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symbolify.py
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symbolify.py
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import struct
import itertools
from collections import defaultdict
from functools import reduce
import basicTypes
import algebra
from instruction import *
buildExpr = algebra.Expression.build
def extend(const):
if const < 0x8000:
return const
else:
return const-0x10000
def moveReg(reg, isFrom):
def foo(instr, history):
if isFrom:
value = history.read(reg)
toWrite = instr.destReg
else:
toWrite = reg
value = history.read(instr.sourceReg)
return InstrResult.register, history.write(toWrite, value)
return foo
def assignReg(w, fmt ,op):
def foo(instr, history):
value = get_value(history, instr)
toWrite = get_toWrite(instr)
return (InstrResult.register, history.write(toWrite, value))
def get_toWrite(instr):
if w == 'T':
return instr.targetReg
elif w == 'D':
return instr.destReg
elif w == 'F':
return instr.fd
elif w == 'C':
return SpecialRegister.Compare
raise Error("Bad w")
def get_value(history, instr):
if fmt == 'S+xI':
return buildExpr(op, history.read(instr.sourceReg, basicTypes.word), algebra.Literal(instr.immediate))
elif fmt == 'S+I':
return buildExpr(op, history.read(instr.sourceReg, basicTypes.word), algebra.Literal(extend(instr.immediate)))
elif fmt == 'f(I)':
return algebra.Literal(op(instr.immediate))
elif fmt == 'F+F':
return buildExpr(op, history.read(instr.fs, basicTypes.single),
history.read(instr.ft, basicTypes.single), flop=True)
elif fmt == '@F':
if op == 'id':
return history.read(instr.fs)
else:
return buildExpr('@', op, history.read(instr.fs))
elif fmt == 'T<<A':
return buildExpr(op, history.read(instr.targetReg, basicTypes.word), algebra.Literal(instr.shift))
elif fmt == 'S+T':
return buildExpr(op, history.read(instr.sourceReg, basicTypes.word),
history.read(instr.targetReg, basicTypes.word))
elif fmt == 'T<<S':
return buildExpr(op, history.read(instr.targetReg, basicTypes.word),
history.read(instr.sourceReg, basicTypes.word))
raise Error("Bad format")
return foo
def loadMemory(datatype):
# TODO:
# account for stack reads at different offsets (ie, loading the low short of a word)
# add datatype memory
def foo(instr, history):
if instr.sourceReg == Register.SP:
#TODO account for more general reads (ie, just the lower bytes of a word)
value = history.read(basicTypes.Stack(extend(instr.immediate)), datatype)
else:
address = buildExpr('+', history.read(instr.sourceReg, basicTypes.address),
algebra.Literal(extend(instr.immediate)))
value = history.lookupAddress(datatype, address)
return InstrResult.register, history.write(instr.targetReg, value)
return foo
def storeMemory(datatype):
def foo(instr, history):
if instr.sourceReg == Register.SP:
return InstrResult.register, history.write(basicTypes.Stack(extend(instr.immediate)),
history.read(instr.targetReg, datatype))
else:
dest = history.lookupAddress(datatype, buildExpr('+',
history.read(instr.sourceReg, basicTypes.address),
algebra.Literal(extend(instr.immediate))))
return InstrResult.write, history.read(instr.targetReg, dest.type), dest
return foo
def branchMaker(comp, withZero, likely = False):
def doBranch(instr, history):
if instr.opcode == MainOp.BEQ and instr.sourceReg == instr.targetReg:
return InstrResult.jump, None, extend(instr.immediate)
return (InstrResult.likely if likely else InstrResult.branch,
buildExpr(comp,
history.read(instr.sourceReg, basicTypes.word),
history.read(Register.R0 if withZero else instr.targetReg, basicTypes.word)),
extend(instr.immediate))
return doBranch
def MFC_python(instr, history):
if instr.cop == 0:
raise Exception("COP0 unimplemented")
if instr.cop == 1:
return InstrResult.register, history.write(instr.targetReg, history.read(instr.fs))
def MTC_python(instr, history):
if instr.cop == 0:
raise Exception("COP0 unimplemented")
if instr.cop == 1:
return InstrResult.register, history.write(instr.fs, history.read(instr.targetReg))
InstrResult = Enum('InstrResult', 'none register read write function branch likely jump end unhandled')
conversionList = {
MainOp.JAL: lambda instr,regs: (InstrResult.function, 0x80000000 + instr.target),
#note that branches are written negated, the 'if' code is the code immediately following
MainOp.BEQ: branchMaker('!=', withZero = False),
MainOp.BEQL: branchMaker('!=', withZero = False, likely = True),
MainOp.BNE: branchMaker('==', False),
MainOp.BNEL: branchMaker('==', False, True),
MainOp.BLEZ: branchMaker('>', True),
MainOp.BGTZ: branchMaker('<=', True),
MainOp.ADDIU: assignReg('T','S+I','+'),
MainOp.SLTI: assignReg('T','S+I','<'),
MainOp.SLTIU: assignReg('T','S+xI','<'),
MainOp.ANDI: assignReg('T','S+xI','&'),
MainOp.ORI: assignReg('T','S+xI','|'),
MainOp.XORI: assignReg('T','S+xI','^'),
MainOp.LUI: assignReg('T','f(I)',lambda x: x << 16),
MainOp.LB: loadMemory(basicTypes.byte),
MainOp.LH: loadMemory(basicTypes.short),
MainOp.LW: loadMemory(basicTypes.word),
MainOp.LBU: loadMemory(basicTypes.ubyte),
MainOp.LHU: loadMemory(basicTypes.ushort),
MainOp.SB: storeMemory(basicTypes.byte),
MainOp.SH: storeMemory(basicTypes.short),
MainOp.SW: storeMemory(basicTypes.word),
MainOp.LWC1: loadMemory(basicTypes.single),
MainOp.SWC1: storeMemory(basicTypes.single),
MainOp.SDC1: storeMemory(basicTypes.double),
MainOp.LDC1: loadMemory(basicTypes.double),
RegOp.SLL: assignReg('D','T<<A','<<'),
RegOp.SRL: assignReg('D','T<<A','>>'),
RegOp.SRA: assignReg('D','T<<A','>a'),
RegOp.SLLV: assignReg('D', 'T<<S', '<<'),
RegOp.JR: lambda instr, history: (InstrResult.end,) if instr.sourceReg == Register.RA else (InstrResult.unhandled, buildExpr('@','JR',history.read(instr.sourceReg))),
RegOp.JALR: lambda instr, history: (InstrResult.function, '{}'.format(history.read(instr.sourceReg, basicTypes.address))),
RegOp.ADD: assignReg('D','S+T','+'),
RegOp.ADDU: assignReg('D','S+T','+'),
RegOp.SUB: assignReg('D','S+T','-'),
RegOp.SUBU: assignReg('D','S+T','-'),
RegOp.MFHI: moveReg(SpecialRegister.MultHi, isFrom = True),
RegOp.MTHI: moveReg(SpecialRegister.MultHi, False),
RegOp.MFLO: moveReg(SpecialRegister.MultLo, True),
RegOp.MTLO: moveReg(SpecialRegister.MultLo, False),
RegOp.DIV: assignReg('D','S+T','/'),
RegOp.AND: assignReg('D','S+T','&'),
RegOp.OR: assignReg('D','S+T','|'),
RegOp.XOR: assignReg('D','S+T','^'),
RegOp.NOR: assignReg('D', 'S+T', 'NOR'),
RegOp.SLT: assignReg('D','S+T','<'),
RegOp.SLTU: assignReg('D','S+T','<'),
FloatOp.ADD: assignReg('F','F+F','+'),
FloatOp.SUB: assignReg('F','F+F','-'),
FloatOp.MUL: assignReg('F','F+F','*'),
FloatOp.DIV: assignReg('F','F+F','/'),
FloatOp.SQRT: assignReg('F','@F','sqrt'),
FloatOp.ABS: assignReg('F','@F','abs'),
FloatOp.MOV: assignReg('F','@F','id'), #lol
FloatOp.NEG: assignReg('F','@F','neg'),
FloatOp.ROUND_W: assignReg('F','@F','round'),
FloatOp.TRUNC_W: assignReg('F','@F','trunc'),
FloatOp.CEIL_W: assignReg('F','@F','ceil'),
FloatOp.FLOOR_W: assignReg('F','@F','floor'),
FloatOp.CVT_S: assignReg('F','@F','id'),
FloatOp.CVT_D: assignReg('F','@F','id'),
FloatOp.CVT_W: assignReg('F','@F','id'),
FloatOp.C_EQ: assignReg('C', 'F+F', '=='),
FloatOp.C_LE: assignReg('C', 'F+F', '<='),
FloatOp.C_LT: assignReg('C', 'F+F', '<'),
CopOp.MFC: MFC_python,
CopOp.MTC: MTC_python,
