1 | \newcommand{\Alt}{ \mid\!\!\mid } |
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2 | |
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3 | % CerCo compiler architecture |
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4 | % Description of languages |
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5 | % Target hardware description |
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6 | |
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7 | \section{Compiler architecture} |
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8 | \label{sect.compiler.architecture} |
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9 | |
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10 | In this section we give an overview of the architecture of the CerCo verified C compiler. |
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11 | We discuss the compiler's intermediate languages, the optimisations and other transforms that occur at each intermediate language, and discuss the compiler's target hardware: the MCS-51 8-bit microprocessor. |
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12 | |
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13 | Many of the intermediate languages used in the CerCo verified C compiler are inspired by analogous languages in the CompCert verified C compiler, and a compiler written by Fran\s{c}ois Pottier---used for teaching compiler construction to undergraduates. |
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14 | Where appropriate, we make reference to the source documentation of these two compilers, to explain our intermediate languages. |
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15 | |
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16 | Note: though many of the compiler intermediate languages (especially in the front end) are shared with CompCert, the architecture of the CerCo compiler is different in quite a substantial way from that of CompCert. |
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17 | In particular, the CompCert compiler's backend `linearises' its code much earlier, compared to our own. |
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18 | Indeed, as explained below, the CerCo compiler works with a control-flow graph based representation of the program almost until producing machine code, only linearising in the translation from LTL to LIN intermediate languages. |
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19 | This is merely a design variation in our two compilers, and is not motivated by any real technical issue pertinent to the proof of correctness, or due to the lifting of cost models. |
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20 | |
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21 | \subsection{Compiler front-end} |
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22 | |
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23 | The compiler front-end lowers a program written in C to a low-level language of control-flow graphs, ready for the entry-point of our compiler backend. |
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24 | In total, there are three intermediate languages in the front-end. |
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25 | |
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26 | The first translation step of the compiler lowers the full C language to a high-level intermediate language, Clight---this language will be explained further below. |
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27 | This translation phase is unverified, using the CIL C parsing utility~\cite{cil02} to handle the intricacies of parsing C. |
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28 | We produce a Clight AST directly from a C source file, using this tool. |
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29 | As this translation step is unverified we do not expand any further on it here, and only note its existence. |
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30 | |
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31 | \paragraph{Clight} is a large subset of the C language, developed by the CompCert team for use in the CompCert verified C compiler, that we adopt as the source language of our compiler. |
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32 | We refer to~\cite{compcert} for a formal definition of the Clight language. |
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33 | |
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34 | Briefly, Clight features most of the types and operators of C, and includes pointer arithmetic, pointers to functions, and \texttt{struct} and \texttt{union} types, as well as all of C's control structures. |
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35 | The language is classically structured with expressions, statements, functions, and whole programs. |
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36 | Clight expressions are side-effect free, which means that side-effect operators ($\texttt{=}$,$\texttt{+=}$,$\texttt{++}$, and so on) and function calls within expressions are not supported. |
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37 | This is the key difference between the full C programming language and Clight. |
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38 | |
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39 | In order to limit the implementation effort of verifying the CerCo compiler, our current compiler for Clight does {\em not} cover the operators relating to the floating point type {\tt float}. |
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40 | |
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41 | \paragraph{Cminor} is a simple, low-level imperative language, comparable to a stripped-down, typeless variant of C. |
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42 | The Cminor intermediate language again is taken directly from the CompCert verified C compiler, and we refer to the CompCert project for its formal definition. |
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43 | Like Clight, the Cminor language is structured into expressions, statements, functions, and whole programs. |
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44 | Control flow constructs are now presented in a simpler form, compared to Clight. |
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45 | In particular, Cminor provides only a single, generic `loop' construct, into which the different looping constructs of Clight must be translated. |
