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bit_generator
BitGenerator base class and SeedSequence used to seed the BitGenerators.

SeedSequence is derived from Melissa E. O'Neill's C++11 `std::seed_seq`
implementation, as it has a lot of nice properties that we want.

https://gist.github.com/imneme/540829265469e673d045
http://www.pcg-random.org/posts/developing-a-seed_seq-alternative.html

The MIT License (MIT)

Copyright (c) 2015 Melissa E. O'Neill
Copyright (c) 2019 NumPy Developers

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in
all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.
numpy.random.bit_generatorbit_generator.pyxstringsource__reduce____module____doc____name____qualname____dict__[0-9]+0xABC
    Abstract base class for seed sequences.

    ``BitGenerator`` implementations should treat any object that adheres to
    this interface as a seed sequence.

    See Also
    --------
    SeedSequence, SeedlessSeedSequence
    
    Abstract base class for seed sequences that can spawn.
    BitGenerator is a base class and cannot be instantized Coerce an input to a uint32 array.

    If a `uint32` array, pass it through directly.
    If a non-negative integer, then break it up into `uint32` words, lowest
    bits first.
    If a string starting with "0x", then interpret as a hex integer, as above.
    If a string of decimal digits, interpret as a decimal integer, as above.
    If a sequence of ints or strings, interpret each element as above and
    concatenate.

    Note that the handling of `int64` or `uint64` arrays are not just
    straightforward views as `uint32` arrays. If an element is small enough to
    fit into a `uint32`, then it will only take up one `uint32` element in the
    output. This is to make sure that the interpretation of a sequence of
    integers is the same regardless of numpy's default integer type, which
    differs on different platforms.

    Parameters
    ----------
    x : int, str, sequence of int or str

    Returns
    -------
    seed_array : uint32 array

    Examples
    --------
    >>> import numpy as np
    >>> from numpy.random.bit_generator import _coerce_to_uint32_array
    >>> _coerce_to_uint32_array(12345)
    array([12345], dtype=uint32)
    >>> _coerce_to_uint32_array('12345')
    array([12345], dtype=uint32)
    >>> _coerce_to_uint32_array('0x12345')
    array([74565], dtype=uint32)
    >>> _coerce_to_uint32_array([12345, '67890'])
    array([12345, 67890], dtype=uint32)
    >>> _coerce_to_uint32_array(np.array([12345, 67890], dtype=np.uint32))
    array([12345, 67890], dtype=uint32)
    >>> _coerce_to_uint32_array(np.array([12345, 67890], dtype=np.int64))
    array([12345, 67890], dtype=uint32)
    >>> _coerce_to_uint32_array([12345, 0x10deadbeef, 67890, 0xdeadbeef])
    array([     12345, 3735928559,         16,      67890, 3735928559],
          dtype=uint32)
    >>> _coerce_to_uint32_array(1234567890123456789012345678901234567890)
    array([3460238034, 2898026390, 3235640248, 2697535605,          3],
          dtype=uint32)
    DECIMAL_REISeedSequenceISeedSequence.generate_stateISpawnableSeedSequenceISpawnableSeedSequence.spawnImportErrorIncompatible checksums (%s vs 0xd41d8cd = ())Incompatible checksums (%s vs 0xf88304a = (entropy, n_children_spawned, pool, pool_size, spawn_key))LockNotImplementedErrorNot implemented in base BitGeneratorPickleErrorSeedSequenceSeedSequence expects int or sequence of ints for entropy not {}SeedlessSeedSequenceSeedlessSequenceSystemRandomThe size of the entropy pool should be at least TypeErrorValueError
(,)abcabstractmethod__all__arrarrayastypebase__bit_generator_ctorcline_in_tracebackcnt_coerce_to_uint32_array (line 85)compileconcatenatecopycycle    entropy=errstateexpected non-negative integerformatgetrandbitsignore__import__itertools__main__match__metaclass__methodnn_children    n_children_spawned=n_words__new__npnumpy.core.multiarray failed to importnumpy.core.umath failed to importonly support uint32 or uint64outputover_picklepickle    pool_size=__prepare____pyx_PickleError__pyx_checksum__pyx_result__pyx_state__pyx_type__pyx_vtable__randbitsrandomrangere__reduce_ex__registersecretsseedseed must be integerseedless SeedSequences cannot generate stateselfsize    spawn_key=startswithsubseqssys__test__threading<u4<u8uint32uint64unrecognized seed stringupdatevviewxzeros__getstate____setstate__stateBitGeneratorgenerate_statespawn__reduce_cython____setstate_cython__entropyspawn_keypool_sizen_children_spawnednumpydtype_int_to_uint32_array_coerce_to_uint32_array__pyx_unpickle_SeedlessSeedSequence__pyx_unpickle_SeedSequencenamenumpy/random/bit_generator.cloader__loader__origin__file__parent__package__submodule_search_locations__path__Interpreter change detected - this module can only be loaded into one interpreter per process.Module 'bit_generator' has already been imported. Re-initialisation is not supported.builtinscython_runtime__builtins__init numpy.random.bit_generator%d.%d%scompiletime version %s of module '%.100s' does not match runtime version %sbit_generator.pxd__init__.pxd_cython_0_29_24Shared Cython type %.200s is not a type objectShared Cython type %.200s has the wrong size, try recompilingcython_function_or_method<cyfunction %U at %p>%.200s() takes no arguments (%zd given)%.200s() takes exactly one argument (%zd given)Bad call flags in __Pyx_CyFunction_Call. METH_OLDARGS is no longer supported!%.200s() takes no keyword argumentsfunc_docfunc_name__self__func_dictfunc_globals__globals__func_closure__closure__func_code__code__func_defaults__defaults____kwdefaults____annotations____name__ must be set to a string object__qualname__ must be set to a string objectfunction's dictionary may not be deletedsetting function's dictionary to a non-dict__defaults__ must be set to a tuple object__kwdefaults__ must be set to a dict object__annotations__ must be set to a dict object4294967296numpy.random.bit_generator.BitGenerator
    BitGenerator(seed=None)

