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fmha_i8_quant_deviation.py
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fmha_i8_quant_deviation.py
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import numpy as np
import matplotlib.pyplot as plt
fig1, ax1 = plt.subplots()
fig2, ax2 = plt.subplots()
SOFTMAX_QUANT_SCALE = 127
SEQLEN = 512
HEAD_DIM = 64
f_q = np.random.randn(SEQLEN, HEAD_DIM)
f_k = np.random.randn(SEQLEN, HEAD_DIM)
f_v = np.random.randn(SEQLEN, HEAD_DIM)
# GEMM1
f_s = np.matmul(f_q, np.transpose(f_k), dtype = np.float32) / np.sqrt(HEAD_DIM)
f_p = np.zeros_like(f_s)
# Softmax
for row in range(SEQLEN):
row_max = np.max(f_s[row]) # scalar
row_exp = np.exp(f_s[row] - row_max) # vector
row_exp_sum = np.sum(row_exp) # scalar
f_p[row] = row_exp/row_exp_sum
ax2.hist(f_p.flatten(),1000)
# GEMM2
f_o_ref = np.matmul(f_p, f_v, dtype = np.float32) # Ground truth
def quantize_to_int8(tensor, clip_max, quant_range = 127):
scale = quant_range / clip_max
min_bound = - quant_range
max_bound = quant_range
outputs = np.clip((tensor.astype(np.float32) * scale).round(), min_bound, max_bound)
quant_tensor = outputs.astype(np.int8)
return quant_tensor
def quantize_to_uint8(tensor, clip_max, quant_range = 255): #
scale = quant_range / clip_max
max_bound = quant_range
outputs = np.clip((tensor.astype(np.float32) * scale).round(), 0, max_bound)
quant_tensor = outputs.astype(np.uint8)
return quant_tensor
# input quant arguments
q_amax = np.abs(f_q).max()
k_amax = np.abs(f_k).max()
v_amax = np.abs(f_v).max()
p_amax_ref = np.abs(f_p).max() # potential
o_amax = np.abs(f_o_ref).max()
i8_q = quantize_to_int8(f_q, q_amax)
i8_k = quantize_to_int8(f_k, k_amax)
i8_v = quantize_to_int8(f_v, v_amax)
# C1 GEMM1
i32_s = np.matmul(i8_q, np.transpose(i8_k), dtype = np.int32)
f_s = (i32_s * q_amax/127 * k_amax/127) / np.sqrt(HEAD_DIM)
f_p = np.zeros_like(f_s, dtype=np.float32)
# C1 Softmax
p_amax = 1
for row in range(SEQLEN):
row_max = np.max(f_s[row]) # scalar
row_exp = np.exp(f_s[row] - row_max) # vector
row_exp_sum = np.sum(row_exp) # scalar
f_p[row] = row_exp/row_exp_sum
i8_p = quantize_to_uint8(f_p, p_amax, SOFTMAX_QUANT_SCALE)
# C1 GEMM2
i32_o = np.matmul(i8_p, i8_v, dtype = np.int32) # int8 result for case 1
f_o1 = i32_o * p_amax/SOFTMAX_QUANT_SCALE * v_amax/127
f_o1_diff_row_abs = np.linalg.norm(f_o1-f_o_ref, ord=2, axis=1)/ np.linalg.norm(f_o_ref, ord=2, axis=1)
ax1.plot(np.arange(SEQLEN),f_o1_diff_row_abs)
# C2 GEMM1
i32_s = np.matmul(i8_q, np.transpose(i8_k), dtype = np.int32)
f_s = (i32_s * q_amax/127 * k_amax/127) / np.sqrt(HEAD_DIM)
f_p = np.zeros_like(f_s, dtype=np.float32)
# C2 Softmax
p_amax = p_amax_ref
for row in range(SEQLEN):
row_max = np.max(f_s[row]) # scalar
row_exp = np.exp(f_s[row] - row_max) # vector
row_exp_sum = np.sum(row_exp) # scalar
f_p[row] = row_exp/row_exp_sum
i8_p = quantize_to_uint8(f_p, p_amax, SOFTMAX_QUANT_SCALE)
# C2 GEMM2
i32_o = np.matmul(i8_p, i8_v, dtype = np.int32) # int8 result for case 1
f_o2 = i32_o * p_amax/SOFTMAX_QUANT_SCALE * v_amax/127
f_o2_diff_row_abs = np.linalg.norm(f_o2-f_o_ref, ord=2, axis=1)/ np.linalg.norm(f_o_ref, ord=2, axis=1)
ax1.plot(np.arange(SEQLEN),f_o2_diff_row_abs)
# C3 GEMM1
i32_s = np.matmul(i8_q, np.transpose(i8_k), dtype = np.int32)
f_s = (i32_s * q_amax/127 * k_amax/127) / np.sqrt(HEAD_DIM)
f_p = np.zeros_like(f_s, dtype=np.float32)
# C3 Softmax
ui8_p = np.zeros_like(f_p, dtype=np.uint8)
p_amax = np.zeros(SEQLEN, dtype=np.float32)
for row in range(SEQLEN):
row_max = np.max(f_s[row]) # scalar
row_exp = np.exp(f_s[row] - row_max) # vector
row_exp_sum = np.sum(row_exp) # scalar
f_p[row] = row_exp/row_exp_sum
p_amax[row] = np.max(f_p[row])
ui8_p[row] = quantize_to_uint8(f_p[row], p_amax[row], SOFTMAX_QUANT_SCALE)
# C3 GEMM2
i32_o = np.matmul(ui8_p, i8_v, dtype = np.int32) # int8 result for case 1
f_o3 = np.matmul(np.diag(p_amax/SOFTMAX_QUANT_SCALE), i32_o) * v_amax/127
f_o3_diff_row_abs = np.linalg.norm(f_o3-f_o_ref, ord=2, axis=1)/ np.linalg.norm(f_o_ref, ord=2, axis=1)
ax1.plot(np.arange(SEQLEN),f_o3_diff_row_abs)
ax1.set_ylabel("Deviation (%)")
ax1.set_xlabel("Token ID")
ax1.legend(["worst case", "static quantization", "dynamic quantization"])
plt.show()