Basic type system working

examples/math.ang

@@ -1,206 +0,0 @@
-
-PI := 3.14159265358979323
-E := 2.718281828459045235360287471352
-
-# abs(x)
-# x: number
-#   Get the absolute value of a number. If x is negative, the returned
-#   value is positive and equal to `-x`. If x is positive or zero, the
-#   returned value is x.
-func abs(x) {
-    # if the number is negative
-    if x < 0 {
-        # negate it so it's positive
-        return -x
-    }
-
-    return x
-}
-
-MAX_SQRT_DX := 0.0000001
-
-# sqrt(x)
-# x: number
-#   Calculate the approximate square root using newton's method until
-#   the accuracy has increased by less than the variable `MAX_SQRT_DX`.
-func sqrt(x) {
-    ng := x
-    g := 1
-
-    while abs(g - ng) > MAX_SQRT_DX {
-        g = ng
-
-        # create new guess
-        ng = (g + x / g) / 2
-    }
-
-    return g
-}
-
-# floor(x)
-# x: number
-#   Return the whole number part of the number. if x is a whole number,
-#   the returned value is x. If x is not a whole number, the closest
-#   whole number which is less than or equal to x is returned.
-func floor(x) {
-    # todo
-}
-
-# ceil(x)
-# x: number
-#   Return the whole number part of the number. if x is a whole number,
-#   the returned value is x. If x is not a whole number, the closest
-#   whole number which is greater than or equal to x is returned.
-func ceil(x) {
-    # todo
-}
-
-# round(x)
-# x: number
-#   Return the closest whole number to the value x.
-func round(x) {
-    f := floor(x)
-
-    if x - f > 0.5 {
-        return f + 1
-    }
-
-    return f
-}
-
-# 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) {
-    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)
-# x: number; an angle in radians
-#   Get the cosine of an angle (in radians). https://en.wikipedia.org/wiki/Sine_and_cosine
-func cos(x) {
-    # todo
-}
-
-# tan(x)
-# x: number; an angle in radians
-#   Get the tangent of an angle. https://en.wikipedia.org/wiki/Tangent
-func tan(x) {
-    # todo
-}
-
-# mod(x, n)
-# x: number; any number
-# n: number; the number to divide by
-#   Return the rest from a division of x by n.
-func mod(x, n) {
-    if x == 0 {
-        return 0
-    }
-
-    if x < 0 {
-        while x + n <= 0 {
-            x = x + n
-        }
-    } else {
-        while x - n >= 0 {
-            x = x - n
-        }
-    }
-
-    return x
-}
-
-# ln(x)
-# x: number; any number
-#   Get the approximate value of the natural logarithm
-#   This function uses newton's method to approximate.
-LN_ACC := 0.000000001
-func ln(x) {
-    pg := 0
-    g := 1
-
-    while abs(pg - g) > LN_ACC {
-        pg = g
-        g = pg + x / exp(pg) - 1
-    }
-
-    return g
-}
-
-# sm_exp(x)
-# x: number; any number between 0 and 1
-#   Get an approximate value of e raised to the power of x.
-#   This value is only reasonable if 0<x<1.
-#   It is approximated using the taylor series of e**x.
-SM_EXP_ACC := 0.00000000001
-func sm_exp(x) {
-    p_tot := 0
-    tot := 1
-    n := 1
-    x_pow := x
-    f := 1
-    while abs(tot - p_tot) > SM_EXP_ACC {
-        p_tot = tot
-        t := x_pow / f
-        tot = tot + t
-        f = f * (n+1)
-        x_pow = x_pow * x
-        n = n + 1
-    }
-
-    return tot
-}
-
-# exp(x)
-# x: number; any number
-#   Get an approximate value of e raised to the power of x.
-func exp(x) {
-    n := abs(x)
-    tot := 1
-    while n >= 1 {
-        tot = tot * E
-        n = n - 1
-    }
-
-    if n > 0 {
-        tot = tot * sm_exp(n)
-    }
-
-    if x < 0 {
-        return 1/tot
-    } else {
-        return tot
-    }
-}
-
-# pow(x, p)
-# x: number; any number. The base
-# p: number; the value of the exponent
-#   Raise any number to any power (x^p)
-func pow(x, p) {
-    return exp(p*ln(x))
-}

examples/pi-approx.py

@@ -0,0 +1,36 @@
+terms = 100000
+
+tot = 0
+
+n = 1
+while n <= terms:
+    tot = tot + 1 / (n*n)
+    n = n + 1
+
+tot = tot * 6
+
+# get the absolute value of a number
+def abs(x):
+	if x < 0:
+		return -x
+	return x
+
+# calculate an approximation of the square root of tot using
+# newton's method.
+# see: https://en.wikipedia.org/wiki/Newton's_method
+# The required accuracy
+SQRT_ACC = 0.00000001
+def sqrt(x):
+    pg = 0 # previous guess
+    g = 1 # current guess
+
+    while abs(pg - g) >= SQRT_ACC:
+        pg = g
+        g = (pg + tot/pg)/2
+
+    return g
+
+tot = sqrt(tot)
+
+# output the result
+print(tot)

examples/pøck.ang

@@ -0,0 +1,16 @@
+import "math.ang"
+
+func r_x(t) {
+    return 8*(exp(-t) - t)
+}
+
+func r_y(t) {
+    return 5*(exp(-t) - t)
+}
+
+func r(t) {
+    return format("(%s, %s)", [r_x(t), r_y(t)])
+}
+
+write(r(1))
+write()