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# Copyright (C) 2020 Arm Limited or its affiliates. All rights reserved.
#
# Copyright 2015 The Gemmlowp Authors. All Rights Reserved.
#
# SPDX-License-Identifier: Apache-2.0
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
#
# Description:
# Contains various fixed point math functions based on the gemmlowp fixed
# point implementation.
import numpy as np
def saturating_rounding_mul(a, b):
assert np.int32(a) == a
assert np.int32(b) == b
if a == b and a == np.iinfo(np.int32).min:
return np.int32(np.iinfo(np.int32).max)
ab = np.int64(a) * np.int64(b)
nudge = (1 << 30) if ab >= 0 else (1 - (1 << 30))
result = np.int32(np.right_shift(ab + nudge, 31))
if result < 0:
result += 1
return result
def shift_left(a, offset):
assert np.int32(a) == a
assert offset >= 0
a_info = np.iinfo(a)
shifted = a * (1 << offset)
if shifted < a_info.min:
return np.int32(a_info.min)
elif shifted > a_info.max:
return np.int32(a_info.max)
else:
return np.int32(shifted)
def rounding_divide_by_pot(x, exponent):
assert np.int32(x) == x
assert np.int32(exponent) == exponent
mask = (1 << exponent) - 1
remainder = x & mask
threshold = mask >> 1
if x < 0:
threshold += 1
result = x >> exponent
if remainder > threshold:
result += 1
return result
def saturating_rounding_multiply_by_pot(exponent, x):
assert np.int32(x) == x
assert np.int32(exponent) == exponent
threshold = (1 << (np.iinfo(np.int32).bits - 1 - exponent)) - 1
if x > threshold:
return np.iinfo(np.int32).max
elif x < -threshold:
return np.iinfo(np.int32).min
else:
return shift_left(x, exponent)
def rescale(integer_bits_src, integer_bits_dst, x):
assert np.int32(integer_bits_src) == integer_bits_src
assert np.int32(integer_bits_dst) == integer_bits_dst
assert np.int32(x) == x
exponent = integer_bits_src - integer_bits_dst
result = saturating_rounding_multiply_by_pot(exponent, x)
return result
# Input Q0.31
def exp_on_interval_between_negative_one_quarter_and_0_excl(a):
assert np.int32(a) == a
assert -1 << (31 - 2) <= a < 0
offset = 28
constant_term = 1895147668
constant_1_over_3 = 715827883
x = a + (1 << offset)
x2 = saturating_rounding_mul(x, x)
x3 = saturating_rounding_mul(x2, x)
x4 = saturating_rounding_mul(x2, x2)
x4_over_4 = rounding_divide_by_pot(x4, 2)
x4_over_24_plus_x3_over_6_plus_x2_over_2 = rounding_divide_by_pot(
saturating_rounding_mul((x4_over_4 + x3), constant_1_over_3) + x2, 1
)
return np.int32(
constant_term + saturating_rounding_mul(constant_term, x + x4_over_24_plus_x3_over_6_plus_x2_over_2)
)
# Input Q5.26
def exp_on_negative_values(a):
assert np.int32(a) == a
assert a <= 0
one_quarter = np.int32(16777216)
mask = np.int32(16777215)
a_mod_quarter_minus_one_quarter = np.int32((a & mask) - one_quarter)
result = exp_on_interval_between_negative_one_quarter_and_0_excl(rescale(5, 0, a_mod_quarter_minus_one_quarter))
remainder = np.int32(a_mod_quarter_minus_one_quarter - a)
def exp_barrel_shifter(exponent, multiplier, result):
fractional_bits = 26
integer_bits = 5
shift = fractional_bits + exponent if integer_bits > exponent else 0
if remainder & (1 << shift):
return saturating_rounding_mul(result, multiplier)
else:
return result
result = exp_barrel_shifter(-2, 1672461947, result)
result = exp_barrel_shifter(-1, 1302514674, result)
result = exp_barrel_shifter(+0, 790015084, result)
result = exp_barrel_shifter(+1, 290630308, result)
result = exp_barrel_shifter(+2, 39332535, result)
result = exp_barrel_shifter(+3, 720401, result)
result = exp_barrel_shifter(+4, 242, result)
if a == 0:
return np.iinfo(np.int32).max
else:
return result
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