CopOp.BCF: lambda instr,history: (InstrResult.branch, history.read(SpecialRegister.Compare), extend(instr.target)),
CopOp.BCT: lambda instr,history: (InstrResult.branch, history.read(SpecialRegister.Compare).negated(), extend(instr.target)),
CopOp.BCFL: lambda instr,history: (InstrResult.likely, history.read(SpecialRegister.Compare), extend(instr.target)),
CopOp.BCTL: lambda instr,history: (InstrResult.likely, history.read(SpecialRegister.Compare).negated(), extend(instr.target)),
CopOp.CFC: lambda instr,regs: None,
CopOp.CTC: lambda instr,regs: None,
SpecialOp.NOP: lambda instr,history: (InstrResult.none,),
SpecialOp.BGEZL: branchMaker('<', withZero = True, likely = True),
SpecialOp.BGEZ: branchMaker('<', withZero = True),
SpecialOp.BLTZ: branchMaker('>=', withZero = True),
}
class Branch(dict):
"""A particular path taken through the program"""
def __init__(self, choices = {}, lineNumber = 0):
self.line = lineNumber
super(Branch, self).__init__(choices)
self.hashValue = hash(','.join('%x%s' % (c,'T' if self[c] else 'F') for c in sorted(self.keys())))
def branchOff(self, split, stayed, currLine = 0):
copy = self.copy()
copy[split] = stayed
return Branch(copy, currLine)
def implies(self, other):
for ch in other:
if ch in self and self[ch] == other[ch]:
continue
else:
return False
return True
def isCompatibleWith(self, other):
for ch in self:
if ch in other and self[ch] != other[ch]:
return False
return True
def tryMerge(self, other):
diff = -1
for ch in self:
if not ch in other:
return -1
if other[ch] != self[ch]:
if diff >= 0:
return -1
else:
diff = ch
return diff
def givenNot(self, badList):
drop = []
for br in badList:
if len(br) == 1:
drop.extend(br)
return self.without(drop)
def without(self, avoid):
return Branch({x:self[x] for x in self if x not in avoid}, self.line)
def __hash__(self):
return self.hashValue
def __eq__(self, other):
return self.implies(other) and other.implies(self)
def __repr__(self):
return '(%s)' % ' and '.join([('not 'if not self[c] else '') + 'cmp_%s' % hex(4*c)[2:] for c in self])
class Context:
def __init__(self, branchList = None, line = 0):
"""Merge the list of branches into something a bit more friendly."""
self.line = line
if not branchList:
self.cnf = [Branch()]
return
allChoices = set()
for br in branchList:
for ch in br:
allChoices.add(ch)
allChoices = sorted(allChoices)
#kinda sorta Quine-McCluskey
byLenbyOnes = defaultdict(lambda: defaultdict(dict))
prime = set()
for br in branchList:
byLenbyOnes[len(br)][sum(1 for ch in br if br[ch])][br]= False
bottom = max(byLenbyOnes.keys())
for L in range(bottom, -1, -1):
for ones in range(L+1):
for lower in byLenbyOnes[L][ones]:
for upper in byLenbyOnes[L][ones+1]:
# find True/False differences
index = lower.tryMerge(upper)
if index >= 0:
byLenbyOnes[L][ones][lower] = True
byLenbyOnes[L][ones+1][upper] = True
newOnes = ones-1 if lower[index] else ones
byLenbyOnes[L-1][newOnes][lower.without([index])] = False
if not byLenbyOnes[L][ones][lower]:
prime.add(lower)
if len(prime) == 1:
self.cnf = list(prime)
else:
prime = sorted(prime, key = lambda x:(min(x), len(x)))
self.cnf = []
for br in prime:
self.cnf.append(br.givenNot(self.cnf))
def implies(self, other):
"""Check if this context implies the other one, and if so return the relative conditions"""
# There are combinations of context that will make the "relative" result nonsensical,
# I'm not certain if they will actually appear. For instance,
# self = (x and not y and z) or (x and y and not z)
# other = (x and not y) or (x and y)
# self does imply other, but relative will be an empty context
relative = []
for base in self.cnf:
options = [target for target in other.cnf if base.implies(target)]
if options:
