Proper rounding implementation (#23)

* Implement math.round(x): nearest integer, halfway away from zero

   ...in accordance with Basisregelwerk page 13 ("Rundungen").

   The previous implementation relies on `string.format("%.0f", x)` whose
behaviour is inconsistent accross Lua versions.

* Use math.round() over common.round() in trivial cases
* common.render_delta(): use math.round()
* common.render_delta() used to generate the wrong sign for non-zero
  values in [-0.5, 0.5].
- Emit "&" and the integral value with a single tex.sprint() since the latter
  can't result in special characters.
* Remove common.round()

src/common.lua

@@ -1,3 +1,4 @@
+require("stdext")
 local data = require("data")
 local schema = require("schema")
 
@@ -264,11 +265,6 @@ function common.checkboxlist(items)
   end
 end
 
-function common.round(v, down)
-  local delta = down and -0.0001 or 0.0001 -- round up at 0.5 unless down given
-  return tonumber(string.format("%.0f", v + delta))
-end
-
 function common.ritualkenntnis(items, count)
   tex.sprint([[{\normalfont\normalsize\setlength{\arrayrulewidth}{1pt}
     \begin{NiceTabular}{p{3.7cm}@{(}x{3.2cm}@{):\hspace{2pt}}x{0.7cm}x{0.5cm}}]])
@@ -355,15 +351,17 @@ end
 
 function common.render_delta(input)
   if type(input) == "number" then
-    if input < 0 then
-      tex.sprint(-2, "−")
-    elseif input > 0 then
-      tex.sprint(-2, "+")
+    local sign
+    if input >= 0.5 then
+      sign = "+"
+    elseif input <= -0.5 then
+      sign = "−"
+    else
+      sign = ""
     end
-    tex.sprint(common.round(math.abs(input)))
-  else
-    tex.sprint(-2, input)
+    input = string.format("%s%d", sign, math.round(math.abs(input)))
   end
+  tex.sprint(-2, input)
 end
 
 function common.merkmalliste(input, zauber)
@@ -501,7 +499,7 @@ function common.schaden.render(tp)
     elseif tp.die ~= nil then
       tex.sprint(-2, "+")
     end
-    tex.sprint(-2, common.round(math.abs(tp.num)))
+    tex.sprint(-2, math.round(math.abs(tp.num)))
   end
 end
 

src/frontseite.lua

@@ -1,6 +1,7 @@
 local data = require("data")
 local common = require("common")
 local schema = require("schema")
+require("stdext")
 
 local frontseite = {}
 
@@ -213,7 +214,7 @@ function eigenschaften.rechts(self)
                 if data.Nachteile.Glasknochen then
                   base = base - 2
                 end
-                tex.sprint(-2, common.round(base))
+                tex.sprint(-2, math.round(base))
               end
             end
             tex.sprint([[\\\hline\end{tabular}}\egroup\par]])
@@ -261,4 +262,4 @@ end
 
