扩展#
BitGenerator 的设计旨在通过高性能Python的标准工具（如numba和Cython）进行扩展.`Generator` 对象也可以与用户提供的 BitGenerator 一起使用,只要这些 BitGenerator 导出一小部分必需的函数.
Numba#
Numba 可以与 CTypes 或 CFFI 一起使用.当前版本的 BitGenerators 都通过这两种接口导出了一小部分函数.
这个例子展示了如何使用 numba 通过一个纯 Python 实现来生成高斯样本,然后进行编译.随机数由 ctypes.next_double 提供.
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 都允许在编译 file distributions.c 成 DLL 或 so 后,直接在 Numba 中使用更复杂的分布.在下面的 Examples 部分中有一个展示如何使用更复杂分布的示例.
Cython#
Cython 可以用来解包 BitGenerator 提供的 PyCapsule.这个例子使用了 PCG64 和上面的例子.使用 Cython 编写高性能代码的常见注意事项——移除边界检查和环绕,提供数组对齐信息——仍然适用.
#!/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
BitGenerator 也可以通过 bitgen_t 结构体的成员直接访问.
@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 可以直接访问 numpy/random/c_distributions.pxd 中的函数.这需要与位于 numpy/random/lib 中的 npyrandom 库链接.
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
请参阅 通过 Cython 扩展 numpy.random 以获取这些示例的完整列表以及一个最小的 setup.py 来构建 c-extension 模块.
CFFI#
CFFI 可以用来直接访问 include/numpy/random/distributions.h 中的函数.需要对头文件进行一些”处理”:
"""
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)
一旦头文件被 ffi.cdef 解析,函数可以直接从 _generator 共享对象中访问,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 BitGenerators#
Generator 可以与用户提供的 BitGenerator 一起使用.编写新的 BitGenerator 的最简单方法是检查现有 BitGenerator 的 pyx 文件.必须提供的关键结构是包含 bitgen_t 类型结构指针的 PyCapsule 的 capsule.
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;
提供了5个指针.第一个是指向`BitGenerator`使用的数据结构的透明指针.接下来的三个是函数指针,分别返回下一个64位和32位无符号整数、下一个随机双精度数和下一个原始值.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.`Generator`内部的函数使用这个结构,如下所示
bitgen_state->next_uint64(bitgen_state->state)