'''
The ``mod`` module provides the classes which implement the
`OpenDP Programming Framework <../../user/programming-framework/index.html>`_,
as well as utilities for enabling features and finding parameter values.
The classes here correspond to other top-level modules: For example,
instances of :py:class:`opendp.mod.Domain` are either inputs or outputs for functions in :py:mod:`opendp.domains`.
'''
from __future__ import annotations
import ctypes
from typing import Any, Literal, Type, TypeVar, Union, Tuple, Callable, Optional, overload, TYPE_CHECKING
from opendp._lib import AnyMeasurement, AnyTransformation, AnyDomain, AnyMetric, AnyMeasure, AnyFunction
# https://mypy.readthedocs.io/en/stable/runtime_troubles.html#import-cycles
if TYPE_CHECKING:
from opendp.typing import RuntimeType # pragma: no cover
[docs]
class Measurement(ctypes.POINTER(AnyMeasurement)): # type: ignore[misc]
"""A differentially private unit of computation.
A measurement contains a function and a privacy relation.
The function releases a differentially-private release.
The privacy relation maps from an input metric to an output measure.
See the `Measurement <../../user/programming-framework/core-structures.html#measurement>`_
section in the Programming Framework docs for more context.
Functions for creating measurements are in :py:mod:`opendp.measurements`.
:example:
>>> import opendp.prelude as dp
>>> dp.enable_features("contrib")
>>> # create an instance of Measurement using a constructor from the meas module
>>> base_dl: dp.Measurement = dp.m.make_base_discrete_laplace(
... dp.atom_domain(T=int), dp.absolute_distance(T=int),
... scale=2.)
>>> # invoke the measurement (invoke and __call__ are equivalent)
>>> print('explicit: ', base_dl.invoke(100)) # -> 101 # doctest: +ELLIPSIS
explicit: ...
>>> print('concise: ', base_dl(100)) # -> 99 # doctest: +ELLIPSIS
concise: ...
>>> # check the measurement's relation at
>>> # (1, 0.5): (AbsoluteDistance<u32>, MaxDivergence)
>>> assert base_dl.check(1, 0.5)
>>> # chain with a transformation from the trans module
>>> chained = (
... (dp.vector_domain(dp.atom_domain(T=int)), dp.symmetric_distance()) >>
... dp.t.then_count() >>
... base_dl
... )
>>> # the resulting measurement has the same features
>>> print('dp count: ', chained([1, 2, 3])) # -> 4 # doctest: +ELLIPSIS
dp count: ...
>>> # check the chained measurement's relation at
>>> # (1, 0.5): (SymmetricDistance, MaxDivergence)
>>> assert chained.check(1, 0.5)
"""
_type_ = AnyMeasurement
def __call__(self, arg):
from opendp.core import measurement_invoke
return measurement_invoke(self, arg)
[docs]
def invoke(self, arg):
"""Create a differentially-private release with `arg`.
If `self` is (d_in, d_out)-close, then each invocation of this function is a d_out-DP release.
:param arg: Input to the measurement.
:return: differentially-private release
:raises OpenDPException: packaged error from the core OpenDP library
"""
from opendp.core import measurement_invoke
return measurement_invoke(self, arg)
[docs]
def map(self, d_in):
"""Map an input distance `d_in` to an output distance."""
from opendp.core import measurement_map
return measurement_map(self, d_in)
[docs]
def check(self, d_in, d_out, *, debug=False) -> bool:
"""Check if the measurement is (`d_in`, `d_out`)-close.
If true, implies that if the distance between inputs is at most `d_in`, then the privacy usage is at most `d_out`.
See also :func:`~Transformation.check`, a similar check for transformations.
:param d_in: Distance in terms of the input metric.
:param d_out: Distance in terms of the output measure.
:param debug: Enable to raise Exceptions to help identify why the privacy relation failed.
:return: If True, a release is differentially private at `d_in`, `d_out`.
