| AIfES 2 2.0.0

Functions
aimath_q7_default.h File Reference

Math functions for Q7 data type, default implementation. More...

Go to the source code of this file.

## Functions
void | aimath_q7_default_linear32 (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_default_linear32_bt (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_default_mat_mul (const aitensor_t *a, const aitensor_t *b, aitensor_t *result)
| Performs a matrix multiplication of Q7 matrices a and b. More...
void | aimath_q7_default_multiply (const aitensor_t *a, const aitensor_t *b, aitensor_t *result)
| Performs an element wise multiplication of Q7 tensors a and b (Hadamard product) More...
void | aimath_q7_default_scalar_mul (const void *scalar, const aitensor_t *a, aitensor_t *result)
| Performs a scalar multiplication (scaling) of Q7 tensor a and a scalar. More...
void | aimath_q7_default_tensor_add_different_shift (const aitensor_t *a, const aitensor_t *b, aitensor_t *result)
| Performs an element wise addition of Q7 tensors a and b with different shifts. More...
void | aimath_q7_default_tensor_add_same_shift (const aitensor_t *a, const aitensor_t *b, aitensor_t *result)
| Performs an element wise addition of Q7 tensors a and b with same shifts. More...
void | aimath_q7_default_tensor_sub_different_shift (const aitensor_t *a, const aitensor_t *b, aitensor_t *result)
| Performs an element wise addition of Q7 tensors a and b with different shifts. More...
void | aimath_q7_default_tensor_sub_same_shift (const aitensor_t *a, const aitensor_t *b, aitensor_t *result)
| Performs an element wise subtraction of Q7 tensors a and b with same shifts. More...
void | aimath_q7_default_copy_tensor (const aitensor_t *from, aitensor_t *to)
| Performs an element wise copy of Q7 tensors. More...
void | aimath_q7_default_transpose_vector (aitensor_t *vector)
| Transposes a Q7 vector. More...
void | aimath_q7_default_transpose_matrix (aitensor_t *x)
| Transpose a Q7 tensor. More...
void | aimath_q7_default_sigmoid (const aitensor_t *x, aitensor_t *result)
| Calculates the sigmoid of each element in a Q7 tensor. More...
void | aimath_q7_default_relu (const aitensor_t *x, aitensor_t *result)
| Calculates the rectifier (ReLU) value of each element in a Q7 tensor. More...
void | aimath_q7_default_d_relu (const aitensor_t *x, aitensor_t *result)
| Calculates the rectifier (ReLU) derivative of each element in a Q7 tensor. More...
void | aimath_q7_default_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_default_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_default_tanh (const aitensor_t *x, aitensor_t *result)
| Calculates the tanh of each element in a Q7 tensor. More...
void | aimath_q7_default_softsign (const aitensor_t *x, aitensor_t *result)
| Calculates the softsign value of each element in a Q7 tensor. More...
void | aimath_q7_default_softmax (const aitensor_t *x, aitensor_t *result)
| Calculates the softmax value of each batch element (row) of a Q7 tensor. More...
void | aimath_q7_default_zero_tensor (aitensor_t *tensor)
| Fills a Q7 tensor with zeros. More...
void | aimath_q7_default_init_zeros (aitensor_t *tensor)
| Fills a Q7 tensor with zeros. More...

## Detailed Description

Math functions for Q7 data type, default implementation.

Version
  2.2.0

Copyright
  Copyright (C) 2020-2023 Fraunhofer Institute for Microelectronic Circuits and Systems. All rights reserved.
  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 can be used when no hardware specific implementation is available.

## Function Documentation

## ◆ aimath_q7_default_copy_tensor()

void aimath_q7_default_copy_tensor | ( | const aitensor_t * | from,
|  | aitensor_t * | to
| ) |  |

Performs an element wise copy of Q7 tensors.

\[ to \leftarrow from \]

Dimension, shape and quantization parameters of from and to tensors have to be the same.