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46 | Switch statements are also present, but in a semi-explicit jump-table form. |
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47 | |
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48 | In Cminor, stack operations are made explicit, and one must know which variables are stored on the stack when translating from Clight to Cminor. |
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49 | This information is produced by a static analysis that determines the variables whose address may be `taken'. |
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50 | When translating from Clight to Cminor, space is reserved for local arrays and structures. |
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51 | In a second step, the proper compilation of Clight programs into Cminor programs is performed: consisting mainly of the translation of Clight control structures to the more primitive control-flow constructs available in Cminor. |
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52 | |
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53 | \paragraph{RTLabs} is the last architecture independent language in the compilation process. |
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54 | It is a rather straightforward abstraction of the architecture-dependent RTL intermediate language used in the CompCert project. |
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55 | |
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56 | RTLabs is intended to ease retargeting of the compiler---should that be desired---by factorising some work common to the various target assembly languages, for example optimisations. |
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57 | In RTLAbs the structure of Cminor expressions is lost. |
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58 | This may have a negative impact on the instruction selection steps that follow in the compiler backend. |
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59 | However, the subtleties of instruction selection seem rather orthogonal to our goals, and we deem the possibility of retargeting easily the compiler more important than the efficiency of the generated code. |
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60 | |
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61 | In RTLAbs, programs are represented as \emph{control flow graphs}, or CFGs for short. |
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62 | We associate with the nodes of the graphs instructions reflecting commands of the Cminor language. |
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63 | As usual, commands that change the control flow of the program (e.g. loops, conditionals) are translated by inserting suitable branching instructions in the CFG. |
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64 | |
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65 | Local variables are now represented by \emph{pseudo registers}. |
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66 | The number of available pseudo registers is unbounded. |
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67 | Eventually these pseudo registers will be replaced by real (machine) registers or stack slots, in the compiler backend. |
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68 | |
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69 | Translating Cminor programs to RTLAbs consists of transforming Cminor commands into a CFG form. |
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70 | Most commands are sequential and have a rather straightforward linear translation. |
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71 | However, a conditional is translated into a branch instruction, whilst a loop is translated using a back-edge in the CFG. |
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72 | |
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73 | \subsection{Compiler back-end} |
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74 | |
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75 | \paragraph{RTL} is the first architecture-dependant intermediate language of our compiler, and the entry point of the compiler back end. |
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76 | RTL programs are structured as CFGs, like RTLabs. |
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77 | |
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78 | The syntax of RTL is very close to RTLAbs, but now MCS-51 instructions are made explicit. |
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79 | Type information completely disappears: everything is represented using 32-bit words. |
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80 | Moreover, each global variable of a program is associated to a fixed offset, as we begin to fix the eventual memory layout of the program in the processor's memory. |
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81 | The syntax of the RTL language is provided in Table~\ref{RTL:syntax}. |
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82 | Within the grammar $\textit{unop}$, $\textit{binop}$, $\textit{uncon}$, and $\textit{bincon}$, represent the sets of unary operations, binary operations, unary conditions and binary conditions of the MCS-51 machine code language, lifted into RTL, respectively. |
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83 | |
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84 | \begin{table} |
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85 | {\footnotesize |
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86 | \[ |
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87 | \begin{array}{lllllll} |
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88 | \textit{size} & ::= & \textsf{Byte} \Alt \textsf{HalfWord} \Alt \textsf{Word} & \qquad |
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89 | \textit{fun\_ref} & ::= & \textit{fun\_name} \Alt \textit{psd\_reg} |
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90 | \end{array} |
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91 | \] |
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92 | |
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93 | \[ |
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94 | \begin{array}{llll} |
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95 | \textit{instruction} & ::= & \Alt \textsf{skip} \rightarrow \textit{node} & |
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96 | \quad \mbox{(no instruction)}\\ |