:rtype: bool
"""
from opendp.core import measurement_check
if debug:
return measurement_check(self, d_in, d_out)
try:
return measurement_check(self, d_in, d_out)
except OpenDPException as err:
if err.variant == "RelationDebug":
return False
raise
def __rshift__(self, other: Union["Function", "Transformation"]) -> "Measurement":
if isinstance(other, Transformation):
other = other.function
if not isinstance(other, Function):
from opendp.core import new_function
other = new_function(other, TO="ExtrinsicObject")
if isinstance(other, Function):
from opendp.combinators import make_chain_pm
return make_chain_pm(other, self)
raise ValueError(f"rshift expected a postprocessing transformation, got {other}")
@property
def input_domain(self) -> "Domain":
from opendp.core import measurement_input_domain
return measurement_input_domain(self)
@property
def input_metric(self) -> "Metric":
from opendp.core import measurement_input_metric
return measurement_input_metric(self)
@property
def input_space(self) -> Tuple["Domain", "Metric"]:
return self.input_domain, self.input_metric
@property
def output_measure(self) -> "Measure":
from opendp.core import measurement_output_measure
return measurement_output_measure(self)
@property
def function(self) -> "Function":
from opendp.core import measurement_function
return measurement_function(self)
@property
def input_distance_type(self) -> Union["RuntimeType", str]:
"""Retrieve the distance type of the input metric.
This may be any integral type for dataset metrics, or any numeric type for sensitivity metrics.
:return: distance type
"""
from opendp.core import measurement_input_distance_type
from opendp.typing import RuntimeType
return RuntimeType.parse(measurement_input_distance_type(self))
@property
def output_distance_type(self) -> Union["RuntimeType", str]:
"""Retrieve the distance type of the output measure.
This is the type that the budget is expressed in.
:return: distance type
"""
from opendp.core import measurement_output_distance_type
from opendp.typing import RuntimeType
return RuntimeType.parse(measurement_output_distance_type(self))
@property
def input_carrier_type(self) -> Union["RuntimeType", str]:
"""Retrieve the carrier type of the input domain.
Any member of the input domain is a member of the carrier type.
:return: carrier type
"""
from opendp.core import measurement_input_carrier_type
from opendp.typing import RuntimeType
return RuntimeType.parse(measurement_input_carrier_type(self))
def _depends_on(self, *args):
"""Extends the memory lifetime of args to the lifetime of self."""
setattr(self, "_dependencies", args)
def __del__(self):
try:
from opendp.core import _measurement_free
_measurement_free(self)
except (ImportError, TypeError):
# an example error that this catches:
# ImportError: sys.meta_path is None, Python is likely shutting down
pass
def __str__(self) -> str:
return f"Measurement(\n input_domain = {self.input_domain}, \n input_metric = {self.input_metric}, \n output_measure = {self.output_measure}\n)" # pragma: no cover
from typing import cast
Transformation = cast(Type[Transformation], Transformation) # type: ignore[misc]
[docs]
class Queryable(object):
def __init__(self, value):
self.value = value
def __call__(self, query):
from opendp.core import queryable_eval
return queryable_eval(self.value, query)
[docs]
def eval(self, query):
from opendp.core import queryable_eval # pragma: no cover
return queryable_eval(self.value, query) # pragma: no cover
@property
def query_type(self):
from opendp.core import queryable_query_type
from opendp.typing import RuntimeType
return RuntimeType.parse(queryable_query_type(self.value))
def __str__(self):
return f"Queryable(Q={self.query_type})"
def _depends_on(self, *args):
"""Extends the memory lifetime of args to the lifetime of self."""
setattr(self, "_dependencies", args)
[docs]
class Function(ctypes.POINTER(AnyFunction)): # type: ignore[misc]
'''
See the `Function <../../user/programming-framework/supporting-elements.html#function>`_
section in the Programming Framework docs for more context.
'''
_type_ = AnyFunction
def __call__(self, arg):
from opendp.core import function_eval
return function_eval(self, arg)
def _depends_on(self, *args):
"""Extends the memory lifetime of args to the lifetime of self."""
setattr(self, "_dependencies", args)
def __del__(self):
try:
from opendp.core import _function_free
_function_free(self)
except (ImportError, TypeError):
# an example error that this catches:
# ImportError: sys.meta_path is None, Python is likely shutting down
pass
[docs]
class Domain(ctypes.POINTER(AnyDomain)): # type: ignore[misc]
'''
See the `Domain <../../user/programming-framework/supporting-elements.html#domain>`_
section in the Programming Framework docs for more context.
