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vm.py
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vm.py
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# ####### dev hack flags ###############
verify_stack_after_op = False
# ######################################
from ethereum import utils
import copy
from ethereum import opcodes
import time
from ethereum.slogging import get_logger
from ethereum.utils import to_string, zpad, encode_int, encode_hex, ascii_chr
log_log = get_logger('eth.vm.log')
log_vm_exit = get_logger('eth.vm.exit')
log_vm_op = get_logger('eth.vm.op')
log_vm_op_stack = get_logger('eth.vm.op.stack')
log_vm_op_memory = get_logger('eth.vm.op.memory')
log_vm_op_storage = get_logger('eth.vm.op.storage')
TT256 = 2 ** 256
TT256M1 = 2 ** 256 - 1
TT255 = 2 ** 255
stackencode = lambda v: encode_hex(zpad(encode_int(v), 32))
def memview(mem):
"""sliced view on memory similar to geth
"""
assert len(mem) % 32 == 0
m = []
for i in range(len(mem) / 32):
m.append("".join([encode_hex(ascii_chr(x)) for x in mem[i * 32:i * 32 + 32]]))
return m
def storage_view(storage_dict):
d = storage_dict.copy()
# FIXME: why is there `"0x": "0x08fa01"` in initialized storage?
if "0x" in d:
# popping in order to align with geth traces
d.pop("0x")
return {stackencode(int(k, 16)): stackencode(int(v, 16)) for k, v in d.items()}
class CallData(object):
def __init__(self, parent_memory, offset=0, size=None):
self.data = parent_memory
self.offset = offset
self.size = len(self.data) if size is None else size
self.rlimit = self.offset + self.size
def extract_all(self):
d = self.data[self.offset: self.offset + self.size]
d += [0] * (self.size - len(d))
return b''.join([ascii_chr(x) for x in d])
def extract32(self, i):
if i >= self.size:
return 0
o = self.data[self.offset + i: min(self.offset + i + 32, self.rlimit)]
return utils.bytearray_to_int(o + [0] * (32 - len(o)))
def extract_copy(self, mem, memstart, datastart, size):
for i in range(size):
if datastart + i < self.size:
mem[memstart + i] = self.data[self.offset + datastart + i]
else:
mem[memstart + i] = 0
class Message(object):
def __init__(self, sender, to, value, gas, data, depth=1,
code_address=None, is_create=False, transfers_value=True):
self.sender = sender
self.to = to
self.value = value
self.gas = gas
self.data = data
self.depth = depth
self.logs = []
self.code_address = code_address
self.is_create = is_create
self.transfers_value = transfers_value
def __repr__(self):
return '<Message(to:%s...)>' % self.to[:8]
class Compustate():
def __init__(self, **kwargs):
self.memory = []
self.stack = []
self.pc = 0
self.gas = 0
for kw in kwargs:
setattr(self, kw, kwargs[kw])
# Preprocesses code, and determines which locations are in the middle
# of pushdata and thus invalid
def preprocess_code(code):
assert isinstance(code, bytes)
code = memoryview(code).tolist()
ops = []
i = 0
while i < len(code):
o = copy.copy(opcodes.opcodes.get(code[i], ['INVALID', 0, 0, 0]) + [code[i], 0])
ops.append(o)
if o[0][:4] == 'PUSH':
for j in range(int(o[0][4:])):
i += 1
byte = code[i] if i < len(code) else 0
o[-1] = (o[-1] << 8) + byte
if i < len(code):
ops.append(['INVALID', 0, 0, 0, byte, 0])
i += 1
return ops
def vm_exception(error, **kargs):
log_vm_exit.trace('EXCEPTION', cause=error, **kargs)
return 0, 0, []
def peaceful_exit(cause, gas, data, **kargs):
