Merge remote-tracking branch 'refs/remotes/origin/main'

MiniC/Lib/Dominators.py

@@ -0,0 +1,128 @@
+"""
+Utility functions to work with dominators in a :py:class:`CFG <Lib.CFG.CFG>`.
+
+Do not hesitate to look at the source of the functions
+to get a better understanding of the algorithms.
+"""
+
+from typing import Dict, Set
+from graphviz import Digraph
+from Lib.CFG import Block, CFG
+
+
+def computeDom(cfg: CFG) -> Dict[Block, Set[Block]]:
+    """
+    `computeDom(cfg)` computes the table associating blocks to their
+    dominators in `cfg`.
+    It works by solving the equation system.
+
+    This is an helper function called during SSA entry.
+    """
+    all_blocks: Set[Block] = set(cfg.get_blocks())
+    dominators: Dict[Block, Set[Block]] = dict()
+    for b in all_blocks:
+        if b.get_in():  # If b has some predecessor
+            dominators[b] = all_blocks
+        else:  # If b has no predecessors
+            dominators[b] = {b}
+    new_dominators: Dict[Block, Set[Block]] = dict()
+    while True:
+        for b in all_blocks:
+            if b.get_in():
+                dom_preds = [dominators[b2] for b2 in b.get_in()]
+                new_dominators[b] = {b}.union(set.intersection(*dom_preds))
+            else:
+                new_dominators[b] = {b}
+        if dominators == new_dominators:
+            break
+        else:
+            dominators = new_dominators
+            new_dominators = dict()
+    return dominators
+
+
+def printDT(filename: str, graph: Dict[Block, Set[Block]]) -> None:  # pragma: no cover
+    """Display a graphical rendering of the given domination tree."""
+    dot = Digraph()
+    for k in graph:
+        dot.node(str(k.get_label()))
+    for k in graph:
+        for v in graph[k]:
+            dot.edge(str(k.get_label()), str(v.get_label()))
+    dot.render(filename, view=True)
+
+
+def computeDT(cfg: CFG, dominators: Dict[Block, Set[Block]],
+              dom_graphs: bool, basename: str) -> Dict[Block, Set[Block]]:
+    """
+    `computeDT(cfg, dominators)` computes the domination tree of `cfg`
+    using the previously computed `dominators`.
+    It returns `DT`, a dictionary which associates a block with its children
+    in the dominator tree.
+
+    This is an helper function called during SSA entry.
+    """
+    # First, compute the immediate dominators
+    idominators: Dict[Block, Block] = {}
+    for b, doms in dominators.items():
+        # The immediate dominator of b is the unique vertex n ≠ b
+        # which dominates b and is dominated by all vertices in Dom(b) − b.
+        strict_doms = doms - {b}
+        idoms = set()
+        for n in strict_doms:
+            if strict_doms.issubset(dominators[n]):
+                idoms.add(n)
+        if idoms:
+            assert (len(idoms) == 1)
+            idominators[b] = idoms.pop()
+    # Then, simply inverse the relation to obtain the domination tree
+    DT = {b: set() for b in cfg.get_blocks()}
+    for i, idominator in idominators.items():
+        DT[idominator].add(i)
+    # Print the domination tree if asked
+    if dom_graphs:
+        s = "{}.{}.ssa.DT.dot".format(basename, cfg.fdata.get_name())
+        print("SSA - domination tree graph:", s)
+        printDT(s, DT)
+    return DT
+
+
+def _computeDF_at_block(
+        cfg: CFG,
+        dominators: Dict[Block, Set[Block]],
+        DT: Dict[Block, Set[Block]],
+        b: Block,
+        DF: Dict[Block, Set[Block]]) -> None:
+    """
+    `_computeDF_at_block(...)` computes the dominance frontier at the given block,
+    by updating `DF`.
+
+    This is an helper function called during SSA entry.
+    """
+    S: Set[Block] = {succ for succ in cfg.out_blocks(b) if succ not in DT[b]}
+    for b_succ in DT[b]:
+        _computeDF_at_block(cfg, dominators, DT, b_succ, DF)
+        for b_frontier in DF[b_succ]:
+            if b not in (dominators[b_frontier] - {b_frontier}):
+                S.add(b_frontier)
+    DF[b] = S
+
+
+def computeDF(cfg: CFG, dominators: Dict[Block, Set[Block]],
+              DT: Dict[Block, Set[Block]], dom_graphs: bool, basename: str
+              ) -> Dict[Block, Set[Block]]:
+    """
+    `computeDF(...)` computes the dominance frontier of a CFG.
+    It returns `DF` which associates a block to its frontier.
+
+    This is an helper function called during SSA entry.
+    """
+    DF: Dict[Block, Set[Block]] = dict()
+    for b_entry in cfg.get_entries():
+        _computeDF_at_block(cfg, dominators, DT, b_entry, DF)
+    # Print the domination frontier on the CFG if asked
+    if dom_graphs:
+        s = "{}.{}.ssa.DF.dot".format(basename, cfg.fdata.get_name())
+        print("SSA - dominance frontier graph:", s)
+        cfg.print_dot(s, DF, True)
+    return DF

MiniC/Lib/Graphes.py

@@ -0,0 +1,306 @@
+""" Python Classes for Oriented and Non Oriented Graphs
+"""
+
+from graphviz import Digraph  # for dot output
+from typing import List, Dict, Set, Tuple, Any
+
+
+class GraphError(Exception):
+    """Exception raised for self loops.
+    """
+
+    message: str
+
+    def __init__(self, message: str):
+        self.message = message
+
+
+class GeneralGraph(object):
+    """
+    General class regrouping similarities
+    between directed and non oriented graphs.
+    The only differences between the two are:
+
+    - how to compute the set of edges
+    - how to add an edge
+    - how to print the graph
+    - how to delete a vertex
+    - how to delete an edge
+    - we only color undirected graphs
+    """
+
+    graph_dict: Dict[Any, Set]
+
+    def __init__(self, graph_dict=None):
+        """
+        Initializes a graph object.
+        If no dictionary or None is given,
+        an empty dictionary will be used.
+        """
+        if graph_dict is None:
+            graph_dict = {}
+        self.graph_dict = graph_dict
+
+    def vertices(self) -> List[Any]:
+        """Return the vertices of a graph."""
+        return list(self.graph_dict.keys())
+
+    def add_vertex(self, vertex: Any) -> None:
+        """
+        If the vertex "vertex" is not in
+        self.graph_dict, a key "vertex" with an empty
+        list as a value is added to the dictionary.
+        Otherwise nothing has to be done.
+        """
+        if vertex not in self.graph_dict:
+            self.graph_dict[vertex] = set()
+
+    def edges(self) -> List[Set]:
+        """Return the edges of the graph."""
+        return []
+
+    def __str__(self):
+        res = "vertices: "
+        for k in self.graph_dict:
+            res += str(k) + " "
+        res += "\nedges: "
+        for edge in self.edges():
+            res += str(edge) + " "
+        return res
+
+    def dfs_traversal(self, root: Any) -> List[Any]:
+        """
+        Compute a depth first search of the graph,
+        from the vertex root.
+        """
+        seen: List[Any] = []
+        todo: List[Any] = [root]
+        while len(todo) > 0:  # while todo ...
+            current = todo.pop()
+            seen.append(current)
+            for neighbour in self.graph_dict[current]:
+                if neighbour not in seen:
+                    todo.append(neighbour)
+        return seen
+
+    def is_reachable_from(self, v1: Any, v2: Any) -> bool:
+        """True if there is a path from v1 to v2."""
+        return v2 in self.dfs_traversal(v1)
+
+    def connected_components(self) -> List[List[Any]]:
+        """
+        Compute the list of all connected components of the graph,
+        each component being a list of vetices.
+        """
+        components: List[List[Any]] = []
+        done: List[Any] = []
+        for v in self.vertices():
+            if v not in done:
+                v_comp = self.dfs_traversal(v)
+                components.append(v_comp)
+                done.extend(v_comp)
+        return components
+
+    def bfs_traversal(self, root: Any) -> List[Any]:
+        """
+        Compute a breadth first search of the graph,
+        from the vertex root.
+        """
+        seen: List[Any] = []
+        todo: List[Any] = [root]
+        while len(todo) > 0:  # while todo ...
+            current = todo.pop(0)  # list.pop(0): for dequeuing (on the left...) !
+            seen.append(current)
+            for neighbour in self.graph_dict[current]:
+                if neighbour not in seen:
+                    todo.append(neighbour)
+        return seen
+
+
+class Graph(GeneralGraph):
+    """Class for non oriented graphs."""
+
+    def edges(self) -> List[Set]:
+        """
+        A static method generating the set of edges
+        (they appear twice in the dictionnary).
+        Return a list of sets.
+        """
+        edges = []
+        for vertex in self.graph_dict:
+            for neighbour in self.graph_dict[vertex]:
+                if {neighbour, vertex} not in edges:
+                    edges.append({vertex, neighbour})
+        return edges
+
+    def add_edge(self, edge: Tuple[Any, Any]) -> None:
+        """
+        Add an edge in the graph.
+        edge should be a pair and not (c,c)
+        (we call g.add_edge((v1,v2)))
+        """
+        (vertex1, vertex2) = edge
+        if vertex1 == vertex2:
+            raise GraphError("Cannot add a self loop on vertex {} in an unoriented graph.".format(
+                             str(vertex1)))
+        if vertex1 in self.graph_dict:
+            self.graph_dict[vertex1].add(vertex2)
+        else:
+            self.graph_dict[vertex1] = {vertex2}
+        if vertex2 in self.graph_dict:
+            self.graph_dict[vertex2].add(vertex1)
+        else:
+            self.graph_dict[vertex2] = {vertex1}
+
+    def print_dot(self, name: str, colors={}) -> None:
+        """Print the graph."""
+        color_names = ['red', 'blue', 'green', 'yellow', 'cyan', 'magenta'] + \
+            [f"grey{i}" for i in range(0, 100, 10)]
+        color_shapes = ['ellipse', 'polygon', 'box', 'circle', 'egg', 'pentagon', 'hexagon']
+        dot = Digraph(comment='Conflict Graph')
+        for k in self.graph_dict:
+            shape = None
+            if not colors:
+                color = "red"  # Graph not colored: red for everyone
+            elif k not in colors:
+                color = "grey"  # Node not colored: grey
+            else:
+                n = colors[k]
+                if n < len(color_names):
+                    color = color_names[colors[k]]
+                else:
+                    color = "black"  # Too many colors anyway, it won't be readable.
+                shape = color_shapes[n % len(color_shapes)]
+            dot.node(str(k), color=color, shape=shape)
+        for (v1, v2) in self.edges():
+            dot.edge(str(v1), str(v2), dir="none")
+        # print(dot.source)
+        dot.render(name, view=True)  # print in pdf
+
+    def delete_vertex(self, vertex: Any) -> None:
+        """Delete a vertex and all the adjacent edges."""
+        gdict = self.graph_dict
+        for neighbour in gdict[vertex]:
+            gdict[neighbour].remove(vertex)
+        del gdict[vertex]
+
+    def delete_edge(self, edge: Tuple[Any, Any]):
+        """Delete an edge."""
+        (v1, v2) = edge
+        self.graph_dict[v1].remove(v2)
+        self.graph_dict[v2].remove(v1)
+
+    def color(self) -> Dict[Any, int]:
+        """
+        Color the graph with an unlimited number of colors.
+        Return a dict vertex -> color, where color is an integer (0, 1, ...).
+        """
+        coloring, _, _ = self.color_with_k_colors()
+        return coloring
+
+    # see algo of the course
+    def color_with_k_colors(self, K=None, avoidingnodes=()) -> Tuple[Dict[Any, int], bool, List]:
+        """
+        Color with <= K colors (if K is unspecified, use unlimited colors).
+
+        Return 3 values:
+
+        - a dict vertex -> color
+        - a Boolean, True if the coloring succeeded
+        - the set of nodes actually colored
+
+        Do not color vertices belonging to avoidingnodes.
+
+        Continue even if the algo fails.
+        """
+        if K is None:
+            K = len(self.graph_dict)
+        todo_vertices = []
+        is_total = True
+        gcopy = Graph(self.graph_dict.copy())
+        # suppress nodes that are not to be considered.
+        for node in avoidingnodes:
+            gcopy.delete_vertex(node)
+        # append nodes in the list according to their degree and node number:
+        while gcopy.graph_dict:
+            todo = list(gcopy.graph_dict)
+            todo.sort(key=lambda v: (len(gcopy.graph_dict[v]), str(v)))
+            lower = todo[0]
+            todo_vertices.append(lower)
+            gcopy.delete_vertex(lower)
+        # Now reverse the list: first elements are those with higher degree
+        # print(todo_vertices)
+        todo_vertices.reverse()  # in place reversal
+        # print(todo_vertices)
+        coloring = {}
+        colored_nodes = []
+        # gdict will be the coloring map to return
+        gdict = self.graph_dict
+        for v in todo_vertices:
+            seen_neighbours = [x for x in gdict[v] if x in coloring]
+            choose_among = [i for i in range(K) if not (
+                i in [coloring[v1] for v1 in seen_neighbours])]
+            if choose_among:
+                # if the node can be colored, I choose the minimal color.
+                color = min(choose_among)
+                coloring[v] = color
+                colored_nodes.append(v)
+            else:
+                # if I cannot color some node, the coloring is not Total
+                # but I continue
+                is_total = False
+        return (coloring, is_total, colored_nodes)
+
+
+class DiGraph(GeneralGraph):
+    """Class for directed graphs."""
+
+    def neighbourhoods(self) -> List[Tuple[Any, Set]]:
+        """Return all neighbourhoods in the graph."""
+        return list(self.graph_dict.items())
+
+    def edges(self) -> List[Tuple[Any, Any]]:
+        """ A static method generating the set of edges"""
+        edges = []
+        for vertex in self.graph_dict:
+            for neighbour in self.graph_dict[vertex]:
+                edges.append((vertex, neighbour))
+        return edges
+
+    def add_edge(self, edge: Tuple[Any, Any]) -> None:
+        """
+        Add an edge in the graph.
+        edge should be a pair and not (c,c)
+        (we call g.add_edge((v1,v2)))
+        """
+        (vertex1, vertex2) = edge
+        if vertex1 in self.graph_dict:
+            self.graph_dict[vertex1].add(vertex2)
+        else:
+            self.graph_dict[vertex1] = {vertex2}
+        if vertex2 not in self.graph_dict:
+            self.graph_dict[vertex2] = set()
+
+    def print_dot(self, name: str) -> None:
+        """Print the graph."""
+        dot = Digraph(comment='Conflict Graph')
+        for k in self.graph_dict:
+            shape = None
+            color = "grey"
+            dot.node(str(k), color=color, shape=shape)
+        for (v1, v2) in self.edges():
+            dot.edge(str(v1), str(v2), dir="none")
+        # print(dot.source)
+        dot.render(name, view=True)  # print in pdf
+
+    def delete_vertex(self, vertex: Any) -> None:
+        """Delete a vertex and all the adjacent edges."""
+        for node, neighbours in self.graph_dict.items():
+            if vertex in neighbours:
+                neighbours.remove(vertex)
+        del self.graph_dict[vertex]
+
+    def delete_edge(self, edge: Tuple[Any, Any]) -> None:
+        """Delete an edge."""
+        (v1, v2) = edge
+        self.graph_dict[v1].remove(v2)

MiniC/Lib/PhiNode.py

@@ -0,0 +1,58 @@
+"""
+Classes for φ nodes in a RiscV CFG :py:class:`CFG <Lib.CFG.CFG>` under SSA Form:
+:py:class:`PhiNode` for a statement of the form temp_x = φ(temp_0, ..., temp_n).
+These particular kinds of statements are expected to be in the field
+b._phis for a :py:class:`Block <Lib.CFG.Block>` b.
+"""
+
+from dataclasses import dataclass
+from typing import Dict
+
+from Lib.Operands import Operand, Temporary, DataLocation, Renamer
+from Lib.Statement import Statement, Label
+
+
+@dataclass
+class PhiNode(Statement):
+    """
+    A φ node is a renaming in the CFG, of the form temp_x = φ(temp_0, ..., temp_n).
+    The field var contains the variable temp_x.
+    The field srcs relies for each precedent block in the CFG, identified with its label,
+    the variable temp_i of the φ node.
+    """
+    var: DataLocation
+    srcs: Dict[Label, Operand]
+
+    def defined(self):
+        """Return the variable defined by the φ node."""
+        return [self.var]
+
+    def used(self) -> Dict[Label, Operand]:
+        """
+        Return the dictionnary associating for each previous block the corresponding variable.
+        """
+        return self.srcs
+
+    def rename(self, renamer: Renamer) -> None:
+        """Rename the variable defined by the φ node with a fresh name."""
+        if isinstance(self.var, Temporary):
+            self.var = renamer.fresh(self.var)
+
+    def rename_from(self, renamer: Renamer, label: Label) -> None:
+        """Rename the variable associated to the block identified by `label`."""
+        if label in self.srcs:
+            t = self.srcs[label]
+            if isinstance(t, Temporary):
+                if renamer.defined(t):
+                    self.srcs[label] = renamer.replace(t)
+                else:
+                    del self.srcs[label]
+
+    def __str__(self):
+        return "{} = φ({})".format(self.var, self.srcs)
+
+    def __hash__(self):
+        return hash((self.var, *self.srcs.items()))
+
+    def printIns(self, stream):
+        print('        # ' + str(self), file=stream)

MiniC/MiniCC.py

@@ -5,8 +5,9 @@ Usage:
     python3 MiniCC.py --mode <mode> <filename>
     python3 MiniCC.py --help
 """
-import traceback
 from typing import cast
+from enum import Enum
+
 from MiniCLexer import MiniCLexer
 from MiniCParser import MiniCParser
 from TP03.MiniCTypingVisitor import MiniCTypingVisitor, MiniCTypeError
@@ -14,12 +15,11 @@ from TP03.MiniCInterpretVisitor import MiniCInterpretVisitor
 from Lib.Errors import (MiniCUnsupportedError, MiniCInternalError,
                         MiniCRuntimeError, AllocationError)
 
-from enum import Enum
-import argparse
-
 from antlr4 import FileStream, CommonTokenStream
 from antlr4.error.ErrorListener import ErrorListener
 
+from argparse import ArgumentParser
+from traceback import print_exc
 import os
 import sys
 
@@ -52,7 +52,7 @@ def valid_modes():
         return modes
 
     try:
-        import TP05.SSA  # type: ignore[import]
+        import TP05.EnterSSA  # type: ignore[import]
         modes.append('codegen-ssa')
     except ImportError:
         return modes
@@ -84,7 +84,7 @@ class CountErrorListener(ErrorListener):
 
 def main(inputname, reg_alloc, mode,
          typecheck=True, stdout=False, output_name=None, debug=False,
-         debug_graphs=False, ssa_graphs=False):
+         debug_graphs=False, ssa_graphs=False, dom_graphs=False):
     (basename, rest) = os.path.splitext(inputname)
     if mode.is_codegen():
         if stdout:
@@ -144,22 +144,19 @@ def main(inputname, reg_alloc, mode,
                 code = function
             else:
                 from TP04.BuildCFG import build_cfg  # type: ignore[import]
-                from Lib.CFG import CFG  # type: ignore[import]
                 code = build_cfg(function)
-                assert (isinstance(code, CFG))
             if debug_graphs:
                 s = "{}.{}.dot".format(basename, code.fdata.get_name())
                 print("CFG:", s)
                 code.print_dot(s, view=True)
             if mode.value >= Mode.SSA.value:
-                from TP05.SSA import enter_ssa  # type: ignore[import]
+                from TP05.EnterSSA import enter_ssa  # type: ignore[import]
                 from Lib.CFG import CFG  # type: ignore[import]
-
-                DF = enter_ssa(cast(CFG, code), basename, debug, ssa_graphs)
+                enter_ssa(cast(CFG, code), dom_graphs, basename)
                 if ssa_graphs:
-                    s = "{}.{}.ssa.dot".format(basename, code.fdata.get_name())
+                    s = "{}.{}.enterssa.dot".format(basename, code.fdata.get_name())
                     print("SSA:", s)
-                    code.print_dot(s, DF, True)
+                    code.print_dot(s, view=True)
                 if mode == Mode.OPTIM:
                     from TPoptim.OptimSSA import OptimSSA  # type: ignore[import]
                     OptimSSA(cast(CFG, code), debug=debug)
@@ -207,8 +204,8 @@ liveness file not found for {}.".format(form))
                 allocator.prepare()
             if mode.value >= Mode.SSA.value:
                 from Lib.CFG import CFG  # type: ignore[import]
-                from TP05.SSA import exit_ssa  # type: ignore[import]
-                exit_ssa(cast(CFG, code))
+                from TP05.ExitSSA import exit_ssa  # type: ignore[import]
+                exit_ssa(cast(CFG, code), reg_alloc == 'smart')
                 comment += " with SSA"
             if allocator:
                 allocator.rewriteCode(code)
@@ -233,7 +230,7 @@ if __name__ == '__main__':
 
     modes = valid_modes()
 
-    parser = argparse.ArgumentParser(description='Generate code for .c file')
+    parser = ArgumentParser(description='CAP/MIF08 MiniCC compiler')
 
     parser.add_argument('filename', type=str,
                         help='Source file.')
@@ -265,7 +262,10 @@ if __name__ == '__main__':
     if "codegen-ssa" in modes:
         parser.add_argument('--ssa-graphs', action='store_true',
                             default=False,
-                            help='Display SSA graphs (DT, DF).')
+                            help='Display the CFG at SSA entry and exit.')
+        parser.add_argument('--dom-graphs', action='store_true',
+                            default=False,
+                            help='Display dominance-related graphs (DT, DF).')
 
     args = parser.parse_args()
     reg_alloc = args.reg_alloc if "codegen-linear" in modes else None
@@ -273,6 +273,7 @@ if __name__ == '__main__':
     outfile = args.output if "codegen-linear" in modes else None
     graphs = args.graphs if "codegen-cfg" in modes else False
     ssa_graphs = args.ssa_graphs if "codegen-ssa" in modes else False
+    dom_graphs = args.dom_graphs if "codegen-ssa" in modes else False
 
     if reg_alloc is None and "codegen" in args.mode:
         print("error: the following arguments is required: --reg-alloc")
@@ -308,10 +309,10 @@ if __name__ == '__main__':
         main(args.filename, reg_alloc, mode,
              typecheck,
              to_stdout, outfile, args.debug,
-             graphs, ssa_graphs)
+             graphs, ssa_graphs, dom_graphs)
     except MiniCUnsupportedError as e:
         print(e)
         exit(5)
     except (MiniCInternalError, AllocationError):
-        traceback.print_exc()
+        print_exc()
         exit(4)

MiniC/README-SSA.md

@@ -0,0 +1,20 @@
+# MiniC Compiler 
+LAB5a (Control Flow Graph in SSA Form) & LAB5b (Smart Register Allocation), CAP 2022-23
+
+# Authors
+
+YOUR NAME HERE
+
+# Contents
+
+TODO:
+- Explain any design choices you may have made.
+- Do not forget to remove all debug traces from your code!
+
+# Test design 
+
+TODO: give the main objectives of your tests.
+
+# Known bugs
+
+TODO: bugs you could not fix (if any).

