From ef317f20689409f54bdc6706a6b72cf84a070596 Mon Sep 17 00:00:00 2001 From: Yury Katkov Date: Wed, 4 Sep 2024 19:47:26 +0300 Subject: [PATCH] [NeoML] JIT readme (#566) * Add readme for JIT. Signed-off-by: Yury Katkov * [NeoMathEngineAvx] Add JIT.en.md docs Signed-off-by: Kirill Golikov * [NeoMathEngineAvx] Update JIT.md Signed-off-by: Kirill Golikov --------- Signed-off-by: Yury Katkov Signed-off-by: Kirill Golikov Co-authored-by: Kirill Golikov --- .../src/CPU/x86/avx/src/docs/JIT.en.md | 270 ++++++++++++++++++ .../src/CPU/x86/avx/src/docs/JIT.ru.md | 255 +++++++++++++++++ .../src/CPU/x86/avx/src/docs/RestOfLstm.pdf | Bin 0 -> 290595 bytes 3 files changed, 525 insertions(+) create mode 100644 NeoMathEngine/src/CPU/x86/avx/src/docs/JIT.en.md create mode 100644 NeoMathEngine/src/CPU/x86/avx/src/docs/JIT.ru.md create mode 100644 NeoMathEngine/src/CPU/x86/avx/src/docs/RestOfLstm.pdf diff --git a/NeoMathEngine/src/CPU/x86/avx/src/docs/JIT.en.md b/NeoMathEngine/src/CPU/x86/avx/src/docs/JIT.en.md new file mode 100644 index 000000000..677116227 --- /dev/null +++ b/NeoMathEngine/src/CPU/x86/avx/src/docs/JIT.en.md @@ -0,0 +1,270 @@ +# NeoMathEngineAvx Module + +## Introduction +The NeoMathEngineAvx module is designed to accelerate certain NeoML methods by implementing them using the AVX/AVX2/FMA instruction sets. +This allows the code to run on relatively older x86_64 processors (Haswell and newer) as well as AMD processors that support the corresponding instruction sets. + +Currently, the module implements 3 main subsystems: direct convolution, matrix multiplication kernels, and a set of various primitives used in neural networks. + +The matrix multiplication kernels are written using intrinsic calls for use in the `CMatrixMultiplier` class. +According to benchmarks, matrix multiplication with these kernels performs better than MKL on AMD processors but generally lags behind MKL on Intel processors, even with the same AVX/AVX2/FMA instruction set. + +Direct convolution and primitives are implemented using the OpenSource library [xbyak](https://github.com/herumi/xbyak). +This library enables the generation of machine instructions at runtime, so we will refer to this technology as the **JIT compiler** or simply **JIT**. +One of the notable features of `xbyak` is its straightforward API, which allows writing code that closely resembles Intel assembly syntax. +The main advantages of the JIT compiler are the minimization of conditional jumps, the calculation of all offsets, and the substitution of constant values at the JIT code compilation stage, as well as loop unrolling for better pipeline code prefetching. + +## Module Descriptions + +### Matrix Multiplication Kernels +This part is pure C++ and does not need further description in this document. + +### Forward Convolution +Originally, this module was written using intrinsic calls but was later transitioned to JIT. +However, the implementation as a template class remained, although it is no longer necessary because template parameters do not affect the JIT code generation time, and templates are no longer needed after code generation. +*In the future, it would be beneficial to remove template parameters from the class to simplify the code.* + +JIT code for **Forward Convolution** is generated separately for each descriptor, as it depends on various descriptor parameters. +This is one of those cases where acceleration is achieved partly through the use of pre-known constants and offsets in the instructions. +The functionality of this module was previously described for intrinsic implementations, and the JIT version has not fundamentally changed the core logic. + +The workings of JIT will be discussed in the next section. + +### Primitives +JIT is a very unconventional way of writing code: on one hand, you write the logic of the JIT compiler in C++, benefiting from all the advantages and new features of the language; +on the other hand, you write code that is similar to assembly language, resulting in compact and relatively optimized code (though not always readable for an unprepared programmer). +Most importantly, you write code knowing the conditions under which it will run: how many times, with which variables/constants, etc., thus enabling you to achieve maximum performance. +These 3 aspects help in significantly improving performance. + +### Preparation and Reference Materials +1. Start by familiarizing yourself with the basics of Assembler language and Intel syntax. +2. Read the documentation on [xbyak](https://github.com/herumi/xbyak); it is quite concise and well-structured with examples. +3. For documentation on assembly instructions, I mainly used the following sites: + * [x86 and amd64 instruction reference](https://www.felixcloutier.com/x86/index.html) + * [Intel® Intrinsics