log_vm_exit.trace('EXIT', cause=cause, **kargs)
return 1, gas, data
def vm_execute(ext, msg, code):
code_cache = {}
# precompute trace flag
# if we trace vm, we're in slow mode anyway
trace_vm = log_vm_op.is_active('trace')
# Using a mutable object for the bound logger in order to share it 'nonlocal'
# this is necessary, because in the trace scenario we need to
# accumulate gasCost
trace = []
# we have this function nested in order to share the `trace` instance
def mem_extend(mem, compustate, op, start, sz):
memfee = None
if sz:
oldsize = len(mem) // 32
old_totalfee = oldsize * opcodes.GMEMORY + \
oldsize ** 2 // opcodes.GQUADRATICMEMDENOM
newsize = utils.ceil32(start + sz) // 32
# if newsize > 524288:
# raise Exception("Memory above 16 MB per call not supported by this VM")
new_totalfee = newsize * opcodes.GMEMORY + \
newsize ** 2 // opcodes.GQUADRATICMEMDENOM
if old_totalfee < new_totalfee:
memfee = new_totalfee - old_totalfee
if compustate.gas < memfee:
compustate.gas = 0
return False
use_gas(memfee)
m_extend = (newsize - oldsize) * 32
mem.extend([0] * m_extend)
else:
memfee = 0
if trace:
trace[0] = trace[0].bind(memory=memview(mem),
# preserve gasCost in context when
# binding memory
gasCost=trace[0].context.get('gasCost', 0),
gas=compustate.gas)
return True
# we have this function nested in order to share the `trace` instance
def data_copy(compustate, size):
if size:
copyfee = opcodes.GCOPY * utils.ceil32(size) // 32
if compustate.gas < copyfee:
compustate.gas = 0
return False
use_gas(copyfee)
return True
# we have this function nested in order to share the `trace` instance
def use_gas(amount):
"""manipulating compustate.gas should be done through this method!
(since this allows us to update the actual used gas per step
"""
compustate.gas -= amount
if trace:
trace[0] = trace[0].bind(
gasCost=trace[0].context.get('gasCost', 0) + amount,
gas=compustate.gas)
compustate = Compustate(gas=msg.gas)
stk = compustate.stack
mem = compustate.memory
if code in code_cache:
processed_code = code_cache[code]
else:
processed_code = preprocess_code(code)
code_cache[code] = processed_code
codelen = len(processed_code)
s = time.time()
assert s
op = None
steps = 0
# `try`'ing here in order to `finally` being able to trace RETURN
try:
while 1:
if trace_vm:
if trace:
trace[0].trace('vm')
trace = [log_vm_op.bind()]
# print 'op: ', op, time.time() - s
# s = time.time()
# stack size limit error
if compustate.pc >= codelen:
return peaceful_exit('CODE OUT OF RANGE', compustate.gas, [])
op, in_args, out_args, fee, opcode, pushval = \
processed_code[compustate.pc]
# out of gas error
if fee > compustate.gas:
return vm_exception('OUT OF GAS')
# empty stack error
if in_args > len(compustate.stack):
return vm_exception('INSUFFICIENT STACK',
op=op, needed=to_string(in_args),
available=to_string(len(compustate.stack)))
if len(compustate.stack) - in_args + out_args > 1024:
return vm_exception('STACK SIZE LIMIT EXCEEDED',
op=op,
pre_height=to_string(len(compustate.stack)))
# Apply operation
use_gas(fee)
compustate.pc += 1
if trace_vm:
# if trace:
# trace[0].trace('vm')
# trace = [log_vm_op.bind()]
# trace.context = dict()
"""
This diverges from normal logging, as we use the logging namespace
only to decide which features get logged in 'eth.vm.op'
i.e. tracing can not be activated by activating a sub