MiniC/TP05/EnterSSA.py

@@ -0,0 +1,70 @@
+"""
+CAP, SSA Intro, Elimination and Optimisations
+Functions to convert a CFG into SSA Form.
+"""
+
+from typing import List, Dict, Set
+from Lib.CFG import Block, CFG
+from Lib.Operands import Renamer
+from Lib.Statement import Instruction
+from Lib.PhiNode import PhiNode
+from Lib.Dominators import computeDom, computeDT, computeDF
+
+
+def insertPhis(cfg: CFG, DF: Dict[Block, Set[Block]]) -> None:
+    """
+    `insertPhis(CFG, DF)` inserts phi nodes in `cfg` where needed.
+    At this point, phi nodes will look like `temp_x = φ(temp_x, ..., temp_x)`.
+
+    This is an helper function called during SSA entry.
+    """
+    for var, defs in cfg.gather_defs().items():
+        has_phi: Set[Block] = set()
+        queue: List[Block] = list(defs)
+        while queue:
+            d = queue.pop(0)
+            for b in DF[d]:
+                if b not in has_phi:
+                    # TODO add a phi node in block `b` (Lab 5a, Exercise 4)
+                    raise NotImplementedError("insertPhis")
+
+
+def rename_block(cfg: CFG, DT: Dict[Block, Set[Block]], renamer: Renamer, b: Block) -> None:
+    """
+    Rename variables from block b.
+
+    This is an auxiliary function for `rename_variables`.
+    """
+    renamer = renamer.copy()
+    for i in b.get_all_statements():
+        if isinstance(i, Instruction | PhiNode):
+            i.rename(renamer)
+    for succ in cfg.out_blocks(b):
+        for i in succ._phis:
+            assert (isinstance(i, PhiNode))
+            i.rename_from(renamer, b.get_label())
+    # TODO recursive call(s) of rename_block (Lab 5a, Exercise 5)
+
+
+def rename_variables(cfg: CFG, DT: Dict[Block, Set[Block]]) -> None:
+    """
+    Rename variables in the CFG, to transform `temp_x = φ(temp_x, ..., temp_x)`
+    into `temp_x = φ(temp_0, ... temp_n)`.
+
+    This is an helper function called during SSA entry.
+    """
+    renamer = Renamer(cfg.fdata._pool)
+    # TODO initial call(s) to rename_block (Lab 5a, Exercise 5)
+
+
+def enter_ssa(cfg: CFG, dom_graphs=False, basename="prog") -> None:
+    """
+    Convert the CFG `cfg` into SSA Form:
+    compute the dominance frontier, then insert phi nodes and finally
+    rename variables accordingly.
+
+    `dom_graphs` indicates if we have to print the domination graphs.
+    `basename` is used for the names of the produced graphs.
+    """
+    # TODO implement this function (Lab 5a, Exercise 2)
+    raise NotImplementedError("enter_ssa")

MiniC/TP05/ExitSSA.py

@@ -0,0 +1,48 @@
+"""
+CAP, SSA Intro, Elimination and Optimisations
+Functions to convert a CFG out of SSA Form.
+"""
+
+from typing import cast, List, Set, Tuple
+from Lib import RiscV
+from Lib.Graphes import DiGraph
+from Lib.CFG import Block, BlockInstr, CFG
+from Lib.Operands import (
+    Register, DataLocation,
+    Temporary)
+from Lib.Statement import AbsoluteJump
+from Lib.Terminator import BranchingTerminator, Return
+from Lib.PhiNode import PhiNode
+
+
+def generate_moves_from_phis(phis: List[PhiNode], parent: Block) -> List[BlockInstr]:
+    """
+    `generate_moves_from_phis(phis, parent)` builds a list of move instructions
+    to be inserted in a new block between `parent` and the block with phi nodes
+    `phis`.
+
+    This is an helper function called during SSA exit.
+    """
+    moves: List[BlockInstr] = []
+    # TODO compute 'moves', a list of 'mv' instructions to insert under parent
+    # (Lab 5a, Exercise 6)
+    return moves
+
+
+def exit_ssa(cfg: CFG, is_smart: bool) -> None:
+    """
+    `exit_ssa(cfg)` replaces phi nodes with move instructions to exit SSA form.
+
+    `is_smart` is set to true when smart register allocation is enabled (Lab 5b).
+    """
+    for b in cfg.get_blocks():
+        phis = cast(List[PhiNode], b._phis)  # Use cast for Pyright
+        b._phis = []  # Remove all phi nodes in the block
+        parents: List[Block] = b.get_in().copy()  # Copy as we modify it by adding blocks
+        for parent in parents:
+            moves = generate_moves_from_phis(phis, parent)
+            # TODO Add the block containing 'moves' to 'cfg'
+            # and update edges and jumps accordingly (Lab 5a, Exercise 6)
+            raise NotImplementedError("exit_ssa")
+
+

MiniC/TP05/tests/students/README.md

@@ -0,0 +1 @@
+Add your own tests in this directory.

PLANNING.md

@@ -76,9 +76,17 @@ _Academic first semester 2022-2023_
 
   * Control Flow Graph [TP04b](MiniC/TP04/tp4b.pdf).
   * Code in [MiniC/TP04/](MiniC/TP04/).
-  * Documentation [here](docs/index.html).
+  * Documentation (updated) [here](docs/index.html).
 
 - :book: 7th Course session: Friday 14/10/2022, 10:15. Amphi B (Gabriel Radanne)
 
   * SSA [slides in english](course/cap_cours06a_ssa.pdf).
 
+# Week 7:
+
+- :hammer: Lab 5a: Wednesday 19/10/2021, 10h15-12h15. Rooms A1 (Nicolas Chappe) & B2 (Rémi Di Guardia)
+
+  * Control Flow Graph under SSA Form [TP05a](MiniC/TP05/tp5a.pdf).
+  * Code in [MiniC/TP05/](MiniC/TP05/).
+  * Documentation (updated) [here](docs/index.html).
+

docs/_modules/Lib/Allocator.html

@@ -42,10 +42,13 @@
 <li class="toctree-l1"><a class="reference internal" href="../../api/Lib.RiscV.html">Base library - RISC-V instructions</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../api/Lib.Operands.html">Base library - Operands</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../api/Lib.FunctionData.html">Base library - Function data</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../api/Lib.Graphes.html">Base library - Graphs</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../api/Lib.LinearCode.html">Linear intermediate representation</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../api/Lib.Allocator.html">Temporary allocation</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../api/Lib.CFG.html">Control Flow Graph - CFG and Basic blocks</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../api/Lib.Terminator.html">Control Flow Graph - Terminators</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../api/Lib.Dominators.html">SSA form - Dominance frontier</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../api/Lib.PhiNode.html">SSA form - Phi Nodes</a></li>
 </ul>
 
         </div>

docs/_modules/Lib/CFG.html

@@ -42,10 +42,13 @@
 <li class="toctree-l1"><a class="reference internal" href="../../api/Lib.RiscV.html">Base library - RISC-V instructions</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../api/Lib.Operands.html">Base library - Operands</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../api/Lib.FunctionData.html">Base library - Function data</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../api/Lib.Graphes.html">Base library - Graphs</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../api/Lib.LinearCode.html">Linear intermediate representation</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../api/Lib.Allocator.html">Temporary allocation</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../api/Lib.CFG.html">Control Flow Graph - CFG and Basic blocks</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../api/Lib.Terminator.html">Control Flow Graph - Terminators</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../api/Lib.Dominators.html">SSA form - Dominance frontier</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../api/Lib.PhiNode.html">SSA form - Phi Nodes</a></li>
 </ul>
 
         </div>
@@ -334,7 +337,6 @@
         <span class="c1"># nodes</span>
         <span class="k">for</span> <span class="n">name</span><span class="p">,</span> <span class="n">blk</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">_blocks</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
             <span class="k">if</span> <span class="n">DF</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
-                <span class="nb">print</span><span class="p">(</span><span class="nb">str</span><span class="p">(</span><span class="n">name</span><span class="p">),</span> <span class="n">blk</span><span class="o">.</span><span class="n">_label</span><span class="p">)</span>
                 <span class="n">df_str</span> <span class="o">=</span> <span class="s2">&quot;</span><span class="si">{}</span><span class="s2">&quot;</span> <span class="k">if</span> <span class="n">blk</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">DF</span> <span class="ow">or</span> <span class="ow">not</span> <span class="nb">len</span><span class="p">(</span><span class="n">DF</span><span class="p">[</span><span class="n">blk</span><span class="p">])</span> <span class="k">else</span> <span class="nb">str</span><span class="p">(</span><span class="n">DF</span><span class="p">[</span><span class="n">blk</span><span class="p">])</span>
                 <span class="n">df_lab</span> <span class="o">=</span> <span class="n">blk</span><span class="o">.</span><span class="n">to_dot</span><span class="p">()</span> <span class="o">+</span> <span class="s2">&quot;</span><span class="se">\n\n</span><span class="s2">Dominance frontier:</span><span class="se">\n</span><span class="s2">&quot;</span> <span class="o">+</span> <span class="n">df_str</span>
             <span class="k">else</span><span class="p">:</span>

docs/_modules/Lib/Dominators.html

@@ -0,0 +1,236 @@
+<!DOCTYPE html>
+<html class="writer-html5" lang="en" >
+<head>
+  <meta charset="utf-8" />
+  <meta name="viewport" content="width=device-width, initial-scale=1.0" />
+  <title>Lib.Dominators &mdash; MiniC  documentation</title>
+      <link rel="stylesheet" href="../../_static/pygments.css" type="text/css" />
+      <link rel="stylesheet" href="../../_static/css/theme.css" type="text/css" />
+  <!--[if lt IE 9]>
+    <script src="../../_static/js/html5shiv.min.js"></script>
+  <![endif]-->
+  
+        <script data-url_root="../../" id="documentation_options" src="../../_static/documentation_options.js"></script>
+        <script src="../../_static/jquery.js"></script>
+        <script src="../../_static/underscore.js"></script>
+        <script src="../../_static/_sphinx_javascript_frameworks_compat.js"></script>
+        <script src="../../_static/doctools.js"></script>
+    <script src="../../_static/js/theme.js"></script>
+    <link rel="index" title="Index" href="../../genindex.html" />
+    <link rel="search" title="Search" href="../../search.html" /> 
+</head>
+
+<body class="wy-body-for-nav"> 
+  <div class="wy-grid-for-nav">
+    <nav data-toggle="wy-nav-shift" class="wy-nav-side">
+      <div class="wy-side-scroll">
+        <div class="wy-side-nav-search" >
+            <a href="../../index.html" class="icon icon-home"> MiniC
+          </a>
+<div role="search">
+  <form id="rtd-search-form" class="wy-form" action="../../search.html" method="get">
+    <input type="text" name="q" placeholder="Search docs" />
+    <input type="hidden" name="check_keywords" value="yes" />
+    <input type="hidden" name="area" value="default" />
+  </form>
+</div>
+        </div><div class="wy-menu wy-menu-vertical" data-spy="affix" role="navigation" aria-label="Navigation menu">
+              <p class="caption" role="heading"><span class="caption-text">Contents:</span></p>
+<ul>
+<li class="toctree-l1"><a class="reference internal" href="../../api/Lib.Errors.html">Base library - Errors</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../api/Lib.Statement.html">Base library - Statement</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../api/Lib.RiscV.html">Base library - RISC-V instructions</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../api/Lib.Operands.html">Base library - Operands</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../api/Lib.FunctionData.html">Base library - Function data</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../api/Lib.Graphes.html">Base library - Graphs</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../api/Lib.LinearCode.html">Linear intermediate representation</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../api/Lib.Allocator.html">Temporary allocation</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../api/Lib.CFG.html">Control Flow Graph - CFG and Basic blocks</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../api/Lib.Terminator.html">Control Flow Graph - Terminators</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../api/Lib.Dominators.html">SSA form - Dominance frontier</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../api/Lib.PhiNode.html">SSA form - Phi Nodes</a></li>
+</ul>
+
+        </div>
+      </div>
+    </nav>
+
+    <section data-toggle="wy-nav-shift" class="wy-nav-content-wrap"><nav class="wy-nav-top" aria-label="Mobile navigation menu" >
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+      <li><a href="../../index.html" class="icon icon-home"></a> &raquo;</li>
+          <li><a href="../index.html">Module code</a> &raquo;</li>
+      <li>Lib.Dominators</li>
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+      </li>
+  </ul>
+  <hr/>
+</div>
+          <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article">
+           <div itemprop="articleBody">
+             
+  <h1>Source code for Lib.Dominators</h1><div class="highlight"><pre>
+<span></span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">Utility functions to work with dominators in a :py:class:`CFG &lt;Lib.CFG.CFG&gt;`.</span>
+
+<span class="sd">Do not hesitate to look at the source of the functions</span>
+<span class="sd">to get a better understanding of the algorithms.</span>
+<span class="sd">&quot;&quot;&quot;</span>
+
+<span class="kn">from</span> <span class="nn">typing</span> <span class="kn">import</span> <span class="n">Dict</span><span class="p">,</span> <span class="n">Set</span>
+<span class="kn">from</span> <span class="nn">graphviz</span> <span class="kn">import</span> <span class="n">Digraph</span>
+<span class="kn">from</span> <span class="nn">Lib.CFG</span> <span class="kn">import</span> <span class="n">Block</span><span class="p">,</span> <span class="n">CFG</span>
+
+
+<div class="viewcode-block" id="computeDom"><a class="viewcode-back" href="../../api/Lib.Dominators.html#Lib.Dominators.computeDom">[docs]</a><span class="k">def</span> <span class="nf">computeDom</span><span class="p">(</span><span class="n">cfg</span><span class="p">:</span> <span class="n">CFG</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">Dict</span><span class="p">[</span><span class="n">Block</span><span class="p">,</span> <span class="n">Set</span><span class="p">[</span><span class="n">Block</span><span class="p">]]:</span>
+    <span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    `computeDom(cfg)` computes the table associating blocks to their</span>
+<span class="sd">    dominators in `cfg`.</span>
+<span class="sd">    It works by solving the equation system.</span>
+
+<span class="sd">    This is an helper function called during SSA entry.</span>
+<span class="sd">    &quot;&quot;&quot;</span>
+    <span class="n">all_blocks</span><span class="p">:</span> <span class="n">Set</span><span class="p">[</span><span class="n">Block</span><span class="p">]</span> <span class="o">=</span> <span class="nb">set</span><span class="p">(</span><span class="n">cfg</span><span class="o">.</span><span class="n">get_blocks</span><span class="p">())</span>
+    <span class="n">dominators</span><span class="p">:</span> <span class="n">Dict</span><span class="p">[</span><span class="n">Block</span><span class="p">,</span> <span class="n">Set</span><span class="p">[</span><span class="n">Block</span><span class="p">]]</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">()</span>
+    <span class="k">for</span> <span class="n">b</span> <span class="ow">in</span> <span class="n">all_blocks</span><span class="p">:</span>
+        <span class="k">if</span> <span class="n">b</span><span class="o">.</span><span class="n">get_in</span><span class="p">():</span>  <span class="c1"># If b has some predecessor</span>
+            <span class="n">dominators</span><span class="p">[</span><span class="n">b</span><span class="p">]</span> <span class="o">=</span> <span class="n">all_blocks</span>
+        <span class="k">else</span><span class="p">:</span>  <span class="c1"># If b has no predecessors</span>
+            <span class="n">dominators</span><span class="p">[</span><span class="n">b</span><span class="p">]</span> <span class="o">=</span> <span class="p">{</span><span class="n">b</span><span class="p">}</span>
+    <span class="n">new_dominators</span><span class="p">:</span> <span class="n">Dict</span><span class="p">[</span><span class="n">Block</span><span class="p">,</span> <span class="n">Set</span><span class="p">[</span><span class="n">Block</span><span class="p">]]</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">()</span>
+    <span class="k">while</span> <span class="kc">True</span><span class="p">:</span>
+        <span class="k">for</span> <span class="n">b</span> <span class="ow">in</span> <span class="n">all_blocks</span><span class="p">:</span>
+            <span class="k">if</span> <span class="n">b</span><span class="o">.</span><span class="n">get_in</span><span class="p">():</span>
+                <span class="n">dom_preds</span> <span class="o">=</span> <span class="p">[</span><span class="n">dominators</span><span class="p">[</span><span class="n">b2</span><span class="p">]</span> <span class="k">for</span> <span class="n">b2</span> <span class="ow">in</span> <span class="n">b</span><span class="o">.</span><span class="n">get_in</span><span class="p">()]</span>
+                <span class="n">new_dominators</span><span class="p">[</span><span class="n">b</span><span class="p">]</span> <span class="o">=</span> <span class="p">{</span><span class="n">b</span><span class="p">}</span><span class="o">.</span><span class="n">union</span><span class="p">(</span><span class="nb">set</span><span class="o">.</span><span class="n">intersection</span><span class="p">(</span><span class="o">*</span><span class="n">dom_preds</span><span class="p">))</span>
+            <span class="k">else</span><span class="p">:</span>
+                <span class="n">new_dominators</span><span class="p">[</span><span class="n">b</span><span class="p">]</span> <span class="o">=</span> <span class="p">{</span><span class="n">b</span><span class="p">}</span>
+        <span class="k">if</span> <span class="n">dominators</span> <span class="o">==</span> <span class="n">new_dominators</span><span class="p">:</span>
+            <span class="k">break</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="n">dominators</span> <span class="o">=</span> <span class="n">new_dominators</span>
+            <span class="n">new_dominators</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">()</span>
+    <span class="k">return</span> <span class="n">dominators</span></div>
+
+
+<div class="viewcode-block" id="printDT"><a class="viewcode-back" href="../../api/Lib.Dominators.html#Lib.Dominators.printDT">[docs]</a><span class="k">def</span> <span class="nf">printDT</span><span class="p">(</span><span class="n">filename</span><span class="p">:</span> <span class="nb">str</span><span class="p">,</span> <span class="n">graph</span><span class="p">:</span> <span class="n">Dict</span><span class="p">[</span><span class="n">Block</span><span class="p">,</span> <span class="n">Set</span><span class="p">[</span><span class="n">Block</span><span class="p">]])</span> <span class="o">-&gt;</span> <span class="kc">None</span><span class="p">:</span>  <span class="c1"># pragma: no cover</span>
+    <span class="sd">&quot;&quot;&quot;Display a graphical rendering of the given domination tree.&quot;&quot;&quot;</span>
+    <span class="n">dot</span> <span class="o">=</span> <span class="n">Digraph</span><span class="p">()</span>
+    <span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="n">graph</span><span class="p">:</span>
+        <span class="n">dot</span><span class="o">.</span><span class="n">node</span><span class="p">(</span><span class="nb">str</span><span class="p">(</span><span class="n">k</span><span class="o">.</span><span class="n">get_label</span><span class="p">()))</span>
+    <span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="n">graph</span><span class="p">:</span>
+        <span class="k">for</span> <span class="n">v</span> <span class="ow">in</span> <span class="n">graph</span><span class="p">[</span><span class="n">k</span><span class="p">]:</span>
+            <span class="n">dot</span><span class="o">.</span><span class="n">edge</span><span class="p">(</span><span class="nb">str</span><span class="p">(</span><span class="n">k</span><span class="o">.</span><span class="n">get_label</span><span class="p">()),</span> <span class="nb">str</span><span class="p">(</span><span class="n">v</span><span class="o">.</span><span class="n">get_label</span><span class="p">()))</span>
+    <span class="n">dot</span><span class="o">.</span><span class="n">render</span><span class="p">(</span><span class="n">filename</span><span class="p">,</span> <span class="n">view</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span></div>
+
+
+<div class="viewcode-block" id="computeDT"><a class="viewcode-back" href="../../api/Lib.Dominators.html#Lib.Dominators.computeDT">[docs]</a><span class="k">def</span> <span class="nf">computeDT</span><span class="p">(</span><span class="n">cfg</span><span class="p">:</span> <span class="n">CFG</span><span class="p">,</span> <span class="n">dominators</span><span class="p">:</span> <span class="n">Dict</span><span class="p">[</span><span class="n">Block</span><span class="p">,</span> <span class="n">Set</span><span class="p">[</span><span class="n">Block</span><span class="p">]],</span>
+              <span class="n">dom_graphs</span><span class="p">:</span> <span class="nb">bool</span><span class="p">,</span> <span class="n">basename</span><span class="p">:</span> <span class="nb">str</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">Dict</span><span class="p">[</span><span class="n">Block</span><span class="p">,</span> <span class="n">Set</span><span class="p">[</span><span class="n">Block</span><span class="p">]]:</span>
+    <span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    `computeDT(cfg, dominators)` computes the domination tree of `cfg`</span>
+<span class="sd">    using the previously computed `dominators`.</span>
+<span class="sd">    It returns `DT`, a dictionary which associates a block with its children</span>
+<span class="sd">    in the dominator tree.</span>
+
+<span class="sd">    This is an helper function called during SSA entry.</span>
+<span class="sd">    &quot;&quot;&quot;</span>
+    <span class="c1"># First, compute the immediate dominators</span>
+    <span class="n">idominators</span><span class="p">:</span> <span class="n">Dict</span><span class="p">[</span><span class="n">Block</span><span class="p">,</span> <span class="n">Block</span><span class="p">]</span> <span class="o">=</span> <span class="p">{}</span>
+    <span class="k">for</span> <span class="n">b</span><span class="p">,</span> <span class="n">doms</span> <span class="ow">in</span> <span class="n">dominators</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
+        <span class="c1"># The immediate dominator of b is the unique vertex n ≠ b</span>
+        <span class="c1"># which dominates b and is dominated by all vertices in Dom(b) − b.</span>
+        <span class="n">strict_doms</span> <span class="o">=</span> <span class="n">doms</span> <span class="o">-</span> <span class="p">{</span><span class="n">b</span><span class="p">}</span>
+        <span class="n">idoms</span> <span class="o">=</span> <span class="nb">set</span><span class="p">()</span>
+        <span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="n">strict_doms</span><span class="p">:</span>
+            <span class="k">if</span> <span class="n">strict_doms</span><span class="o">.</span><span class="n">issubset</span><span class="p">(</span><span class="n">dominators</span><span class="p">[</span><span class="n">n</span><span class="p">]):</span>
+                <span class="n">idoms</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
+        <span class="k">if</span> <span class="n">idoms</span><span class="p">:</span>
+            <span class="k">assert</span> <span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">idoms</span><span class="p">)</span> <span class="o">==</span> <span class="mi">1</span><span class="p">)</span>
+            <span class="n">idominators</span><span class="p">[</span><span class="n">b</span><span class="p">]</span> <span class="o">=</span> <span class="n">idoms</span><span class="o">.</span><span class="n">pop</span><span class="p">()</span>
+    <span class="c1"># Then, simply inverse the relation to obtain the domination tree</span>
+    <span class="n">DT</span> <span class="o">=</span> <span class="p">{</span><span class="n">b</span><span class="p">:</span> <span class="nb">set</span><span class="p">()</span> <span class="k">for</span> <span class="n">b</span> <span class="ow">in</span> <span class="n">cfg</span><span class="o">.</span><span class="n">get_blocks</span><span class="p">()}</span>
+    <span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">idominator</span> <span class="ow">in</span> <span class="n">idominators</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
+        <span class="n">DT</span><span class="p">[</span><span class="n">idominator</span><span class="p">]</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
+    <span class="c1"># Print the domination tree if asked</span>
+    <span class="k">if</span> <span class="n">dom_graphs</span><span class="p">:</span>
+        <span class="n">s</span> <span class="o">=</span> <span class="s2">&quot;</span><span class="si">{}</span><span class="s2">.</span><span class="si">{}</span><span class="s2">.ssa.DT.dot&quot;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">basename</span><span class="p">,</span> <span class="n">cfg</span><span class="o">.</span><span class="n">fdata</span><span class="o">.</span><span class="n">get_name</span><span class="p">())</span>
+        <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;SSA - domination tree graph:&quot;</span><span class="p">,</span> <span class="n">s</span><span class="p">)</span>
+        <span class="n">printDT</span><span class="p">(</span><span class="n">s</span><span class="p">,</span> <span class="n">DT</span><span class="p">)</span>
+    <span class="k">return</span> <span class="n">DT</span></div>
+
+
+<span class="k">def</span> <span class="nf">_computeDF_at_block</span><span class="p">(</span>
+        <span class="n">cfg</span><span class="p">:</span> <span class="n">CFG</span><span class="p">,</span>
+        <span class="n">dominators</span><span class="p">:</span> <span class="n">Dict</span><span class="p">[</span><span class="n">Block</span><span class="p">,</span> <span class="n">Set</span><span class="p">[</span><span class="n">Block</span><span class="p">]],</span>
+        <span class="n">DT</span><span class="p">:</span> <span class="n">Dict</span><span class="p">[</span><span class="n">Block</span><span class="p">,</span> <span class="n">Set</span><span class="p">[</span><span class="n">Block</span><span class="p">]],</span>
+        <span class="n">b</span><span class="p">:</span> <span class="n">Block</span><span class="p">,</span>
+        <span class="n">DF</span><span class="p">:</span> <span class="n">Dict</span><span class="p">[</span><span class="n">Block</span><span class="p">,</span> <span class="n">Set</span><span class="p">[</span><span class="n">Block</span><span class="p">]])</span> <span class="o">-&gt;</span> <span class="kc">None</span><span class="p">:</span>
+    <span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    `_computeDF_at_block(...)` computes the dominance frontier at the given block,</span>
+<span class="sd">    by updating `DF`.</span>
+
+<span class="sd">    This is an helper function called during SSA entry.</span>
+<span class="sd">    &quot;&quot;&quot;</span>
+    <span class="n">S</span><span class="p">:</span> <span class="n">Set</span><span class="p">[</span><span class="n">Block</span><span class="p">]</span> <span class="o">=</span> <span class="p">{</span><span class="n">succ</span> <span class="k">for</span> <span class="n">succ</span> <span class="ow">in</span> <span class="n">cfg</span><span class="o">.</span><span class="n">out_blocks</span><span class="p">(</span><span class="n">b</span><span class="p">)</span> <span class="k">if</span> <span class="n">succ</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">DT</span><span class="p">[</span><span class="n">b</span><span class="p">]}</span>
+    <span class="k">for</span> <span class="n">b_succ</span> <span class="ow">in</span> <span class="n">DT</span><span class="p">[</span><span class="n">b</span><span class="p">]:</span>
+        <span class="n">_computeDF_at_block</span><span class="p">(</span><span class="n">cfg</span><span class="p">,</span> <span class="n">dominators</span><span class="p">,</span> <span class="n">DT</span><span class="p">,</span> <span class="n">b_succ</span><span class="p">,</span> <span class="n">DF</span><span class="p">)</span>
+        <span class="k">for</span> <span class="n">b_frontier</span> <span class="ow">in</span> <span class="n">DF</span><span class="p">[</span><span class="n">b_succ</span><span class="p">]:</span>
+            <span class="k">if</span> <span class="n">b</span> <span class="ow">not</span> <span class="ow">in</span> <span class="p">(</span><span class="n">dominators</span><span class="p">[</span><span class="n">b_frontier</span><span class="p">]</span> <span class="o">-</span> <span class="p">{</span><span class="n">b_frontier</span><span class="p">}):</span>
+                <span class="n">S</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">b_frontier</span><span class="p">)</span>
+    <span class="n">DF</span><span class="p">[</span><span class="n">b</span><span class="p">]</span> <span class="o">=</span> <span class="n">S</span>
+
+
+<div class="viewcode-block" id="computeDF"><a class="viewcode-back" href="../../api/Lib.Dominators.html#Lib.Dominators.computeDF">[docs]</a><span class="k">def</span> <span class="nf">computeDF</span><span class="p">(</span><span class="n">cfg</span><span class="p">:</span> <span class="n">CFG</span><span class="p">,</span> <span class="n">dominators</span><span class="p">:</span> <span class="n">Dict</span><span class="p">[</span><span class="n">Block</span><span class="p">,</span> <span class="n">Set</span><span class="p">[</span><span class="n">Block</span><span class="p">]],</span>
+              <span class="n">DT</span><span class="p">:</span> <span class="n">Dict</span><span class="p">[</span><span class="n">Block</span><span class="p">,</span> <span class="n">Set</span><span class="p">[</span><span class="n">Block</span><span class="p">]],</span> <span class="n">dom_graphs</span><span class="p">:</span> <span class="nb">bool</span><span class="p">,</span> <span class="n">basename</span><span class="p">:</span> <span class="nb">str</span>
+              <span class="p">)</span> <span class="o">-&gt;</span> <span class="n">Dict</span><span class="p">[</span><span class="n">Block</span><span class="p">,</span> <span class="n">Set</span><span class="p">[</span><span class="n">Block</span><span class="p">]]:</span>
+    <span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    `computeDF(...)` computes the dominance frontier of a CFG.</span>
+<span class="sd">    It returns `DF` which associates a block to its frontier.</span>
+
+<span class="sd">    This is an helper function called during SSA entry.</span>
+<span class="sd">    &quot;&quot;&quot;</span>
+    <span class="n">DF</span><span class="p">:</span> <span class="n">Dict</span><span class="p">[</span><span class="n">Block</span><span class="p">,</span> <span class="n">Set</span><span class="p">[</span><span class="n">Block</span><span class="p">]]</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">()</span>
+    <span class="k">for</span> <span class="n">b_entry</span> <span class="ow">in</span> <span class="n">cfg</span><span class="o">.</span><span class="n">get_entries</span><span class="p">():</span>
+        <span class="n">_computeDF_at_block</span><span class="p">(</span><span class="n">cfg</span><span class="p">,</span> <span class="n">dominators</span><span class="p">,</span> <span class="n">DT</span><span class="p">,</span> <span class="n">b_entry</span><span class="p">,</span> <span class="n">DF</span><span class="p">)</span>
+    <span class="c1"># Print the domination frontier on the CFG if asked</span>
+    <span class="k">if</span> <span class="n">dom_graphs</span><span class="p">:</span>
+        <span class="n">s</span> <span class="o">=</span> <span class="s2">&quot;</span><span class="si">{}</span><span class="s2">.</span><span class="si">{}</span><span class="s2">.ssa.DF.dot&quot;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">basename</span><span class="p">,</span> <span class="n">cfg</span><span class="o">.</span><span class="n">fdata</span><span class="o">.</span><span class="n">get_name</span><span class="p">())</span>
+        <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;SSA - dominance frontier graph:&quot;</span><span class="p">,</span> <span class="n">s</span><span class="p">)</span>
+        <span class="n">cfg</span><span class="o">.</span><span class="n">print_dot</span><span class="p">(</span><span class="n">s</span><span class="p">,</span> <span class="n">DF</span><span class="p">,</span> <span class="kc">True</span><span class="p">)</span>
+    <span class="k">return</span> <span class="n">DF</span></div>
+</pre></div>
+
+           </div>
+          </div>
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docs/_modules/Lib/Errors.html