    Base Class for generic BitGenerators, which provide a stream
    of random bits based on different algorithms. Must be overridden.

    Parameters
    ----------
    seed : {None, int, array_like[ints], SeedSequence}, optional
        A seed to initialize the `BitGenerator`. If None, then fresh,
        unpredictable entropy will be pulled from the OS. If an ``int`` or
        ``array_like[ints]`` is passed, then it will be passed to
        ~`numpy.random.SeedSequence` to derive the initial `BitGenerator` state.
        One may also pass in a `SeedSequence` instance.

    Attributes
    ----------
    lock : threading.Lock
        Lock instance that is shared so that the same BitGenerator can
        be used in multiple Generators without corrupting the state. Code that
        generates values from a bit generator should hold the bit generator's
        lock.

    See Also
    --------
    SeedSequence
    random_raw_benchmarknumpy.random.bit_generator.BitGenerator.__getstate__numpy.random.bit_generator.BitGenerator.__setstate__numpy.random.bit_generator.BitGenerator.__reduce__numpy.random.bit_generator.BitGenerator.random_raw%.200s() keywords must be strings%s() got an unexpected keyword argument '%U'%s() got multiple values for keyword argument '%U'at leastat mostexactly%.200s() takes %.8s %zd positional argument%.1s (%zd given)snumpy.random.bit_generator.BitGenerator._benchmark
        Get or set the PRNG state

        The base BitGenerator.state must be overridden by a subclass

        Returns
        -------
        state : dict
            Dictionary containing the information required to describe the
            state of the PRNG
        ctypes
        ctypes interface

        Returns
        -------
        interface : namedtuple
            Named tuple containing ctypes wrapper

            * state_address - Memory address of the state struct
            * state - pointer to the state struct
            * next_uint64 - function pointer to produce 64 bit integers
            * next_uint32 - function pointer to produce 32 bit integers
            * next_double - function pointer to produce doubles
            * bitgen - pointer to the bit generator struct
        cffi
        CFFI interface

        Returns
        -------
        interface : namedtuple
            Named tuple containing CFFI wrapper

