Merge branch 'native-complex'

This makes Complex a class purely defined in Perl 6, to avoid oddnesses where
methods defined in the parrot Complex PMC would not be overridable from
withing Perl 6.

colomon++ gets much credit for working on this branch.

Test.pm

@@ -84,7 +84,7 @@ multi sub isnt(Object $got, Object $expected, $desc) is export(:DEFAULT) {
 multi sub isnt(Object $got, Object $expected) is export(:DEFAULT) { isnt($got, $expected, ''); }
 
 multi sub is_approx(Object $got, Object $expected, $desc) is export(:DEFAULT) {
-    my $test = abs($got - $expected) <= 0.00001;
+    my $test = ($got - $expected).abs <= 0.00001;
     proclaim(?$test, $desc);
 }
 

build/Makefile.in

@@ -93,7 +93,6 @@ BUILTINS_PIR = \
   src/classes/Num.pir \
   src/classes/Int.pir \
   src/classes/Order.pir \
-  src/classes/Complex.pir \
   src/classes/IO.pir \
   src/classes/List.pir \
   src/classes/Array.pir \

src/builtins/any-num.pir

@@ -22,24 +22,12 @@ the size of that file down and to emphasize their generic,
 .loadlib 'math_ops'
 .sub 'onload' :anon :init :load
     $P0 = get_hll_namespace ['Any']
-    '!EXPORT'('abs,int,log,polar,sqrt,truncate,unpolar', 'from'=>$P0)
+    '!EXPORT'('int,polar,truncate', 'from'=>$P0)
 
     ##  pre-seed a random number generator
     'srand'()
 .end
 
-
-=item abs()
-
-=cut
-
-.namespace ['Any']
-.sub 'abs' :method :multi(_)
-    $N0 = self
-    $N1 = abs $N0
-    .return ($N1)
-.end
-
 .namespace ['Any']
 .sub 'int' :method :multi(_)
     "die"("the int() sub and .int method have been replaced by the .Int method")
@@ -51,23 +39,6 @@ the size of that file down and to emphasize their generic,
 .end
 
 
-=item log
-
- our Num multi Num::log         ( Num $x: Num :$base )
- our Num multi Math::Basic::log ( Num $x, Num :$base )
-
-Logarithm of base C<$base>, default Natural. Calling with C<$x == 0> is an
-error.
-
-=cut
-
-.sub 'log' :method :multi(_)
-    $N0 = self
-    $N1 = ln $N0
-    .return ($N1)
-.end
-
-
 =item polar
 
 =cut
@@ -79,18 +50,6 @@ error.
 .end
 
 
-=item sqrt()
-
-=cut
-
-.namespace ['Any']
-.sub 'sqrt' :method :multi(_)
-    $N0 = self
-    $N1 = sqrt $N0
-    .return ($N1)
-.end
-
-
 =item srand()
 