@@ -42,10 +42,13 @@
 <li class="toctree-l1"><a class="reference internal" href="../../api/Lib.RiscV.html">Base library - RISC-V instructions</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../api/Lib.Operands.html">Base library - Operands</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../api/Lib.FunctionData.html">Base library - Function data</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../api/Lib.Graphes.html">Base library - Graphs</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../api/Lib.LinearCode.html">Linear intermediate representation</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../api/Lib.Allocator.html">Temporary allocation</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../api/Lib.CFG.html">Control Flow Graph - CFG and Basic blocks</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../api/Lib.Terminator.html">Control Flow Graph - Terminators</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../api/Lib.Dominators.html">SSA form - Dominance frontier</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../api/Lib.PhiNode.html">SSA form - Phi Nodes</a></li>
 </ul>
 
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docs/_modules/Lib/FunctionData.html

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 <li class="toctree-l1"><a class="reference internal" href="../../api/Lib.FunctionData.html">Base library - Function data</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../api/Lib.Graphes.html">Base library - Graphs</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../api/Lib.LinearCode.html">Linear intermediate representation</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../api/Lib.Allocator.html">Temporary allocation</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../api/Lib.CFG.html">Control Flow Graph - CFG and Basic blocks</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../api/Lib.Terminator.html">Control Flow Graph - Terminators</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../api/Lib.Dominators.html">SSA form - Dominance frontier</a></li>
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 </ul>
 
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docs/_modules/Lib/Graphes.html

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+<!DOCTYPE html>
+<html class="writer-html5" lang="en" >
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+  <meta name="viewport" content="width=device-width, initial-scale=1.0" />
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+              <p class="caption" role="heading"><span class="caption-text">Contents:</span></p>
+<ul>
+<li class="toctree-l1"><a class="reference internal" href="../../api/Lib.Errors.html">Base library - Errors</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../api/Lib.Statement.html">Base library - Statement</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../api/Lib.RiscV.html">Base library - RISC-V instructions</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../api/Lib.Operands.html">Base library - Operands</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../api/Lib.FunctionData.html">Base library - Function data</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../api/Lib.Graphes.html">Base library - Graphs</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../api/Lib.LinearCode.html">Linear intermediate representation</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../api/Lib.Allocator.html">Temporary allocation</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../api/Lib.CFG.html">Control Flow Graph - CFG and Basic blocks</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../api/Lib.Terminator.html">Control Flow Graph - Terminators</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../api/Lib.Dominators.html">SSA form - Dominance frontier</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../api/Lib.PhiNode.html">SSA form - Phi Nodes</a></li>
+</ul>
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+      </li>
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+           <div itemprop="articleBody">
+             
+  <h1>Source code for Lib.Graphes</h1><div class="highlight"><pre>
+<span></span><span class="sd">&quot;&quot;&quot; Python Classes for Oriented and Non Oriented Graphs</span>
+<span class="sd">&quot;&quot;&quot;</span>
+
+<span class="kn">from</span> <span class="nn">graphviz</span> <span class="kn">import</span> <span class="n">Digraph</span>  <span class="c1"># for dot output</span>
+<span class="kn">from</span> <span class="nn">typing</span> <span class="kn">import</span> <span class="n">List</span><span class="p">,</span> <span class="n">Dict</span><span class="p">,</span> <span class="n">Set</span><span class="p">,</span> <span class="n">Tuple</span><span class="p">,</span> <span class="n">Any</span>
+
+
+<div class="viewcode-block" id="GraphError"><a class="viewcode-back" href="../../api/Lib.Graphes.html#Lib.Graphes.GraphError">[docs]</a><span class="k">class</span> <span class="nc">GraphError</span><span class="p">(</span><span class="ne">Exception</span><span class="p">):</span>
+    <span class="sd">&quot;&quot;&quot;Exception raised for self loops.</span>
+<span class="sd">    &quot;&quot;&quot;</span>
+
+    <span class="n">message</span><span class="p">:</span> <span class="nb">str</span>
+
+    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">message</span><span class="p">:</span> <span class="nb">str</span><span class="p">):</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">message</span> <span class="o">=</span> <span class="n">message</span></div>
+
+
+<div class="viewcode-block" id="GeneralGraph"><a class="viewcode-back" href="../../api/Lib.Graphes.html#Lib.Graphes.GeneralGraph">[docs]</a><span class="k">class</span> <span class="nc">GeneralGraph</span><span class="p">(</span><span class="nb">object</span><span class="p">):</span>
+    <span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    General class regrouping similarities</span>
+<span class="sd">    between directed and non oriented graphs.</span>
+<span class="sd">    The only differences between the two are:</span>
+
+<span class="sd">    - how to compute the set of edges</span>
+<span class="sd">    - how to add an edge</span>
+<span class="sd">    - how to print the graph</span>
+<span class="sd">    - how to delete a vertex</span>
+<span class="sd">    - how to delete an edge</span>
+<span class="sd">    - we only color undirected graphs</span>
+<span class="sd">    &quot;&quot;&quot;</span>
+
+    <span class="n">graph_dict</span><span class="p">:</span> <span class="n">Dict</span><span class="p">[</span><span class="n">Any</span><span class="p">,</span> <span class="n">Set</span><span class="p">]</span>
+
+    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">graph_dict</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
+        <span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Initializes a graph object.</span>
+<span class="sd">        If no dictionary or None is given,</span>
+<span class="sd">        an empty dictionary will be used.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">if</span> <span class="n">graph_dict</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="n">graph_dict</span> <span class="o">=</span> <span class="p">{}</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">graph_dict</span> <span class="o">=</span> <span class="n">graph_dict</span>
+
+<div class="viewcode-block" id="GeneralGraph.vertices"><a class="viewcode-back" href="../../api/Lib.Graphes.html#Lib.Graphes.GeneralGraph.vertices">[docs]</a>    <span class="k">def</span> <span class="nf">vertices</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">List</span><span class="p">[</span><span class="n">Any</span><span class="p">]:</span>
+        <span class="sd">&quot;&quot;&quot;Return the vertices of a graph.&quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="nb">list</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">graph_dict</span><span class="o">.</span><span class="n">keys</span><span class="p">())</span></div>
+
+<div class="viewcode-block" id="GeneralGraph.add_vertex"><a class="viewcode-back" href="../../api/Lib.Graphes.html#Lib.Graphes.GeneralGraph.add_vertex">[docs]</a>    <span class="k">def</span> <span class="nf">add_vertex</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">vertex</span><span class="p">:</span> <span class="n">Any</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kc">None</span><span class="p">:</span>
+        <span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        If the vertex &quot;vertex&quot; is not in</span>
+<span class="sd">        self.graph_dict, a key &quot;vertex&quot; with an empty</span>
+<span class="sd">        list as a value is added to the dictionary.</span>
+<span class="sd">        Otherwise nothing has to be done.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">if</span> <span class="n">vertex</span> <span class="ow">not</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">graph_dict</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">graph_dict</span><span class="p">[</span><span class="n">vertex</span><span class="p">]</span> <span class="o">=</span> <span class="nb">set</span><span class="p">()</span></div>
+
+<div class="viewcode-block" id="GeneralGraph.edges"><a class="viewcode-back" href="../../api/Lib.Graphes.html#Lib.Graphes.GeneralGraph.edges">[docs]</a>    <span class="k">def</span> <span class="nf">edges</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">List</span><span class="p">[</span><span class="n">Set</span><span class="p">]:</span>
+        <span class="sd">&quot;&quot;&quot;Return the edges of the graph.&quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="p">[]</span></div>
+
+    <span class="k">def</span> <span class="fm">__str__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+        <span class="n">res</span> <span class="o">=</span> <span class="s2">&quot;vertices: &quot;</span>
+        <span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">graph_dict</span><span class="p">:</span>
+            <span class="n">res</span> <span class="o">+=</span> <span class="nb">str</span><span class="p">(</span><span class="n">k</span><span class="p">)</span> <span class="o">+</span> <span class="s2">&quot; &quot;</span>
+        <span class="n">res</span> <span class="o">+=</span> <span class="s2">&quot;</span><span class="se">\n</span><span class="s2">edges: &quot;</span>
+        <span class="k">for</span> <span class="n">edge</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">edges</span><span class="p">():</span>
+            <span class="n">res</span> <span class="o">+=</span> <span class="nb">str</span><span class="p">(</span><span class="n">edge</span><span class="p">)</span> <span class="o">+</span> <span class="s2">&quot; &quot;</span>
+        <span class="k">return</span> <span class="n">res</span>
+
+<div class="viewcode-block" id="GeneralGraph.dfs_traversal"><a class="viewcode-back" href="../../api/Lib.Graphes.html#Lib.Graphes.GeneralGraph.dfs_traversal">[docs]</a>    <span class="k">def</span> <span class="nf">dfs_traversal</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">root</span><span class="p">:</span> <span class="n">Any</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">List</span><span class="p">[</span><span class="n">Any</span><span class="p">]:</span>
+        <span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Compute a depth first search of the graph,</span>
+<span class="sd">        from the vertex root.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="n">seen</span><span class="p">:</span> <span class="n">List</span><span class="p">[</span><span class="n">Any</span><span class="p">]</span> <span class="o">=</span> <span class="p">[]</span>
+        <span class="n">todo</span><span class="p">:</span> <span class="n">List</span><span class="p">[</span><span class="n">Any</span><span class="p">]</span> <span class="o">=</span> <span class="p">[</span><span class="n">root</span><span class="p">]</span>
+        <span class="k">while</span> <span class="nb">len</span><span class="p">(</span><span class="n">todo</span><span class="p">)</span> <span class="o">&gt;</span> <span class="mi">0</span><span class="p">:</span>  <span class="c1"># while todo ...</span>
+            <span class="n">current</span> <span class="o">=</span> <span class="n">todo</span><span class="o">.</span><span class="n">pop</span><span class="p">()</span>
+            <span class="n">seen</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">current</span><span class="p">)</span>
+            <span class="k">for</span> <span class="n">neighbour</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">graph_dict</span><span class="p">[</span><span class="n">current</span><span class="p">]:</span>
+                <span class="k">if</span> <span class="n">neighbour</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">seen</span><span class="p">:</span>
+                    <span class="n">todo</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">neighbour</span><span class="p">)</span>
+        <span class="k">return</span> <span class="n">seen</span></div>
+
+<div class="viewcode-block" id="GeneralGraph.is_reachable_from"><a class="viewcode-back" href="../../api/Lib.Graphes.html#Lib.Graphes.GeneralGraph.is_reachable_from">[docs]</a>    <span class="k">def</span> <span class="nf">is_reachable_from</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">v1</span><span class="p">:</span> <span class="n">Any</span><span class="p">,</span> <span class="n">v2</span><span class="p">:</span> <span class="n">Any</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">bool</span><span class="p">:</span>
+        <span class="sd">&quot;&quot;&quot;True if there is a path from v1 to v2.&quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="n">v2</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">dfs_traversal</span><span class="p">(</span><span class="n">v1</span><span class="p">)</span></div>
+
+<div class="viewcode-block" id="GeneralGraph.connected_components"><a class="viewcode-back" href="../../api/Lib.Graphes.html#Lib.Graphes.GeneralGraph.connected_components">[docs]</a>    <span class="k">def</span> <span class="nf">connected_components</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">List</span><span class="p">[</span><span class="n">List</span><span class="p">[</span><span class="n">Any</span><span class="p">]]:</span>
+        <span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Compute the list of all connected components of the graph,</span>
+<span class="sd">        each component being a list of vetices.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="n">components</span><span class="p">:</span> <span class="n">List</span><span class="p">[</span><span class="n">List</span><span class="p">[</span><span class="n">Any</span><span class="p">]]</span> <span class="o">=</span> <span class="p">[]</span>
+        <span class="n">done</span><span class="p">:</span> <span class="n">List</span><span class="p">[</span><span class="n">Any</span><span class="p">]</span> <span class="o">=</span> <span class="p">[]</span>
+        <span class="k">for</span> <span class="n">v</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">vertices</span><span class="p">():</span>
+            <span class="k">if</span> <span class="n">v</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">done</span><span class="p">:</span>
+                <span class="n">v_comp</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">dfs_traversal</span><span class="p">(</span><span class="n">v</span><span class="p">)</span>
+                <span class="n">components</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">v_comp</span><span class="p">)</span>
+                <span class="n">done</span><span class="o">.</span><span class="n">extend</span><span class="p">(</span><span class="n">v_comp</span><span class="p">)</span>
+        <span class="k">return</span> <span class="n">components</span></div>
+
+<div class="viewcode-block" id="GeneralGraph.bfs_traversal"><a class="viewcode-back" href="../../api/Lib.Graphes.html#Lib.Graphes.GeneralGraph.bfs_traversal">[docs]</a>    <span class="k">def</span> <span class="nf">bfs_traversal</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">root</span><span class="p">:</span> <span class="n">Any</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">List</span><span class="p">[</span><span class="n">Any</span><span class="p">]:</span>
+        <span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Compute a breadth first search of the graph,</span>
+<span class="sd">        from the vertex root.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="n">seen</span><span class="p">:</span> <span class="n">List</span><span class="p">[</span><span class="n">Any</span><span class="p">]</span> <span class="o">=</span> <span class="p">[]</span>
+        <span class="n">todo</span><span class="p">:</span> <span class="n">List</span><span class="p">[</span><span class="n">Any</span><span class="p">]</span> <span class="o">=</span> <span class="p">[</span><span class="n">root</span><span class="p">]</span>
+        <span class="k">while</span> <span class="nb">len</span><span class="p">(</span><span class="n">todo</span><span class="p">)</span> <span class="o">&gt;</span> <span class="mi">0</span><span class="p">:</span>  <span class="c1"># while todo ...</span>
+            <span class="n">current</span> <span class="o">=</span> <span class="n">todo</span><span class="o">.</span><span class="n">pop</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>  <span class="c1"># list.pop(0): for dequeuing (on the left...) !</span>
+            <span class="n">seen</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">current</span><span class="p">)</span>
+            <span class="k">for</span> <span class="n">neighbour</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">graph_dict</span><span class="p">[</span><span class="n">current</span><span class="p">]:</span>
+                <span class="k">if</span> <span class="n">neighbour</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">seen</span><span class="p">:</span>
+                    <span class="n">todo</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">neighbour</span><span class="p">)</span>
+        <span class="k">return</span> <span class="n">seen</span></div></div>
+
+
+<div class="viewcode-block" id="Graph"><a class="viewcode-back" href="../../api/Lib.Graphes.html#Lib.Graphes.Graph">[docs]</a><span class="k">class</span> <span class="nc">Graph</span><span class="p">(</span><span class="n">GeneralGraph</span><span class="p">):</span>
+    <span class="sd">&quot;&quot;&quot;Class for non oriented graphs.&quot;&quot;&quot;</span>
+
+<div class="viewcode-block" id="Graph.edges"><a class="viewcode-back" href="../../api/Lib.Graphes.html#Lib.Graphes.Graph.edges">[docs]</a>    <span class="k">def</span> <span class="nf">edges</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">List</span><span class="p">[</span><span class="n">Set</span><span class="p">]:</span>
+        <span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        A static method generating the set of edges</span>
+<span class="sd">        (they appear twice in the dictionnary).</span>
+<span class="sd">        Return a list of sets.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="n">edges</span> <span class="o">=</span> <span class="p">[]</span>
+        <span class="k">for</span> <span class="n">vertex</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">graph_dict</span><span class="p">:</span>
+            <span class="k">for</span> <span class="n">neighbour</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">graph_dict</span><span class="p">[</span><span class="n">vertex</span><span class="p">]:</span>
+                <span class="k">if</span> <span class="p">{</span><span class="n">neighbour</span><span class="p">,</span> <span class="n">vertex</span><span class="p">}</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">edges</span><span class="p">:</span>
+                    <span class="n">edges</span><span class="o">.</span><span class="n">append</span><span class="p">({</span><span class="n">vertex</span><span class="p">,</span> <span class="n">neighbour</span><span class="p">})</span>
+        <span class="k">return</span> <span class="n">edges</span></div>
+
+<div class="viewcode-block" id="Graph.add_edge"><a class="viewcode-back" href="../../api/Lib.Graphes.html#Lib.Graphes.Graph.add_edge">[docs]</a>    <span class="k">def</span> <span class="nf">add_edge</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">edge</span><span class="p">:</span> <span class="n">Tuple</span><span class="p">[</span><span class="n">Any</span><span class="p">,</span> <span class="n">Any</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="kc">None</span><span class="p">:</span>
+        <span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Add an edge in the graph.</span>
+<span class="sd">        edge should be a pair and not (c,c)</span>
+<span class="sd">        (we call g.add_edge((v1,v2)))</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="p">(</span><span class="n">vertex1</span><span class="p">,</span> <span class="n">vertex2</span><span class="p">)</span> <span class="o">=</span> <span class="n">edge</span>
+        <span class="k">if</span> <span class="n">vertex1</span> <span class="o">==</span> <span class="n">vertex2</span><span class="p">:</span>
+            <span class="k">raise</span> <span class="n">GraphError</span><span class="p">(</span><span class="s2">&quot;Cannot add a self loop on vertex </span><span class="si">{}</span><span class="s2"> in an unoriented graph.&quot;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span>
+                             <span class="nb">str</span><span class="p">(</span><span class="n">vertex1</span><span class="p">)))</span>
+        <span class="k">if</span> <span class="n">vertex1</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">graph_dict</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">graph_dict</span><span class="p">[</span><span class="n">vertex1</span><span class="p">]</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">vertex2</span><span class="p">)</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">graph_dict</span><span class="p">[</span><span class="n">vertex1</span><span class="p">]</span> <span class="o">=</span> <span class="p">{</span><span class="n">vertex2</span><span class="p">}</span>
+        <span class="k">if</span> <span class="n">vertex2</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">graph_dict</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">graph_dict</span><span class="p">[</span><span class="n">vertex2</span><span class="p">]</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">vertex1</span><span class="p">)</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">graph_dict</span><span class="p">[</span><span class="n">vertex2</span><span class="p">]</span> <span class="o">=</span> <span class="p">{</span><span class="n">vertex1</span><span class="p">}</span></div>
+
+<div class="viewcode-block" id="Graph.print_dot"><a class="viewcode-back" href="../../api/Lib.Graphes.html#Lib.Graphes.Graph.print_dot">[docs]</a>    <span class="k">def</span> <span class="nf">print_dot</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">name</span><span class="p">:</span> <span class="nb">str</span><span class="p">,</span> <span class="n">colors</span><span class="o">=</span><span class="p">{})</span> <span class="o">-&gt;</span> <span class="kc">None</span><span class="p">:</span>
+        <span class="sd">&quot;&quot;&quot;Print the graph.&quot;&quot;&quot;</span>
+        <span class="n">color_names</span> <span class="o">=</span> <span class="p">[</span><span class="s1">&#39;red&#39;</span><span class="p">,</span> <span class="s1">&#39;blue&#39;</span><span class="p">,</span> <span class="s1">&#39;green&#39;</span><span class="p">,</span> <span class="s1">&#39;yellow&#39;</span><span class="p">,</span> <span class="s1">&#39;cyan&#39;</span><span class="p">,</span> <span class="s1">&#39;magenta&#39;</span><span class="p">]</span> <span class="o">+</span> \
+            <span class="p">[</span><span class="sa">f</span><span class="s2">&quot;grey</span><span class="si">{</span><span class="n">i</span><span class="si">}</span><span class="s2">&quot;</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">100</span><span class="p">,</span> <span class="mi">10</span><span class="p">)]</span>
+        <span class="n">color_shapes</span> <span class="o">=</span> <span class="p">[</span><span class="s1">&#39;ellipse&#39;</span><span class="p">,</span> <span class="s1">&#39;polygon&#39;</span><span class="p">,</span> <span class="s1">&#39;box&#39;</span><span class="p">,</span> <span class="s1">&#39;circle&#39;</span><span class="p">,</span> <span class="s1">&#39;egg&#39;</span><span class="p">,</span> <span class="s1">&#39;pentagon&#39;</span><span class="p">,</span> <span class="s1">&#39;hexagon&#39;</span><span class="p">]</span>
+        <span class="n">dot</span> <span class="o">=</span> <span class="n">Digraph</span><span class="p">(</span><span class="n">comment</span><span class="o">=</span><span class="s1">&#39;Conflict Graph&#39;</span><span class="p">)</span>
+        <span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">graph_dict</span><span class="p">:</span>
+            <span class="n">shape</span> <span class="o">=</span> <span class="kc">None</span>
+            <span class="k">if</span> <span class="ow">not</span> <span class="n">colors</span><span class="p">:</span>
+                <span class="n">color</span> <span class="o">=</span> <span class="s2">&quot;red&quot;</span>  <span class="c1"># Graph not colored: red for everyone</span>
+            <span class="k">elif</span> <span class="n">k</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">colors</span><span class="p">:</span>
+                <span class="n">color</span> <span class="o">=</span> <span class="s2">&quot;grey&quot;</span>  <span class="c1"># Node not colored: grey</span>
+            <span class="k">else</span><span class="p">:</span>
+                <span class="n">n</span> <span class="o">=</span> <span class="n">colors</span><span class="p">[</span><span class="n">k</span><span class="p">]</span>
+                <span class="k">if</span> <span class="n">n</span> <span class="o">&lt;</span> <span class="nb">len</span><span class="p">(</span><span class="n">color_names</span><span class="p">):</span>
+                    <span class="n">color</span> <span class="o">=</span> <span class="n">color_names</span><span class="p">[</span><span class="n">colors</span><span class="p">[</span><span class="n">k</span><span class="p">]]</span>
+                <span class="k">else</span><span class="p">:</span>
+                    <span class="n">color</span> <span class="o">=</span> <span class="s2">&quot;black&quot;</span>  <span class="c1"># Too many colors anyway, it won&#39;t be readable.</span>
+                <span class="n">shape</span> <span class="o">=</span> <span class="n">color_shapes</span><span class="p">[</span><span class="n">n</span> <span class="o">%</span> <span class="nb">len</span><span class="p">(</span><span class="n">color_shapes</span><span class="p">)]</span>
+            <span class="n">dot</span><span class="o">.</span><span class="n">node</span><span class="p">(</span><span class="nb">str</span><span class="p">(</span><span class="n">k</span><span class="p">),</span> <span class="n">color</span><span class="o">=</span><span class="n">color</span><span class="p">,</span> <span class="n">shape</span><span class="o">=</span><span class="n">shape</span><span class="p">)</span>
+        <span class="k">for</span> <span class="p">(</span><span class="n">v1</span><span class="p">,</span> <span class="n">v2</span><span class="p">)</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">edges</span><span class="p">():</span>
+            <span class="n">dot</span><span class="o">.</span><span class="n">edge</span><span class="p">(</span><span class="nb">str</span><span class="p">(</span><span class="n">v1</span><span class="p">),</span> <span class="nb">str</span><span class="p">(</span><span class="n">v2</span><span class="p">),</span> <span class="nb">dir</span><span class="o">=</span><span class="s2">&quot;none&quot;</span><span class="p">)</span>
+        <span class="c1"># print(dot.source)</span>
+        <span class="n">dot</span><span class="o">.</span><span class="n">render</span><span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="n">view</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>  <span class="c1"># print in pdf</span></div>
+
+<div class="viewcode-block" id="Graph.delete_vertex"><a class="viewcode-back" href="../../api/Lib.Graphes.html#Lib.Graphes.Graph.delete_vertex">[docs]</a>    <span class="k">def</span> <span class="nf">delete_vertex</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">vertex</span><span class="p">:</span> <span class="n">Any</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kc">None</span><span class="p">:</span>
+        <span class="sd">&quot;&quot;&quot;Delete a vertex and all the adjacent edges.&quot;&quot;&quot;</span>
+        <span class="n">gdict</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">graph_dict</span>
+        <span class="k">for</span> <span class="n">neighbour</span> <span class="ow">in</span> <span class="n">gdict</span><span class="p">[</span><span class="n">vertex</span><span class="p">]:</span>
+            <span class="n">gdict</span><span class="p">[</span><span class="n">neighbour</span><span class="p">]</span><span class="o">.</span><span class="n">remove</span><span class="p">(</span><span class="n">vertex</span><span class="p">)</span>
+        <span class="k">del</span> <span class="n">gdict</span><span class="p">[</span><span class="n">vertex</span><span class="p">]</span></div>
+
+<div class="viewcode-block" id="Graph.delete_edge"><a class="viewcode-back" href="../../api/Lib.Graphes.html#Lib.Graphes.Graph.delete_edge">[docs]</a>    <span class="k">def</span> <span class="nf">delete_edge</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">edge</span><span class="p">:</span> <span class="n">Tuple</span><span class="p">[</span><span class="n">Any</span><span class="p">,</span> <span class="n">Any</span><span class="p">]):</span>
+        <span class="sd">&quot;&quot;&quot;Delete an edge.&quot;&quot;&quot;</span>
+        <span class="p">(</span><span class="n">v1</span><span class="p">,</span> <span class="n">v2</span><span class="p">)</span> <span class="o">=</span> <span class="n">edge</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">graph_dict</span><span class="p">[</span><span class="n">v1</span><span class="p">]</span><span class="o">.</span><span class="n">remove</span><span class="p">(</span><span class="n">v2</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">graph_dict</span><span class="p">[</span><span class="n">v2</span><span class="p">]</span><span class="o">.</span><span class="n">remove</span><span class="p">(</span><span class="n">v1</span><span class="p">)</span></div>
+
+<div class="viewcode-block" id="Graph.color"><a class="viewcode-back" href="../../api/Lib.Graphes.html#Lib.Graphes.Graph.color">[docs]</a>    <span class="k">def</span> <span class="nf">color</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">Dict</span><span class="p">[</span><span class="n">Any</span><span class="p">,</span> <span class="nb">int</span><span class="p">]:</span>
+        <span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Color the graph with an unlimited number of colors.</span>
+<span class="sd">        Return a dict vertex -&gt; color, where color is an integer (0, 1, ...).</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="n">coloring</span><span class="p">,</span> <span class="n">_</span><span class="p">,</span> <span class="n">_</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">color_with_k_colors</span><span class="p">()</span>
+        <span class="k">return</span> <span class="n">coloring</span></div>
+
+    <span class="c1"># see algo of the course</span>
+<div class="viewcode-block" id="Graph.color_with_k_colors"><a class="viewcode-back" href="../../api/Lib.Graphes.html#Lib.Graphes.Graph.color_with_k_colors">[docs]</a>    <span class="k">def</span> <span class="nf">color_with_k_colors</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">K</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">avoidingnodes</span><span class="o">=</span><span class="p">())</span> <span class="o">-&gt;</span> <span class="n">Tuple</span><span class="p">[</span><span class="n">Dict</span><span class="p">[</span><span class="n">Any</span><span class="p">,</span> <span class="nb">int</span><span class="p">],</span> <span class="nb">bool</span><span class="p">,</span> <span class="n">List</span><span class="p">]:</span>
+        <span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Color with &lt;= K colors (if K is unspecified, use unlimited colors).</span>
+
+<span class="sd">        Return 3 values:</span>
+
+<span class="sd">        - a dict vertex -&gt; color</span>
+<span class="sd">        - a Boolean, True if the coloring succeeded</span>
+<span class="sd">        - the set of nodes actually colored</span>
+
+<span class="sd">        Do not color vertices belonging to avoidingnodes.</span>
+
+<span class="sd">        Continue even if the algo fails.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">if</span> <span class="n">K</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="n">K</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">graph_dict</span><span class="p">)</span>
+        <span class="n">todo_vertices</span> <span class="o">=</span> <span class="p">[]</span>
+        <span class="n">is_total</span> <span class="o">=</span> <span class="kc">True</span>
+        <span class="n">gcopy</span> <span class="o">=</span> <span class="n">Graph</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">graph_dict</span><span class="o">.</span><span class="n">copy</span><span class="p">())</span>
+        <span class="c1"># suppress nodes that are not to be considered.</span>
+        <span class="k">for</span> <span class="n">node</span> <span class="ow">in</span> <span class="n">avoidingnodes</span><span class="p">:</span>
+            <span class="n">gcopy</span><span class="o">.</span><span class="n">delete_vertex</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
+        <span class="c1"># append nodes in the list according to their degree and node number:</span>
+        <span class="k">while</span> <span class="n">gcopy</span><span class="o">.</span><span class="n">graph_dict</span><span class="p">:</span>
+            <span class="n">todo</span> <span class="o">=</span> <span class="nb">list</span><span class="p">(</span><span class="n">gcopy</span><span class="o">.</span><span class="n">graph_dict</span><span class="p">)</span>
+            <span class="n">todo</span><span class="o">.</span><span class="n">sort</span><span class="p">(</span><span class="n">key</span><span class="o">=</span><span class="k">lambda</span> <span class="n">v</span><span class="p">:</span> <span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">gcopy</span><span class="o">.</span><span class="n">graph_dict</span><span class="p">[</span><span class="n">v</span><span class="p">]),</span> <span class="nb">str</span><span class="p">(</span><span class="n">v</span><span class="p">)))</span>
+            <span class="n">lower</span> <span class="o">=</span> <span class="n">todo</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
+            <span class="n">todo_vertices</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">lower</span><span class="p">)</span>
+            <span class="n">gcopy</span><span class="o">.</span><span class="n">delete_vertex</span><span class="p">(</span><span class="n">lower</span><span class="p">)</span>
+        <span class="c1"># Now reverse the list: first elements are those with higher degree</span>
+        <span class="c1"># print(todo_vertices)</span>
+        <span class="n">todo_vertices</span><span class="o">.</span><span class="n">reverse</span><span class="p">()</span>  <span class="c1"># in place reversal</span>
+        <span class="c1"># print(todo_vertices)</span>
+        <span class="n">coloring</span> <span class="o">=</span> <span class="p">{}</span>
+        <span class="n">colored_nodes</span> <span class="o">=</span> <span class="p">[]</span>
+        <span class="c1"># gdict will be the coloring map to return</span>
+        <span class="n">gdict</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">graph_dict</span>
+        <span class="k">for</span> <span class="n">v</span> <span class="ow">in</span> <span class="n">todo_vertices</span><span class="p">:</span>
+            <span class="n">seen_neighbours</span> <span class="o">=</span> <span class="p">[</span><span class="n">x</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">gdict</span><span class="p">[</span><span class="n">v</span><span class="p">]</span> <span class="k">if</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">coloring</span><span class="p">]</span>
+            <span class="n">choose_among</span> <span class="o">=</span> <span class="p">[</span><span class="n">i</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">K</span><span class="p">)</span> <span class="k">if</span> <span class="ow">not</span> <span class="p">(</span>
+                <span class="n">i</span> <span class="ow">in</span> <span class="p">[</span><span class="n">coloring</span><span class="p">[</span><span class="n">v1</span><span class="p">]</span> <span class="k">for</span> <span class="n">v1</span> <span class="ow">in</span> <span class="n">seen_neighbours</span><span class="p">])]</span>
+            <span class="k">if</span> <span class="n">choose_among</span><span class="p">:</span>
+                <span class="c1"># if the node can be colored, I choose the minimal color.</span>
+                <span class="n">color</span> <span class="o">=</span> <span class="nb">min</span><span class="p">(</span><span class="n">choose_among</span><span class="p">)</span>
+                <span class="n">coloring</span><span class="p">[</span><span class="n">v</span><span class="p">]</span> <span class="o">=</span> <span class="n">color</span>
+                <span class="n">colored_nodes</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">v</span><span class="p">)</span>
+            <span class="k">else</span><span class="p">:</span>
+                <span class="c1"># if I cannot color some node, the coloring is not Total</span>
+                <span class="c1"># but I continue</span>
+                <span class="n">is_total</span> <span class="o">=</span> <span class="kc">False</span>
+        <span class="k">return</span> <span class="p">(</span><span class="n">coloring</span><span class="p">,</span> <span class="n">is_total</span><span class="p">,</span> <span class="n">colored_nodes</span><span class="p">)</span></div></div>
+
+
+<div class="viewcode-block" id="DiGraph"><a class="viewcode-back" href="../../api/Lib.Graphes.html#Lib.Graphes.DiGraph">[docs]</a><span class="k">class</span> <span class="nc">DiGraph</span><span class="p">(</span><span class="n">GeneralGraph</span><span class="p">):</span>
+    <span class="sd">&quot;&quot;&quot;Class for directed graphs.&quot;&quot;&quot;</span>
+
+<div class="viewcode-block" id="DiGraph.neighbourhoods"><a class="viewcode-back" href="../../api/Lib.Graphes.html#Lib.Graphes.DiGraph.neighbourhoods">[docs]</a>    <span class="k">def</span> <span class="nf">neighbourhoods</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">List</span><span class="p">[</span><span class="n">Tuple</span><span class="p">[</span><span class="n">Any</span><span class="p">,</span> <span class="n">Set</span><span class="p">]]:</span>
+        <span class="sd">&quot;&quot;&quot;Return all neighbourhoods in the graph.&quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="nb">list</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">graph_dict</span><span class="o">.</span><span class="n">items</span><span class="p">())</span></div>
+
+<div class="viewcode-block" id="DiGraph.edges"><a class="viewcode-back" href="../../api/Lib.Graphes.html#Lib.Graphes.DiGraph.edges">[docs]</a>    <span class="k">def</span> <span class="nf">edges</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">List</span><span class="p">[</span><span class="n">Tuple</span><span class="p">[</span><span class="n">Any</span><span class="p">,</span> <span class="n">Any</span><span class="p">]]:</span>
+        <span class="sd">&quot;&quot;&quot; A static method generating the set of edges&quot;&quot;&quot;</span>
+        <span class="n">edges</span> <span class="o">=</span> <span class="p">[]</span>
+        <span class="k">for</span> <span class="n">vertex</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">graph_dict</span><span class="p">:</span>
+            <span class="k">for</span> <span class="n">neighbour</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">graph_dict</span><span class="p">[</span><span class="n">vertex</span><span class="p">]:</span>
+                <span class="n">edges</span><span class="o">.</span><span class="n">append</span><span class="p">((</span><span class="n">vertex</span><span class="p">,</span> <span class="n">neighbour</span><span class="p">))</span>
+        <span class="k">return</span> <span class="n">edges</span></div>
+
+<div class="viewcode-block" id="DiGraph.add_edge"><a class="viewcode-back" href="../../api/Lib.Graphes.html#Lib.Graphes.DiGraph.add_edge">[docs]</a>    <span class="k">def</span> <span class="nf">add_edge</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">edge</span><span class="p">:</span> <span class="n">Tuple</span><span class="p">[</span><span class="n">Any</span><span class="p">,</span> <span class="n">Any</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="kc">None</span><span class="p">:</span>
+        <span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Add an edge in the graph.</span>
+<span class="sd">        edge should be a pair and not (c,c)</span>
+<span class="sd">        (we call g.add_edge((v1,v2)))</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="p">(</span><span class="n">vertex1</span><span class="p">,</span> <span class="n">vertex2</span><span class="p">)</span> <span class="o">=</span> <span class="n">edge</span>
+        <span class="k">if</span> <span class="n">vertex1</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">graph_dict</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">graph_dict</span><span class="p">[</span><span class="n">vertex1</span><span class="p">]</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">vertex2</span><span class="p">)</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">graph_dict</span><span class="p">[</span><span class="n">vertex1</span><span class="p">]</span> <span class="o">=</span> <span class="p">{</span><span class="n">vertex2</span><span class="p">}</span>
+        <span class="k">if</span> <span class="n">vertex2</span> <span class="ow">not</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">graph_dict</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">graph_dict</span><span class="p">[</span><span class="n">vertex2</span><span class="p">]</span> <span class="o">=</span> <span class="nb">set</span><span class="p">()</span></div>
+
+<div class="viewcode-block" id="DiGraph.print_dot"><a class="viewcode-back" href="../../api/Lib.Graphes.html#Lib.Graphes.DiGraph.print_dot">[docs]</a>    <span class="k">def</span> <span class="nf">print_dot</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">name</span><span class="p">:</span> <span class="nb">str</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kc">None</span><span class="p">:</span>
+        <span class="sd">&quot;&quot;&quot;Print the graph.&quot;&quot;&quot;</span>
+        <span class="n">dot</span> <span class="o">=</span> <span class="n">Digraph</span><span class="p">(</span><span class="n">comment</span><span class="o">=</span><span class="s1">&#39;Conflict Graph&#39;</span><span class="p">)</span>
+        <span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">graph_dict</span><span class="p">:</span>
+            <span class="n">shape</span> <span class="o">=</span> <span class="kc">None</span>
+            <span class="n">color</span> <span class="o">=</span> <span class="s2">&quot;grey&quot;</span>
+            <span class="n">dot</span><span class="o">.</span><span class="n">node</span><span class="p">(</span><span class="nb">str</span><span class="p">(</span><span class="n">k</span><span class="p">),</span> <span class="n">color</span><span class="o">=</span><span class="n">color</span><span class="p">,</span> <span class="n">shape</span><span class="o">=</span><span class="n">shape</span><span class="p">)</span>
+        <span class="k">for</span> <span class="p">(</span><span class="n">v1</span><span class="p">,</span> <span class="n">v2</span><span class="p">)</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">edges</span><span class="p">():</span>
+            <span class="n">dot</span><span class="o">.</span><span class="n">edge</span><span class="p">(</span><span class="nb">str</span><span class="p">(</span><span class="n">v1</span><span class="p">),</span> <span class="nb">str</span><span class="p">(</span><span class="n">v2</span><span class="p">),</span> <span class="nb">dir</span><span class="o">=</span><span class="s2">&quot;none&quot;</span><span class="p">)</span>
+        <span class="c1"># print(dot.source)</span>
+        <span class="n">dot</span><span class="o">.</span><span class="n">render</span><span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="n">view</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>  <span class="c1"># print in pdf</span></div>
+
+<div class="viewcode-block" id="DiGraph.delete_vertex"><a class="viewcode-back" href="../../api/Lib.Graphes.html#Lib.Graphes.DiGraph.delete_vertex">[docs]</a>    <span class="k">def</span> <span class="nf">delete_vertex</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">vertex</span><span class="p">:</span> <span class="n">Any</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kc">None</span><span class="p">:</span>
+        <span class="sd">&quot;&quot;&quot;Delete a vertex and all the adjacent edges.&quot;&quot;&quot;</span>
+        <span class="k">for</span> <span class="n">node</span><span class="p">,</span> <span class="n">neighbours</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">graph_dict</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
+            <span class="k">if</span> <span class="n">vertex</span> <span class="ow">in</span> <span class="n">neighbours</span><span class="p">:</span>
+                <span class="n">neighbours</span><span class="o">.</span><span class="n">remove</span><span class="p">(</span><span class="n">vertex</span><span class="p">)</span>
+        <span class="k">del</span> <span class="bp">self</span><span class="o">.</span><span class="n">graph_dict</span><span class="p">[</span><span class="n">vertex</span><span class="p">]</span></div>
+
+<div class="viewcode-block" id="DiGraph.delete_edge"><a class="viewcode-back" href="../../api/Lib.Graphes.html#Lib.Graphes.DiGraph.delete_edge">[docs]</a>    <span class="k">def</span> <span class="nf">delete_edge</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">edge</span><span class="p">:</span> <span class="n">Tuple</span><span class="p">[</span><span class="n">Any</span><span class="p">,</span> <span class="n">Any</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="kc">None</span><span class="p">:</span>
+        <span class="sd">&quot;&quot;&quot;Delete an edge.&quot;&quot;&quot;</span>
+        <span class="p">(</span><span class="n">v1</span><span class="p">,</span> <span class="n">v2</span><span class="p">)</span> <span class="o">=</span> <span class="n">edge</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">graph_dict</span><span class="p">[</span><span class="n">v1</span><span class="p">]</span><span class="o">.</span><span class="n">remove</span><span class="p">(</span><span class="n">v2</span><span class="p">)</span></div></div>
+</pre></div>
+
+           </div>
+          </div>
+          <footer>
+
+  <hr/>
+
+  <div role="contentinfo">
+    <p>&#169; Copyright 2022, compil-lyon.</p>
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docs/_modules/Lib/LinearCode.html