            * state_address - Memory address of the state struct
            * state - pointer to the state struct
            * next_uint64 - function pointer to produce 64 bit integers
            * next_uint32 - function pointer to produce 32 bit integers
            * next_double - function pointer to produce doubles
            * bitgen - pointer to the bit generator struct
        _seed_seqlock_ctypes_cfficapsulenumpy.random.bit_generator.BitGenerator.state.__get__calling %R should have returned an instance of BaseException, not %Rraise: exception class must be a subclass of BaseException__del__numpy.random.bit_generator.BitGenerator.state.__set__numpy.random.bit_generator.BitGenerator.ctypes.__get__numpy.random.bit_generator.BitGenerator.cffi.__get____init__numpy.random.bit_generator.BitGenerator.__init__numpy.random.bit_generator.SeedSequence.mix_entropyBuffer has wrong number of dimensions (expected %d, got %d)Item size of buffer (%zd byte%s) does not match size of '%s' (%zd byte%s)buffer dtypeBig-endian buffer not supported on little-endian compilerBuffer acquisition: Expected '{' after 'T'end'Buffer dtype mismatch, expected %s%s%s but got %sBuffer dtype mismatch, expected '%s' but got %s in '%s.%s''bool''char''signed char''unsigned char''short''unsigned short''int''unsigned int''long''unsigned long''long long''unsigned long long''complex float''float''complex double''double''complex long double''long double'a structPython objecta pointera stringunparseable format stringExpected a dimension of size %zu, got %zuExpected %d dimensions, got %dBuffer dtype mismatch; next field is at offset %zd but %zd expectedPython does not define a standard format string size for long double ('g')..Unexpected format string character: '%c'Cannot handle repeated arrays in format stringExpected a dimension of size %zu, got %dExpected a comma in format string, got '%c'Expected %d dimension(s), got %dUnexpected end of format string, expected ')'Does not understand character buffer dtype format string ('%c')npy_uint32Out of bounds on buffer access (axis %d)numpy.random.bit_generator.SeedSequence.get_assembled_entropynumpy.random.bit_generator.SeedSequence
    SeedSequence(entropy=None, *, spawn_key=(), pool_size=4)

    SeedSequence mixes sources of entropy in a reproducible way to set the
    initial state for independent and very probably non-overlapping
    BitGenerators.

    Once the SeedSequence is instantiated, you can call the `generate_state`
    method to get an appropriately sized seed. Calling `spawn(n) <spawn>` will
    create ``n`` SeedSequences that can be used to seed independent
    BitGenerators, i.e. for different threads.

    Parameters
    ----------
    entropy : {None, int, sequence[int]}, optional
        The entropy for creating a `SeedSequence`.
    spawn_key : {(), sequence[int]}, optional
        A third source of entropy, used internally when calling
        `SeedSequence.spawn`
    pool_size : {int}, optional
        Size of the pooled entropy to store. Default is 4 to give a 128-bit
        entropy pool. 8 (for 256 bits) is another reasonable choice if working
        with larger PRNGs, but there is very little to be gained by selecting
        another value.
    n_children_spawned : {int}, optional
        The number of children already spawned. Only pass this if
        reconstructing a `SeedSequence` from a serialized form.

    Notes
    -----

    Best practice for achieving reproducible bit streams is to use
    the default ``None`` for the initial entropy, and then use
    `SeedSequence.entropy` to log/pickle the `entropy` for reproducibility:

