延伸¶

bitgenerator被设计成可以使用高性能Python的标准工具numba和Cython进行扩展。这个 Generator 对象也可以与用户提供的位生成器一起使用，只要这些位生成器导出一小部分所需的函数。

努巴¶

Numba可以与CTypes或CFFI一起使用。两个小比特集的接口函数都通过迭代导出当前所有比特集。

这个例子展示了如何使用一个纯Python实现来生成gaussian样本，然后编译这个实现。随机数由 ctypes.next_double .

import numpy as np
import numba as nb

from numpy.random import PCG64
from timeit import timeit

bit_gen = PCG64()
next_d = bit_gen.cffi.next_double
state_addr = bit_gen.cffi.state_address

def normals(n, state):
    out = np.empty(n)
    for i in range((n + 1) // 2):
        x1 = 2.0 * next_d(state) - 1.0
        x2 = 2.0 * next_d(state) - 1.0
        r2 = x1 * x1 + x2 * x2
        while r2 >= 1.0 or r2 == 0.0:
            x1 = 2.0 * next_d(state) - 1.0
            x2 = 2.0 * next_d(state) - 1.0
            r2 = x1 * x1 + x2 * x2
        f = np.sqrt(-2.0 * np.log(r2) / r2)
        out[2 * i] = f * x1
        if 2 * i + 1 < n:
            out[2 * i + 1] = f * x2
    return out

# Compile using Numba
normalsj = nb.jit(normals, nopython=True)
# Must use state address not state with numba
n = 10000

def numbacall():
    return normalsj(n, state_addr)

rg = np.random.Generator(PCG64())

def numpycall():
    return rg.normal(size=n)

# Check that the functions work
r1 = numbacall()
r2 = numpycall()
assert r1.shape == (n,)
assert r1.shape == r2.shape

t1 = timeit(numbacall, number=1000)
print(f'{t1:.2f} secs for {n} PCG64 (Numba/PCG64) gaussian randoms')
t2 = timeit(numpycall, number=1000)
print(f'{t2:.2f} secs for {n} PCG64 (NumPy/PCG64) gaussian randoms')

CTypes和CFFI都允许在将distributions.c文件编译成 DLL 或 so . 下面的示例展示了如何使用更复杂的分布 examples 下面部分。

赛隆¶

Cython可用于打开 PyCapsule 由位发生器提供。本例使用 PCG64 还有上面的例子。并提供了通常的数组对齐检查——使用Cython来消除代码的高性能限制。

#!/usr/bin/env python3
#cython: language_level=3
"""
This file shows how the to use a BitGenerator to create a distribution.
"""
import numpy as np
cimport numpy as np
cimport cython
from cpython.pycapsule cimport PyCapsule_IsValid, PyCapsule_GetPointer
from libc.stdint cimport uint16_t, uint64_t
from numpy.random cimport bitgen_t
from numpy.random import PCG64
from numpy.random.c_distributions cimport (
      random_standard_uniform_fill, random_standard_uniform_fill_f)


@cython.boundscheck(False)
@cython.wraparound(False)
def uniforms(Py_ssize_t n):
    """
    Create an array of `n` uniformly distributed doubles.
    A 'real' distribution would want to process the values into
    some non-uniform distribution
    """
    cdef Py_ssize_t i
    cdef bitgen_t *rng
    cdef const char *capsule_name = "BitGenerator"
    cdef double[::1] random_values

    x = PCG64()
    capsule = x.capsule
    # Optional check that the capsule if from a BitGenerator
    if not PyCapsule_IsValid(capsule, capsule_name):
        raise ValueError("Invalid pointer to anon_func_state")
    # Cast the pointer
    rng = <bitgen_t *> PyCapsule_GetPointer(capsule, capsule_name)
    random_values = np.empty(n, dtype='float64')
    with x.lock, nogil:
        for i in range(n):
            # Call the function
            random_values[i] = rng.next_double(rng.state)
    randoms = np.asarray(random_values)

    return randoms

还可以使用 bitgen_t 结构。

@cython.boundscheck(False)
@cython.wraparound(False)
def uint10_uniforms(Py_ssize_t n):
    """Uniform 10 bit integers stored as 16-bit unsigned integers"""
    cdef Py_ssize_t i
    cdef bitgen_t *rng
    cdef const char *capsule_name = "BitGenerator"
    cdef uint16_t[::1] random_values
    cdef int bits_remaining
    cdef int width = 10
    cdef uint64_t buff, mask = 0x3FF