@@ -42,10 +42,13 @@
 <li class="toctree-l1"><a class="reference internal" href="../../api/Lib.RiscV.html">Base library - RISC-V instructions</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../api/Lib.Operands.html">Base library - Operands</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../api/Lib.FunctionData.html">Base library - Function data</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../api/Lib.Graphes.html">Base library - Graphs</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../api/Lib.LinearCode.html">Linear intermediate representation</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../api/Lib.Allocator.html">Temporary allocation</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../api/Lib.CFG.html">Control Flow Graph - CFG and Basic blocks</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../api/Lib.Terminator.html">Control Flow Graph - Terminators</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../api/Lib.Dominators.html">SSA form - Dominance frontier</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../api/Lib.PhiNode.html">SSA form - Phi Nodes</a></li>
 </ul>
 
         </div>

docs/_modules/Lib/Operands.html

@@ -42,10 +42,13 @@
 <li class="toctree-l1"><a class="reference internal" href="../../api/Lib.RiscV.html">Base library - RISC-V instructions</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../api/Lib.Operands.html">Base library - Operands</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../api/Lib.FunctionData.html">Base library - Function data</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../api/Lib.Graphes.html">Base library - Graphs</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../api/Lib.LinearCode.html">Linear intermediate representation</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../api/Lib.Allocator.html">Temporary allocation</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../api/Lib.CFG.html">Control Flow Graph - CFG and Basic blocks</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../api/Lib.Terminator.html">Control Flow Graph - Terminators</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../api/Lib.Dominators.html">SSA form - Dominance frontier</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../api/Lib.PhiNode.html">SSA form - Phi Nodes</a></li>
 </ul>
 
         </div>
@@ -204,10 +207,10 @@
 <span class="n">RA</span> <span class="o">=</span> <span class="n">Register</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
 <span class="c1">#:</span>
 <span class="n">SP</span> <span class="o">=</span> <span class="n">Register</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span>
-<span class="c1">#:</span>
-<span class="n">GP</span> <span class="o">=</span> <span class="n">Register</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span>  <span class="c1"># Register not used for this course</span>
-<span class="c1">#:</span>
-<span class="n">TP</span> <span class="o">=</span> <span class="n">Register</span><span class="p">(</span><span class="mi">4</span><span class="p">)</span>  <span class="c1"># Register not used for this course</span>
+<span class="c1">#: Register not used for this course</span>
+<span class="n">GP</span> <span class="o">=</span> <span class="n">Register</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span>
+<span class="c1">#: Register not used for this course</span>
+<span class="n">TP</span> <span class="o">=</span> <span class="n">Register</span><span class="p">(</span><span class="mi">4</span><span class="p">)</span>
 <span class="c1">#:</span>
 <span class="n">A</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">Register</span><span class="p">(</span><span class="n">i</span> <span class="o">+</span> <span class="mi">10</span><span class="p">)</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">8</span><span class="p">))</span>
 <span class="c1">#:</span>
@@ -220,8 +223,8 @@
 <span class="n">A0</span> <span class="o">=</span> <span class="n">A</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>  <span class="c1"># function args/return Values: A0, A1</span>
 <span class="c1">#:</span>
 <span class="n">A1</span> <span class="o">=</span> <span class="n">A</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>
-<span class="c1">#:</span>
-<span class="n">FP</span> <span class="o">=</span> <span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>  <span class="c1"># Frame Pointer = Saved register 0</span>
+<span class="c1">#: Frame Pointer = Saved register 0</span>
+<span class="n">FP</span> <span class="o">=</span> <span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
 
 <span class="c1">#: General purpose registers, usable for the allocator</span>
 <span class="n">GP_REGS</span> <span class="o">=</span> <span class="n">S</span><span class="p">[</span><span class="mi">4</span><span class="p">:]</span> <span class="o">+</span> <span class="n">T</span>  <span class="c1"># s0, s1, s2 and s3 are special</span>