Example:

uint16_t from_shape[2] = {2, 3};
aimath_q7_params_t from_params = {1, 0}; // {shift, zero point}
int8_t from_data[2*3] = { 2, -4, 6,
-8, 10, -12};
aitensor_t from = AITENSOR_2D_Q7(from_shape, &from_params, from_data);
uint16_t to_shape[2] = {2, 3};
aimath_q7_params_t to_params = {1, 0}; // {shift, zero point}
int8_t to_data[2*3];
aitensor_t to = AITENSOR_2D_Q7(to_shape, &to_params, to_data);
aimath_q7_default_copy_tensor(&from, &to);
print_aitensor(&to);
print_aitensor
void print_aitensor(const aitensor_t *tensor)
Printing a tensor to console.
aimath_q7_default_copy_tensor
void aimath_q7_default_copy_tensor(const aitensor_t *from, aitensor_t *to)
Performs an element wise copy of Q7 tensors.
aimath_q7_params
Parameters used for the quantized Q7 values, used as property of a tensor.
Definition: aimath_q7.h:148
aitensor
A tensor in AIfES.
Definition: aifes_math.h:89

Parameters

  *from | Q7 tensor to copy from (N-D tensor)
  *to | Q7 tensor to copy to (N-D tensor)

## ◆ aimath_q7_default_d_relu()

void aimath_q7_default_d_relu | ( | const aitensor_t * | x,
|  | aitensor_t * | result
| ) |  |

Calculates the rectifier (ReLU) derivative of each element in a Q7 tensor.

\[ result_{ij} = \begin{cases} 0 & \text{if } x_i < 0\\ 1 & \text{if } x_i \geq 0 \end{cases} \]

The quantization parameters of the result tensor are set to {shift = 0, zero_point = 0} by the function because the output values are either 0 or 1.

Example:

uint16_t x_shape[2] = {2, 3};
aimath_q7_params_t x_params = {1, 0}; // {shift, zero point}
int8_t x_data[2*3] = { 2, -4, 6,
-8, 10, -12};
aitensor_t x = AITENSOR_2D_Q7(x_shape, &x_params, x_data);
uint16_t result_shape[2] = {2, 3};
aimath_q7_params_t result_params; // {shift, zero point}
int8_t result_data[2*3];
aitensor_t result = AITENSOR_2D_Q7(result_shape, &result_params, result_data);
aimath_q7_default_d_relu(&x, &result);
print_aitensor(&result);
aimath_q7_default_d_relu
void aimath_q7_default_d_relu(const aitensor_t *x, aitensor_t *result)
Calculates the rectifier (ReLU) derivative of each element in a Q7 tensor.

Parameters

  *x | Q7 tensor to calculate the ReLU derivative from (N-D tensor)
  *result | Resulting Q7 tensor (N-D tensor)

## ◆ aimath_q7_default_elu()

void aimath_q7_default_elu | ( | const aitensor_t * | x,
|  | const void * | alpha,
|  | aitensor_t * | result
| ) |  |

Calculates the exponential rectifier (ELU) value of each element in a Q7 tensor.

\[ result_{i} = \begin{cases} \alpha \cdot (e^{x_i} - 1) & \text{if } x_i < 0 \\ x_i & \text{if } x_i \geq 0 \end{cases} \]

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:

uint16_t x_shape[2] = {2, 3};
aimath_q7_params_t x_params = {1, 0}; // {shift, zero point}
int8_t x_data[2*3] = { 2, -4, 6,
-8, 10, -12};
aitensor_t x = AITENSOR_2D_Q7(x_shape, &x_params, x_data);
aiscalar_q7_t alpha = AISCALAR_Q7(1.0f, 0, 0);
uint16_t result_shape[2] = {2, 3};
aimath_q7_params_t result_params; // {shift, zero point}
int8_t result_data[2*3];
aitensor_t result = AITENSOR_2D_Q7(result_shape, &result_params, result_data);
aimath_q7_default_elu(&x, &alpha, &result);
print_aitensor(&result);
aimath_q7_default_elu
void aimath_q7_default_elu(const aitensor_t *x, const void *alpha, aitensor_t *result)
Calculates the exponential rectifier (ELU) value of each element in a Q7 tensor.
aiscalar_q7
Single quantized Q7 value/scalar.
Definition: aimath_q7.h:155

Parameters

  *x | Q7 tensor to calculate the ELU from (N-D tensor)
  *alpha | Scalar \( \alpha \) (type aiscalar_q7_t)
  *result | Resulting Q7 tensor (N-D tensor)

## ◆ aimath_q7_default_init_zeros()

void aimath_q7_default_init_zeros | ( | aitensor_t * | tensor | ) |

Fills a Q7 tensor with zeros.

\[ tensor_{i} = 0 \]

The function sets all tensor elements, the shift and the zero_point to 0.

