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erc20-demurrage-token-archive
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Rehabilitate deployer cli script

This commit is contained in:
lash 2023-02-10 10:05:10 +00:00
parent 5317573b47
commit dc891ce9bb
Signed by: lash
GPG Key ID: 21D2E7BB88C2A746
11 changed files with 886 additions and 221 deletions
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145
python/erc20_demurrage_token/runnable/deploy.py
View File

@ -29,6 +29,21 @@ from chainlib.eth.connection import EthHTTPConnection
from chainlib.eth.tx import receipt
from chainlib.eth.constant import ZERO_ADDRESS
import chainlib.eth.cli
from chainlib.eth.cli.arg import (
Arg,
ArgFlag,
process_args,
)
from chainlib.eth.cli.config import (
Config,
process_config,
)
from chainlib.eth.cli.log import process_log
from chainlib.eth.settings import process_settings
from chainlib.eth.address import to_checksum_address
from chainlib.settings import ChainSettings
from dexif import to_fixed
# local imports
import erc20_demurrage_token
@ -37,7 +52,6 @@ from erc20_demurrage_token import (
DemurrageTokenSettings,
)
logging.basicConfig(level=logging.WARNING)
logg = logging.getLogger()
script_dir = os.path.dirname(__file__)
@ -45,76 +59,103 @@ data_dir = os.path.join(script_dir, '..', 'data')
config_dir = os.path.join(data_dir, 'config')
arg_flags = chainlib.eth.cli.argflag_std_write
def process_config_local(config, arg, args, flags):
config.add(args.token_name, 'TOKEN_NAME')
config.add(args.token_symbol, 'TOKEN_SYMBOL')
config.add(args.token_decimals, 'TOKEN_DECIMALS')
sink_address = to_checksum_address(args.sink_address)
config.add(sink_address, 'TOKEN_SINK_ADDRESS')
config.add(args.redistribution_period, 'TOKEN_REDISTRIBUTION_PERIOD')
v = args.demurrage_level / 1000000
if v >= 1.0:
raise ValueError('demurrage level must be less than 100%')
demurrage_level = to_fixed(v)
config.add(demurrage_level, 'TOKEN_DEMURRAGE_LEVEL')
return config
arg_flags = ArgFlag()
arg = Arg(arg_flags)
flags = arg_flags.STD_WRITE | arg_flags.WALLET
argparser = chainlib.eth.cli.ArgumentParser(arg_flags)
argparser = process_args(argparser, arg, flags)
argparser.add_argument('--name', dest='token_name', type=str, help='Token name')
argparser.add_argument('--symbol', dest='token_symbol', required=True, type=str, help='Token symbol')
argparser.add_argument('--decimals', dest='token_decimals', type=int, help='Token decimals')
argparser.add_argument('--sink-address', dest='sink_address', type=str, help='demurrage level,ppm per minute')
argparser.add_argument('--supply-limit', dest='supply_limit', type=int, help='token supply limit (0 = no limit)')
argparser.add_argument('--redistribution-period', type=int, help='redistribution period, minutes (0 = deactivate)') # default 10080 = week
argparser.add_argument('--multi', action='store_true', help='automatic redistribution')
argparser.add_argument('--demurrage-level', dest='demurrage_level', type=int, help='demurrage level, ppm per minute')
argparser.add_argument('--demurrage-level', dest='demurrage_level', type=int, help='demurrage level, ppm per period')
args = argparser.parse_args()
arg_flags = chainlib.eth.cli.argflag_std_write
logg = process_log(args, logg)
extra_args = {
'redistribution_period': 'TOKEN_REDISTRIBUTION_PERIOD',
'demurrage_level': 'TOKEN_DEMURRAGE_LEVEL',
'supply_limit': 'TOKEN_SUPPLY_LIMIT',
'token_name': 'TOKEN_NAME',
'token_symbol': 'TOKEN_SYMBOL',
'token_decimals': 'TOKEN_DECIMALS',
'sink_address': 'TOKEN_SINK_ADDRESS',
'multi': None,
}
config = chainlib.eth.cli.Config.from_args(args, arg_flags, extra_args=extra_args, default_fee_limit=DemurrageToken.gas(), base_config_dir=config_dir)
if not bool(config.get('TOKEN_NAME')):
logg.info('token name not set, using symbol {} as name'.format(config.get('TOKEN_SYMBOL')))
config.add(config.get('TOKEN_SYMBOL'), 'TOKEN_NAME', True)
if config.get('TOKEN_SUPPLY_LIMIT') == None:
config.add(0, 'TOKEN_SUPPLY_LIMIT', True)
if config.get('TOKEN_REDISTRIBUTION_PERIOD') == None:
config.add(10800, 'TOKEN_REDISTRIBUTION_PERIOD', True)
config = Config()
config = process_config(config, arg, args, flags)
config = process_config_local(config, arg, args, flags)
logg.debug('config loaded:\n{}'.format(config))
wallet = chainlib.eth.cli.Wallet()
wallet.from_config(config)
settings = ChainSettings()
settings = process_settings(settings, config)
logg.debug('settings loaded:\n{}'.format(settings))
rpc = chainlib.eth.cli.Rpc(wallet=wallet)
conn = rpc.connect_by_config(config)
chain_spec = ChainSpec.from_chain_str(config.get('CHAIN_SPEC'))
#extra_args = {
# 'redistribution_period': 'TOKEN_REDISTRIBUTION_PERIOD',
# 'demurrage_level': 'TOKEN_DEMURRAGE_LEVEL',
# 'supply_limit': 'TOKEN_SUPPLY_LIMIT',
# 'token_name': 'TOKEN_NAME',
# 'token_symbol': 'TOKEN_SYMBOL',
# 'token_decimals': 'TOKEN_DECIMALS',
# 'sink_address': 'TOKEN_SINK_ADDRESS',
# 'multi': None,
# }
#config = chainlib.eth.cli.Config.from_args(args, arg_flags, extra_args=extra_args, default_fee_limit=DemurrageToken.gas(), base_config_dir=config_dir)
#
#if not bool(config.get('TOKEN_NAME')):
# logg.info('token name not set, using symbol {} as name'.format(config.get('TOKEN_SYMBOL')))
# config.add(config.get('TOKEN_SYMBOL'), 'TOKEN_NAME', True)
#
#if config.get('TOKEN_SUPPLY_LIMIT') == None:
# config.add(0, 'TOKEN_SUPPLY_LIMIT', True)
#
#if config.get('TOKEN_REDISTRIBUTION_PERIOD') == None:
# config.add(10800, 'TOKEN_REDISTRIBUTION_PERIOD', True)
#logg.debug('config loaded:\n{}'.format(config))
#
#wallet = chainlib.eth.cli.Wallet()
#wallet.from_config(config)
#
#rpc = chainlib.eth.cli.Rpc(wallet=wallet)
#conn = rpc.connect_by_config(config)
#
#chain_spec = ChainSpec.from_chain_str(config.get('CHAIN_SPEC'))
def main():
signer = rpc.get_signer()
signer_address = rpc.get_sender_address()
gas_oracle = rpc.get_gas_oracle()
nonce_oracle = rpc.get_nonce_oracle()
c = DemurrageToken(chain_spec, signer=signer, gas_oracle=gas_oracle, nonce_oracle=nonce_oracle)
settings = DemurrageTokenSettings()
settings.name = config.get('TOKEN_NAME')
settings.symbol = config.get('TOKEN_SYMBOL')
settings.decimals = int(config.get('TOKEN_DECIMALS'))
settings.demurrage_level = int(config.get('TOKEN_DEMURRAGE_LEVEL'))
settings.period_minutes = int(config.get('TOKEN_REDISTRIBUTION_PERIOD'))
settings.sink_address = config.get('TOKEN_SINK_ADDRESS')
conn = settings.get('CONN')
c = DemurrageToken(
settings.get('CHAIN_SPEC'),
signer=settings.get('SIGNER'),
gas_oracle=settings.get('FEE_ORACLE'),
nonce_oracle=settings.get('NONCE_ORACLE'),
)
token_settings = DemurrageTokenSettings()
token_settings.name = config.get('TOKEN_NAME')
token_settings.symbol = config.get('TOKEN_SYMBOL')
token_settings.decimals = int(config.get('TOKEN_DECIMALS'))
token_settings.demurrage_level = int(config.get('TOKEN_DEMURRAGE_LEVEL'))
token_settings.period_minutes = int(config.get('TOKEN_REDISTRIBUTION_PERIOD'))
token_settings.sink_address = config.get('TOKEN_SINK_ADDRESS')
(tx_hash_hex, o) = c.constructor(
signer_address,
settings,
redistribute=config.true('_MULTI'),
cap=int(config.get('TOKEN_SUPPLY_LIMIT')),
settings.get('SENDER_ADDRESS'),
token_settings,
)
if config.get('_RPC_SEND'):
if settings.get('RPC_SEND'):
conn.do(o)
if config.get('_WAIT'):
if config.true('_WAIT'):
r = conn.wait(tx_hash_hex)
if r['status'] == 0:
sys.stderr.write('EVM revert while deploying contract. Wish I had more to tell you')