docs/_modules/Lib/PhiNode.html

@@ -0,0 +1,166 @@
+<!DOCTYPE html>
+<html class="writer-html5" lang="en" >
+<head>
+  <meta charset="utf-8" />
+  <meta name="viewport" content="width=device-width, initial-scale=1.0" />
+  <title>Lib.PhiNode &mdash; MiniC  documentation</title>
+      <link rel="stylesheet" href="../../_static/pygments.css" type="text/css" />
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+              <p class="caption" role="heading"><span class="caption-text">Contents:</span></p>
+<ul>
+<li class="toctree-l1"><a class="reference internal" href="../../api/Lib.Errors.html">Base library - Errors</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../api/Lib.Statement.html">Base library - Statement</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../api/Lib.RiscV.html">Base library - RISC-V instructions</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../api/Lib.Operands.html">Base library - Operands</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../api/Lib.FunctionData.html">Base library - Function data</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../api/Lib.Graphes.html">Base library - Graphs</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../api/Lib.LinearCode.html">Linear intermediate representation</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../api/Lib.Allocator.html">Temporary allocation</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../api/Lib.CFG.html">Control Flow Graph - CFG and Basic blocks</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../api/Lib.Terminator.html">Control Flow Graph - Terminators</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../api/Lib.Dominators.html">SSA form - Dominance frontier</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../api/Lib.PhiNode.html">SSA form - Phi Nodes</a></li>
+</ul>
+
+        </div>
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+           <div itemprop="articleBody">
+             
+  <h1>Source code for Lib.PhiNode</h1><div class="highlight"><pre>
+<span></span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">Classes for φ nodes in a RiscV CFG :py:class:`CFG &lt;Lib.CFG.CFG&gt;` under SSA Form:</span>
+<span class="sd">:py:class:`PhiNode` for a statement of the form temp_x = φ(temp_0, ..., temp_n).</span>
+<span class="sd">These particular kinds of statements are expected to be in the field</span>
+<span class="sd">b._phis for a :py:class:`Block &lt;Lib.CFG.Block&gt;` b.</span>
+<span class="sd">&quot;&quot;&quot;</span>
+
+<span class="kn">from</span> <span class="nn">dataclasses</span> <span class="kn">import</span> <span class="n">dataclass</span>
+<span class="kn">from</span> <span class="nn">typing</span> <span class="kn">import</span> <span class="n">Dict</span>
+
+<span class="kn">from</span> <span class="nn">Lib.Operands</span> <span class="kn">import</span> <span class="n">Operand</span><span class="p">,</span> <span class="n">Temporary</span><span class="p">,</span> <span class="n">DataLocation</span><span class="p">,</span> <span class="n">Renamer</span>
+<span class="kn">from</span> <span class="nn">Lib.Statement</span> <span class="kn">import</span> <span class="n">Statement</span><span class="p">,</span> <span class="n">Label</span>
+
+
+<div class="viewcode-block" id="PhiNode"><a class="viewcode-back" href="../../api/Lib.PhiNode.html#Lib.PhiNode.PhiNode">[docs]</a><span class="nd">@dataclass</span>
+<span class="k">class</span> <span class="nc">PhiNode</span><span class="p">(</span><span class="n">Statement</span><span class="p">):</span>
+    <span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    A φ node is a renaming in the CFG, of the form temp_x = φ(temp_0, ..., temp_n).</span>
+<span class="sd">    The field var contains the variable temp_x.</span>
+<span class="sd">    The field srcs relies for each precedent block in the CFG, identified with its label,</span>
+<span class="sd">    the variable temp_i of the φ node.</span>
+<span class="sd">    &quot;&quot;&quot;</span>
+    <span class="n">var</span><span class="p">:</span> <span class="n">DataLocation</span>
+    <span class="n">srcs</span><span class="p">:</span> <span class="n">Dict</span><span class="p">[</span><span class="n">Label</span><span class="p">,</span> <span class="n">Operand</span><span class="p">]</span>
+
+<div class="viewcode-block" id="PhiNode.defined"><a class="viewcode-back" href="../../api/Lib.PhiNode.html#Lib.PhiNode.PhiNode.defined">[docs]</a>    <span class="k">def</span> <span class="nf">defined</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+        <span class="sd">&quot;&quot;&quot;Return the variable defined by the φ node.&quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">var</span><span class="p">]</span></div>
+
+<div class="viewcode-block" id="PhiNode.used"><a class="viewcode-back" href="../../api/Lib.PhiNode.html#Lib.PhiNode.PhiNode.used">[docs]</a>    <span class="k">def</span> <span class="nf">used</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">Dict</span><span class="p">[</span><span class="n">Label</span><span class="p">,</span> <span class="n">Operand</span><span class="p">]:</span>
+        <span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Return the dictionnary associating for each previous block the corresponding variable.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">srcs</span></div>
+
+<div class="viewcode-block" id="PhiNode.rename"><a class="viewcode-back" href="../../api/Lib.PhiNode.html#Lib.PhiNode.PhiNode.rename">[docs]</a>    <span class="k">def</span> <span class="nf">rename</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">renamer</span><span class="p">:</span> <span class="n">Renamer</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kc">None</span><span class="p">:</span>
+        <span class="sd">&quot;&quot;&quot;Rename the variable defined by the φ node with a fresh name.&quot;&quot;&quot;</span>
+        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">var</span><span class="p">,</span> <span class="n">Temporary</span><span class="p">):</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">var</span> <span class="o">=</span> <span class="n">renamer</span><span class="o">.</span><span class="n">fresh</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">var</span><span class="p">)</span></div>
+
+<div class="viewcode-block" id="PhiNode.rename_from"><a class="viewcode-back" href="../../api/Lib.PhiNode.html#Lib.PhiNode.PhiNode.rename_from">[docs]</a>    <span class="k">def</span> <span class="nf">rename_from</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">renamer</span><span class="p">:</span> <span class="n">Renamer</span><span class="p">,</span> <span class="n">label</span><span class="p">:</span> <span class="n">Label</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kc">None</span><span class="p">:</span>
+        <span class="sd">&quot;&quot;&quot;Rename the variable associated to the block identified by `label`.&quot;&quot;&quot;</span>
+        <span class="k">if</span> <span class="n">label</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">srcs</span><span class="p">:</span>
+            <span class="n">t</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">srcs</span><span class="p">[</span><span class="n">label</span><span class="p">]</span>
+            <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="n">Temporary</span><span class="p">):</span>
+                <span class="k">if</span> <span class="n">renamer</span><span class="o">.</span><span class="n">defined</span><span class="p">(</span><span class="n">t</span><span class="p">):</span>
+                    <span class="bp">self</span><span class="o">.</span><span class="n">srcs</span><span class="p">[</span><span class="n">label</span><span class="p">]</span> <span class="o">=</span> <span class="n">renamer</span><span class="o">.</span><span class="n">replace</span><span class="p">(</span><span class="n">t</span><span class="p">)</span>
+                <span class="k">else</span><span class="p">:</span>
+                    <span class="k">del</span> <span class="bp">self</span><span class="o">.</span><span class="n">srcs</span><span class="p">[</span><span class="n">label</span><span class="p">]</span></div>
+
+    <span class="k">def</span> <span class="fm">__str__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+        <span class="k">return</span> <span class="s2">&quot;</span><span class="si">{}</span><span class="s2"> = φ(</span><span class="si">{}</span><span class="s2">)&quot;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">var</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">srcs</span><span class="p">)</span>
+
+    <span class="k">def</span> <span class="fm">__hash__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+        <span class="k">return</span> <span class="nb">hash</span><span class="p">((</span><span class="bp">self</span><span class="o">.</span><span class="n">var</span><span class="p">,</span> <span class="o">*</span><span class="bp">self</span><span class="o">.</span><span class="n">srcs</span><span class="o">.</span><span class="n">items</span><span class="p">()))</span>
+
+<div class="viewcode-block" id="PhiNode.printIns"><a class="viewcode-back" href="../../api/Lib.PhiNode.html#Lib.PhiNode.PhiNode.printIns">[docs]</a>    <span class="k">def</span> <span class="nf">printIns</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">stream</span><span class="p">):</span>
+        <span class="nb">print</span><span class="p">(</span><span class="s1">&#39;        # &#39;</span> <span class="o">+</span> <span class="nb">str</span><span class="p">(</span><span class="bp">self</span><span class="p">),</span> <span class="n">file</span><span class="o">=</span><span class="n">stream</span><span class="p">)</span></div></div>
+</pre></div>
+
+           </div>
+          </div>
+          <footer>
+
+  <hr/>
+
+  <div role="contentinfo">
+    <p>&#169; Copyright 2022, compil-lyon.</p>
+  </div>
+
+  Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a
+    <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a>
+    provided by <a href="https://readthedocs.org">Read the Docs</a>.
+   
+
+</footer>
+        </div>
+      </div>
+    </section>
+  </div>
+  <script>
+      jQuery(function () {
+          SphinxRtdTheme.Navigation.enable(true);
+      });
+  </script> 
+
+</body>
+</html>

docs/_modules/Lib/RiscV.html

@@ -42,10 +42,13 @@
 <li class="toctree-l1"><a class="reference internal" href="../../api/Lib.RiscV.html">Base library - RISC-V instructions</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../api/Lib.Operands.html">Base library - Operands</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../api/Lib.FunctionData.html">Base library - Function data</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../api/Lib.Graphes.html">Base library - Graphs</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../api/Lib.LinearCode.html">Linear intermediate representation</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../api/Lib.Allocator.html">Temporary allocation</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../api/Lib.CFG.html">Control Flow Graph - CFG and Basic blocks</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../api/Lib.Terminator.html">Control Flow Graph - Terminators</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../api/Lib.Dominators.html">SSA form - Dominance frontier</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../api/Lib.PhiNode.html">SSA form - Phi Nodes</a></li>
 </ul>
 
         </div>
@@ -79,8 +82,7 @@
 <span class="sd">&quot;&quot;&quot;</span>
 
 <span class="kn">from</span> <span class="nn">Lib.Errors</span> <span class="kn">import</span> <span class="n">MiniCInternalError</span>
-<span class="kn">from</span> <span class="nn">Lib.Operands</span> <span class="kn">import</span> <span class="p">(</span>
-    <span class="n">Condition</span><span class="p">,</span> <span class="n">Immediate</span><span class="p">,</span> <span class="n">Operand</span><span class="p">,</span> <span class="n">Function</span><span class="p">,</span> <span class="n">ZERO</span><span class="p">)</span>
+<span class="kn">from</span> <span class="nn">Lib.Operands</span> <span class="kn">import</span> <span class="p">(</span><span class="n">Condition</span><span class="p">,</span> <span class="n">Immediate</span><span class="p">,</span> <span class="n">Operand</span><span class="p">,</span> <span class="n">Function</span><span class="p">)</span>
 <span class="kn">from</span> <span class="nn">Lib.Statement</span> <span class="kn">import</span> <span class="p">(</span><span class="n">Instru3A</span><span class="p">,</span> <span class="n">AbsoluteJump</span><span class="p">,</span> <span class="n">ConditionalJump</span><span class="p">,</span> <span class="n">Label</span><span class="p">)</span>
 
 
@@ -99,7 +101,6 @@
 <span class="sd">    This is a wrapper around bge, bgt, beq, ... c is a Condition, like</span>
 <span class="sd">    Condition(&#39;bgt&#39;), Condition(MiniCParser.EQ), ...</span>
 <span class="sd">    &quot;&quot;&quot;</span>
-    <span class="n">op2</span> <span class="o">=</span> <span class="n">op2</span> <span class="k">if</span> <span class="n">op2</span> <span class="o">!=</span> <span class="n">Immediate</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span> <span class="k">else</span> <span class="n">ZERO</span>
     <span class="k">return</span> <span class="n">ConditionalJump</span><span class="p">(</span><span class="n">cond</span><span class="o">=</span><span class="n">cond</span><span class="p">,</span> <span class="n">op1</span><span class="o">=</span><span class="n">op1</span><span class="p">,</span> <span class="n">op2</span><span class="o">=</span><span class="n">op2</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="n">label</span><span class="p">)</span></div>
 
 

docs/_modules/Lib/Statement.html

@@ -42,10 +42,13 @@
 <li class="toctree-l1"><a class="reference internal" href="../../api/Lib.RiscV.html">Base library - RISC-V instructions</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../api/Lib.Operands.html">Base library - Operands</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../api/Lib.FunctionData.html">Base library - Function data</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../api/Lib.Graphes.html">Base library - Graphs</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../api/Lib.LinearCode.html">Linear intermediate representation</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../api/Lib.Allocator.html">Temporary allocation</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../api/Lib.CFG.html">Control Flow Graph - CFG and Basic blocks</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../api/Lib.Terminator.html">Control Flow Graph - Terminators</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../api/Lib.Dominators.html">SSA form - Dominance frontier</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../api/Lib.PhiNode.html">SSA form - Phi Nodes</a></li>
 </ul>
 
         </div>
@@ -177,7 +180,7 @@
             <span class="n">defs</span> <span class="o">=</span> <span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">args</span><span class="p">()[</span><span class="mi">0</span><span class="p">]]</span>
         <span class="k">return</span> <span class="n">defs</span></div>
 
-<div class="viewcode-block" id="Instruction.used"><a class="viewcode-back" href="../../api/Lib.Statement.html#Lib.Statement.Instruction.used">[docs]</a>    <span class="k">def</span> <span class="nf">used</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<div class="viewcode-block" id="Instruction.used"><a class="viewcode-back" href="../../api/Lib.Statement.html#Lib.Statement.Instruction.used">[docs]</a>    <span class="k">def</span> <span class="nf">used</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">List</span><span class="p">[</span><span class="n">Operand</span><span class="p">]:</span>
         <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">is_read_only</span><span class="p">():</span>
             <span class="n">uses</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">args</span><span class="p">()</span>
         <span class="k">else</span><span class="p">:</span>

docs/_modules/Lib/Terminator.html

@@ -42,10 +42,13 @@
 <li class="toctree-l1"><a class="reference internal" href="../../api/Lib.RiscV.html">Base library - RISC-V instructions</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../api/Lib.Operands.html">Base library - Operands</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../api/Lib.FunctionData.html">Base library - Function data</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../api/Lib.Graphes.html">Base library - Graphs</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../api/Lib.LinearCode.html">Linear intermediate representation</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../api/Lib.Allocator.html">Temporary allocation</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../api/Lib.CFG.html">Control Flow Graph - CFG and Basic blocks</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../api/Lib.Terminator.html">Control Flow Graph - Terminators</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../api/Lib.Dominators.html">SSA form - Dominance frontier</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../api/Lib.PhiNode.html">SSA form - Phi Nodes</a></li>
 </ul>
 
         </div>
@@ -125,7 +128,10 @@
             <span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span>
                 <span class="s2">&quot;substitute: No possible substitution on instruction </span><span class="si">{}</span><span class="s2">&quot;</span>
                 <span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="bp">self</span><span class="p">))</span>
-        <span class="k">return</span> <span class="bp">self</span></div></div>
+        <span class="k">return</span> <span class="bp">self</span></div>
+
+<div class="viewcode-block" id="Return.is_read_only"><a class="viewcode-back" href="../../api/Lib.Terminator.html#Lib.Terminator.Return.is_read_only">[docs]</a>    <span class="k">def</span> <span class="nf">is_read_only</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+        <span class="k">return</span> <span class="kc">True</span></div></div>
 
 
 <div class="viewcode-block" id="BranchingTerminator"><a class="viewcode-back" href="../../api/Lib.Terminator.html#Lib.Terminator.BranchingTerminator">[docs]</a><span class="nd">@dataclass</span><span class="p">(</span><span class="n">init</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span>
@@ -201,7 +207,7 @@
             <span class="k">return</span> <span class="n">BranchingTerminator</span><span class="p">(</span><span class="n">j</span><span class="o">.</span><span class="n">cond</span><span class="p">,</span> <span class="n">j</span><span class="o">.</span><span class="n">op1</span><span class="p">,</span> <span class="n">j</span><span class="o">.</span><span class="n">op2</span><span class="p">,</span> <span class="n">j</span><span class="o">.</span><span class="n">label</span><span class="p">,</span> <span class="n">label_else</span><span class="p">)</span>
         <span class="k">case</span> <span class="n">AbsoluteJump</span><span class="p">():</span>
             <span class="k">return</span> <span class="n">AbsoluteJump</span><span class="p">(</span><span class="n">label</span><span class="o">=</span><span class="n">j</span><span class="o">.</span><span class="n">label</span><span class="p">)</span>
-        <span class="n">case</span> <span class="kc">None</span><span class="p">:</span>
+        <span class="k">case</span> <span class="k">_</span><span class="p">:</span>
             <span class="k">if</span> <span class="n">next_label</span><span class="p">:</span>
                 <span class="k">return</span> <span class="n">AbsoluteJump</span><span class="p">(</span><span class="n">next_label</span><span class="p">)</span>
             <span class="k">else</span><span class="p">:</span>

docs/_modules/index.html

@@ -42,10 +42,13 @@
 <li class="toctree-l1"><a class="reference internal" href="../api/Lib.RiscV.html">Base library - RISC-V instructions</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../api/Lib.Operands.html">Base library - Operands</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../api/Lib.FunctionData.html">Base library - Function data</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../api/Lib.Graphes.html">Base library - Graphs</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../api/Lib.LinearCode.html">Linear intermediate representation</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../api/Lib.Allocator.html">Temporary allocation</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../api/Lib.CFG.html">Control Flow Graph - CFG and Basic blocks</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../api/Lib.Terminator.html">Control Flow Graph - Terminators</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../api/Lib.Dominators.html">SSA form - Dominance frontier</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../api/Lib.PhiNode.html">SSA form - Phi Nodes</a></li>
 </ul>
 
         </div>
@@ -74,10 +77,13 @@
   <h1>All modules for which code is available</h1>
 <ul><li><a href="Lib/Allocator.html">Lib.Allocator</a></li>
 <li><a href="Lib/CFG.html">Lib.CFG</a></li>
+<li><a href="Lib/Dominators.html">Lib.Dominators</a></li>
 <li><a href="Lib/Errors.html">Lib.Errors</a></li>
 <li><a href="Lib/FunctionData.html">Lib.FunctionData</a></li>
+<li><a href="Lib/Graphes.html">Lib.Graphes</a></li>
 <li><a href="Lib/LinearCode.html">Lib.LinearCode</a></li>
 <li><a href="Lib/Operands.html">Lib.Operands</a></li>
+<li><a href="Lib/PhiNode.html">Lib.PhiNode</a></li>
 <li><a href="Lib/RiscV.html">Lib.RiscV</a></li>
 <li><a href="Lib/Statement.html">Lib.Statement</a></li>
 <li><a href="Lib/Terminator.html">Lib.Terminator</a></li>

docs/_sources/api/Lib.Dominators.rst.txt

@@ -0,0 +1,7 @@
+Lib.Dominators module
+=====================
+
+.. automodule:: Lib.Dominators
+   :members:
+   :undoc-members:
+   :show-inheritance:

docs/_sources/api/Lib.Graphes.rst.txt

@@ -0,0 +1,7 @@
+Lib.Graphes module
+==================
+
+.. automodule:: Lib.Graphes
+   :members:
+   :undoc-members:
+   :show-inheritance:

docs/_sources/api/Lib.PhiNode.rst.txt

@@ -0,0 +1,7 @@
+Lib.PhiNode module
+==================
+
+.. automodule:: Lib.PhiNode
+   :members:
+   :undoc-members:
+   :show-inheritance:

docs/_sources/api/Lib.rst.txt

@@ -9,10 +9,13 @@ Submodules
 
    Lib.Allocator
    Lib.CFG
+   Lib.Dominators
    Lib.Errors
    Lib.FunctionData
+   Lib.Graphes
    Lib.LinearCode
    Lib.Operands
+   Lib.PhiNode
    Lib.RiscV
    Lib.Statement
    Lib.Terminator

docs/_sources/index.rst.txt

@@ -15,10 +15,13 @@ Welcome to MiniC's documentation!
    Base library - RISC-V instructions <api/Lib.RiscV>
    Base library - Operands <api/Lib.Operands>
    Base library - Function data <api/Lib.FunctionData>
+   Base library - Graphs <api/Lib.Graphes>
    Linear intermediate representation <api/Lib.LinearCode>
    Temporary allocation <api/Lib.Allocator>
    Control Flow Graph - CFG and Basic blocks <api/Lib.CFG>
    Control Flow Graph - Terminators <api/Lib.Terminator>
+   SSA form - Dominance frontier <api/Lib.Dominators>
+   SSA form - Phi Nodes <api/Lib.PhiNode>
 
 These pages document the various Python sources in the Lib/
 folder of MiniC. You should not have to edit them *at all*.
@@ -36,6 +39,9 @@ and pseudo-instructions, we give you the :doc:`api/Lib.RiscV`.
 RISC-V instructions take arguments of various kinds,
 as defined in the :doc:`api/Lib.Operands`.
 
+At some point, we will need some basic functions about oriented and non oriented graphs,
+those are present in :doc:`api/Lib.Graphes`.
+
 Linear Intermediate representation
 ----------------------------------
 
@@ -54,6 +60,15 @@ Control Flow Graph Intermediate representation
 The classes for the CFG and its basic blocks are in the :doc:`api/Lib.CFG`.
 Each block ends with a terminator, as documented in the :doc:`api/Lib.Terminator`.
 
+SSA form
+--------
+
+The translation of the CFG into SSA form makes use of dominance frontiers.
+Functions to work with dominance are defined in the :doc:`api/Lib.Dominators`.
+
+Phi nodes, a special kind of statement that appears in CFGs in SSA form,
+are defined in the :doc:`api/Lib.PhiNode`.
+
 Indices and tables
 ==================
 

docs/api/Lib.Allocator.html

@@ -45,10 +45,13 @@
 <li class="toctree-l1"><a class="reference internal" href="Lib.RiscV.html">Base library - RISC-V instructions</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Lib.Operands.html">Base library - Operands</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Lib.FunctionData.html">Base library - Function data</a></li>
+<li class="toctree-l1"><a class="reference internal" href="Lib.Graphes.html">Base library - Graphs</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Lib.LinearCode.html">Linear intermediate representation</a></li>
 <li class="toctree-l1 current"><a class="current reference internal" href="#">Temporary allocation</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Lib.CFG.html">Control Flow Graph - CFG and Basic blocks</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Lib.Terminator.html">Control Flow Graph - Terminators</a></li>
+<li class="toctree-l1"><a class="reference internal" href="Lib.Dominators.html">SSA form - Dominance frontier</a></li>
+<li class="toctree-l1"><a class="reference internal" href="Lib.PhiNode.html">SSA form - Phi Nodes</a></li>
 </ul>
 
         </div>

docs/api/Lib.CFG.html

@@ -45,10 +45,13 @@
 <li class="toctree-l1"><a class="reference internal" href="Lib.RiscV.html">Base library - RISC-V instructions</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Lib.Operands.html">Base library - Operands</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Lib.FunctionData.html">Base library - Function data</a></li>
+<li class="toctree-l1"><a class="reference internal" href="Lib.Graphes.html">Base library - Graphs</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Lib.LinearCode.html">Linear intermediate representation</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Lib.Allocator.html">Temporary allocation</a></li>
 <li class="toctree-l1 current"><a class="current reference internal" href="#">Control Flow Graph - CFG and Basic blocks</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Lib.Terminator.html">Control Flow Graph - Terminators</a></li>
+<li class="toctree-l1"><a class="reference internal" href="Lib.Dominators.html">SSA form - Dominance frontier</a></li>
+<li class="toctree-l1"><a class="reference internal" href="Lib.PhiNode.html">SSA form - Phi Nodes</a></li>
 </ul>
 
