浮点数到有符号整数标准化的数字方式

Question

这种标准化的更快的数字方法是什么：

def normalize_vector(x, b, axis):
    """
    Normalize real vector x and outputs an integer vector y.

    Parameters:
        x (numpy.ndarray): Input real vector. (batch_size, seq_len)
        b (int): Unsigned integer defining the scaling factor.
        axis (int/None): if None, perform flatenned version, if axis=-1, perform relative normalization across batch.

    Returns:
        numpy.ndarray: Integer vector y.
    """
    # Find the maximum absolute value in x
    m = np.max(np.abs(x))

    # Process each element in x
    y = []
    for xi in x:
        if xi > 0:
            y.append(int((2**b - 1) * xi / m))
        elif xi < 0:
            y.append(int(-2**b * xi / m))
        else:
            y.append(0)

    return np.array(y)

可以

np.digitize

让它更快吗？

我有类似的问题，但这与NumPy无关。

我也期待它支持批量向量的

axis

参数。

Answer 1

有 np.piecewise

def normalize_vector2(x, b):
    """
    Normalize real vector x and outputs an integer vector y.

    Parameters:
        x (numpy.ndarray): Input real vector. (batch_size, seq_len)
        b (int): Unsigned integer defining the scaling factor.
        axis (int/None): if None, perform flatenned version, if axis=-1, perform relative normalization across batch.

    Returns:
        numpy.ndarray: Integer vector y.
    """
    # Step 1: Find the maximum absolute value in x
    m = np.max(np.abs(x))


    y = np.piecewise(x, [x > 0, x < 0], 
                     [lambda xi: ((2**b - 1) * xi / m), lambda xi: (-2**b * xi / m)])

    return y.astype(int)

比较：

import numpy as np
import time

def normalize_vector2(x, b):
    """
    Normalize real vector x and outputs an integer vector y.

    Parameters:
        x (numpy.ndarray): Input real vector. (batch_size, seq_len)
        b (int): Unsigned integer defining the scaling factor.
        axis (int/None): if None, perform flatenned version, if axis=-1, perform relative normalization across batch.

    Returns:
        numpy.ndarray: Integer vector y.
    """
    # Step 1: Find the maximum absolute value in x
    m = np.max(np.abs(x))


    y = np.piecewise(x, [x > 0, x < 0],
                     [lambda xi: ((2**b - 1) * xi / m), lambda xi: (-2**b * xi / m)])

    return y.astype(int)

def normalize_vector(x, b):
    """
    Normalize real vector x and outputs an integer vector y.

    Parameters:
        x (numpy.ndarray): Input real vector. (batch_size, seq_len)
        b (int): Unsigned integer defining the scaling factor.
        axis (int/None): if None, perform flatenned version, if axis=-1, perform relative normalization across batch.

    Returns:
        numpy.ndarray: Integer vector y.
    """
    # Find the maximum absolute value in x
    m = np.max(np.abs(x))

    # Process each element in x
    y = []
    for xi in x:
        if xi > 0:
            y.append(int((2**b - 1) * xi / m))
        elif xi < 0:
            y.append(int(-2**b * xi / m))
        else:
            y.append(0)

    return np.array(y)

for elements in [100,1000,10000]:
    iterations = int(100000 / elements)
    x = np.random.random(elements) * 256-128

    t1 = time.time()
    for i in range(iterations):
        normalize_vector(x,7)
    t2 = time.time()

    for i in range(iterations):
        normalize_vector2(x, 7)
    t3 = time.time()

    print(f"{(t2-t1)/iterations:.7f}, {elements} elements python: ")
    print(f"{(t3-t2)/iterations:.7f}, {elements} elements numpy")

0.0000596, 100 elements python: 
0.0000300, 100 elements numpy
0.0004920, 1000 elements python: 
0.0000443, 1000 elements numpy
0.0045721, 10000 elements python: 
0.0003924, 10000 elements numpy