19
python/erc20_demurrage_token/token.py
View File

@ -21,10 +21,10 @@ from hexathon import (
add_0x,
strip_0x,
)
from dexif import from_fixed
# local imports
from erc20_demurrage_token.data import data_dir
from erc20_demurrage_token.fixed import from_fixed
logg = logging.getLogger(__name__)
@ -82,10 +82,10 @@ class DemurrageToken(ERC20):
'SingleCap',
]
def constructor(self, sender_address, settings, redistribute=True, cap=0, tx_format=TxFormat.JSONRPC):
def constructor(self, sender_address, settings, cap=0, tx_format=TxFormat.JSONRPC):
if int(cap) < 0:
raise ValueError('cap must be 0 or positive integer')
code = DemurrageToken.bytecode(multi=redistribute, cap=cap>0)
code = DemurrageToken.bytecode()
enc = ABIContractEncoder()
enc.string(settings.name)
enc.string(settings.symbol)
@ -603,18 +603,7 @@ class DemurrageToken(ERC20):
@classmethod
def parse_redistributions(self, v):
return strip_0x(v)
#return DemurrageRedistribution(v)
# d = ABIContractDecoder()
# v = strip_0x(v)
# d.typ(ABIContractType.BYTES32)
# d.typ(ABIContractType.BYTES32)
# d.typ(ABIContractType.BYTES32)
# d.val(v[:64])
# d.val(v[64:128])
# d.val(v[128:192])
# r = d.decode()
# return ''.join(r)
@classmethod
def parse_account_period(self, v):

