[NFC][SYCL] Fix formatting and typos (#5822)

Remove unused header files.

Author: bader

sycl/include/CL/sycl/half_type.hpp

@@ -12,9 +12,6 @@
 #include <CL/sycl/detail/export.hpp>
 #include <CL/sycl/detail/type_traits.hpp>
 
-#include <array>
-#include <cmath>
-#include <cstdint>
 #include <functional>
 #include <iostream>
 #include <limits>
@@ -59,7 +56,7 @@ inline __SYCL_CONSTEXPR_HALF uint16_t float2Half(const float &Val) {
   const uint8_t Exp32 = (Bits & 0x7f800000) >> 23;
   const int16_t Exp32Diff = Exp32 - 127;
 
-  // intialize to 0, covers the case for 0 and small numbers
+  // initialize to 0, covers the case for 0 and small numbers
   uint16_t Exp16 = 0, Frac16 = 0;
 
   if (__builtin_expect(Exp32Diff > 15, 0)) {
@@ -342,7 +339,7 @@ class half {
 #ifndef __SYCL_DEVICE_ONLY__
   // Since StorageT and BIsRepresentationT are different on host, these two
   // helpers are required for 'vec' class
-  constexpr half(const detail::host_half_impl::half_v2 &rhs) : Data(rhs){};
+  constexpr half(const detail::host_half_impl::half_v2 &rhs) : Data(rhs) {}
   constexpr operator detail::host_half_impl::half_v2() const { return Data; }
 #endif // __SYCL_DEVICE_ONLY__