like 'eth.vm.op.stack'
"""
trace_data = {}
trace_data['stack'] = list(map(stackencode, list(compustate.stack)))
# if len(mem):
trace_data['memory'] = memview(mem) if len(mem) else None
trace_data['storage'] = storage_view(ext.log_storage(msg.to))
trace_data['gas'] = compustate.gas
trace_data['gasCost'] = trace[0].context['gasCost'] # keep gasCost in context
trace_data['pc'] = compustate.pc - 1
# if steps == 0:
# trace_data['address'] = encode_hex(msg.to)
trace_data['depth'] = msg.depth
trace_data['op'] = op
trace_data['error'] = ""
# trace_data['steps'] = steps
# trace_data['processed_code'] = processed_code[compustate.pc - 1]
trace[0] = trace[0].bind(**trace_data)
steps += 1
# Invalid operation
if op == 'INVALID':
return vm_exception('INVALID OP', opcode=opcode)
# Valid operations
if opcode < 0x10:
if op == 'STOP':
return peaceful_exit('STOP', compustate.gas, [])
elif op == 'ADD':
stk.append((stk.pop() + stk.pop()) & TT256M1)
elif op == 'SUB':
stk.append((stk.pop() - stk.pop()) & TT256M1)
elif op == 'MUL':
stk.append((stk.pop() * stk.pop()) & TT256M1)
elif op == 'DIV':
s0, s1 = stk.pop(), stk.pop()
stk.append(0 if s1 == 0 else s0 // s1)
elif op == 'MOD':
s0, s1 = stk.pop(), stk.pop()
stk.append(0 if s1 == 0 else s0 % s1)
elif op == 'SDIV':
s0, s1 = utils.to_signed(stk.pop()), utils.to_signed(stk.pop())
stk.append(0 if s1 == 0 else (abs(s0) // abs(s1) *
(-1 if s0 * s1 < 0 else 1)) & TT256M1)
elif op == 'SMOD':
s0, s1 = utils.to_signed(stk.pop()), utils.to_signed(stk.pop())
stk.append(0 if s1 == 0 else (abs(s0) % abs(s1) *
(-1 if s0 < 0 else 1)) & TT256M1)
elif op == 'ADDMOD':
s0, s1, s2 = stk.pop(), stk.pop(), stk.pop()
stk.append((s0 + s1) % s2 if s2 else 0)
elif op == 'MULMOD':
s0, s1, s2 = stk.pop(), stk.pop(), stk.pop()
stk.append((s0 * s1) % s2 if s2 else 0)
elif op == 'EXP':
base, exponent = stk.pop(), stk.pop()
# fee for exponent is dependent on its bytes
# calc n bytes to represent exponent
nbytes = len(encode_int(exponent))
expfee = nbytes * opcodes.GEXPONENTBYTE
if compustate.gas < expfee:
compustate.gas = 0
return vm_exception('OOG EXPONENT')
use_gas(expfee)
stk.append(pow(base, exponent, TT256))
elif op == 'SIGNEXTEND':
s0, s1 = stk.pop(), stk.pop()
if s0 <= 31:
testbit = s0 * 8 + 7
if s1 & (1 << testbit):
stk.append(s1 | (TT256 - (1 << testbit)))
else:
stk.append(s1 & ((1 << testbit) - 1))
else:
stk.append(s1)
elif opcode < 0x20:
if op == 'LT':
stk.append(1 if stk.pop() < stk.pop() else 0)
elif op == 'GT':
stk.append(1 if stk.pop() > stk.pop() else 0)
elif op == 'SLT':
s0, s1 = utils.to_signed(stk.pop()), utils.to_signed(stk.pop())
stk.append(1 if s0 < s1 else 0)
elif op == 'SGT':
s0, s1 = utils.to_signed(stk.pop()), utils.to_signed(stk.pop())
stk.append(1 if s0 > s1 else 0)
elif op == 'EQ':
stk.append(1 if stk.pop() == stk.pop() else 0)
elif op == 'ISZERO':
stk.append(0 if stk.pop() else 1)
elif op == 'AND':
stk.append(stk.pop() & stk.pop())
elif op == 'OR':
stk.append(stk.pop() | stk.pop())
elif op == 'XOR':
stk.append(stk.pop() ^ stk.pop())
elif op == 'NOT':
stk.append(TT256M1 - stk.pop())
elif op == 'BYTE':
s0, s1 = stk.pop(), stk.pop()
if s0 >= 32:
stk.append(0)
else:
stk.append((s1 // 256 ** (31 - s0)) % 256)
elif opcode < 0x40:
if op == 'SHA3':
s0, s1 = stk.pop(), stk.pop()
use_gas(opcodes.GSHA3WORD * (utils.ceil32(s1) // 32))
if compustate.gas < 0:
return vm_exception('OOG PAYING FOR SHA3')
if not mem_extend(mem, compustate, op, s0, s1):
return vm_exception('OOG EXTENDING MEMORY')
data = b''.join(map(ascii_chr, mem[s0: s0 + s1]))
stk.append(utils.big_endian_to_int(utils.sha3(data)))
elif op == 'ADDRESS':
stk.append(utils.coerce_to_int(msg.to))
elif op == 'BALANCE':
addr = utils.coerce_addr_to_hex(stk.pop() % 2 ** 160)
stk.append(ext.get_balance(addr))
elif op == 'ORIGIN':
stk.append(utils.coerce_to_int(ext.tx_origin))
elif op == 'CALLER':
stk.append(utils.coerce_to_int(msg.sender))
elif op == 'CALLVALUE':
stk.append(msg.value)
elif op == 'CALLDATALOAD':
stk.append(msg.data.extract32(stk.pop()))
elif op == 'CALLDATASIZE':
stk.append(msg.data.size)
elif op == 'CALLDATACOPY':
mstart, dstart, size = stk.pop(), stk.pop(), stk.pop()
if not mem_extend(mem, compustate, op, mstart, size):
return vm_exception('OOG EXTENDING MEMORY')
if not data_copy(compustate, size):
return vm_exception('OOG COPY DATA')
msg.data.extract_copy(mem, mstart, dstart, size)
elif op == 'CODESIZE':
stk.append(len(processed_code))
elif op == 'CODECOPY':
start, s1, size = stk.pop(), stk.pop(), stk.pop()
if not mem_extend(mem, compustate, op, start, size):
return vm_exception('OOG EXTENDING MEMORY')
if not data_copy(compustate, size):
return vm_exception('OOG COPY DATA')
for i in range(size):
if s1 + i < len(processed_code):
mem[start + i] = processed_code[s1 + i][4]
else:
mem[start + i] = 0
elif op == 'GASPRICE':
stk.append(ext.tx_gasprice)
elif op == 'EXTCODESIZE':
addr = utils.coerce_addr_to_hex(stk.pop() % 2 ** 160)
stk.append(len(ext.get_code(addr) or b''))
elif op == 'EXTCODECOPY':
addr = utils.coerce_addr_to_hex(stk.pop() % 2 ** 160)
start, s2, size = stk.pop(), stk.pop(), stk.pop()
extcode = ext.get_code(addr) or b''
assert utils.is_string(extcode)
if not mem_extend(mem, compustate, op, start, size):
return vm_exception('OOG EXTENDING MEMORY')
if not data_copy(compustate, size):
return vm_exception('OOG COPY DATA')
for i in range(size):
if s2 + i < len(extcode):
mem[start + i] = utils.safe_ord(extcode[s2 + i])
else:
mem[start + i] = 0
elif opcode < 0x50:
if op == 'BLOCKHASH':
stk.append(utils.big_endian_to_int(ext.block_hash(stk.pop())))
elif op == 'COINBASE':
stk.append(utils.big_endian_to_int(ext.block_coinbase))
elif op == 'TIMESTAMP':
stk.append(ext.block_timestamp)
elif op == 'NUMBER':
stk.append(ext.block_number)
elif op == 'DIFFICULTY':
stk.append(ext.block_difficulty)
elif op == 'GASLIMIT':
stk.append(ext.block_gas_limit)
elif opcode < 0x60:
if op == 'POP':
stk.pop()
elif op == 'MLOAD':
s0 = stk.pop()
if not mem_extend(mem, compustate, op, s0, 32):
return vm_exception('OOG EXTENDING MEMORY')
data = b''.join(map(ascii_chr, mem[s0: s0 + 32]))
stk.append(utils.big_endian_to_int(data))
elif op == 'MSTORE':
s0, s1 = stk.pop(), stk.pop()
if not mem_extend(mem, compustate, op, s0, 32):
return vm_exception('OOG EXTENDING MEMORY')
v = s1
for i in range(31, -1, -1):
mem[s0 + i] = v % 256
v //= 256
elif op == 'MSTORE8':
s0, s1 = stk.pop(), stk.pop()
if not mem_extend(mem, compustate, op, s0, 1):
return vm_exception('OOG EXTENDING MEMORY')
mem[s0] = s1 % 256
elif op == 'SLOAD':
stk.append(ext.get_storage_data(msg.to, stk.pop()))
elif op == 'SSTORE':
s0, s1 = stk.pop(), stk.pop()
if ext.get_storage_data(msg.to, s0):
gascost = opcodes.GSTORAGEMOD if s1 else opcodes.GSTORAGEKILL