2
python/erc20_demurrage_token/unittest/__init__.py
View File

@ -1 +1 @@
from .newbase import *
from .base import *

167
python/erc20_demurrage_token/unittest/base.py
View File

@ -1,6 +1,7 @@
# standard imports
import logging
import os
import math
# external imports
from chainlib.eth.unittest.ethtester import EthTesterCase
@ -19,6 +20,7 @@ from erc20_demurrage_token import (
DemurrageTokenSettings,
DemurrageToken,
)
from dexif import *
logg = logging.getLogger()
@ -26,12 +28,12 @@ logg = logging.getLogger()
TAX_LEVEL = int(10000 * 2) # 2%
# calc "1-(0.98)^(1/518400)" <- 518400 = 30 days of blocks
# 0.00000003897127107225
#PERIOD = int(60/BLOCKTIME) * 60 * 24 * 30 # month
PERIOD = 10
PERIOD = 43200
class TestTokenDeploy:
"""tax level is ppm, 1000000 = 100%"""
def __init__(self, rpc, token_symbol='FOO', token_name='Foo Token', sink_address=ZERO_ADDRESS, supply=10**12, tax_level=TAX_LEVEL, period=PERIOD):
self.tax_level = tax_level
self.period_seconds = period * 60
@ -40,7 +42,8 @@ class TestTokenDeploy:
self.settings.name = token_name
self.settings.symbol = token_symbol
self.settings.decimals = 6
self.settings.demurrage_level = tax_level * (10 ** 32)
tax_level_input = to_fixed((1 - (tax_level / 1000000)) ** (1 / period))
self.settings.demurrage_level = tax_level_input
self.settings.period_minutes = period
self.settings.sink_address = sink_address
self.sink_address = self.settings.sink_address
@ -58,24 +61,13 @@ class TestTokenDeploy:
self.start_time = int(r['timestamp'])
self.default_supply = supply
self.default_supply_cap = int(self.default_supply * 10)
self.default_supply_cap = 0
def deploy(self, rpc, deployer_address, interface, mode, supply_cap=10**12):
def deploy(self, rpc, deployer_address, interface, supply_cap=0):
tx_hash = None
o = None
logg.debug('mode {} {}'.format(mode, self.settings))
self.mode = mode
if mode == 'MultiNocap':
(tx_hash, o) = interface.constructor(deployer_address, self.settings, redistribute=True, cap=0)
elif mode == 'SingleNocap':
(tx_hash, o) = interface.constructor(deployer_address, self.settings, redistribute=False, cap=0)
elif mode == 'MultiCap':
(tx_hash, o) = interface.constructor(deployer_address, self.settings, redistribute=True, cap=supply_cap)
elif mode == 'SingleCap':
(tx_hash, o) = interface.constructor(deployer_address, self.settings, redistribute=False, cap=supply_cap)
else:
raise ValueError('Invalid mode "{}", valid are {}'.format(mode, DemurrageToken.valid_modes))
(tx_hash, o) = interface.constructor(deployer_address, self.settings, redistribute=False, cap=0)
r = rpc.do(o)
o = receipt(tx_hash)
@ -95,13 +87,6 @@ class TestDemurrage(EthTesterCase):
def setUp(self):
super(TestDemurrage, self).setUp()
# token_deploy = TestTokenDeploy()
# self.settings = token_deploy.settings
# self.sink_address = token_deploy.sink_address
# self.start_block = token_deploy.start_block
# self.start_time = token_deploy.start_time
# self.default_supply = self.default_supply
# self.default_supply_cap = self.default_supply_cap
period = PERIOD
try:
period = getattr(self, 'period')
@ -115,8 +100,8 @@ class TestDemurrage(EthTesterCase):
self.start_time = None
def deploy(self, interface, mode):
self.address = self.deployer.deploy(self.rpc, self.accounts[0], interface, mode, supply_cap=self.default_supply_cap)
def deploy(self, interface):
self.address = self.deployer.deploy(self.rpc, self.accounts[0], interface, supply_cap=self.default_supply_cap)
self.start_block = self.deployer.start_block
self.start_time = self.deployer.start_time
self.tax_level = self.deployer.tax_level
@ -126,6 +111,17 @@ class TestDemurrage(EthTesterCase):
logg.debug('contract address {} start block {} start time {}'.format(self.address, self.start_block, self.start_time))
def assert_within(self, v, target, tolerance_ppm):
lower_target = target - (target * (tolerance_ppm / 1000000))
higher_target = target + (target * (tolerance_ppm / 1000000))
#self.assertGreaterEqual(v, lower_target)
#self.assertLessEqual(v, higher_target)
if v >= lower_target and v <= higher_target:
logg.debug('asserted within {} <= {} <= {}'.format(lower_target, v, higher_target))
return
raise AssertionError('{} not within lower {} and higher {}'.format(v, lower_target, higher_target))
def assert_within_lower(self, v, target, tolerance_ppm):
lower_target = target - (target * (tolerance_ppm / 1000000))
self.assertGreaterEqual(v, lower_target)
@ -133,6 +129,12 @@ class TestDemurrage(EthTesterCase):
logg.debug('asserted within lower {} <= {} <= {}'.format(lower_target, v, target))
def assert_equal_decimals(self, v, target, precision):
target = int(target * (10 ** precision))
target = target / (10 ** precision)
self.assertEqual(v, target)
def tearDown(self):
pass
@ -145,115 +147,4 @@ class TestDemurrageDefault(TestDemurrage):
nonce_oracle = RPCNonceOracle(self.accounts[0], self.rpc)
c = DemurrageToken(self.chain_spec, signer=self.signer, nonce_oracle=nonce_oracle)
self.mode = os.environ.get('ERC20_DEMURRAGE_TOKEN_TEST_MODE')
if self.mode == None:
self.mode = 'MultiNocap'
logg.debug('executing test setup default mode {}'.format(self.mode))
self.deploy(c, self.mode)
logg.info('deployed with mode {}'.format(self.mode))
class TestDemurrageSingle(TestDemurrage):
def setUp(self):
super(TestDemurrageSingle, self).setUp()
nonce_oracle = RPCNonceOracle(self.accounts[0], self.rpc)
c = DemurrageToken(self.chain_spec, signer=self.signer, nonce_oracle=nonce_oracle)
self.mode = os.environ.get('ERC20_DEMURRAGE_TOKEN_TEST_MODE')
single_valid_modes = [
'SingleNocap',
'SingleCap',
]
if self.mode != None:
if self.mode not in single_valid_modes:
raise ValueError('Invalid mode "{}" for "single" contract tests, valid are {}'.format(self.mode, single_valid_modes))
else:
self.mode = 'SingleNocap'
logg.debug('executing test setup demurragesingle mode {}'.format(self.mode))
self.deploy(c, self.mode)
logg.info('deployed with mode {}'.format(self.mode))
class TestDemurrageCap(TestDemurrage):
def setUp(self):
super(TestDemurrageCap, self).setUp()
nonce_oracle = RPCNonceOracle(self.accounts[0], self.rpc)
c = DemurrageToken(self.chain_spec, signer=self.signer, nonce_oracle=nonce_oracle)
self.mode = os.environ.get('ERC20_DEMURRAGE_TOKEN_TEST_MODE')
cap_valid_modes = [
'MultiCap',
'SingleCap',
]
if self.mode != None:
if self.mode not in cap_valid_modes:
raise ValueError('Invalid mode "{}" for "cap" contract tests, valid are {}'.format(self.mode, cap_valid_modes))
else:
self.mode = 'MultiCap'
logg.debug('executing test setup demurragecap mode {}'.format(self.mode))
self.deploy(c, self.mode)
logg.info('deployed with mode {}'.format(self.mode))
class TestDemurrageUnit(TestDemurrage):
def setUp(self):
self.period = 1
self.period_seconds = self.period * 60
self.tax_level = TAX_LEVEL
super(TestDemurrageUnit, self).setUp()
nonce_oracle = RPCNonceOracle(self.accounts[0], self.rpc)
self.settings = DemurrageTokenSettings()
self.settings.name = 'Foo Token'
self.settings.symbol = 'FOO'
self.settings.decimals = 6
self.settings.demurrage_level = self.tax_level * (10 ** 32)
self.settings.period_minutes = int(self.period_seconds/60)
self.settings.sink_address = self.accounts[9]
self.sink_address = self.settings.sink_address
o = block_latest()
self.start_block = self.rpc.do(o)
o = block_by_number(self.start_block, include_tx=False)
r = self.rpc.do(o)
try:
self.start_time = int(r['timestamp'], 16)
except TypeError:
self.start_time = int(r['timestamp'])
self.default_supply = 1000000000000
self.default_supply_cap = int(self.default_supply * 10)
nonce_oracle = RPCNonceOracle(self.accounts[0], self.rpc)
c = DemurrageToken(self.chain_spec, signer=self.signer, nonce_oracle=nonce_oracle)
self.mode = os.environ.get('ERC20_DEMURRAGE_TOKEN_TEST_MODE')
unit_valid_modes = [
'SingleNocap',
'SingleCap',
]
if self.mode != None:
if self.mode not in unit_valid_modes:
raise ValueError('Invalid mode "{}" for "unit" contract tests, valid are {}'.format(self.mode, unit_valid_modes))
else:
self.mode = 'SingleNocap'
logg.debug('executing test setup unit mode {}'.format(self.mode))
self.deploy(c, self.mode)
logg.info('deployed with mode {}'.format(self.mode))
self.deploy(c)