Guide](https://www.intel.com/content/www/us/en/docs/intrinsics-guide/index.html) + * [X86-64_Instruction_Encoding](https://wiki.osdev.org/X86-64_Instruction_Encoding) - useful for understanding addressing modes in command formation. + +That should cover everything needed for confident work with `xbyak`. + +### Issues or peculiarities encountered when using xbyak +I believe this section should be placed BEFORE the description of working with `xbyak`. + +1. **Mixing AVX and SSE Instructions:** + During execution, mixing AVX and SSE instructions can cause significant performance degradation due to potential reloading of the SIMD instruction module. + More details on this can be found in the [Intel® 64 and IA - 32 Architectures Optimization Reference Manual](https://www.intel.com/content/dam/www/public/us/en/documents/manuals/64-ia-32-architectures-optimization-manual.pdf), + Section 11.3 **MIXING AVX CODE WITH SSE CODE**: *Assembly/Compiler Coding Rule 72. (H impact, H generality) Add the VZEROUPPER instruction after 256-bit AVX instructions are executed and before any function call that might execute SSE code.* + *Add VZEROUPPER at the end of any function that uses 256-bit AVX instructions.* + +2. **Error Checking in xbyak:** + `xbyak` has the beneficial feature of making it very difficult to form incorrect instructions. Inside function calls, there are numerous checks to prevent the use of incorrect operands in instructions. + +3. **Challenges with Prefetch Instructions:** + Gaining performance improvements from using prefetch instructions is challenging. + This is because modern processors have very effective hardware implementations for memory access pattern recognition and automatically prefetch necessary blocks. + +### Description of the `CPrimitivesJit` class + +#### General Information +The class interface implements 2 mechanisms for calling primitive functions: +1. Directly invoking the method (JIT implementation of the LSTM network), +2. Obtaining a pointer to a specific primitive (allows for seamless replacement of primitive calls in the `CCpuMathEngine` class). + +The greatest performance gains can be achieved for computation-intensive operations. +For this reason, simple primitives often show unstable performance compared to SSE intrinsic implementations, as memory access time, particularly cache misses, can cause significant performance variability. + +### Container `gens` holding JIT code for primitive functions +All implemented JIT functions are listed in the `TPrimitive` enum. +The class defines a `CGenerator` structure, which essentially is an instance of the `Xbyak::CodeGenerator` class responsible for generating JIT code. +The **`gens`** array stores all generated JIT primitives, and their generation occurs upon the first access to a particular primitive in the `GetFunctionRawPtr()` method. + +### Constants Table +The constants table is defined using **`TTableKey`** keys and two containers: **`table`** and **`tableOffsets`**. +This table allows for centralized storage of all constants needed for executing JIT code and provides easy access to them. +Since it is not possible to directly set the initializing value of `ymm` registers in instruction code, they must be loaded from memory. +Centralizing all constants in one place benefits cache performance. + +The constants table is initialized once in the `CPrimitivesJit` constructor by calling the `initTable` method. +In each JIT function, the address of the constants table (if used) is located in the `regTablePtr` register (**`r10`**). +The address for initializing `ymm` registers can be obtained using the `getOfft` or `getAddr` methods, passing the necessary offsets. +The `getAddr` method returns the direct address descriptor `Xbyak::Address`, which implements relative addressing (relative to the `regTablePtr` register). + +### Structure of Primitive Functions +JIT primitives are created in the template method `initPrimitive`, which +* either directly contains the JIT function generation code +* or serves as a wrapper for another template method with the name `init...`, which generalizes the implementation of similar functions (typically basic mathematical primitives). + +Nevertheless, the following essential steps can be highlighted: +* **Creating an instance of the `CGenerator` class**: + - This is used for generating JIT code. +* **Defining registers that need to be preserved before executing the function `preservedReg64` and `preservedYmm`**: + - For Windows and Unix, these are different sets of registers; more details can be found in the calling conventions for the specific OS. +* **Calling the mandatory `Prologue` method**: + - This method adds the necessary prologue for any function, saves the required registers on the stack, and calculates the address descriptor pointing to the stack area containing the function arguments (if any). +* **Defining registers used inside the function