feat: adjust overlays

overlays/fcitx5/rime-data-flypy/share/rime-data/lua/calculator_translator.lua

@@ -0,0 +1,402 @@
+-- Rime Script >https://github.com/baopaau/rime-lua-collection/blob/master/calculator_translator.lua
+-- 簡易計算器（執行任何Lua表達式）
+--
+-- 格式：=<exp>
+-- Lambda語法糖：\<arg>.<exp>|
+--
+-- 例子：
+-- =1+1 輸出 2
+-- =floor(9^(8/7)*cos(deg(6))) 輸出 -3
+-- =e^pi>pi^e 輸出 true
+-- =max({1,7,2}) 輸出 7
+-- =map({1,2,3},\x.x^2|) 輸出 {1, 4, 9}
+-- =map(range(-5,5),\x.x*pi/4|,deriv(sin)) 輸出 {-0.7071, -1, -0.7071, 0, 0.7071, 1, 0.7071, 0, -0.7071, -1}
+-- =$(range(-5,5,0.01))(map,\x.-60*x^2-16*x+20|)(max)() 輸出 21.066
+-- =test(\x.trunc(sin(x),1e-3)==trunc(deriv(cos)(x),1e-3)|,range(-2,2,0.1)) 輸出 true
+--
+-- 安装：
+-- - 將本文件保存至 <rime>/lua/
+-- - 在 <rime>/rime.lua 新增一行：
+--   `calculator_translator = require("calculator_translator")`
+-- - 在 <rime>/<schema>.schema.yaml 新增：
+--   `engine/translators/@next: lua_translator@calculator_translator`
+--   `recognizer/patterns/expression: "^=.*$"`
+-- 註：
+-- - <rime> 替換爲RIME的共享目錄
+-- - <schema> 替換爲自己的方案ID
+-- - 如目錄／文件不存在，請自行創建
+
+-- 定義全局函數、常數（注意命名空間污染）
+cos = math.cos
+sin = math.sin
+tan = math.tan
+acos = math.acos
+asin = math.asin
+atan = math.atan
+rad = math.rad
+deg = math.deg
+
+abs = math.abs
+floor = math.floor
+ceil = math.ceil
+mod = math.fmod
+trunc = function (x, dc)
+  if dc == nil then
+    return math.modf(x)
+  end
+  return x - mod(x, dc)
+end
+
+round = function (x, dc)
+  dc = dc or 1
+  local dif = mod(x, dc)
+  if abs(dif) > dc / 2 then
+    return x < 0 and x - dif - dc or x - dif + dc
+  end
+  return x - dif
+end
+
+random = math.random
+randomseed = math.randomseed
+
+inf = math.huge
+MAX_INT = math.maxinteger
+MIN_INT = math.mininteger
+pi = math.pi
+sqrt = math.sqrt
+exp = math.exp
+e = exp(1)
+ln = math.log
+log = function (x, base)
+  base = base or 10
+  return ln(x)/ln(base)
+end
+
+min = function (arr)
+  local m = inf
+  for k, x in ipairs(arr) do
+   m = x < m and x or m
+  end
+  return m
+end
+
+max = function (arr)
+  local m = -inf
+  for k, x in ipairs(arr) do
+   m = x > m and x or m
+  end
+  return m
+end
+
+sum = function (t)
+  local acc = 0
+  for k,v in ipairs(t) do
+    acc = acc + v
+  end
+  return acc
+end
+
+avg = function (t)
+  return sum(t) / #t
+end
+
+isinteger = function (x)
+  return math.fmod(x, 1) == 0
+end
+
+-- iterator . array
+array = function (...)
+  local arr = {}
+  for v in ... do
+    arr[#arr + 1] = v
+  end
+  return arr
+end
+
+-- iterator <- [form, to)
+irange = function (from, to, step)
+  if to == nil then
+    to = from
+    from = 0
+  end
+  step = step or 1
+  local i = from - step
+  to = to - step
+  return function()
+    if i < to then
+      i = i + step
+      return i
+    end
+  end
+end
+
+-- array <- [form, to)
+range = function (from, to, step)
+  return array(irange(from, to, step))
+end
+
+-- array . reversed iterator
+irev = function (arr)
+  local i = #arr + 1
+  return function()
+    if i > 1 then
+      i = i - 1
+      return arr[i]
+    end
+  end
+end
+
+-- array . reversed array
+arev = function (arr)
+  return array(irev(arr))
+end
+
+test = function (f, t)
+  for k,v in ipairs(t) do
+    if not f(v) then
+      return false
+    end
+  end
+  return true
+end
+
+-- # Functional
+map = function (t, ...)
+  local ta = {}
+  for k,v in pairs(t) do
+    local tmp = v
+    for _,f in pairs({...}) do tmp = f(tmp) end
+    ta[k] = tmp
+  end
+  return ta
+end
+
+filter = function (t, ...)
+  local ta = {}
+  local i = 1
+  for k,v in pairs(t) do
+    local erase = false
+    for _,f in pairs({...}) do
+      if not f(v) then
+        erase = true
+        break
+      end
+    end
+    if not erase then
+	  ta[i] = v
+	  i = i + 1
+    end
+  end
+  return ta
+end
+
+-- e.g: foldr({2,3},\n,x.x^n|,2) = 81
+foldr = function (t, f, acc)
+  for k,v in pairs(t) do
+    acc = f(acc, v)
+  end
+  return acc
+end
+
+-- e.g: foldl({2,3},\n,x.x^n|,2) = 512
+foldl = function (t, f, acc)
+  for v in irev(t) do
+    acc = f(acc, v)
+  end
+  return acc
+end
+
+-- 調用鏈生成函數（HOF for method chaining）
+-- e.g: chain(range(-5,5))(map,\x.x/5|)(map,sin)(map,\x.e^x*10|)(map,floor)()
+--    = floor(map(map(map(range(-5,5),\x.x/5|),sin),\x.e^x*10|))
+--    = {4, 4, 5, 6, 8, 10, 12, 14, 17, 20}
+-- 可以用 $ 代替 chain
+chain = function (t)
+  local ta = t
+  local function cf(f, ...)
