New examples.

examples.md

@@ -49,10 +49,12 @@ for plotting or rendering graphics.
 -   [Matrix multiplication](examples/matrix-multiplication.html)
 -   [Pairwise L₁ distances](examples/pairwise-l1.html)
 -   [Outer product](examples/outer-product.html)
+-   [Comparing arrays for equality](examples/array-equality.html)
 -   [Searching](examples/searching.html)
 -   [Computing histograms](examples/histograms.html)
 -   [Moving average](examples/moving-average.html)
 -   [Means](examples/means.html)
+-   [Integer logarithm](examples/integer-logarithm.html)
 -   [Radix sort](examples/radix-sort.html)
 -   [Radix sort by key](examples/radix-sort-key.html)
 -   [Merge sort](examples/merge-sort.html)

examples/3d-vectors.fut

@@ -146,7 +146,7 @@ module f64_3d = mk_vspace_3d f64
 -- {x = -3.0f64, y = 6.0f64, z = -3.0f64}
 -- ```
 
--- # See also
+-- ## See also
 --
 -- [Dex: Multi-step ray tracer](dex-raytrace.html)
 --

examples/array-equality.fut

@@ -0,0 +1,34 @@
+-- # Comparing arrays for equality
+
+-- To compare two one-dimensional arrays for equality, we can compare
+-- them elementwise, yielding an array of `bool`s, then use `and` to
+-- check whether all those elements are true:
+
+def eq_arr_i32 [n] (a: [n]i32) (b: [n]i32) : bool =
+  and (map2 (==) a b)
+
+-- This function requires us to already know that the arrays have the
+-- same size. We can also write a variant that does not have this
+-- requirement, but instead checks for the size explicitly and then
+-- uses a [size coercion](size-coercions.html):
+
+def eq_arr_i32_any [n] [m] (a: [n]i32) (b: [m]i32) : bool =
+  n == m && eq_arr_i32 a (b :> [n]i32)
+
+-- This implementation is still restricted to arrays of integers. We
+-- can make a polymorphic one that expects the user to provide an
+-- equality function:
+
+def eq_arr 'a [n] [m] (eq: a -> a -> bool) (a: [n]a) (b: [m]a) : bool =
+  n == m && and (map2 eq a (b :> [n]a))
+
+-- This can then be used to define a function that works for
+-- two-dimensional arrays:
+
+def eq_arr_2d 'a [n1] [n2] [m1] [m2]
+              (eq: a -> a -> bool) (a: [n1][n2]a) (b: [m1][m2]a) : bool =
+  n1 == m1 && n2 == m2 && eq_arr (eq_arr eq) a (b :> [n1][n2]a)
+
+-- ## See also
+--
+-- [Searching](searching.html).

examples/integer-logarithm.fut

@@ -0,0 +1,15 @@
+-- # Integer logarithm
+--
+-- The base-2 integer logarithm can be computed by counting the number
+-- of leading *zero bits* in the integer, through the `clz` builtin
+-- function. For example for 64-bit integers:
+
+def ilog2 (n: i64) : i64 = i64.i32 (63 - i64.clz n)
+
+-- > ilog2 127
+
+-- > ilog2 128
+
+-- ## See also
+--
+-- [Merge sort](merge-sort.html).

examples/size-coercions.fut

@@ -19,4 +19,4 @@ def B = [1,2,3] ++ [4,5,6] :> [6]i32
 
 -- # See also
 --
--- [Complex ranges](complex-ranges.html)
+-- [Complex ranges](complex-ranges.html), [Comparing arrays for equality](array-equality.html).