11
python/erc20_demurrage_token/unittest/newbase.py
View File

@ -20,19 +20,12 @@ from erc20_demurrage_token import (
DemurrageTokenSettings,
DemurrageToken,
)
from erc20_demurrage_token.fixed import (
to_fixed,
from_fixed,
)
from dexif import *
logg = logging.getLogger()
#BLOCKTIME = 5 # seconds
TAX_LEVEL = int(10000 * 2) # 2%
# calc "1-(0.98)^(1/518400)" <- 518400 = 30 days of blocks
# 0.00000003897127107225
PERIOD = 43200
PERIOD = 43200 # 30 days in minutes
class TestTokenDeploy:

1
python/requirements.txt
View File

@ -1,3 +1,4 @@
chainlib-eth~=0.4.11
eth-erc20~=0.5.0
funga-eth~=0.6.0
dexif~=0.0.1

2
python/tests/test_period.py
View File

@ -18,11 +18,11 @@ from chainlib.eth.contract import (
)
from hexathon import same as hex_same
from hexathon import strip_0x
from dexif import from_fixed
# local imports
from erc20_demurrage_token import DemurrageToken
from erc20_demurrage_token import DemurrageRedistribution
from erc20_demurrage_token.fixed import from_fixed
# test imports
from erc20_demurrage_token.unittest import TestDemurrageDefault

4
python/tests/test_redistribution_single.py
View File

@ -18,10 +18,10 @@ from hexathon import (
add_0x,
same as hex_same,
)
from dexif import from_fixed
# local imports
from erc20_demurrage_token import DemurrageToken
from erc20_demurrage_token.fixed import from_fixed
# test imports
from erc20_demurrage_token.unittest import TestDemurrageDefault
@ -63,7 +63,6 @@ class TestRedistribution(TestDemurrageDefault):
o = c.to_redistribution_demurrage_modifier(self.address, redistribution, sender_address=self.accounts[0])
r = self.rpc.do(o)
#demurrage = c.parse_to_redistribution_item(r)
demurrage = from_fixed(r)
o = c.redistributions(self.address, i-1, sender_address=self.accounts[0])
@ -71,7 +70,6 @@ class TestRedistribution(TestDemurrageDefault):
o = c.to_redistribution_demurrage_modifier(self.address, redistribution, sender_address=self.accounts[0])
r = self.rpc.do(o)
#demurrage_previous = c.parse_to_redistribution_item(r)
demurrage_previous = from_fixed(r)
o = c.balance_of(self.address, self.sink_address, sender_address=self.accounts[0])

2
python/tests/test_redistribution_unit.py
View File

@ -16,10 +16,10 @@ from hexathon import (
strip_0x,
add_0x,
)
from dexif import to_fixed
# local imports
from erc20_demurrage_token import DemurrageToken
from erc20_demurrage_token.fixed import to_fixed
from erc20_demurrage_token import DemurrageRedistribution
# test imports

2
python/tests/test_single.py
View File

@ -13,13 +13,13 @@ from hexathon import (
strip_0x,
add_0x,
)
from dexif import to_fixed
# local imports
from erc20_demurrage_token import DemurrageToken
# test imports
from erc20_demurrage_token.unittest import TestDemurrageDefault
from erc20_demurrage_token.fixed import to_fixed
logging.basicConfig(level=logging.DEBUG)
logg = logging.getLogger()

