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include/ck_tile/core/utility/bit_cast.hpp

@@ -0,0 +1,19 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2024, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck_tile/core/config.hpp"
+
+namespace ck_tile {
+
+template <typename Y, typename X>
+CK_TILE_HOST_DEVICE constexpr Y bit_cast(const X& x)
+{
+    static_assert(__has_builtin(__builtin_bit_cast), "");
+    static_assert(sizeof(X) == sizeof(Y), "Do not support cast between different size of type");
+
+    return __builtin_bit_cast(Y, x);
+}
+
+} // namespace ck_tile

include/ck_tile/core/utility/functional.hpp

@@ -0,0 +1,194 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2024, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck_tile/core/config.hpp"
+#include "ck_tile/core/container/sequence.hpp"
+#include "ck_tile/core/numeric/integer.hpp"
+#include "ck_tile/core/numeric/integral_constant.hpp"
+#include <stdint.h>
+#include <utility>
+
+namespace ck_tile {
+
+namespace detail {
+
+struct swallow
+{
+    template <typename... Ts>
+    CK_TILE_HOST_DEVICE constexpr swallow(Ts&&...)
+    {
+    }
+};
+
+template <class>
+struct static_for_impl;
+
+template <index_t... Is>
+struct static_for_impl<sequence<Is...>>
+{
+    template <class F>
+    CK_TILE_HOST_DEVICE constexpr void operator()(F f) const
+    {
+        swallow{(f(number<Is>{}), 0)...};
+    }
+};
+
+} // namespace detail
+
+// F signature: F(number<Iter>)
+template <index_t NBegin, index_t NEnd, index_t Increment>
+struct static_for
+{
+    CK_TILE_HOST_DEVICE constexpr static_for()
+    {
+        static_assert(Increment != 0 && (NEnd - NBegin) % Increment == 0,
+                      "Wrong! should satisfy (NEnd - NBegin) % Increment == 0");
+        static_assert((Increment > 0 && NBegin <= NEnd) || (Increment < 0 && NBegin >= NEnd),
+                      "wrongs! should (Increment > 0 && NBegin <= NEnd) || (Increment < 0 && "
+                      "NBegin >= NEnd)");
+    }
+
+    template <class F>
+    CK_TILE_HOST_DEVICE constexpr void operator()(F f) const
+    {
+        detail::static_for_impl<typename arithmetic_sequence_gen<NBegin, NEnd, Increment>::type>{}(
+            f);
+    }
+};
+
+struct identity
+{
+    template <typename T>
+    CK_TILE_HOST_DEVICE constexpr T&& operator()(T&& arg) const noexcept
+    {
+        return std::forward<T>(arg);
+    }
+};
+
+namespace detail {
+
+// RemainLengths: sequence<...>
+// Orders: sequence<...>
+template <class RemainLengths, class Orders>
+struct static_ford_impl
+{
+    CK_TILE_HOST_DEVICE constexpr static_ford_impl()
+    {
+        static_assert(RemainLengths::size() > 0, "wrong! should not get here");
+    }
+
+    // F signature: F(sequence<...>)
+    // CurrentOrderedId: sequence<...>
+    template <class F, class CurrentOrderedId>
+    CK_TILE_HOST_DEVICE constexpr void operator()(F f, CurrentOrderedId) const
+    {
+        static_for<0, RemainLengths::front(), 1>{}([=](auto I) {
+            static_ford_impl<decltype(RemainLengths::pop_front()), Orders>{}(
+                f, CurrentOrderedId::push_back(I));
+        });
+    }
+};
+
+template <class Orders>
+struct static_ford_impl<sequence<>, Orders>
+{
+    // F signature: F(sequence<...>)