relative.append(min([base.without(target) for target in options], key=len))
else:
return False, None
return True, Context(relative)
def isCompatibleWith(self, other):
"""Check if any branch could satisfy both contexts"""
for base in self.cnf:
if [t for t in other.cnf if base.isCompatibleWith(t)]:
return True
return False
def processElif(self, badList):
"""What parts of this matter, given that other is NOT true"""
dropped = [br.without(badList) for br in self.cnf]
for br in dropped:
if len(br) == 1:
badList.extend(br)
return Context(dropped)
def isTrivial(self):
return len(self.cnf) == 1 and not self.cnf[0]
def __repr__(self):
return ' or '.join(str(br) for br in self.cnf)
class VariableState:
def __init__(self, name, value, context):
self.name = name
self.value = value
self.context = context
self.explicit = False
def __repr__(self):
return '{} = {} ({})'.format(self.name, self.value, self.context)
class VariableHistory:
def __init__(self, bindings, args = []):
self.states = defaultdict(list)
self.bindings = bindings
self.argList = [] #arguments beyond the given ones
self.now = Context([Branch()])
self.write(Register.R0, algebra.Literal(0))
self.write(Register.SP, algebra.Symbol('SP'))
self.write(Register.RA, algebra.Symbol('RA'))
self.write(SpecialRegister.Compare, algebra.Symbol('bad_CC'))
for reg, name, fmt in args:
showName = name if name else VariableHistory.getName(reg)
self.argList.append(reg)
self.write(reg, algebra.Symbol(showName, fmt))
def read(self, var, fmt = basicTypes.unknown):
"""Retrive (an appropriate representation of) the value in a register and track its usage
var should be a register or Stack() object
Depending on the expected format, the stored value may be altered substantially
"""
if var == Register.R0: #zero is zero, shouldn't remember type info
return algebra.Literal(0)
if var in self.states:
uncertain = False
for st in reversed(self.states[var]):
if self.now.implies(st.context)[0]: # this state definitely occurred
if uncertain:
st.explicit = True
break
else:
if isinstance(st.value, algebra.Literal):
if isinstance(fmt, basicTypes.EnumType):
st.value = self.getEnumValue(fmt, st.value.value)
elif basicTypes.isIndexable(fmt):
st.value = self.lookupAddress(fmt, st.value)
elif st.value.type in [basicTypes.unknown, basicTypes.bad]:
st.value.type = fmt
return st.value
elif self.now.isCompatibleWith(st.context):
st.explicit = True
uncertain = True
return algebra.Symbol(VariableHistory.getName(var), fmt)
else:
symName = VariableHistory.getName(var)
if VariableHistory.couldBeArg(var):
self.argList.append(var)
symName = 'arg_' + symName
self.states[var].append(VariableState(self.getName(var), algebra.Symbol(symName, fmt), self.now))
return self.states[var][-1].value
def write(self, var, value):
self.states[var].append(VariableState(self.getName(var), value, self.now))
return self.states[var][-1]
def markBad(self, var):
self.write(var, algebra.Symbol('bad_%s' % VariableHistory.getName(var), basicTypes.bad))
def isValid(self, var):
"""Determine if reading from the variable makes sense, mainly for function arguments"""
# has the function been touched at all?
if var not in self.states:
return False
# have we marked it as "bad" -
try:
return self.states[var][-1].value.type != basicTypes.bad
except:
# TODO: check that a value is set along all branches, unsure how often this will come up
return True
def lookupAddress(self, fmt, address):
"""Find data of an appropriate format at a (possibly symbolic) address
fmt can influence the results
lookupAddress(single, address_of_v) -> v.x
lookupAddress(Vector, address_of_v) -> v
if fmt is unknown (or no match is found), ?????
