1.5*size, depth = 0,
                commands = {
                    push,
                        right1mu,
                        push, up1size, slot, pop,
                        right2muw,
                        push, up4size, slot, pop,
                        right2muw,
                        push, up7size, slot, pop,
                        right1mu,
                    pop
                }
            }
        else
            characters[unicode] = {
                width = 3*w + 2*3*mu, height = h, depth = d,
                commands = { push, slot, right3mu, slot, right3mu, slot, pop }
            }
        end
    end
end

local function vertbar(main,characters,id,size,parent,scale,unicode)
    local cp = characters[parent]
    if cp then
        local sc = scale * size
        local pc = { "slot", id, parent }
        characters[unicode] = {
            width    = cp.width,
            height   = cp.height + sc,
            depth    = cp.depth + sc,
            commands = {
                push, { "down", -sc }, pc, pop,
                push, { "down",  sc }, pc, pop,
                                       pc,
            },
            next = cp.next -- can be extensible
        }
        cp.next = unicode
    end
end

local function jointwo(main,characters,id,size,unicode,u1,d12,u2)
    local c1, c2 = characters[u1], characters[u2]
    if c1 and c2 then
        local w1, w2 = c1.width, c2.width
        local mu = size/18
        characters[unicode] = {
            width    = w1 + w2 - d12*mu,
            height   = max(c1.height or 0, c2.height or 0),
            depth    = max(c1.depth or 0, c2.depth or 0),
            commands = {
                { "slot", id, u1 },
                { "right", -d12*mu } ,
                { "slot", id, u2 },
            }
        }
    end
end

local function jointhree(main,characters,id,size,unicode,u1,d12,u2,d23,u3)
    local c1, c2, c3 = characters[u1], characters[u2], characters[u3]
    if c1 and c2 and c3 then
        local w1, w2, w3 = c1.width, c2.width, c3.width
        local mu = size/18
        characters[unicode] = {
            width    = w1 + w2 + w3 - d12*mu - d23*mu,
            height   = max(c1.height or 0, c2.height or 0, c3.height or 0),
            depth    = max(c1.depth or 0, c2.depth or 0, c3.depth or 0),
            commands = {
                { "slot", id, u1 },
                { "right", - d12*mu } ,
                { "slot", id, u2 },
                { "right", - d23*mu },
                { "slot", id, u3 },
            }
        }
    end
end

local function stack(main,characters,id,size,unicode,u1,d12,u2)
    local c1, c2 = characters[u1], characters[u2]
    if c1 and c2 then
        local w1, w2 = c1.width, c2.width
        local h1, h2 = c1.height, c2.height
        local d1, d2 = c1.depth, c2.depth
        local mu = size/18
        characters[unicode] = {
            width    = w1,
            height   = h1 + h2 + d12,
            depth    = d1,
            commands = {
                { "slot", id, u1 },
                { "right", - w1/2 - w2/2 } ,
                { "down", -h1 + d2 -d12*mu } ,
                { "slot", id, u2 },
            }
        }
    end
end

