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AIfES 2 2.0.0
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Math functions for Q7 data type using AVR pgmspace.h library for constant data storage. More...
Go to the source code of this file.
Functions | |
void | aimath_q7_avr_pgm_linear32_1 (const aitensor_t *a, const aitensor_t *b, const aitensor_t *c, aitensor_t *result) |
Performs a matrix multiplication of Q7 matrices a and b and adds a Q31 vector c to each row. More... | |
void | aimath_q7_avr_pgm_linear32_2 (const aitensor_t *a, const aitensor_t *b, const aitensor_t *c, aitensor_t *result) |
Performs a matrix multiplication of Q7 matrices a and b and adds a Q31 vector c to each row. More... | |
void | aimath_q7_avr_pgm_linear32_bt_1 (const aitensor_t *a, const aitensor_t *b, const aitensor_t *c, aitensor_t *result) |
Performs a matrix multiplication of Q7 matrices a and b (transposed) and adds a Q31 vector c to each row. More... | |
void | aimath_q7_avr_pgm_linear32_bt_2 (const aitensor_t *a, const aitensor_t *b, const aitensor_t *c, aitensor_t *result) |
Performs a matrix multiplication of Q7 matrices a and b and adds a Q31 vector c to each row. More... | |
void | aimath_q7_avr_pgm_relu (const aitensor_t *x, aitensor_t *result) |
Calculates the rectifier (ReLU) value of each element in a Q7 tensor. More... | |
void | aimath_q7_avr_pgm_leaky_relu (const aitensor_t *x, const void *alpha, aitensor_t *result) |
Calculates the leaky rectifier (leaky ReLU) value of each element in a Q7 tensor. More... | |
void | aimath_q7_avr_pgm_elu (const aitensor_t *x, const void *alpha, aitensor_t *result) |
Calculates the exponential rectifier (ELU) value of each element in a Q7 tensor. More... | |
void | aimath_q7_avr_pgm_sigmoid (const aitensor_t *x, aitensor_t *result) |
Calculates the sigmoid of each element in a Q7 tensor. More... | |
void | aimath_q7_avr_pgm_tanh (const aitensor_t *x, aitensor_t *result) |
Calculates the tanh of each element in a Q7 tensor. More... | |
void | aimath_q7_avr_pgm_softsign (const aitensor_t *x, aitensor_t *result) |
Calculates the softsign value of each element in a Q7 tensor. More... | |
void | aimath_q7_avr_pgm_softmax (const aitensor_t *x, aitensor_t *result) |
Calculates the softmax value of each batch element (row) of a Q7 tensor. More... | |
Math functions for Q7 data type using AVR pgmspace.h library for constant data storage.
AIfES is free software: you can redistribute it and/or modify it under the terms of the GNU Affero General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.
This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Affero General Public License for more details.
You should have received a copy of the GNU Affero General Public License along with this program. If not, see https://www.gnu.org/licenses/.
These functions modify the default implementation of the Q7 math functions to work with parameters, stored in the program memory of AVR controllers.
The library avr/pgmspace.h is required.
void aimath_q7_avr_pgm_elu | ( | const aitensor_t * | x, |
const void * | alpha, | ||
aitensor_t * | result | ||
) |
Calculates the exponential rectifier (ELU) value of each element in a Q7 tensor.
The quantization parameters x must be defined constant in PROGMEM.
This function wraps the function aimath_f32_default_elu() internally.
\[ result_{i} = \begin{cases} \alpha \cdot (e^{x_i} - 1) & \text{if } x_i < 0 \\ x_i & \text{if } x_i \geq 0 \end{cases} \]
The ELU is calculated with a piecewise linear approximation to avoid using exponential functions.
\[ result_{i} = \begin{cases} x_i & \text{if } 0 \leq x_i\\ \alpha \cdot 0.625 \cdot x_i & \text{if } -1 \leq x < 0\\ \alpha \cdot (0.25 \cdot x_i - 0.375) & \text{if } -2 \leq x < -1\\ \alpha \cdot (0.09375 \cdot x_i - 0.6875) & \text{if } -3 \leq x < -2\\ \alpha \cdot (0.03125 \cdot x_i - 0.875) & \text{if } -4 \leq x < -3\\ - \alpha & \text{if } x < -4 \end{cases} \]
The quantization parameters of the result tensor are set to {shift = x.shift, zero_point = x.zero_point} by the function because the output values are in the interval (max(-alpha, min(x)), max(x)].
