the static single assignment book

SSA-based Compiler Design

• © 2022
• Fabrice Rastello 0 ,
• Florent Bouchez Tichadou 1

Inria, Grenoble, France

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University of Grenoble Alpes, Grenoble, France

• Provides first single-source reference to widely adopted, static-single assignment (SSA) form of compiler design
• Offers readers state-of-the-art, advanced compiler optimization techniques
• Includes content from globally recognized compiler research centers and engineering practitioners

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Table of contents (24 chapters)

Front matter, vanilla ssa, introduction.

• Jeremy Singer

Properties and Flavours

• Philip Brisk, Fabrice Rastello

Standard Construction and Destruction Algorithms

• Jeremy Singer, Fabrice Rastello

Advanced Construction Algorithms for SSA

• Dibyendu Das, Upadrasta Ramakrishna, Vugranam C. Sreedhar

SSA Reconstruction

• Sebastian Hack

Functional Representations of SSA

• Lennart Beringer
• Markus Schordan, Fabrice Rastello

Propagating Information Using SSA

• Florian Brandner, Diego Novillo
• Benoît Boissinot, Fabrice Rastello

Loop Tree and Induction Variables

• Sebastian Pop, Albert Cohen

Redundancy Elimination

• Vivek Sarkar, Fabrice Rastello

Static Single Information Form

• Fernando Magno Quintão Pereira, Fabrice Rastello

Graphs and Gating Functions

• James Stanier, Fabrice Rastello

Psi-SSA Form

• François de Ferrière

Hashed SSA Form: HSSA

• Massimiliano Mantione, Fred Chow
• Engineering a Compiler
• Modern Compiler Design
• static-single assignment compiler
• SSA Form and Code Generation

About this book

This book provides readers with a single-source reference to static-single assignment

(SSA)-based compiler design. It is the first (and up to now only) book that covers

in a deep and comprehensive way how an optimizing compiler can be designed using

the SSA form. After introducing vanilla SSA and its main properties, the authors

describe several compiler analyses and optimizations under this form. They illustrate

how compiler design can be made simpler and more efficient, thanks to the SSA form.

This book also serves as a valuable text/reference for lecturers, making the teaching of

compilers simpler and more effective. Coverage also includes advanced topics, such as

code generation, aliasing, predication and more, making this book a valuable reference

for advanced students and practicing engineers.

Editors and Affiliations

Fabrice Rastello

Florent Bouchez Tichadou

About the editors

Fabrice Rastello is an Inria research director and the leader of the CORSE (Compiler Optimization and Runtime SystEms) Inria team. His expertize includes automatic parallelization (PhD thesis on tiling as a loop transformations), and compiler back-end optimizations (engineer at STMicroelectronics’s compiler group + researcher at Inria). Among others, he advised several PhD thesis so as to fully revisit register allocation for JIT compilation in the light of Static Single Assignment (SSA) properties. He likes mixing theory (mostly graphs, algorithmic, and algebra) and practice (industrial transfer). His current research topics include: (i) combining run-time techniques with static compilation, hybrid compilation being an example of such approach he is trying to promote; (ii) performance debugging through static and dynamic (binary instrumentation) analysis; (iii) revisiting compilers infrastructure for pattern specific programs.

Florent Bouchez Tichadou received his Ph.D. in computer science in 2009 at the ENS Lyon in France, working on program compilation. He was then a post-doctoral fellow at the Indian Institute of Science (IISc) in Bangalore, India. He worked for three years at Kalray, a startup company in the Grenoble area in France. Since 2013, he is an assistant professor at the Université Grenoble Alpes (UGA).

Bibliographic Information

Book Title : SSA-based Compiler Design

Editors : Fabrice Rastello, Florent Bouchez Tichadou

DOI : https://doi.org/10.1007/978-3-030-80515-9

Publisher : Springer Cham

eBook Packages : Computer Science , Computer Science (R0)

Copyright Information : The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022

Hardcover ISBN : 978-3-030-80514-2 Published: 09 December 2022

Softcover ISBN : 978-3-030-80517-3 Published: 09 December 2023

eBook ISBN : 978-3-030-80515-9 Published: 08 December 2022

Edition Number : 1

Number of Pages : XVII, 382

Number of Illustrations : 116 b/w illustrations, 32 illustrations in colour

Topics : Circuits and Systems , Programming Languages, Compilers, Interpreters , Processor Architectures

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SSA-based Compiler Design 1st ed. 2022 Edition

Purchase options and add-ons.