"""
base = None
memOffset = 0
others = []
if isinstance(address, algebra.Literal):
memOffset = address.value
elif isinstance(address, algebra.Expression) and address.op == '+':
memOffset = address.constant.value if address.constant else 0
for term in address.args:
if isinstance(term.type, basicTypes.Pointer):
if base:
raise Exception('adding pointers')
base = term
else:
others.append(term)
elif isinstance(address.type, basicTypes.Pointer):
if basicTypes.isIndexable(address.type.pointedType):
base = address
memOffset = 0
else:
return algebra.Symbol(address.type.target if address.type.target else address.name,
address.type.pointedType)
if not base:
#check for trig lookup
if fmt == basicTypes.single and memOffset in self.bindings['trigtables']:
try:
angle = others[0].args[0].args[0]
return algebra.Symbol('{}Table({})'.format(self.bindings['trigtables'][memOffset], angle))
except:
pass
pair = self.relativeToGlobals(memOffset)
if pair:
base = algebra.Symbol('raw', basicTypes.Pointer(pair[0].type, pair[0].name))
memOffset = pair[1]
else:
# no idea what we are looking at, process it anyway
return buildExpr('@', fmt, address)
if basicTypes.isIndexable(base.type.pointedType):
if memOffset >= self.getSize(base.type.pointedType):
raise Exception('trying to look up address {:#x} in {} (only {:#x} bytes)'.format(
memOffset, base.type.pointedType, self.getSize(base.type.pointedType)))
if base.type.target:
return self.subLookup(fmt, algebra.Symbol(base.type.target, base.type.pointedType), memOffset, others)
else:
return self.subLookup(fmt, base, memOffset, others)
elif base.type.target and memOffset == 0 and not others:
return algebra.Symbol(base.type.target, base.type.pointedType)
else:
return buildExpr('@', fmt, address)
def relativeToGlobals(self, offset):
try:
bestOffset = max(x for x in self.bindings['globals'] if x <= offset)
except ValueError:
return None # nothing less than this value
base = algebra.Symbol(*self.bindings['globals'][bestOffset])
relOffset = offset - bestOffset
if relOffset >= self.getSize(base.type):
return None
else:
return base, relOffset
def subLookup(self, fmt, base, address, others = []):
"""Recursively find data at the given address from the start of a type"""
if isinstance(base.type, basicTypes.Array):
spacing = self.getSize(base.type.pointedType)
index = algebra.Literal(address//spacing)
canIndex = True
for o in others:
if (isinstance(o, algebra.Expression) and o.op == '*'
and o.constant and o.constant.value == spacing):
index = buildExpr('+', index, algebra.Expression.arithmeticMerge('*', o.args))
else:
canIndex = False
break
if canIndex:
element = buildExpr('[', base, index)
if basicTypes.isIndexable(base.type.pointedType):
return self.subLookup(fmt, element, address % spacing)
else:
return element
else:
return buildExpr('@',fmt, algebra.Expression.arithmeticMerge('+', [base, algebra.Literal(address)] + others))
parentStruct = None
if isinstance(base.type, basicTypes.Pointer):
parentStruct = base.type.pointedType
elif isinstance(base.type, str):
parentStruct = base.type
if parentStruct and parentStruct in self.bindings['structs']:
members = self.bindings['structs'][parentStruct].members
try:
bestOffset = max(x for x in members if x <= address)
except ValueError: # nothing less
pass
else:
newBase = buildExpr('.', base, algebra.Symbol(*members[bestOffset]))
if address < bestOffset + self.getSize(newBase.type):
if basicTypes.isIndexable(newBase.type):
return self.subLookup(fmt, newBase, address - bestOffset, others)
if not others:
#TODO account for reading the lower short of a word, etc.