 frontseite.eigenschaften = eigenschaften
 
-return frontseite
+return frontseite

src/kampfbogen.lua

@@ -1,3 +1,4 @@
+require("stdext")
 local data = require("data")
 local common = require("common")
 local schemadef = require("schemadef")
@@ -14,7 +15,7 @@ local function calc_be(input)
   if string.find(input, "^BEx") then
     return be * input:sub(4)
   elseif string.find(input, "^BE%-") then
-    return common.round(math.max(0, be - tonumber(input:sub(4))))
+    return math.round(math.max(0, be - tonumber(input:sub(4))))
   elseif string.find(input, "^BE") then
     return be
   else
@@ -158,14 +159,14 @@ nahkampf_render[11]= {false, function(v, talent, ebe)
   if talent == nil or #talent < 4 or atb == "" or #v < 8 then
     return
   end
-  tex.sprint(-2, atpa_mod(atb - common.round(ebe/2, true), talent.AT, v["TP/KK Schwelle"], v["TP/KK Schritt"], v["WM AT"], art(v), talent.Spezialisierungen))
+  tex.sprint(-2, atpa_mod(atb - ebe // 2, talent.AT, v["TP/KK Schwelle"], v["TP/KK Schritt"], v["WM AT"], art(v), talent.Spezialisierungen))
 end}
 nahkampf_render[12]= {false, function(v, talent, ebe)
   local pab = data:cur("PA")
   if talent == nil or #talent < 5 or pab == "" or #v < 9 then
     return
   end
-  tex.sprint(-2, atpa_mod(pab - common.round(ebe/2), data.PA(talent), v["TP/KK Schwelle"], v["TP/KK Schritt"], v["WM PA"], art(v), talent.Spezialisierungen))
+  tex.sprint(-2, atpa_mod(pab - (ebe + 1) // 2, data.PA(talent), v["TP/KK Schwelle"], v["TP/KK Schritt"], v["WM PA"], art(v), talent.Spezialisierungen))
 end}
 nahkampf_render[13]= {false, function(v, talent, ebe)
   if #v < 6 then
@@ -252,7 +253,7 @@ local waffenlos_render = {
         added = added + 1
       end
     end
-    tex.sprint(-2, atpa_mod(atb - common.round(ebe/2, true), talent.AT, v["TP/KK Schwelle"], v["TP/KK Schritt"], 0))
+    tex.sprint(-2, atpa_mod(atb - ebe // 2, talent.AT, v["TP/KK Schwelle"], v["TP/KK Schritt"], 0))
   end},
   [6]= {false, function(v, talent, ebe)
     local pab = data:cur("PA")
@@ -266,7 +267,7 @@ local waffenlos_render = {
         added = added + 1
       end
     end
-    tex.sprint(-2, atpa_mod(pab - common.round(ebe/2), data.PA(talent), v["TP/KK Schwelle"], v["TP/KK Schritt"], 0))
+    tex.sprint(-2, atpa_mod(pab - (ebe + 1) // 2, data.PA(talent), v["TP/KK Schwelle"], v["TP/KK Schritt"], 0))
   end},
   [7]= {false, function(v, talent, ebe)
     tp = common.schaden.mod({dice=1, die=6, num=0}, v["TP/KK Schwelle"], v["TP/KK Schritt"])
@@ -404,13 +405,12 @@ end
 
 function kampfbogen.energieleiste(label, val)
   tex.sprint(-2, label)
-  num = tonumber(val)
-  if num == nil then
+  val = tonumber(val)
+  if val == nil then
     tex.sprint("&&&&")
   else
     for i=1,4 do
-      tex.sprint("&")
-      tex.sprint(-2, common.round(num/i))
+      tex.sprint("&", math.round(val / i))
     end
   end
   tex.sprint("&")

src/skt.lua

@@ -1,3 +1,5 @@
+require("stdext")
+
 local skt = {
   spalte = {
     {n="A*", f=1}, {n="A", f=1, [31] = 50}, {n="B", f=2}, {n="C", f=3}, {n="D", f=4, [28] = 170, [31] = 200}, {n="E", f=5, [8] = 48}, {n="F", f=7.5, [30] = 350, [31] = 375}, {n="G", f=10, [30] = 480, [31] = 500}, {n="H", f=20, [2] = 35, [6] = 140, [24] = 720, [27] = 830, [31] = 1000}
@@ -52,7 +54,7 @@ function skt.spalte:effektiv(basis, zielwert, methode)
 end
 
 function skt.faktor:apply(value)
-  return math.floor(value * self[1] + 0.5)
+  return math.round(value * self[1])
 end
 
 for _, f in ipairs(skt.faktor) do
@@ -61,11 +63,9 @@ end
 
 function skt:kosten(spalte, zielwert)
   local index = self.spalte:num(spalte)
-  if zielwert > 31 then
-    zielwert = 31
-  end
+  zielwert = math.min(zielwert, 31)
   if zielwert <= 0 then
-    return 5 * math.floor(self.spalte[index].f + 0.5)
+    return 5 * math.round(self.spalte[index].f)
   end
   if index == 1 then
     return math.max(self:kosten("A", zielwert) - 2, 1)
@@ -74,14 +74,14 @@ function skt:kosten(spalte, zielwert)
   if explicit ~= nil then
     return explicit
   end
-  local val = tonumber(string.format("%.0f", 0.8 * self.spalte[index].f * zielwert^1.2))
+  local val = math.round(0.8 * self.spalte[index].f * zielwert^1.2)
 
   if val > 200 then
-    val = math.floor((val + 5) / 10) * 10
+    val = math.round(val / 10) * 10
   elseif val > 50 then
-    val = math.floor((val + 2) / 5) * 5
+    val = math.round(val / 5) * 5
   end
   return val
 end
 