This book provides readers with a single-source reference to static-single assignment

(SSA)-based compiler design. It is the first (and up to now only) book that covers

in a deep and comprehensive way how an optimizing compiler can be designed using

the SSA form. After introducing vanilla SSA and its main properties, the authors

describe several compiler analyses and optimizations under this form. They illustrate

how compiler design can be made simpler and more efficient, thanks to the SSA form.

This book also serves as a valuable text/reference for lecturers, making the teaching of

compilers simpler and more effective. Coverage also includes advanced topics, such as

code generation, aliasing, predication and more, making this book a valuable reference

for advanced students and practicing engineers.

• ISBN-10 303080514X
• ISBN-13 978-3030805142
• Edition 1st ed. 2022
• Publisher Springer
• Publication date December 9, 2022
• Language English
• Dimensions 6.14 x 0.88 x 9.21 inches
• Print length 399 pages
• See all details

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From the back cover.

This book provides readers with a single-source reference to static-single assignment (SSA)-based compiler design. It is the first (and up to now only) book that covers in a deep and comprehensive way how an optimizing compiler can be designed using the SSA form. After introducing vanilla SSA and its main properties, the authors describe several compiler analyses and optimizations under this form. They illustrate how compiler design can be made simpler and more efficient, thanks to the SSA form. This book also serves as a valuable text/reference for lecturers, making the teaching of compilers simpler and more effective. Coverage also includes advanced topics, such as code generation, aliasing, predication and more, making this book a valuable reference for advancedstudents and practicing engineers.

• Provides the first, single-source reference to the widely adopted, static-single assignment (SSA) form of compiler design;
• Offers readers state-of-the-art, advanced compiler optimization techniques;
• Includes contributions by subject experts from globally recognized compiler research centers and engineering practitioners at companies such as Google, Facebook, IBM, and Amazon;
• Employs a textbook style of presentation throughout, with coherent and uniform structure, sequence, terminology, and notations;
• Offers valuable content both for lecturers (such as vanilla SSA, construction, destruction, propagation, liveness) and advanced compiler developers (including if-conversion, code-selection, hardware compilation, scalar evolution, register allocation, Gated-SSA, Psi-SSA, Hashed-SSA, Array-SSA, SSI).

About the Author

Fabrice Rastello is an Inria research director and the leader of the CORSE (Compiler Optimization and Runtime SystEms) Inria team. His expertize includes automatic parallelization (PhD thesis on tiling as a loop transformations), and compiler back-end optimizations (engineer at STMicroelectronics’s compiler group + researcher at Inria). Among others, he advised several PhD thesis so as to fully revisit register allocation for JIT compilation in the light of Static Single Assignment (SSA) properties. He likes mixing theory (mostly graphs, algorithmic, and algebra) and practice (industrial transfer). His current research topics include: (i) combining run-time techniques with static compilation, hybrid compilation being an example of such approach he is trying to promote; (ii) performance debugging through static and dynamic (binary instrumentation) analysis; (iii) revisiting compilers infrastructure for pattern specific programs.

Florent Bouchez Tichadou received his Ph.D. in computer science in 2009 at the ENS Lyon in France, working on program compilation. He was then a post-doctoral fellow at the Indian Institute of Science (IISc) in Bangalore, India. He worked for three years at Kalray, a startup company in the Grenoble area in France. Since 2013, he is an assistant professor at the Université Grenoble Alpes (UGA).

Product details

• Publisher ‏ : ‎ Springer; 1st ed. 2022 edition (December 9, 2022)
• Language ‏ : ‎ English
• Hardcover ‏ : ‎ 399 pages
• ISBN-10 ‏ : ‎ 303080514X
• ISBN-13 ‏ : ‎ 978-3030805142
• Item Weight ‏ : ‎ 1.62 pounds
• Dimensions ‏ : ‎ 6.14 x 0.88 x 9.21 inches
• #103 in Compiler Design
• #118 in Software Programming Compilers
• #230 in Computer Hardware Design & Architecture

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Lesson 6: Static Single Assignment

• discussion thread
• static single assignment
• SSA slides from Todd Mowry at CMU another presentation of the pseudocode for various algorithms herein
• Revisiting Out-of-SSA Translation for Correctness, Code Quality, and Efficiency by Boissinot on more sophisticated was to translate out of SSA form
• tasks due March 8

You have undoubtedly noticed by now that many of the annoying problems in implementing analyses & optimizations stem from variable name conflicts. Wouldn’t it be nice if every assignment in a program used a unique variable name? Of course, people don’t write programs that way, so we’re out of luck. Right?