Example:
*x | Q7 tensor to calculate the ELU from (N-D tensor) (quantization parameters const in PROGMEM) |
*alpha | Scalar \( \alpha \) (type aiscalar_q7_t) |
*result | Resulting Q7 tensor (N-D tensor) |
void aimath_q7_avr_pgm_leaky_relu | ( | const aitensor_t * | x, |
const void * | alpha, | ||
aitensor_t * | result | ||
) |
Calculates the leaky rectifier (leaky ReLU) value of each element in a Q7 tensor.
The quantization parameters x must be defined constant in PROGMEM.
This function wraps the function aimath_f32_default_leaky_relu() internally.
\[ result_{i} = \begin{cases} \alpha \cdot x_i & \text{if } x_i < 0 \\ x_i & \text{if } x_i \geq 0 \end{cases} \]
The quantization parameters of the result tensor are set to {shift = x.shift, zero_point = x.zero_point} by the function because the output values are in the interval (alpha * min(x), max(x)].
Example:
*x | Q7 tensor to calculate the leaky ReLU from (N-D tensor) (quantization parameters const in PROGMEM) |
*alpha | Scalar \( \alpha \) (type aiscalar_q7_t) for the leakage |
*result | Resulting Q7 tensor (N-D tensor) |
void aimath_q7_avr_pgm_linear32_1 | ( | const aitensor_t * | a, |
const aitensor_t * | b, | ||
const aitensor_t * | c, | ||
aitensor_t * | result | ||
) |
Performs a matrix multiplication of Q7 matrices a and b and adds a Q31 vector c to each row.
The data of b and c and the quantization parameters of a, b, c and result must be defined constant in PROGMEM.
Same functionality as aimath_f32_default_linear32().
The addition of the horizontal vector c is performed via broadcast, i.e. element wise in each column Mathematically this broadcast is equal to multiplying c with an vertical vector (with the same number of elements as c) and adding the result to a * b.
** The quantization parameters of the vector c have to be {zero_point = 0, shift = a.shift + b.shift}! **
\[ result = a \cdot b + \left( \begin{array}{c} 1 \\ 1 \\ \vdots \\ 1 \\ \end{array}\right) \cdot c \]
Example:
*a | Q7 matrix a (2D tensor of shape [N x K]) (quantization parameters const in PROGMEM) |
*b | Q7 matrix b (2D tensor of shape [K x M]) (data and quantization parameters const in PROGMEM) |
*c | Q31 vector c (2D tensor of shape [1 x M]) (data and quantization parameters const in PROGMEM) |
*result | Resulting Q7 matrix (2D tensor of shape [N x M]) (quantization parameters const in PROGMEM) |
void aimath_q7_avr_pgm_linear32_2 | ( | const aitensor_t * | a, |
const aitensor_t * | b, | ||
const aitensor_t * | c, | ||
aitensor_t * | result | ||
) |
Performs a matrix multiplication of Q7 matrices a and b and adds a Q31 vector c to each row.
The data of b and c and the quantization parameters of b, c and result (not of a!) must be defined constant in PROGMEM.
Same functionality as aimath_f32_default_linear32().
The addition of the horizontal vector c is performed via broadcast, i.e. element wise in each column Mathematically this broadcast is equal to multiplying c with an vertical vector (with the same number of elements as c) and adding the result to a * b.
