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-rw-r--r--tex/context/base/util-dim.lua898
1 files changed, 449 insertions, 449 deletions
diff --git a/tex/context/base/util-dim.lua b/tex/context/base/util-dim.lua
index bbfeae7d4..47b2706b7 100644
--- a/tex/context/base/util-dim.lua
+++ b/tex/context/base/util-dim.lua
@@ -1,449 +1,449 @@
-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
-
---this might become another namespace
-
-number = number or { }
-local number = number
-
-number.tonumberf = function(n) return match(format("%.20f",n),"(.-0?)0*$") end -- one zero too much but alas
-number.tonumberg = function(n) return format("%.20g",n) end
-
-local dimenfactors = allocate {
- ["pt"] = 1/65536,
- ["in"] = ( 100/ 7227)/65536,
- ["cm"] = ( 254/ 7227)/65536,
- ["mm"] = ( 2540/ 7227)/65536,
- ["sp"] = 1, -- 65536 sp in 1pt
- ["bp"] = ( 7200/ 7227)/65536,
- ["pc"] = ( 1/ 12)/65536,
- ["dd"] = ( 1157/ 1238)/65536,
- ["cc"] = ( 1157/14856)/65536,
- ["nd"] = (20320/21681)/65536,
- ["nc"] = ( 5080/65043)/65536
-}
-
---~ print(table.serialize(dimenfactors))
---~
---~ %.99g:
---~
---~ t={
---~ ["bp"]=1.5201782378580324e-005,
---~ ["cc"]=1.1883696112892098e-006,
---~ ["cm"]=5.3628510057769479e-007,
---~ ["dd"]=1.4260435335470516e-005,
---~ ["em"]=0.000152587890625,
---~ ["ex"]=6.103515625e-005,
---~ ["in"]=2.1113586636917117e-007,
---~ ["mm"]=5.3628510057769473e-008,
---~ ["nc"]=1.1917446679504327e-006,
---~ ["nd"]=1.4300936015405194e-005,
---~ ["pc"]=1.2715657552083333e-006,
---~ ["pt"]=1.52587890625e-005,
---~ ["sp"]=1,
---~ }
---~
---~ patched %s and tonumber
---~
---~ t={
---~ ["bp"]=0.00001520178238,
---~ ["cc"]=0.00000118836961,
---~ ["cm"]=0.0000005362851,
---~ ["dd"]=0.00001426043534,
---~ ["em"]=0.00015258789063,
---~ ["ex"]=0.00006103515625,
---~ ["in"]=0.00000021113587,
---~ ["mm"]=0.00000005362851,
---~ ["nc"]=0.00000119174467,
---~ ["nd"]=0.00001430093602,
---~ ["pc"]=0.00000127156576,
---~ ["pt"]=0.00001525878906,
---~ ["sp"]=1,
---~ }
-
---[[ldx--
-<p>A conversion function that takes a number, unit (string) and optional
-format (string) is implemented using this table.</p>
---ldx]]--
-
-
-local function numbertodimen(n,unit,fmt)
- if type(n) == 'string' then
- return n
- else
- unit = unit or 'pt'
- if not fmt then
- fmt = "%s%s"
- elseif fmt == true then
- fmt = "%0.5f%s"
- end
- return format(fmt,n*dimenfactors[unit],unit)
- -- if fmt then
- -- return format(fmt,n*dimenfactors[unit],unit)
- -- else
- -- return match(format("%.20f",n*dimenfactors[unit]),"(.-0?)0*$") .. 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
-
-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 type(unit) == "function" then
- k = value/unit()
- else
- k = value/unit
- 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
- if type(str) == "number" then
- return str
- else
- local k = known[str]
- if not k then
- local value, unit = lpegmatch(dimenpair,str)
- if value and unit then
- k = value/unit -- to be considered: round
- else
- k = 0
- end
- -- print(str,value,unit)
- 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/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 tex.hsize
