[EK-VT] Adding a workgroup class to VecUtils

This diff adds a new class called `WorkgroupSize` to the `VecUtils` header file. The `WorkgroupSize` class takes three `uint32_t` values as parameters and stores them in a single `uint32_t` variable using bitwise operations. This class is used in the Vulkan backend to specify the size of a workgroup for a given operation.

Differential Revision: [D70021019](https://our.internmc.facebook.com/intern/diff/D70021019/)

ghstack-source-id: 267790990
Pull Request resolved: #8632

Author: trivedivivek

backends/vulkan/runtime/utils/VecUtils.h

@@ -479,5 +479,49 @@ inline int64_t multiply_integers(Iter begin, Iter end) {
       begin, end, static_cast<int64_t>(1), std::multiplies<>());
 }
 
+class WorkgroupSize final {
+  uint32_t val;
+
+ public:
+  explicit WorkgroupSize() : val(0) {}
+  explicit WorkgroupSize(const uint32_t x, const uint32_t y, const uint32_t z) {
+    // shift numbers by multiple of 11 bits, since each local workgroup axis can
+    // be 1024 at most and which is 0x400. only z axis can't store 1024, because
+    // it would overflow uint32_t storage.
+    if (z == 1024) {
+      throw std::runtime_error(
+          "Workgroup size in z axis cannot be 1024 because it would overflow uint32_t storage");
+    }
+    val = x | (y << 11) | (z << 22);
+  }
+
+  explicit WorkgroupSize(const uvec3& vec) {
+    // shift numbers by multiple of 11 bits, since each local workgroup axis can
+    // be 1024 at most and which is 0x400. only z axis can't store 1024, because
+    // it would overflow uint32_t storage.
+    if (z == 1024) {
+      throw std::runtime_error(
+          "Workgroup size in z axis cannot be 1024 because it would overflow uint32_t storage");
+    }
+    val = vec[0u] | (vec[1u] << 11) | (vec[2u] << 22);
+  }
+
+  explicit inline operator uvec3() const {
+    return {
+        val & 0x7ffu,
+        (val >> 11) & 0x7ffu,
+        (val >> 22),
+    };
+  }
+
+  explicit inline operator uint32_t() const {
+    return val;
+  }
+
+  inline constexpr uint32_t operator[](const int idx) const {
+    return (val >> (11 * idx)) & 0x7ffu;
+  }
+};
+
 } // namespace utils
 } // namespace vkcompute