util-dim.lua / last modification: 2020-01-30 14:16
if not modules then modules = { } end modules ['util-dim'] = {
    version   = 1.001,
    comment   = "support for dimensions",
    author    = "Hans Hagen, PRAGMA-ADE, Hasselt NL",
    copyright = "PRAGMA ADE / ConTeXt Development Team",
    license   = "see context related readme files"
}

--[[ldx--
<p>Internally <l n='luatex'/> work with scaled point, which are
represented by integers. However, in practice, at east at the
<l n='tex'/> end we work with more generic units like points (pt). Going
from scaled points (numbers) to one of those units can be
done by using the conversion factors collected in the following
table.</p>
--ldx]]--

local format, match, gsub, type, setmetatable = string.format, string.match, string.gsub, type, setmetatable
local P, S, R, Cc, C, lpegmatch = lpeg.P, lpeg.S, lpeg.R, lpeg.Cc, lpeg.C, lpeg.match

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

local texget            = tex and tex.get or function() return 65536*10*100 end

local p_stripzeros      = lpeg.patterns.stripzeros

--this might become another namespace

number = number or { }
local number = number

number.tonumberf = function(n) return lpegmatch(p_stripzeros,format("%.20f",n)) end
number.tonumberg = function(n) return format("%.20g",n) end

local dimenfactors = allocate {
    ["pt"] =             1/65536,
    ["in"] = (  100/ 7227)/65536,
    ["cm"] = (  254/ 7227)/65536,
    ["mm"] = ( 2540/ 7227)/65536,
    ["sp"] =                   1, -- 65536 sp in 1pt
    ["bp"] = ( 7200/ 7227)/65536,
    ["pc"] = (    1/   12)/65536,
    ["dd"] = ( 1157/ 1238)/65536,
    ["cc"] = ( 1157/14856)/65536,
    ["nd"] = (20320/21681)/65536,
    ["nc"] = ( 5080/65043)/65536
}

-- print(table.serialize(dimenfactors))
--
--  %.99g:
--
--  t={
--   ["bp"]=1.5201782378580324e-005,
--   ["cc"]=1.1883696112892098e-006,
--   ["cm"]=5.3628510057769479e-007,
--   ["dd"]=1.4260435335470516e-005,
--   ["em"]=0.000152587890625,
--   ["ex"]=6.103515625e-005,
--   ["in"]=2.1113586636917117e-007,
--   ["mm"]=5.3628510057769473e-008,
--   ["nc"]=1.1917446679504327e-006,
--   ["nd"]=1.4300936015405194e-005,
--   ["pc"]=1.2715657552083333e-006,
--   ["pt"]=1.52587890625e-005,
--   ["sp"]=1,
--  }
--
--  patched %s and tonumber
--
--  t={
--   ["bp"]=0.00001520178238,
--   ["cc"]=0.00000118836961,
--   ["cm"]=0.0000005362851,
--   ["dd"]=0.00001426043534,
--   ["em"]=0.00015258789063,
--   ["ex"]=0.00006103515625,
--   ["in"]=0.00000021113587,
--   ["mm"]=0.00000005362851,
--   ["nc"]=0.00000119174467,
--   ["nd"]=0.00001430093602,
--   ["pc"]=0.00000127156576,
--   ["pt"]=0.00001525878906,
--   ["sp"]=1,
--  }

--[[ldx--
<p>A conversion function that takes a number, unit (string) and optional
format (string) is implemented using this table.</p>
--ldx]]--

local f_none = formatters["%s%s"]
local f_true = formatters["%0.5F%s"]

local function numbertodimen(n,unit,fmt) -- will be redefined later !
    if type(n) == 'string' then
        return n
    else
        unit = unit or 'pt'
        n = n * dimenfactors[unit]
        if not fmt then
            fmt = f_none(n,unit)
        elseif fmt == true then
            fmt = f_true(n,unit)
        else
            return formatters[fmt](n,unit)
        end
    end
end

--[[ldx--
<p>We collect a bunch of converters in the <type>number</type> namespace.</p>
--ldx]]--

number.maxdimen     = 1073741823
number.todimen      = numbertodimen
number.dimenfactors = dimenfactors

function number.topoints      (n,fmt) return numbertodimen(n,"pt",fmt) end
function number.toinches      (n,fmt) return numbertodimen(n,"in",fmt) end
function number.tocentimeters (n,fmt) return numbertodimen(n,"cm",fmt) end
function number.tomillimeters (n,fmt) return numbertodimen(n,"mm",fmt) end
function number.toscaledpoints(n,fmt) return numbertodimen(n,"sp",fmt) end
function number.toscaledpoints(n)     return            n .. "sp"      end
function number.tobasepoints  (n,fmt) return numbertodimen(n,"bp",fmt) end
function number.topicas       (n,fmt) return numbertodimen(n "pc",fmt) end
function number.todidots      (n,fmt) return numbertodimen(n,"dd",fmt) end
function number.tociceros     (n,fmt) return numbertodimen(n,"cc",fmt) end
function number.tonewdidots   (n,fmt) return numbertodimen(n,"nd",fmt) end
function number.tonewciceros  (n,fmt) return numbertodimen(n,"nc",fmt) end