+    // OrderedId: sequence<...>
+    template <class F, class OrderedId>
+    CK_TILE_HOST_DEVICE constexpr void operator()(F f, OrderedId) const
+    {
+        // retrive unordered Id
+        f(OrderedId::reorder_old_to_new(Orders{}));
+    }
+};
+
+} // namespace detail
+
+// Lengths is sequence<...>, it is the length of each dimension for
+// N-dimensional loop
+// Orders is sequence<...>, it is the order of dimension in which static_ford
+// will loop over each
+// dimension
+template <class Lengths,
+          class Orders = typename arithmetic_sequence_gen<0, Lengths::size(), 1>::type>
+struct static_ford
+{
+    CK_TILE_HOST_DEVICE constexpr static_ford()
+    {
+        static_assert(Lengths::size() > 0, "wrong! Lengths is empty");
+        static_assert(Lengths::size() == Orders::size(), "wrong! inconsistent size");
+    }
+
+    // F signature: F(sequence<...> multi_id)
+    // multi_id is the unordered multi-index
+    template <class F>
+    CK_TILE_HOST_DEVICE constexpr void operator()(F f) const
+    {
+        constexpr auto ordered_lengths = Lengths::reorder_new_to_old(Orders{});
+        detail::static_ford_impl<decltype(ordered_lengths), Orders>{}(f, sequence<>{});
+    }
+};
+
+namespace detail {
+
+template <typename Indices>
+struct unpack_impl;
+
+template <index_t... Is>
+struct unpack_impl<sequence<Is...>>
+{
+    template <typename F, typename X>
+    CK_TILE_HOST_DEVICE constexpr auto operator()(F&& f, X&& x) const
+    {
+#if 0
+        return std::forward<F>(f)(std::forward<X>(x).at(number<Is>{})...);
+#else
+        return std::forward<F>(f)(std::forward<X>(x).template at<Is>()...);
+#endif
+    }
+};
+
+template <typename Seq0, typename Seq1>
+struct unpack2_impl;
+
+// TODO: remove this, after properly implementing unpack that takes any number of containers
+template <index_t... Is, index_t... Js>
+struct unpack2_impl<sequence<Is...>, sequence<Js...>>
+{
+    template <typename F, typename X, typename Y>
+    CK_TILE_HOST_DEVICE constexpr auto operator()(F&& f, X&& x, Y&& y) const
+    {
+#if 0
+        return std::forward<F>(f)(std::forward<X>(x).at(number<Is>{})...,
+                                  std::forward<Y>(y).at(number<Js>{})...);
+#else
+        return std::forward<F>(f)(std::forward<X>(x).template at<Is>()...,
+                                  std::forward<Y>(y).template at<Js>()...);
+#endif
+    }
+};
+
+} // namespace detail
+
+template <typename F, typename X>
+CK_TILE_HOST_DEVICE constexpr auto unpack(F&& f, X&& x)
+{
+    using X_ = remove_reference_t<X>;
+    return detail::unpack_impl<typename arithmetic_sequence_gen<0, X_::size(), 1>::type>{}(
+        std::forward<F>(f), std::forward<X>(x));
+}
+
+// TODO: properly implement unpack that takes any number of containers
+template <typename F, typename X, typename Y>
+CK_TILE_HOST_DEVICE constexpr auto unpack2(F&& f, X&& x, Y&& y)
+{
+    using X_ = remove_reference_t<X>;
+    using Y_ = remove_reference_t<Y>;
+    return detail::unpack2_impl<typename arithmetic_sequence_gen<0, X_::size(), 1>::type,
+                                typename arithmetic_sequence_gen<0, Y_::size(), 1>::type>{}(
+        std::forward<F>(f), std::forward<X>(x), std::forward<Y>(y));
+}
+
+} // namespace ck_tile