return newBase
if others:
return buildExpr('@', fmt, algebra.arithmeticMerge('+', [base, algebra.Literal(address)] + others))
else:
return buildExpr('.', base, algebra.Symbol('{}_{:#x}'.format(basicTypes.getCode(fmt), address), fmt))
def getEnumValue(self, fmt, val):
try:
subname = self.bindings['enums'][fmt.enum].values[val]
except:
subname = '_{:#x}'.format(val)
return buildExpr('.', fmt.enum, algebra.Symbol(subname, fmt))
@staticmethod
def getName(var):
try:
return var.name
except:
try:
return 'stack_%x' % var.offset
except:
return var
def getSize(self, t):
try:
return t.size
except:
if isinstance(t, basicTypes.Pointer):
return 4
if isinstance(t, basicTypes.Flag):
return t.base.size
if isinstance(t, basicTypes.Array):
return t.length * self.getSize(t.pointedType)
if t in self.bindings['structs']:
return self.bindings['structs'][t].size
if isinstance(t, basicTypes.EnumType):
return self.getSize(self.bindings['enums'][t.enum].base)
print('failed to size', t)
@staticmethod
def couldBeArg(var):
if var in [Register.A0, Register.A1, Register.A2, Register.A3, FloatRegister.F12, FloatRegister.F14]:
return True
return isinstance(var, basicTypes.Stack) and var.offset in range(0x10,0x20)
class CodeBlock:
def __init__(self, context, parent = None, relative = None):
self.code = []
self.context = context
self.parent = parent
self.relative = relative
self.children = []
self.elifAccumulator = []
self.elseRelative = None
def makeSymbolic(name, mipsData, bindings, arguments = []):
"""Produce symbolic representation of the logic of a MIPS function"""
address, mips, loops = mipsData
baseBranch = Branch()
currContext = Context([baseBranch]) #no branches yet
branchList = [baseBranch] #branches and their current lines
updates = set()
booleans = {} #will hold the symbols associated with branches
delayed = None
mainCode = CodeBlock(currContext)
currBlock = mainCode
history = VariableHistory(bindings, arguments)
for lineNum, instr in enumerate(mips):
if lineNum in updates:
# different set of active branches, start a new block of code
newContext = Context([b for b in branchList if 0 <= b.line <= lineNum], lineNum)
newParent = currBlock
while True:
imp, rel = newContext.implies(newParent.context)
if imp:
break
else:
newParent = newParent.parent
currBlock = CodeBlock(newContext, newParent, rel)
# continue an elif chain, or start a new one
if newParent.children and not rel.isCompatibleWith(newParent.children[-1].relative):
currBlock.elseRelative = rel.processElif(newParent.elifAccumulator)
else:
newParent.elifAccumulator = [list(br)[0] for br in rel.cnf if len(br) == 1]
newParent.children.append(currBlock)
history.now = newContext
#TODO prune now-irrelevant choices from branches so this doesn't take forever on long functions
try:
result = conversionList[instr.opcode](instr, history)
except ValueError:
currBlock.code.append((InstrResult.unhandled, instr))
else:
if result[0] in [InstrResult.branch, InstrResult.likely, InstrResult.jump]:
if result[1]:
booleans[lineNum] = result[1]
delayed = (result[0], lineNum + 1 + result[-1])
continue
elif result[0] in [InstrResult.function, InstrResult.end]:
delayed = result
continue
elif result[0] != InstrResult.none:
currBlock.code.append(result)
if delayed:
if delayed[0] in [InstrResult.branch, InstrResult.likely, InstrResult.jump]:
branchType, branchDest = delayed
currBranches = [x for x in branchList if 0 <= x.line <= lineNum-1]
if branchType == InstrResult.jump:
for b in currBranches:
b.line = branchDest
updates.add(branchDest)
else:
for b in currBranches:
b.line = -1
branchList.append(b.branchOff(lineNum-1, True, lineNum+1))
branchList.append(b.branchOff(lineNum-1, False, branchDest))
updates.add(lineNum+1)
updates.add(branchDest)
elif delayed[0] == InstrResult.function:
argList = []
funcCall = delayed[1]
if funcCall in bindings['functions']:
title = bindings['functions'][funcCall].name
for reg, argName, fmt in bindings['functions'][funcCall].args:
argList.append((argName, history.read(reg, fmt)))
history.markBad(reg)
else:
try:
title = 'fn%06x' % funcCall
except:
title = funcCall
for reg in [Register.A0, FloatRegister.F12, Register.A1, FloatRegister.F14, Register.A2, Register.A3]:
if history.isValid(reg):
argList.append((reg.name, history.read(reg)))
history.markBad(reg)
for s in (basicTypes.Stack(i) for i in range(0x10, 0x28, 4)):
if history.isValid(s):
argList.append(('stack_{:x}'.format(s.offset), history.read(s)))
history.markBad(s)
else:
break
marker = algebra.Symbol('returnValue_{:x}'.format((lineNum - 1)*4), basicTypes.bad)
currBlock.code.append((InstrResult.function, title, argList, marker))
history.write(Register.V0, marker)
history.write(FloatRegister.F0, marker)
elif delayed[0] == InstrResult.end:
if history.isValid(Register.V0):
returnValue = history.read(Register.V0)
elif history.isValid(FloatRegister.F0):
returnValue = history.read(FloatRegister.F0)
else:
returnValue = None
currBlock.code.append((InstrResult.end, returnValue))
delayed = None
return mainCode, history, booleans