Implement guarded fixed-point arithmetic

This commit is contained in:
RunasSudo 2021-01-14 22:31:24 +11:00
parent f724ae0b93
commit f534c983cd
Signed by: RunasSudo
GPG Key ID: 7234E476BF21C61A
15 changed files with 243 additions and 20 deletions

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@ -21,7 +21,7 @@ pyRCV2 accepts data in the [BLT file format](http://www.dia.govt.nz/diawebsite.N
pyRCV2 is highly customisable, including options for:
* different quotas and quota rules (e.g. exact Droop, Hare) or progressively reducing quota
* calculations using fixed-point arithmetic or exact rational numbers
* calculations using fixed-point arithmetic, guarded fixed-point ([quasi-exact](http://www.votingmatters.org.uk/ISSUE24/I24P2.pdf)) or exact rational numbers
* different tie breaking rules (backwards, random, manual) with auditable deterministic random number generation
* extensible API for other counting methods

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@ -18,6 +18,7 @@ This functionality is not available on the Python command line.
This dropdown allows you to select how numbers (vote totals, etc.) are represented internally in memory. The options are:
* *Fixed*: Numbers are represented as fixed-precision decimals, up to a certain number of decimal places (default: 5).
* *Fixed (guarded)*: Numbers are represented as fixed-precision decimals with ‘guard digits’ – also known as [‘quasi-exact’ arithmetic](http://www.votingmatters.org.uk/ISSUE24/I24P2.pdf). If *n* decimal places are requested, numbers are represented up to 2*n* decimal places, and two values are considered equal if the absolute difference is less than (10^-*n*)/2.
* *Rational*: Numbers are represented exactly as fractions, resulting in the elimination of rounding error, but increasing computational complexity when the number of surplus transfers is very large.
* *Native*: Numbers are represented as native integers or floating-point numbers. This is fast, but not recommended as unexpectedly large rounding errors may be introduced in some circumstances.

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@ -139,6 +139,7 @@
<option value="native">Native</option>
<option value="rational">Rational</option>
<option value="fixed" selected>Fixed</option>
<option value="gfixed">Fixed (guarded)</option>
</select>
</label>
<label>

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@ -93,7 +93,7 @@ function changePreset() {
document.getElementById('chkBulkElection').checked = true;
document.getElementById('chkBulkExclusion').checked = false;
document.getElementById('chkDeferSurpluses').checked = false;
document.getElementById('selNumbers').value = 'fixed';
document.getElementById('selNumbers').value = 'gfixed';
document.getElementById('txtDP').value = '9';
document.getElementById('txtPPDP').value = '2';
document.getElementById('chkRoundQuota').checked = false;

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@ -33,6 +33,10 @@ onmessage = function(evt) {
py.pyRCV2.numbers.set_numclass(py.pyRCV2.numbers.Fixed);
py.pyRCV2.numbers.set_dps(evt.data.data.fixedDPs);
}
if (evt.data.data.numbers === 'gfixed') {
py.pyRCV2.numbers.set_numclass(py.pyRCV2.numbers.FixedGuarded);
py.pyRCV2.numbers.set_dps(evt.data.data.fixedDPs);
}
ppDPs = evt.data.data.ppDPs;

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@ -34,7 +34,7 @@ def add_parser(subparsers):
parser.add_argument('--no-bulk-elect', action='store_true', help='disable bulk election unless absolutely required')
parser.add_argument('--bulk-exclude', action='store_true', help='use bulk exclusion')
parser.add_argument('--defer-surpluses', action='store_true', help='defer surplus transfers if possible')
parser.add_argument('--numbers', '-n', choices=['fixed', 'rational', 'native'], default='fixed', help='numbers mode (default: fixed)')
parser.add_argument('--numbers', '-n', choices=['fixed', 'gfixed', 'rational', 'native'], default='fixed', help='numbers mode (default: fixed)')
parser.add_argument('--decimals', type=int, default=5, help='decimal places if --numbers fixed (default: 5)')
#parser.add_argument('--no-round-quota', action='store_true', help='do not round the quota')
parser.add_argument('--round-quota', type=int, help='round quota to specified decimal places')
@ -102,6 +102,9 @@ def main(args):
elif args.numbers == 'fixed':
pyRCV2.numbers.set_numclass(pyRCV2.numbers.Fixed)
pyRCV2.numbers.set_dps(args.decimals)
elif args.numbers == 'gfixed':
pyRCV2.numbers.set_numclass(pyRCV2.numbers.FixedGuarded)
pyRCV2.numbers.set_dps(args.decimals)
with open(args.file, 'r') as f:
election = pyRCV2.blt.readBLT(f.read())