Example:

uint16_t tensor_shape[2] = {2, 3};
aimath_q7_params_t tensor_params;
int8_t tensor_data[2*3];
aitensor_t tensor = AITENSOR_2D_Q7(tensor_shape, &tensor_params, tensor_data);
aimath_q7_default_init_zeros(&tensor);
print_aitensor(&tensor);
aimath_q7_default_init_zeros
void aimath_q7_default_init_zeros(aitensor_t *tensor)
Fills a Q7 tensor with zeros.

Parameters

  *tensor | Q7 tensor to set to zero (N-D tensor)

## ◆ aimath_q7_default_leaky_relu()

void aimath_q7_default_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.

\[ result_{i} = \begin{cases} \alpha \cdot x_i & \text{if } x_i < 0 \\ x_i & \text{if } x_i \geq 0 \end{cases} \]

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:

uint16_t x_shape[2] = {2, 3};
aimath_q7_params_t x_params = {6, 0}; // {shift, zero point}
int8_t x_data[2*3] = { 2, -4, 6,
-8, 10, -12};
aitensor_t x = AITENSOR_2D_Q7(x_shape, &x_params, x_data);
aiscalar_q7_t alpha = AISCALAR_Q7(0.01f, 10, 0);
uint16_t result_shape[2] = {2, 3};
aimath_q7_params_t result_params; // {shift, zero point}
int8_t result_data[2*3];
aitensor_t result = AITENSOR_2D_Q7(result_shape, &result_params, result_data);
aimath_q7_default_leaky_relu(&x, &alpha, &result);
print_aitensor(&result);
aimath_q7_default_leaky_relu
void aimath_q7_default_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.

Parameters

  *x | Q7 tensor to calculate the leaky ReLU from (N-D tensor)
  *alpha | Scalar \( \alpha \) (type aiscalar_q7_t) for the leakage
  *result | Resulting Q7 tensor (N-D tensor)

## ◆ aimath_q7_default_linear32()

void aimath_q7_default_linear32 | ( | 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 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 \( a \cdot b \).

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:

\[ a = \left( \begin{array}{rrr} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{array}\right) \]

\[ b = \left( \begin{array}{rr} 1 & 0 \\ 0 & 1 \\ 0 & 0 \end{array}\right) \]

\[ c = \left( \begin{array}{rr} 2 & 5 \end{array}\right) \]

\[ result = a \cdot b + \left( \begin{array}{r} 1 \\ 1 \\ 1 \\ \end{array}\right) \cdot c \]

\[ = \left( \begin{array}{rr} 1 & 2 \\ 4 & 5 \\ 7 & 8 \end{array}\right) + \left( \begin{array}{rr} 2 & 5 \\ 2 & 5 \\ 2 & 5 \end{array}\right) \]

\[ = \left( \begin{array}{rr} 3 & 7 \\ 6 & 10 \\ 9 & 13 \end{array}\right) \]

Example:

uint16_t a_shape[2] = {3, 3};
aimath_q7_params_t a_params = {1, 0}; // {shift, zero point}
int8_t a_data[3*3] = { 2, 4, 6,
8, 10, 12,
14, 16, 18};
aitensor_t a = AITENSOR_2D_Q7(a_shape, &a_params, a_data);
uint16_t b_shape[2] = {3, 2};
aimath_q7_params_t b_params = {2, 0}; // {shift, zero point}
int8_t b_data[3*2] = {4, 0,
0, 4,
0, 0};
aitensor_t b = AITENSOR_2D_Q7(b_shape, &b_params, b_data);
uint16_t c_shape[2] = {1, 2};
aimath_q31_params_t c_params = {3, 0}; // {shift, zero point}
int32_t c_data[1*2] = {16, 40};
aitensor_t c = AITENSOR_2D_Q31(c_shape, &c_params, c_data);
uint16_t result_shape[2] = {3, 2};
aimath_q7_params_t result_params = {1, 0}; // {shift, zero point}
int8_t result_data[3*2];
aitensor_t result = AITENSOR_2D_Q7(result_shape, &result_params, result_data);
aimath_q7_default_linear32(&a, &b, &c, &result);
print_aitensor(&result);
aimath_q7_default_linear32
void aimath_q7_default_linear32(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.
aimath_q31_params
Parameters used for the quantized Q31 values, used as property of a tensor.
Definition: aimath_q31.h:149