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97 | & & \Alt \textit{psd\_reg} := n |
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98 | \rightarrow \textit{node} & \quad \mbox{(constant)}\\ |
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99 | & & \Alt \textit{psd\_reg} := \textit{unop}(\textit{psd\_reg}) |
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100 | \rightarrow \textit{node} & \quad \mbox{(unary operation)}\\ |
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101 | & & \Alt \textit{psd\_reg} := |
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102 | \textit{binop}(\textit{psd\_reg},\textit{psd\_reg}) |
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103 | \rightarrow \textit{node} & \quad |
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104 | \mbox{(binary operation)}\\ |
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105 | & & \Alt \textit{psd\_reg} := \textsf{\&globals}[n] |
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106 | \rightarrow \textit{node} & |
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107 | \quad \mbox{(address of a global)}\\ |
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108 | & & \Alt \textit{psd\_reg} := \textsf{\&locals}[n] |
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109 | \rightarrow \textit{node} & |
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110 | \quad \mbox{(address of a local)}\\ |
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111 | & & \Alt \textit{psd\_reg} := \textit{fun\_name} |
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112 | \rightarrow \textit{node} & |
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113 | \quad \mbox{(address of a function)}\\ |
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114 | & & \Alt \textit{psd\_reg} := |
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115 | \textit{size}(\textit{psd\_reg}[n]) |
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116 | \rightarrow \textit{node} & \quad \mbox{(memory load)}\\ |
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117 | & & \Alt \textit{size}(\textit{psd\_reg}[n]) := |
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118 | \textit{psd\_reg} |
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119 | \rightarrow \textit{node} & \quad \mbox{(memory store)}\\ |
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120 | & & \Alt \textit{psd\_reg} := \textit{fun\_ref}({\it psd\_reg^*}) |
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121 | \rightarrow \textit{node} & |
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122 | \quad \mbox{(function call)}\\ |
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123 | & & \Alt \textit{fun\_ref}({\it psd\_reg^*}) |
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124 | & \quad \mbox{(function tail call)}\\ |
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125 | & & \Alt \textsf{test}\ \textit{uncon}(\textit{psd\_reg}) \rightarrow |
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126 | \textit{node}, \textit{node} & \quad |
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127 | \mbox{(branch unary condition)}\\ |
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128 | & & \Alt \textsf{test}\ \textit{bincon}(\textit{psd\_reg},\textit{psd\_reg}) |
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129 | \rightarrow \textit{node}, \textit{node} & \quad |
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130 | \mbox{(branch binary condition)}\\ |
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131 | & & \Alt \textsf{return}\ \textit{psd\_reg}? & \quad |
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132 | \mbox{(return)} |
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133 | \end{array} |
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134 | \] |
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135 | |
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136 | \[ |
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137 | \begin{array}{lllllll} |
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138 | \textit{fun\_def} & ::= & \textit{fun\_name}(\textit{psd\_reg}^*) & \qquad |
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139 | \textit{program} & ::= & \textsf{globals}: n\\ |
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140 | & & \textsf{result:} \textit{psd\_reg}? & \qquad |
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141 | & & \textit{fun\_def}^*\\ |
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142 | & & \textsf{locals:} \textit{psd\_reg}^*\\ |
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143 | & & \textsf{stack:} n\\ |
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144 | & & \textsf{entry:} \textit{node}\\ |
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145 | & & \textsf{exit:} \textit{node}\\ |
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146 | & & (\textit{node:} \textit{instruction})^* |
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147 | \end{array} |
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148 | \]} |
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149 | \caption{Syntax of the RTL language}\label{RTL:syntax} |
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150 | \end{table} |
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151 | |
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152 | Translating from RTLabs into RTL is mostly straightforward. |
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153 | An RTLAbs instruction is often directly translated to a corresponding MCS-51 instruction. |
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154 | However, there are a few exceptions: some RTLAbs instructions are expanded into multiple MCS-51 instructions. |
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155 | When the translation of an RTLAbs instruction requires more than a few simple MCS-51 instructions, we generate a function implementing the RTLabs instruction, place it in the program's preamble before the entry point, and generate a call to the relevant function, instead of directly generating the instruction sequence. |
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156 | |
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157 | \paragraph{ERTL} programs are again structured as CFGs. |
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158 | In ERTL, calling conventions of the MCS-51 machine language are made explicit. |
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159 | We provide the syntax of the language in Table~\ref{ERTL:syntax}. |