include/ck_tile/core/utility/limits.hpp

@@ -0,0 +1,75 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2024, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck_tile/core/config.hpp"
+#include <limits>
+#include <stdint.h>
+
+namespace ck_tile {
+
+template <typename T>
+struct numeric_limits
+{
+    // minimum finite value, or minimum positive normalized value for float
+    CK_TILE_HOST_DEVICE static constexpr T min() { return std::numeric_limits<T>::min(); }
+
+    // minumum finite value
+    CK_TILE_HOST_DEVICE static constexpr T lowest() { return std::numeric_limits<T>::lowest(); }
+
+    // maximum finite value
+    CK_TILE_HOST_DEVICE static constexpr T max() { return std::numeric_limits<T>::max(); }
+
+    // difference between 1.0 and next value representable by float
+    CK_TILE_HOST_DEVICE static constexpr T epsilon() { return std::numeric_limits<T>::epsilon(); }
+
+    // maximum rounding error
+    CK_TILE_HOST_DEVICE static constexpr T round_error()
+    {
+        return std::numeric_limits<T>::round_error();
+    }
+
+    // positive infinity value
+    CK_TILE_HOST_DEVICE static constexpr T infinity() { return std::numeric_limits<T>::infinity(); }
+
+    // quiet NaN
+    CK_TILE_HOST_DEVICE static constexpr T quiet_NaN()
+    {
+        return std::numeric_limits<T>::quiet_NaN();
+    }
+
+    // signaling NaN
+    CK_TILE_HOST_DEVICE static constexpr T signaling_NaN()
+    {
+        return std::numeric_limits<T>::signaling_NaN();
+    }
+
+    // smallest positive subnormal value
+    CK_TILE_HOST_DEVICE static constexpr T denorm_min()
+    {
+        return std::numeric_limits<T>::denorm_min();
+    }
+};
+
+template <typename T>
+struct numeric_utils;
+
+template <>
+struct numeric_utils<float>
+{
+    static constexpr int exp            = 8;
+    static constexpr int mant           = 23;
+    static constexpr int bias           = 127;
+    static constexpr uint32_t nan_mask  = 0x7F800000;
+    static constexpr uint32_t head_mask = 0xFF800000;
+    static constexpr uint32_t mant_mask = 0x7FFFFF;
+    static constexpr uint32_t exp_mask  = 0xFF;
+    static constexpr uint32_t Inf       = 0x7F800000;
+    static constexpr uint32_t NegInf    = 0xFF800000;
+    static constexpr uint32_t NaN       = 0x7F800001;
+    static constexpr uint32_t Neg0      = 0x80000000;
+    using bitwise_type                  = uint32_t;
+};
+
+} // namespace ck_tile