Functions for creating domains are in :py:mod:`opendp.domains`.
'''
_type_ = AnyDomain
[docs]
def member(self, val):
from opendp.domains import member
return member(self, val)
@property
def type(self) -> Union["RuntimeType", str]:
from opendp.domains import domain_type
from opendp.typing import RuntimeType
return RuntimeType.parse(domain_type(self))
@property
def carrier_type(self) -> Union["RuntimeType", str]:
from opendp.domains import domain_carrier_type
from opendp.typing import RuntimeType
return RuntimeType.parse(domain_carrier_type(self))
@property
def descriptor(self) -> Any:
from opendp.domains import _user_domain_descriptor
return _user_domain_descriptor(self)
def __str__(self):
from opendp.domains import domain_debug
return domain_debug(self)
def __del__(self):
try:
from opendp.domains import _domain_free
_domain_free(self)
except (ImportError, TypeError):
# an example error that this catches:
# ImportError: sys.meta_path is None, Python is likely shutting down
pass
def __repr__(self) -> str:
return str(self)
def __eq__(self, other) -> bool:
# TODO: consider adding ffi equality
return str(self) == str(other)
def __hash__(self) -> int:
return hash(str(self))
def _depends_on(self, *args):
"""Extends the memory lifetime of args to the lifetime of self."""
setattr(self, "_dependencies", args)
[docs]
class Metric(ctypes.POINTER(AnyMetric)): # type: ignore[misc]
'''
See the `Metric <../../user/programming-framework/supporting-elements.html#metric>`_
section in the Programming Framework docs for more context.
Functions for creating metrics are in :py:mod:`opendp.metrics`.
'''
_type_ = AnyMetric
@property
def type(self):
from opendp.metrics import metric_type
from opendp.typing import RuntimeType
return RuntimeType.parse(metric_type(self))
@property
def distance_type(self) -> Union["RuntimeType", str]:
from opendp.metrics import metric_distance_type
from opendp.typing import RuntimeType
return RuntimeType.parse(metric_distance_type(self))
def __str__(self):
from opendp.metrics import metric_debug
return metric_debug(self)
def __del__(self):
try:
from opendp.metrics import _metric_free
_metric_free(self)
except (ImportError, TypeError):
# an example error that this catches:
# ImportError: sys.meta_path is None, Python is likely shutting down
pass
def __repr__(self) -> str:
return str(self)
def __eq__(self, other) -> bool:
# TODO: consider adding ffi equality
return str(self) == str(other)
def __hash__(self) -> int:
return hash(str(self))
[docs]
class Measure(ctypes.POINTER(AnyMeasure)): # type: ignore[misc]
'''
See the `Measure <../../user/programming-framework/supporting-elements.html#measure>`_
section in the Programming Framework docs for more context.
Functions for creating measures are in :py:mod:`opendp.measures`.
'''
_type_ = AnyMeasure
@property
def type(self):
from opendp.measures import measure_type
from opendp.typing import RuntimeType
return RuntimeType.parse(measure_type(self))
@property
def distance_type(self) -> Union["RuntimeType", str]:
from opendp.measures import measure_distance_type
from opendp.typing import RuntimeType
return RuntimeType.parse(measure_distance_type(self))
def __str__(self):
from opendp.measures import measure_debug
return measure_debug(self)
def __del__(self):
try:
from opendp.measures import _measure_free
_measure_free(self)
except (ImportError, TypeError):
# an example error that this catches:
# ImportError: sys.meta_path is None, Python is likely shutting down
pass
def __eq__(self, other):
return str(self) == str(other)
def __hash__(self) -> int:
return hash(str(self))
[docs]
class SMDCurve(object):
def __init__(self, curve):
self.curve = curve
[docs]
def epsilon(self, delta):
from opendp._data import smd_curve_epsilon
return smd_curve_epsilon(self.curve, delta)
[docs]
class PartialConstructor(object):
def __init__(self, constructor):
self.constructor = constructor
def __call__(self, input_domain: Domain, input_metric: Metric):
return self.constructor(input_domain, input_metric)
def __rshift__(self, other):
return PartialConstructor(lambda input_domain, input_metric: self(input_domain, input_metric) >> other) # pragma: no cover
def __rrshift__(self, other):
if isinstance(other, tuple) and list(map(type, other)) == [Domain, Metric]:
return self(other[0], other[1])
raise TypeError(f"Cannot chain {type(self)} with {type(other)}")
[docs]
class UnknownTypeException(Exception):
pass
[docs]
class OpenDPException(Exception):
"""General exception for errors originating from the underlying OpenDP library.
