diff options
author | Marius <mariausol@gmail.com> | 2013-05-19 20:40:34 +0300 |
---|---|---|
committer | Marius <mariausol@gmail.com> | 2013-05-19 20:40:34 +0300 |
commit | 13ec4b540e0d46c97fd7b089e0b7413da81e0a9f (patch) | |
tree | bebfa563a17c06b3bd3bf8f6f4ba6d025e00d107 /tex/context/base/util-dim.lua | |
parent | 69ad13650cda027526271179e95b5294694143a1 (diff) | |
download | context-13ec4b540e0d46c97fd7b089e0b7413da81e0a9f.tar.gz |
beta 2013.05.19 19:27
Diffstat (limited to 'tex/context/base/util-dim.lua')
-rw-r--r-- | tex/context/base/util-dim.lua | 898 |
1 files changed, 449 insertions, 449 deletions
diff --git a/tex/context/base/util-dim.lua b/tex/context/base/util-dim.lua index 47b2706b7..bbfeae7d4 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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