include/ck_tile/core/utility/magic_div.hpp

@@ -0,0 +1,261 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2023, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck_tile/core/config.hpp"
+#include "ck_tile/core/container/tuple.hpp"
+#include "ck_tile/core/numeric/integral_constant.hpp"
+#include "ck_tile/core/utility/bit_cast.hpp"
+#include "ck_tile/core/utility/type_traits.hpp"
+#include <stdint.h>
+
+namespace ck_tile {
+
+// magic number division
+// Caution:
+//   1. For uint32_t as dividend: magic number division implementation being used would produce
+//   correct result if the dividend is uint32_t and its value is within 31-bit value range.
+//   2. For int32_t as dividendd: magic number division for int32_t dividened has not been
+//   implemented, the int32_t dividend would be bit-wise interpreted as uint32_t and magic number
+//   division implementation for uint32_t is then used. Therefore, dividend value need to be
+//   non-negative.
+// TODO:
+//   1. Implement magic number divison for int32_t
+//   2. Implement magic number divison for unit32_t with 32-bit value range
+struct magic_division32_bit_range
+{
+    // uint32_t
+    CK_TILE_HOST_DEVICE static constexpr auto calculate_magic_numbers(uint32_t divisor)
+    {
+        // WARNING: magic division is only valid for division inside this range.
+        // assert(divisor >= 1 && divisor <= INT32_MAX)
+
+        uint32_t shift_u32 = 0;
+
+        while((1U << shift_u32) < divisor)
+        {
+            shift_u32++;
+        };
+
+        uint64_t tmp_u64        = ((1UL << shift_u32) - divisor) << 32;
+        uint32_t multiplier_u32 = tmp_u64 / divisor + 1;
+
+        return make_tuple(multiplier_u32, shift_u32);
+    }
+
+    // integral_constant<uint32_t, .>
+    template <uint32_t Divisor, typename = std::enable_if_t<(0 < Divisor)>>
+    CK_TILE_HOST_DEVICE static constexpr auto
+        calculate_magic_numbers(integral_constant<uint32_t, Divisor>)
+    {
+        constexpr auto tmp = calculate_magic_numbers(uint32_t{Divisor});
+
+        constexpr uint32_t multiplier = tmp[number<0>{}];
+        constexpr uint32_t shift      = tmp[number<1>{}];
+
+        return make_tuple(integral_constant<uint32_t, multiplier>{},
+                          integral_constant<uint32_t, shift>{});
+    }
+
+    // integral_constant<int32_t, .>
+    template <int32_t Divisor>
+    CK_TILE_HOST_DEVICE static constexpr auto
+        calculate_magic_numbers(integral_constant<int32_t, Divisor>)
+    {
+        return calculate_magic_numbers(integral_constant<uint32_t, Divisor>{});
+    }
+
+    // magic division for uint32_t
+    CK_TILE_DEVICE static constexpr uint32_t
+    do_magic_division(uint32_t dividend, uint32_t multiplier, uint32_t shift)
+    {
+        uint32_t tmp = __umulhi(dividend, multiplier);
+        return (tmp + dividend) >> shift;
+    }
+
+    CK_TILE_HOST static constexpr uint32_t
+    do_magic_division(uint32_t dividend, uint32_t multiplier, uint32_t shift)
+    {
+        uint32_t tmp = (static_cast<uint64_t>(dividend) * multiplier) >> 32;
+        return (tmp + dividend) >> shift;
+    }
+
+    // magic division for int32_t
+    // HACK: use dividend_i32 as if it's uint32_t, dividend_i32 need to be
+    // non-negative for result to be correct
+    // TODO: figure out how to do magic number divison for int32_t as dividended
+    CK_TILE_DEVICE static constexpr int32_t
+    do_magic_division(int32_t dividend_i32, uint32_t multiplier, uint32_t shift)
+    {
+        uint32_t dividend_u32 = bit_cast<uint32_t>(dividend_i32);
+        uint32_t tmp          = __umulhi(dividend_u32, multiplier);
+        return (tmp + dividend_u32) >> shift;
+    }
+
+    CK_TILE_HOST static constexpr int32_t
+    do_magic_division(int32_t dividend_i32, uint32_t multiplier, uint32_t shift)
+    {
+        uint32_t dividend_u32 = bit_cast<uint32_t>(dividend_i32);
+        uint32_t tmp          = (static_cast<uint64_t>(dividend_u32) * multiplier) >> 32;
+        return (tmp + dividend_u32) >> shift;
+    }
+};
+
+// magic number division
+// This version on works for divisor and dividended between [0, 1 << 16]
+struct magic_division16_bit_range
+{
+    // uint32_t
+    CK_TILE_HOST_DEVICE static constexpr auto calculate_magic_numbers(uint32_t divisor)
+    {
+        // WARNING: magic division is only valid for division inside this range.
+        // assert(divisor >= 1 && divisor <= (1U << 16));
+
+        uint32_t shift_u32 = 0;
+
+        while((1U << shift_u32) < divisor)
+        {
+            shift_u32++;
+        };
+
+        uint32_t one            = 1;
