Merge pull request #2327 from perl6/normalized-ZDRs

Normalized ZDRs

Author: zoffixznet

doc/Language/numerics.pod6

@@ -270,11 +270,11 @@ In many languages division by zero is an immediate exception. In Perl 6, what
 happens depends on what you're dividing and how you use the result.
 
 Perl 6 follows L<IEEE 754-2008 Standard for Floating-Point Arithmetic|https://en.wikipedia.org/wiki/IEEE_754>, but for historical reasons
-6.c language does not comply fully. L<Num> division by zero produces a
-L<Failure>, while L<Complex> division by zero produces C<NaN> components,
-regardless of what the numerator is.
+6.c and 6.d language versions do not comply fully. L<Num> division by zero
+produces a L<Failure>, while L<Complex> division by zero produces C<NaN>
+components, regardless of what the numerator is.
 
-As of 6.d language, both L<Num> and L<Complex> division by zero will produce a
+As of 6.e language, both L<Num> and L<Complex> division by zero will produce a
 -L<Inf|/type/Num#Inf>, C<+Inf>, or L<NaN> depending on whether the numerator was
 negative, positive, or zero, respectively (for L<Complex> the real and imaginary
 components are L<Num> and are considered separately).
@@ -289,7 +289,9 @@ which can be explosive.
 
 A Zero-Denominator Rational is a numeric that does role L<Rational>, which
 among core numerics would be L<Rat> and L<FatRat> objects, which
-has denominator of zero.
+has denominator of zero. The numerator of such Rationals is normalized
+to C<-1>, C<0>, or C<1> depending on whether the original numerator
+is negative, zero or positive, respectively.
 
 Operations that can be performed without requiring actual division to occur are
 non-explosive. For example, you can separately examine L<numerator> and

doc/Type/Rational.pod6

@@ -24,7 +24,10 @@ Please note that, since C<DeT> is by default equal to C<NuT>, in this case both
 =for code :skip-test
 method new(NuT:D: $numerator, DeT:D: $denominator --> Rational:D)
 
-Creates a new rational object from numerator and denominator.
+Creates a new rational object from numerator and denominator, which it
+normalizes to the lowest terms. The C<$denominator> can be zero, in which
+case the numerator is normalized to C<-1>, C<0>, or C<1> depending on whether
+the original is negative, zero, or positive, respectively.
 
 =head2 method Bool
 
@@ -56,6 +59,24 @@ If L<denominator> is C<0>, returns C<Inf>, C<-Inf>, or C<NaN>, based on
 whether L<numerator> is a positive number, negative number, or C<0>,
 respectively.
 
+=head2 method ceiling
+
+Defined as:
+
+    method ceiling(Rational:D: --> Int:D)
+
+Return the smallest integer not greater than the invocant. If L<denominator>
+is zero, L<fails|/routine/fail> with C<X::Numeric::DivideByZero>.
+
+=head2 method floor
+
+Defined as:
+
+    method floor(Rational:D: --> Int:D)
+
+Return the largest integer not greater than the invocant. If L<denominator>
+is zero, L<fails|/routine/fail> with C<X::Numeric::DivideByZero>.
+
 =head2 method isNaN
 
 =for code