[Base] Clock reworked.

- Time progression is now equal and in sync on all threads.
- Floating point imprecisions do not interfere with timing.

src/xenia/base/math.h

@@ -2,7 +2,7 @@
  ******************************************************************************
  * Xenia : Xbox 360 Emulator Research Project                                 *
  ******************************************************************************
- * Copyright 2014 Ben Vanik. All rights reserved.                             *
+ * Copyright 2019 Ben Vanik. All rights reserved.                             *
  * Released under the BSD license - see LICENSE in the root for more details. *
  ******************************************************************************
  */
@@ -15,6 +15,7 @@
 #include <cstdint>
 #include <cstring>
 #include <limits>
+#include <numeric>
 #include <type_traits>
 #include "xenia/base/platform.h"
 
@@ -59,6 +60,34 @@ T next_pow2(T value) {
   return value;
 }
 
+#if __cpp_lib_gcd_lcm
+template <typename T>
+inline constexpr T greatest_common_divisor(T a, T b) {
+  return std::gcd(a, b);
+}
+#else
+template <typename T>
+constexpr T greatest_common_divisor(T a, T b) {
+  // Use the Euclid algorithm to calculate the greatest common divisor
+  while (b) {
+    a = std::exchange(b, a % b);
+  }
+  return a;
+}
+#endif
+
+template <typename T>
+inline constexpr void reduce_fraction(T& numerator, T& denominator) {
+  auto gcd = greatest_common_divisor(numerator, denominator);
+  numerator /= gcd;
+  denominator /= gcd;
+}
+
+template <typename T>
+inline constexpr void reduce_fraction(std::pair<T, T>& fraction) {
+  reduce_fraction<T>(fraction.first, fraction.second);
+}
+
 constexpr uint32_t make_bitmask(uint32_t a, uint32_t b) {
   return (static_cast<uint32_t>(-1) >> (31 - b)) & ~((1u << a) - 1);
 }