** The quantization parameters of the vector c have to be {zero_point = 0, shift = a.shift + b.shift}! **
\[ result = a \cdot b + \left( \begin{array}{c} 1 \\ 1 \\ \vdots \\ 1 \\ \end{array}\right) \cdot c \]
Example:
*a | Q7 matrix a (2D tensor of shape [N x K]) |
*b | Q7 matrix b (2D tensor of shape [K x M]) (data and quantization parameters const in PROGMEM) |
*c | Q31 vector c (2D tensor of shape [1 x M]) (data and quantization parameters const in PROGMEM) |
*result | Resulting Q7 matrix (2D tensor of shape [N x M]) (quantization parameters const in PROGMEM) |
void aimath_q7_avr_pgm_linear32_bt_1 | ( | const aitensor_t * | a, |
const aitensor_t * | b, | ||
const aitensor_t * | c, | ||
aitensor_t * | result | ||
) |
Performs a matrix multiplication of Q7 matrices a and b (transposed) and adds a Q31 vector c to each row.
The data of b and c and the quantization parameters of a, b, c and result must be defined constant in PROGMEM.
The b matrix has to be transposed.
Same functionality as aimath_f32_default_linear32_bt().
The addition of the horizontal vector c is performed via broadcast, i.e. element wise in each column Mathematically this broadcast is equal to multiplying c with an vertical vector (with the same number of elements as c) and adding the result to \( a * b^T \).
The quantization parameters of the vector c have to be {zero_point = 0, shift = a.shift + b.shift}!
\[ result = a \cdot b^T + \left( \begin{array}{c} 1 \\ 1 \\ \vdots \\ 1 \\ \end{array}\right) \cdot c \]
Example:
*a | Q7 matrix a (2D tensor of shape [N x K]) (quantization parameters const in PROGMEM) |
*b | Q7 matrix b (2D tensor of shape [M x K]) (data and quantization parameters const in PROGMEM) |
*c | Q31 vector c (2D tensor of shape [1 x M]) (data and quantization parameters const in PROGMEM) |
*result | Resulting Q7 matrix (2D tensor of shape [N x M]) (quantization parameters const in PROGMEM) |
void aimath_q7_avr_pgm_linear32_bt_2 | ( | const aitensor_t * | a, |
const aitensor_t * | b, | ||
const aitensor_t * | c, | ||
aitensor_t * | result | ||
) |
Performs a matrix multiplication of Q7 matrices a and b and adds a Q31 vector c to each row.
The data of b and c and the quantization parameters of b, c and result (not of a!) must be defined constant in PROGMEM.
The b matrix has to be transposed.
Same functionality as aimath_f32_default_linear32().
The addition of the horizontal vector c is performed via broadcast, i.e. element wise in each column Mathematically this broadcast is equal to multiplying c with an vertical vector (with the same number of elements as c) and adding the result to \( a * b^T \).
** The quantization parameters of the vector c have to be {zero_point = 0, shift = a.shift + b.shift}! **
\[ result = a \cdot b^T + \left( \begin{array}{c} 1 \\ 1 \\ \vdots \\ 1 \\ \end{array}\right) \cdot c \]
Example:
*a | Q7 matrix a (2D tensor of shape [N x K]) |
*b | Q7 matrix b (2D tensor of shape [M x K]) (data and quantization parameters const in PROGMEM) |
*c | Q31 vector c (2D tensor of shape [1 x M]) (data and quantization parameters const in PROGMEM) |
*result | Resulting Q7 matrix (2D tensor of shape [N x M]) (quantization parameters const in PROGMEM) |
void aimath_q7_avr_pgm_relu | ( | const aitensor_t * | x, |
aitensor_t * | result | ||
) |
Calculates the rectifier (ReLU) value of each element in a Q7 tensor.
The quantization parameters x must be defined constant in PROGMEM.
This function wraps the function aimath_f32_default_relu() internally.
\[ result_{i} = max(0, x_{i}) \]
The quantization parameters of the result tensor are set to {shift = x.shift, zero_point = x.zero_point} by the function because the output values are in the interval [0, max(x)].
Example:
*x | Q7 tensor to calculate the ReLU from (N-D tensor) (quantization parameters const in PROGMEM) |
*result | Resulting Q7 tensor (N-D tensor) |
void aimath_q7_avr_pgm_sigmoid | ( | const aitensor_t * | x, |
aitensor_t * | result | ||
) |
Calculates the sigmoid of each element in a Q7 tensor.
The quantization parameters x must be defined constant in PROGMEM.