-return skt
+return skt

src/stdext.lua

@@ -0,0 +1,10 @@
+-- Rounds to the nearest integer. Halfway cases are arounded _away_ from zero.
+function math.round(x)
+  local integral, fractional = math.modf(x)
+  if fractional >= 0.5 then
+    return integral + 1
+  elseif fractional <= -0.5 then
+    return integral - 1
+  end
+  return integral
+end

src/talentbogen.lua

@@ -1,6 +1,7 @@
 local schema = require("schema")
 local data = require("data")
 local common = require("common")
+require("stdext")
 
 local talent = {}
 
@@ -187,7 +188,7 @@ function talent.meta(v)
     ::found::
   end
   if sum ~= nil and #v[5] > 0 then
-    tex.sprint(-2, common.round(sum / #v[5]))
+    tex.sprint(-2, math.round(sum / #v[5]))
   end
 end
 
@@ -379,4 +380,4 @@ function talentbogen.gruppen()
 end
 
 
-return talentbogen
+return talentbogen

src/values.lua

@@ -1,3 +1,4 @@
+require("stdext")
 local d = require("schemadef")
 local schema = assert(loadfile("schema.lua", "t"))(false)
 local skt = require("skt")
@@ -134,7 +135,7 @@ function getter_map.sparse(val, div)
   if val == 0 then
     return ""
   end
-  return tonumber(string.format("%.0f", val/div + 0.0001)) -- round up at 0.5
+  return math.round(val / div)
 end
 
 values.sparse = getter_map.sparse
@@ -515,13 +516,12 @@ function values:gesamtRuestung(teile, decimals)
   end
   if gRS == nil then return nil, nil end
   gRS = gRS/20
-  gBE = gBE/20 - sterne
-  if gBE < 0 then gBE = 0 end
-  if decimals then
-    return gRS, gBE
-  else
-    return tonumber(string.format("%.0f", gRS + 0.0001)), tonumber(string.format("%.0f", gBE + 0.0001))
+  gBE = math.max(gBE/20 - sterne, 0)
+  if not decimals then
+    gRS = math.round(gRS)
+    gBE = math.round(gBE)
   end
+  return gRS, gBE
 end
 
 function values:ap_mod(kosten)
@@ -756,9 +756,11 @@ function values:spezialisierung(e)
   end
   event[1] = event[1] .. e.Fertigkeit .. ", " .. e.Methode .. "): " .. e.Name
   ziel.Spezialisierungen:append(e.Name)
-  local ap = #ziel.Spezialisierungen * 20 * math.floor(skt.spalte[skt.spalte:num(spalte)].f + 0.5)
+  local ap = (
+    #ziel.Spezialisierungen * 20
+      * math.round(skt.spalte[skt.spalte:num(spalte)].f))
   if e.Methode == "SE" then
-    ap = math.floor(ap / 2 + 0.5)
+    ap = math.round(ap / 2)
   end
   event[2] = -1 * ap
   event[3] = faktor
@@ -924,7 +926,7 @@ function values:aktiviere(e)
   elseif smt.name == "Ritual" then
     ap = e.Subjekt.Lernkosten
     if e.Methode == "SE" then
-      ap = math.floor((ap / 2) + 0.51)
+      ap = math.round(ap / 2)
     end
     faktor = self:tgruppe_faktor("Zauber")
     self.Magie.Rituale:append(e.Subjekt, e.Sortierung)
@@ -1062,7 +1064,7 @@ function values:senkung(e)
   if found == nil then
     tex.error("\n[Senkung] unbekannte Schlechte Eigenschaft: '" .. e.Name .. "'")
   end
-  local ap = math.floor((found.Wert - e.Zielwert) * 50 * found.GP + 0.5)
+  local ap = math.round((found.Wert - e.Zielwert) * 50 * found.GP)
   if e.Zielwert == 0 then
     event[1] = event[1] .. ": Schlechte Eigenschaft mit Wert " .. found.Wert .. " entfernt"
     table.remove(self.Nachteile.Eigenschaften.value, found_index)
@@ -1213,4 +1215,4 @@ for _, e in ipairs(schema.Ereignisse:instance()) do
   table.insert(values.Ereignisse, event)
 end
 
-return values
+return values

src/zauberdokument.lua

@@ -1,3 +1,4 @@
+require("stdext")
 local data = require("data")
 local common = require("common")
 
@@ -16,7 +17,7 @@ function zauberdokument.asp_regeneration()
     end
     local mr = data.SF.Magisch.MeisterlicheRegeneration
     if mr ~= nil then
-      val.num = val.num + 3 + math.floor((data:cur(mr) + 1)/3)
+      val.num = val.num + 3 + math.round(data:cur(mr) / 3)
       tex.sprint(-2, val.num)
     else
       local reg = data.SF.Magisch:getlist("Regeneration")
@@ -30,4 +31,4 @@ function zauberdokument.asp_regeneration()
   end
 end
 
-return zauberdokument
+return zauberdokument