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/**
* @file
* @brief Basic operations on generic types.
*/
#pragma once
#include <cuda_bf16.h>
#include <limits>
#include "base_types.cuh"
namespace kittens {
/**
* @namespace base_ops
*
* @brief A namespace for operations on basic data types.
*/
namespace base_ops {
/* ---------- CONST OPS ---------- */
/**
* @brief Represents the zero constant operation.
*
* This operation returns the zero value of the specified type.
*
* @tparam T The data type for which to return the zero value.
* @return The zero value of type T.
*/
struct zero {
template<typename T, typename... args> __device__ static inline constexpr T op(args... _) { return base_types::constants<T>::zero(); }
};
/**
* @brief Represents the one constant operation.
*
* This operation returns the one value of the specified type.
*
* @tparam T The data type for which to return the one value.
* @return The one value of type T.
*/
struct one {
template<typename T, typename... args> __device__ static inline constexpr T op(args... _) { return base_types::constants<T>::one(); }
};
/**
* @brief Represents the positive infinity constant operation.
*
* This operation returns the positive infinity value of the specified type.
*
* @tparam T The data type for which to return the positive infinity value.
* @return The positive infinity value of type T.
*/
struct pos_infty {
template<typename T, typename... args> __device__ static inline constexpr T op(args... _) { return base_types::constants<T>::pos_infty(); }
};
/**
* @brief Represents the negative infinity constant operation.
*
* This operation returns the negative infinity value of the specified type.
*
* @tparam T The data type for which to return the negative infinity value.
* @return The negative infinity value of type T.
*/
struct neg_infty {
template<typename T, typename... args> __device__ static inline constexpr T op(args... _) { return base_types::constants<T>::neg_infty(); }
};
/* ---------- UNARY OPS ---------- */
/**
* @brief Exponential function operation.
*
* This operation calculates the exponential of the input value.
*
* @tparam T The data type of the input and output values.
* @param x[in] The input value.
* @return The exponential of the input value.
*/
struct exp {
template<typename T> static __device__ inline T op(const T &x) { return exp(x); }
};
template<> __device__ inline float exp::op<float> (const float &x ) { return __expf(x); }
template<> __device__ inline float2 exp::op<float2>(const float2 &x) { return float2{__expf(x.x), __expf(x.y)}; }
template<> __device__ inline bf16 exp::op<bf16> (const bf16 &x ) { return hexp(x); }
template<> __device__ inline bf16_2 exp::op<bf16_2>(const bf16_2 &x) { return h2exp(x); }
template<> __device__ inline half exp::op<half> (const half &x ) { return hexp(x); }
template<> __device__ inline half_2 exp::op<half_2>(const half_2 &x) { return h2exp(x); }
/**
* @brief Exponential function operation, in base 2
*
* This operation calculates the exponential of the input value, in base 2.
*
* @tparam T The data type of the input and output values.
* @param x[in] The input value.
* @return The exponential of the input value.
*/
struct exp2 {
template<typename T> static __device__ inline T op(const T &x) { return exp2f(x); }
};
template<> __device__ inline float exp2::op<float> (const float &x ) { return exp2f(x); }
template<> __device__ inline float2 exp2::op<float2>(const float2 &x) { return float2{exp2f(x.x), exp2f(x.y)}; }
template<> __device__ inline bf16 exp2::op<bf16> (const bf16 &x ) { return hexp2(x); }
template<> __device__ inline bf16_2 exp2::op<bf16_2>(const bf16_2 &x) { return h2exp2(x); }
template<> __device__ inline half exp2::op<half> (const half &x ) { return hexp2(x); }
template<> __device__ inline half_2 exp2::op<half_2>(const half_2 &x) { return h2exp2(x); }
/**
* @brief Natural log function operation.
*
* This operation calculates the natural logarithm of the input value.
*
* @tparam T The data type of the input and output values.
* @param x[in] The input value.
* @return The natural logarithm of the input value.
*/
struct log {
template<typename T> static __device__ inline T op(const T &x) { return log(x); }
};
template<> __device__ inline float log::op<float> (const float &x ) { return __logf(x); }
template<> __device__ inline float2 log::op<float2>(const float2 &x) { return float2{__logf(x.x), __logf(x.y)}; }
template<> __device__ inline bf16 log::op<bf16> (const bf16 &x ) { return hlog(x); }
template<> __device__ inline bf16_2 log::op<bf16_2>(const bf16_2 &x) { return h2log(x); }
template<> __device__ inline half log::op<half> (const half &x ) { return hlog(x); }
template<> __device__ inline half_2 log::op<half_2>(const half_2 &x) { return h2log(x); }
/**
* @brief Logarithm base 2 operation.