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160 | |
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161 | The main difference between RTL and ERTL is the elimination of pseudo registers, and the use of hardware registers to pass arguments to functions. |
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162 | Parameters are now passed in fixed hardware registers, tied directly to our target hardware. |
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163 | If there are too many parameters, the remaining arguments to be passed are spilled, and are stored in the stack. |
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164 | |
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165 | Further, we now enforce a convention that certain other now-explicit hardware registers are used for certain tasks. |
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166 | We fix registers holding the result of a function, holding the base address of the program's global variables, holding the address of the top of the stack. |
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167 | We also make explicit that some registers must be saved and restored when entering or returning from a function, to avoid clobbering. |
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168 | |
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169 | ERTL function calls do not list their parameters anymore---they merely assert the number of arguments that are being passed. |
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170 | Two new instructions are provided to allocate and deallocate on the stack some space needed by a function to execute. |
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171 | Along with these two instructions come two instructions to fetch or assign a value in the parameter sections of the stack; these instructions cannot yet be translated using regular load and store instructions. |
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172 | This is because we do not know the final size of the stack area of each function at this point in the compilation chain. |
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173 | |
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174 | Note that the ERTL function return instruction has a boolean argument that indicates whether the result of the function may be used later or not. |
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175 | This is exploited in certain optimisations. |
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176 | |
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177 | \begin{table} |
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178 | {\footnotesize |
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179 | \[ |
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180 | \begin{array}{lllllll} |
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181 | \textit{size} & ::= & \textsf{Byte} \Alt \textsf{HalfWord} \Alt \textsf{Word} & \qquad |
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182 | \textit{fun\_ref} & ::= & \textit{fun\_name} \Alt \textit{psd\_reg} |
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183 | \end{array} |
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184 | \] |
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185 | |
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186 | \[ |
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187 | \begin{array}{llll} |
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188 | \textit{instruction} & ::= & \Alt \textsf{skip} \rightarrow \textit{node} & |
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189 | \quad \mbox{(no instruction)}\\ |
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190 | & & \Alt \textsf{NewFrame} \rightarrow \textit{node} & |
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191 | \quad \mbox{(frame creation)}\\ |
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192 | & & \Alt \textsf{DelFrame} \rightarrow \textit{node} & |
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193 | \quad \mbox{(frame deletion)}\\ |
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194 | & & \Alt \textit{psd\_reg} := \textsf{stack}[\textit{slot}, n] |
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195 | \rightarrow \textit{node} & |
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196 | \quad \mbox{(stack load)}\\ |
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197 | & & \Alt \textsf{stack}[\textit{slot}, n] := \textit{psd\_reg} |
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198 | \rightarrow \textit{node} & |
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199 | \quad \mbox{(stack store)}\\ |
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200 | & & \Alt \textit{hdw\_reg} := \textit{psd\_reg} |
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201 | \rightarrow \textit{node} & |
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202 | \quad \mbox{(pseudo to hardware)}\\ |
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203 | & & \Alt \textit{psd\_reg} := \textit{hdw\_reg} |
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204 | \rightarrow \textit{node} & |
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205 | \quad \mbox{(hardware to pseudo)}\\ |
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206 | & & \Alt \textit{psd\_reg} := n |
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207 | \rightarrow \textit{node} & \quad \mbox{(constant)}\\ |
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208 | & & \Alt \textit{psd\_reg} := \textit{unop}(\textit{psd\_reg}) |
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209 | \rightarrow \textit{node} & \quad \mbox{(unary operation)}\\ |
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210 | & & \Alt \textit{psd\_reg} := |
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211 | \textit{binop}(\textit{psd\_reg},\textit{psd\_reg}) |
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212 | \rightarrow \textit{node} & \quad |
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213 | \mbox{(binary operation)}\\ |
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214 | & & \Alt \textit{psd\_reg} := \textit{fun\_name} |
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215 | \rightarrow \textit{node} & |
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216 | \quad \mbox{(address of a function)}\\ |
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217 | & & \Alt \textit{psd\_reg} := |
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218 | \textit{size}(\textit{psd\_reg}[n]) |