and their initialization**: + - Initialization either from registers or from stack values, it is also important to understand the calling convention here. + For example, Windows passes only 4 arguments through registers, while Unix passes 6. + Additionally, if arguments are multiplied by floating-point values, they would stored in different `xmm` registers in Windows and Unix. + If there are more function arguments than the allocated registers, the remaining arguments are passed via the stack. + Windows also has a `ShadowSpace` concept: 32-byte reserved area on the stack before the arguments. +* **Implementing a lambda function**: + - This lambda performs the core computational operations for the primitive. +* **Batch processing input data with loop unrolling:** + - The lambda function from the previous step is applied to it. + The number of elements that can be unrolled in one loop iteration is determined by the number of `ymm` registers involved and the number of elements in typical use cases. + For complex primitives like `Exp`, `Sigmoid`, `Tanh`, and `RestOfLstm`, which use many `ymm` registers, no more than 2 values are processed at a time. +* **Handling tail of input data**: + - If the length of the input data is not a multiple of 8, tail values are processed separately. + Tail handling differs only in that data reading and writing are performed with a mask. +* **Calling the mandatory `Epilogue` method**: + - This restores previously saved registers, executes the required `VZEROUPPER` instruction (as mentioned earlier), and restores the frame and stack pointers (using the `leave` instruction). + +For simpler primitives, there is not much additional detail. +The batch processing code for varying numbers of input data is unified and implemented in the `insertSimpleMathFunction()` function. + +### Description of Complex Primitives +Complex primitives consist of other primitives (**Sigmoid** and **RestOfLstm**) or are computed using polynomials (**Tanh** and **Exp**). +These primitives use many `ymm` registers to process a block of 8 input values, typically unrolling no more than 2 such blocks at a time. + +In the `insertPrimitive` function, which processes 2 blocks (2 input `ymm`), we would have to write each line twice, and have another similar function that processes only 1 block at a time. +Such an approach would inevitably lead to code divergence and hard-to-detect bugs, so in these primitives we operate not with individual `ymm`, but with the `ymmVec_t` vector. +During initialization we either manually check how many blocks should be processed: +``` +ymmVec_t forget = wholeYmmNumber == 2 ? ymmVec_t{ ymm0, ymm1 } : ymmVec_t{ ymm0 }; +``` +or use a special function `initFromAux()`, which slices the auxiliary register vector `ymmAux` into small blocks, each of which matches the size of the input data (`ymmSrc`). + +Such manipulation of `ymm` vectors required us to overload various methods of the `Xbyak::CodeGenerator` class responsible for generating instructions. +These overloaded functions are defined in the base class `CJitCommon`. +To enable single-line function overloading, we had to define several macros and template functions for different numbers and combinations of arguments. +As a result, we achieved a syntax similar to what `xbyak` offers for working with register vectors. + +#### Tanh +The computation of the hyperbolic tangent (`tanh`) function is described in detail through comments. + +Segments based the Argument's range: +1. **Linear Segment:** + - `[0; linear_ubound]`, where `tanh(x) = x`. + +2. **Polynomial Segments:** + - `[linear_ubound; 0x1.8p-12]` is the first half of a binom. + - `[0x1.8p-12; 0x1.0p-11], ..., [0x1.8p2; 0x1.0p3]` are 29 half-binoms. + - `[0x1.0p3; saturation_ubound]` + - This gives a total of 31 intervals where `tanh` is calculated using a 6th-degree polynomial. + +3. **Saturation Segment:** + - `[0x1.205966p3; saturation_ubound]`, where `tanh(x) = 1`. + +The other steps in code for computing `tanh(x)` are: +1. **Discard the sign:** + - The absolute value of the argument is used for the computation, and the sign is reintroduced at the end. + +2. **Determine the polynomial segment:** + - Identify which polynomial segment the argument falls into. + +3. **Compute `tanh` using a polynomial:** + - For polynomial segment `tanh(x)` is computed using a polynomial approximation. + +4. **Handle Linear and Saturation Segments:** + - For the linear segment, simply use `x`, and for the saturation segment, use `1`. + +5. **Return the sign:** + - Add the sign back to the computed result. + +#### Exp +The exponential function (`exp`) is computed using a polynomial approximation. +To calculate `exp(x)`, the argument is split into 2 parts based on `ln(2)`: + +1. **Decompose the Argument:** + - The result of `x / ln(2)` is split into its integer part `n` and the remainder `r`: + ``` + x = n * ln(2) + r + exp(x) = exp(n * ln(2) + r) = exp(ln(2))^n * exp(r) = 2^n * exp(r) + ``` + - Hence, `2^n` is calculated using a shift operation, and `exp(r)` is approximated using a polynomial on the interval `[0; ln(2)]`. + +2. **Limit Argument to Avoid Overflow:** + - Before calculating the exponent, limit the argument from above and below to avoid overflow. + Constants `ExpFltMax` and `ExpFltMin` are specified in hex format. If `ExpFltMax` is increased by one, the result will be `inf` on overflow, which does not agree with the similar result in MKL. + +**Function Operations:** +1. Save a mask for a value less than `ExpFltMin`, and at the end of the function use it to set corresponding results to zero: + ``` + gen.vcmpltps(ymmMask, ymmSrc, getAddr(TTableKey::ExpFltMin)); + ``` +2. Limit the argument `x` from above and below and cache this value to use further + ``` + gen.vminps(ymmSrc, ymmSrc, getAddr(TTableKey::ExpFltMax)); + gen.vmaxps(ymmSrc, ymmSrc, getAddr(TTableKey::ExpFltMin)); + gen.vmovups(ymmAux1, ymmSrc); + ``` +3. Calculate the integer part of the division `x / ln(2)`, adding `0.5` to shift the remainder of the division to the zero region for a more accurate calculation of the polynomial. + ``` + n = round( x / ln(2) + 0.5 ) = round( x * log2(e) + 0.5 ) + ``` +4. Calculate the remainder `r = x - n * ln(2)` +5. In case `n == 128`, to avoid an overflow when calculating `2^n`, so need to do the following: + ``` + exp(x) = 2^n * exp(r) = 2^(n-1) * exp(r) * 2 + ``` + the expression `2^(n-1) * exp(r)` will be less than `2^127` and as a result there will be no overflow. + + Calculate `2^(n-1)` using the shift operation, adding `ExpBias` to maintain the floating point format: + ``` + gen.vsubps( ymmSrc, ymmSrc, getAddr( TTableKey::One ) ); + gen.vcvtps2dq( ymmAux2, ymmSrc ); + gen.vpaddd( ymmAux2, ymmAux2, getAddr( TTableKey::ExpBias ) ); + gen.vpslld( ymmAux2, ymmAux2, MantissaNumBits ); + ``` +6. Apply the mask obtained in step 1, zeroing out the values that are less than `ExpFltMin` + ``` + gen.vxorps( ymmSrc, ymmSrc, ymmSrc ); + gen.vblendvps( ymmAux2, ymmAux2, ymmSrc, ymmMask ); + ``` +7. Calculate `exp(r)` using a polynomial +8. Multiply the obtained value first by `2^(n-1)` then by `2` to avoid the problem obtained in step 5. + +#### Sigmoid +The Sigmoid function is computed using the exponential function as follows: + +$\[ \text{sigmoid}(x) = \frac{\exp(x)}{1 + \exp(x)} \]$ + +**In the Method `insertPrimitive`:** + +- **Initialization of Registers:** + - The final register `ymmAux` is pre-initialized to ones. + This is because `insertPrimitive` is also used in `insertPrimitive`, and pre-initializing `ymmAux` simplifies the logic and avoids redundant operations. + +- **Functional Object `afterPrologue`:** + - To maintain the unified method approach in `initActivationFunction()`, a parameter `afterPrologue` is added. + This parameter is a functional object that is invoked after the prologue to initialize the `ymmAux` register with ones for the sigmoid function. + +#### RestOfLstm +The implementation of the `RestOfLstm` primitive might appear complex, but it can be better understood with the aid of a diagram [RestOfLstm.pdf](https://github.com/neoml-lib/neoml/NeoMathEngine/src/CPU/x86/avx/src/docs/RestOfLstm.pdf). + +![image](https://github.com/user-attachments/assets/d64e8bbf-e023-40f0-ad27-7cedca41db4b) + +This diagram represents the classic LSTM cell and its implementation, broken down into 3 blocks. +Each block is designed to use the maximum number of `ymm` registers (up to 16) while avoiding excessive register usage. + +Each block is labeled with the number of `ymm` registers used *at the input*, *maximum within* the block, and *at the output*. + +The main executions are performed in the lambda function `insertCode()`, which processes 1 or 2 `ymm` input registers at a time. + +The LSTM layer is recurrent, with an outer loop for processing 1 LSTM step and inner loops for handling data in chunks (first 16 values, then 8, and finally the remainder). +```cpp + // *** Main loop *** + gen.StartDownCountLoop(regObjectsCount, 1); + + // ... Inner processing of 1 LSTM step + + // *** Stop Main loop *** + gen.StopDownCountLoop(); +``` + +After each inner loop, pointers are nullified. +Methods `StartDownCountLoop()` and `StopDownCountLoop()` are designed to handle nested loops by managing labels for transitions in the stack and tracking the nesting level. + +## Conclusion +The JIT primitives were designed to be scalable and easy to extend by new primitives. However, the code could benefit from refactoring: +1. Consider limiting access to primitives solely through pointer retrieval and removing multi-threading support if not needed. +2. The method `insertSimpleMathFunction()` standardizes loop unrolling for simple mathematical primitives, could be extended to handle