*
* This operation calculates the logarithm base 2 of the input value.
*
* @tparam T The data type of the input and output values.
* @param x[in] The input value.
* @return The logarithm base 2 of the input value.
*/
struct log2 {
template<typename T> static __device__ inline T op(const T &x) { return log2(x); }
};
template<> __device__ inline float log2::op<float> (const float &x ) { return __log2f(x); }
template<> __device__ inline float2 log2::op<float2>(const float2 &x) { return float2{__log2f(x.x), __log2f(x.y)}; }
template<> __device__ inline bf16 log2::op<bf16> (const bf16 &x ) { return hlog2(x); }
template<> __device__ inline bf16_2 log2::op<bf16_2>(const bf16_2 &x) { return h2log2(x); }
template<> __device__ inline half log2::op<half> (const half &x ) { return hlog2(x); }
template<> __device__ inline half_2 log2::op<half_2>(const half_2 &x) { return h2log2(x); }
/**
* @brief Absolute value operation.
*
* This operation calculates the absolute value of the input.
*
* @tparam T The data type of the input and output values.
* @param x[in] The input value.
* @return The absolute value of the input.
*/
struct abs {
template<typename T> static __device__ inline T op(const T &x) { return abs(x); }
};
template<> __device__ inline float abs::op<float> (const float &x ) { return fabsf(x); }
template<> __device__ inline float2 abs::op<float2>(const float2 &x) { return float2{fabsf(x.x), fabsf(x.y)}; }
template<> __device__ inline bf16 abs::op<bf16> (const bf16 &x ) { return __habs(x); }
template<> __device__ inline bf16_2 abs::op<bf16_2>(const bf16_2 &x) { return __habs2(x); }
template<> __device__ inline half abs::op<half> (const half &x ) { return __habs(x); }
template<> __device__ inline half_2 abs::op<half_2>(const half_2 &x) { return __habs2(x); }
/**
* @brief Rectified Linear Unit (ReLU) operation.
*
* This operation applies the ReLU function to the input, which is the
* maximum of zero and the input value.
*
* @tparam T The data type of the input and output values.
* @param x[in] The input value.
* @return The result of ReLU function applied to the input.
*/
struct relu {
template<typename T> static __device__ inline T op(const T &x) { return max(x, base_types::constants<T>::zero()); }
};
template<> __device__ inline float relu::op<float> (const float &x ) { return max(x, 0.f); }
template<> __device__ inline float2 relu::op<float2>(const float2 &x) { return float2{max(x.x, 0.f), max(x.y, 0.f)}; }
template<> __device__ inline bf16 relu::op<bf16> (const bf16 &x ) { return __hmax(x, base_types::constants<bf16>::zero()); }
template<> __device__ inline bf16_2 relu::op<bf16_2>(const bf16_2 &x) { return __hmax2(x, base_types::constants<bf16_2>::zero()); }
template<> __device__ inline half relu::op<half> (const half &x ) { return __hmax(x, base_types::constants<half>::zero()); }
template<> __device__ inline half_2 relu::op<half_2>(const half_2 &x) { return __hmax2(x, base_types::constants<half_2>::zero()); }
/**
* @brief Copy operation.
*
* This operation returns the input value unchanged.
*
* @tparam T The data type of the input and output values.
* @param a[in] The input value.
* @return The same value as the input.
*/
struct copy { // for non-compile-time setters.
template<typename T> static __device__ inline T op(const T &a) { return a; }
};
/* ---------- BINARY OPS ---------- */
/**
* @brief Copy2 operation.
*
* This operation returns the second input value unchanged.
*
* @tparam T The data type of the input and output values.
* @param a[in] The first input value (ignored).
* @param b[in] The second input value.
* @return The same value as the second input.
*/
struct copy2 { // this turns out to be a slightly hacky op that makes some code cleaner :/
template<typename T> static __device__ inline T op(const T &a, const T &b) { return b; }
};
/**
* @brief Sum operation.
*
* This operation calculates the sum of two input values.
*
* @tparam T The data type of the input and output values.
* @param a[in] The first input value.
* @param b[in] The second input value.
* @return The sum of the input values.