Wrong! Many compilers convert programs into static single assignment (SSA) form, which does exactly what it says: it ensures that, globally, every variable has exactly one static assignment location. (Of course, that statement might be executed multiple times, which is why it’s not dynamic single assignment.) In Bril terms, we convert a program like this:

Into a program like this, by renaming all the variables:

Of course, things will get a little more complicated when there is control flow. And because real machines are not SSA, using separate variables (i.e., memory locations and registers) for everything is bound to be inefficient. The idea in SSA is to convert general programs into SSA form, do all our optimization there, and then convert back to a standard mutating form before we generate backend code.

Just renaming assignments willy-nilly will quickly run into problems. Consider this program:

If we start renaming all the occurrences of a , everything goes fine until we try to write that last print a . Which “version” of a should it use?

To match the expressiveness of unrestricted programs, SSA adds a new kind of instruction: a ϕ-node . ϕ-nodes are flow-sensitive copy instructions: they get a value from one of several variables, depending on which incoming CFG edge was most recently taken to get to them.

In Bril, a ϕ-node appears as a phi instruction:

The phi instruction chooses between any number of variables, and it picks between them based on labels. If the program most recently executed a basic block with the given label, then the phi instruction takes its value from the corresponding variable.

You can write the above program in SSA like this:

It can also be useful to see how ϕ-nodes crop up in loops.

(An aside: some recent SSA-form IRs, such as MLIR and Swift’s IR , use an alternative to ϕ-nodes called basic block arguments . Instead of making ϕ-nodes look like weird instructions, these IRs bake the need for ϕ-like conditional copies into the structure of the CFG. Basic blocks have named parameters, and whenever you jump to a block, you must provide arguments for those parameters. With ϕ-nodes, a basic block enumerates all the possible sources for a given variable, one for each in-edge in the CFG; with basic block arguments, the sources are distributed to the “other end” of the CFG edge. Basic block arguments are a nice alternative for “SSA-native” IRs because they avoid messy problems that arise when needing to treat ϕ-nodes differently from every other kind of instruction.)

Bril in SSA

Bril has an SSA extension . It adds support for a phi instruction. Beyond that, SSA form is just a restriction on the normal expressiveness of Bril—if you solemnly promise never to assign statically to the same variable twice, you are writing “SSA Bril.”

The reference interpreter has built-in support for phi , so you can execute your SSA-form Bril programs without fuss.

The SSA Philosophy

In addition to a language form, SSA is also a philosophy! It can fundamentally change the way you think about programs. In the SSA philosophy:

• definitions == variables
• instructions == values
• arguments == data flow graph edges

In LLVM, for example, instructions do not refer to argument variables by name—an argument is a pointer to defining instruction.

Converting to SSA

To convert to SSA, we want to insert ϕ-nodes whenever there are distinct paths containing distinct definitions of a variable. We don’t need ϕ-nodes in places that are dominated by a definition of the variable. So what’s a way to know when control reachable from a definition is not dominated by that definition? The dominance frontier!

We do it in two steps. First, insert ϕ-nodes:

Then, rename variables:

Converting from SSA

Eventually, we need to convert out of SSA form to generate efficient code for real machines that don’t have phi -nodes and do have finite space for variable storage.

The basic algorithm is pretty straightforward. If you have a ϕ-node:

Then there must be assignments to x and y (recursively) preceding this statement in the CFG. The paths from x to the phi -containing block and from y to the same block must “converge” at that block. So insert code into the phi -containing block’s immediate predecessors along each of those two paths: one that does v = id x and one that does v = id y . Then you can delete the phi instruction.

This basic approach can introduce some redundant copying. (Take a look at the code it generates after you implement it!) Non-SSA copy propagation optimization can work well as a post-processing step. For a more extensive take on how to translate out of SSA efficiently, see “Revisiting Out-of-SSA Translation for Correctness, Code Quality, and Efficiency” by Boissinot et al.