The variant attribute corresponds to `one of the following variants <https://github.com/opendp/opendp/blob/53ec58d01762ca5ceee08590d7e7b725bbdafcf6/rust/opendp/src/error.rs#L46-L87>`_ and can be matched on.
Error variants may change in library updates.
See `Rust ErrorVariant <https://docs.rs/opendp/latest/opendp/error/enum.ErrorVariant.html>`_ for values variant may take on.
"""
raw_traceback: Optional[str]
def __init__(self, variant: str, message: Optional[str] = None, raw_traceback: Optional[str] = None):
self.variant = variant
self.message = message
self.raw_traceback = raw_traceback
[docs]
def raw_frames(self): # pragma: no cover
import re
return re.split(r"\s*[0-9]+: ", self.raw_traceback or "")
[docs]
def frames(self): # pragma: no cover
def format_frame(frame):
return "\n ".join(l.strip() for l in frame.split("\n"))
return [format_frame(f) for f in self.raw_frames() if f.startswith("opendp") or f.startswith("<opendp")]
def __str__(self) -> str: # pragma: no cover
response = ''
if self.raw_traceback and 'rust-stack-trace' in GLOBAL_FEATURES:
# join and split by newlines because frames may be multi-line
lines = "\n".join(self.frames()[::-1]).split('\n')
response += "Continued Rust stack trace:\n" + '\n'.join(' ' + line for line in lines)
response += '\n ' + self.variant
if self.message:
response += f'("{self.message}")'
return response
GLOBAL_FEATURES = set()
[docs]
def enable_features(*features: str) -> None:
GLOBAL_FEATURES.update(set(features))
[docs]
def disable_features(*features: str) -> None:
GLOBAL_FEATURES.difference_update(set(features))
[docs]
def assert_features(*features: str) -> None:
for feature in features:
assert feature in GLOBAL_FEATURES, f"Attempted to use function that requires {feature}, but {feature} is not enabled. See https://github.com/opendp/opendp/discussions/304, then call enable_features(\"{feature}\")"
M = TypeVar("M", Transformation, Measurement)
[docs]
def binary_search_chain(
make_chain: Callable[[float], M],
d_in: Any, d_out: Any,
bounds: Tuple[float, float] | None = None,
T=None) -> M:
"""Find the highest-utility (`d_in`, `d_out`)-close Transformation or Measurement.
Searches for the numeric parameter to `make_chain` that results in a computation
that most tightly satisfies `d_out` when datasets differ by at most `d_in`,
then returns the Transformation or Measurement corresponding to said parameter.
See `binary_search_param` to retrieve the discovered parameter instead of the complete computation chain.
:param make_chain: a function that takes a number and returns a Transformation or Measurement
:param d_in: how far apart input datasets can be
:param d_out: how far apart output datasets or distributions can be
:param bounds: a 2-tuple of the lower and upper bounds on the input of `make_chain`
:param T: type of argument to `make_chain`, one of {float, int}
:return: a chain parameterized at the nearest passing value to the decision point of the relation
:rtype: Union[Transformation, Measurement]
:raises TypeError: if the type is not inferrable (pass T) or the type is invalid
:raises ValueError: if the predicate function is constant, bounds cannot be inferred, or decision boundary is not within `bounds`.
:examples:
Find a base_laplace measurement with the smallest noise scale that is still (d_in, d_out)-close.
