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perl/Examples/Chap6/Newton.pm

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+
+
+###
+### Newton.pm
+###
+
+## Chapter 6 section 6
+
+sub sqrt2 {
+  my $g = 2;   # Initial guess
+  until (close_enough($g*$g, 2)) {
+    $g = ($g*$g + 2) / (2*$g);
+  }
+  $g;
+}
+
+sub close_enough {
+  my ($a, $b) = @_;
+  return abs($a - $b) < 1e-12;
+}
+sub sqrtn {
+  my $n = shift;
+  my $g = $n;   # Initial guess
+  until (close_enough($g*$g, $n)) {
+    $g = ($g*$g + $n) / (2*$g);
+  }
+  $g;
+}
+
+
+## Chapter 6 section 6.1
+
+use Stream 'iterate_function';
+
+sub sqrt_stream {
+  my $n = shift;
+  iterate_function (sub { my $g = shift;
+                         ($g*$g + $n) / (2*$g);
+                        },
+                    $n);
+}
+
+1;
+
+
+## Chapter 6 section 6.2
+
+sub slope {
+  my ($f, $x) = @_;
+  my $e = 0.00000095367431640625;
+  ($f->($x+$e) - $f->($x-$e)) / (2*$e);
+}
+
+
+## Chapter 6 section 6.2
+
+# Return a stream of numbers $x that make $f->($x) close to 0
+sub solve {
+  my $f = shift;
+  my $guess = shift || 1;
+  iterate_function(sub { my $g = shift;
+                         $g - $f->($g)/slope($f, $g);
+                       },
+                   $guess);
+}