Tutorial: Rewrite using conventions enabled by CMake 3.23

This is a full re-write of the CMake Tutorial for CMake 3.23, both
the functionality it provides, as well as the modern workflows that
developers use when interfacing with CMake.

Issue: #22663, #23086, #23799, #26053, #26105, #26153, #26914

Help/guide/tutorial/Step9/MathFunctions/MathFunctions.cxx

@@ -1,19 +1,101 @@
-#include "MathFunctions.h"
-
 #include <cmath>
+#include <format>
 
-#ifdef USE_MYMATH
-#  include "mysqrt.h"
+#include <MathLogger.h>
+
+#ifdef TUTORIAL_USE_SSE2
+#  include <emmintrin.h>
 #endif
 
+namespace {
+
+mathlogger::Logger Logger;
+
+#if defined(TUTORIAL_USE_GNU_BUILTIN)
+typedef double v2df __attribute__((vector_size(16)));
+
+double gnu_mysqrt(double x)
+{
+  v2df root = __builtin_ia32_sqrtsd(v2df{ x, 0.0 });
+  double result = root[0];
+  Logger.Log(std::format("Computed sqrt of {} to be {} with GNU-builtins\n", x,
+                         result));
+  return result;
+}
+#elif defined(TUTORIAL_USE_SSE2)
+double sse2_mysqrt(double x)
+{
+  __m128d root = _mm_sqrt_sd(_mm_setzero_pd(), _mm_set_sd(x));
+  double result = _mm_cvtsd_f64(root);
+  Logger.Log(
+    std::format("Computed sqrt of {} to be {} with SSE2\n", x, result));
+  return result;
+}
+#endif
+
+// a hack square root calculation using simple operations
+double fallback_mysqrt(double x)
+{
+  if (x <= 0) {
+    return 0;
+  }
+
+  double result = x;
+
+  // do ten iterations
+  for (int i = 0; i < 10; ++i) {
+    if (result <= 0) {
+      result = 0.1;
+    }
+    double delta = x - (result * result);
+    result = result + 0.5 * delta / result;
+
+    Logger.Log(std::format("Computing sqrt of {} to be {}\n", x, result));
+  }
+  return result;
+}
+
+#include <SqrtTable.h>
+
+double table_sqrt(double x)
+{
+  double result = sqrtTable[static_cast<int>(x)];
+  // do ten iterations
+  for (int i = 0; i < 10; ++i) {
+    if (result <= 0) {
+      result = 0.1;
+    }
+    double delta = x - (result * result);
+    result = result + 0.5 * delta / result;
+  }
+  Logger.Log(
+    std::format("Computed sqrt of {} to be {} with TableSqrt\n", x, result));
+  return result;
+}
+
+double mysqrt(double x)
+{
+  if (x >= 1 && x < 10) {
+    return table_sqrt(x);
+  }
+
+#if defined(TUTORIAL_USE_GNU_BUILTIN)
+  return gnu_mysqrt(x);
+#elif defined(TUTORIAL_USE_SSE2)
+  return sse2_mysqrt(x);
+#else
+  return fallback_mysqrt(x);
+#endif
+}
+}
+
 namespace mathfunctions {
 double sqrt(double x)
 {
-// which square root function should we use?
-#ifdef USE_MYMATH
-  return detail::mysqrt(x);
-#else
+#ifdef TUTORIAL_USE_STD_SQRT
   return std::sqrt(x);
+#else
+  return mysqrt(x);
 #endif
 }
 }