complex primitives similarly. diff --git a/NeoMathEngine/src/CPU/x86/avx/src/docs/JIT.ru.md b/NeoMathEngine/src/CPU/x86/avx/src/docs/JIT.ru.md new file mode 100644 index 000000000..a78c0bc4f --- /dev/null +++ b/NeoMathEngine/src/CPU/x86/avx/src/docs/JIT.ru.md @@ -0,0 +1,255 @@ +# Модуль NeoMathEngineAvx + +## Введение +Модуль **NeoMathEngineAvx** предназначен для ускорения отдельных методов NeoML путём реализации их с использованием набора инструкци AVX/AVX2/FMA. +Это позволяет запускать код как на уже довольно старых процессорах x86_64 (Haswell и старше), так и на AMD процессорах, поддерживающих соответствующий набор инструкций. + +В данный момент в модуле реализовано глобально 3 подсистемы: прямая свёртка, ядра для матричного умножения и набор различных примитивов, используемых в нейросетях. + +Ядра для матричного умножения написаны с применением intrinsic вызовов для использования в классе `CMatrixMultiplier`. +По результатам замеров матричное умножение с использованием данных ядер выигрывает у MKL на AMD процессорах, но в целом проигрывает MKL на Intel даже с тем же набором инструкций AVX/AVX2/FMA. + +Прямая свёртка и примитивы реализованы уже с использованием OpenSource библиотеки [xbyak](https://github.com/herumi/xbyak). +Эта библиотека позволяет генерировать машинные инструкции в рантайме, поэтому в дальнейшем будем именовать данную технологию **JIT компилятором** или просто **JIT**. +Одна из замечательных особенностей `xbyak` - это простая реализации API, которая позволяет писать код очень приближенный по виду и структуре в синтаксису ассемблера от Intel. +Основные преимущества JIT компилятора - это минимизация условных переходов, расчёт всех смещений и подстановка константных значений на этапе компиляции JIT кода, а так же разворачивание циклов для лучшей предвыборки кода конвейером. + +## Описание модулей + +### Matrix Multiplication Kernels +Тут чистый C++, смысла описывать этот модуль в данном документе нет. + +### Forward Convolution +Изначально модуль писался с применением intrinsic вызовов, но впоследствии был переведён на JIT. +Однако реализация в виде шаблонного класса осталась, хотя в ней уже нет никакой необходимости, так как в целом время на время генерации JIT кода шаблонные параметры не влияют, а после генерации кода шаблоны уже не нужны. +*В будущем хорошо бы убрать шаблонные параметры из класса, чтобы упростить код" + +JIT код для **Forward Convolution** генерируется отдельно для каждого дескриптора, так как он зависит от различных параметров дескриптора. +Это тот случай, когда ускорение достигается при помощи использования в инструкциях известных заранее констант и смещений. +Работа данного модуля уже описывалась при реализации на intrinsic-ах, и основную логику JIT не поменял. + +О том, как работает JIT будет рассказано в следующем разделе. + +### Primitives +JIT - очень необычный способ написания кода: с одной стороны, логика работы JIT компилятора пишется на C++, пользуясь всеми преимуществами и новыми фишками этого языка; +с другой стороны, код пишется как бы на ассемблере, получая компактный и довольно оптимальный код (хотя и не всегда читаемый для неподготовленного программиста). +Самое главное, что код пишется исходя из условий, при которых он будет запускаться: сколько раз, с какими переменными/константами и т.д.; это позволяет обеспечить максимальную производительность. +Данные 3 аспекта позволяют добиваться значительных успехов в улучшении производительности. + +### Подготовка и ссылочные материалы +1. Для начала нужно ознакомится с базовыми аспектами языка Assembler и с его Intel синтаксисом. +2. Нужно почитать документацию на [xbyak](https://github.com/herumi/xbyak), там довольно небольшой объём, и он хорошо структурирован и сопровождён примерами. +3. Для поиска документации на ассемблерные инструкции я пользовался в основном следующими сайтами: + * [x86 and amd64 instruction reference](https://www.felixcloutier.com/x86/index.html) + * [Intel® Intrinsics Guide](https://www.intel.com/content/www/us/en/docs/intrinsics-guide/index.html) + * [X86-64_Instruction_Encoding](https://wiki.osdev.org/X86-64_Instruction_Encoding) - полезно для понимания режима адресации при формировании команд. + +Вот, вроде и всё, что нужно для уверенной работы с `xbyak`. + +### Проблемы или особенности, с которыми столкнулись при использовании xbyak +Считаю, что данный раздел следует поместить ДО описания работы с `xbyak`. + +1. В процессе работы нельзя смешивать инструкции AVX и SSE, т.к. это приводит к фатальному замедлению, которое может быть вызвано перегрузкой модуля SIMD инструкций. + Более подробно про этом можно почитать [Intel® 64 and IA - 32 Architectures Optimization Reference Manual](https://www.intel.com/content/dam/www/public/us/en/documents/manuals/64-ia-32-architectures-optimization-manual.pdf), + раздел 11.3 **MIXING AVX CODE WITH SSE CODE**: *Assembly/Compiler Coding Rule 72. (H impact, H generality) Add VZEROUPPER instruction after 256-bit AVX instructions are executed and before any function call that might execute SSE code.