Move complex<Half> from Half.h to complex.h (#140565)

Executing on old TODO on the way to sharing Half.h with ExecuTorch.

Differential Revision: [D65888037](https://our.internmc.facebook.com/intern/diff/D65888037/)
Pull Request resolved: https://github.com/pytorch/pytorch/pull/140565
Approved by: https://github.com/ezyang, https://github.com/malfet
ghstack dependencies: #140564

c10/util/Half.h

@@ -12,7 +12,6 @@
 #include <c10/macros/Export.h>
 #include <c10/macros/Macros.h>
 #include <c10/util/bit_cast.h>
-#include <c10/util/complex.h>
 #include <c10/util/floating_point_utils.h>
 #include <type_traits>
 
@@ -385,56 +384,6 @@ struct alignas(2) Half {
 #endif
 };
 
-// TODO : move to complex.h
-template <>
-struct alignas(4) complex<Half> {
-  Half real_;
-  Half imag_;
-
-  // Constructors
-  complex() = default;
-  // Half constructor is not constexpr so the following constructor can't
-  // be constexpr
-  C10_HOST_DEVICE explicit inline complex(const Half& real, const Half& imag)
-      : real_(real), imag_(imag) {}
-  C10_HOST_DEVICE inline complex(const c10::complex<float>& value)
-      : real_(value.real()), imag_(value.imag()) {}
-
-  // Conversion operator
-  inline C10_HOST_DEVICE operator c10::complex<float>() const {
-    return {real_, imag_};
-  }
-
-  constexpr C10_HOST_DEVICE Half real() const {
-    return real_;
-  }
-  constexpr C10_HOST_DEVICE Half imag() const {
-    return imag_;
-  }
-
-  C10_HOST_DEVICE complex<Half>& operator+=(const complex<Half>& other) {
-    real_ = static_cast<float>(real_) + static_cast<float>(other.real_);
-    imag_ = static_cast<float>(imag_) + static_cast<float>(other.imag_);
-    return *this;
-  }
-
-  C10_HOST_DEVICE complex<Half>& operator-=(const complex<Half>& other) {
-    real_ = static_cast<float>(real_) - static_cast<float>(other.real_);
-    imag_ = static_cast<float>(imag_) - static_cast<float>(other.imag_);
-    return *this;
-  }
-
-  C10_HOST_DEVICE complex<Half>& operator*=(const complex<Half>& other) {
-    auto a = static_cast<float>(real_);
-    auto b = static_cast<float>(imag_);
-    auto c = static_cast<float>(other.real());
-    auto d = static_cast<float>(other.imag());
-    real_ = a * c - b * d;
-    imag_ = a * d + b * c;
-    return *this;
-  }
-};
-
 C10_API inline std::ostream& operator<<(std::ostream& out, const Half& value) {
   out << (float)value;
   return out;

c10/util/complex.h

@@ -3,6 +3,7 @@
 #include <complex>
 
 #include <c10/macros/Macros.h>
+#include <c10/util/Half.h>
 
 #if defined(__CUDACC__) || defined(__HIPCC__)
 #include <thrust/complex.h>
@@ -606,6 +607,55 @@ C10_HOST_DEVICE complex<T> polar(const T& r, const T& theta = T()) {
 #endif
 }
 
+template <>
+struct alignas(4) complex<Half> {
+  Half real_;
+  Half imag_;
+
+  // Constructors
+  complex() = default;
+  // Half constructor is not constexpr so the following constructor can't
+  // be constexpr
+  C10_HOST_DEVICE explicit inline complex(const Half& real, const Half& imag)
+      : real_(real), imag_(imag) {}
+  C10_HOST_DEVICE inline complex(const c10::complex<float>& value)
+      : real_(value.real()), imag_(value.imag()) {}
+
+  // Conversion operator
+  inline C10_HOST_DEVICE operator c10::complex<float>() const {
+    return {real_, imag_};
+  }
+
+  constexpr C10_HOST_DEVICE Half real() const {
+    return real_;
+  }
+  constexpr C10_HOST_DEVICE Half imag() const {
+    return imag_;
+  }
+
+  C10_HOST_DEVICE complex<Half>& operator+=(const complex<Half>& other) {
+    real_ = static_cast<float>(real_) + static_cast<float>(other.real_);
+    imag_ = static_cast<float>(imag_) + static_cast<float>(other.imag_);
+    return *this;
+  }
+
+  C10_HOST_DEVICE complex<Half>& operator-=(const complex<Half>& other) {
+    real_ = static_cast<float>(real_) - static_cast<float>(other.real_);
+    imag_ = static_cast<float>(imag_) - static_cast<float>(other.imag_);
+    return *this;
+  }
+
+  C10_HOST_DEVICE complex<Half>& operator*=(const complex<Half>& other) {
+    auto a = static_cast<float>(real_);
+    auto b = static_cast<float>(imag_);
+    auto c = static_cast<float>(other.real());
+    auto d = static_cast<float>(other.imag());
+    real_ = a * c - b * d;
+    imag_ = a * d + b * c;
+    return *this;
+  }
+};
+
 } // namespace c10
 
 C10_CLANG_DIAGNOSTIC_POP()

torch/csrc/utils/byte_order.cpp

@@ -1,4 +1,5 @@
 #include <c10/util/BFloat16.h>
+#include <c10/util/complex.h>
 #include <c10/util/irange.h>
 #include <torch/csrc/utils/byte_order.h>