[SYCL][COMPAT] Add math extend_v*2 to SYCLCompat (intel#13953)

This PR adds math `extend_v*2` operators _(18 in total)_ along with
unit-tests for signed and unsigned `int32` cases.

---------

Co-authored-by: Alberto Cabrera Pérez <alberto.cabrera@intel.com>
Co-authored-by: Joe Todd <joe.todd@codeplay.com>

sycl/doc/syclcompat/README.md

@@ -1771,7 +1771,7 @@ struct sub_sat {
 } // namespace syclcompat
 ```
 
-Finally, the math header provides a set of functions to extend 32-bit operations
+The math header provides a set of functions to extend 32-bit operations
 to 33 bit, and handle sign extension internally. There is support for `add`,
 `sub`, `absdiff`, `min` and `max` operations. Each operation provides overloads
 to include a second, separate, `BinaryOperation` after the first, and include
@@ -1855,6 +1855,244 @@ inline constexpr RetT extend_max_sat(AT a, BT b, CT c,
                                      BinaryOperation second_op);
 ```
 
+Another set of vectorized extend 32-bit operations is provided in the math 
+header.These APIs treat each of the 32-bit operands as 2-elements vector 
+(16-bits each) while handling sign extension to 17-bits internally. There is 
+support for `add`, `sub`, `absdiff`, `min`, `max` and `avg` binary operations. 
+Each operation provides has a `_sat` variat which determines if the returning 
+value is saturated or not, and a `_add` variant that computes the binary sum 
+of the the initial operation outputs and a third operand. 
+
+```cpp
+/// Compute vectorized addition of \p a and \p b, with each value treated as a
+/// 2 elements vector type and extend each element to 17 bit.
+/// \tparam [in] RetT The type of the return value, can only be 32 bit integer
+/// \tparam [in] AT The type of the first value, can only be 32 bit integer
+/// \tparam [in] BT The type of the second value, can only be 32 bit integer
+/// \param [in] a The first value
+/// \param [in] b The second value
+/// \param [in] c The third value
+/// \returns The extend vectorized addition of the two values
+template <typename RetT, typename AT, typename BT>
+inline constexpr RetT extend_vadd2(AT a, BT b, RetT c);
+
+/// Compute vectorized addition of \p a and \p b, with each value treated as a 2
+/// elements vector type and extend each element to 17 bit. Then add each half
+/// of the result and add with \p c.
+/// \tparam [in] RetT The type of the return value, can only be 32 bit integer
+/// \tparam [in] AT The type of the first value, can only be 32 bit integer
+/// \tparam [in] BT The type of the second value, can only be 32 bit integer
+/// \param [in] a The first value
+/// \param [in] b The second value
+/// \param [in] c The third value
+/// \returns The addition of each half of extend vectorized addition of the two
+/// values and the third value
+template <typename RetT, typename AT, typename BT>
+inline constexpr RetT extend_vadd2_add(AT a, BT b, RetT c);
+
+/// Compute vectorized addition of \p a and \p b with saturation, with each
+/// value treated as a 2 elements vector type and extend each element to 17 bit.
+/// \tparam [in] RetT The type of the return value, can only be 32 bit integer
+/// \tparam [in] AT The type of the first value, can only be 32 bit integer
+/// \tparam [in] BT The type of the second value, can only be 32 bit integer
+/// \param [in] a The first value
+/// \param [in] b The second value
+/// \param [in] c The third value
+/// \returns The extend vectorized addition of the two values with saturation
+template <typename RetT, typename AT, typename BT>
+inline constexpr RetT extend_vadd2_sat(AT a, BT b, RetT c);
+
+/// Compute vectorized subtraction of \p a and \p b, with each value treated as
+/// a 2 elements vector type and extend each element to 17 bit.
+/// \tparam [in] RetT The type of the return value, can only be 32 bit integer
+/// \tparam [in] AT The type of the first value, can only be 32 bit integer
+/// \tparam [in] BT The type of the second value, can only be 32 bit integer
+/// \param [in] a The first value
+/// \param [in] b The second value
+/// \param [in] c The third value
+/// \returns The extend vectorized subtraction of the two values
+template <typename RetT, typename AT, typename BT>
+inline constexpr RetT extend_vsub2(AT a, BT b, RetT c);
+
+/// Compute vectorized subtraction of \p a and \p b, with each value treated as
+/// a 2 elements vector type and extend each element to 17 bit. Then add each
+/// half of the result and add with \p c.
+/// \tparam [in] RetT The type of the return value, can only be 32 bit integer
+/// \tparam [in] AT The type of the first value, can only be 32 bit integer
+/// \tparam [in] BT The type of the second value, can only be 32 bit integer
+/// \param [in] a The first value
+/// \param [in] b The second value