752
solidity/aux/ABDKMath64x64.sol Normal file
View File

@ -0,0 +1,752 @@
// SPDX-License-Identifier: BSD-4-Clause
/*
* ABDK Math 64.64 Smart Contract Library. Copyright © 2019 by ABDK Consulting.
* Author: Mikhail Vladimirov <mikhail.vladimirov@gmail.com>
*/
pragma solidity ^0.8.0;
/**
* Smart contract library of mathematical functions operating with signed
* 64.64-bit fixed point numbers. Signed 64.64-bit fixed point number is
* basically a simple fraction whose numerator is signed 128-bit integer and
* denominator is 2^64. As long as denominator is always the same, there is no
* need to store it, thus in Solidity signed 64.64-bit fixed point numbers are
* represented by int128 type holding only the numerator.
*/
library ABDKMath64x64 {
/*
* Minimum value signed 64.64-bit fixed point number may have.
*/
int128 private constant MIN_64x64 = -0x80000000000000000000000000000000;
/*
* Maximum value signed 64.64-bit fixed point number may have.
*/
int128 private constant MAX_64x64 = 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF;
/**
* Convert signed 256-bit integer number into signed 64.64-bit fixed point
* number. Revert on overflow.
*
* @param x signed 256-bit integer number
* @return signed 64.64-bit fixed point number
*/
function fromInt (int256 x) internal pure returns (int128) {
unchecked {
require (x >= -0x8000000000000000 && x <= 0x7FFFFFFFFFFFFFFF);
return int128 (x << 64);
}
}
/**
* Convert signed 64.64 fixed point number into signed 64-bit integer number
* rounding down.
*
* @param x signed 64.64-bit fixed point number
* @return signed 64-bit integer number
*/
function toInt (int128 x) internal pure returns (int64) {
unchecked {
return int64 (x >> 64);
}
}
/**
* Convert unsigned 256-bit integer number into signed 64.64-bit fixed point
* number. Revert on overflow.
*
* @param x unsigned 256-bit integer number
* @return signed 64.64-bit fixed point number
*/
function fromUInt (uint256 x) internal pure returns (int128) {
unchecked {
require (x <= 0x7FFFFFFFFFFFFFFF);
return int128 (int256 (x << 64));
}
}
/**
* Convert signed 64.64 fixed point number into unsigned 64-bit integer
* number rounding down. Revert on underflow.
*
* @param x signed 64.64-bit fixed point number
* @return unsigned 64-bit integer number
*/
function toUInt (int128 x) internal pure returns (uint64) {
unchecked {
require (x >= 0);
return uint64 (uint128 (x >> 64));
}
}
/**
* Convert signed 128.128 fixed point number into signed 64.64-bit fixed point
* number rounding down. Revert on overflow.
*
* @param x signed 128.128-bin fixed point number
* @return signed 64.64-bit fixed point number
*/
function from128x128 (int256 x) internal pure returns (int128) {
unchecked {
int256 result = x >> 64;
require (result >= MIN_64x64 && result <= MAX_64x64);
return int128 (result);
}
}
/**
* Convert signed 64.64 fixed point number into signed 128.128 fixed point
* number.
*
* @param x signed 64.64-bit fixed point number
* @return signed 128.128 fixed point number
*/
function to128x128 (int128 x) internal pure returns (int256) {
unchecked {
return int256 (x) << 64;
}
}
/**
* Calculate x + y. Revert on overflow.
*
* @param x signed 64.64-bit fixed point number
* @param y signed 64.64-bit fixed point number
* @return signed 64.64-bit fixed point number
*/
function add (int128 x, int128 y) internal pure returns (int128) {
unchecked {
int256 result = int256(x) + y;
require (result >= MIN_64x64 && result <= MAX_64x64);
return int128 (result);
}
}
/**
* Calculate x - y. Revert on overflow.
*
* @param x signed 64.64-bit fixed point number
* @param y signed 64.64-bit fixed point number
* @return signed 64.64-bit fixed point number
*/
function sub (int128 x, int128 y) internal pure returns (int128) {
unchecked {
int256 result = int256(x) - y;
require (result >= MIN_64x64 && result <= MAX_64x64);
return int128 (result);
}
}
/**
* Calculate x * y rounding down. Revert on overflow.
*
* @param x signed 64.64-bit fixed point number
* @param y signed 64.64-bit fixed point number
* @return signed 64.64-bit fixed point number
*/
function mul (int128 x, int128 y) internal pure returns (int128) {
unchecked {
int256 result = int256(x) * y >> 64;
require (result >= MIN_64x64 && result <= MAX_64x64);
return int128 (result);
}
}
/**
* Calculate x * y rounding towards zero, where x is signed 64.64 fixed point
* number and y is signed 256-bit integer number. Revert on overflow.
*
* @param x signed 64.64 fixed point number
* @param y signed 256-bit integer number
* @return signed 256-bit integer number
*/
function muli (int128 x, int256 y) internal pure returns (int256) {
unchecked {
if (x == MIN_64x64) {
require (y >= -0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF &&
y <= 0x1000000000000000000000000000000000000000000000000);
return -y << 63;
} else {
bool negativeResult = false;
if (x < 0) {
x = -x;
negativeResult = true;
}
if (y < 0) {
y = -y; // We rely on overflow behavior here
negativeResult = !negativeResult;
}
uint256 absoluteResult = mulu (x, uint256 (y));
if (negativeResult) {
require (absoluteResult <=
0x8000000000000000000000000000000000000000000000000000000000000000);
return -int256 (absoluteResult); // We rely on overflow behavior here
} else {
require (absoluteResult <=
0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF);
return int256 (absoluteResult);
}
}
}
}
/**
* Calculate x * y rounding down, where x is signed 64.64 fixed point number
* and y is unsigned 256-bit integer number. Revert on overflow.
*
* @param x signed 64.64 fixed point number
