Data update

Task/Test-integerness/Ada/test-integerness.ada

@@ -0,0 +1,49 @@
+--  Big_Numbers is an Ada 2022 unit
+
+with Ada.Numerics.Big_Numbers.Big_Integers,
+     Ada.Numerics.Big_Numbers.Big_Reals,
+     Ada.Numerics.Generic_Complex_Types,
+     Ada.Text_IO;
+
+use Ada.Numerics.Big_Numbers.Big_Integers,
+    Ada.Numerics.Big_Numbers.Big_Reals,
+    Ada.Text_IO;
+
+procedure Test_Integer is
+   --  These are the only numerical types defined in package
+   --  "Standard" which is always incuded. 'Base also covers anything
+   --  with the same Base types.
+   function Is_Integer (N : Integer'Base) return Boolean is (True);
+   function Is_Integer (N : Float'Base) return Boolean is (Float'Base'Floor (N) = N);
+
+   --  Additional types defined in the standard library.
+   function Is_Integer (N : Big_Integer) return Boolean is (True);
+
+   --  The type says real, but these are rational approximations of
+   --  real numbers.
+   function Is_Integer (N : Big_Real) return Boolean is (Denominator (N) = 1);
+
+   package Complex_Float is new Ada.Numerics.Generic_Complex_Types (Float);
+   use Complex_Float;
+
+   function Is_Integer (N : Complex) return Boolean
+     is (Im (N) = 0.0 and then Is_Integer (Re (N)));
+
+   Int_One : Integer := 1;
+   Flo_One : Float := 1.0;
+   Flo_OneH : Float := 1.5;
+   BInt_One : Big_Integer := To_Big_Integer (1);
+   BFlo_One : Big_Real := To_Big_Real (1);
+   BFlo_OneH : Big_Real := From_String ("1.5");
+   CInt_One : Complex := 1.0 + 0.0 * I;
+   CInt_OneI : Complex := 1.0 + 1.0 * I;
+begin
+   Put_Line (Int_One'Image & " is integer? " & Is_Integer (Int_One)'Image);
+   Put_Line (Flo_One'Image & " is integer? " & Is_Integer (Flo_One)'Image);
+   Put_Line (Flo_OneH'Image & " is integer? " & Is_Integer (Flo_OneH)'Image);
+   Put_Line (BInt_One'Image & " is integer? " & Is_Integer (BInt_One)'Image);
+   Put_Line (BFlo_One'Image & " is integer? " & Is_Integer (BFlo_One)'Image);
+   Put_Line (BFlo_OneH'Image & " is integer? " & Is_Integer (BFlo_OneH)'Image);
+   Put_Line (CInt_One'Image & " is integer? " & Is_Integer (CInt_One)'Image);
+   Put_Line (CInt_OneI'Image & " is integer? " & Is_Integer (CInt_OneI)'Image);
+end Test_Integer;

Task/Test-integerness/DuckDB/test-integerness-1.duckdb

@@ -0,0 +1,3 @@
+create type Complex as struct (r float, i float);
+
+create type Rational as struct (n integer, d integer);

Task/Test-integerness/DuckDB/test-integerness-2.duckdb

@@ -0,0 +1,16 @@
+create or replace function number_integerp(x) as (
+  x = trunc(x)
+);
+
+# Return true iff x has the type signature of a Rational
+# with the denominator dividing the numerator evenly.
+create or replace function rational_integerp(x) as (
+   typeof(x) = 'STRUCT(n INTEGER, d INTEGER)'
+   and x.n % x.d = 0
+);
+
+# Return true if x can be cast to a Complex with
+# the imaginary part equal to 0 and an integer real part.
+create or replace function complex_integerp(x) as (
+  (x::Complex).i = 0 and number_integerp(x.r)
+);

Task/Test-integerness/Pluto/test-integerness.pluto

@@ -0,0 +1,37 @@
+require "complex"
+require "rat"
+require "table2"
+local fmt = require "fmt"
+
+local tests1 = {25.000000, 24.999999, 25.000100}
+local tests2 = {-2.1e120}
+local tests3 = {-5e-2, 0/0, 1/0}
+local tests4 = {complex.of(5, 0), complex.of(5, -5)}
+local tests5 = {rat.of(24, 8), rat.of(-5, 1), rat.of(17, 2)}
+local tests6 = tests1:joined({-5e-2})
+
+print("Using exact arithmetic:\n")
+for tests1 as t do
+    fmt.print("  %-9.6f is integer? %s", t, t % 1 == 0)
+end
+print()
+for tests2 as t do
+    fmt.print("  %-9g is integer? %s", t, t % 1 == 0)
+end
+for tests3 as t do
+    fmt.print("  %-9.6f is integer? %s", t, t % 1 == 0)
+end
+print()
+for tests4 as t do
+    fmt.print("  %-9s is integer? %s", t, t:getReal() % 1 == 0 and t:getImag() == 0)
+end
+print()
+for tests5 as t do
+    fmt.print("  %-9s is integer? %s", t, t:isint())
+end
+print("\nWithin a tolerance of 0.00001:\n")
+local tol = 0.00001
+for tests6 as t do
+    local d = math.abs(t - math.round(t))
+    fmt.print("  %9.6f is integer? %s", t, d <= tol)
+end