* + *Add VZEROUPPER at the end of any function that uses 256-bit AVX instructions.* +2. `xbyak` имеет такую замечательную особенность, что очень трудно сформировать неправильную инструкцию. Внутри вызовов функций имеется множество проверок, которые не позволят вам использовать неправильные операнды внутри инструкции. +3. Получить какой-то прирост скорости при использовании `prefetch` инструкций очень сложно. + Это связано с тем, что современные процессоры имеют очень хорошую аппаратную реализацию поиска закономерностей при доступе к памяти, и автоматически подгружают необходимые блоки. + +### Описание класса `CPrimitivesJit` + +#### Общие положения +В интерфейсе класса реализованы 2 механизма вызова функций примитива: +1. Непосредственно вызов метода (JIT реализация сетки LSTM), +2. Через указатель на конкретный примитив (позволяет безболезненно подменить вызовы примитивов в классе `CCpuMathEngine`). + +Наибольшее ускорение можно достичь для ёмких операций с точки зрения вычисления. +По этой причине простые примитивы показывают весьма нестабильное ускорение относительно реализации с sse intrinsic-ами, т.к. основное время занимает доступ к памяти и в случае промахов кэша результат замера производительности может сильно гулять. + +### Контейнер `gens`, хранящий JIT код функций примитивов +Все реализованные JIT функции перечислены в enum-е `TPrimitive`. +В классе определена структура `CGenerator`, которая по сути своей является экземпляром класса `Xbyak::CodeGenerator`, отвечающий за формирование JIT кода. +Массив **`gens`** хранит все сгенерированные JIT примитивы, их генерация происходит при первом обращении к данному примитиву в методе `GetFunctionRawPtr()`. + +### Таблица констант +Таблица констант определяется при помощи ключей **`TTableKey`** и двух контейнеров **`table`** и **`tableOffsets`**. +Эта таблица позволяет хранить в одном месте все константы, которые нужны при выполнении JIT кода и иметь к ним лёгкий доступ. +Т.к. невозможно напрямую задать инициализирующее значение `ymm` регистра в коде инструкции, приходится производить загрузку их из памяти. +Локализация всех констант в одном месте благоприятно сказывается на работе с кэшем. + +Таблица констант инициализируется один раз в конструкторе `CPrimitivesJit` вызовом метода `initTable`. +В каждой JIT функции адрес таблицы констант (если он используется) находится в регистре `regTablePtr` (**`r10`**). +Получить этот адрес для инициализации `ymm` регистра можно при помощи методов `getOfft` или `getAddr`, передавая при этом необходимые смещения. +Метод `getAddr` возвращает непосредственный дескриптор адреса `Xbyak::Address` реализующего механизм относительной адресации (относительно регистра `regTablePtr`). + +### Структура функции примитива +JIT примитивы создаются в шаблонном методе `initPrimitive`, который +* либо непосредственно содержит код генерации JIT функции, +* либо является обёрткой для другого шаблонного метода с именем `init...`, который обобщает реализацию похожих функций (как правило, простейших математических примитивов). + +Тем не менее можно выделить следующие обязательные шаги: +* **Создание экземпляра класса `CGenerator`**. +* **Определение регистров, что должны быть сохранены перед выполнением функции `preservedReg64` и `preservedYmm`**: + - Для Windows и Unix это разные наборы регистров, более подробно про них можно узнать в соглашении о вызовах для конкретной ОС. +* **Вызов обязательного метода `Prologue`**: + - В котором добавляется необходимая преамбула для любой функции, на стеке сохраняются необходимые регистры, а также высчитывается дескриптор адреса, указывающий на область стека, содержащую аргументы вызываемой функции (если такие есть). +* **Определение регистров, используемых внутри функции и их инициализация**: + - Инициализация либо регистрами, либо значениями из стека, тут тоже важно изучить соглашение о вызовах функции. + Например, Windows передаёт через регистры только 4 аргумента в то время, как Unix передаёт 6. + К тому же, если аргументы перемежаются значениями с плавающей точкой, то эти значения также содержатся в разных `xmm` регистрах для Windows и Unix. + Если аргументов функции больше, чем число отведённых на это регистров, то остальные аргументы передаются через стек. + Ещё в Windows есть такое понятие как `ShadowSpace` - зарезервированная область на стеке перед аргументами размером в 32 байта. +* **Реализация lambda функции**: + - Лямбда выполняет основные вычислительные операции для данного примитива. +* **Пакетная обработка входных значений с разворачиванием циклов (unrolling loop)**: + - Для этого применяется лямбда функция из предыдущего пункта. + Количество элементов, которые можно развернуть в одном цикле, определяется