擴充#
The BitGenerator 的設計使其可使用高效能 Python 的標準工具 (numba 和 Cython) 進行擴充。Generator 物件也可以與使用者提供的 BitGenerator 一起使用，只要這些 BitGenerator 匯出一小組必要的功能即可。
Numba#
Numba 可以與 CTypes 或 CFFI 一起使用。目前版本的 BitGenerator 皆透過這兩種介面匯出一小組功能。
這個範例示範如何使用 numba 透過純 Python 實作產生高斯樣本，然後進行編譯。隨機數由 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 都允許在將 distributions.c 檔案編譯成 DLL 或 so 後，更複雜的分佈直接在 Numba 中使用。下方範例章節中有一個範例展示如何使用更複雜的分佈。
Cython#
Cython 可用於解壓縮 BitGenerator 提供的 PyCapsule。此範例使用 PCG64 和上述範例。使用 Cython 撰寫高效能程式碼時的常見注意事項 (移除邊界檢查和環繞、提供陣列對齊資訊) 仍然適用。
#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
也可以使用 bitgen_t 結構的成員直接存取 BitGenerator。
@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 可用於直接存取 numpy/random/c_distributions.pxd 中的函數。這需要連結到位於 numpy/random/lib 中的 npyrandom 程式庫。
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
請參閱 透過 Cython 擴充 numpy.random，以取得這些範例的完整列表和用於建置 c 擴充模組的最小 setup.py。
CFFI#
CFFI 可用於直接存取 include/numpy/random/distributions.h 中的函數。標頭檔需要進行一些「調整」。
"""
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)
一旦標頭由 ffi.cdef 解析，即可使用 BitGenerator.cffi 介面，直接從 _generator 共用物件存取這些函數。
# 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 可以與使用者提供的 BitGenerator 一起使用。撰寫新的 BitGenerator 最簡單的方式是檢查現有 BitGenerator 之一的 pyx 檔案。必須提供的關鍵結構是 capsule，其中包含指向 bitgen_t 類型結構指標的 PyCapsule，
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;
其中提供 5 個指標。第一個是不透明指標，指向 BitGenerator 使用的資料結構。接下來三個是函數指標，分別傳回下一個 64 位元和 32 位元無號整數、下一個隨機雙精度浮點數和下一個原始值。最後一個函數用於測試，因此如果不需要，可以設定為下一個 64 位元無號整數函數。Generator 內部的函數會使用此結構，如下所示：
bitgen_state->next_uint64(bitgen_state->state)