    >>> sq1 = np.random.SeedSequence()
    >>> sq1.entropy
    243799254704924441050048792905230269161  # random
    >>> sq2 = np.random.SeedSequence(sq1.entropy)
    >>> np.all(sq1.generate_state(10) == sq2.generate_state(10))
    True
    numpy.random.bit_generator.SeedSequence.__repr__join() result is too long for a Python string00010203040506070809101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899numpy.random.bit_generator.SeedSequence.generate_state%.200s object is not an iteratorvalue too large to convert to uint32_tcan't convert negative value to uint32_tintan integer is required__int__ returned non-int (type %.200s).  The ability to return an instance of a strict subclass of int is deprecated, and may be removed in a future version of Python.__%.4s__ returned non-%.4s (type %.200s)numpy.random.bit_generator.SeedSequence.spawnnumpy.random.bit_generator.SeedSequence.__reduce_cython__Expected %.16s, got %.200stuplenumpy.random.bit_generator.SeedSequence.__setstate_cython__'NoneType' object is not subscriptableobject of type 'NoneType' has no len()numpy.random.bit_generator.__pyx_unpickle_SeedSequence__set_statehasattr(): attribute name must be stringpoolnumpy.random.bit_generator.SeedSequence.state.__get__numpy.random.bit_generator.SeedSequence.pool_size.__get__numpy.random.bit_generator.SeedSequence.n_children_spawned.__get__numpy.random.bit_generator.SeedSequence.__init__Missing type objectCannot convert %.200s to %.200sUnable to initialize pickling for %snumpy.random.bit_generator.SeedlessSequencenumpy.random.bit_generator.SeedlessSeedSequence
    A seed sequence for BitGenerators with no need for seed state.

    See Also
    --------
    SeedSequence, ISeedSequence
    numpy.random.bit_generator.SeedlessSeedSequence.generate_statenumpy.random.bit_generator.SeedlessSeedSequence.spawnnumpy.random.bit_generator.SeedlessSeedSequence.__reduce_cython__numpy.random.bit_generator.SeedlessSeedSequence.__setstate_cython__numpy.random.bit_generator.__pyx_unpickle_SeedlessSeedSequence__set_statetypeflatiterbroadcastndarraygenericnumberintegersignedintegerunsignedintegerinexactfloatingcomplexfloatingflexiblecharacterufunc%.200s.%.200s is not a type object%.200s.%.200s size changed, may indicate binary incompatibility. Expected %zd from C header, got %zd from PyObject%s.%s size changed, may indicate binary incompatibility. Expected %zd from C header, got %zd from PyObjectnumpy.random._commonPOISSON_LAM_MAXdoubleLEGACY_POISSON_LAM_MAXMAXSIZEuint64_t__pyx_capi__%.200s does not export expected C variable %.200sC variable %.200s.%.200s has wrong signature (expected %.500s, got %.500s)benchmarkPyObject *(bitgen_t *, PyObject *, Py_ssize_t, PyObject *)PyObject *(bitgen_t *, PyObject *, PyObject *, PyObject *)prepare_cffiPyObject *(bitgen_t *)prepare_ctypes%.200s does not export expected C function %.200sC function %.200s.%.200s has wrong signature (expected %.500s, got %.500s)cannot import name %S%s (%s:%d)name '%U' is not defined while calling a Python objectNULL result without error in PyObject_Callnumpy.import_arraynumpy.core._multiarray_umath_ARRAY_API_ARRAY_API not found_ARRAY_API is not PyCapsule object_ARRAY_API is NULL pointermodule compiled against ABI version 0x%x but this version of numpy is 0x%xmodule compiled against API version 0x%x but this version of numpy is 0x%xFATAL: module compiled as unknown endianFATAL: module compiled as little endian, but detected different endianness at runtimenumpy.random.bit_generator._int_to_uint32_arraynumpy.random.bit_generator._coerce_to_uint32_arraymetaclass conflict: the metaclass of a derived class must be a (non-strict) subclass of the metaclasses of all its basesnumpy.random.bit_generator.ISeedSequence.generate_statenumpy.random.bit_generator.__defaults__numpy.random.bit_generator.ISpawnableSeedSequence.spawnnumpy.random.bit_generator.__pyx_unpickle_SeedlessSeedSequencenumpy.random.bit_generator.__pyx_unpickle_SeedSequence
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        random_raw(self, size=None)

        Return randoms as generated by the underlying BitGenerator

        Parameters
        ----------
        size : int or tuple of ints, optional
            Output shape.  If the given shape is, e.g., ``(m, n, k)``, then
            ``m * n * k`` samples are drawn.  Default is None, in which case a
            single value is returned.
        output : bool, optional
            Output values.  Used for performance testing since the generated
            values are not returned.

        Returns
        -------
        out : uint or ndarray
            Drawn samples.