• One thing to watch out for: a tricky part of the translation from the pseudocode to the real world is dealing with variables that are undefined along some paths.
• Previous 6120 adventurers have found that it can be surprisingly difficult to get this right. Leave yourself plenty of time, and test thoroughly.
• You will want to make sure the output of your “to SSA” pass is actually in SSA form. There’s a really simple is_ssa.py script that can check that for you.
• You’ll also want to make sure that programs do the same thing when converted to SSA form and back again. Fortunately, brili supports the phi instruction, so you can interpret your SSA-form programs if you want to check the midpoint of that round trip.
• For bonus “points,” implement global value numbering for SSA-form Bril code.

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Static Single Assignment was presented in 1988 by Barry K. Rosen, Mark N, Wegman, and F. Kenneth Zadeck. 

In compiler design, Static Single Assignment ( shortened SSA) is a means of structuring the IR (intermediate representation) such that every variable is allotted a value only once and every variable is defined before it’s use. The prime use of SSA is it simplifies and improves the results of compiler optimisation algorithms, simultaneously by simplifying the variable properties. Some Algorithms improved by application of SSA – 

• Constant Propagation –   Translation of calculations from runtime to compile time. E.g. – the instruction v = 2*7+13 is treated like v = 27
• Value Range Propagation –   Finding the possible range of values a calculation could result in.
• Dead Code Elimination – Removing the code which is not accessible and will have no effect on results whatsoever.
• Strength Reduction – Replacing computationally expensive calculations by inexpensive ones.
• Register Allocation – Optimising the use of registers for calculations.

Any code can be converted to SSA form by simply replacing the target variable of each code segment with a new variable and substituting each use of a variable with the new edition of the variable reaching that point. Versions are created by splitting the original variables existing in IR and are represented by original name with a subscript such that every variable gets its own version.

Example #1:

Convert the following code segment to SSA form:

Here x,y,z,s,p,q are original variables and x 2 , s 2 , s 3 , s 4 are versions of x and s. 

Example #2:

Here a,b,c,d,e,q,s are original variables and a 2 , q 2 , q 3 are versions of a and q. 

Phi function and SSA codes

The three address codes may also contain goto statements, and thus a variable may assume value from two different paths.

Consider the following example:-

Example #3:

When we try to convert the above three address code to SSA form, the output looks like:-

Attempt #3:

We need to be able to decide what value shall y take, out of x 1 and x 2 . We thus introduce the notion of phi functions, which resolves the correct value of the variable from two different computation paths due to branching.

Hence, the correct SSA codes for the example will be:-

Solution #3:

Thus, whenever a three address code has a branch and control may flow along two different paths, we need to use phi functions for appropriate addresses.

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《Static Single Assignment Book》- 中文翻译

CnTransGroup/StaticSingleAssignmentBookChinese

Folders and files, repository files navigation, 《static single assignment book》翻译.

英文版PDF，仅供翻译参考

• 1.2 SSA的非形式化语义
• 1.3 与传统数据流分析的比较
• 1.4 此情此景此SSA
• 2.1 Def-use和use-def链
• 2.3 严格SSA形式和支配属性
• 第三章 SSA构造和解构算法
• 第四章 SSA高级构造算法
• 第五章 再谈SSA解构
• 第六章 SSA的函数式表示
• 第八章 基于SSA传播信息
• 第十章 Loop tree和归纳变量
• 第十三章 静态单赋值信息
• 第十四章 图和Gating函数
• 第十五章 Psi-SSA形式
• 第十六章 哈希化SSA形式：HSSA
• 第十七章 数组SSA形式
• 第十八章 SSA形式和代码生成
• 第二十一章 机器代码生成期的SSA解构
• 第二十二章 寄存器分配
• 第二十三章 基于SSA的硬件编译
• 第二十四章 为PHP开发基于SSA的编译器

译者纯粹出于学习目的与个人兴趣翻译本书，不追求任何经济利益。译者保留对此版本译文的署名权，其他权利以原作者和出版社的主张为准。本译文只供学习研究参考之用，不得公开传播发行或用于商业用途。有能力阅读英文书籍者请购买正版支持。

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