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@ -14,6 +14,8 @@
# You should have received a copy of the GNU Affero General Public License
# along with this program. If not, see <https://www.gnu.org/licenses/>.
DEBUG_MEEK = False
__pragma__ = lambda x: None
from pyRCV2.method.base_stv import BaseSTVCounter, STVException
@ -170,7 +172,9 @@ class MeekSTVCounter(BaseSTVCounter):
# Recompute keep values
for candidate, count_card in has_surplus:
__pragma__('opov')
count_card.keep_value *= self.quota / count_card.votes
# Perform in steps to avoid rounding error
count_card.keep_value *= self.quota
count_card.keep_value /= count_card.votes
__pragma__('noopov')
# Redistribute votes
@ -182,6 +186,9 @@ class MeekSTVCounter(BaseSTVCounter):
__pragma__('opov')
has_surplus = [(c, cc) for c, cc in self.candidates.items() if cc.state == CandidateState.ELECTED and cc.votes / self.quota > self._quota_tolerance]
__pragma__('noopov')
if DEBUG_MEEK:
break
if num_iterations == 1:
self.logs.append('Surpluses distributed, requiring 1 iteration.')

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@ -20,17 +20,23 @@ __pragma__('skip')
is_py = True
__pragma__('noskip')
# CLASS DEFINITIONS
if is_py:
__pragma__('skip')
from pyRCV2.numbers.fixed_py import Fixed, set_dps, get_dps
from pyRCV2.numbers.fixed_py import Fixed, _fixed_set_dps
from pyRCV2.numbers.gfixed_py import FixedGuarded, _gfixed_set_dps
from pyRCV2.numbers.native_py import Native
from pyRCV2.numbers.rational_py import Rational
__pragma__('noskip')
else: # pragma: no cover
from pyRCV2.numbers.fixed_js import Fixed, set_dps, get_dps
from pyRCV2.numbers.fixed_js import Fixed, _fixed_set_dps
from pyRCV2.numbers.gfixed_js import FixedGuarded, _gfixed_set_dps
from pyRCV2.numbers.native_js import Native
from pyRCV2.numbers.rational_js import Rational
# GLOBALS
_numclass = Native
def set_numclass(cls):
@ -39,3 +45,17 @@ def set_numclass(cls):
def Num(val):
return _numclass(val)
_dps = 6
def set_dps(dps):
global _dps
_dps = dps
if _numclass is Fixed:
_fixed_set_dps(dps)
elif _numclass is FixedGuarded:
_gfixed_set_dps(dps)
def get_dps():
return _dps

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@ -158,6 +158,10 @@ class BaseNum:
self.impl = self._truediv_impl(self.impl, other.impl)
return self
def __idiv__(self, other):
# For Transcrypt
return self.__itruediv__(other)
def __floor__(self):
return self.round(0, self.ROUND_DOWN)

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@ -18,12 +18,9 @@ from pyRCV2.numbers.base import BaseNum, compatible_types
Big.DP = 6
def set_dps(dps):
def _fixed_set_dps(dps):
Big.DP = dps
def get_dps():
return Big.DP
class Fixed(BaseNum):
"""
Wrapper for big.js (fixed-point arithmetic)

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@ -18,17 +18,12 @@ from pyRCV2.numbers.base import BasePyNum, compatible_types
import decimal
_dps = 6
_quantize_exp = decimal.Decimal('10') ** -_dps
_quantize_exp = decimal.Decimal('10') ** -6
def set_dps(dps):
global _dps, _quantize_exp
_dps = dps
def _fixed_set_dps(dps):
global _quantize_exp
_quantize_exp = decimal.Decimal('10') ** -dps
def get_dps():
return _dps
class Fixed(BasePyNum):
"""
Wrapper for Python Decimal (for fixed-point arithmetic)