refund = 0 if s1 else opcodes.GSTORAGEREFUND
else:
gascost = opcodes.GSTORAGEADD if s1 else opcodes.GSTORAGEMOD
refund = 0
if compustate.gas < gascost:
return vm_exception('OUT OF GAS')
use_gas(gascost)
ext.add_refund(refund) # adds neg gascost as a refund if below zero
ext.set_storage_data(msg.to, s0, s1)
elif op == 'JUMP':
compustate.pc = stk.pop()
opnew = processed_code[compustate.pc][0] if \
compustate.pc < len(processed_code) else 'STOP'
if opnew != 'JUMPDEST':
return vm_exception('BAD JUMPDEST')
elif op == 'JUMPI':
s0, s1 = stk.pop(), stk.pop()
if s1:
compustate.pc = s0
opnew = processed_code[compustate.pc][0] if \
compustate.pc < len(processed_code) else 'STOP'
if opnew != 'JUMPDEST':
return vm_exception('BAD JUMPDEST')
elif op == 'PC':
stk.append(compustate.pc - 1)
elif op == 'MSIZE':
stk.append(len(mem))
elif op == 'GAS':
stk.append(compustate.gas) # AFTER subtracting cost 1
elif op[:4] == 'PUSH':
pushnum = int(op[4:])
compustate.pc += pushnum
stk.append(pushval)
elif op[:3] == 'DUP':
depth = int(op[3:])
stk.append(stk[-depth])
elif op[:4] == 'SWAP':
depth = int(op[4:])
temp = stk[-depth - 1]
stk[-depth - 1] = stk[-1]
stk[-1] = temp
elif op[:3] == 'LOG':
"""
0xa0 ... 0xa4, 32/64/96/128/160 + len(data) gas
a. Opcodes LOG0...LOG4 are added, takes 2-6 stack arguments
MEMSTART MEMSZ (TOPIC1) (TOPIC2) (TOPIC3) (TOPIC4)
b. Logs are kept track of during tx execution exactly the same way as suicides
(except as an ordered list, not a set).
Each log is in the form [address, [topic1, ... ], data] where:
* address is what the ADDRESS opcode would output
* data is mem[MEMSTART: MEMSTART + MEMSZ]
* topics are as provided by the opcode
c. The ordered list of logs in the transaction are expressed as [log0, log1, ..., logN].
"""
depth = int(op[3:])
mstart, msz = stk.pop(), stk.pop()
topics = [stk.pop() for x in range(depth)]
use_gas(msz * opcodes.GLOGBYTE)
if not mem_extend(mem, compustate, op, mstart, msz):
return vm_exception('OOG EXTENDING MEMORY')
data = b''.join(map(ascii_chr, mem[mstart: mstart + msz]))
ext.log(msg.to, topics, data)
log_log.trace('LOG', to=encode_hex(msg.to), topics=topics, data=list(map(utils.safe_ord, data)))
# print('LOG', msg.to, topics, list(map(ord, data)))
elif op == 'CREATE':
value, mstart, msz = stk.pop(), stk.pop(), stk.pop()
if not mem_extend(mem, compustate, op, mstart, msz):
return vm_exception('OOG EXTENDING MEMORY')
if ext.get_balance(msg.to) >= value and msg.depth < 1024:
cd = CallData(mem, mstart, msz)
create_msg = Message(msg.to, b'', value, compustate.gas, cd, msg.depth + 1)
o, gas, addr = ext.create(create_msg)
if o:
stk.append(utils.coerce_to_int(addr))
compustate.gas = gas
else:
stk.append(0)
compustate.gas = 0
else:
stk.append(0)
elif op == 'CALL':
gas, to, value, meminstart, meminsz, memoutstart, memoutsz = \
stk.pop(), stk.pop(), stk.pop(), stk.pop(), stk.pop(), stk.pop(), stk.pop()
if not mem_extend(mem, compustate, op, meminstart, meminsz) or \
not mem_extend(mem, compustate, op, memoutstart, memoutsz):
return vm_exception('OOG EXTENDING MEMORY')
to = encode_int(to)
to = ((b'\x00' * (32 - len(to))) + to)[12:]
extra_gas = (not ext.account_exists(to)) * opcodes.GCALLNEWACCOUNT + \
(value > 0) * opcodes.GCALLVALUETRANSFER
submsg_gas = gas + opcodes.GSTIPEND * (value > 0)
if compustate.gas < gas + extra_gas:
return vm_exception('OUT OF GAS', needed=gas + extra_gas)
if ext.get_balance(msg.to) >= value and msg.depth < 1024:
use_gas(gas + extra_gas)
cd = CallData(mem, meminstart, meminsz)
call_msg = Message(msg.to, to, value, submsg_gas, cd,
msg.depth + 1, code_address=to)
result, gas, data = ext.msg(call_msg)
if result == 0:
stk.append(0)
else:
stk.append(1)
use_gas(-gas) # refund
for i in range(min(len(data), memoutsz)):
mem[memoutstart + i] = data[i]
else:
use_gas(gas + extra_gas - submsg_gas)
stk.append(0)
elif op == 'CALLCODE' or op == 'DELEGATECALL':
if op == 'CALLCODE':
gas, to, value, meminstart, meminsz, memoutstart, memoutsz = \
stk.pop(), stk.pop(), stk.pop(), stk.pop(), stk.pop(), stk.pop(), stk.pop()
else:
gas, to, meminstart, meminsz, memoutstart, memoutsz = \
stk.pop(), stk.pop(), stk.pop(), stk.pop(), stk.pop(), stk.pop()
value = 0
if not mem_extend(mem, compustate, op, meminstart, meminsz) or \
not mem_extend(mem, compustate, op, memoutstart, memoutsz):
return vm_exception('OOG EXTENDING MEMORY')
extra_gas = (value > 0) * opcodes.GCALLVALUETRANSFER
submsg_gas = gas + opcodes.GSTIPEND * (value > 0)
if compustate.gas < gas + extra_gas:
return vm_exception('OUT OF GAS', needed=gas + extra_gas)
if ext.get_balance(msg.to) >= value and msg.depth < 1024:
use_gas(gas + extra_gas)
to = encode_int(to)
to = ((b'\x00' * (32 - len(to))) + to)[12:]
cd = CallData(mem, meminstart, meminsz)
if ext.post_homestead_hardfork() and op == 'DELEGATECALL':
call_msg = Message(msg.sender, msg.to, msg.value, submsg_gas, cd,
msg.depth + 1, code_address=to, transfers_value=False)
elif op == 'DELEGATECALL':
return vm_exception('OPCODE INACTIVE')
else:
call_msg = Message(msg.to, msg.to, value, submsg_gas, cd,
msg.depth + 1, code_address=to)
result, gas, data = ext.msg(call_msg)
if result == 0:
stk.append(0)
else:
stk.append(1)
use_gas(-gas) # refund
for i in range(min(len(data), memoutsz)):
mem[memoutstart + i] = data[i]
else:
use_gas(gas + extra_gas - submsg_gas)
stk.append(0)
elif op == 'RETURN':
s0, s1 = stk.pop(), stk.pop()
if not mem_extend(mem, compustate, op, s0, s1):
return vm_exception('OOG EXTENDING MEMORY')
return peaceful_exit('RETURN', compustate.gas, mem[s0: s0 + s1])
elif op == 'SUICIDE':
to = encode_int(stk.pop())
to = ((b'\x00' * (32 - len(to))) + to)[12:]
xfer = ext.get_balance(msg.to)
ext.set_balance(to, ext.get_balance(to) + xfer)
ext.set_balance(msg.to, 0)
ext.add_suicide(msg.to)
# print('suiciding %s %s %d' % (msg.to, to, xfer))
return 1, compustate.gas, []
# this is slow!
# for a in stk:
# assert is_numeric(a), (op, stk)
# assert a >= 0 and a < 2 ** 256, (a, op, stk)
finally:
if trace_vm:
trace[0].trace('return')
class VmExtBase():
def __init__(self):
self.get_code = lambda addr: b''
self.get_balance = lambda addr: 0
self.set_balance = lambda addr, balance: 0
self.set_storage_data = lambda addr, key, value: 0
self.get_storage_data = lambda addr, key: 0
self.log_storage = lambda addr: 0
self.add_suicide = lambda addr: 0
self.add_refund = lambda x: 0
self.block_prevhash = 0
self.block_coinbase = 0
self.block_timestamp = 0
self.block_number = 0
self.block_difficulty = 0
self.block_gas_limit = 0
self.log = lambda addr, topics, data: 0
self.tx_origin = b'0' * 40
self.tx_gasprice = 0
self.create = lambda msg: 0, 0, 0
self.call = lambda msg: 0, 0, 0
self.sendmsg = lambda msg: 0, 0, 0