+/// \param [in] c The third value
+/// \returns The addition of each half of extend vectorized subtraction of the
+/// two values and the third value
+template <typename RetT, typename AT, typename BT>
+inline constexpr RetT extend_vsub2_add(AT a, BT b, RetT c);
+
+/// Compute vectorized subtraction of \p a and \p b with saturation, with each
+/// value treated as a 2 elements vector type and extend each element to 17 bit.
+/// \tparam [in] RetT The type of the return value, can only be 32 bit integer
+/// \tparam [in] AT The type of the first value, can only be 32 bit integer
+/// \tparam [in] BT The type of the second value, can only be 32 bit integer
+/// \param [in] a The first value
+/// \param [in] b The second value
+/// \param [in] c The third value
+/// \returns The extend vectorized subtraction of the two values with saturation
+template <typename RetT, typename AT, typename BT>
+inline constexpr RetT extend_vsub2_sat(AT a, BT b, RetT c);
+
+/// Compute vectorized abs_diff of \p a and \p b, with each value treated as a 2
+/// elements vector type and extend each element to 17 bit.
+/// \tparam [in] RetT The type of the return value, can only be 32 bit integer
+/// \tparam [in] AT The type of the first value, can only be 32 bit integer
+/// \tparam [in] BT The type of the second value, can only be 32 bit integer
+/// \param [in] a The first value
+/// \param [in] b The second value
+/// \param [in] c The third value
+/// \returns The extend vectorized abs_diff of the two values
+template <typename RetT, typename AT, typename BT>
+inline constexpr RetT extend_vabsdiff2(AT a, BT b, RetT c);
+
+/// Compute vectorized abs_diff of \p a and \p b, with each value treated as a 2
+/// elements vector type and extend each element to 17 bit. Then add each half
+/// of the result and add with \p c.
+/// \tparam [in] RetT The type of the return value, can only be 32 bit integer
+/// \tparam [in] AT The type of the first value, can only be 32 bit integer
+/// \tparam [in] BT The type of the second value, can only be 32 bit integer
+/// \param [in] a The first value
+/// \param [in] b The second value
+/// \param [in] c The third value
+/// \returns The addition of each half of extend vectorized abs_diff of the
+/// two values and the third value
+template <typename RetT, typename AT, typename BT>
+inline constexpr RetT extend_vabsdiff2_add(AT a, BT b, RetT c);
+
+/// Compute vectorized abs_diff of \p a and \p b with saturation, with each
+/// value treated as a 2 elements vector type and extend each element to 17 bit.
+/// \tparam [in] RetT The type of the return value, can only be 32 bit integer
+/// \tparam [in] AT The type of the first value, can only be 32 bit integer
+/// \tparam [in] BT The type of the second value, can only be 32 bit integer
+/// \param [in] a The first value
+/// \param [in] b The second value
+/// \param [in] c The third value
+/// \returns The extend vectorized abs_diff of the two values with saturation
+template <typename RetT, typename AT, typename BT>
+inline constexpr RetT extend_vabsdiff2_sat(AT a, BT b, RetT c);
+
+/// Compute vectorized minimum of \p a and \p b, with each value treated as a 2
+/// elements vector type and extend each element to 17 bit.
+/// \tparam [in] RetT The type of the return value, can only be 32 bit integer
+/// \tparam [in] AT The type of the first value, can only be 32 bit integer
+/// \tparam [in] BT The type of the second value, can only be 32 bit integer
+/// \param [in] a The first value
+/// \param [in] b The second value
+/// \param [in] c The third value
+/// \returns The extend vectorized minimum of the two values
+template <typename RetT, typename AT, typename BT>
+inline constexpr RetT extend_vmin2(AT a, BT b, RetT c);
+
+/// Compute vectorized minimum of \p a and \p b, with each value treated as a 2
+/// elements vector type and extend each element to 17 bit. Then add each half
+/// of the result and add with \p c.
+/// \tparam [in] RetT The type of the return value, can only be 32 bit integer
+/// \tparam [in] AT The type of the first value, can only be 32 bit integer
+/// \tparam [in] BT The type of the second value, can only be 32 bit integer
+/// \param [in] a The first value
+/// \param [in] b The second value
+/// \param [in] c The third value
+/// \returns The addition of each half of extend vectorized minimum of the
+/// two values and the third value
+template <typename RetT, typename AT, typename BT>
+inline constexpr RetT extend_vmin2_add(AT a, BT b, RetT c);
+
+/// Compute vectorized minimum of \p a and \p b with saturation, with each value
+/// treated as a 2 elements vector type and extend each element to 17 bit.
+/// \tparam [in] RetT The type of the return value, can only be 32 bit integer