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@ -0,0 +1,93 @@
# pyRCV2: Preferential vote counting
# Copyright © 2020–2021 Lee Yingtong Li (RunasSudo)
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU Affero General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Affero General Public License for more details.
#
# You should have received a copy of the GNU Affero General Public License
# along with this program. If not, see <https://www.gnu.org/licenses/>.
from pyRCV2.numbers.base import BaseNum, compatible_types
Big.DP = 12
_pos_epsilon = Big('10').pow(-6).div('2')
_neg_epsilon = _pos_epsilon.times('-1')
def _gfixed_set_dps(dps):
global _pos_epsilon, _neg_epsilon
Big.DP = 2 * dps
_pos_epsilon = Big('10').pow(-dps).div('2')
_neg_epsilon = _pos_epsilon.times('-1')
class FixedGuarded(BaseNum):
"""
Wrapper for big.js (fixed-point arithmetic)
Implements guarded (quasi-exact) fixed-point
"""
@classmethod
def _to_impl(cls, value):
"""Implements BaseNum._to_impl"""
return Big(value).round(Big.DP)
def pp(self, dp):
"""Implements BaseNum.pp"""
return self.impl.toFixed(dp)
@classmethod
def _add_impl(cls, i1, i2):
"""Implements BaseNum._add_impl"""
return i1.plus(i2)
@classmethod
def _sub_impl(cls, i1, i2):
"""Implements BaseNum._sub_impl"""
return i1.minus(i2)
@classmethod
def _mul_impl(cls, i1, i2):
"""Implements BaseNum._mul_impl"""
return i1.times(i2)
@classmethod
def _truediv_impl(cls, i1, i2):
"""Implements BaseNum._truediv_impl"""
return i1.div(i2)
@compatible_types
def __eq__(self, other):
"""Implements BaseNum.__eq__"""
diff = self.impl.minus(other.impl)
return diff.lt(_pos_epsilon) and diff.gt(_neg_epsilon)
@compatible_types
def __gt__(self, other):
"""Implements BaseNum.__gt__"""
diff = self.impl.minus(other.impl)
return diff.gt(_pos_epsilon)
@compatible_types
def __ge__(self, other):
"""Implements BaseNum.__ge__"""
diff = self.impl.minus(other.impl)
return diff.gt(_neg_epsilon)
@compatible_types
def __lt__(self, other):
"""Implements BaseNum.__lt__"""
diff = self.impl.minus(other.impl)
return diff.lt(_neg_epsilon)
@compatible_types
def __le__(self, other):
"""Implements BaseNum.__le__"""
diff = self.impl.minus(other.impl)
return diff.lt(_pos_epsilon)
def __pow__(self, power):
"""Implements BaseNum.__pow__"""
return FixedGuarded._from_impl(self.impl.pow(power))
def round(self, dps, mode):
"""Implements BaseNum.round"""
return FixedGuarded._from_impl(self.impl.round(dps, mode))

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@ -0,0 +1,92 @@
# pyRCV2: Preferential vote counting
# Copyright © 2020–2021 Lee Yingtong Li (RunasSudo)
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU Affero General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Affero General Public License for more details.
#
# You should have received a copy of the GNU Affero General Public License
# along with this program. If not, see <https://www.gnu.org/licenses/>.
from pyRCV2.numbers.base import BasePyNum, compatible_types
import decimal
_quantize_exp = decimal.Decimal('10') ** -12
_pos_epsilon = decimal.Decimal('10') ** -6 / decimal.Decimal('2')
_neg_epsilon = -_pos_epsilon
def _gfixed_set_dps(dps):
global _quantize_exp
_quantize_exp = decimal.Decimal('10') ** -(2 * dps)
_pos_epsilon = decimal.Decimal('10') ** -dps / decimal.Decimal('2')
_neg_epsilon = -_pos_epsilon
class FixedGuarded(BasePyNum):
"""
Wrapper for Python Decimal (for fixed-point arithmetic)
Implements guarded (quasi-exact) fixed-point
"""
_py_class = decimal.Decimal # For BasePyNum
ROUND_DOWN = decimal.ROUND_DOWN
ROUND_HALF_UP = decimal.ROUND_HALF_UP
ROUND_HALF_EVEN = decimal.ROUND_HALF_EVEN
ROUND_UP = decimal.ROUND_UP
@classmethod
def _to_impl(cls, value):
"""Overrides BasePyNum._to_impl"""
return decimal.Decimal(value).quantize(_quantize_exp)
@classmethod
def _truediv_impl(cls, i1, i2):
"""Overrides BasePyNum._truediv_impl"""
return (i1 / i2).quantize(_quantize_exp)
@compatible_types
def __eq__(self, other):
"""Overrides BasePyNum.__eq__"""
diff = self.impl - other.impl
return diff < _pos_epsilon and diff > _neg_epsilon
@compatible_types
def __ne__(self, other):
"""Overrides BasePyNum.__ne__"""
return not self.__eq__(other)
@compatible_types
def __gt__(self, other):
"""Overrides BasePyNum.__gt__"""
diff = self.impl - other.impl
return diff > _pos_epsilon
@compatible_types
def __ge__(self, other):
"""Overrides BasePyNum.__ge__"""
diff = self.impl - other.impl
return diff > _neg_epsilon
@compatible_types
def __lt__(self, other):
"""Overrides BasePyNum.__lt__"""
diff = self.impl - other.impl
return diff < _neg_epsilon
@compatible_types
def __le__(self, other):
"""Overrides BasePyNum.__le__"""
diff = self.impl - other.impl
return diff < _pos_epsilon
@compatible_types
def __itruediv__(self, other):
"""Overrides BasePyNum.__itruediv__"""
self.impl = (self.impl / other.impl).quantize(_quantize_exp)
return self
def round(self, dps, mode):
"""Implements BaseNum.round"""
return FixedGuarded._from_impl(self.impl.quantize(decimal.Decimal('10') ** -dps, mode))