         </div>

docs/api/Lib.Dominators.html

@@ -0,0 +1,152 @@
+<!DOCTYPE html>
+<html class="writer-html5" lang="en" >
+<head>
+  <meta charset="utf-8" /><meta name="generator" content="Docutils 0.17.1: http://docutils.sourceforge.net/" />
+
+  <meta name="viewport" content="width=device-width, initial-scale=1.0" />
+  <title>Lib.Dominators module &mdash; MiniC  documentation</title>
+      <link rel="stylesheet" href="../_static/pygments.css" type="text/css" />
+      <link rel="stylesheet" href="../_static/css/theme.css" type="text/css" />
+  <!--[if lt IE 9]>
+    <script src="../_static/js/html5shiv.min.js"></script>
+  <![endif]-->
+  
+        <script data-url_root="../" id="documentation_options" src="../_static/documentation_options.js"></script>
+        <script src="../_static/jquery.js"></script>
+        <script src="../_static/underscore.js"></script>
+        <script src="../_static/_sphinx_javascript_frameworks_compat.js"></script>
+        <script src="../_static/doctools.js"></script>
+    <script src="../_static/js/theme.js"></script>
+    <link rel="index" title="Index" href="../genindex.html" />
+    <link rel="search" title="Search" href="../search.html" />
+    <link rel="next" title="Lib.PhiNode module" href="Lib.PhiNode.html" />
+    <link rel="prev" title="Lib.Terminator module" href="Lib.Terminator.html" /> 
+</head>
+
+<body class="wy-body-for-nav"> 
+  <div class="wy-grid-for-nav">
+    <nav data-toggle="wy-nav-shift" class="wy-nav-side">
+      <div class="wy-side-scroll">
+        <div class="wy-side-nav-search" >
+            <a href="../index.html" class="icon icon-home"> MiniC
+          </a>
+<div role="search">
+  <form id="rtd-search-form" class="wy-form" action="../search.html" method="get">
+    <input type="text" name="q" placeholder="Search docs" />
+    <input type="hidden" name="check_keywords" value="yes" />
+    <input type="hidden" name="area" value="default" />
+  </form>
+</div>
+        </div><div class="wy-menu wy-menu-vertical" data-spy="affix" role="navigation" aria-label="Navigation menu">
+              <p class="caption" role="heading"><span class="caption-text">Contents:</span></p>
+<ul class="current">
+<li class="toctree-l1"><a class="reference internal" href="Lib.Errors.html">Base library - Errors</a></li>
+<li class="toctree-l1"><a class="reference internal" href="Lib.Statement.html">Base library - Statement</a></li>
+<li class="toctree-l1"><a class="reference internal" href="Lib.RiscV.html">Base library - RISC-V instructions</a></li>
+<li class="toctree-l1"><a class="reference internal" href="Lib.Operands.html">Base library - Operands</a></li>
+<li class="toctree-l1"><a class="reference internal" href="Lib.FunctionData.html">Base library - Function data</a></li>
+<li class="toctree-l1"><a class="reference internal" href="Lib.Graphes.html">Base library - Graphs</a></li>
+<li class="toctree-l1"><a class="reference internal" href="Lib.LinearCode.html">Linear intermediate representation</a></li>
+<li class="toctree-l1"><a class="reference internal" href="Lib.Allocator.html">Temporary allocation</a></li>
+<li class="toctree-l1"><a class="reference internal" href="Lib.CFG.html">Control Flow Graph - CFG and Basic blocks</a></li>
+<li class="toctree-l1"><a class="reference internal" href="Lib.Terminator.html">Control Flow Graph - Terminators</a></li>
+<li class="toctree-l1 current"><a class="current reference internal" href="#">SSA form - Dominance frontier</a></li>
+<li class="toctree-l1"><a class="reference internal" href="Lib.PhiNode.html">SSA form - Phi Nodes</a></li>
+</ul>
+
+        </div>
+      </div>
+    </nav>
+
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+  <section id="module-Lib.Dominators">
+<span id="lib-dominators-module"></span><h1>Lib.Dominators module<a class="headerlink" href="#module-Lib.Dominators" title="Permalink to this heading"></a></h1>
+<p>Utility functions to work with dominators in a <a class="reference internal" href="Lib.CFG.html#Lib.CFG.CFG" title="Lib.CFG.CFG"><code class="xref py py-class docutils literal notranslate"><span class="pre">CFG</span></code></a>.</p>
+<p>Do not hesitate to look at the source of the functions
+to get a better understanding of the algorithms.</p>
+<dl class="py function">
+<dt class="sig sig-object py" id="Lib.Dominators.computeDom">
+<span class="sig-prename descclassname"><span class="pre">Lib.Dominators.</span></span><span class="sig-name descname"><span class="pre">computeDom</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">cfg</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference internal" href="Lib.CFG.html#Lib.CFG.CFG" title="Lib.CFG.CFG"><span class="pre">CFG</span></a></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">Dict</span><span class="p"><span class="pre">[</span></span><a class="reference internal" href="Lib.CFG.html#Lib.CFG.Block" title="Lib.CFG.Block"><span class="pre">Block</span></a><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">Set</span><span class="p"><span class="pre">[</span></span><a class="reference internal" href="Lib.CFG.html#Lib.CFG.Block" title="Lib.CFG.Block"><span class="pre">Block</span></a><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">]</span></span></span></span><a class="reference internal" href="../_modules/Lib/Dominators.html#computeDom"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#Lib.Dominators.computeDom" title="Permalink to this definition"></a></dt>
+<dd><p><cite>computeDom(cfg)</cite> computes the table associating blocks to their
+dominators in <cite>cfg</cite>.
+It works by solving the equation system.</p>
+<p>This is an helper function called during SSA entry.</p>
+</dd></dl>
+
+<dl class="py function">
+<dt class="sig sig-object py" id="Lib.Dominators.printDT">
+<span class="sig-prename descclassname"><span class="pre">Lib.Dominators.</span></span><span class="sig-name descname"><span class="pre">printDT</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">filename</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">str</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">graph</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Dict</span><span class="p"><span class="pre">[</span></span><a class="reference internal" href="Lib.CFG.html#Lib.CFG.Block" title="Lib.CFG.Block"><span class="pre">Block</span></a><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">Set</span><span class="p"><span class="pre">[</span></span><a class="reference internal" href="Lib.CFG.html#Lib.CFG.Block" title="Lib.CFG.Block"><span class="pre">Block</span></a><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">]</span></span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">None</span></span></span><a class="reference internal" href="../_modules/Lib/Dominators.html#printDT"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#Lib.Dominators.printDT" title="Permalink to this definition"></a></dt>
+<dd><p>Display a graphical rendering of the given domination tree.</p>
+</dd></dl>
+
+<dl class="py function">
+<dt class="sig sig-object py" id="Lib.Dominators.computeDT">
+<span class="sig-prename descclassname"><span class="pre">Lib.Dominators.</span></span><span class="sig-name descname"><span class="pre">computeDT</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">cfg</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference internal" href="Lib.CFG.html#Lib.CFG.CFG" title="Lib.CFG.CFG"><span class="pre">CFG</span></a></span></em>, <em class="sig-param"><span class="n"><span class="pre">dominators</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Dict</span><span class="p"><span class="pre">[</span></span><a class="reference internal" href="Lib.CFG.html#Lib.CFG.Block" title="Lib.CFG.Block"><span class="pre">Block</span></a><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">Set</span><span class="p"><span class="pre">[</span></span><a class="reference internal" href="Lib.CFG.html#Lib.CFG.Block" title="Lib.CFG.Block"><span class="pre">Block</span></a><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">]</span></span></span></em>, <em class="sig-param"><span class="n"><span class="pre">dom_graphs</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">bool</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">basename</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">str</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">Dict</span><span class="p"><span class="pre">[</span></span><a class="reference internal" href="Lib.CFG.html#Lib.CFG.Block" title="Lib.CFG.Block"><span class="pre">Block</span></a><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">Set</span><span class="p"><span class="pre">[</span></span><a class="reference internal" href="Lib.CFG.html#Lib.CFG.Block" title="Lib.CFG.Block"><span class="pre">Block</span></a><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">]</span></span></span></span><a class="reference internal" href="../_modules/Lib/Dominators.html#computeDT"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#Lib.Dominators.computeDT" title="Permalink to this definition"></a></dt>
+<dd><p><cite>computeDT(cfg, dominators)</cite> computes the domination tree of <cite>cfg</cite>
+using the previously computed <cite>dominators</cite>.
+It returns <cite>DT</cite>, a dictionary which associates a block with its children
+in the dominator tree.</p>
+<p>This is an helper function called during SSA entry.</p>
+</dd></dl>
+
+<dl class="py function">
+<dt class="sig sig-object py" id="Lib.Dominators.computeDF">
+<span class="sig-prename descclassname"><span class="pre">Lib.Dominators.</span></span><span class="sig-name descname"><span class="pre">computeDF</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">cfg</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference internal" href="Lib.CFG.html#Lib.CFG.CFG" title="Lib.CFG.CFG"><span class="pre">CFG</span></a></span></em>, <em class="sig-param"><span class="n"><span class="pre">dominators</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Dict</span><span class="p"><span class="pre">[</span></span><a class="reference internal" href="Lib.CFG.html#Lib.CFG.Block" title="Lib.CFG.Block"><span class="pre">Block</span></a><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">Set</span><span class="p"><span class="pre">[</span></span><a class="reference internal" href="Lib.CFG.html#Lib.CFG.Block" title="Lib.CFG.Block"><span class="pre">Block</span></a><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">]</span></span></span></em>, <em class="sig-param"><span class="n"><span class="pre">DT</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Dict</span><span class="p"><span class="pre">[</span></span><a class="reference internal" href="Lib.CFG.html#Lib.CFG.Block" title="Lib.CFG.Block"><span class="pre">Block</span></a><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">Set</span><span class="p"><span class="pre">[</span></span><a class="reference internal" href="Lib.CFG.html#Lib.CFG.Block" title="Lib.CFG.Block"><span class="pre">Block</span></a><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">]</span></span></span></em>, <em class="sig-param"><span class="n"><span class="pre">dom_graphs</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">bool</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">basename</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">str</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">Dict</span><span class="p"><span class="pre">[</span></span><a class="reference internal" href="Lib.CFG.html#Lib.CFG.Block" title="Lib.CFG.Block"><span class="pre">Block</span></a><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">Set</span><span class="p"><span class="pre">[</span></span><a class="reference internal" href="Lib.CFG.html#Lib.CFG.Block" title="Lib.CFG.Block"><span class="pre">Block</span></a><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">]</span></span></span></span><a class="reference internal" href="../_modules/Lib/Dominators.html#computeDF"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#Lib.Dominators.computeDF" title="Permalink to this definition"></a></dt>
+<dd><p><cite>computeDF(…)</cite> computes the dominance frontier of a CFG.
+It returns <cite>DF</cite> which associates a block to its frontier.</p>
+<p>This is an helper function called during SSA entry.</p>
+</dd></dl>
+
+</section>
+
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+<li class="toctree-l1"><a class="reference internal" href="Lib.Dominators.html">SSA form - Dominance frontier</a></li>
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+<li class="toctree-l1"><a class="reference internal" href="Lib.PhiNode.html">SSA form - Phi Nodes</a></li>
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+<li class="toctree-l1"><a class="reference internal" href="Lib.Dominators.html">SSA form - Dominance frontier</a></li>
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+             
+  <section id="module-Lib.Graphes">
+<span id="lib-graphes-module"></span><h1>Lib.Graphes module<a class="headerlink" href="#module-Lib.Graphes" title="Permalink to this heading"></a></h1>
+<p>Python Classes for Oriented and Non Oriented Graphs</p>
+<dl class="py exception">
+<dt class="sig sig-object py" id="Lib.Graphes.GraphError">
+<em class="property"><span class="pre">exception</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">Lib.Graphes.</span></span><span class="sig-name descname"><span class="pre">GraphError</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">message</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">str</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/Lib/Graphes.html#GraphError"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#Lib.Graphes.GraphError" title="Permalink to this definition"></a></dt>
+<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">Exception</span></code></p>
+<p>Exception raised for self loops.</p>
+<dl class="py attribute">
+<dt class="sig sig-object py" id="Lib.Graphes.GraphError.message">
+<span class="sig-name descname"><span class="pre">message</span></span><em class="property"><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="pre">str</span></em><a class="headerlink" href="#Lib.Graphes.GraphError.message" title="Permalink to this definition"></a></dt>
+<dd></dd></dl>
+
+</dd></dl>
+
+<dl class="py class">
+<dt class="sig sig-object py" id="Lib.Graphes.GeneralGraph">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">Lib.Graphes.</span></span><span class="sig-name descname"><span class="pre">GeneralGraph</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">graph_dict</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/Lib/Graphes.html#GeneralGraph"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#Lib.Graphes.GeneralGraph" title="Permalink to this definition"></a></dt>
+<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">object</span></code></p>
+<p>General class regrouping similarities
+between directed and non oriented graphs.
+The only differences between the two are:</p>
+<ul class="simple">
+<li><p>how to compute the set of edges</p></li>
+<li><p>how to add an edge</p></li>
+<li><p>how to print the graph</p></li>
+<li><p>how to delete a vertex</p></li>
+<li><p>how to delete an edge</p></li>
+<li><p>we only color undirected graphs</p></li>
+</ul>
+<dl class="py attribute">
+<dt class="sig sig-object py" id="Lib.Graphes.GeneralGraph.graph_dict">
+<span class="sig-name descname"><span class="pre">graph_dict</span></span><em class="property"><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="pre">Dict</span><span class="p"><span class="pre">[</span></span><span class="pre">Any</span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">Set</span><span class="p"><span class="pre">]</span></span></em><a class="headerlink" href="#Lib.Graphes.GeneralGraph.graph_dict" title="Permalink to this definition"></a></dt>
+<dd></dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="Lib.Graphes.GeneralGraph.vertices">
+<span class="sig-name descname"><span class="pre">vertices</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">List</span><span class="p"><span class="pre">[</span></span><span class="pre">Any</span><span class="p"><span class="pre">]</span></span></span></span><a class="reference internal" href="../_modules/Lib/Graphes.html#GeneralGraph.vertices"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#Lib.Graphes.GeneralGraph.vertices" title="Permalink to this definition"></a></dt>
+<dd><p>Return the vertices of a graph.</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="Lib.Graphes.GeneralGraph.add_vertex">
+<span class="sig-name descname"><span class="pre">add_vertex</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">vertex</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Any</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">None</span></span></span><a class="reference internal" href="../_modules/Lib/Graphes.html#GeneralGraph.add_vertex"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#Lib.Graphes.GeneralGraph.add_vertex" title="Permalink to this definition"></a></dt>
+<dd><p>If the vertex “vertex” is not in
+self.graph_dict, a key “vertex” with an empty
+list as a value is added to the dictionary.
+Otherwise nothing has to be done.</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="Lib.Graphes.GeneralGraph.edges">
+<span class="sig-name descname"><span class="pre">edges</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">List</span><span class="p"><span class="pre">[</span></span><span class="pre">Set</span><span class="p"><span class="pre">]</span></span></span></span><a class="reference internal" href="../_modules/Lib/Graphes.html#GeneralGraph.edges"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#Lib.Graphes.GeneralGraph.edges" title="Permalink to this definition"></a></dt>
+<dd><p>Return the edges of the graph.</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="Lib.Graphes.GeneralGraph.dfs_traversal">
+<span class="sig-name descname"><span class="pre">dfs_traversal</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">root</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Any</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">List</span><span class="p"><span class="pre">[</span></span><span class="pre">Any</span><span class="p"><span class="pre">]</span></span></span></span><a class="reference internal" href="../_modules/Lib/Graphes.html#GeneralGraph.dfs_traversal"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#Lib.Graphes.GeneralGraph.dfs_traversal" title="Permalink to this definition"></a></dt>
+<dd><p>Compute a depth first search of the graph,
+from the vertex root.</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="Lib.Graphes.GeneralGraph.is_reachable_from">
+<span class="sig-name descname"><span class="pre">is_reachable_from</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">v1</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Any</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">v2</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Any</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">bool</span></span></span><a class="reference internal" href="../_modules/Lib/Graphes.html#GeneralGraph.is_reachable_from"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#Lib.Graphes.GeneralGraph.is_reachable_from" title="Permalink to this definition"></a></dt>
+<dd><p>True if there is a path from v1 to v2.</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="Lib.Graphes.GeneralGraph.connected_components">
+<span class="sig-name descname"><span class="pre">connected_components</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">List</span><span class="p"><span class="pre">[</span></span><span class="pre">List</span><span class="p"><span class="pre">[</span></span><span class="pre">Any</span><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">]</span></span></span></span><a class="reference internal" href="../_modules/Lib/Graphes.html#GeneralGraph.connected_components"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#Lib.Graphes.GeneralGraph.connected_components" title="Permalink to this definition"></a></dt>
+<dd><p>Compute the list of all connected components of the graph,
+each component being a list of vetices.</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="Lib.Graphes.GeneralGraph.bfs_traversal">
+<span class="sig-name descname"><span class="pre">bfs_traversal</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">root</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Any</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">List</span><span class="p"><span class="pre">[</span></span><span class="pre">Any</span><span class="p"><span class="pre">]</span></span></span></span><a class="reference internal" href="../_modules/Lib/Graphes.html#GeneralGraph.bfs_traversal"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#Lib.Graphes.GeneralGraph.bfs_traversal" title="Permalink to this definition"></a></dt>
+<dd><p>Compute a breadth first search of the graph,
+from the vertex root.</p>
+</dd></dl>
+
+</dd></dl>
+
+<dl class="py class">
+<dt class="sig sig-object py" id="Lib.Graphes.Graph">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">Lib.Graphes.</span></span><span class="sig-name descname"><span class="pre">Graph</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">graph_dict</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/Lib/Graphes.html#Graph"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#Lib.Graphes.Graph" title="Permalink to this definition"></a></dt>
+<dd><p>Bases: <a class="reference internal" href="#Lib.Graphes.GeneralGraph" title="Lib.Graphes.GeneralGraph"><code class="xref py py-class docutils literal notranslate"><span class="pre">GeneralGraph</span></code></a></p>
+<p>Class for non oriented graphs.</p>
+<dl class="py method">
+<dt class="sig sig-object py" id="Lib.Graphes.Graph.edges">
+<span class="sig-name descname"><span class="pre">edges</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">List</span><span class="p"><span class="pre">[</span></span><span class="pre">Set</span><span class="p"><span class="pre">]</span></span></span></span><a class="reference internal" href="../_modules/Lib/Graphes.html#Graph.edges"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#Lib.Graphes.Graph.edges" title="Permalink to this definition"></a></dt>
+<dd><p>A static method generating the set of edges
+(they appear twice in the dictionnary).
+Return a list of sets.</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="Lib.Graphes.Graph.add_edge">
+<span class="sig-name descname"><span class="pre">add_edge</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">edge</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Tuple</span><span class="p"><span class="pre">[</span></span><span class="pre">Any</span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">Any</span><span class="p"><span class="pre">]</span></span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">None</span></span></span><a class="reference internal" href="../_modules/Lib/Graphes.html#Graph.add_edge"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#Lib.Graphes.Graph.add_edge" title="Permalink to this definition"></a></dt>
+<dd><p>Add an edge in the graph.
+edge should be a pair and not (c,c)
+(we call g.add_edge((v1,v2)))</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="Lib.Graphes.Graph.print_dot">
+<span class="sig-name descname"><span class="pre">print_dot</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">name</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">str</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">colors</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">{}</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">None</span></span></span><a class="reference internal" href="../_modules/Lib/Graphes.html#Graph.print_dot"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#Lib.Graphes.Graph.print_dot" title="Permalink to this definition"></a></dt>
+<dd><p>Print the graph.</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="Lib.Graphes.Graph.delete_vertex">
+<span class="sig-name descname"><span class="pre">delete_vertex</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">vertex</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Any</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">None</span></span></span><a class="reference internal" href="../_modules/Lib/Graphes.html#Graph.delete_vertex"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#Lib.Graphes.Graph.delete_vertex" title="Permalink to this definition"></a></dt>
+<dd><p>Delete a vertex and all the adjacent edges.</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="Lib.Graphes.Graph.delete_edge">
+<span class="sig-name descname"><span class="pre">delete_edge</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">edge</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Tuple</span><span class="p"><span class="pre">[</span></span><span class="pre">Any</span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">Any</span><span class="p"><span class="pre">]</span></span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/Lib/Graphes.html#Graph.delete_edge"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#Lib.Graphes.Graph.delete_edge" title="Permalink to this definition"></a></dt>
+<dd><p>Delete an edge.</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="Lib.Graphes.Graph.color">
+<span class="sig-name descname"><span class="pre">color</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">Dict</span><span class="p"><span class="pre">[</span></span><span class="pre">Any</span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">int</span><span class="p"><span class="pre">]</span></span></span></span><a class="reference internal" href="../_modules/Lib/Graphes.html#Graph.color"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#Lib.Graphes.Graph.color" title="Permalink to this definition"></a></dt>
+<dd><p>Color the graph with an unlimited number of colors.
+Return a dict vertex -&gt; color, where color is an integer (0, 1, …).</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="Lib.Graphes.Graph.color_with_k_colors">
+<span class="sig-name descname"><span class="pre">color_with_k_colors</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">K</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">avoidingnodes</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">()</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">Tuple</span><span class="p"><span class="pre">[</span></span><span class="pre">Dict</span><span class="p"><span class="pre">[</span></span><span class="pre">Any</span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">int</span><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">bool</span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">List</span><span class="p"><span class="pre">]</span></span></span></span><a class="reference internal" href="../_modules/Lib/Graphes.html#Graph.color_with_k_colors"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#Lib.Graphes.Graph.color_with_k_colors" title="Permalink to this definition"></a></dt>
+<dd><p>Color with &lt;= K colors (if K is unspecified, use unlimited colors).</p>
+<p>Return 3 values:</p>
+<ul class="simple">
+<li><p>a dict vertex -&gt; color</p></li>
+<li><p>a Boolean, True if the coloring succeeded</p></li>
+<li><p>the set of nodes actually colored</p></li>
+</ul>
+<p>Do not color vertices belonging to avoidingnodes.</p>
+<p>Continue even if the algo fails.</p>
+</dd></dl>
+
+</dd></dl>
+
+<dl class="py class">
+<dt class="sig sig-object py" id="Lib.Graphes.DiGraph">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">Lib.Graphes.</span></span><span class="sig-name descname"><span class="pre">DiGraph</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">graph_dict</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/Lib/Graphes.html#DiGraph"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#Lib.Graphes.DiGraph" title="Permalink to this definition"></a></dt>
+<dd><p>Bases: <a class="reference internal" href="#Lib.Graphes.GeneralGraph" title="Lib.Graphes.GeneralGraph"><code class="xref py py-class docutils literal notranslate"><span class="pre">GeneralGraph</span></code></a></p>
+<p>Class for directed graphs.</p>
+<dl class="py method">
+<dt class="sig sig-object py" id="Lib.Graphes.DiGraph.neighbourhoods">
+<span class="sig-name descname"><span class="pre">neighbourhoods</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">List</span><span class="p"><span class="pre">[</span></span><span class="pre">Tuple</span><span class="p"><span class="pre">[</span></span><span class="pre">Any</span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">Set</span><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">]</span></span></span></span><a class="reference internal" href="../_modules/Lib/Graphes.html#DiGraph.neighbourhoods"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#Lib.Graphes.DiGraph.neighbourhoods" title="Permalink to this definition"></a></dt>
+<dd><p>Return all neighbourhoods in the graph.</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="Lib.Graphes.DiGraph.edges">
+<span class="sig-name descname"><span class="pre">edges</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">List</span><span class="p"><span class="pre">[</span></span><span class="pre">Tuple</span><span class="p"><span class="pre">[</span></span><span class="pre">Any</span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">Any</span><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">]</span></span></span></span><a class="reference internal" href="../_modules/Lib/Graphes.html#DiGraph.edges"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#Lib.Graphes.DiGraph.edges" title="Permalink to this definition"></a></dt>
+<dd><p>A static method generating the set of edges</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="Lib.Graphes.DiGraph.add_edge">
+<span class="sig-name descname"><span class="pre">add_edge</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">edge</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Tuple</span><span class="p"><span class="pre">[</span></span><span class="pre">Any</span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">Any</span><span class="p"><span class="pre">]</span></span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">None</span></span></span><a class="reference internal" href="../_modules/Lib/Graphes.html#DiGraph.add_edge"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#Lib.Graphes.DiGraph.add_edge" title="Permalink to this definition"></a></dt>
+<dd><p>Add an edge in the graph.
+edge should be a pair and not (c,c)
+(we call g.add_edge((v1,v2)))</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="Lib.Graphes.DiGraph.print_dot">
+<span class="sig-name descname"><span class="pre">print_dot</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">name</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">str</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">None</span></span></span><a class="reference internal" href="../_modules/Lib/Graphes.html#DiGraph.print_dot"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#Lib.Graphes.DiGraph.print_dot" title="Permalink to this definition"></a></dt>
+<dd><p>Print the graph.</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="Lib.Graphes.DiGraph.delete_vertex">
+<span class="sig-name descname"><span class="pre">delete_vertex</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">vertex</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Any</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">None</span></span></span><a class="reference internal" href="../_modules/Lib/Graphes.html#DiGraph.delete_vertex"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#Lib.Graphes.DiGraph.delete_vertex" title="Permalink to this definition"></a></dt>
+<dd><p>Delete a vertex and all the adjacent edges.</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="Lib.Graphes.DiGraph.delete_edge">
+<span class="sig-name descname"><span class="pre">delete_edge</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">edge</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Tuple</span><span class="p"><span class="pre">[</span></span><span class="pre">Any</span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">Any</span><span class="p"><span class="pre">]</span></span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">None</span></span></span><a class="reference internal" href="../_modules/Lib/Graphes.html#DiGraph.delete_edge"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#Lib.Graphes.DiGraph.delete_edge" title="Permalink to this definition"></a></dt>
+<dd><p>Delete an edge.</p>
+</dd></dl>
+
+</dd></dl>
+
+</section>
+
+
+           </div>
+          </div>
+          <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer">
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docs/api/Lib.LinearCode.html

@@ -20,7 +20,7 @@
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     <link rel="next" title="Lib.Allocator module" href="Lib.Allocator.html" />
-    <link rel="prev" title="Lib.FunctionData module" href="Lib.FunctionData.html" /> 
+    <link rel="prev" title="Lib.Graphes module" href="Lib.Graphes.html" /> 
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@@ -45,10 +45,13 @@
 <li class="toctree-l1"><a class="reference internal" href="Lib.RiscV.html">Base library - RISC-V instructions</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Lib.Operands.html">Base library - Operands</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Lib.FunctionData.html">Base library - Function data</a></li>
+<li class="toctree-l1"><a class="reference internal" href="Lib.Graphes.html">Base library - Graphs</a></li>
 <li class="toctree-l1 current"><a class="current reference internal" href="#">Linear intermediate representation</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Lib.Allocator.html">Temporary allocation</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Lib.CFG.html">Control Flow Graph - CFG and Basic blocks</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Lib.Terminator.html">Control Flow Graph - Terminators</a></li>
+<li class="toctree-l1"><a class="reference internal" href="Lib.Dominators.html">SSA form - Dominance frontier</a></li>
+<li class="toctree-l1"><a class="reference internal" href="Lib.PhiNode.html">SSA form - Phi Nodes</a></li>
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@@ -157,7 +160,7 @@ instruction is replaced by this list.</p>
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docs/api/Lib.Operands.html

@@ -45,10 +45,13 @@
 <li class="toctree-l1"><a class="reference internal" href="Lib.RiscV.html">Base library - RISC-V instructions</a></li>
 <li class="toctree-l1 current"><a class="current reference internal" href="#">Base library - Operands</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Lib.FunctionData.html">Base library - Function data</a></li>
+<li class="toctree-l1"><a class="reference internal" href="Lib.Graphes.html">Base library - Graphs</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Lib.LinearCode.html">Linear intermediate representation</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Lib.Allocator.html">Temporary allocation</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Lib.CFG.html">Control Flow Graph - CFG and Basic blocks</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Lib.Terminator.html">Control Flow Graph - Terminators</a></li>
+<li class="toctree-l1"><a class="reference internal" href="Lib.Dominators.html">SSA form - Dominance frontier</a></li>
+<li class="toctree-l1"><a class="reference internal" href="Lib.PhiNode.html">SSA form - Phi Nodes</a></li>
 </ul>
 
         </div>
@@ -155,12 +158,14 @@ or a place in memory (offset).</p>
 <dl class="py data">
 <dt class="sig sig-object py" id="Lib.Operands.GP">
 <span class="sig-prename descclassname"><span class="pre">Lib.Operands.</span></span><span class="sig-name descname"><span class="pre">GP</span></span><a class="headerlink" href="#Lib.Operands.GP" title="Permalink to this definition"></a></dt>
-<dd></dd></dl>
+<dd><p>Register not used for this course</p>
+</dd></dl>
 
 <dl class="py data">
 <dt class="sig sig-object py" id="Lib.Operands.TP">
 <span class="sig-prename descclassname"><span class="pre">Lib.Operands.</span></span><span class="sig-name descname"><span class="pre">TP</span></span><a class="headerlink" href="#Lib.Operands.TP" title="Permalink to this definition"></a></dt>
-<dd></dd></dl>
+<dd><p>Register not used for this course</p>
+</dd></dl>
 
 <dl class="py data">
 <dt class="sig sig-object py" id="Lib.Operands.A">
@@ -190,7 +195,8 @@ or a place in memory (offset).</p>
 <dl class="py data">
 <dt class="sig sig-object py" id="Lib.Operands.FP">
 <span class="sig-prename descclassname"><span class="pre">Lib.Operands.</span></span><span class="sig-name descname"><span class="pre">FP</span></span><em class="property"><span class="w"> </span><span class="p"><span class="pre">=</span></span><span class="w"> </span><span class="pre">fp</span></em><a class="headerlink" href="#Lib.Operands.FP" title="Permalink to this definition"></a></dt>
-<dd></dd></dl>
+<dd><p>Frame Pointer = Saved register 0</p>
+</dd></dl>
 
