roots and tests

src/core/Complex.pm

@@ -83,6 +83,17 @@ my class Complex is Numeric {
         Complex.new($mag * $!im.cos, $mag * $!im.sin);
     }
 
+    method roots(Complex:D: Int $n) {
+        return $NaN if $n < 1;
+        return self if $n == 1;
+        for $!re, $!im {
+            return $NaN if $_ eq 'Inf' || $_ eq '-Inf' || $_ eq 'NaN';
+        }
+
+        my ($mag, $angle) = self.polar;
+        $mag **= 1e0 / $n;
+        (^$n).map: { $mag.unpolar( ($angle + $_ * 2e0 * pi) / $n) };
+    }
 }
 
 multi sub prefix:<->(Complex \$a) {

src/core/Numeric.pm

@@ -1,3 +1,5 @@
+class Complex { ... }
+
 # XXX role Numeric { ... }
 my class Numeric {
     method Numeric() { self }
@@ -14,6 +16,7 @@ my class Numeric {
     multi method exp(Numeric $base) {
         self.exp * $base.log;
     }
+    method roots(Cool $n) { self.Complex.roots($n.Int) }
     multi method Bool(Numeric:D:) { self != 0 }
 
     multi method gist(Numeric:D:) { self.Str }
@@ -61,6 +64,10 @@ proto sub sqrt(|$) {*}
 multi sub sqrt(Numeric \$x) { $x.sqrt }
 multi sub sqrt(Cool \$x)    { $x.Numeric.sqrt }
 
+proto sub roots($, $)        { * }
+multi sub roots($x, Cool $n) { $x.Numeric.Complex.roots($n.Int) }
+multi sub roots($x, Numeric $n) { $x.Numeric.Complex.roots($n.Int) }
+
 proto infix:<+>(|$)          { * }
 multi infix:<+>($x = 0)      { $x.Numeric }
 multi infix:<+>(\$a, \$b)    { $a.Numeric + $b.Numeric }

src/core/Real.pm

@@ -18,6 +18,7 @@ my class Real {
     method cis() {
         Complex.new(self.cos, self.sin);
     }
+    method Complex() { Complex.new(self.Num, 0e0) }
     multi method log()           { self.Bridge.log               }
     multi method log(Real $base) { self.Bridge.log($base.Bridge) }
     multi method exp()           { self.Bridge.exp               }

t/spectest.data

@@ -527,7 +527,7 @@ S32-num/power.t
 # S32-num/rand.t
 S32-num/rat.t
 # S32-num/real-bridge.t
-# S32-num/roots.t
+S32-num/roots.t
 # S32-num/rounders.t
 # S32-num/sign.t
 S32-num/sqrt.t