* @param y unsigned 256-bit integer number
* @return unsigned 256-bit integer number
*/
function mulu (int128 x, uint256 y) internal pure returns (uint256) {
unchecked {
if (y == 0) return 0;
require (x >= 0);
uint256 lo = (uint256 (int256 (x)) * (y & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF)) >> 64;
uint256 hi = uint256 (int256 (x)) * (y >> 128);
require (hi <= 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF);
hi <<= 64;
require (hi <=
0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF - lo);
return hi + lo;
}
}
/**
* Calculate x / y rounding towards zero. Revert on overflow or when y is
* zero.
*
* @param x signed 64.64-bit fixed point number
* @param y signed 64.64-bit fixed point number
* @return signed 64.64-bit fixed point number
*/
function div (int128 x, int128 y) internal pure returns (int128) {
unchecked {
require (y != 0);
int256 result = (int256 (x) << 64) / y;
require (result >= MIN_64x64 && result <= MAX_64x64);
return int128 (result);
}
}
/**
* Calculate x / y rounding towards zero, where x and y are signed 256-bit
* integer numbers. Revert on overflow or when y is zero.
*
* @param x signed 256-bit integer number
* @param y signed 256-bit integer number
* @return signed 64.64-bit fixed point number
*/
function divi (int256 x, int256 y) internal pure returns (int128) {
unchecked {
require (y != 0);
bool negativeResult = false;
if (x < 0) {
x = -x; // We rely on overflow behavior here
negativeResult = true;
}
if (y < 0) {
y = -y; // We rely on overflow behavior here
negativeResult = !negativeResult;
}
uint128 absoluteResult = divuu (uint256 (x), uint256 (y));
if (negativeResult) {
require (absoluteResult <= 0x80000000000000000000000000000000);
return -int128 (absoluteResult); // We rely on overflow behavior here
} else {
require (absoluteResult <= 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF);
return int128 (absoluteResult); // We rely on overflow behavior here
}
}
}
/**
* Calculate x / y rounding towards zero, where x and y are unsigned 256-bit
* integer numbers. Revert on overflow or when y is zero.
*
* @param x unsigned 256-bit integer number
* @param y unsigned 256-bit integer number
* @return signed 64.64-bit fixed point number
*/
function divu (uint256 x, uint256 y) internal pure returns (int128) {
unchecked {
require (y != 0);
uint128 result = divuu (x, y);
require (result <= uint128 (MAX_64x64));
return int128 (result);
}
}
/**
* Calculate -x. Revert on overflow.
*
* @param x signed 64.64-bit fixed point number
* @return signed 64.64-bit fixed point number
*/
function neg (int128 x) internal pure returns (int128) {
unchecked {
require (x != MIN_64x64);
return -x;
}
}
/**
* Calculate |x|. Revert on overflow.
*
* @param x signed 64.64-bit fixed point number
* @return signed 64.64-bit fixed point number
*/
function abs (int128 x) internal pure returns (int128) {
unchecked {
require (x != MIN_64x64);
return x < 0 ? -x : x;
}
}
/**
* Calculate 1 / x rounding towards zero. Revert on overflow or when x is
* zero.
*
* @param x signed 64.64-bit fixed point number
* @return signed 64.64-bit fixed point number
*/
function inv (int128 x) internal pure returns (int128) {
unchecked {
require (x != 0);
int256 result = int256 (0x100000000000000000000000000000000) / x;
require (result >= MIN_64x64 && result <= MAX_64x64);
return int128 (result);
}
}
/**
* Calculate arithmetics average of x and y, i.e. (x + y) / 2 rounding down.
*
* @param x signed 64.64-bit fixed point number
* @param y signed 64.64-bit fixed point number
* @return signed 64.64-bit fixed point number
*/
function avg (int128 x, int128 y) internal pure returns (int128) {
unchecked {
return int128 ((int256 (x) + int256 (y)) >> 1);
}
}
/**
* Calculate geometric average of x and y, i.e. sqrt (x * y) rounding down.
* Revert on overflow or in case x * y is negative.
*
* @param x signed 64.64-bit fixed point number
* @param y signed 64.64-bit fixed point number
* @return signed 64.64-bit fixed point number
*/
function gavg (int128 x, int128 y) internal pure returns (int128) {
unchecked {
int256 m = int256 (x) * int256 (y);
require (m >= 0);
require (m <
0x4000000000000000000000000000000000000000000000000000000000000000);
return int128 (sqrtu (uint256 (m)));
}
}
/**
* Calculate x^y assuming 0^0 is 1, where x is signed 64.64 fixed point number
* and y is unsigned 256-bit integer number. Revert on overflow.
*
* @param x signed 64.64-bit fixed point number
* @param y uint256 value
* @return signed 64.64-bit fixed point number
*/
function pow (int128 x, uint256 y) internal pure returns (int128) {
unchecked {
bool negative = x < 0 && y & 1 == 1;
uint256 absX = uint128 (x < 0 ? -x : x);
uint256 absResult;
absResult = 0x100000000000000000000000000000000;
if (absX <= 0x10000000000000000) {
absX <<= 63;
while (y != 0) {
if (y & 0x1 != 0) {
absResult = absResult * absX >> 127;
}
absX = absX * absX >> 127;
if (y & 0x2 != 0) {
absResult = absResult * absX >> 127;
}
absX = absX * absX >> 127;
if (y & 0x4 != 0) {
absResult = absResult * absX >> 127;
}
absX = absX * absX >> 127;
if (y & 0x8 != 0) {
absResult = absResult * absX >> 127;
}
absX = absX * absX >> 127;
y >>= 4;
}
absResult >>= 64;
} else {
uint256 absXShift = 63;
if (absX < 0x1000000000000000000000000) { absX <<= 32; absXShift -= 32; }
if (absX < 0x10000000000000000000000000000) { absX <<= 16; absXShift -= 16; }
if (absX < 0x1000000000000000000000000000000) { absX <<= 8; absXShift -= 8; }
if (absX < 0x10000000000000000000000000000000) { absX <<= 4; absXShift -= 4; }