*/
struct sum {
template<typename T> static __device__ inline T op(const T &a, const T &b) { return a+b; }
};
template<> __device__ inline float2 sum::op<float2>(const float2 &a, const float2 &b) {
#ifdef KITTENS_BLACKWELL
float2 c;
asm volatile("add.f32x2 %0, %1, %2;" : "=l"(*(uint64_t*)&c) : "l"(*(uint64_t*)&a), "l"(*(uint64_t*)&b));
return c;
#else
return float2{a.x+b.x, a.y+b.y};
#endif
}
template<> __device__ inline bf16 sum::op<bf16> (const bf16 &a, const bf16 &b) { return __hadd(a, b); }
template<> __device__ inline bf16_2 sum::op<bf16_2>(const bf16_2 &a, const bf16_2 &b) { return __hadd2(a, b); }
template<> __device__ inline half sum::op<half> (const half &a, const half &b) { return __hadd(a, b); }
template<> __device__ inline half_2 sum::op<half_2>(const half_2 &a, const half_2 &b) { return __hadd2(a, b); }
/**
* @brief Subtraction operation.
*
* This operation calculates the difference between two input values.
*
* @tparam T The data type of the input and output values.
* @param a[in] The first input value.
* @param b[in] The second input value.
* @return The difference between the input values.
*/
struct sub {
template<typename T> static __device__ inline T op(const T &a, const T &b) { return a-b; }
};
template<> __device__ inline float2 sub::op<float2>(const float2 &a, const float2 &b) {
#ifdef KITTENS_BLACKWELL
float2 c;
asm volatile("sub.f32x2 %0, %1, %2;" : "=l"(*(uint64_t*)&c) : "l"(*(uint64_t*)&a), "l"(*(uint64_t*)&b));
return c;
#else
return float2{a.x-b.x, a.y-b.y};
#endif
}
template<> __device__ inline bf16 sub::op<bf16> (const bf16 &a, const bf16 &b) { return __hsub(a, b); }
template<> __device__ inline bf16_2 sub::op<bf16_2>(const bf16_2 &a, const bf16_2 &b) { return __hsub2(a, b); }
template<> __device__ inline half sub::op<half> (const half &a, const half &b) { return __hsub(a, b); }
template<> __device__ inline half_2 sub::op<half_2>(const half_2 &a, const half_2 &b) { return __hsub2(a, b); }
/**
* @brief Multiplication operation.
*
* This operation calculates the product of two input values.
*
* @tparam T The data type of the input and output values.
* @param a[in] The first input value.
* @param b[in] The second input value.
* @return The product of the input values.
*/
struct mul {
template<typename T> static __device__ inline T op(const T &a, const T &b) { return a*b; }
};
template<> __device__ inline float2 mul::op<float2>(const float2 &a, const float2 &b) {
#ifdef KITTENS_BLACKWELL
float2 c;
asm volatile("mul.f32x2 %0, %1, %2;" : "=l"(*(uint64_t*)&c) : "l"(*(uint64_t*)&a), "l"(*(uint64_t*)&b));
return c;
#else
return float2{a.x*b.x, a.y*b.y};
#endif
}
template<> __device__ inline bf16 mul::op<bf16> (const bf16 &a, const bf16 &b) { return __hmul(a, b); }
template<> __device__ inline bf16_2 mul::op<bf16_2>(const bf16_2 &a, const bf16_2 &b) { return __hmul2(a, b); }
template<> __device__ inline half mul::op<half> (const half &a, const half &b) { return __hmul(a, b); }
template<> __device__ inline half_2 mul::op<half_2>(const half_2 &a, const half_2 &b) { return __hmul2(a, b); }
/**
* @brief Division operation.
*
* This operation calculates the quotient of two input values.
*
* @tparam T The data type of the input and output values.
* @param a[in] The first input value.
* @param b[in] The second input value.
* @return The quotient of the input values.
*/
struct div {
template<typename T> static __device__ inline T op(const T &a, const T &b) { return a/b; }
};
template<> __device__ inline float2 div::op<float2>(const float2 &a, const float2 &b) { return float2{a.x/b.x, a.y/b.y}; }
template<> __device__ inline bf16 div::op<bf16> (const bf16 &a, const bf16 &b) { return __hdiv(a, b); }
template<> __device__ inline bf16_2 div::op<bf16_2>(const bf16_2 &a, const bf16_2 &b) { return __h2div(a, b); } // this op is a special snowflake
template<> __device__ inline half div::op<half> (const half &a, const half &b) { return __hdiv(a, b); }
template<> __device__ inline half_2 div::op<half_2>(const half_2 &a, const half_2 &b) { return __h2div(a, b); }
/**
* @brief Maximum operation.