function vfmath.addmissing(main,id,size)
    local characters = main.characters
    local shared = main.shared
    local variables = main.goodies.mathematics and main.goodies.mathematics.variables or { }
    local joinrelfactor = variables.joinrelfactor or 3
    for i=0x7A,0x7D do
        make(main,characters,id,size,i,1)
    end
    brace    (main,characters,id,size,0x23DE,0xFF17A,0xFF301,0xFF17D,0xFF17C,0xFF301,0xFF17B)
    brace    (main,characters,id,size,0x23DF,0xFF27C,0xFF401,0xFF27B,0xFF27A,0xFF401,0xFF27D)
    parent   (main,characters,id,size,0x23DC,0xFF17A,0xFF301,0xFF17B)
    parent   (main,characters,id,size,0x23DD,0xFF27C,0xFF401,0xFF27D)
 -- negate   (main,characters,id,size,0x2260,0x003D)
    dots     (main,characters,id,size,0x2026) -- ldots
    dots     (main,characters,id,size,0x22EE) -- vdots
    dots     (main,characters,id,size,0x22EF) -- cdots
    dots     (main,characters,id,size,0x22F1) -- ddots
    dots     (main,characters,id,size,0x22F0) -- udots
    minus    (main,characters,id,size,0xFF501)
    arrow    (main,characters,id,size,0x2190,0x2190,0xFF501,true)  -- left
    arrow    (main,characters,id,size,0x2192,0x2192,0xFF501,false) -- right
    vertbar  (main,characters,id,size,0x0007C,0.10,0xFF601) -- big  : 0.85 bodyfontsize
    vertbar  (main,characters,id,size,0xFF601,0.30,0xFF602) -- Big  : 1.15 bodyfontsize
    vertbar  (main,characters,id,size,0xFF602,0.30,0xFF603) -- bigg : 1.45 bodyfontsize
    vertbar  (main,characters,id,size,0xFF603,0.30,0xFF604) -- Bigg : 1.75 bodyfontsize
    vertbar  (main,characters,id,size,0x02016,0.10,0xFF605)
    vertbar  (main,characters,id,size,0xFF605,0.30,0xFF606)
    vertbar  (main,characters,id,size,0xFF606,0.30,0xFF607)
    vertbar  (main,characters,id,size,0xFF607,0.30,0xFF608)
    jointwo  (main,characters,id,size,0x21A6,0xFE321,0,0x02192)                       -- \mapstochar\rightarrow
    jointwo  (main,characters,id,size,0x21A9,0x02190,joinrelfactor,0xFE323)           -- \leftarrow\joinrel\rhook
    jointwo  (main,characters,id,size,0x21AA,0xFE322,joinrelfactor,0x02192)           -- \lhook\joinrel\rightarrow
    stack    (main,characters,id,size,0x2259,0x0003D,3,0x02227)                       -- \buildrel\wedge\over=
    jointwo  (main,characters,id,size,0x22C8,0x022B3,joinrelfactor,0x022B2)           -- \mathrel\triangleright\joinrel\mathrel\triangleleft (4 looks better than 3)
    jointwo  (main,characters,id,size,0x2260,0x00338,0,0x0003D)                       -- \not\equal
    jointwo  (main,characters,id,size,0x2284,0x00338,0,0x02282)                       -- \not\subset
    jointwo  (main,characters,id,size,0x2285,0x00338,0,0x02283)                       -- \not\supset
    jointwo  (main,characters,id,size,0x22A7,0x0007C,joinrelfactor,0x0003D)           -- \mathrel|\joinrel=
    jointwo  (main,characters,id,size,0x27F5,0x02190,joinrelfactor,0x0002D)           -- \leftarrow\joinrel\relbar
    jointwo  (main,characters,id,size,0x27F6,0x0002D,joinrelfactor,0x02192)           -- \relbar\joinrel\rightarrow
    jointwo  (main,characters,id,size,0x27F7,0x02190,joinrelfactor,0x02192)           -- \leftarrow\joinrel\rightarrow
    jointwo  (main,characters,id,size,0x27F8,0x021D0,joinrelfactor,0x0003D)           -- \Leftarrow\joinrel\Relbar
    jointwo  (main,characters,id,size,0x27F9,0x0003D,joinrelfactor,0x021D2)           -- \Relbar\joinrel\Rightarrow
    jointwo  (main,characters,id,size,0x27FA,0x021D0,joinrelfactor,0x021D2)           -- \Leftarrow\joinrel\Rightarrow
    jointhree(main,characters,id,size,0x27FB,0x02190,joinrelfactor,0x0002D,0,0xFE324) -- \leftarrow\joinrel\relbar\mapsfromchar
    jointhree(main,characters,id,size,0x27FC,0xFE321,0,0x0002D,joinrelfactor,0x02192) -- \mapstochar\relbar\joinrel\rightarrow
    jointwo  (main,characters,id,size,0x2254,0x03A,0,0x03D)                           -- := (≔)

 -- raise    (main,characters,id,size,0x02032,0xFE325,1) -- prime
 -- raise    (main,characters,id,size,0x02033,0xFE325,2) -- double prime
 -- raise    (main,characters,id,size,0x02034,0xFE325,3) -- triple prime

    -- there are more (needs discussion first):

 -- characters[0x20D6] = characters[0x2190]
 -- characters[0x20D7] = characters[0x2192]

    characters[0x02B9] = characters[0x2032] -- we're nice

end

local unique = 0 -- testcase: \startTEXpage \math{!\text{-}\text{-}\text{-}} \stopTEXpage

local reported = { }
local reverse  = { } -- index -> unicode

setmetatableindex(reverse, function(t,name)
    if trace_virtual then
        report_virtual("initializing math vector '%s'",name)
    end
    local m, r = mathencodings[name], { }
    for u, i in next, m do
        r[i] = u
    end
    reverse[name] = r
    return r
end)