- if type(d) == "string" then
- d = stringtodimen(d)
- end
- return (n/100) * d
-end
-
-number["%"] = number.percent
+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
+
+--this might become another namespace
+
+number = number or { }
+local number = number
+
+number.tonumberf = function(n) return match(format("%.20f",n),"(.-0?)0*$") end -- one zero too much but alas
+number.tonumberg = function(n) return format("%.20g",n) end
+
+local dimenfactors = allocate {
+ ["pt"] = 1/65536,
+ ["in"] = ( 100/ 7227)/65536,
+ ["cm"] = ( 254/ 7227)/65536,
+ ["mm"] = ( 2540/ 7227)/65536,
+ ["sp"] = 1, -- 65536 sp in 1pt
+ ["bp"] = ( 7200/ 7227)/65536,
+ ["pc"] = ( 1/ 12)/65536,
+ ["dd"] = ( 1157/ 1238)/65536,
+ ["cc"] = ( 1157/14856)/65536,
+ ["nd"] = (20320/21681)/65536,
+ ["nc"] = ( 5080/65043)/65536
+}
+
+--~ print(table.serialize(dimenfactors))
+--~
+--~ %.99g:
+--~
+--~ t={
+--~ ["bp"]=1.5201782378580324e-005,
+--~ ["cc"]=1.1883696112892098e-006,
+--~ ["cm"]=5.3628510057769479e-007,
+--~ ["dd"]=1.4260435335470516e-005,
+--~ ["em"]=0.000152587890625,
+--~ ["ex"]=6.103515625e-005,
+--~ ["in"]=2.1113586636917117e-007,
+--~ ["mm"]=5.3628510057769473e-008,
+--~ ["nc"]=1.1917446679504327e-006,
+--~ ["nd"]=1.4300936015405194e-005,
+--~ ["pc"]=1.2715657552083333e-006,
+--~ ["pt"]=1.52587890625e-005,
+--~ ["sp"]=1,
+--~ }
+--~
+--~ patched %s and tonumber
+--~
+--~ t={
+--~ ["bp"]=0.00001520178238,
+--~ ["cc"]=0.00000118836961,
+--~ ["cm"]=0.0000005362851,
+--~ ["dd"]=0.00001426043534,
+--~ ["em"]=0.00015258789063,
+--~ ["ex"]=0.00006103515625,
+--~ ["in"]=0.00000021113587,
+--~ ["mm"]=0.00000005362851,
+--~ ["nc"]=0.00000119174467,
+--~ ["nd"]=0.00001430093602,
+--~ ["pc"]=0.00000127156576,
+--~ ["pt"]=0.00001525878906,
+--~ ["sp"]=1,
+--~ }
+
+--[[ldx--
+<p>A conversion function that takes a number, unit (string) and optional
+format (string) is implemented using this table.</p>
+--ldx]]--
+
+
+local function numbertodimen(n,unit,fmt)
+ if type(n) == 'string' then
+ return n
+ else
+ unit = unit or 'pt'
+ if not fmt then
+ fmt = "%s%s"
+ elseif fmt == true then
+ fmt = "%0.5f%s"
+ end
+ return format(fmt,n*dimenfactors[unit],unit)
+ -- if fmt then
+ -- return format(fmt,n*dimenfactors[unit],unit)
+ -- else
+ -- return match(format("%.20f",n*dimenfactors[unit]),"(.-0?)0*$") .. 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
+
+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 type(unit) == "function" then
+ k = value/unit()
+ else
+ k = value/unit
+ 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
+ if type(str) == "number" then
+ return str
+ else
+ local k = known[str]
+ if not k then
+ local value, unit = lpegmatch(dimenpair,str)
+ if value and unit then
+ k = value/unit -- to be considered: round
+ else
+ k = 0
+ end
+ -- print(str,value,unit)
+ 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/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 tex.hsize
+ if type(d) == "string" then
+ d = stringtodimen(d)
+ end
+ return (n/100) * d
+end
+
+number["%"] = number.percent
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