+/// \tparam [in] AT The type of the first value, can only be 32 bit integer
+/// \tparam [in] BT The type of the second value, can only be 32 bit integer
+/// \param [in] a The first value
+/// \param [in] b The second value
+/// \param [in] c The third value
+/// \returns The extend vectorized minimum of the two values with saturation
+template <typename RetT, typename AT, typename BT>
+inline constexpr RetT extend_vmin2_sat(AT a, BT b, RetT c);
+
+/// Compute vectorized maximum of \p a and \p b, with each value treated as a 2
+/// elements vector type and extend each element to 17 bit.
+/// \tparam [in] RetT The type of the return value, can only be 32 bit integer
+/// \tparam [in] AT The type of the first value, can only be 32 bit integer
+/// \tparam [in] BT The type of the second value, can only be 32 bit integer
+/// \param [in] a The first value
+/// \param [in] b The second value
+/// \param [in] c The third value
+/// \returns The extend vectorized maximum of the two values
+template <typename RetT, typename AT, typename BT>
+inline constexpr RetT extend_vmax2(AT a, BT b, RetT c);
+
+/// Compute vectorized maximum of \p a and \p b, with each value treated as a 2
+/// elements vector type and extend each element to 17 bit. Then add each half
+/// of the result and add with \p c.
+/// \tparam [in] RetT The type of the return value, can only be 32 bit integer
+/// \tparam [in] AT The type of the first value, can only be 32 bit integer
+/// \tparam [in] BT The type of the second value, can only be 32 bit integer
+/// \param [in] a The first value
+/// \param [in] b The second value
+/// \param [in] c The third value
+/// \returns The addition of each half of extend vectorized maximum of the
+/// two values and the third value
+template <typename RetT, typename AT, typename BT>
+inline constexpr RetT extend_vmax2_add(AT a, BT b, RetT c);
+
+/// Compute vectorized maximum of \p a and \p b with saturation, with each value
+/// treated as a 2 elements vector type and extend each element to 17 bit.
+/// \tparam [in] RetT The type of the return value, can only be 32 bit integer
+/// \tparam [in] AT The type of the first value, can only be 32 bit integer
+/// \tparam [in] BT The type of the second value, can only be 32 bit integer
+/// \param [in] a The first value
+/// \param [in] b The second value
+/// \param [in] c The third value
+/// \returns The extend vectorized maximum of the two values with saturation
+template <typename RetT, typename AT, typename BT>
+inline constexpr RetT extend_vmax2_sat(AT a, BT b, RetT c);
+
+/// Compute vectorized average of \p a and \p b, with each value treated as a 2
+/// elements vector type and extend each element to 17 bit.
+/// \tparam [in] RetT The type of the return value, can only be 32 bit integer
+/// \tparam [in] AT The type of the first value, can only be 32 bit integer
+/// \tparam [in] BT The type of the second value, can only be 32 bit integer
+/// \param [in] a The first value
+/// \param [in] b The second value
+/// \param [in] c The third value
+/// \returns The extend vectorized average of the two values
+template <typename RetT, typename AT, typename BT>
+inline constexpr RetT extend_vavrg2(AT a, BT b, RetT c);
+
+/// Compute vectorized average of \p a and \p b, with each value treated as a 2
+/// elements vector type and extend each element to 17 bit. Then add each half
+/// of the result and add with \p c.
+/// \tparam [in] RetT The type of the return value, can only be 32 bit integer
+/// \tparam [in] AT The type of the first value, can only be 32 bit integer
+/// \tparam [in] BT The type of the second value, can only be 32 bit integer
+/// \param [in] a The first value
+/// \param [in] b The second value
+/// \param [in] c The third value
+/// \returns The addition of each half of extend average maximum of the
+/// two values and the third value
+template <typename RetT, typename AT, typename BT>
+inline constexpr RetT extend_vavrg2_add(AT a, BT b, RetT c);
+
+/// Compute vectorized average of \p a and \p b with saturation, with each value
+/// treated as a 2 elements vector type and extend each element to 17 bit.
+/// \tparam [in] RetT The type of the return value, can only be 32 bit integer
+/// \tparam [in] AT The type of the first value, can only be 32 bit integer
+/// \tparam [in] BT The type of the second value, can only be 32 bit integer
+/// \param [in] a The first value
+/// \param [in] b The second value
+/// \param [in] c The third value
+/// \returns The extend vectorized average of the two values with saturation
+template <typename RetT, typename AT, typename BT>
+inline constexpr RetT extend_vavrg2_sat(AT a, BT b, RetT c);
+```
+
 ## Sample Code
 
 Below is a simple linear algebra sample, which computes `y = mx + b` implemented