>>> from typing import List
>>> import opendp.prelude as dp
>>> dp.enable_features("floating-point", "contrib")
...
>>> # The majority of the chain only needs to be defined once.
>>> pre = (
... dp.space_of(List[float]) >>
... dp.t.then_clamp(bounds=(0., 1.)) >>
... dp.t.then_resize(size=10, constant=0.) >>
... dp.t.then_mean()
... )
...
>>> # Find a value in `bounds` that produces a (`d_in`, `d_out`)-chain nearest the decision boundary.
>>> # The lambda function returns the complete computation chain when given a single numeric parameter.
>>> chain = dp.binary_search_chain(
... lambda s: pre >> dp.m.then_base_laplace(scale=s),
... d_in=1, d_out=1.)
...
>>> # The resulting computation chain is always (`d_in`, `d_out`)-close, but we can still double-check:
>>> assert chain.check(1, 1.)
Build a (2 neighboring, 1. epsilon)-close sized bounded sum with discrete_laplace(100.) noise.
It should have the widest possible admissible clamping bounds (-b, b).
>>> def make_sum(b):
... space = dp.vector_domain(dp.atom_domain((-b, b)), 10_000), dp.symmetric_distance()
... return space >> dp.t.then_sum() >> dp.m.then_laplace(100.)
...
>>> # `meas` is a Measurement with the widest possible clamping bounds.
>>> meas = dp.binary_search_chain(make_sum, d_in=2, d_out=1., bounds=(0, 10_000))
...
>>> # If you want the discovered clamping bound, use `binary_search_param` instead.
"""
return make_chain(binary_search_param(make_chain, d_in, d_out, bounds, T))
[docs]
def binary_search_param(
make_chain: Callable[[float], Union[Transformation, Measurement]],
d_in: Any, d_out: Any,
bounds: Tuple[float, float] | None = None,
T=None) -> float:
"""Solve for the ideal constructor argument to `make_chain`.
Optimizes a parameterized chain `make_chain` within float or integer `bounds`,
subject to the chained relation being (`d_in`, `d_out`)-close.
:param make_chain: a function that takes a number and returns a Transformation or Measurement
:param d_in: how far apart input datasets can be
:param d_out: how far apart output datasets or distributions can be
:param bounds: a 2-tuple of the lower and upper bounds on the input of `make_chain`
:param T: type of argument to `make_chain`, one of {float, int}
:return: the nearest passing value to the decision point of the relation
:raises TypeError: if the type is not inferrable (pass T) or the type is invalid
:raises ValueError: if the predicate function is constant, bounds cannot be inferred, or decision boundary is not within `bounds`.
:example:
>>> import opendp.prelude as dp
...
>>> # Find a value in `bounds` that produces a (`d_in`, `d_out`)-chain nearest the decision boundary.
>>> # The first argument is any function that returns your complete computation chain
>>> # when passed a single numeric parameter.
...
>>> def make_fixed_laplace(scale):
... # fixes the input domain and metric, but parameterizes the noise scale
... return dp.m.make_base_laplace(dp.atom_domain(T=float), dp.absolute_distance(T=float), scale)
...
>>> scale = dp.binary_search_param(make_fixed_laplace, d_in=0.1, d_out=1.)
>>> assert scale == 0.1
>>> # Constructing the same chain with the discovered parameter will always be (0.1, 1.)-close.
>>> assert make_fixed_laplace(scale).check(0.1, 1.)
A policy research organization wants to know the smallest sample size necessary to release an "accurate" epsilon=1 DP mean income.
Determine the smallest dataset size such that, with 95% confidence,
the DP release differs from the clipped dataset's mean by no more than 1000.
Assume that neighboring datasets have a symmetric distance at most 2.
Also assume a clipping bound of 500,000.
>>> # we first work out the necessary noise scale to satisfy the above constraints.
>>> necessary_scale = dp.accuracy_to_laplacian_scale(accuracy=1000., alpha=.05)
...
>>> # we then write a function that make a computation chain with a given data size
>>> def make_mean(data_size):
... return (
... (dp.vector_domain(dp.atom_domain(bounds=(0., 500_000.)), data_size), dp.symmetric_distance()) >>
... dp.t.then_mean() >>
... dp.m.then_base_laplace(necessary_scale)
... )
...