function vfmath.define(specification,set,goodies)
    local name = specification.name -- symbolic name
    local size = specification.size -- given size
    local loaded, fontlist, names, main = { }, { }, { }, nil
    local start = (trace_virtual or trace_timings) and os.clock()
    local okset, n = { }, 0
    for s=1,#set do
        local ss = set[s]
        local ssname = ss.name
        if add_optional and ss.optional then
            if trace_virtual then
                report_virtual("loading font %s subfont %s with name %s at %s is skipped",name,s,ssname,size)
            end
        else
            if ss.features then
                ssname = ssname .. "*" .. ss.features
            end
            if ss.main then
                main = s
            end
            local alreadyloaded = names[ssname] -- for px we load one twice (saves .04 sec)
            local f, id
            if alreadyloaded then
                f, id = alreadyloaded.f, alreadyloaded.id
                if trace_virtual then
                    report_virtual("loading font %s subfont %s with name %s is reused",name,s,ssname)
                end
            else
                f, id = fonts.constructors.readanddefine(ssname,size)
                names[ssname] = { f = f, id = id }
            end
            if not f or id == 0 then
                report_virtual("loading font %s subfont %s with name %s at %s is skipped, not found",name,s,ssname,size)
            else
                n = n + 1
                okset[n] = ss
                loaded[n] = f
                fontlist[n] = { id = id, size = size }
                if not shared[s] then
                    shared[n] = { }
                end
                if trace_virtual then
                    report_virtual("loading font %s subfont %s with name %s at %s as id %s using encoding %s",name,s,ssname,size,id,ss.vector or "none")
                end
                if not ss.checked then
                    ss.checked = true
                    local vector = mathencodings[ss.vector]
                    if vector then
                        -- we resolve named glyphs only once as we can assume that vectors
                        -- are unique to a font set (when we read an afm we get those names
                        -- mapped onto the private area)
                        for unicode, index in next, vector do
                            if not tonumber(index) then
                                local u = f.unicodes
                                u = u and u[index]
                                if u then
                                    if trace_virtual then
                                        report_virtual("resolving name %s to %s",index,u)
                                    end
                                else
                                    report_virtual("unable to resolve name %s",index)
                                end
                                vector[unicode] = u
                            end
                        end
                    end
                end
            end
        end
    end
    -- beware, loaded[1] is already passed to tex (we need to make a simple copy then .. todo)
    local parent         = loaded[1] -- a text font
    local characters     = { }
    local parameters     = { }
    local mathparameters = { }
    local descriptions   = { }
    local metadata       = { }
    local properties     = { }
    local goodies        = { }
    local main           = {
        metadata         = metadata,
        properties       = properties,
        characters       = characters,
        descriptions     = descriptions,
        parameters       = parameters,
        mathparameters   = mathparameters,
        fonts            = fontlist,
        goodies          = goodies,
    }
    --
    --
    for key, value in next, parent do
        if type(value) ~= "table" then
            main[key] = value
        end
    end
    --
    if parent.characters then
        for unicode, character in next, parent.characters do
            characters[unicode] = character
        end
    else
        report_virtual("font %s has no characters",name)
    end
    --
    if parent.parameters then
        for key, value in next, parent.parameters do
            parameters[key] = value
        end
    else
        report_virtual("font %s has no parameters",name)
    end
    --
    local description = { name = "<unset>" }
    setmetatableindex(descriptions,function() return description end)
    --
    if parent.properties then
        setmetatableindex(properties,parent.properties)
    end
    --
    if parent.goodies then
        setmetatableindex(goodies,parent.goodies)
    end
    --
    properties.virtualized = true
    properties.hasitalics  = true
    properties.hasmath     = true
    --
    local fullname = properties.fullname -- parent via mt
    if fullname then
        unique = unique + 1
        properties.fullname = fullname .. "-" .. unique
    end
    --
    -- we need to set some values in main as well (still?)
    --
    main.fullname      = properties.fullname
    main.type          = "virtual"
    main.nomath        = false
    --
    parameters.x_height = parameters.x_height or 0
    --
    local already_reported = false
    for s=1,n do
        local ss, fs = okset[s], loaded[s]
        if not fs then
            -- skip, error
        elseif add_optional and ss.optional then
            -- skip, redundant
        else
            local newparameters = fs.parameters
            if not newparameters then
                report_virtual("font %s, no parameters set",name)
            elseif ss.extension then
                mathparameters.math_x_height          = newparameters.x_height or 0        -- math_x_height          : height of x
                mathparameters.default_rule_thickness = newparameters[ 8]      or 0        -- default_rule_thickness : thickness of \over bars
                mathparameters.big_op_spacing1        = newparameters[ 9]      or 0        -- big_op_spacing1        : minimum clearance above a displayed op
                mathparameters.big_op_spacing2        = newparameters[10]      or 0        -- big_op_spacing2        : minimum clearance below a displayed op
                mathparameters.big_op_spacing3        = newparameters[11]      or 0        -- big_op_spacing3        : minimum baselineskip above displayed op
                mathparameters.big_op_spacing4        = newparameters[12]      or 0        -- big_op_spacing4        : minimum baselineskip below displayed op
                mathparameters.big_op_spacing5        = newparameters[13]      or 0        -- big_op_spacing5        : padding above and below displayed limits
            --  report_virtual("loading and virtualizing font %s at size %s, setting ex parameters",name,size)
            elseif ss.parameters then