+    if f ~= nil then
+      ta = f(ta, ...)
+      return cf
+    else
+      return ta
+    end
+  end
+  return cf
+end
+
+-- # Statistics
+fac = function (n)
+  local acc = 1
+  for i = 2,n do
+    acc = acc * i
+  end
+  return acc
+end
+
+nPr = function (n, r)
+  return fac(n) / fac(n - r)
+end
+
+nCr = function (n, r)
+  return nPr(n,r) / fac(r)
+end
+
+MSE = function (t)
+  local ss = 0
+  local s = 0
+  local n = #t
+  for k,v in ipairs(t) do
+    ss = ss + v*v
+    s = s + v
+  end
+  return sqrt((n*ss - s*s) / (n*n))
+end
+
+-- # Linear Algebra
+
+
+-- # Calculus
+-- Linear approximation
+lapproxd = function (f, delta)
+  local delta = delta or 1e-8
+  return function (x)
+           return (f(x+delta) - f(x)) / delta
+         end
+end
+
+-- Symmetric approximation
+sapproxd = function (f, delta)
+  local delta = delta or 1e-8
+  return function (x)
+           return (f(x+delta) - f(x-delta)) / delta / 2
+         end
+end
+
+-- 近似導數
+deriv = function (f, delta, dc)
+  dc = dc or 1e-4
+  local fd = sapproxd(f, delta)
+  return function (x)
+           return round(fd(x), dc)
+         end
+end
+
+-- Trapezoidal rule
+trapzo = function (f, a, b, n)
+  local dif = b - a
+  local acc = 0
+  for i = 1, n-1 do
+    acc = acc + f(a + dif * (i/n))
+  end
+  acc = acc * 2 + f(a) + f(b)
+  acc = acc * dif / n / 2
+  return acc
+end
+
+-- 近似積分
+integ = function (f, delta, dc)
+  delta = delta or 1e-4
+  dc = dc or 1e-4
+  return function (a, b)
+           if b == nil then
+             b = a
+             a = 0
+           end
+           local n = round(abs(b - a) / delta)
+           return round(trapzo(f, a, b, n), dc)
+         end
+end
+
+-- Runge-Kutta
+rk4 = function (f, timestep)
+  local timestep = timestep or 0.01
+  return function (start_x, start_y, time)
+           local x = start_x
+           local y = start_y
+           local t = time
+           -- loop until i >= t
+           for i = 0, t, timestep do
+             local k1 = f(x, y)
+             local k2 = f(x + (timestep/2), y + (timestep/2)*k1)
+             local k3 = f(x + (timestep/2), y + (timestep/2)*k2)
+             local k4 = f(x + timestep, y + timestep*k3)
+             y = y + (timestep/6)*(k1 + 2*k2 + 2*k3 + k4)
+             x = x + timestep
+           end
+           return y
+         end
+end
+
+
+-- # System
+date = os.date
+time = os.time
+path = function ()
+  return debug.getinfo(1).source:match("@?(.*/)")
+end
+
+
+local function serialize(obj)
+  local type = type(obj)
+  if type == "number" then
+    return isinteger(obj) and floor(obj) or obj
+  elseif type == "boolean" then
+    return tostring(obj)
+  elseif type == "string" then
+    return '"'..obj..'"'
+  elseif type == "table" then
+    local str = "{"
+    local i = 1
+    for k, v in pairs(obj) do
+      if i ~= k then  
+        str = str.."["..serialize(k).."]="
+      end
+      str = str..serialize(v)..", "  
+      i = i + 1
+    end
+    str = str:len() > 3 and str:sub(0,-3) or str
+    return str.."}"
+  elseif pcall(obj) then -- function類型
+    return "callable"
+  end
+  return obj
+end
+
+-- greedy：隨時求值（每次變化都會求值，否則結尾爲特定字符時求值）
+local greedy = true
+
+local function calculator_translator(input, seg)
+  if string.sub(input, 1, 1) ~= "=" then return end
+  
+  local expfin = greedy or string.sub(input, -1, -1) == ";"
+  local exp = (greedy or not expfin) and string.sub(input, 2, -1) or string.sub(input, 2, -2)
+  
+  -- 空格輸入可能
+  exp = exp:gsub("#", " ")
+  
+       
+  if not expfin then return end
+  
+  local expe = exp
+  -- 鏈式調用語法糖
+  expe = expe:gsub("%$", " chain ")
+  -- lambda語法糖
+  do
+    local count
+    repeat
+      expe, count = expe:gsub("\\%s*([%a%d%s,_]-)%s*%.(.-)|", " (function (%1) return %2 end) ")
+    until count == 0
+  end
+  --yield(Candidate("number", seg.start, seg._end, expe, "展開"))
+  
+  -- 防止危險操作，禁用os和io命名空間
+  if expe:find("i?os?%.") then return end
+  -- return語句保證了只有合法的Lua表達式才可執行
+  local result = load("return "..expe)()
+  if result == nil then return end
+  
+  result = serialize(result)
+  yield(Candidate("number", seg.start, seg._end, exp.."="..result, ""))
+end
+
+return calculator_translator