computation_practice

@@ -10,6 +10,17 @@ local function cup(x)

     end

 end

+local function ztable(x)

+    -- Sergei Winitzki's 2003 approximation of erf

+    local a = 0.140012

+    local function erf(x)

+        return math.abs(x) / (x == 0 and 1 or x) *

+            math.sqrt(1 - math.exp(-x^2 * (4 / math.pi + a * x^2) / (1 + a * x^2)))

+    end

+    local rev = erf(x / math.sqrt(2))

+    return (rev + 1) / 2

+end

+

 local TYPES = {

     ln = {

         -- how to generate the problem (returns problem-object)

@@ -31,10 +42,25 @@ local TYPES = {

         func = math.sin,

         score = function(p, g) return -(math.log(math.abs(math.sin(p) - g), 10) + 1.5)^3 end

     },

+    normalcdf = {

+        gen = function()

+            return 5 * math.random() - 2.5

+        end,

+        disp = "z = %.2f, percentile",

+        func = ztable,

+        score = function(p, g) return -(math.log(math.abs(ztable(p) - g), 10) + 1.5)^3 end

+    },

 }

-local TYPE = TYPES.sin

+local TYPE = TYPES[arg[1]]

+if not TYPE then

+    if arg[1] then

+        io.write(string.format("unknown problem type %s\n", arg[1]))

+        os.exit(false)

+    else

+        TYPE = TYPES.normalcdf

+    end

+end

 local TIME = 30

 local ts = 0

@@ -45,7 +71,7 @@ while os.time() - st < TIME do

     local ans = TYPE.func(rp)

     io.write(string.format(TYPE.disp .. " ? ", cup(rp)))

     io.flush()

-    inp = tonumber(io.read("l")) or 0

+    local inp = tonumber(io.read("l")) or 0

     local sc = TYPE.score(rp, inp)

     if sc > 0 then

         io.write(string.format("✓ correct (%.3f)\n", ans))