                mathparameters.x_height      = newparameters.x_height or mathparameters.x_height
                mathparameters.x_height      = mathparameters.x_height or fp.x_height or 0 -- x_height               : height of x
                mathparameters.num1          = newparameters[ 8] or 0                      -- num1                   : numerator shift-up in display styles
                mathparameters.num2          = newparameters[ 9] or 0                      -- num2                   : numerator shift-up in non-display, non-\atop
                mathparameters.num3          = newparameters[10] or 0                      -- num3                   : numerator shift-up in non-display \atop
                mathparameters.denom1        = newparameters[11] or 0                      -- denom1                 : denominator shift-down in display styles
                mathparameters.denom2        = newparameters[12] or 0                      -- denom2                 : denominator shift-down in non-display styles
                mathparameters.sup1          = newparameters[13] or 0                      -- sup1                   : superscript shift-up in uncramped display style
                mathparameters.sup2          = newparameters[14] or 0                      -- sup2                   : superscript shift-up in uncramped non-display
                mathparameters.sup3          = newparameters[15] or 0                      -- sup3                   : superscript shift-up in cramped styles
                mathparameters.sub1          = newparameters[16] or 0                      -- sub1                   : subscript shift-down if superscript is absent
                mathparameters.sub2          = newparameters[17] or 0                      -- sub2                   : subscript shift-down if superscript is present
                mathparameters.sup_drop      = newparameters[18] or 0                      -- sup_drop               : superscript baseline below top of large box
                mathparameters.sub_drop      = newparameters[19] or 0                      -- sub_drop               : subscript baseline below bottom of large box
                mathparameters.delim1        = newparameters[20] or 0                      -- delim1                 : size of \atopwithdelims delimiters in display styles
                mathparameters.delim2        = newparameters[21] or 0                      -- delim2                 : size of \atopwithdelims delimiters in non-displays
                mathparameters.axis_height   = newparameters[22] or 0                      -- axis_height            : height of fraction lines above the baseline
            --  report_virtual("loading and virtualizing font %s at size %s, setting sy parameters",name,size)
            end
            local vectorname = ss.vector
            if vectorname then
                local offset = 0xFF000
                local vector = mathencodings[vectorname]
                local rotcev = reverse[vectorname]
                local isextension = ss.extension
                if vector and rotcev then
                    local fc, fd, si = fs.characters, fs.descriptions, shared[s]
                    local skewchar = ss.skewchar
                    for unicode, index in next, vector do
                        local fci = fc[index]
                        if not fci then
                            local fontname = fs.properties.name or "unknown"
                            local rf = reported[fontname]
                            if not rf then rf = { } reported[fontname] = rf end
                            local rv = rf[vectorname]
                            if not rv then rv = { } rf[vectorname] = rv end
                            local ru = rv[unicode]
                            if not ru then
                                if trace_virtual then
                                    report_virtual( "unicode point U+%05X has no index %04X in vector %s for font %s",unicode,index,vectorname,fontname)
                                elseif not already_reported then
                                    report_virtual( "the mapping is incomplete for '%s' at %s",name,number.topoints(size))
                                    already_reported = true
                                end
                                rv[unicode] = true
                            end
                        else
                            local ref = si[index]
                            if not ref then
                                ref = { { 'slot', s, index } }
                                si[index] = ref
                            end
                            local kerns = fci.kerns
                            local width = fci.width
                            local italic = fci.italic
                            if italic and isextension then
                                -- int_a^b
                                width = width + italic
                            end
                            if kerns then
                                local krn = { }
                                for k, v in next, kerns do -- kerns is sparse
                                    local rk = rotcev[k]
                                    if rk then
                                        krn[rk] = v -- kerns[k]
                                    end
                                end
                                if not next(krn) then
                                    krn = nil
                                end
                                local t = {
                                    width    = width,
                                    height   = fci.height,
                                    depth    = fci.depth,
                                    italic   = italic,
                                    kerns    = krn,
                                    commands = ref,
                                }
                                if skewchar then
                                    local k = kerns[skewchar]
                                    if k then
                                        t.top_accent = width/2 + k
                                    end
                                end
                                characters[unicode] = t
                            else
                                characters[unicode] = {
                                    width    = width,
                                    height   = fci.height,
                                    depth    = fci.depth,
                                    italic   = italic,
                                    commands = ref,
                                }
                            end
--~ report_virtual("%05X %s %s",unicode,fci.height or "NO HEIGHT",fci.depth or "NO DEPTH")
                        end
                    end
                    if isextension then