--[[ldx--
<p>More interesting it to implement a (sort of) dimen datatype, one
that permits calculations too. First we define a function that
converts a string to scaledpoints. We use <l n='lpeg'/>. We capture
a number and optionally a unit. When no unit is given a constant
capture takes place.</p>
--ldx]]--

local amount = (S("+-")^0 * R("09")^0 * P(".")^0 * R("09")^0) + Cc("0")
local unit   = R("az")^1 + P("%")

local dimenpair = amount/tonumber * (unit^1/dimenfactors + Cc(1)) -- tonumber is new

lpeg.patterns.dimenpair = dimenpair

local splitter = amount/tonumber * C(unit^1)

function number.splitdimen(str)
    return lpegmatch(splitter,str)
end

--[[ldx--
<p>We use a metatable to intercept errors. When no key is found in
the table with factors, the metatable will be consulted for an
alternative index function.</p>
--ldx]]--

setmetatableindex(dimenfactors, function(t,s)
 -- error("wrong dimension: " .. (s or "?")) -- better a message
    return false
end)

--[[ldx--
<p>We redefine the following function later on, so we comment it
here (which saves us bytecodes.</p>
--ldx]]--

-- function string.todimen(str)
--     if type(str) == "number" then
--         return str
--     else
--         local value, unit = lpegmatch(dimenpair,str)
--         return value/unit
--     end
-- end
--
-- local stringtodimen = string.todimen

local stringtodimen -- assigned later (commenting saves bytecode)

local amount = S("+-")^0 * R("09")^0 * S(".,")^0 * R("09")^0
local unit   = P("pt") + P("cm") + P("mm") + P("sp") + P("bp") + P("in")  +
               P("pc") + P("dd") + P("cc") + P("nd") + P("nc")

local validdimen = amount * unit

lpeg.patterns.validdimen = validdimen

--[[ldx--
<p>This converter accepts calls like:</p>

<typing>
string.todimen("10")
string.todimen(".10")
string.todimen("10.0")
string.todimen("10.0pt")
string.todimen("10pt")
string.todimen("10.0pt")
</typing>

<p>With this in place, we can now implement a proper datatype for dimensions, one
that permits us to do this:</p>

<typing>
s = dimen "10pt" + dimen "20pt" + dimen "200pt"
        - dimen "100sp" / 10 + "20pt" + "0pt"
</typing>

<p>We create a local metatable for this new type:</p>
--ldx]]--

local dimensions = { }

--[[ldx--
<p>The main (and globally) visible representation of a dimen is defined next: it is
a one-element table. The unit that is returned from the match is normally a number
(one of the previously defined factors) but we also accept functions. Later we will
see why. This function is redefined later.</p>
--ldx]]--

-- function dimen(a)
--     if a then
--         local ta= type(a)
--         if ta == "string" then
--             local value, unit = lpegmatch(pattern,a)
--             if type(unit) == "function" then
--                 k = value/unit()
--             else
--                 k = value/unit
--             end
--             a = k
--         elseif ta == "table" then
--             a = a[1]
--         end
--         return setmetatable({ a }, dimensions)
--     else
--         return setmetatable({ 0 }, dimensions)
--     end
-- end

--[[ldx--
<p>This function return a small hash with a metatable attached. It is
through this metatable that we can do the calculations. We could have
shared some of the code but for reasons of speed we don't.</p>
--ldx]]--

function dimensions.__add(a, b)
    local ta, tb = type(a), type(b)
    if ta == "string" then a = stringtodimen(a) elseif ta == "table" then a = a[1] end
    if tb == "string" then b = stringtodimen(b) elseif tb == "table" then b = b[1] end
    return setmetatable({ a + b }, dimensions)
end

function dimensions.__sub(a, b)
    local ta, tb = type(a), type(b)
    if ta == "string" then a = stringtodimen(a) elseif ta == "table" then a = a[1] end
    if tb == "string" then b = stringtodimen(b) elseif tb == "table" then b = b[1] end
    return setmetatable({ a - b }, dimensions)
end

function dimensions.__mul(a, b)
    local ta, tb = type(a), type(b)
    if ta == "string" then a = stringtodimen(a) elseif ta == "table" then a = a[1] end
    if tb == "string" then b = stringtodimen(b) elseif tb == "table" then b = b[1] end
    return setmetatable({ a * b }, dimensions)
end

function dimensions.__div(a, b)
    local ta, tb = type(a), type(b)
    if ta == "string" then a = stringtodimen(a) elseif ta == "table" then a = a[1] end
    if tb == "string" then b = stringtodimen(b) elseif tb == "table" then b = b[1] end
    return setmetatable({ a / b }, dimensions)
end

function dimensions.__unm(a)
    local ta = type(a)
    if ta == "string" then a = stringtodimen(a) elseif ta == "table" then a = a[1] end
    return setmetatable({ - a }, dimensions)
end