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@ -26,8 +26,8 @@ from pyRCV2.ties import TiesBackwards
def test_meekm():
"""Compare count of meekm.blt with model result produced by Hill et al. reference implementation"""
pyRCV2.numbers.set_numclass(pyRCV2.numbers.Fixed)
pyRCV2.numbers.set_dps(9)
pyRCV2.numbers.set_numclass(pyRCV2.numbers.FixedGuarded)
pyRCV2.numbers.set_dps(4)
with open('tests/data/meekm.blt', 'r') as f:
election = pyRCV2.blt.readBLT(f.read())

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@ -44,6 +44,7 @@ def maketst(numbers, dps, method, result):
test_fixed2_add_py, test_fixed2_add_js = maketst('Fixed', 2, '__add__', '356.57')
test_fixed1_add_py, test_fixed1_add_js = maketst('Fixed', 1, '__add__', '356.6')
test_fixed0_add_py, test_fixed0_add_js = maketst('Fixed', 0, '__add__', '356')
test_gfixed2_add_py, test_gfixed2_add_js = maketst('FixedGuarded', 2, '__add__', '356.57')
test_rational_add_py, test_rational_add_js = maketst('Rational', 0, '__add__', '356.57')
def maketst_round(numbers, dps, num, dps_round, mode_round, result):
@ -70,6 +71,11 @@ test_fixed_round2_py, test_fixed_round2_js = maketst_round('Fixed', 5, '3141.59'
test_fixed_round3_py, test_fixed_round3_js = maketst_round('Fixed', 5, '3141.45', 1, 'ROUND_HALF_EVEN', '3141.4')
test_fixed_round4_py, test_fixed_round4_js = maketst_round('Fixed', 5, '3141.45', 1, 'ROUND_HALF_UP', '3141.5')
test_gfixed_round1_py, test_gfixed_round1_js = maketst_round('FixedGuarded', 5, '3141.59', 1, 'ROUND_DOWN', '3141.5')
test_gfixed_round2_py, test_gfixed_round2_js = maketst_round('FixedGuarded', 5, '3141.59', 1, 'ROUND_UP', '3141.6')
test_gfixed_round3_py, test_gfixed_round3_js = maketst_round('FixedGuarded', 5, '3141.45', 1, 'ROUND_HALF_EVEN', '3141.4')
test_gfixed_round4_py, test_gfixed_round4_js = maketst_round('FixedGuarded', 5, '3141.45', 1, 'ROUND_HALF_UP', '3141.5')
test_native_round1_py, test_native_round1_js = maketst_round('Native', 0, '3141.59', 1, 'ROUND_DOWN', '3141.5')
test_native_round2_py, test_native_round2_js = maketst_round('Native', 0, '3141.59', 1, 'ROUND_UP', '3141.6')
test_native_round3_py, _ = maketst_round('Native', 0, '3141.45', 1, 'ROUND_HALF_EVEN', '3141.4')