This function wraps the function aimath_f32_default_sigmoid() internally.
\[ result_{i} = \sigma(x_{i}) = \frac{1}{1 + e^{-x_{i}}} \]
The sigmoid is calculated with a piecewise linear approximation (PLAN) to avoid using exponential functions.
\[ result_{i} = \sigma_{PLAN}(x_i) = \begin{cases} 1 & \text{if } 5 \leq x_i\\ 0.03125 \cdot |x_i| + 0.84375 & \text{if } 2.375 \leq x_i < 5\\ 0.0125 \cdot |x_i| + 0.625 & \text{if } 1 \leq x_i < 2.375\\ 0.25 \cdot |x_i| + 0.5 & \text{if } 0 \leq x_i < 1\\ 1 - \sigma_{PLAN}(- x_i) & \text{if } x_i < 0\\ \end{cases} \]
The quantization parameters of the result tensor are set to {shift = 8, zero_point = -2^7} by the function because the output values are in the interval (0, 1).
Example:
*x | Q7 tensor to calculate the sigmoid from (N-D tensor) (quantization parameters const in PROGMEM) |
*result | Resulting Q7 tensor (N-D tensor) |
void aimath_q7_avr_pgm_softmax | ( | const aitensor_t * | x, |
aitensor_t * | result | ||
) |
Calculates the softmax value of each batch element (row) of a Q7 tensor.
The quantization parameters x must be defined constant in PROGMEM.
This function wraps the function aimath_f32_default_softmax() internally.
\[ result_{i} = \frac{e^{x_i}}{\sum_{j=1}^{K} e^{x_j}} \]
The quantization parameters of the result tensor are set to {shift = 8, zero_point = -128} by the function because the output values are in the interval (0, 1).
Example:
*x | Q7 tensor to calculate the softmax from (N-D tensor) (quantization parameters const in PROGMEM) |
*result | Resulting Q7 tensor (N-D tensor) |
void aimath_q7_avr_pgm_softsign | ( | const aitensor_t * | x, |
aitensor_t * | result | ||
) |
Calculates the softsign value of each element in a Q7 tensor.
The quantization parameters x must be defined constant in PROGMEM.
This function wraps the function aimath_f32_default_softsign() internally.
\[ result_{i} = \frac {x_i} {1 + |x_i|} \]
The quantization parameters of the result tensor are set to {shift = 7, zero_point = 0} by the function because the output values are in the interval (-1, 1).
Example:
*x | Q7 tensor to calculate the softsign from (N-D tensor) (quantization parameters const in PROGMEM) |
*result | Resulting Q7 tensor (N-D tensor) |
void aimath_q7_avr_pgm_tanh | ( | const aitensor_t * | x, |
aitensor_t * | result | ||
) |
Calculates the tanh of each element in a Q7 tensor.
The quantization parameters x must be defined constant in PROGMEM.
This function wraps the function aimath_f32_default_tanh() internally.
\[ result_{i} = \tanh(x_{i}) = \frac{e^{x_i} - e^{-x_i}}{e^{x_i} + e^{-x_i}} \]
The tanh is calculated with a piecewise linear approximation (PLA) to avoid using exponential functions.
\[ result_{i} = \tanh_{PLA}(x_i) = 2 \cdot \sigma(2x_i) - 1 = \begin{cases} 1 & \text{if } 5 \leq x_i\\ 0.0625 \cdot |x_i| + 0.6875 & \text{if } 2.375 \leq x_i < 5\\ 0.25 \cdot |x_i| + 0.25 & \text{if } 1 \leq x_i < 2.375\\ 0.5 \cdot |x_i| & \text{if } 0 \leq x_i < 1\\ - \tanh_{PLA}(- x_i) & \text{if } x_i < 0\\ \end{cases} \]
The quantization parameters of the result tensor are set to {shift = 7, zero_point = 0} by the function because the output values are in the interval (-1, 1).
Example:
*x | Q7 tensor to calculate the tanh from (N-D tensor) (quantization parameters const in PROGMEM) |
*result | Resulting Q7 tensor (N-D tensor) |