add pdf and cdf functions

util.lua

@@ -1,12 +1,14 @@
 -- TODO: reorganize function order.
 
 local assert = assert
+local exp = math.exp
 local ipairs = ipairs
 local log = math.log
 local max = math.max
 local min = math.min
 local open = io.open
 local pairs = pairs
+local pi = math.pi
 local random = math.random
 local select = select
 local sort = table.sort
@@ -173,6 +175,26 @@ local function exists(fn)
     end
 end
 
+local function pdf(x, mean, std)
+    -- probability density function for a normal distribution.
+    mean = mean or 0
+    std = std or 1
+    if mean == 0 and std == 1 then
+        return 0.39894228040143 * exp(x * x * -0.5)
+    end
+    local var = std * std
+    return 1 / sqrt(2 * pi * var) * exp((x - mean) * (x - mean) / (-2 * var))
+end
+
+local function cdf(x)
+    -- a very rough approximation of the
+    -- cumulative distribution function for a normal distribution.
+    -- absolute error peaks at plus-or-minus 1.654.
+    -- i don't remember where this is from.
+    local sign = x >= 0 and 1 or -1
+    return 0.5 * (1 + sign * sqrt(1 - exp(-2 / pi * x * x)))
+end
+
 return {
     signbyte=signbyte,
     boolean_xor=boolean_xor,
@@ -195,4 +217,6 @@ return {
     rbool=rbool,
     argsort=argsort,
     exists=exists,
+    pdf=pdf,
+    cdf=cdf,
 }