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219 | \rightarrow \textit{node} & \quad \mbox{(memory load)}\\ |
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220 | & & \Alt \textit{size}(\textit{psd\_reg}[n]) := |
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221 | \textit{psd\_reg} |
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222 | \rightarrow \textit{node} & \quad \mbox{(memory store)}\\ |
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223 | & & \Alt \textit{fun\_ref}(n) \rightarrow \textit{node} & |
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224 | \quad \mbox{(function call)}\\ |
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225 | & & \Alt \textit{fun\_ref}(n) |
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226 | & \quad \mbox{(function tail call)}\\ |
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227 | & & \Alt \textsf{test}\ \textit{uncon}(\textit{psd\_reg}) \rightarrow |
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228 | \textit{node}, \textit{node} & \quad |
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229 | \mbox{(branch unary condition)}\\ |
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230 | & & \Alt \textsf{test}\ \textit{bincon}(\textit{psd\_reg},\textit{psd\_reg}) |
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231 | \rightarrow \textit{node}, \textit{node} & \quad |
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232 | \mbox{(branch binary condition)}\\ |
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233 | & & \Alt \textsf{return}\ b & \quad \mbox{(return)} |
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234 | \end{array} |
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235 | \] |
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236 | |
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237 | \[ |
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238 | \begin{array}{lllllll} |
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239 | \textit{fun\_def} & ::= & \textit{fun\_name}(n) & \qquad |
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240 | \textit{program} & ::= & \textsf{globals}: n\\ |
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241 | & & \textsf{locals:} \textit{psd\_reg}^* & \qquad |
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242 | & & \textit{fun\_def}^*\\ |
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243 | & & \textsf{stack:} n\\ |
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244 | & & \textsf{entry:} \textit{node}\\ |
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245 | & & (\textit{node:} \textit{instruction})^* |
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246 | \end{array} |
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247 | \]} |
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248 | \caption{Syntax of the ERTL language}\label{ERTL:syntax} |
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249 | \end{table} |
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250 | |
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251 | The majority of the work involved in translating from RTL to ERTL involves making the MCS-51 calling conventions explicit. |
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252 | These conventions appear when entering, calling and leaving a function, and when referencing a global variable or the address of a local variable. |
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253 | |
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254 | At this point, we also perform a \emph{liveness analysis} on ERTL to replace unused instructions by a $\textsf{skip}$, or dummy instruction with no effect on the program state. |
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255 | Our analysis declares an instruction as unused when it performs an assignment on a register that will not be read afterwards. |
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256 | The result of this liveness analysis is also exploited by the \emph{register allocation} algorithm whose result is to efficiently associate a physical location (a hardware register or an address in the stack) to each pseudo register of the input RTL program. |
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257 | |
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258 | \paragraph{LTL} |
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259 | |
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260 | \paragraph{LIN} |
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261 | |
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262 | \subsection{Target hardware} |
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263 | |
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264 | \subsubsection{LTL} |
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265 | |
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266 | As in ERTL, the structure of LTL programs is based on CFGs. Pseudo |
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267 | registers are not used anymore; instead, they are replaced by physical locations |
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268 | (a hardware register or an address in the stack). |
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269 | |
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270 | \paragraph{Syntax.} |
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271 | Except for a few exceptions, the instructions of the language are those of |
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272 | ERTL with hardware registers replacing pseudo registers. Calling and |
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273 | returning conventions were explicited in ERTL; thus, function calls and |
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274 | returns do not need parameters in LTL. The syntax is defined in table |
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275 | \ref{LTL:syntax}. |
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276 | |
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277 | \begin{table} |
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278 | {\footnotesize |
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279 | \[ |
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280 | \begin{array}{lllllll} |
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281 | \textit{size} & ::= & \textsf{Byte} \Alt \textsf{HalfWord} \Alt \textsf{Word} & \qquad |
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282 | \textit{fun\_ref} & ::= & \textit{fun\_name} \Alt \textit{hdw\_reg} |