                        -- todo: if multiple ex, then 256 offsets per instance
                        local extension = mathencodings["large-to-small"]
                        local variants_done = fs.variants_done
                        for index, fci in next, fc do -- the raw ex file
                            if type(index) == "number" then
                                local ref = si[index]
                                if not ref then
                                    ref = { { 'slot', s, index } }
                                    si[index] = ref
                                end
                                local italic = fci.italic
                                local t = {
                                    width    = fci.width + italic, -- watch this !
                                    height   = fci.height,
                                    depth    = fci.depth,
                                    italic   = italic,
                                    commands = ref,
                                }
                                local n = fci.next
                                if n then
                                    t.next = offset + n
                                elseif variants_done then
                                    local vv = fci.vert_variants
                                    if vv then
                                        t.vert_variants = vv
                                    end
                                    local hv = fci.horiz_variants
                                    if hv then
                                        t.horiz_variants = hv
                                    end
                                else
                                    local vv = fci.vert_variants
                                    if vv then
                                        for i=1,#vv do
                                            local vvi = vv[i]
                                            vvi.glyph = vvi.glyph + offset
                                        end
                                        t.vert_variants = vv
                                    end
                                    local hv = fci.horiz_variants
                                    if hv then
                                        for i=1,#hv do
                                            local hvi = hv[i]
                                            hvi.glyph = hvi.glyph + offset
                                        end
                                        t.horiz_variants = hv
                                    end
                                end
                                characters[offset + index] = t
                            end
                        end
                        fs.variants_done = true
                        for unicode, index in next, extension do
                            local cu = characters[unicode]
                            if cu then
                                cu.next = offset + index
                            else
                                local fci = fc[index]
                                if not fci then
                                    -- do nothing
                                else
                                    -- probably never entered
                                    local ref = si[index]
                                    if not ref then
                                        ref = { { 'slot', s, index } }
                                        si[index] = ref
                                    end
                                    local kerns = fci.kerns
                                    if kerns then
                                        local krn = { }
--~                                         for k=1,#kerns do
--~                                             krn[offset + k] = kerns[k]
--~                                         end
                                        for k, v in next, kerns do -- is kerns sparse?
                                            krn[offset + k] = v
                                        end
                                        characters[unicode] = {
                                            width    = fci.width,
                                            height   = fci.height,
                                            depth    = fci.depth,
                                            italic   = fci.italic,
                                            commands = ref,
                                            kerns    = krn,
                                            next     = offset + index,
                                        }
                                    else
                                        characters[unicode] = {
                                            width    = fci.width,
                                            height   = fci.height,
                                            depth    = fci.depth,
                                            italic   = fci.italic,
                                            commands = ref,
                                            next     = offset + index,
                                        }
                                    end
                                end
                            end
                        end
                    end
                else
                    report_virtual("error in loading %s: problematic vector %s",name,vectorname)
                end
            end
            mathematics.extras.copy(main) --not needed here (yet)
        end
    end
    --
    fontlist[#fontlist+1] = {
        id   = font.nextid(),
        size = size,
    }
    --
    main.mathparameters = mathparameters -- still traditional ones
    vfmath.addmissing(main,#fontlist,size)
    mathematics.addfallbacks(main)
    --
    main.properties.math_is_scaled = true -- signal
    fonts.constructors.assignmathparameters(main,main)
    --
    main.MathConstants = main.mathparameters -- we directly pass it to TeX (bypasses the scaler) so this is needed
-- inspect(main.MathConstants)
    --
    if trace_virtual or trace_timings then
        report_virtual("loading and virtualizing font %s at size %s took %0.3f seconds",name,size,os.clock()-start)
    end
    --
    return main
end

function mathematics.makefont(name,set,goodies)
    fonts.definers.methods.variants[name] = function(specification)
        return vfmath.define(specification,set,goodies)
    end
end

-- helpers

function vfmath.setletters(font_encoding, name, uppercase, lowercase)
    local enc = font_encoding[name]
    for i = 0,25 do
        enc[uppercase+i] = i + 0x41
        enc[lowercase+i] = i + 0x61
    end
end

function vfmath.setdigits(font_encoding, name, digits)
    local enc = font_encoding[name]
    for i = 0,9 do
        enc[digits+i] = i + 0x30
    end
end