        Notes
        -----
        This method directly exposes the the raw underlying pseudo-random
        number generator. All values are returned as unsigned 64-bit
        values irrespective of the number of bits produced by the PRNG.

        See the class docstring for the number of bits returned.
        Used in testsøH8H`GØGÈHæç
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        generate_state(n_words, dtype=np.uint32)

        Return the requested number of words for PRNG seeding.

        A BitGenerator should call this method in its constructor with
        an appropriate `n_words` parameter to properly seed itself.

        Parameters
        ----------
        n_words : int
        dtype : np.uint32 or np.uint64, optional
            The size of each word. This should only be either `uint32` or
            `uint64`. Strings (`'uint32'`, `'uint64'`) are fine. Note that
            requesting `uint64` will draw twice as many bits as `uint32` for
            the same `n_words`. This is a convenience for `BitGenerator`s that
            express their states as `uint64` arrays.

        Returns
        -------
        state : uint32 or uint64 array, shape=(n_words,)
        
        spawn(n_children)

        Spawn a number of child `SeedSequence` s by extending the
        `spawn_key`.

        Parameters
        ----------
        n_children : int

        Returns
        -------
        seqs : list of `SeedSequence` s
        HˆGGIPHøGÌÏ
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HˆG Coerce an input to a uint32 array.

    If a `uint32` array, pass it through directly.
    If a non-negative integer, then break it up into `uint32` words, lowest
    bits first.
    If a string starting with "0x", then interpret as a hex integer, as above.
    If a string of decimal digits, interpret as a decimal integer, as above.
    If a sequence of ints or strings, interpret each element as above and
    concatenate.

    Note that the handling of `int64` or `uint64` arrays are not just
    straightforward views as `uint32` arrays. If an element is small enough to
    fit into a `uint32`, then it will only take up one `uint32` element in the
    output. This is to make sure that the interpretation of a sequence of
    integers is the same regardless of numpy's default integer type, which
    differs on different platforms.

    Parameters
    ----------
    x : int, str, sequence of int or str

    Returns
    -------
    seed_array : uint32 array

    Examples
    --------
    >>> import numpy as np
    >>> from numpy.random.bit_generator import _coerce_to_uint32_array
    >>> _coerce_to_uint32_array(12345)
    array([12345], dtype=uint32)
    >>> _coerce_to_uint32_array('12345')
    array([12345], dtype=uint32)
    >>> _coerce_to_uint32_array('0x12345')
    array([74565], dtype=uint32)
    >>> _coerce_to_uint32_array([12345, '67890'])
    array([12345, 67890], dtype=uint32)
    >>> _coerce_to_uint32_array(np.array([12345, 67890], dtype=np.uint32))
    array([12345, 67890], dtype=uint32)
    >>> _coerce_to_uint32_array(np.array([12345, 67890], dtype=np.int64))
    array([12345, 67890], dtype=uint32)
    >>> _coerce_to_uint32_array([12345, 0x10deadbeef, 67890, 0xdeadbeef])
    array([     12345, 3735928559,         16,      67890, 3735928559],
          dtype=uint32)
    >>> _coerce_to_uint32_array(1234567890123456789012345678901234567890)
    array([3460238034, 2898026390, 3235640248, 2697535605,          3],
          dtype=uint32)
    
        generate_state(n_words, dtype=np.uint32)

        Return the requested number of words for PRNG seeding.

        A BitGenerator should call this method in its constructor with
        an appropriate `n_words` parameter to properly seed itself.

        Parameters
        ----------
        n_words : int
        dtype : np.uint32 or np.uint64, optional
            The size of each word. This should only be either `uint32` or
            `uint64`. Strings (`'uint32'`, `'uint64'`) are fine. Note that
            requesting `uint64` will draw twice as many bits as `uint32` for
            the same `n_words`. This is a convenience for `BitGenerator`s that
            express their states as `uint64` arrays.

        Returns
        -------
        state : uint32 or uint64 array, shape=(n_words,)
        àHHˆG
        spawn(n_children)

        Spawn a number of child `SeedSequence` s by extending the
        `spawn_key`.

        Parameters
        ----------
        n_children : int

        Returns
        -------
        seqs : list of `SeedSequence` s
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