+        uint32_t multiplier_u32 = ((one << 16) * ((one << shift_u32) - divisor)) / divisor + 1;
+
+        return make_tuple(multiplier_u32, shift_u32);
+    }
+
+    // integral_constant<uint32_t, .>
+    template <uint32_t Divisor>
+    CK_TILE_HOST_DEVICE static constexpr auto
+        calculate_magic_numbers(integral_constant<uint32_t, Divisor>)
+    {
+        constexpr auto tmp = calculate_magic_numbers(uint32_t{Divisor});
+
+        constexpr uint32_t multiplier = tmp[number<0>{}];
+        constexpr uint32_t shift      = tmp[number<1>{}];
+
+        return make_tuple(integral_constant<uint32_t, multiplier>{},
+                          integral_constant<uint32_t, shift>{});
+    }
+
+    // integral_constant<int32_t, .>
+    template <int32_t Divisor>
+    CK_TILE_HOST_DEVICE static constexpr auto
+        calculate_magic_numbers(integral_constant<int32_t, Divisor>)
+    {
+        return calculate_magic_numbers(integral_constant<uint32_t, Divisor>{});
+    }
+
+    // magic division for uint32_t
+    CK_TILE_DEVICE static constexpr uint32_t
+    do_magic_division(uint32_t dividend, uint32_t multiplier, uint32_t shift)
+    {
+        uint32_t tmp = (dividend * multiplier) >> 16;
+        return (tmp + dividend) >> shift;
+    }
+
+    CK_TILE_HOST static constexpr uint32_t
+    do_magic_division(uint32_t dividend, uint32_t multiplier, uint32_t shift)
+    {
+        uint32_t tmp = (dividend * multiplier) >> 16;
+        return (tmp + dividend) >> shift;
+    }
+
+    // magic division for int32_t
+    // HACK: use dividend_i32 as if it's uint32_t, dividend_i32 need to be
+    // non-negative for result to be correct
+    // TODO: figure out how to do magic number divison for int32_t as dividended
+    CK_TILE_DEVICE static constexpr int32_t
+    do_magic_division(int32_t dividend_i32, uint32_t multiplier, uint32_t shift)
+    {
+        uint32_t dividend_u32 = bit_cast<uint32_t>(dividend_i32);
+        uint32_t tmp          = (dividend_u32 * multiplier) >> 16;
+        return (tmp + dividend_u32) >> shift;
+    }
+
+    CK_TILE_HOST static constexpr int32_t
+    do_magic_division(int32_t dividend_i32, uint32_t multiplier, uint32_t shift)
+    {
+        uint32_t dividend_u32 = bit_cast<uint32_t>(dividend_i32);
+        uint32_t tmp          = (dividend_u32 * multiplier) >> 16;
+        return (tmp + dividend_u32) >> shift;
+    }
+};
+
+// use 32bit version
+using magic_division = magic_division32_bit_range;
+
+struct mdiv
+{
+    // 1 dword -> 3 dword storage
+    uint32_t divisor;
+    uint32_t multiplier;
+    uint32_t shift; // TODO: 8 bit is enough
+
+    // prefer construct on host
+    CK_TILE_HOST_DEVICE mdiv(uint32_t divisor_) : divisor(divisor_)
+    {
+        auto tmp = magic_division::calculate_magic_numbers(divisor_);
+
+        multiplier = tmp[number<0>{}];
+        shift      = tmp[number<1>{}];
+    }
+
+    CK_TILE_HOST_DEVICE mdiv() : divisor(0), multiplier(0), shift(0) {}
+
+    CK_TILE_HOST_DEVICE void update(uint32_t divisor_)
+    {
+        divisor  = divisor_;
+        auto tmp = magic_division::calculate_magic_numbers(divisor_);
+
+        multiplier = tmp[number<0>{}];
+        shift      = tmp[number<1>{}];
+    }
+
+    CK_TILE_HOST_DEVICE uint32_t div(uint32_t dividend_) const
+    {
+        return magic_division::do_magic_division(dividend_, multiplier, shift);
+    }
+
+    CK_TILE_HOST_DEVICE void
+    divmod(uint32_t dividend_, uint32_t& quotient_, uint32_t& remainder_) const
+    {
+        quotient_  = div(dividend_);
+        remainder_ = dividend_ - (quotient_ * divisor);
+    }
+
+    CK_TILE_HOST_DEVICE uint32_t get() const { return divisor; }
+};
+
+struct mdiv2
+{
+    // 1 dword -> 2 dword storage, divisor need compute from runtime
+    uint32_t multiplier;
+    uint32_t shift; // TODO: 8 bit is enough
+
+    // prefer construct on host
+    CK_TILE_HOST_DEVICE mdiv2(uint32_t divisor_)
+    {
+        auto tmp = magic_division::calculate_magic_numbers(divisor_);
+
+        multiplier = tmp[number<0>{}];
+        shift      = tmp[number<1>{}];
+    }
+
+    CK_TILE_HOST_DEVICE mdiv2() : multiplier(0), shift(0) {}
+
+    CK_TILE_HOST_DEVICE uint32_t div(uint32_t dividend_) const
+    {
+        return magic_division::do_magic_division(dividend_, multiplier, shift);
+    }
+
+    CK_TILE_HOST_DEVICE void
+    divmod(uint32_t dividend_, uint32_t divisor_, uint32_t& quotient_, uint32_t& remainder_) const
+    {
+        quotient_  = div(dividend_);
+        remainder_ = dividend_ - (quotient_ * divisor_);
+    }
+};
+
+} // namespace ck_tile