 <dl class="py data">
 <dt class="sig sig-object py" id="Lib.Operands.GP_REGS">

docs/api/Lib.PhiNode.html

@@ -0,0 +1,169 @@
+<!DOCTYPE html>
+<html class="writer-html5" lang="en" >
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+  <title>Lib.PhiNode module &mdash; MiniC  documentation</title>
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+              <p class="caption" role="heading"><span class="caption-text">Contents:</span></p>
+<ul class="current">
+<li class="toctree-l1"><a class="reference internal" href="Lib.Errors.html">Base library - Errors</a></li>
+<li class="toctree-l1"><a class="reference internal" href="Lib.Statement.html">Base library - Statement</a></li>
+<li class="toctree-l1"><a class="reference internal" href="Lib.RiscV.html">Base library - RISC-V instructions</a></li>
+<li class="toctree-l1"><a class="reference internal" href="Lib.Operands.html">Base library - Operands</a></li>
+<li class="toctree-l1"><a class="reference internal" href="Lib.FunctionData.html">Base library - Function data</a></li>
+<li class="toctree-l1"><a class="reference internal" href="Lib.Graphes.html">Base library - Graphs</a></li>
+<li class="toctree-l1"><a class="reference internal" href="Lib.LinearCode.html">Linear intermediate representation</a></li>
+<li class="toctree-l1"><a class="reference internal" href="Lib.Allocator.html">Temporary allocation</a></li>
+<li class="toctree-l1"><a class="reference internal" href="Lib.CFG.html">Control Flow Graph - CFG and Basic blocks</a></li>
+<li class="toctree-l1"><a class="reference internal" href="Lib.Terminator.html">Control Flow Graph - Terminators</a></li>
+<li class="toctree-l1"><a class="reference internal" href="Lib.Dominators.html">SSA form - Dominance frontier</a></li>
+<li class="toctree-l1 current"><a class="current reference internal" href="#">SSA form - Phi Nodes</a></li>
+</ul>
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+           <div itemprop="articleBody">
+             
+  <section id="module-Lib.PhiNode">
+<span id="lib-phinode-module"></span><h1>Lib.PhiNode module<a class="headerlink" href="#module-Lib.PhiNode" title="Permalink to this heading"></a></h1>
+<p>Classes for φ nodes in a RiscV CFG <a class="reference internal" href="Lib.CFG.html#Lib.CFG.CFG" title="Lib.CFG.CFG"><code class="xref py py-class docutils literal notranslate"><span class="pre">CFG</span></code></a> under SSA Form:
+<a class="reference internal" href="#Lib.PhiNode.PhiNode" title="Lib.PhiNode.PhiNode"><code class="xref py py-class docutils literal notranslate"><span class="pre">PhiNode</span></code></a> for a statement of the form temp_x = φ(temp_0, …, temp_n).
+These particular kinds of statements are expected to be in the field
+b._phis for a <a class="reference internal" href="Lib.CFG.html#Lib.CFG.Block" title="Lib.CFG.Block"><code class="xref py py-class docutils literal notranslate"><span class="pre">Block</span></code></a> b.</p>
+<dl class="py class">
+<dt class="sig sig-object py" id="Lib.PhiNode.PhiNode">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">Lib.PhiNode.</span></span><span class="sig-name descname"><span class="pre">PhiNode</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">var</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference internal" href="Lib.Operands.html#Lib.Operands.DataLocation" title="Lib.Operands.DataLocation"><span class="pre">DataLocation</span></a></span></em>, <em class="sig-param"><span class="n"><span class="pre">srcs</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Dict</span><span class="p"><span class="pre">[</span></span><a class="reference internal" href="Lib.Statement.html#Lib.Statement.Label" title="Lib.Statement.Label"><span class="pre">Label</span></a><span class="p"><span class="pre">,</span></span><span class="w"> </span><a class="reference internal" href="Lib.Operands.html#Lib.Operands.Operand" title="Lib.Operands.Operand"><span class="pre">Operand</span></a><span class="p"><span class="pre">]</span></span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/Lib/PhiNode.html#PhiNode"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#Lib.PhiNode.PhiNode" title="Permalink to this definition"></a></dt>
+<dd><p>Bases: <a class="reference internal" href="Lib.Statement.html#Lib.Statement.Statement" title="Lib.Statement.Statement"><code class="xref py py-class docutils literal notranslate"><span class="pre">Statement</span></code></a></p>
+<p>A φ node is a renaming in the CFG, of the form temp_x = φ(temp_0, …, temp_n).
+The field var contains the variable temp_x.
+The field srcs relies for each precedent block in the CFG, identified with its label,
+the variable temp_i of the φ node.</p>
+<dl class="py attribute">
+<dt class="sig sig-object py" id="Lib.PhiNode.PhiNode.var">
+<span class="sig-name descname"><span class="pre">var</span></span><em class="property"><span class="p"><span class="pre">:</span></span><span class="w"> </span><a class="reference internal" href="Lib.Operands.html#Lib.Operands.DataLocation" title="Lib.Operands.DataLocation"><span class="pre">DataLocation</span></a></em><a class="headerlink" href="#Lib.PhiNode.PhiNode.var" title="Permalink to this definition"></a></dt>
+<dd></dd></dl>
+
+<dl class="py attribute">
+<dt class="sig sig-object py" id="Lib.PhiNode.PhiNode.srcs">
+<span class="sig-name descname"><span class="pre">srcs</span></span><em class="property"><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="pre">Dict</span><span class="p"><span class="pre">[</span></span><a class="reference internal" href="Lib.Statement.html#Lib.Statement.Label" title="Lib.Statement.Label"><span class="pre">Label</span></a><span class="p"><span class="pre">,</span></span><span class="w"> </span><a class="reference internal" href="Lib.Operands.html#Lib.Operands.Operand" title="Lib.Operands.Operand"><span class="pre">Operand</span></a><span class="p"><span class="pre">]</span></span></em><a class="headerlink" href="#Lib.PhiNode.PhiNode.srcs" title="Permalink to this definition"></a></dt>
+<dd></dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="Lib.PhiNode.PhiNode.defined">
+<span class="sig-name descname"><span class="pre">defined</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="../_modules/Lib/PhiNode.html#PhiNode.defined"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#Lib.PhiNode.PhiNode.defined" title="Permalink to this definition"></a></dt>
+<dd><p>Return the variable defined by the φ node.</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="Lib.PhiNode.PhiNode.used">
+<span class="sig-name descname"><span class="pre">used</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">Dict</span><span class="p"><span class="pre">[</span></span><a class="reference internal" href="Lib.Statement.html#Lib.Statement.Label" title="Lib.Statement.Label"><span class="pre">Label</span></a><span class="p"><span class="pre">,</span></span><span class="w"> </span><a class="reference internal" href="Lib.Operands.html#Lib.Operands.Operand" title="Lib.Operands.Operand"><span class="pre">Operand</span></a><span class="p"><span class="pre">]</span></span></span></span><a class="reference internal" href="../_modules/Lib/PhiNode.html#PhiNode.used"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#Lib.PhiNode.PhiNode.used" title="Permalink to this definition"></a></dt>
+<dd><p>Return the dictionnary associating for each previous block the corresponding variable.</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="Lib.PhiNode.PhiNode.rename">
+<span class="sig-name descname"><span class="pre">rename</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">renamer</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference internal" href="Lib.Operands.html#Lib.Operands.Renamer" title="Lib.Operands.Renamer"><span class="pre">Renamer</span></a></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">None</span></span></span><a class="reference internal" href="../_modules/Lib/PhiNode.html#PhiNode.rename"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#Lib.PhiNode.PhiNode.rename" title="Permalink to this definition"></a></dt>
+<dd><p>Rename the variable defined by the φ node with a fresh name.</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="Lib.PhiNode.PhiNode.rename_from">
+<span class="sig-name descname"><span class="pre">rename_from</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">renamer</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference internal" href="Lib.Operands.html#Lib.Operands.Renamer" title="Lib.Operands.Renamer"><span class="pre">Renamer</span></a></span></em>, <em class="sig-param"><span class="n"><span class="pre">label</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference internal" href="Lib.Statement.html#Lib.Statement.Label" title="Lib.Statement.Label"><span class="pre">Label</span></a></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">None</span></span></span><a class="reference internal" href="../_modules/Lib/PhiNode.html#PhiNode.rename_from"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#Lib.PhiNode.PhiNode.rename_from" title="Permalink to this definition"></a></dt>
+<dd><p>Rename the variable associated to the block identified by <cite>label</cite>.</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="Lib.PhiNode.PhiNode.printIns">
+<span class="sig-name descname"><span class="pre">printIns</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">stream</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/Lib/PhiNode.html#PhiNode.printIns"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#Lib.PhiNode.PhiNode.printIns" title="Permalink to this definition"></a></dt>
+<dd><p>Print the statement on the given output.
+Should never be called on the base class.</p>
+</dd></dl>
+
+</dd></dl>
+
+</section>
+
+
+           </div>
+          </div>
+          <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer">
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+    </div>
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docs/api/Lib.RiscV.html

@@ -45,10 +45,13 @@
 <li class="toctree-l1 current"><a class="current reference internal" href="#">Base library - RISC-V instructions</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Lib.Operands.html">Base library - Operands</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Lib.FunctionData.html">Base library - Function data</a></li>
+<li class="toctree-l1"><a class="reference internal" href="Lib.Graphes.html">Base library - Graphs</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Lib.LinearCode.html">Linear intermediate representation</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Lib.Allocator.html">Temporary allocation</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Lib.CFG.html">Control Flow Graph - CFG and Basic blocks</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Lib.Terminator.html">Control Flow Graph - Terminators</a></li>
+<li class="toctree-l1"><a class="reference internal" href="Lib.Dominators.html">SSA form - Dominance frontier</a></li>
+<li class="toctree-l1"><a class="reference internal" href="Lib.PhiNode.html">SSA form - Phi Nodes</a></li>
 </ul>
 
         </div>

docs/api/Lib.Statement.html

@@ -45,10 +45,13 @@
 <li class="toctree-l1"><a class="reference internal" href="Lib.RiscV.html">Base library - RISC-V instructions</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Lib.Operands.html">Base library - Operands</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Lib.FunctionData.html">Base library - Function data</a></li>
+<li class="toctree-l1"><a class="reference internal" href="Lib.Graphes.html">Base library - Graphs</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Lib.LinearCode.html">Linear intermediate representation</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Lib.Allocator.html">Temporary allocation</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Lib.CFG.html">Control Flow Graph - CFG and Basic blocks</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Lib.Terminator.html">Control Flow Graph - Terminators</a></li>
+<li class="toctree-l1"><a class="reference internal" href="Lib.Dominators.html">SSA form - Dominance frontier</a></li>
+<li class="toctree-l1"><a class="reference internal" href="Lib.PhiNode.html">SSA form - Phi Nodes</a></li>
 </ul>
 
         </div>
@@ -194,7 +197,7 @@ and others are source.</p>
 
 <dl class="py method">
 <dt class="sig sig-object py" id="Lib.Statement.Instruction.used">
-<span class="sig-name descname"><span class="pre">used</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="../_modules/Lib/Statement.html#Instruction.used"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#Lib.Statement.Instruction.used" title="Permalink to this definition"></a></dt>
+<span class="sig-name descname"><span class="pre">used</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">List</span><span class="p"><span class="pre">[</span></span><a class="reference internal" href="Lib.Operands.html#Lib.Operands.Operand" title="Lib.Operands.Operand"><span class="pre">Operand</span></a><span class="p"><span class="pre">]</span></span></span></span><a class="reference internal" href="../_modules/Lib/Statement.html#Instruction.used"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#Lib.Statement.Instruction.used" title="Permalink to this definition"></a></dt>
 <dd><p>Operands used (read) in this instruction</p>
 </dd></dl>
 

docs/api/Lib.Terminator.html

@@ -19,6 +19,7 @@
     <script src="../_static/js/theme.js"></script>
     <link rel="index" title="Index" href="../genindex.html" />
     <link rel="search" title="Search" href="../search.html" />
+    <link rel="next" title="Lib.Dominators module" href="Lib.Dominators.html" />
     <link rel="prev" title="Lib.CFG module" href="Lib.CFG.html" /> 
 </head>
 
@@ -44,10 +45,13 @@
 <li class="toctree-l1"><a class="reference internal" href="Lib.RiscV.html">Base library - RISC-V instructions</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Lib.Operands.html">Base library - Operands</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Lib.FunctionData.html">Base library - Function data</a></li>
+<li class="toctree-l1"><a class="reference internal" href="Lib.Graphes.html">Base library - Graphs</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Lib.LinearCode.html">Linear intermediate representation</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Lib.Allocator.html">Temporary allocation</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Lib.CFG.html">Control Flow Graph - CFG and Basic blocks</a></li>
 <li class="toctree-l1 current"><a class="current reference internal" href="#">Control Flow Graph - Terminators</a></li>
+<li class="toctree-l1"><a class="reference internal" href="Lib.Dominators.html">SSA form - Dominance frontier</a></li>
+<li class="toctree-l1"><a class="reference internal" href="Lib.PhiNode.html">SSA form - Phi Nodes</a></li>
 </ul>
 
         </div>
@@ -125,6 +129,11 @@ Should never be called on the base class.</p>
 <span class="sig-name descname"><span class="pre">substitute</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">subst</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Dict</span><span class="p"><span class="pre">[</span></span><a class="reference internal" href="Lib.Operands.html#Lib.Operands.Operand" title="Lib.Operands.Operand"><span class="pre">Operand</span></a><span class="p"><span class="pre">,</span></span><span class="w"> </span><a class="reference internal" href="Lib.Operands.html#Lib.Operands.Operand" title="Lib.Operands.Operand"><span class="pre">Operand</span></a><span class="p"><span class="pre">]</span></span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/Lib/Terminator.html#Return.substitute"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#Lib.Terminator.Return.substitute" title="Permalink to this definition"></a></dt>
 <dd></dd></dl>
 
+<dl class="py method">
+<dt class="sig sig-object py" id="Lib.Terminator.Return.is_read_only">
+<span class="sig-name descname"><span class="pre">is_read_only</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="../_modules/Lib/Terminator.html#Return.is_read_only"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#Lib.Terminator.Return.is_read_only" title="Permalink to this definition"></a></dt>
+<dd></dd></dl>
+
 </dd></dl>
 
 <dl class="py class">
@@ -200,6 +209,7 @@ to the potential label next_label.</p>
           </div>
           <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer">
         <a href="Lib.CFG.html" class="btn btn-neutral float-left" title="Lib.CFG module" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a>
+        <a href="Lib.Dominators.html" class="btn btn-neutral float-right" title="Lib.Dominators module" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a>
     </div>
 
   <hr/>

docs/api/Lib.html

@@ -43,10 +43,13 @@
 <li class="toctree-l1"><a class="reference internal" href="Lib.RiscV.html">Base library - RISC-V instructions</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Lib.Operands.html">Base library - Operands</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Lib.FunctionData.html">Base library - Function data</a></li>
+<li class="toctree-l1"><a class="reference internal" href="Lib.Graphes.html">Base library - Graphs</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Lib.LinearCode.html">Linear intermediate representation</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Lib.Allocator.html">Temporary allocation</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Lib.CFG.html">Control Flow Graph - CFG and Basic blocks</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Lib.Terminator.html">Control Flow Graph - Terminators</a></li>
+<li class="toctree-l1"><a class="reference internal" href="Lib.Dominators.html">SSA form - Dominance frontier</a></li>
+<li class="toctree-l1"><a class="reference internal" href="Lib.PhiNode.html">SSA form - Phi Nodes</a></li>
 </ul>
 
         </div>
@@ -81,10 +84,13 @@
 <ul>
 <li class="toctree-l1"><a class="reference internal" href="Lib.Allocator.html">Lib.Allocator module</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Lib.CFG.html">Lib.CFG module</a></li>
+<li class="toctree-l1"><a class="reference internal" href="Lib.Dominators.html">Lib.Dominators module</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Lib.Errors.html">Lib.Errors module</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Lib.FunctionData.html">Lib.FunctionData module</a></li>
+<li class="toctree-l1"><a class="reference internal" href="Lib.Graphes.html">Lib.Graphes module</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Lib.LinearCode.html">Lib.LinearCode module</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Lib.Operands.html">Lib.Operands module</a></li>
+<li class="toctree-l1"><a class="reference internal" href="Lib.PhiNode.html">Lib.PhiNode module</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Lib.RiscV.html">Lib.RiscV module</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Lib.Statement.html">Lib.Statement module</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Lib.Terminator.html">Lib.Terminator module</a></li>

docs/api/modules.html

@@ -43,10 +43,13 @@
 <li class="toctree-l1"><a class="reference internal" href="Lib.RiscV.html">Base library - RISC-V instructions</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Lib.Operands.html">Base library - Operands</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Lib.FunctionData.html">Base library - Function data</a></li>
+<li class="toctree-l1"><a class="reference internal" href="Lib.Graphes.html">Base library - Graphs</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Lib.LinearCode.html">Linear intermediate representation</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Lib.Allocator.html">Temporary allocation</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Lib.CFG.html">Control Flow Graph - CFG and Basic blocks</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Lib.Terminator.html">Control Flow Graph - Terminators</a></li>
+<li class="toctree-l1"><a class="reference internal" href="Lib.Dominators.html">SSA form - Dominance frontier</a></li>
+<li class="toctree-l1"><a class="reference internal" href="Lib.PhiNode.html">SSA form - Phi Nodes</a></li>
 </ul>
 
         </div>
@@ -81,10 +84,13 @@
 <li class="toctree-l2"><a class="reference internal" href="Lib.html#submodules">Submodules</a><ul>
 <li class="toctree-l3"><a class="reference internal" href="Lib.Allocator.html">Lib.Allocator module</a></li>
 <li class="toctree-l3"><a class="reference internal" href="Lib.CFG.html">Lib.CFG module</a></li>
+<li class="toctree-l3"><a class="reference internal" href="Lib.Dominators.html">Lib.Dominators module</a></li>
 <li class="toctree-l3"><a class="reference internal" href="Lib.Errors.html">Lib.Errors module</a></li>
 <li class="toctree-l3"><a class="reference internal" href="Lib.FunctionData.html">Lib.FunctionData module</a></li>
+<li class="toctree-l3"><a class="reference internal" href="Lib.Graphes.html">Lib.Graphes module</a></li>
 <li class="toctree-l3"><a class="reference internal" href="Lib.LinearCode.html">Lib.LinearCode module</a></li>
 <li class="toctree-l3"><a class="reference internal" href="Lib.Operands.html">Lib.Operands module</a></li>
+<li class="toctree-l3"><a class="reference internal" href="Lib.PhiNode.html">Lib.PhiNode module</a></li>
 <li class="toctree-l3"><a class="reference internal" href="Lib.RiscV.html">Lib.RiscV module</a></li>
 <li class="toctree-l3"><a class="reference internal" href="Lib.Statement.html">Lib.Statement module</a></li>
 <li class="toctree-l3"><a class="reference internal" href="Lib.Terminator.html">Lib.Terminator module</a></li>

docs/genindex.html

@@ -42,10 +42,13 @@
 <li class="toctree-l1"><a class="reference internal" href="api/Lib.RiscV.html">Base library - RISC-V instructions</a></li>
 <li class="toctree-l1"><a class="reference internal" href="api/Lib.Operands.html">Base library - Operands</a></li>
 <li class="toctree-l1"><a class="reference internal" href="api/Lib.FunctionData.html">Base library - Function data</a></li>
+<li class="toctree-l1"><a class="reference internal" href="api/Lib.Graphes.html">Base library - Graphs</a></li>
 <li class="toctree-l1"><a class="reference internal" href="api/Lib.LinearCode.html">Linear intermediate representation</a></li>
 <li class="toctree-l1"><a class="reference internal" href="api/Lib.Allocator.html">Temporary allocation</a></li>
 <li class="toctree-l1"><a class="reference internal" href="api/Lib.CFG.html">Control Flow Graph - CFG and Basic blocks</a></li>
 <li class="toctree-l1"><a class="reference internal" href="api/Lib.Terminator.html">Control Flow Graph - Terminators</a></li>
+<li class="toctree-l1"><a class="reference internal" href="api/Lib.Dominators.html">SSA form - Dominance frontier</a></li>
+<li class="toctree-l1"><a class="reference internal" href="api/Lib.PhiNode.html">SSA form - Phi Nodes</a></li>
 </ul>
 
         </div>
@@ -79,6 +82,7 @@
  | <a href="#B"><strong>B</strong></a>
  | <a href="#C"><strong>C</strong></a>
  | <a href="#D"><strong>D</strong></a>
+ | <a href="#E"><strong>E</strong></a>
  | <a href="#F"><strong>F</strong></a>
  | <a href="#G"><strong>G</strong></a>
  | <a href="#I"><strong>I</strong></a>
@@ -92,6 +96,7 @@
  | <a href="#S"><strong>S</strong></a>
  | <a href="#T"><strong>T</strong></a>
  | <a href="#U"><strong>U</strong></a>
+ | <a href="#V"><strong>V</strong></a>
  | <a href="#X"><strong>X</strong></a>
  | <a href="#Z"><strong>Z</strong></a>
  
@@ -114,7 +119,13 @@
       <li><a href="api/Lib.LinearCode.html#Lib.LinearCode.LinearCode.add_comment">add_comment() (Lib.LinearCode.LinearCode method)</a>
 </li>
       <li><a href="api/Lib.CFG.html#Lib.CFG.CFG.add_edge">add_edge() (Lib.CFG.CFG method)</a>
+
+      <ul>
+        <li><a href="api/Lib.Graphes.html#Lib.Graphes.DiGraph.add_edge">(Lib.Graphes.DiGraph method)</a>
 </li>
+        <li><a href="api/Lib.Graphes.html#Lib.Graphes.Graph.add_edge">(Lib.Graphes.Graph method)</a>
+</li>
+      </ul></li>
       <li><a href="api/Lib.CFG.html#Lib.CFG.Block.add_instruction">add_instruction() (Lib.CFG.Block method)</a>
 
       <ul>
@@ -128,6 +139,8 @@
       <li><a href="api/Lib.LinearCode.html#Lib.LinearCode.LinearCode.add_label">add_label() (Lib.LinearCode.LinearCode method)</a>
 </li>
       <li><a href="api/Lib.Operands.html#Lib.Operands.TemporaryPool.add_tmp">add_tmp() (Lib.Operands.TemporaryPool method)</a>
+</li>
+      <li><a href="api/Lib.Graphes.html#Lib.Graphes.GeneralGraph.add_vertex">add_vertex() (Lib.Graphes.GeneralGraph method)</a>
 </li>
       <li><a href="api/Lib.Errors.html#Lib.Errors.AllocationError">AllocationError</a>
 </li>
@@ -153,10 +166,12 @@
 <h2 id="B">B</h2>
 <table style="width: 100%" class="indextable genindextable"><tr>
   <td style="width: 33%; vertical-align: top;"><ul>
-      <li><a href="api/Lib.CFG.html#Lib.CFG.Block">Block (class in Lib.CFG)</a>
+      <li><a href="api/Lib.Graphes.html#Lib.Graphes.GeneralGraph.bfs_traversal">bfs_traversal() (Lib.Graphes.GeneralGraph method)</a>
 </li>
   </ul></td>
   <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="api/Lib.CFG.html#Lib.CFG.Block">Block (class in Lib.CFG)</a>
+</li>
       <li><a href="api/Lib.Terminator.html#Lib.Terminator.BranchingTerminator">BranchingTerminator (class in Lib.Terminator)</a>
 </li>
   </ul></td>
@@ -168,10 +183,22 @@
       <li><a href="api/Lib.RiscV.html#Lib.RiscV.call">call() (in module Lib.RiscV)</a>
 </li>
       <li><a href="api/Lib.CFG.html#Lib.CFG.CFG">CFG (class in Lib.CFG)</a>
+</li>
+      <li><a href="api/Lib.Graphes.html#Lib.Graphes.Graph.color">color() (Lib.Graphes.Graph method)</a>
+</li>
+      <li><a href="api/Lib.Graphes.html#Lib.Graphes.Graph.color_with_k_colors">color_with_k_colors() (Lib.Graphes.Graph method)</a>
 </li>
       <li><a href="api/Lib.Statement.html#Lib.Statement.Comment">Comment (class in Lib.Statement)</a>
 </li>
       <li><a href="api/Lib.Statement.html#Lib.Statement.Comment.comment">comment (Lib.Statement.Comment attribute)</a>
+</li>
+      <li><a href="api/Lib.Dominators.html#Lib.Dominators.computeDF">computeDF() (in module Lib.Dominators)</a>
+</li>
+      <li><a href="api/Lib.Dominators.html#Lib.Dominators.computeDom">computeDom() (in module Lib.Dominators)</a>
+</li>
+  </ul></td>
+  <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="api/Lib.Dominators.html#Lib.Dominators.computeDT">computeDT() (in module Lib.Dominators)</a>
 </li>
       <li><a href="api/Lib.Statement.html#Lib.Statement.ConditionalJump.cond">cond (Lib.Statement.ConditionalJump attribute)</a>
 
@@ -179,13 +206,13 @@
         <li><a href="api/Lib.Terminator.html#Lib.Terminator.BranchingTerminator.cond">(Lib.Terminator.BranchingTerminator attribute)</a>
 </li>
       </ul></li>
-  </ul></td>
-  <td style="width: 33%; vertical-align: top;"><ul>
       <li><a href="api/Lib.Operands.html#Lib.Operands.Condition">Condition (class in Lib.Operands)</a>
 </li>
       <li><a href="api/Lib.RiscV.html#Lib.RiscV.conditional_jump">conditional_jump() (in module Lib.RiscV)</a>
 </li>
       <li><a href="api/Lib.Statement.html#Lib.Statement.ConditionalJump">ConditionalJump (class in Lib.Statement)</a>
+</li>
+      <li><a href="api/Lib.Graphes.html#Lib.Graphes.GeneralGraph.connected_components">connected_components() (Lib.Graphes.GeneralGraph method)</a>
 </li>
       <li><a href="api/Lib.Operands.html#Lib.Operands.Renamer.copy">copy() (Lib.Operands.Renamer method)</a>
 </li>
@@ -200,18 +227,50 @@
       <li><a href="api/Lib.Operands.html#Lib.Operands.Renamer.defined">defined() (Lib.Operands.Renamer method)</a>
 