Parameters

  *a | Q7 matrix a (2D tensor of shape [N x K])
  *b | Q7 matrix b (2D tensor of shape [K x M])
  *c | Q31 vector c (2D tensor of shape [1 x M] or 1D tensor of shape [M])
  *result | Resulting Q7 matrix (2D tensor of shape [N x M])

## ◆ aimath_q7_default_linear32_bt()

void aimath_q7_default_linear32_bt | ( | 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.

Same operation as aimath_q7_default_linear32() but with a transposed b matrix.

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 \( a \cdot b^T \).

** 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:

\[ a = \left( \begin{array}{rrr} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{array}\right) \]

\[ b = \left( \begin{array}{rr} 1 & 0 & 0 \\ 0 & 1 & 0 \end{array}\right) \]

\[ c = \left( \begin{array}{rr} 2 & 5 \end{array}\right) \]

\[ result = a \cdot b^T + \left( \begin{array}{r} 1 \\ 1 \\ 1 \\ \end{array}\right) \cdot c \]

\[ = \left( \begin{array}{rr} 1 & 2 \\ 4 & 5 \\ 7 & 8 \end{array}\right) + \left( \begin{array}{rr} 2 & 5 \\ 2 & 5 \\ 2 & 5 \end{array}\right) \]

\[ = \left( \begin{array}{rr} 3 & 7 \\ 6 & 10 \\ 9 & 13 \end{array}\right) \]

Example:

uint16_t a_shape[2] = {3, 3};
aimath_q7_params_t a_params = {1, 0}; // {shift, zero point}
int8_t a_data[3*3] = { 2, 4, 6,
8, 10, 12,
14, 16, 18};
aitensor_t a = AITENSOR_2D_Q7(a_shape, &a_params, a_data);
uint16_t b_shape[2] = {2, 3};
aimath_q7_params_t b_params = {2, 0}; // {shift, zero point}
int8_t b_data[2*3] = {4, 0, 0,
0, 4, 0};
aitensor_t b = AITENSOR_2D_Q7(b_shape, &b_params, b_data);
uint16_t c_shape[2] = {1, 2};
aimath_q31_params_t c_params = {3, 0}; // {shift, zero point}
int32_t c_data[1*2] = {16, 40};
aitensor_t c = AITENSOR_2D_Q31(c_shape, &c_params, c_data);
uint16_t result_shape[2] = {3, 2};
aimath_q7_params_t result_params = {1, 0}; // {shift, zero point}
int8_t result_data[3*2];
aitensor_t result = AITENSOR_2D_Q7(result_shape, &result_params, result_data);
aimath_q7_default_linear32_bt(&a, &b, &c, &result);
print_aitensor(&result);
aimath_q7_default_linear32_bt
void aimath_q7_default_linear32_bt(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 eac...

Parameters

  *a | Q7 matrix a (2D tensor of shape [N x K])
  *b | Q7 matrix b (2D tensor of shape [M x K])
  *c | Q31 vector c (2D tensor of shape [1 x M] or 1D tensor of shape [M])
  *result | Resulting Q7 matrix (2D tensor of shape [N x M])

## ◆ aimath_q7_default_mat_mul()

void aimath_q7_default_mat_mul | ( | const aitensor_t * | a,
|  | const aitensor_t * | b,
|  | aitensor_t * | result
| ) |  |

Performs a matrix multiplication of Q7 matrices a and b.

\[ result = a \cdot b \]