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283 | \end{array} |
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284 | \] |
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285 | |
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286 | \[ |
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287 | \begin{array}{llll} |
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288 | \textit{instruction} & ::= & \Alt \textsf{skip} \rightarrow \textit{node} & |
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289 | \quad \mbox{(no instruction)}\\ |
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290 | & & \Alt \textsf{NewFrame} \rightarrow \textit{node} & |
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291 | \quad \mbox{(frame creation)}\\ |
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292 | & & \Alt \textsf{DelFrame} \rightarrow \textit{node} & |
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293 | \quad \mbox{(frame deletion)}\\ |
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294 | & & \Alt \textit{hdw\_reg} := n |
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295 | \rightarrow \textit{node} & \quad \mbox{(constant)}\\ |
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296 | & & \Alt \textit{hdw\_reg} := \textit{unop}(\textit{hdw\_reg}) |
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297 | \rightarrow \textit{node} & \quad \mbox{(unary operation)}\\ |
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298 | & & \Alt \textit{hdw\_reg} := |
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299 | \textit{binop}(\textit{hdw\_reg},\textit{hdw\_reg}) |
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300 | \rightarrow \textit{node} & \quad |
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301 | \mbox{(binary operation)}\\ |
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302 | & & \Alt \textit{hdw\_reg} := \textit{fun\_name} |
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303 | \rightarrow \textit{node} & |
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304 | \quad \mbox{(address of a function)}\\ |
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305 | & & \Alt \textit{hdw\_reg} := \textit{size}(\textit{hdw\_reg}[n]) |
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306 | \rightarrow \textit{node} & \quad \mbox{(memory load)}\\ |
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307 | & & \Alt \textit{size}(\textit{hdw\_reg}[n]) := \textit{hdw\_reg} |
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308 | \rightarrow \textit{node} & \quad \mbox{(memory store)}\\ |
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309 | & & \Alt \textit{fun\_ref}() \rightarrow \textit{node} & |
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310 | \quad \mbox{(function call)}\\ |
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311 | & & \Alt \textit{fun\_ref}() |
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312 | & \quad \mbox{(function tail call)}\\ |
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313 | & & \Alt \textsf{test}\ \textit{uncon}(\textit{hdw\_reg}) \rightarrow |
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314 | \textit{node}, \textit{node} & \quad |
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315 | \mbox{(branch unary condition)}\\ |
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316 | & & \Alt \textsf{test}\ \textit{bincon}(\textit{hdw\_reg},\textit{hdw\_reg}) |
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317 | \rightarrow \textit{node}, \textit{node} & \quad |
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318 | \mbox{(branch binary condition)}\\ |
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319 | & & \Alt \textsf{return} & \quad \mbox{(return)} |
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320 | \end{array} |
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321 | \] |
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322 | |
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323 | \[ |
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324 | \begin{array}{lllllll} |
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325 | \textit{fun\_def} & ::= & \textit{fun\_name}(n) & \qquad |
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326 | \textit{program} & ::= & \textsf{globals}: n\\ |
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327 | & & \textsf{locals:} n & \qquad |
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328 | & & \textit{fun\_def}^*\\ |
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329 | & & \textsf{stack:} n\\ |
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330 | & & \textsf{entry:} \textit{node}\\ |
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331 | & & (\textit{node:} \textit{instruction})^* |
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332 | \end{array} |
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333 | \]} |
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334 | \caption{Syntax of the LTL language}\label{LTL:syntax} |
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335 | \end{table} |
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336 | |
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337 | \paragraph{Translation of ERTL to LTL.} The translation relies on the |
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338 | results of the liveness analysis and of the register allocation. Unused |
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339 | instructions are eliminated and each pseudo register is replaced by a physical |
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340 | location. In LTL, the size of the stack frame of a function is known; |
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341 | instructions intended to load or store values in the stack are translated |
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342 | using regular load and store instructions. |
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343 | |
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344 | \paragraph{Optimizations.} A \emph{graph compression} algorithm removes empty |
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345 | instructions generated by previous compilation passes and by the liveness |
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346 | analysis. |
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347 | |
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348 | \subsubsection{LIN} |
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349 | |