*
* This operation calculates the maximum of two input values.
*
* @tparam T The data type of the input and output values.
* @param a[in] The first input value.
* @param b[in] The second input value.
* @return The maximum of the input values.
*/
struct max {
template<typename T> static __device__ inline T op(const T &a, const T &b) { return ::max(a, b); }
};
template<> __device__ inline float2 max::op<float2>(const float2 &a, const float2 &b) { return float2{::max(a.x, b.x), ::max(a.y, b.y)}; }
template<> __device__ inline bf16 max::op<bf16> (const bf16 &a, const bf16 &b) { return __hmax(a, b); }
template<> __device__ inline bf16_2 max::op<bf16_2>(const bf16_2 &a, const bf16_2 &b) { return __hmax2(a, b); }
template<> __device__ inline half max::op<half> (const half &a, const half &b) { return __hmax(a, b); }
template<> __device__ inline half_2 max::op<half_2>(const half_2 &a, const half_2 &b) { return __hmax2(a, b); }
/**
* @brief Minimum operation.
*
* This operation calculates the minimum of two input values.
*
* @tparam T The data type of the input and output values.
* @param a[in] The first input value.
* @param b[in] The second input value.
* @return The minimum of the input values.
*/
struct min {
template<typename T> static __device__ inline T op(const T &a, const T &b) { return ::min(a, b); }
};
template<> __device__ inline float2 min::op<float2>(const float2 &a, const float2 &b) { return float2{::min(a.x, b.x), ::min(a.y, b.y)}; }
template<> __device__ inline bf16 min::op<bf16> (const bf16 &a, const bf16 &b) { return __hmin(a, b); }
template<> __device__ inline bf16_2 min::op<bf16_2>(const bf16_2 &a, const bf16_2 &b) { return __hmin2(a, b); }
template<> __device__ inline half min::op<half> (const half &a, const half &b) { return __hmin(a, b); }
template<> __device__ inline half_2 min::op<half_2>(const half_2 &a, const half_2 &b) { return __hmin2(a, b); }
/* ---------- TERNARY OPS ---------- */
/**
* @brief Fused multiply-add operation A * B + C.
*
* This operation performs a fused multiply-add, computing (A * B) + C with only one rounding.
*
* @tparam T The data type of the input and output values.
* @param a[in] The first input value.
* @param b[in] The second input value.
* @param c[in] The third input value to be added.
* @return The result of the fused multiply-add operation.
*/
struct fma_AxBtC {
template<typename T> static __device__ inline T op(const T &a, const T &b, const T &c) {
return sum::op<T>(mul::op<T>(a, b), c);
}
};
template<> __device__ inline float2 fma_AxBtC::op<float2>(const float2 &a, const float2 &b, const float2 &c) {
#ifdef KITTENS_BLACKWELL
float2 d;
asm volatile("fma.rn.f32x2 %0, %1, %2, %3;" : "=l"(*(uint64_t*)&d) : "l"(*(uint64_t*)&a), "l"(*(uint64_t*)&b), "l"(*(uint64_t*)&c));
return d;
#else
return float2{a.x*b.x+c.x, a.y*b.y+c.y};
#endif
}
/**
* @brief Fused multiply-add operation A * C + B.
*
* This operation performs a fused multiply-add, computing (A * C) + B with only one rounding.
* This is particularly useful for attention mechanisms in neural networks.
*
* @tparam T The data type of the input and output values.
* @param a[in] The first input value.
* @param b[in] The third input value to be added.
* @param c[in] The second input value.
* @return The result of the fused multiply-add operation.
*/
struct fma_AxCtB { // this is the one needed for attention
template<typename T> static __device__ inline T op(const T &a, const T &b, const T &c) {
return sum::op<T>(mul::op<T>(a, c), b);
}
};
template<> __device__ inline float2 fma_AxCtB::op<float2>(const float2 &a, const float2 &b, const float2 &c) {
#ifdef KITTENS_BLACKWELL
float2 d;
asm volatile("fma.rn.f32x2 %0, %1, %2, %3;" : "=l"(*(uint64_t*)&d) : "l"(*(uint64_t*)&a), "l"(*(uint64_t*)&c), "l"(*(uint64_t*)&b));
return d;
#else
return float2{a.x*c.x+b.x, a.y*c.y+b.y};
#endif
}
} // namespace base_ops
} // namespace kittens