if (absX < 0x40000000000000000000000000000000) { absX <<= 2; absXShift -= 2; }
if (absX < 0x80000000000000000000000000000000) { absX <<= 1; absXShift -= 1; }
uint256 resultShift = 0;
while (y != 0) {
require (absXShift < 64);
if (y & 0x1 != 0) {
absResult = absResult * absX >> 127;
resultShift += absXShift;
if (absResult > 0x100000000000000000000000000000000) {
absResult >>= 1;
resultShift += 1;
}
}
absX = absX * absX >> 127;
absXShift <<= 1;
if (absX >= 0x100000000000000000000000000000000) {
absX >>= 1;
absXShift += 1;
}
y >>= 1;
}
require (resultShift < 64);
absResult >>= 64 - resultShift;
}
int256 result = negative ? -int256 (absResult) : int256 (absResult);
require (result >= MIN_64x64 && result <= MAX_64x64);
return int128 (result);
}
}
/**
* Calculate sqrt (x) rounding down. Revert if x < 0.
*
* @param x signed 64.64-bit fixed point number
* @return signed 64.64-bit fixed point number
*/
function sqrt (int128 x) internal pure returns (int128) {
unchecked {
require (x >= 0);
return int128 (sqrtu (uint256 (int256 (x)) << 64));
}
}
/**
* Calculate binary logarithm of x. Revert if x <= 0.
*
* @param x signed 64.64-bit fixed point number
* @return signed 64.64-bit fixed point number
*/
function log_2 (int128 x) internal pure returns (int128) {
unchecked {
require (x > 0);
int256 msb = 0;
int256 xc = x;
if (xc >= 0x10000000000000000) { xc >>= 64; msb += 64; }
if (xc >= 0x100000000) { xc >>= 32; msb += 32; }
if (xc >= 0x10000) { xc >>= 16; msb += 16; }
if (xc >= 0x100) { xc >>= 8; msb += 8; }
if (xc >= 0x10) { xc >>= 4; msb += 4; }
if (xc >= 0x4) { xc >>= 2; msb += 2; }
if (xc >= 0x2) msb += 1; // No need to shift xc anymore
int256 result = msb - 64 << 64;
uint256 ux = uint256 (int256 (x)) << uint256 (127 - msb);
for (int256 bit = 0x8000000000000000; bit > 0; bit >>= 1) {
ux *= ux;
uint256 b = ux >> 255;
ux >>= 127 + b;
result += bit * int256 (b);
}
return int128 (result);
}
}
/**
* Calculate natural logarithm of x. Revert if x <= 0.
*
* @param x signed 64.64-bit fixed point number
* @return signed 64.64-bit fixed point number
*/
function ln (int128 x) internal pure returns (int128) {
unchecked {
require (x > 0);
return int128 (int256 (
uint256 (int256 (log_2 (x))) * 0xB17217F7D1CF79ABC9E3B39803F2F6AF >> 128));
}
}
/**
* Calculate binary exponent of x. Revert on overflow.
*
* @param x signed 64.64-bit fixed point number
* @return signed 64.64-bit fixed point number
*/
function exp_2 (int128 x) internal pure returns (int128) {
unchecked {
require (x < 0x400000000000000000); // Overflow
if (x < -0x400000000000000000) return 0; // Underflow
uint256 result = 0x80000000000000000000000000000000;
if (x & 0x8000000000000000 > 0)
result = result * 0x16A09E667F3BCC908B2FB1366EA957D3E >> 128;
if (x & 0x4000000000000000 > 0)
result = result * 0x1306FE0A31B7152DE8D5A46305C85EDEC >> 128;
if (x & 0x2000000000000000 > 0)
result = result * 0x1172B83C7D517ADCDF7C8C50EB14A791F >> 128;
if (x & 0x1000000000000000 > 0)
result = result * 0x10B5586CF9890F6298B92B71842A98363 >> 128;
if (x & 0x800000000000000 > 0)
result = result * 0x1059B0D31585743AE7C548EB68CA417FD >> 128;
if (x & 0x400000000000000 > 0)
result = result * 0x102C9A3E778060EE6F7CACA4F7A29BDE8 >> 128;
if (x & 0x200000000000000 > 0)
result = result * 0x10163DA9FB33356D84A66AE336DCDFA3F >> 128;
if (x & 0x100000000000000 > 0)
result = result * 0x100B1AFA5ABCBED6129AB13EC11DC9543 >> 128;
if (x & 0x80000000000000 > 0)
result = result * 0x10058C86DA1C09EA1FF19D294CF2F679B >> 128;
if (x & 0x40000000000000 > 0)
result = result * 0x1002C605E2E8CEC506D21BFC89A23A00F >> 128;
if (x & 0x20000000000000 > 0)
result = result * 0x100162F3904051FA128BCA9C55C31E5DF >> 128;
if (x & 0x10000000000000 > 0)
result = result * 0x1000B175EFFDC76BA38E31671CA939725 >> 128;
if (x & 0x8000000000000 > 0)
result = result * 0x100058BA01FB9F96D6CACD4B180917C3D >> 128;
if (x & 0x4000000000000 > 0)
result = result * 0x10002C5CC37DA9491D0985C348C68E7B3 >> 128;
if (x & 0x2000000000000 > 0)
result = result * 0x1000162E525EE054754457D5995292026 >> 128;
if (x & 0x1000000000000 > 0)
result = result * 0x10000B17255775C040618BF4A4ADE83FC >> 128;
if (x & 0x800000000000 > 0)
result = result * 0x1000058B91B5BC9AE2EED81E9B7D4CFAB >> 128;
if (x & 0x400000000000 > 0)
result = result * 0x100002C5C89D5EC6CA4D7C8ACC017B7C9 >> 128;
if (x & 0x200000000000 > 0)
result = result * 0x10000162E43F4F831060E02D839A9D16D >> 128;
if (x & 0x100000000000 > 0)
result = result * 0x100000B1721BCFC99D9F890EA06911763 >> 128;
if (x & 0x80000000000 > 0)
result = result * 0x10000058B90CF1E6D97F9CA14DBCC1628 >> 128;
if (x & 0x40000000000 > 0)
result = result * 0x1000002C5C863B73F016468F6BAC5CA2B >> 128;
if (x & 0x20000000000 > 0)
result = result * 0x100000162E430E5A18F6119E3C02282A5 >> 128;
if (x & 0x10000000000 > 0)
result = result * 0x1000000B1721835514B86E6D96EFD1BFE >> 128;
if (x & 0x8000000000 > 0)
result = result * 0x100000058B90C0B48C6BE5DF846C5B2EF >> 128;
if (x & 0x4000000000 > 0)
result = result * 0x10000002C5C8601CC6B9E94213C72737A >> 128;
if (x & 0x2000000000 > 0)
result = result * 0x1000000162E42FFF037DF38AA2B219F06 >> 128;
if (x & 0x1000000000 > 0)
result = result * 0x10000000B17217FBA9C739AA5819F44F9 >> 128;
if (x & 0x800000000 > 0)
result = result * 0x1000000058B90BFCDEE5ACD3C1CEDC823 >> 128;
if (x & 0x400000000 > 0)
result = result * 0x100000002C5C85FE31F35A6A30DA1BE50 >> 128;
if (x & 0x200000000 > 0)
result = result * 0x10000000162E42FF0999CE3541B9FFFCF >> 128;
if (x & 0x100000000 > 0)