>>> # solve for the smallest dataset size that admits a (2 neighboring, 1. epsilon)-close measurement
>>> dp.binary_search_param(
... make_mean,
... d_in=2, d_out=1.,
... bounds=(1, 1000000))
1498
"""
# one might think running scipy.optimize.brent* would be better, but
# 1. benchmarking showed no difference or minor regressions
# 2. brentq is more complicated
return binary_search(lambda param: make_chain(param).check(d_in, d_out), bounds, T)
# when return sign is false, only return float
@overload
def binary_search(
predicate: Callable[[float], bool],
bounds: Tuple[float, float] | None = ...,
T: Type[float] | None = ...,
return_sign: Literal[False] = False) -> float:
...
# when setting return sign to true as a keyword argument, return both
@overload
def binary_search(
predicate: Callable[[float], bool],
bounds: Tuple[float, float] | None = ...,
T: Type[float] | None = ...,
*, # see https://stackoverflow.com/questions/66435480/overload-following-optional-argument
return_sign: Literal[True]) -> Tuple[float, int]:
...
# when setting return sign to true as a positional argument, return both
@overload
def binary_search(
predicate: Callable[[float], bool],
bounds: Tuple[float, float] | None,
T: Type[float] | None,
return_sign: Literal[True]) -> Tuple[float, int]:
...
[docs]
def binary_search(
predicate: Callable[[float], bool],
bounds: Tuple[float, float] | None = None,
T: Type[float] | None = None,
return_sign: bool = False) -> float | Tuple[float, int]:
"""Find the closest passing value to the decision boundary of `predicate`.
If bounds are not passed, conducts an exponential search.
:param predicate: a monotonic unary function from a number to a boolean
:param bounds: a 2-tuple of the lower and upper bounds to the input of `predicate`
:param T: type of argument to `predicate`, one of {float, int}
:param return_sign: if True, also return the direction away from the decision boundary
:return: the discovered parameter within the bounds
:raises TypeError: if the type is not inferrable (pass T) or the type is invalid
:raises ValueError: if the predicate function is constant, bounds cannot be inferred, or decision boundary is not within `bounds`.
:example:
>>> from opendp.mod import binary_search
>>> binary_search(lambda x: x >= 5.)
5.0
>>> binary_search(lambda x: x <= 5.)
5.0
>>> binary_search(lambda x: x > 5, T=int)
6
>>> binary_search(lambda x: x < 5, T=int)
4
Find epsilon usage of the gaussian(scale=1.) mechanism applied on a dp mean.
Assume neighboring datasets differ by up to three additions/removals, and fix delta to 1e-8.
>>> # build a histogram that emits float counts
>>> import opendp.prelude as dp
>>> input_space = dp.vector_domain(dp.atom_domain(bounds=(0., 100.)), 1000), dp.symmetric_distance()
>>> dp_mean = dp.c.make_fix_delta(dp.c.make_zCDP_to_approxDP(
... input_space >> dp.t.then_mean() >> dp.m.then_gaussian(1.)),
... 1e-8
... )
...
>>> dp.binary_search(
... lambda d_out: dp_mean.check(3, (d_out, 1e-8)),
... bounds = (0., 1.))
0.5235561269546629
Find the L2 distance sensitivity of a histogram when neighboring datasets differ by up to 3 additions/removals.
>>> from opendp.transformations import make_count_by_categories
>>> histogram = dp.t.make_count_by_categories(
... dp.vector_domain(dp.atom_domain(T=str)), dp.symmetric_distance(),
... categories=["a"], MO=dp.L2Distance[int])
...