тем, сколько регистров `ymm` участвует в обработке, а также тем, сколько элементов содержится в типовых случаях использования. + Например, для сложных примитивов `Exp`, `Sigmoid`, `Tanh` и `RestOfLstm`, где задействовано много регистров `ymm`, не обрабатываем за раз более 2 значений. +* **Выполняем обработку 'хвоста' входных данных** + - В случае, если длинна входных данных не кратна 8, производится обработка хвостовых значений отдельно. + Она отличается только тем, что чтение и запись данных производится по маске. +* **Вызов обязательного метода `Epilogue`**: + - В котором восстанавливаются сохранённые ранее регистры, вызывается обязательная инструкция `VZEROUPPER`, о которой говорилось выше, а также восстанавливается указатели фрейма и стека (инструкция leave). + +Для простейших примитивов добавить к предыдущему описанию особо нечего. +Код, выполняющий пакетную обработку для разного количества входных данных, унифицирован и реализован в функции `insertSimpleMathFunction()` + +### Описание сложных примитивов +Сложные примитивы состоят из других примитивов (**Sigmoid** и **RestOfLstm**) или вычисляются при помощи полинома (**Tanh** и **Exp**). +Такие примитивы используют много регистров `ymm` для вычисления одного блока из 8 входных значений, а потому разворачивают за раз как правило не более 2 таких блоков. + +В функции `insertPrimitive`, которая обрабатывает 2 блока (2 входных `ymm`), пришлось бы каждую строчку писать дважды, и иметь ещё такую же функцию, которая обрабатывала только 1 блок за раз. +Подобный подход неминуемо привёл бы к расхождению кода и появлению трудно-детектируемых багов, поэтому в этих примитивах оперируем не отдельными `ymm`, а вектором `ymmVec_t`. +При инициализации либо вручную проверяем сколько блоков должны обработать: +``` + ymmVec_t forget = wholeYmmNumber == 2 ? ymmVec_t{ ymm0, ymm1 } : ymmVec_t{ ymm0 }; +``` +либо используем специальную функцию `initFromAux()`, которая нарезает вектор вспомогательных регистров `ymmAux` на небольшие блоки, каждый из которых по размеру равен размеру входных данных (`ymmSrc`). + +Подобное оперирование векторами `ymm` заставило нас перегрузить различные методы класса `Xbyak::CodeGenerator`, отвечающие за генерацию инструкций. +Эти перегруженные функции определены в базовом классе `CJitCommon`. +Чтобы иметь возможность перегрузить функцию в одну строчку, пришлось определить ряд дефайнов и шаблонных функций для разного количества и комбинации аргументов. +Как итог, получили возможность использовать синтаксис, идентичный тому, что есть в `xbyak` для работы с векторами регистров. + +#### Tanh +Вычисление данного примитива подробно расписано в комментариях. + +Весь диапазон значений аргумента бьётся на отрезки: +1. **Линейный участок:** + - `[0; linear_ubound]`, где `tanh(x) = x` + +2. **Полиномиальные участки:** + - `[linear_ubound; 0x1.8p-12]` - часть половины бинады + - `[0x1.8p-12; 0x1.0p-11], ..., [0x1.8p2; 0x1.0p3]` - 29 половин бинад + - `[0x1.0p3; saturation_ubound]` + - Итого, 31 интервал, где значение тангенса вычисляется полиномом 6-й степени. + +3. **Участок насыщения:** + - `[0x1.205966p3; saturation_ubound]` - участок насыщения, где `tanh(x) = 1`. + +Остальные действия понятны из кода: +1. **Отбрасываем знак**, чтобы потом добавить его к ответу. +2. **Вычисляем номер бинады**, что соответствует данному аргументу. +3. **Вычисляем `tanh` при помощи полинома**, вычисляем значение гиперболического тангенса. +4. **Обработка линейного участка и участка насыщения**, подставляем значение `x` на линейном участке, и `1` и участке насыщения. +5. **Возвращаем знак** к вычисленному результату. + +#### Exp +Экспонента также вычисляется полиномом. +Для вычисления экспоненты разбиваем аргумент на 2 части, поделив его на `ln(2)`. + +1. **Разложим аргумент:** + - Результат деления `x / ln(2)` будет целая часть `n` и остаток `r`, таким образом можно обратно выразить: + ``` + x = n * ln(2) + r + exp(x) = exp(n * ln(2) + r) = exp(ln(2))^n * exp(r) = 2^n * exp(r) + ``` + - Затем `2^n` считается элементарно сдвигом, а `exp(r)` считается полиномом на отрезке `[0;ln(2)]`. + +2. **Ограничим аргумент, чтобы избежать переполнения:** + - Перед вычислением экспоненты нужно ограничить аргумент сверху и снизу, чтобы не получить переполнение. + Константы `ExpFltMax` и `ExpFltMin` заданы в hex формате. Если `ExpFltMax` увеличить на 1, то при переполнении получим `inf`, что не согласуется с аналогичным результатом у MKL. + +**Операции в функции:** +1. Сохраняем маску для значения меньше `ExpFltMin`, в конце функции по этой маске заполним соответствующие результаты нулями. + ``` + gen.vcmpltps( ymmMask, ymmSrc, getAddr( TTableKey::ExpFltMin ) ); + ``` +2. Ограничиваем аргумент `x` сверху и снизу и кэшируем значение для последующего использования. + ``` + gen.vminps( ymmSrc, ymmSrc, getAddr( TTableKey::ExpFltMax ) ); + gen.vmaxps( ymmSrc, ymmSrc, getAddr( TTableKey::ExpFltMin ) ); + gen.vmovups( ymmAux1, ymmSrc ); + ``` +3. Вычисляем целую часть от деления `x / ln(2)`, при этом прибавляя `0.5`, чтобы сместить остаток от деления в область нуля для более точного вычисления полинома. + ``` + n = round( x / ln(2) + 0.5 ) = round( x * log2(e) + 0.5 ) + ``` +4. Вычисляем остаток `r = x - n * ln(2)` +5. В случае, если `n == 128`, получим переполнение при вычислении `2^n`, поэтому поступим следующим образом: + ``` + exp(x) = 2^n * exp(r) = 2^(n-1) * exp(r) * 2 + ``` + Выражение `2^(n-1) * exp(r)` будет меньше `2^127` и в итоге переполнения не будет. + + Вычислим `2^(n-1)` при помощи операции сдвига, добавив `ExpBias`, чтобы соблюсти формат числа с плавающей точкой: + ``` + gen.vsubps( ymmSrc, ymmSrc, getAddr( TTableKey::One ) ); + gen.vcvtps2dq( ymmAux2, ymmSrc ); + gen.vpaddd( ymmAux2, ymmAux2, getAddr( TTableKey::ExpBias ) ); + gen.vpslld( ymmAux2, ymmAux2, MantissaNumBits ); + ``` +6. Применим маску полученную в шаге 1, обнулив значения, которые меньше `ExpFltMin` + ``` + gen.vxorps( ymmSrc, ymmSrc, ymmSrc ); + gen.vblendvps( ymmAux2, ymmAux2, ymmSrc, ymmMask ); + ``` +7. Посчитаем `exp(r)` при помощи полинома +8. Домножим полученное значение сначала на `2^(n-1)` потом на `2`, чтобы избежать проблемы, полученной в шаге 5. + +#### Sigmoid +Примитив Sigmoid по определению считается при помощи экспоненты: + +$\[ \text{sigmoid}(x) = \frac{\exp(x)}{1 + \exp(x)} \]$ + +**В методе `insertPrimitive`:** + +- **Инициализация регистров:** + - Последний регистр `ymmAux` уже инициализирован единицами. + Это сделано потому, что `insertPrimitive` также активно используется в методе `insertPrimitive`, и подобное допущение позволяем избежать лишних действий. + +- **Функциональный объект `afterPrologue`:** + - Чтобы не порушить концепцию унифицированных методов в `initActivationFunction()` был добавлен параметр `afterPrologue`. + Он является функциональным объектом и вызывается после добавления пролога для инициализации последнего регистра `ymmAux` единицами для примитива Сигмоиды. + +#### RestOfLstm +Выглядит реализация данного примитива очень громоздко и страшно, но всё становится более понятным, если взглянуть на схему [RestOfLstm.pdf](https://github.com/neoml-lib/neoml/NeoMathEngine/src/CPU/x86/avx/src/docs/RestOfLstm.pdf). + +![image](https://github.com/user-attachments/assets/d64e8bbf-e023-40f0-ad27-7cedca41db4b) + +На схеме представлено классическое изображение LSTM ячейки и её реализация в коде, разбитая на 3 блока. +Блоки выбирались из того соображения, чтобы внутри них одновременно использовалось бы максимальное количество регистров `ymm`, но не больше 16 штук. + +Каждый блок сопровождён отметкой о количестве используемых регистров **на входе блока**, **максимальное число внутри** блока и **на выходе блока**. + +Основные вычисления происходят внутри lambda функции `insertCode()`, которая за раз может обрабатывать 1 или 2 входных регистра `ymm` + +Слой LSTM рекуррентный, внешний цикл выполняет обработку 1 шага LSTM ячейки несколькими внутренними циклами, которые просто оптимально обрабатывают данные сначала по 16 значений, потом по 8, потом что осталось. +```cpp + // *** Main loop *** + gen.StartDownCountLoop( regObjectsCount, 1 ); + + // ... Внутренняя обработка 1 шага LSTM + + // *** Stop Main loop *** + gen.StopDownCountLoop(); +``` + +После каждого внутреннего цикла обновляем указатели. +Методы `StartDownCountLoop()` и `StopDownCountLoop()` реализованы таким способом, что позволяют организовывать вложенные циклы, сохраняя лэйблы для переходов в стеке и отслеживая уровень вложенности. + +## Заключение +В целом работу с JIT примитивами планировалось сделать максимально масштабируемой для возможности добавления новых примитивов, но всё равно код уже заслуживает рефакторинга: +1. Можно оставить механизм доступа к примитивам только через получение указателей. +2. Метод `insertSimpleMathFunction()` унифицирует разворачивание циклов для блоков различной длинны и обработку хвостовых значений в простейших математических примитивах, подобный механизм хорошо бы перенести и на сложные примитивы. diff --git a/NeoMathEngine/src/CPU/x86/avx/src/docs/RestOfLstm.pdf b/NeoMathEngine/src/CPU/x86/avx/src/docs/RestOfLstm.pdf new file mode 100644 index 0000000000000000000000000000000000000000..dc40655d26889efc81069b578cc933aa491db848 GIT binary patch literal 290595 zcmeFa1yo&0wm*z}@Sp)M?(PtRdvHi_zqq@*27LAu+}$wgz)q! zqq3_FkWpCALC?b4m{DHO7-$b*0aYt9KG(A{rUF{gt0++e7?m9C91R?l?SMc>m8QQFkdUIW1T(47|Gm+c-d{iYpgz;-}TyYC}b1ln6W+8F@tLC;r}(>DVe zIDm4JmY|nn2e5w|;kN=efcxhHGb;d;9$xrc9Wy%slzuL90+_$Q>-So20P`=}vM>Wc z>904lumV8o=OR0R_EX0ig7A zEjNJm7hSP213>AowQQ^aQ2M#Z4q*F5S8SXBQ2M!+8^HF9uGpCYp!C;Tc2)o={aggi z>My!t=LCS#&$ZkD_Fr_x!3+Q;Q0=p4jG`_M;z|yB4nPoj#FaP!-&=_*aRIpga)+3; z)dTIsm;uZ`HIlcpHc$dOXfT4fnNb<&;_#hdLf`)gfBz%-z%-09KtoeKA!`>6P;X2C 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