result = result * 0x100000000B17217F80F4EF5AADDA45554 >> 128;
if (x & 0x80000000 > 0)
result = result * 0x10000000058B90BFBF8479BD5A81B51AD >> 128;
if (x & 0x40000000 > 0)
result = result * 0x1000000002C5C85FDF84BD62AE30A74CC >> 128;
if (x & 0x20000000 > 0)
result = result * 0x100000000162E42FEFB2FED257559BDAA >> 128;
if (x & 0x10000000 > 0)
result = result * 0x1000000000B17217F7D5A7716BBA4A9AE >> 128;
if (x & 0x8000000 > 0)
result = result * 0x100000000058B90BFBE9DDBAC5E109CCE >> 128;
if (x & 0x4000000 > 0)
result = result * 0x10000000002C5C85FDF4B15DE6F17EB0D >> 128;
if (x & 0x2000000 > 0)
result = result * 0x1000000000162E42FEFA494F1478FDE05 >> 128;
if (x & 0x1000000 > 0)
result = result * 0x10000000000B17217F7D20CF927C8E94C >> 128;
if (x & 0x800000 > 0)
result = result * 0x1000000000058B90BFBE8F71CB4E4B33D >> 128;
if (x & 0x400000 > 0)
result = result * 0x100000000002C5C85FDF477B662B26945 >> 128;
if (x & 0x200000 > 0)
result = result * 0x10000000000162E42FEFA3AE53369388C >> 128;
if (x & 0x100000 > 0)
result = result * 0x100000000000B17217F7D1D351A389D40 >> 128;
if (x & 0x80000 > 0)
result = result * 0x10000000000058B90BFBE8E8B2D3D4EDE >> 128;
if (x & 0x40000 > 0)
result = result * 0x1000000000002C5C85FDF4741BEA6E77E >> 128;
if (x & 0x20000 > 0)
result = result * 0x100000000000162E42FEFA39FE95583C2 >> 128;
if (x & 0x10000 > 0)
result = result * 0x1000000000000B17217F7D1CFB72B45E1 >> 128;
if (x & 0x8000 > 0)
result = result * 0x100000000000058B90BFBE8E7CC35C3F0 >> 128;
if (x & 0x4000 > 0)
result = result * 0x10000000000002C5C85FDF473E242EA38 >> 128;
if (x & 0x2000 > 0)
result = result * 0x1000000000000162E42FEFA39F02B772C >> 128;
if (x & 0x1000 > 0)
result = result * 0x10000000000000B17217F7D1CF7D83C1A >> 128;
if (x & 0x800 > 0)
result = result * 0x1000000000000058B90BFBE8E7BDCBE2E >> 128;
if (x & 0x400 > 0)
result = result * 0x100000000000002C5C85FDF473DEA871F >> 128;
if (x & 0x200 > 0)
result = result * 0x10000000000000162E42FEFA39EF44D91 >> 128;
if (x & 0x100 > 0)
result = result * 0x100000000000000B17217F7D1CF79E949 >> 128;
if (x & 0x80 > 0)
result = result * 0x10000000000000058B90BFBE8E7BCE544 >> 128;
if (x & 0x40 > 0)
result = result * 0x1000000000000002C5C85FDF473DE6ECA >> 128;
if (x & 0x20 > 0)
result = result * 0x100000000000000162E42FEFA39EF366F >> 128;
if (x & 0x10 > 0)
result = result * 0x1000000000000000B17217F7D1CF79AFA >> 128;
if (x & 0x8 > 0)
result = result * 0x100000000000000058B90BFBE8E7BCD6D >> 128;
if (x & 0x4 > 0)
result = result * 0x10000000000000002C5C85FDF473DE6B2 >> 128;
if (x & 0x2 > 0)
result = result * 0x1000000000000000162E42FEFA39EF358 >> 128;
if (x & 0x1 > 0)
result = result * 0x10000000000000000B17217F7D1CF79AB >> 128;
result >>= uint256 (int256 (63 - (x >> 64)));
require (result <= uint256 (int256 (MAX_64x64)));
return int128 (int256 (result));
}
}
/**
* Calculate natural exponent of x. Revert on overflow.
*
* @param x signed 64.64-bit fixed point number
* @return signed 64.64-bit fixed point number
*/
function exp (int128 x) internal pure returns (int128) {
unchecked {
require (x < 0x400000000000000000); // Overflow
if (x < -0x400000000000000000) return 0; // Underflow
return exp_2 (
int128 (int256 (x) * 0x171547652B82FE1777D0FFDA0D23A7D12 >> 128));
}
}
/**
* Calculate x / y rounding towards zero, where x and y are unsigned 256-bit
* integer numbers. Revert on overflow or when y is zero.
*
* @param x unsigned 256-bit integer number
* @param y unsigned 256-bit integer number
* @return unsigned 64.64-bit fixed point number
*/
function divuu (uint256 x, uint256 y) private pure returns (uint128) {
unchecked {
require (y != 0);
uint256 result;
if (x <= 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF)
result = (x << 64) / y;
else {
uint256 msb = 192;
uint256 xc = x >> 192;
if (xc >= 0x100000000) { xc >>= 32; msb += 32; }
if (xc >= 0x10000) { xc >>= 16; msb += 16; }
if (xc >= 0x100) { xc >>= 8; msb += 8; }
if (xc >= 0x10) { xc >>= 4; msb += 4; }
if (xc >= 0x4) { xc >>= 2; msb += 2; }
if (xc >= 0x2) msb += 1; // No need to shift xc anymore
result = (x << 255 - msb) / ((y - 1 >> msb - 191) + 1);
require (result <= 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF);
uint256 hi = result * (y >> 128);
uint256 lo = result * (y & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF);
uint256 xh = x >> 192;
uint256 xl = x << 64;
if (xl < lo) xh -= 1;
xl -= lo; // We rely on overflow behavior here
lo = hi << 128;
if (xl < lo) xh -= 1;
xl -= lo; // We rely on overflow behavior here
assert (xh == hi >> 128);
result += xl / y;
}
require (result <= 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF);
return uint128 (result);
}
}
/**
* Calculate sqrt (x) rounding down, where x is unsigned 256-bit integer
* number.
*
* @param x unsigned 256-bit integer number
* @return unsigned 128-bit integer number
*/
function sqrtu (uint256 x) private pure returns (uint128) {
unchecked {
if (x == 0) return 0;
else {
uint256 xx = x;
uint256 r = 1;
if (xx >= 0x100000000000000000000000000000000) { xx >>= 128; r <<= 64; }
if (xx >= 0x10000000000000000) { xx >>= 64; r <<= 32; }
if (xx >= 0x100000000) { xx >>= 32; r <<= 16; }
if (xx >= 0x10000) { xx >>= 16; r <<= 8; }
if (xx >= 0x100) { xx >>= 8; r <<= 4; }
if (xx >= 0x10) { xx >>= 4; r <<= 2; }
if (xx >= 0x4) { r <<= 1; }
r = (r + x / r) >> 1;
r = (r + x / r) >> 1;
r = (r + x / r) >> 1;
r = (r + x / r) >> 1;
r = (r + x / r) >> 1;
r = (r + x / r) >> 1;
r = (r + x / r) >> 1; // Seven iterations should be enough
uint256 r1 = x / r;
return uint128 (r < r1 ? r : r1);
}
}
}
}