Example:

uint16_t a_shape[2] = {3, 3};
aimath_q7_params_t a_params = {1, 0}; // {shift, zero point}
int8_t a_data[3*3] = { 2, 4, 6,
8, 10, 12,
14, 16, 18};
aitensor_t a = AITENSOR_2D_Q7(a_shape, &a_params, a_data);
uint16_t b_shape[2] = {3, 2};
aimath_q7_params_t b_params = {2, 0}; // {shift, zero point}
int8_t b_data[3*2] = {4, 0,
0, 4,
0, 0};
aitensor_t b = AITENSOR_2D_Q7(b_shape, &b_params, b_data);
uint16_t result_shape[2] = {3, 2};
aimath_q7_params_t result_params = {1, 0}; // {shift, zero point}
int8_t result_data[3*2];
aitensor_t result = AITENSOR_2D_Q7(result_shape, &result_params, result_data);
aimath_q7_default_mat_mul(&a, &b, &result);
print_aitensor(&result);
aimath_q7_default_mat_mul
void aimath_q7_default_mat_mul(const aitensor_t *a, const aitensor_t *b, aitensor_t *result)
Performs a matrix multiplication of Q7 matrices a and b.

Parameters

  *a | Q7 matrix a (2D tensor of shape [N x K])
  *b | Q7 matrix b (2D tensor of shape [K x M])
  *result | Resulting Q7 matrix of the multiplication (2D tensor of shape [N x M])

## ◆ aimath_q7_default_multiply()

void aimath_q7_default_multiply | ( | const aitensor_t * | a,
|  | const aitensor_t * | b,
|  | aitensor_t * | result
| ) |  |

Performs an element wise multiplication of Q7 tensors a and b (Hadamard product)

\[ result = a \circ b \]

Example:

uint16_t a_shape[2] = {2, 3};
aimath_q7_params_t a_params = {1, 0}; // {shift, zero point}
int8_t a_data[2*3] = { 2, -4, 6,
-8, 10, -12};
aitensor_t a = AITENSOR_2D_Q7(a_shape, &a_params, a_data);
uint16_t b_shape[2] = {2, 3};
aimath_q7_params_t b_params = {2, 0}; // {shift, zero point}
int8_t b_data[2*3] = { 4, -8, 12,
-16, 20, -24};
aitensor_t b = AITENSOR_2D_Q7(b_shape, &b_params, b_data);
uint16_t result_shape[2] = {2, 3};
aimath_q7_params_t result_params = {1, 0}; // {shift, zero point}
int8_t result_data[2*3];
aitensor_t result = AITENSOR_2D_Q7(result_shape, &result_params, result_data);
aimath_q7_default_multiply(&a, &b, &result);
print_aitensor(&result);
aimath_q7_default_multiply
void aimath_q7_default_multiply(const aitensor_t *a, const aitensor_t *b, aitensor_t *result)
Performs an element wise multiplication of Q7 tensors a and b (Hadamard product)

Parameters

  *a | Q7 tensor a (N-D tensor)
  *b | Q7 tensor b (N-D tensor)
  *result | Resulting Q7 tensor of the element wise multiplication (N-D tensor)

## ◆ aimath_q7_default_relu()

void aimath_q7_default_relu | ( | const aitensor_t * | x,
|  | aitensor_t * | result
| ) |  |

Calculates the rectifier (ReLU) value of each element in a Q7 tensor.

\[ result_{i} = max(0, x_{i}) \]

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:

uint16_t x_shape[2] = {2, 3};
aimath_q7_params_t x_params = {1, 0}; // {shift, zero point}
int8_t x_data[2*3] = { 2, -4, 6,
-8, 10, -12};
aitensor_t x = AITENSOR_2D_Q7(x_shape, &x_params, x_data);
uint16_t result_shape[2] = {2, 3};
aimath_q7_params_t result_params;
int8_t result_data[2*3];
aitensor_t result = AITENSOR_2D_Q7(result_shape, &result_params, result_data);
aimath_q7_default_relu(&x, &result);
print_aitensor(&result);
aimath_q7_default_relu
void aimath_q7_default_relu(const aitensor_t *x, aitensor_t *result)
Calculates the rectifier (ReLU) value of each element in a Q7 tensor.