    x = PCG64()
    capsule = x.capsule
    if not PyCapsule_IsValid(capsule, capsule_name):
        raise ValueError("Invalid pointer to anon_func_state")
    rng = <bitgen_t *> PyCapsule_GetPointer(capsule, capsule_name)
    random_values = np.empty(n, dtype='uint16')
    # Best practice is to release GIL and acquire the lock
    bits_remaining = 0
    with x.lock, nogil:
        for i in range(n):
            if bits_remaining < width:
                buff = rng.next_uint64(rng.state)
            random_values[i] = buff & mask
            buff >>= width

    randoms = np.asarray(random_values)
    return randoms

Cython可以用来直接访问 numpy/random/c_distributions.pxd . 这需要与 npyrandom 类库位于 numpy/random/lib .

def uniforms_ex(bit_generator, Py_ssize_t n, dtype=np.float64):
    """
    Create an array of `n` uniformly distributed doubles via a "fill" function.

    A 'real' distribution would want to process the values into
    some non-uniform distribution

    Parameters
    ----------
    bit_generator: BitGenerator instance
    n: int
        Output vector length
    dtype: {str, dtype}, optional
        Desired dtype, either 'd' (or 'float64') or 'f' (or 'float32'). The
        default dtype value is 'd'
    """
    cdef Py_ssize_t i
    cdef bitgen_t *rng
    cdef const char *capsule_name = "BitGenerator"
    cdef np.ndarray randoms

    capsule = bit_generator.capsule
    # Optional check that the capsule if from a BitGenerator
    if not PyCapsule_IsValid(capsule, capsule_name):
        raise ValueError("Invalid pointer to anon_func_state")
    # Cast the pointer
    rng = <bitgen_t *> PyCapsule_GetPointer(capsule, capsule_name)

    _dtype = np.dtype(dtype)
    randoms = np.empty(n, dtype=_dtype)
    if _dtype == np.float32:
        with bit_generator.lock:
            random_standard_uniform_fill_f(rng, n, <float*>np.PyArray_DATA(randoms))
    elif _dtype == np.float64:
        with bit_generator.lock:
            random_standard_uniform_fill(rng, n, <double*>np.PyArray_DATA(randoms))
    else:
        raise TypeError('Unsupported dtype %r for random' % _dtype)
    return randoms

见延伸 numpy.random 西顿大道有关这些示例的完整列表和 setup.py 构建c扩展模块。

CFFI¶

CFFI可用于直接访问 include/numpy/random/distributions.h . 需要对头文件进行一些“按摩”：

"""
Use cffi to access any of the underlying C functions from distributions.h
"""
import os
import numpy as np
import cffi
from .parse import parse_distributions_h
ffi = cffi.FFI()

inc_dir = os.path.join(np.get_include(), 'numpy')

# Basic numpy types
ffi.cdef('''
    typedef intptr_t npy_intp;
    typedef unsigned char npy_bool;

''')

parse_distributions_h(ffi, inc_dir)

一旦标头被 ffi.cdef ，可以直接从 _generator 共享对象，使用 BitGenerator.cffi 接口。

# Compare the distributions.h random_standard_normal_fill to
# Generator.standard_random
bit_gen = np.random.PCG64()
rng = np.random.Generator(bit_gen)
state = bit_gen.state

interface = rng.bit_generator.cffi
n = 100
vals_cffi = ffi.new('double[%d]' % n)
lib.random_standard_normal_fill(interface.bit_generator, n, vals_cffi)

# reset the state
bit_gen.state = state

vals = rng.standard_normal(n)

for i in range(n):
    assert vals[i] == vals_cffi[i]

新的位发生器¶

Generator 可与用户提供的 BitGenerator 编写一个新的位生成器最简单的方法是检查一个现有位生成器的pyx文件。必须提供的关键结构是 capsule 其中包含 PyCapsule 类型的结构指针 bitgen_t ，

typedef struct bitgen {
  void *state;
  uint64_t (*next_uint64)(void *st);
  uint32_t (*next_uint32)(void *st);
  double (*next_double)(void *st);
  uint64_t (*next_raw)(void *st);
} bitgen_t;

它提供了5个指针。第一个是指向位生成器使用的数据结构的不透明指针。下三个是函数指针，返回下一个64位和32位无符号整数、下一个随机双精度和下一个原始值。最后一个函数用于测试，因此如果不需要，可以设置为下一个64位无符号整数函数。内部功能 Generator 如中所示使用此结构

bitgen_state->next_uint64(bitgen_state->state)

实例¶

C API用于随机通过Numba延伸