tweak: save some progress.

wip/nim/makefile

@@ -0,0 +1,2 @@
+build: samples.nim
+	nim c samples.nim

wip/nim/samples.nim

@@ -1,32 +1,64 @@
-import std/random
 import std/math
+import std/random
+
 # randomize()
 
-proc pow2(x:float, y:int): float = 
-  return pow(x, float(y))
+## Basic math functions
+proc factorial(n: int): int = 
+  if n == 0 or n < 0: 
+    return 1
+  else:
+    return n * factorial(n - 1)
 
 proc sine(x: float): float = 
-  let n = 100
+  let n = 8
+  # ^ Taylor will converge really quickly
+  # notice that the factorial of 17 is 
+  # already pretty gigantic
   var acc = 0.0
   for i in 0..n:
-    let k = 2*n + 1
-    let taylor = pow2(x, k) / float(k)
+    var k = 2*i + 1
+    var taylor = pow(-1, i.float) * pow(x, k.float) / factorial(k).float 
+    acc = acc + taylor
+  return acc 
+
+# Helpers for calculating the log function
+
+## Arithmetic-geomtric mean
+proc ag(x: float, y: float): float = 
+  let n = 100
+  var a = (x + y)/2.0
+  var b = sqrt(x * y)
+  for i in 0..n:
+    let temp = a
+    a = (a+b)/2.0
+    b = sqrt(b*temp)
+  return a
+
+## Find m such that x * 2^m > 2^100
+
+proc log_slow(x: float): float = 
+  # See: <https://en.wikipedia.org/wiki/Natural_logarithm#High_precision>
+  var y = x - 1 
+  let n = 100000000
+  var acc = 0.0
+  for i in 1..n:
+    let taylor = pow(-1.0, float(i+1)) * pow(y, i.float) / i.float
     acc = acc + taylor
   return acc 
 
 proc log(x: float): float = 
-  var y = x - 1 
-  let n = 1000
-  for i in 1..n:
-    let taylor = pow2(-1.0, n+1) * pow2(y, n) / float(n)
-    result = result + taylor
-  return result
+  return 1 
 
+## Test these functions
+echo factorial(5)
+echo sine(1.0)
+echo log(1.0)
+echo log(2.0)
+
+## Distribution functions
 proc normal(): float = 
   let u1 = rand(1.0)
   let u2 = rand(1.0)
   let z = 1
   # see https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform#Basic_form
-
-
-echo sine(0.1)

wip/nim/sums/sums.nim

@@ -1,5 +1,4 @@
 import std/math
-# randomize()
 
 proc factorial(n: int): int = 
   if n == 0 or n < 0: 
@@ -19,5 +18,5 @@ proc sine(x: float): float =
     acc = acc + taylor
   return acc 
 
-# echo factorial(17)
+echo factorial(17)
 echo sine(1.0)