Some more code samples for ch2

Author: robot-dreams

ch2-distance.cpp

@@ -0,0 +1,26 @@
+#include <iostream>
+#include "my_intrinsics.h"
+#include "my_type_functions.h"
+
+using namespace std;
+
+template<typename F>
+    requires(Transformation(F))
+DistanceType(F) distance(Domain(F) x, Domain(F) y, F f)
+{
+    typedef DistanceType(F) N;
+    N n = N(0);
+    while (x != y) {
+        x = f(x);
+        n = n + N(1);
+    }
+    return n;
+}
+
+int increment(int x) {
+    return x + 1;
+}
+
+int main() {
+    cout << distance(0, 2, increment) << endl;
+}

ch2-orbit_structure.cpp

@@ -0,0 +1,90 @@
+#include <iostream>
+#include <set>
+#include "my_intrinsics.h"
+#include "my_type_functions.h"
+
+using namespace std;
+
+template<typename F, typename P>
+    requires(Transformation(F) && UnaryPredicate(P) &&
+        Domain(F) == Domain(P))
+Domain(F) connection_point_naive(Domain(F) x, F f, P p)
+{
+    set<Domain(F)> seen;
+    while (p(x) && seen.find(x) == seen.end()) {
+        seen.insert(x);
+        x = f(x);
+    }
+    return x;
+}
+
+template<typename F, typename P>
+    requires(Transformation(F) && UnaryPredicate(P) &&
+        Domain(F) == Domain(P))
+Domain(F) collision_point(const Domain(F)& x, F f, P p)
+{
+    // Preconditions:
+    // - p(x) if and only if f(x) is defined
+    if (!p(x)) return x;
+
+    Domain(F) slow = x;         // slow = f^0(x)
+    Domain(F) fast = f(x);      // fast = f^1(x)
+                                // n <- 0 (completed iterations)
+    while (fast != slow) {      // slow = f^n(x)     ^ fast = f^{2n+1}(x)
+        slow = f(slow);         // slow = f^{n+1}(x) ^ fast = f^{2n+3}(x)
+        if (!p(fast)) return fast;
+        fast = f(fast);         // slow = f^n(x)     ^ fast = f^{2n+2}(x)
+        if (!p(fast)) return fast;
+        fast = f(fast);         // slow = f^n(x)     ^ fast = f^{2n+3}(x)
+                                // n <- n + 1
+    }
+    return fast;                // slow = f^n(x)     ^ fast = f^{2n+1}(x)
+    // Postconditions:
+    // - return value is terminal point or collision point
+}
+
+template<typename F, typename P>
+    requires(Transformation(F) && UnaryPredicate(P) &&
+        Domain(F) == Domain(P))
+bool terminating(const Domain(F)& x, F f, P p)
+{
+    // Preconditions:
+    // - p(x) if and only if f(x) is defined
+    return !p(collision_point(x, f, p));
+}
+
+template<typename F>
+    requires(Transformation(F))
+Domain(F)
+collision_point_nonterminating_orbit(const Domain(F)& x, F f)
+{
+    Domain(F) slow = x;         // slow = f^0(x)
+    Domain(F) fast = f(x);      // fast = f^1(x)
+                                // n <- 0 (completed iterations)
+    while (fast != slow) {      // slow = f^n(x)     ^ fast = f^{2n+1}(x)
+        slow = f(slow);         // slow = f^{n+1}(x) ^ fast = f^{2n+1}(x)
+        fast = f(fast);         // slow = f^{n+1}(x) ^ fast = f^{2n+2}(x)
+        fast = f(fast);         // slow = f^{n+1}(x) ^ fast = f^{2n+3}(x)
+                                // n <- n + 1
+    }
+    return fast;                // slow = f^n(x)     ^ fast = f^{2n+1}(x)
+    // Postconditions:
+    // - return value is collision point
+}
+
+template<int modulus>
+int mod_increment(int x)
+{
+    return (x + 1) % modulus;
+}
+
+template<int modulus>
+bool mod_valid(int x)
+{
+    return x >= 0 && x < modulus;
+}
+
+int main() {
+    cout << collision_point(0, mod_increment<13>, mod_valid<13>) << endl;
+    cout << collision_point_nonterminating_orbit(0, mod_increment<13>) << endl;
+}

ch2-power_unary.cpp

@@ -0,0 +1,43 @@
+#include <iostream>
+#include <sstream>
+#include <string>
+#include "my_intrinsics.h"
+#include "my_type_functions.h"
+
+using namespace std;
+
+template<typename F, typename N>
+    requires(Transformation(F) && Integer(N))
+Domain(F) power_unary(Domain(F) x, N n, F f)
+{
+    // Preconditions:
+    // - n >= 0
+    // - (forall i in N) 0 < i <= n implies f^i(x) is defined
+    while (n > N(0)) {
+        x = f(x);
+        n = n - N(1);
+    }
+    return x;
+}
+
+string heighway_dragon_step(string input) {
+    stringstream appender;
+    for (int i = 0; i < input.length(); i++) {
+        switch(input[i]) {
+            case 'a':
+                appender << "aRbFR";
+                break;
+            case 'b':
+                appender << "LFaLb";
+                break;
+            default:
+                appender << input[i];
+        }
+    }
+    return appender.str();
+}
+
+int main() {
+    cout << power_unary("Fa", 10, heighway_dragon_step).length() << endl;
+}
+