       <ul>
+        <li><a href="api/Lib.PhiNode.html#Lib.PhiNode.PhiNode.defined">(Lib.PhiNode.PhiNode method)</a>
+</li>
         <li><a href="api/Lib.Statement.html#Lib.Statement.Instruction.defined">(Lib.Statement.Instruction method)</a>
 </li>
         <li><a href="api/Lib.Statement.html#Lib.Statement.Statement.defined">(Lib.Statement.Statement method)</a>
+</li>
+      </ul></li>
+      <li><a href="api/Lib.Graphes.html#Lib.Graphes.DiGraph.delete_edge">delete_edge() (Lib.Graphes.DiGraph method)</a>
+
+      <ul>
+        <li><a href="api/Lib.Graphes.html#Lib.Graphes.Graph.delete_edge">(Lib.Graphes.Graph method)</a>
 </li>
       </ul></li>
   </ul></td>
   <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="api/Lib.Graphes.html#Lib.Graphes.DiGraph.delete_vertex">delete_vertex() (Lib.Graphes.DiGraph method)</a>
+
+      <ul>
+        <li><a href="api/Lib.Graphes.html#Lib.Graphes.Graph.delete_vertex">(Lib.Graphes.Graph method)</a>
+</li>
+      </ul></li>
+      <li><a href="api/Lib.Graphes.html#Lib.Graphes.GeneralGraph.dfs_traversal">dfs_traversal() (Lib.Graphes.GeneralGraph method)</a>
+</li>
+      <li><a href="api/Lib.Graphes.html#Lib.Graphes.DiGraph">DiGraph (class in Lib.Graphes)</a>
+</li>
       <li><a href="api/Lib.RiscV.html#Lib.RiscV.div">div() (in module Lib.RiscV)</a>
 </li>
   </ul></td>
 </tr></table>
 
+<h2 id="E">E</h2>
+<table style="width: 100%" class="indextable genindextable"><tr>
+  <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="api/Lib.Graphes.html#Lib.Graphes.DiGraph.edges">edges() (Lib.Graphes.DiGraph method)</a>
+
+      <ul>
+        <li><a href="api/Lib.Graphes.html#Lib.Graphes.GeneralGraph.edges">(Lib.Graphes.GeneralGraph method)</a>
+</li>
+        <li><a href="api/Lib.Graphes.html#Lib.Graphes.Graph.edges">(Lib.Graphes.Graph method)</a>
+</li>
+      </ul></li>
+  </ul></td>
+</tr></table>
+
 <h2 id="F">F</h2>
 <table style="width: 100%" class="indextable genindextable"><tr>
   <td style="width: 33%; vertical-align: top;"><ul>
@@ -248,6 +307,8 @@
 <table style="width: 100%" class="indextable genindextable"><tr>
   <td style="width: 33%; vertical-align: top;"><ul>
       <li><a href="api/Lib.CFG.html#Lib.CFG.CFG.gather_defs">gather_defs() (Lib.CFG.CFG method)</a>
+</li>
+      <li><a href="api/Lib.Graphes.html#Lib.Graphes.GeneralGraph">GeneralGraph (class in Lib.Graphes)</a>
 </li>
       <li><a href="api/Lib.CFG.html#Lib.CFG.Block.get_all_statements">get_all_statements() (Lib.CFG.Block method)</a>
 </li>
@@ -269,10 +330,10 @@
 </li>
       <li><a href="api/Lib.CFG.html#Lib.CFG.CFG.get_entries">get_entries() (Lib.CFG.CFG method)</a>
 </li>
-  </ul></td>
-  <td style="width: 33%; vertical-align: top;"><ul>
       <li><a href="api/Lib.CFG.html#Lib.CFG.Block.get_in">get_in() (Lib.CFG.Block method)</a>
 </li>
+  </ul></td>
+  <td style="width: 33%; vertical-align: top;"><ul>
       <li><a href="api/Lib.LinearCode.html#Lib.LinearCode.LinearCode.get_instructions">get_instructions() (Lib.LinearCode.LinearCode method)</a>
 </li>
       <li><a href="api/Lib.CFG.html#Lib.CFG.Block.get_label">get_label() (Lib.CFG.Block method)</a>
@@ -294,6 +355,12 @@
       <li><a href="api/Lib.Operands.html#Lib.Operands.GP">GP (in module Lib.Operands)</a>
 </li>
       <li><a href="api/Lib.Operands.html#Lib.Operands.GP_REGS">GP_REGS (in module Lib.Operands)</a>
+</li>
+      <li><a href="api/Lib.Graphes.html#Lib.Graphes.Graph">Graph (class in Lib.Graphes)</a>
+</li>
+      <li><a href="api/Lib.Graphes.html#Lib.Graphes.GeneralGraph.graph_dict">graph_dict (Lib.Graphes.GeneralGraph attribute)</a>
+</li>
+      <li><a href="api/Lib.Graphes.html#Lib.Graphes.GraphError">GraphError</a>
 </li>
   </ul></td>
 </tr></table>
@@ -311,12 +378,18 @@
       </ul></li>
       <li><a href="api/Lib.Statement.html#Lib.Statement.Instru3A">Instru3A (class in Lib.Statement)</a>
 </li>
-  </ul></td>
-  <td style="width: 33%; vertical-align: top;"><ul>
       <li><a href="api/Lib.Statement.html#Lib.Statement.Instruction">Instruction (class in Lib.Statement)</a>
 </li>
-      <li><a href="api/Lib.Statement.html#Lib.Statement.Instruction.is_read_only">is_read_only() (Lib.Statement.Instruction method)</a>
+  </ul></td>
+  <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="api/Lib.Graphes.html#Lib.Graphes.GeneralGraph.is_reachable_from">is_reachable_from() (Lib.Graphes.GeneralGraph method)</a>
 </li>
+      <li><a href="api/Lib.Statement.html#Lib.Statement.Instruction.is_read_only">is_read_only() (Lib.Statement.Instruction method)</a>
+
+      <ul>
+        <li><a href="api/Lib.Terminator.html#Lib.Terminator.Return.is_read_only">(Lib.Terminator.Return method)</a>
+</li>
+      </ul></li>
       <li><a href="api/Lib.CFG.html#Lib.CFG.Block.iter_statements">iter_statements() (Lib.CFG.Block method)</a>
 
       <ul>
@@ -380,6 +453,13 @@
 
       <ul>
         <li><a href="api/Lib.CFG.html#module-Lib.CFG">module</a>
+</li>
+      </ul></li>
+      <li>
+    Lib.Dominators
+
+      <ul>
+        <li><a href="api/Lib.Dominators.html#module-Lib.Dominators">module</a>
 </li>
       </ul></li>
       <li>
@@ -396,6 +476,13 @@
 
       <ul>
         <li><a href="api/Lib.FunctionData.html#module-Lib.FunctionData">module</a>
+</li>
+      </ul></li>
+      <li>
+    Lib.Graphes
+
+      <ul>
+        <li><a href="api/Lib.Graphes.html#module-Lib.Graphes">module</a>
 </li>
       </ul></li>
       <li>
@@ -410,6 +497,13 @@
 
       <ul>
         <li><a href="api/Lib.Operands.html#module-Lib.Operands">module</a>
+</li>
+      </ul></li>
+      <li>
+    Lib.PhiNode
+
+      <ul>
+        <li><a href="api/Lib.PhiNode.html#module-Lib.PhiNode">module</a>
 </li>
       </ul></li>
       <li>
@@ -445,6 +539,8 @@
 <h2 id="M">M</h2>
 <table style="width: 100%" class="indextable genindextable"><tr>
   <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="api/Lib.Graphes.html#Lib.Graphes.GraphError.message">message (Lib.Graphes.GraphError attribute)</a>
+</li>
       <li><a href="api/Lib.Errors.html#Lib.Errors.MiniCInternalError">MiniCInternalError</a>
 </li>
       <li><a href="api/Lib.Errors.html#Lib.Errors.MiniCRuntimeError">MiniCRuntimeError</a>
@@ -462,14 +558,20 @@
         <li><a href="api/Lib.Allocator.html#module-Lib.Allocator">Lib.Allocator</a>
 </li>
         <li><a href="api/Lib.CFG.html#module-Lib.CFG">Lib.CFG</a>
+</li>
+        <li><a href="api/Lib.Dominators.html#module-Lib.Dominators">Lib.Dominators</a>
 </li>
         <li><a href="api/Lib.Errors.html#module-Lib.Errors">Lib.Errors</a>
 </li>
         <li><a href="api/Lib.FunctionData.html#module-Lib.FunctionData">Lib.FunctionData</a>
+</li>
+        <li><a href="api/Lib.Graphes.html#module-Lib.Graphes">Lib.Graphes</a>
 </li>
         <li><a href="api/Lib.LinearCode.html#module-Lib.LinearCode">Lib.LinearCode</a>
 </li>
         <li><a href="api/Lib.Operands.html#module-Lib.Operands">Lib.Operands</a>
+</li>
+        <li><a href="api/Lib.PhiNode.html#module-Lib.PhiNode">Lib.PhiNode</a>
 </li>
         <li><a href="api/Lib.RiscV.html#module-Lib.RiscV">Lib.RiscV</a>
 </li>
@@ -492,11 +594,13 @@
   <td style="width: 33%; vertical-align: top;"><ul>
       <li><a href="api/Lib.Allocator.html#Lib.Allocator.NaiveAllocator">NaiveAllocator (class in Lib.Allocator)</a>
 </li>
-  </ul></td>
-  <td style="width: 33%; vertical-align: top;"><ul>
       <li><a href="api/Lib.Statement.html#Lib.Statement.Label.name">name (Lib.Statement.Label attribute)</a>
 </li>
+  </ul></td>
+  <td style="width: 33%; vertical-align: top;"><ul>
       <li><a href="api/Lib.Operands.html#Lib.Operands.Condition.negate">negate() (Lib.Operands.Condition method)</a>
+</li>
+      <li><a href="api/Lib.Graphes.html#Lib.Graphes.DiGraph.neighbourhoods">neighbourhoods() (Lib.Graphes.DiGraph method)</a>
 </li>
   </ul></td>
 </tr></table>
@@ -530,6 +634,8 @@
 <h2 id="P">P</h2>
 <table style="width: 100%" class="indextable genindextable"><tr>
   <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="api/Lib.PhiNode.html#Lib.PhiNode.PhiNode">PhiNode (class in Lib.PhiNode)</a>
+</li>
       <li><a href="api/Lib.Allocator.html#Lib.Allocator.Allocator.prepare">prepare() (Lib.Allocator.Allocator method)</a>
 
       <ul>
@@ -545,14 +651,22 @@
       <li><a href="api/Lib.CFG.html#Lib.CFG.CFG.print_dot">print_dot() (Lib.CFG.CFG method)</a>
 
       <ul>
+        <li><a href="api/Lib.Graphes.html#Lib.Graphes.DiGraph.print_dot">(Lib.Graphes.DiGraph method)</a>
+</li>
+        <li><a href="api/Lib.Graphes.html#Lib.Graphes.Graph.print_dot">(Lib.Graphes.Graph method)</a>
+</li>
         <li><a href="api/Lib.LinearCode.html#Lib.LinearCode.LinearCode.print_dot">(Lib.LinearCode.LinearCode method)</a>
 </li>
       </ul></li>
   </ul></td>
   <td style="width: 33%; vertical-align: top;"><ul>
-      <li><a href="api/Lib.Statement.html#Lib.Statement.Comment.printIns">printIns() (Lib.Statement.Comment method)</a>
+      <li><a href="api/Lib.Dominators.html#Lib.Dominators.printDT">printDT() (in module Lib.Dominators)</a>
+</li>
+      <li><a href="api/Lib.PhiNode.html#Lib.PhiNode.PhiNode.printIns">printIns() (Lib.PhiNode.PhiNode method)</a>
 
       <ul>
+        <li><a href="api/Lib.Statement.html#Lib.Statement.Comment.printIns">(Lib.Statement.Comment method)</a>
+</li>
         <li><a href="api/Lib.Statement.html#Lib.Statement.Instruction.printIns">(Lib.Statement.Instruction method)</a>
 </li>
         <li><a href="api/Lib.Statement.html#Lib.Statement.Label.printIns">(Lib.Statement.Label method)</a>
@@ -578,9 +692,11 @@
 </li>
       <li><a href="api/Lib.CFG.html#Lib.CFG.CFG.remove_edge">remove_edge() (Lib.CFG.CFG method)</a>
 </li>
-      <li><a href="api/Lib.Statement.html#Lib.Statement.AbsoluteJump.rename">rename() (Lib.Statement.AbsoluteJump method)</a>
+      <li><a href="api/Lib.PhiNode.html#Lib.PhiNode.PhiNode.rename">rename() (Lib.PhiNode.PhiNode method)</a>
 
       <ul>
+        <li><a href="api/Lib.Statement.html#Lib.Statement.AbsoluteJump.rename">(Lib.Statement.AbsoluteJump method)</a>
+</li>
         <li><a href="api/Lib.Statement.html#Lib.Statement.ConditionalJump.rename">(Lib.Statement.ConditionalJump method)</a>
 </li>
         <li><a href="api/Lib.Statement.html#Lib.Statement.Instru3A.rename">(Lib.Statement.Instru3A method)</a>
@@ -594,6 +710,8 @@
       </ul></li>
   </ul></td>
   <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="api/Lib.PhiNode.html#Lib.PhiNode.PhiNode.rename_from">rename_from() (Lib.PhiNode.PhiNode method)</a>
+</li>
       <li><a href="api/Lib.Operands.html#Lib.Operands.Renamer">Renamer (class in Lib.Operands)</a>
 </li>
       <li><a href="api/Lib.Allocator.html#Lib.Allocator.Allocator.replace">replace() (Lib.Allocator.Allocator method)</a>
@@ -626,10 +744,12 @@
 </li>
       <li><a href="api/Lib.Operands.html#Lib.Operands.SP">SP (in module Lib.Operands)</a>
 </li>
-      <li><a href="api/Lib.Statement.html#Lib.Statement.Statement">Statement (class in Lib.Statement)</a>
+      <li><a href="api/Lib.PhiNode.html#Lib.PhiNode.PhiNode.srcs">srcs (Lib.PhiNode.PhiNode attribute)</a>
 </li>
   </ul></td>
   <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="api/Lib.Statement.html#Lib.Statement.Statement">Statement (class in Lib.Statement)</a>
+</li>
       <li><a href="api/Lib.RiscV.html#Lib.RiscV.sub">sub() (in module Lib.RiscV)</a>
 </li>
       <li><a href="api/Lib.Statement.html#Lib.Statement.AbsoluteJump.substitute">substitute() (Lib.Statement.AbsoluteJump method)</a>
@@ -678,15 +798,29 @@
 <h2 id="U">U</h2>
 <table style="width: 100%" class="indextable genindextable"><tr>
   <td style="width: 33%; vertical-align: top;"><ul>
-      <li><a href="api/Lib.Statement.html#Lib.Statement.Instruction.used">used() (Lib.Statement.Instruction method)</a>
+      <li><a href="api/Lib.PhiNode.html#Lib.PhiNode.PhiNode.used">used() (Lib.PhiNode.PhiNode method)</a>
 
       <ul>
+        <li><a href="api/Lib.Statement.html#Lib.Statement.Instruction.used">(Lib.Statement.Instruction method)</a>
+</li>
         <li><a href="api/Lib.Statement.html#Lib.Statement.Statement.used">(Lib.Statement.Statement method)</a>
 </li>
       </ul></li>
   </ul></td>
 </tr></table>
 
+<h2 id="V">V</h2>
+<table style="width: 100%" class="indextable genindextable"><tr>
+  <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="api/Lib.PhiNode.html#Lib.PhiNode.PhiNode.var">var (Lib.PhiNode.PhiNode attribute)</a>
+</li>
+  </ul></td>
+  <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="api/Lib.Graphes.html#Lib.Graphes.GeneralGraph.vertices">vertices() (Lib.Graphes.GeneralGraph method)</a>
+</li>
+  </ul></td>
+</tr></table>
+
 <h2 id="X">X</h2>
 <table style="width: 100%" class="indextable genindextable"><tr>
   <td style="width: 33%; vertical-align: top;"><ul>

docs/index.html

@@ -44,10 +44,13 @@
 <li class="toctree-l1"><a class="reference internal" href="api/Lib.RiscV.html">Base library - RISC-V instructions</a></li>
 <li class="toctree-l1"><a class="reference internal" href="api/Lib.Operands.html">Base library - Operands</a></li>
 <li class="toctree-l1"><a class="reference internal" href="api/Lib.FunctionData.html">Base library - Function data</a></li>
+<li class="toctree-l1"><a class="reference internal" href="api/Lib.Graphes.html">Base library - Graphs</a></li>
 <li class="toctree-l1"><a class="reference internal" href="api/Lib.LinearCode.html">Linear intermediate representation</a></li>
 <li class="toctree-l1"><a class="reference internal" href="api/Lib.Allocator.html">Temporary allocation</a></li>
 <li class="toctree-l1"><a class="reference internal" href="api/Lib.CFG.html">Control Flow Graph - CFG and Basic blocks</a></li>
 <li class="toctree-l1"><a class="reference internal" href="api/Lib.Terminator.html">Control Flow Graph - Terminators</a></li>
+<li class="toctree-l1"><a class="reference internal" href="api/Lib.Dominators.html">SSA form - Dominance frontier</a></li>
+<li class="toctree-l1"><a class="reference internal" href="api/Lib.PhiNode.html">SSA form - Phi Nodes</a></li>
 </ul>
 
         </div>
@@ -84,10 +87,13 @@
 <li class="toctree-l1"><a class="reference internal" href="api/Lib.RiscV.html">Base library - RISC-V instructions</a></li>
 <li class="toctree-l1"><a class="reference internal" href="api/Lib.Operands.html">Base library - Operands</a></li>
 <li class="toctree-l1"><a class="reference internal" href="api/Lib.FunctionData.html">Base library - Function data</a></li>
+<li class="toctree-l1"><a class="reference internal" href="api/Lib.Graphes.html">Base library - Graphs</a></li>
 <li class="toctree-l1"><a class="reference internal" href="api/Lib.LinearCode.html">Linear intermediate representation</a></li>
 <li class="toctree-l1"><a class="reference internal" href="api/Lib.Allocator.html">Temporary allocation</a></li>
 <li class="toctree-l1"><a class="reference internal" href="api/Lib.CFG.html">Control Flow Graph - CFG and Basic blocks</a></li>
 <li class="toctree-l1"><a class="reference internal" href="api/Lib.Terminator.html">Control Flow Graph - Terminators</a></li>
+<li class="toctree-l1"><a class="reference internal" href="api/Lib.Dominators.html">SSA form - Dominance frontier</a></li>
+<li class="toctree-l1"><a class="reference internal" href="api/Lib.PhiNode.html">SSA form - Phi Nodes</a></li>
 </ul>
 </div>
 <p>These pages document the various Python sources in the Lib/
@@ -101,6 +107,8 @@ Instead, to easily create such statements for standard RISC-V assembly instructi
 and pseudo-instructions, we give you the <a class="reference internal" href="api/Lib.RiscV.html"><span class="doc">Lib.RiscV module</span></a>.</p>
 <p>RISC-V instructions take arguments of various kinds,
 as defined in the <a class="reference internal" href="api/Lib.Operands.html"><span class="doc">Lib.Operands module</span></a>.</p>
+<p>At some point, we will need some basic functions about oriented and non oriented graphs,
+those are present in <a class="reference internal" href="api/Lib.Graphes.html"><span class="doc">Lib.Graphes module</span></a>.</p>
 </section>
 <section id="linear-intermediate-representation">
 <h2>Linear Intermediate representation<a class="headerlink" href="#linear-intermediate-representation" title="Permalink to this heading"></a></h2>
@@ -117,6 +125,13 @@ you should understand the naive allocator in the <a class="reference internal" h
 <p>The classes for the CFG and its basic blocks are in the <a class="reference internal" href="api/Lib.CFG.html"><span class="doc">Lib.CFG module</span></a>.
 Each block ends with a terminator, as documented in the <a class="reference internal" href="api/Lib.Terminator.html"><span class="doc">Lib.Terminator module</span></a>.</p>
 </section>
+<section id="ssa-form">
+<h2>SSA form<a class="headerlink" href="#ssa-form" title="Permalink to this heading"></a></h2>
+<p>The translation of the CFG into SSA form makes use of dominance frontiers.
+Functions to work with dominance are defined in the <a class="reference internal" href="api/Lib.Dominators.html"><span class="doc">Lib.Dominators module</span></a>.</p>
+<p>Phi nodes, a special kind of statement that appears in CFGs in SSA form,
+are defined in the <a class="reference internal" href="api/Lib.PhiNode.html"><span class="doc">Lib.PhiNode module</span></a>.</p>
+</section>
 </section>
 <section id="indices-and-tables">
 <h1>Indices and tables<a class="headerlink" href="#indices-and-tables" title="Permalink to this heading"></a></h1>

docs/py-modindex.html

@@ -45,10 +45,13 @@
 <li class="toctree-l1"><a class="reference internal" href="api/Lib.RiscV.html">Base library - RISC-V instructions</a></li>
 <li class="toctree-l1"><a class="reference internal" href="api/Lib.Operands.html">Base library - Operands</a></li>
 <li class="toctree-l1"><a class="reference internal" href="api/Lib.FunctionData.html">Base library - Function data</a></li>
+<li class="toctree-l1"><a class="reference internal" href="api/Lib.Graphes.html">Base library - Graphs</a></li>
 <li class="toctree-l1"><a class="reference internal" href="api/Lib.LinearCode.html">Linear intermediate representation</a></li>
 <li class="toctree-l1"><a class="reference internal" href="api/Lib.Allocator.html">Temporary allocation</a></li>
 <li class="toctree-l1"><a class="reference internal" href="api/Lib.CFG.html">Control Flow Graph - CFG and Basic blocks</a></li>
 <li class="toctree-l1"><a class="reference internal" href="api/Lib.Terminator.html">Control Flow Graph - Terminators</a></li>
+<li class="toctree-l1"><a class="reference internal" href="api/Lib.Dominators.html">SSA form - Dominance frontier</a></li>
+<li class="toctree-l1"><a class="reference internal" href="api/Lib.PhiNode.html">SSA form - Phi Nodes</a></li>
 </ul>
 
         </div>
@@ -101,6 +104,11 @@
        <td>&#160;&#160;&#160;
        <a href="api/Lib.CFG.html#module-Lib.CFG"><code class="xref">Lib.CFG</code></a></td><td>
        <em></em></td></tr>
+     <tr class="cg-1">
+       <td></td>
+       <td>&#160;&#160;&#160;
+       <a href="api/Lib.Dominators.html#module-Lib.Dominators"><code class="xref">Lib.Dominators</code></a></td><td>
+       <em></em></td></tr>
      <tr class="cg-1">
        <td></td>
        <td>&#160;&#160;&#160;
@@ -111,6 +119,11 @@
        <td>&#160;&#160;&#160;
        <a href="api/Lib.FunctionData.html#module-Lib.FunctionData"><code class="xref">Lib.FunctionData</code></a></td><td>
        <em></em></td></tr>
+     <tr class="cg-1">
+       <td></td>
+       <td>&#160;&#160;&#160;
+       <a href="api/Lib.Graphes.html#module-Lib.Graphes"><code class="xref">Lib.Graphes</code></a></td><td>
+       <em></em></td></tr>
      <tr class="cg-1">
        <td></td>
        <td>&#160;&#160;&#160;
@@ -121,6 +134,11 @@
        <td>&#160;&#160;&#160;
        <a href="api/Lib.Operands.html#module-Lib.Operands"><code class="xref">Lib.Operands</code></a></td><td>
        <em></em></td></tr>
+     <tr class="cg-1">
+       <td></td>
+       <td>&#160;&#160;&#160;
+       <a href="api/Lib.PhiNode.html#module-Lib.PhiNode"><code class="xref">Lib.PhiNode</code></a></td><td>
+       <em></em></td></tr>
      <tr class="cg-1">
        <td></td>
        <td>&#160;&#160;&#160;

docs/search.html

@@ -45,10 +45,13 @@
 <li class="toctree-l1"><a class="reference internal" href="api/Lib.RiscV.html">Base library - RISC-V instructions</a></li>
 <li class="toctree-l1"><a class="reference internal" href="api/Lib.Operands.html">Base library - Operands</a></li>
 <li class="toctree-l1"><a class="reference internal" href="api/Lib.FunctionData.html">Base library - Function data</a></li>
+<li class="toctree-l1"><a class="reference internal" href="api/Lib.Graphes.html">Base library - Graphs</a></li>
 <li class="toctree-l1"><a class="reference internal" href="api/Lib.LinearCode.html">Linear intermediate representation</a></li>
 <li class="toctree-l1"><a class="reference internal" href="api/Lib.Allocator.html">Temporary allocation</a></li>
 <li class="toctree-l1"><a class="reference internal" href="api/Lib.CFG.html">Control Flow Graph - CFG and Basic blocks</a></li>
 <li class="toctree-l1"><a class="reference internal" href="api/Lib.Terminator.html">Control Flow Graph - Terminators</a></li>
+<li class="toctree-l1"><a class="reference internal" href="api/Lib.Dominators.html">SSA form - Dominance frontier</a></li>
+<li class="toctree-l1"><a class="reference internal" href="api/Lib.PhiNode.html">SSA form - Phi Nodes</a></li>
 </ul>
 
         </div>