Update and add examples

examples/importing.ang

@@ -0,0 +1,3 @@
+import "math.ang"
+
+write(sqrt(2))

examples/list.ang

@@ -0,0 +1,51 @@
+
+# Empty list
+write([])
+
+# List with items
+write([3, 1, 4, 1, 5, 9, 2, 6, 5])
+
+# List with items of different types
+write(["", "私はかっこいいです。", true, nil, nil, 1, 2])
+
+a := []
+
+a = a.append(1)
+a = a.append(2)
+
+write(a)
+
+
+list := []
+
+n := 0
+x := 0
+while n < 100 {
+    x = x + 2*n + 1
+
+    list = list.append(x)
+    n = n + 1
+}
+
+write(list)
+write(list.map(func(a) {
+    return a - 1
+}))
+write(list.length())
+write(list.at(69))
+
+other := []
+
+a := 1
+while a <= 10 {
+    other = other.append(a)
+    a = a + 1
+}
+
+sum := other.reduce(func(tot, x) {
+    return tot + x
+}, 0)
+
+write(sum)
+
+assert(sum == a*(a-1)/2)

examples/math.ang

@@ -71,8 +71,31 @@ func round(x) {
 # sin(x)
 # x: number; an angle in radians
 #   Get the sine of an angle (in radians). https://en.wikipedia.org/wiki/Sine_and_cosine
+#   TODO: use hashmap with precomputed values and linear interpolation
 func sin(x) {
-    # todo
+    f := 1
+    x = mod(x, 2*PI)
+    if x > PI {
+        x = -x
+        f = -1
+    }
+
+    # compute sine with a taylor series mock function of sine (valid between -pi and +pi)
+    tot := x
+    l := 1
+    i := 1
+    s := -1
+
+    while i <= 19 {
+        i = i + 2
+        l = s * l * x / i / (i-1)
+
+        tot = tot + l
+
+        s = -s
+    }
+
+    return tot*f
 }
 
 # cos(x)

examples/pi-approx.ang

@@ -4,7 +4,7 @@
 # see: https://en.wikipedia.org/wiki/Basel_problem
 
 # The amount of terms
-terms := 100000000
+terms := 1000000
 
 # The running sum of terms
 tot := 0