include/ck_tile/core/utility/random.hpp

@@ -0,0 +1,64 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2023, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck_tile/core/config.hpp"
+#include "ck_tile/core/numeric/half.hpp"
+#include <stdint.h>
+#include <tuple>
+#include <type_traits>
+
+namespace ck_tile {
+
+// return 0 if data is not fp16 or fp32
+template <typename T, uint32_t seed_>
+struct prand_generator_t
+{
+    CK_TILE_HOST_DEVICE uint32_t operator()(int id, T val, uint32_t seed = seed_)
+    {
+        std::ignore = id;
+        std::ignore = val;
+        std::ignore = seed;
+        return 0;
+    }
+};
+
+// version for fp32
+template <uint32_t seed_>
+struct prand_generator_t<float, seed_>
+{
+    CK_TILE_HOST_DEVICE uint32_t operator()(int id, float val, uint32_t seed = seed_)
+    {
+        uint32_t x         = *(reinterpret_cast<uint32_t*>(&val));
+        uint32_t drop_bits = uint32_t(x) & 0xFFFFu;
+        drop_bits ^= x >> 16;
+        drop_bits = ((drop_bits & 31) << 11) | (drop_bits >> 5);
+        drop_bits *= 0x7000149;
+        // NOTE: If id is in 64 bit, we are only using lower 32 bit.
+        //       So, it can have an effect of using same id for multiple elements when the id is
+        //       very large!
+        uint32_t rng = (drop_bits ^ 0x13371337 ^ (id * 229791) ^ seed);
+        return rng;
+    }
+};
+
+// version for fp16
+template <uint32_t seed_>
+struct prand_generator_t<half_t, seed_>
+{
+    CK_TILE_HOST_DEVICE uint32_t operator()(int id, half_t val, uint32_t seed = seed_)
+    {
+        uint16_t x         = *(reinterpret_cast<uint16_t*>(&val));
+        uint32_t drop_bits = uint32_t(x) & 0xFFFFu;
+        drop_bits          = ((drop_bits & 31) << 11) | (drop_bits >> 5);
+        drop_bits *= 0x7000149;
+        // NOTE: If id is in 64 bit, we are only using lower 32 bit.
+        //       So, it can have an effect of using same id for multiple elements when the id is
+        //       very large!
+        uint32_t rng = (drop_bits ^ 0x13371337 ^ (id * 229791) ^ seed);
+        return rng;
+    }
+};
+
+} // namespace ck_tile

include/ck_tile/core/utility/to_sequence.hpp

@@ -0,0 +1,72 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2024, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+#include "ck_tile/core/container/sequence.hpp"
+// TODO: use c++20 nontype template with struct to implement this
+
+#if 1
+// clang happen to support this feature (__cpp_generic_lambdas >= 201707) in c++17 mode
+#define TO_SEQUENCE(a, n)                                                                      \
+    _Pragma("clang diagnostic push")                                                           \
+        _Pragma("clang diagnostic ignored \"-Wc++20-extensions\"")[a]<ck_tile::index_t... Is>( \
+            ck_tile::sequence<Is...>)                                                          \
+    {                                                                                          \
+        return ck_tile::sequence<a.at(ck_tile::number<Is>{})...>{};                            \
+    }                                                                                          \
+    (make_index_sequence<n>{}) _Pragma("clang diagnostic pop")
+
+#else
+// Macro function
+// convert constexpr array to sequence, both a/n need to be constexpr (can't be a rvalue like 2)
+#define TO_SEQUENCE(a, n)                                                                     \
+    [a, n] {                                                                                  \
+        static_assert(a.size() >= n, "wrong! out of bound");                                  \
+        static_assert(n <= 10, "not implemented");                                            \
+        if constexpr(n == 0)                                                                  \
+        {                                                                                     \
+            return ck_tile::sequence<>{};                                                     \
+        }                                                                                     \
+        else if constexpr(n == 1)                                                             \
+        {                                                                                     \
+            return ck_tile::sequence<a[0]>{};                                                 \
+        }                                                                                     \
+        else if constexpr(n == 2)                                                             \
+        {                                                                                     \
+            return ck_tile::sequence<a[0], a[1]>{};                                           \
+        }                                                                                     \
+        else if constexpr(n == 3)                                                             \
+        {                                                                                     \
+            return ck_tile::sequence<a[0], a[1], a[2]>{};                                     \
+        }                                                                                     \
+        else if constexpr(n == 4)                                                             \
+        {                                                                                     \
+            return ck_tile::sequence<a[0], a[1], a[2], a[3]>{};                               \
+        }                                                                                     \
+        else if constexpr(n == 5)                                                             \
+        {                                                                                     \
+            return ck_tile::sequence<a[0], a[1], a[2], a[3], a[4]>{};                         \
+        }                                                                                     \
+        else if constexpr(n == 6)                                                             \
+        {                                                                                     \
+            return ck_tile::sequence<a[0], a[1], a[2], a[3], a[4], a[5]>{};                   \
+        }                                                                                     \
+        else if constexpr(n == 7)                                                             \
+        {                                                                                     \
+            return ck_tile::sequence<a[0], a[1], a[2], a[3], a[4], a[5], a[6]>{};             \
+        }                                                                                     \
+        else if constexpr(n == 8)                                                             \
+        {                                                                                     \
+            return ck_tile::sequence<a[0], a[1], a[2], a[3], a[4], a[5], a[6], a[7]>{};       \
+        }                                                                                     \
+        else if constexpr(n == 9)                                                             \
+        {                                                                                     \
+            return ck_tile::sequence<a[0], a[1], a[2], a[3], a[4], a[5], a[6], a[7], a[8]>{}; \
+        }                                                                                     \
+        else if constexpr(n == 10)                                                            \
+        {                                                                                     \
+            return ck_tile::                                                                  \
+                sequence<a[0], a[1], a[2], a[3], a[4], a[5], a[6], a[7], a[8], a[9]>{};       \
+        }                                                                                     \
+    }()
+#endif