--[[ldx--
<p>It makes no sense to implement the power and modulo function but
the next two do make sense because they permits is code like:</p>

<typing>
local a, b = dimen "10pt", dimen "11pt"
...
if a > b then
    ...
end
</typing>
--ldx]]--

-- makes no sense: dimensions.__pow and dimensions.__mod

function dimensions.__lt(a, b)
    return a[1] < b[1]
end

function dimensions.__eq(a, b)
    return a[1] == b[1]
end

--[[ldx--
<p>We also need to provide a function for conversion to string (so that
we can print dimensions). We print them as points, just like <l n='tex'/>.</p>
--ldx]]--

function dimensions.__tostring(a)
    return a[1]/65536 .. "pt" -- instead of todimen(a[1])
end

--[[ldx--
<p>Since it does not take much code, we also provide a way to access
a few accessors</p>

<typing>
print(dimen().pt)
print(dimen().sp)
</typing>
--ldx]]--

function dimensions.__index(tab,key)
    local d = dimenfactors[key]
    if not d then
        error("illegal property of dimen: " .. key)
        d = 1
    end
    return 1/d
end

--[[ldx--
<p>In the converter from string to dimension we support functions as
factors. This is because in <l n='tex'/> we have a few more units:
<type>ex</type> and <type>em</type>. These are not constant factors but
depend on the current font. They are not defined by default, but need
an explicit function call. This is because at the moment that this code
is loaded, the relevant tables that hold the functions needed may not
yet be available.</p>
--ldx]]--

   dimenfactors["ex"] =  4 * 1/65536 --   4pt
   dimenfactors["em"] = 10 * 1/65536 --  10pt
-- dimenfactors["%"]  =  4 * 1/65536 -- 400pt/100

--[[ldx--
<p>The previous code is rather efficient (also thanks to <l n='lpeg'/>) but we
can speed it up by caching converted dimensions. On my machine (2008) the following
loop takes about 25.5 seconds.</p>

<typing>
for i=1,1000000 do
    local s = dimen "10pt" + dimen "20pt" + dimen "200pt"
        - dimen "100sp" / 10 + "20pt" + "0pt"
end
</typing>

<p>When we cache converted strings this becomes 16.3 seconds. In order not
to waste too much memory on it, we tag the values of the cache as being
week which mean that the garbage collector will collect them in a next
sweep. This means that in most cases the speed up is mostly affecting the
current couple of calculations and as such the speed penalty is small.</p>

<p>We redefine two previous defined functions that can benefit from
this:</p>
--ldx]]--

local known = { } setmetatable(known, { __mode = "v" })

function dimen(a)
    if a then
        local ta= type(a)
        if ta == "string" then
            local k = known[a]
            if k then
                a = k
            else
                local value, unit = lpegmatch(dimenpair,a)
                if value and unit then
                    k = value/unit -- to be considered: round
                else
                    k = 0
                end
                known[a] = k
                a = k
            end
        elseif ta == "table" then
            a = a[1]
        end
        return setmetatable({ a }, dimensions)
    else
        return setmetatable({ 0 }, dimensions)
    end
end

function string.todimen(str) -- maybe use tex.sp when available
    local t = type(str)
    if t == "number" then
        return str
    else
        local k = known[str]
        if not k then
            if t == "string" then
                local value, unit = lpegmatch(dimenpair,str)
                if value and unit then
                    k = value/unit -- to be considered: round
                else
                    k = 0
                end
            else
                k = 0
            end
            known[str] = k
        end
        return k
    end
end

-- local known = { }
--
-- function string.todimen(str) -- maybe use tex.sp
--     local k = known[str]
--     if not k then
--         k = tex.sp(str)
--         known[str] = k
--     end
--     return k
-- end

stringtodimen = string.todimen -- local variable defined earlier

function number.toscaled(d)
    return format("%0.5f",d/0x10000) -- 2^16
end

--[[ldx--
<p>In a similar fashion we can define a glue datatype. In that case we
probably use a hash instead of a one-element table.</p>
--ldx]]--

--[[ldx--
<p>Goodie:s</p>
--ldx]]--

function number.percent(n,d) -- will be cleaned up once luatex 0.30 is out
    d = d or texget("hsize")
    if type(d) == "string" then
        d = stringtodimen(d)
    end
    return (n/100) * d
end

number["%"] = number.percent