本文则以一个程序来说明量化的具体计算过程：
import numpy as np
def quantization(x, s, z, alpha_q, beta_q):
x_q = np.round(1 / s * x + z, decimals=0)
x_q = np.clip(x_q, a_min=alpha_q, a_max=beta_q)
return x_q
def quantization_int8(x, s, z):
x_q = quantization(x, s, z, alpha_q=-128, beta_q=127)
x_q = x_q.astype(np.int8)
return x_q
def quantization_uint8(x, s, z):
x_q = quantization(x, s, z, alpha_q=0, beta_q=255)
x_q = x_q.astype(np.uint8)
return x_q
def dequantization(x_q, s, z):
x = s * (x_q - z)
x = x.astype(np.float32)
return x
def generate_quantization_constants(alpha, beta, alpha_q, beta_q):
# Affine quantization mapping
s = (beta - alpha) / (beta_q - alpha_q)
z = int((beta * alpha_q - alpha * beta_q) / (beta - alpha))
return s, z
def generate_quantization_int8_constants(alpha, beta):
b = 8
alpha_q = -2**(b - 1)
beta_q = 2**(b - 1) - 1
s, z = generate_quantization_constants(alpha=alpha,
beta=beta,
alpha_q=alpha_q,
beta_q=beta_q)
return s, z
def generate_quantization_uint8_constants(alpha, beta):
b = 8
alpha_q = 0
beta_q = 2**(b) - 1
s, z = generate_quantization_constants(alpha=alpha,
beta=beta,
alpha_q=alpha_q,
beta_q=beta_q)
return s, z
def relu(x, z_x, z_y, k):
x = np.clip(x, a_min=z_x, a_max=None)
y = z_y + k * (x - z_x)
return y
def quantization_relu_uint8(x, s_x, z_x, s_y, z_y):
y = relu(x=X_q, z_x=z_X, z_y=z_Y, k=s_X / s_Y)
y = y.astype(np.uint8)
return y
if __name__ == "__main__":
# Set random seed for reproducibility
random_seed = 0
np.random.seed(random_seed)
# Random matrices
m = 2
n = 4
alpha_X = -60.0
beta_X = 60.0
s_X, z_X = generate_quantization_int8_constants(alpha=alpha_X, beta=beta_X)
X = np.random.uniform(low=alpha_X, high=beta_X,
size=(m, n)).astype(np.float32)
X_q = quantization_int8(x=X, s=s_X, z=z_X)
alpha_Y = 0.0
beta_Y = 200.0
s_Y, z_Y = generate_quantization_uint8_constants(alpha=alpha_Y,
beta=beta_Y)
Y_expected = relu(x=X, z_x=0, z_y=0, k=1)
Y_q_expected = quantization_uint8(x=Y_expected, s=s_Y, z=z_Y)
print("X:")
print(X)
print("X_q:")
print(X_q)
print("Expected Y:")
print(Y_expected)
print("Expected Y_q:")
print(Y_q_expected)
Y_q_simulated = quantization_relu_uint8(x=X,
s_x=s_X,
z_x=z_X,
s_y=s_Y,
z_y=z_Y)
Y_simulated = dequantization(x_q=Y_q_simulated, s=s_Y, z=z_Y)
print("Y from ReLU:")
print(Y_simulated)
print("Y_q from Quantized ReLU:")
print(Y_q_simulated)
用python2执行上述程序：