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350 | In LIN, the structure of a program is no longer based on CFGs. Every function |
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351 | is represented as a sequence of instructions. |
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352 | |
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353 | \paragraph{Syntax.} |
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354 | The instructions of LIN are very close to those of LTL. \emph{Program |
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355 | labels}, \emph{gotos} and branch instructions handle the changes in the |
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356 | control flow. The syntax of LIN programs is shown in table \ref{LIN:syntax}. |
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357 | |
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358 | \begin{table} |
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359 | {\footnotesize |
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360 | \[ |
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361 | \begin{array}{lllllll} |
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362 | \textit{size} & ::= & \textsf{Byte} \Alt \textsf{HalfWord} \Alt \textsf{Word} & \qquad |
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363 | \textit{fun\_ref} & ::= & \textit{fun\_name} \Alt \textit{hdw\_reg} |
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364 | \end{array} |
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365 | \] |
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366 | |
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367 | \[ |
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368 | \begin{array}{llll} |
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369 | \textit{instruction} & ::= & \Alt \textsf{NewFrame} & |
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370 | \quad \mbox{(frame creation)}\\ |
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371 | & & \Alt \textsf{DelFrame} & |
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372 | \quad \mbox{(frame deletion)}\\ |
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373 | & & \Alt \textit{hdw\_reg} := n & \quad \mbox{(constant)}\\ |
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374 | & & \Alt \textit{hdw\_reg} := \textit{unop}(\textit{hdw\_reg}) |
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375 | & \quad \mbox{(unary operation)}\\ |
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376 | & & \Alt \textit{hdw\_reg} := |
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377 | \textit{binop}(\textit{hdw\_reg},\textit{hdw\_reg}) |
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378 | & \quad \mbox{(binary operation)}\\ |
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379 | & & \Alt \textit{hdw\_reg} := \textit{fun\_name} |
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380 | & \quad \mbox{(address of a function)}\\ |
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381 | & & \Alt \textit{hdw\_reg} := \textit{size}(\textit{hdw\_reg}[n]) |
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382 | & \quad \mbox{(memory load)}\\ |
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383 | & & \Alt \textit{size}(\textit{hdw\_reg}[n]) := \textit{hdw\_reg} |
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384 | & \quad \mbox{(memory store)}\\ |
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385 | & & \Alt \textsf{call}\ \textit{fun\_ref} |
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386 | & \quad \mbox{(function call)}\\ |
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387 | & & \Alt \textsf{tailcall}\ \textit{fun\_ref} |
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388 | & \quad \mbox{(function tail call)}\\ |
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389 | & & \Alt \textit{uncon}(\textit{hdw\_reg}) \rightarrow |
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390 | \textit{node} & \quad |
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391 | \mbox{(branch unary condition)}\\ |
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392 | & & \Alt \textit{bincon}(\textit{hdw\_reg},\textit{hdw\_reg}) |
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393 | \rightarrow \textit{node} & \quad |
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394 | \mbox{(branch binary condition)}\\ |
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395 | & & \Alt \textit{mips\_label:} & \quad \mbox{(MCS-51 label)}\\ |
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396 | & & \Alt \textsf{goto}\ \textit{mips\_label} & \quad \mbox{(goto)}\\ |
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397 | & & \Alt \textsf{return} & \quad \mbox{(return)} |
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398 | \end{array} |
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399 | \] |
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400 | |
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401 | \[ |
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402 | \begin{array}{lllllll} |
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403 | \textit{fun\_def} & ::= & \textit{fun\_name}(n) & \qquad |
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404 | \textit{program} & ::= & \textsf{globals}: n\\ |
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405 | & & \textsf{locals:} n & \qquad |
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406 | & & \textit{fun\_def}^*\\ |
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407 | & & \textit{instruction}^* |
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408 | \end{array} |
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409 | \]} |
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410 | \caption{Syntax of the LIN language}\label{LIN:syntax} |
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411 | \end{table} |
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412 | |
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413 | \paragraph{Translation of LTL to LIN.} |
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414 | This translation amounts to transform in an efficient way the graph structure of |
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415 | functions into a linear structure of sequential instructions. |
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416 | |
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417 | \subsubsection{ASM} |
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