Parameters

  *x | Q7 tensor to calculate the ReLU from (N-D tensor)
  *result | Resulting Q7 tensor (N-D tensor)

## ◆ aimath_q7_default_scalar_mul()

void aimath_q7_default_scalar_mul | ( | const void * | scalar,
|  | const aitensor_t * | a,
|  | aitensor_t * | result
| ) |  |

Performs a scalar multiplication (scaling) of Q7 tensor a and a scalar.

\[ result = scalar \cdot a \]

Example:

uint16_t a_shape[2] = {2, 3};
aimath_q7_params_t a_params = {1, 0}; // {shift, zero point}
int8_t a_data[2*3] = { 2, -4, 6,
-8, 10, -12};
aitensor_t a = AITENSOR_2D_Q7(a_shape, &a_params, a_data);
aiscalar_q7_t scalar = AISCALAR_Q7(0.1f, 7, 0); // (value, shift, zero_point)
uint16_t result_shape[2] = {2, 3};
aimath_q7_params_t result_params = {7, 0}; // {shift, zero point}
int8_t result_data[2*3];
aitensor_t result = AITENSOR_2D_Q7(result_shape, &result_params, result_data);
aimath_q7_default_scalar_mul(&scalar, &a, &result);
print_aitensor(&result);
aimath_q7_default_scalar_mul
void aimath_q7_default_scalar_mul(const void *scalar, const aitensor_t *a, aitensor_t *result)
Performs a scalar multiplication (scaling) of Q7 tensor a and a scalar.

Parameters

  *scalar | Scalar (type aiscalar_q7_t)
  *a | Q7 tensor a (N-D tensor)
  *result | Resulting Q7 tensor of the scalar multiplication (N-D tensor)

## ◆ aimath_q7_default_sigmoid()

void aimath_q7_default_sigmoid | ( | const aitensor_t * | x,
|  | aitensor_t * | result
| ) |  |

Calculates the sigmoid of each element in a Q7 tensor.

\[ result_{i} = \sigma(x_{i}) = \frac{1}{1 + e^{-x_{i}}} \]

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:

uint16_t x_shape[2] = {2, 3};
aimath_q7_params_t x_params = {1, 0}; // {shift, zero point}
int8_t x_data[2*3] = { 2, -4, 6,
-8, 10, -12};
aitensor_t x = AITENSOR_2D_Q7(x_shape, &x_params, x_data);
uint16_t result_shape[2] = {2, 3};
aimath_q7_params_t result_params;
int8_t result_data[2*3];
aitensor_t result = AITENSOR_2D_Q7(result_shape, &result_params, result_data);
aimath_q7_default_sigmoid(&x, &result);
print_aitensor(&result);
aimath_q7_default_sigmoid
void aimath_q7_default_sigmoid(const aitensor_t *x, aitensor_t *result)
Calculates the sigmoid of each element in a Q7 tensor.

See also
  Sigmoid PLAN: https://www.researchgate.net/figure/Comparative-representation-of-the-sigmoid-function-and-PLAN-approximation_fig7_228618304

Parameters

  *x | Q7 tensor to calculate the sigmoid from (N-D tensor)
  *result | Resulting Q7 tensor (N-D tensor)

## ◆ aimath_q7_default_softmax()

void aimath_q7_default_softmax | ( | const aitensor_t * | x,
|  | aitensor_t * | result
| ) |  |

Calculates the softmax value of each batch element (row) of a Q7 tensor.

\[ result_{i} = \frac{e^{x_i}}{\sum_{j=1}^{K} e^{x_j}} \]

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:

uint16_t x_shape[2] = {2, 3};
aimath_q7_params_t x_params = {1, 0}; // {shift, zero point}
int8_t x_data[2*3] = { 2, -4, 6,
-8, 10, -12};
aitensor_t x = AITENSOR_2D_Q7(x_shape, &x_params, x_data);
uint16_t result_shape[2] = {2, 3};
aimath_q7_params_t result_params;
int8_t result_data[2*3];
aitensor_t result = AITENSOR_2D_Q7(result_shape, &result_params, result_data);
aimath_q7_default_softmax(&x, &result);
print_aitensor(&result);
aimath_q7_default_softmax
void aimath_q7_default_softmax(const aitensor_t *x, aitensor_t *result)
Calculates the softmax value of each batch element (row) of a Q7 tensor.

