September Morn Update

Task/Safe-addition/C++/safe-addition.cpp

@@ -0,0 +1,43 @@
+#include <iostream>
+#include <tuple>
+
+union conv {
+    int i;
+    float f;
+};
+
+float nextUp(float d) {
+    if (isnan(d) || d == -INFINITY || d == INFINITY) return d;
+    if (d == 0.0) return FLT_EPSILON;
+
+    conv c;
+    c.f = d;
+    c.i++;
+
+    return c.f;
+}
+
+float nextDown(float d) {
+    if (isnan(d) || d == -INFINITY || d == INFINITY) return d;
+    if (d == 0.0) return -FLT_EPSILON;
+
+    conv c;
+    c.f = d;
+    c.i--;
+
+    return c.f;
+}
+
+auto safeAdd(float a, float b) {
+    return std::make_tuple(nextDown(a + b), nextUp(a + b));
+}
+
+int main() {
+    float a = 1.20f;
+    float b = 0.03f;
+
+    auto result = safeAdd(a, b);
+    printf("(%f + %f) is in the range (%0.16f, %0.16f)\n", a, b, std::get<0>(result), std::get<1>(result));
+
+    return 0;
+}

Task/Safe-addition/Perl-6/safe-addition.pl6

@@ -0,0 +1,28 @@
+say "Floating points: (Nums)";
+say "Error: " ~ (2**-53).Num;
+
+sub infix:<±+> (Num $a, Num $b) {
+    my \ε = (2**-53).Num;
+    $a - ε + $b, $a + ε + $b,
+}
+
+printf "%4.16f .. %4.16f\n", (1.14e0 ±+ 2e3);
+
+say "\nRationals:";
+
+say ".1 + .2 is exactly equal to .3: ", .1 + .2 === .3;
+
+say "\nLarge denominators require explicit coercion to FatRats:";
+say "Sum of inverses of the first 500 natural numbers:";
+my $sum = sum (1..500).map: { FatRat.new(1,$_) };
+say $sum;
+say $sum.nude;
+
+{
+    say "\nRat stringification may not show full precision for terminating fractions by default.";
+    say "Use a module to get full precision.";
+    use Rat::Precise; # module loading is scoped to the enclosing block
+    my $rat = 1.5**63;
+    say "\nPerl 6 default stringification for 1.5**63:\n" ~ $rat; # standard stringification
+    say "\nRat::Precise stringification for 1.5**63:\n" ~$rat.precise; # full precision
+}

Task/Safe-addition/Perl/safe-addition.pl

@@ -0,0 +1,11 @@
+use strict;
+use warnings;
+use Data::IEEE754::Tools <nextUp nextDown>;
+
+sub safe_add {
+    my($a,$b) = @_;
+    my $c = $a + $b;
+    return $c, nextDown($c), nextUp($c)
+}
+
+printf "%.17f (%.17f, %.17f)\n", safe_add (1/9,1/7);