include/ck_tile/core/utility/type_convert.hpp

@@ -0,0 +1,57 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2023, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include <stdint.h>
+#include <tuple>
+#include <type_traits>
+#include "ck_tile/core/config.hpp"
+#include "ck_tile/core/numeric/half.hpp"
+#include "ck_tile/core/numeric/bfloat16.hpp"
+#include "ck_tile/core/numeric/float8.hpp"
+
+namespace ck_tile {
+
+// Convert X to Y, both X and Y are non-const data types.
+template <typename Y,
+          typename X,
+          std::enable_if_t<!(std::is_const_v<Y> || std::is_const_v<X>), bool> = false>
+CK_TILE_HOST_DEVICE constexpr Y type_convert(X x)
+{
+    static_assert(!std::is_reference_v<Y> && !std::is_reference_v<X>);
+
+    return static_cast<Y>(x);
+}
+
+// Convert X to Y, either X or Y is a const data type.
+template <typename Y,
+          typename X,
+          std::enable_if_t<std::is_const_v<Y> || std::is_const_v<X>, bool> = false>
+CK_TILE_HOST_DEVICE constexpr Y type_convert(X x)
+{
+    static_assert(!std::is_reference_v<Y> && !std::is_reference_v<X>);
+
+    using non_const_y = std::remove_const_t<Y>;
+    using non_const_x = std::remove_const_t<X>;
+    return static_cast<Y>(type_convert<non_const_y, non_const_x>(x));
+}
+
+#define CK_TILE_TYPE_CONVERT(dtype_, stype_)                                           \
+    template <>                                                                        \
+    inline CK_TILE_HOST_DEVICE constexpr dtype_ type_convert<dtype_, stype_>(stype_ x) \
+    {                                                                                  \
+        return stype_##_to_##dtype_(x);                                                \
+    }
+
+CK_TILE_TYPE_CONVERT(float, fp16_t)
+CK_TILE_TYPE_CONVERT(float, bf16_t)
+CK_TILE_TYPE_CONVERT(float, fp8_t)
+CK_TILE_TYPE_CONVERT(float, bf8_t)
+
+CK_TILE_TYPE_CONVERT(fp16_t, float)
+CK_TILE_TYPE_CONVERT(bf16_t, float)
+CK_TILE_TYPE_CONVERT(fp8_t, float)
+CK_TILE_TYPE_CONVERT(bf8_t, float)
+
+} // namespace ck_tile

include/ck_tile/core/utility/type_traits.hpp

@@ -0,0 +1,46 @@
+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2024, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck_tile/core/config.hpp"
+#include <type_traits>
+#include <stdint.h>
+
+namespace ck_tile {
+
+// remove_cvref_t
+template <typename T>
+using remove_reference_t = typename std::remove_reference<T>::type;
+
+template <typename T>
+using remove_cv_t = typename std::remove_cv<T>::type;
+
+template <typename T>
+using remove_cvref_t = remove_cv_t<std::remove_reference_t<T>>;
+
+template <typename T>
+using remove_pointer_t = typename std::remove_pointer<T>::type;
+
+namespace impl {
+template <typename T>
+struct is_static_impl
+{
+    static constexpr bool value = std::is_arithmetic<T>::v ? false : T::is_static();
+};
+} // namespace impl
+
+template <typename T>
+using is_static = impl::is_static_impl<remove_cvref_t<T>>;
+
+template <typename T>
+inline constexpr bool is_static_v = is_static<T>::value;
+
+// TODO: deprecate this
+template <typename T>
+using is_known_at_compile_time = is_static<T>;
+// TODO: if evaluating a rvalue, e.g. a const integer
+// , this helper will also return false, which is not good(?)
+//       do we need something like is_constexpr()?
+
+} // namespace ck_tile