>>> dp.binary_search(
... lambda d_out: histogram.check(3, d_out),
... bounds = (0, 100))
3
"""
if bounds is None:
bounds = exponential_bounds_search(predicate, T) # type: ignore
if bounds is None:
raise ValueError("unable to infer bounds")
if len(set(map(type, bounds))) != 1:
raise TypeError("bounds must share the same type")
lower, upper = sorted(bounds)
maximize = predicate(lower) # if the lower bound passes, we should maximize
minimize = predicate(upper) # if the upper bound passes, we should minimize
if maximize == minimize:
raise ValueError("the decision boundary of the predicate is outside the bounds")
if isinstance(lower, float):
tolerance = 0.
half = lambda x: x / 2.
elif isinstance(lower, int):
tolerance = 1 # the lower and upper bounds never meet due to int truncation
half = lambda x: x // 2
else:
raise TypeError("bounds must be either float or int")
mid = lower
while upper - lower > tolerance:
new_mid = lower + half(upper - lower) # avoid overflow
# avoid an infinite loop from float roundoff
if new_mid == mid:
break
mid = new_mid
if predicate(mid) == minimize:
upper = mid
else:
lower = mid
# one bound is always false, the other true. Return the truthy bound
value = upper if minimize else lower
# optionally return sign
if return_sign:
return value, 1 if minimize else -1 # type: ignore
return value
[docs]
def exponential_bounds_search(
predicate: Callable[[Union[float, int]], bool],
T: Optional[Union[Type[float], Type[int]]]) -> Optional[Union[Tuple[float, float], Tuple[int, int]]]:
"""Determine bounds for a binary search via an exponential search,
in large bands of [2^((k - 1)^2), 2^(k^2)] for k in [0, 8).
Will attempt to recover once if `predicate` throws an exception,
by searching bands on the ok side of the exception boundary.
:param predicate: a monotonic unary function from a number to a boolean
:param T: type of argument to predicate, one of {float, int}
:return: a tuple of float or int bounds that the decision boundary lies within
:raises TypeError: if the type is not inferrable (pass T)
:raises ValueError: if the predicate function is constant
"""
# try to infer T
if T is None:
def check_type(v):
try:
predicate(v)
except TypeError as e:
return False
except OpenDPException as e:
if "No match for concrete type" in (e.message or ""):
return False
return True
if check_type(0.):
T = float
elif check_type(0):
T = int
else:
raise TypeError("unable to infer type `T`; pass the type `T` or bounds")
# core search functionality
def signed_band_search(center, at_center, sign):
"""identify which band (of eight) the decision boundary lies in,
starting from `center` in the direction indicated by `sign`"""
if T == int:
# searching bands of [(k - 1) * 2^16, k * 2^16].
# center + 1 included because zero is prone to error
bands = [center, center + 1, *(center + sign * 2 ** 16 * k for k in range(1, 9))]
elif T == float:
# searching bands of [2^((k - 1)^2), 2^(k^2)].
# exponent has ten bits (2.^1024 overflows) so k must be in [0, 32).
# unlikely to need numbers greater than 2**64, and to avoid overflow from shifted centers,
# only check k in [0, 8). Set your own bounds if this is not sufficient
bands = [center, *(center + sign * 2. ** k ** 2 for k in range(1024 // 32 // 4))]
else:
raise TypeError(f"unknown type {T}. Must be one of int, float")
for i in range(1, len(bands)):
# looking for a change in sign that indicates the decision boundary is within this band
if at_center != predicate(bands[i]):
# return the band
return tuple(sorted(bands[i - 1:i + 1]))
# No band found!
return None
center = {int: 0, float: 0.}[T]
try:
at_center = predicate(center)
# search positive bands, then negative bands
return signed_band_search(center, at_center, 1) or signed_band_search(center, at_center, -1)
except Exception:
pass
# predicate has thrown an exception
# 1. Treat exceptions as a secondary decision boundary, and find the edge value
# 2. Return a bound by searching from the exception edge, in the direction away from the exception
def exception_predicate(v):
try:
predicate(v)
return True
except Exception:
return False
exception_bounds = exponential_bounds_search(exception_predicate, T=T)
if exception_bounds is None:
try:
predicate(center)
except Exception:
raise ValueError(f"predicate always fails. An example traceback is shown above at {center}.")
center, sign = binary_search(exception_predicate, bounds=exception_bounds, T=T, return_sign=True)
at_center = predicate(center)
return signed_band_search(center, at_center, sign)