 =cut
@@ -134,116 +93,6 @@ error.
     .return ($I0)
 .end
 
-
-=item unpolar($angle)
-
-=cut
-
-=item roots
-
- our Array multi Num::roots ( Complex $z, Int $n )
-
-Returns an Array consisting of the $n roots of a Complex number $z, where $n is
-a positive integer. For any Complex number $z ( which includes real numbers and
-integers as a subset ) there are a set of $n numbers W such that $w_k ** $n = $z,
-or in set theory notation:
-
-W = { $w_i : $w_i ** $n = $z and 0 <= i <= n-1 } .
-
-These can be written in terms of the multiple-valued complex logarithm:
-
-exp[1/$n*(Log($z)]
-
-which is equal to
-
-$w_k = exp[1/$n*(log($r)+i*($theta + 2*k*pi))] where k = 0,1,2,..., n-1
-
-where ($r,$theta) = $z.polar . The angle $theta returned is always in the
-interval -pi <= $theta <= pi .
-
-=cut
-
-.sub 'roots' :method
-    .param int n
-    .local num pi, r, theta
-    .local pmc x, result, roots
-    x        = self
-    pi       = atan 1
-    pi      *= 4
-    roots    = root_new ['parrot';'FixedPMCArray']
-  if n > 0 goto positive
-    roots    = 1                # single element array
-    roots[0] = 'NaN'
-    goto done
-  positive:
-    roots    = n                # fix array size to n
-  if n > 1 goto general
-    roots[0] = x
-    goto done
-  general:
-    div $N0, 1, n
-    $I0   = 0
-    $I1   = isa x, 'Complex'
-  unless $I1 goto real
-    $N6   = x[0]
-    $N7   = x[1]
-    theta = atan $N7, $N6       # angle of polar representation
-    $N6  *= $N6
-    $N7  *= $N7
-    $N8   = $N6 + $N7
-    r     = sqrt $N8            # radius of polar representation
-    $N1   = ln r
-    goto loop
- real:
-    $N4  = x
-    $N4  = abs $N4              # if x < 0 we rotate by exp(i pi/n) later on
-    $N1   = ln $N4              # ln(abs(x)) = ln(r)
- loop:
-   if $I0 >= n goto done
-    $P2    = root_new ['parrot';'Complex']   # this can surely be optimized
-    $N3    = $N0
-    $N3   *= 2
-    $N3   *= pi
-    $N3   *= $I0
-    $P2[1] = $N3                # 2*$I0*pi/n
-    $N5    = $P2[1]
-  unless $I1 goto rotate_negative_reals
-    $N8    = $N0
-    $N8   *= theta              # theta/n
-    $N5   += $N8                # 2*$I0*pi/n + theta/n
-    goto exponentiate
- rotate_negative_reals:         # we must rotate answer since we factored out (-1)^(1/n)
-    if x > 0 goto exponentiate
-    div $N4, pi, n
-    $N5 += $N4                  # exp( i pi / n ) = (-1)^(1/n) (principle root)
-  exponentiate:
-    $N9        = $N0
-    $N9       *= $N1            # 1/n*ln(r)
-    $P2[0]     = $N9
-    $P2[1]     = $N5
-    $P2        = $P2.'exp'()    # exp(1/n*(ln(r)+i*(theta + 2*k*pi)))
-    roots[$I0] = $P2
-    inc $I0
-    goto loop
-  done:
-    .return (roots)
-.end
-
-.sub 'unpolar' :method
-    .param num angle
-    .local num mag
-    .local pmc result
-    mag = self
-    result = root_new ['parrot';'Complex']
-    $N0 = cos angle
-    $N0 *= mag
-    result[0] = $N0
-    $N0 = sin angle
-    $N0 *= mag
-    result[1] = $N0
-    .return (result)
-.end
-
 =back
 
 =cut

src/builtins/math.pir

@@ -15,15 +15,6 @@ src/builtins/math.pir - Perl6 math functions
 ## TODO: figure out what to get working, in order to uncomment the following
 ## .namespace [ 'Math::Basic' ]
 
-
-.sub 'roots' :multi(_, 'Integer')
-    .param pmc x
-    .param int n
-    .local pmc result
-     result = x.'roots'(n)
-    .return (result)
-.end
-
 =item sign
 
  our Int multi Num::sign ( Num  $x )
@@ -58,37 +49,6 @@ Returns the sign of $x, i.e +1 for positive numbers (including Inf), zero for ze
 .end
 
 
-=item exp
-
- our Num multi Num::exp         ( Num $exponent: Num :$base = Num::e )
- our Num multi Math::Basic::exp ( Num $exponent, Num :$base = Num::e )
-
-Performs similar to C<$base ** $exponent>. C<$base> defaults to the
-constant I<e>.
-
-=cut
-
-.sub 'exp' :multi(_)
-    .param num a
-    a = exp a
-    .return (a)
-.end
-
-
-=item log10
-
- &log10 := &log.assuming:base(10);
-
-Returns the base 10 logarithm of $x.
-
-=cut
-
-.sub 'log10'
-    .param num a
-    $N0 = log10 a
-    .return ($N0)
-.end
-
 
 =item e
 
@@ -234,10 +194,6 @@ Note that you get one C<srand()> for free when you start a Perl program, so
 you I<must> call C<srand()> yourself if you wish to specify a deterministic seed
 (or if you wish to be differently nondeterministic).
 
-=item i
-
- constant Complex Complex::i = Complex::sqrt(-1);
-
 =back
 
 =cut