Parameters

  *x | Q7 tensor to calculate the softmax from (N-D tensor)
  *result | Resulting Q7 tensor (N-D tensor)

## ◆ aimath_q7_default_softsign()

void aimath_q7_default_softsign | ( | const aitensor_t * | x,
|  | aitensor_t * | result
| ) |  |

Calculates the softsign value of each element in a Q7 tensor.

\[ result_{i} = \frac {x_i} {1 + |x_i|} \]

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:

uint16_t x_shape[2] = {2, 3};
aimath_q7_params_t x_params = {1, 0}; // {shift, zero point}
int8_t x_data[2*3] = { 2, -4, 6,
-8, 10, -12};
aitensor_t x = AITENSOR_2D_Q7(x_shape, &x_params, x_data);
uint16_t result_shape[2] = {2, 3};
aimath_q7_params_t result_params;
int8_t result_data[2*3];
aitensor_t result = AITENSOR_2D_Q7(result_shape, &result_params, result_data);
aimath_q7_default_softsign(&x, &result);
print_aitensor(&result);
aimath_q7_default_softsign
void aimath_q7_default_softsign(const aitensor_t *x, aitensor_t *result)
Calculates the softsign value of each element in a Q7 tensor.

Parameters

  *x | Q7 tensor to calculate the softsign from (N-D tensor)
  *result | Resulting Q7 tensor (N-D tensor)

## ◆ aimath_q7_default_tanh()

void aimath_q7_default_tanh | ( | const aitensor_t * | x,
|  | aitensor_t * | result
| ) |  |

Calculates the tanh of each element in a Q7 tensor.

\[ result_{i} = \tanh(x_{i}) = \frac{e^{x_i} - e^{-x_i}}{e^{x_i} + e^{-x_i}} \]

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:

uint16_t x_shape[2] = {2, 3};
aimath_q7_params_t x_params = {1, 0}; // {shift, zero point}
int8_t x_data[2*3] = { 2, -4, 6,
-8, 10, -12};
aitensor_t x = AITENSOR_2D_Q7(x_shape, &x_params, x_data);
uint16_t result_shape[2] = {2, 3};
aimath_q7_params_t result_params;
int8_t result_data[2*3];
aitensor_t result = AITENSOR_2D_Q7(result_shape, &result_params, result_data);
aimath_q7_default_tanh(&x, &result);
print_aitensor(&result);
aimath_q7_default_tanh
void aimath_q7_default_tanh(const aitensor_t *x, aitensor_t *result)
Calculates the tanh of each element in a Q7 tensor.

See also
  Sigmoid PLAN: https://www.researchgate.net/figure/Comparative-representation-of-the-sigmoid-function-and-PLAN-approximation_fig7_228618304

Parameters

  *x | Q7 tensor to calculate the tanh from (N-D tensor)
  *result | Resulting Q7 tensor (N-D tensor)

## ◆ aimath_q7_default_tensor_add_different_shift()

void aimath_q7_default_tensor_add_different_shift | ( | const aitensor_t * | a,
|  | const aitensor_t * | b,
|  | aitensor_t * | result
| ) |  |

Performs an element wise addition of Q7 tensors a and b with different shifts.

\[ result = a + b \]

The tensors a, b and result can have different shifts. The function will rescale the tensors internally to perform the addition. If a, b and result have the same shift, use aimath_q7_default_tensor_add_same_shift() instead because it is more efficient.

Example:

uint16_t a_shape[2] = {2, 3};
aimath_q7_params_t a_params = {1, 0}; // {shift, zero point}
int8_t a_data[2*3] = { 2, -4, 6,
-8, 10, -12};
aitensor_t a = AITENSOR_2D_Q7(a_shape, &a_params, a_data);
uint16_t b_shape[2] = {2, 3};
aimath_q7_params_t b_params = {2, 0}; // {shift, zero point}
int8_t b_data[2*3] = { 4, -8, 12,
-16, 20, -24};
aitensor_t b = AITENSOR_2D_Q7(b_shape, &b_params, b_data);
uint16_t result_shape[2] = {2, 3};
aimath_q7_params_t result_params = {0, 0}; // {shift, zero point}
int8_t result_data[2*3];
aitensor_t result = AITENSOR_2D_Q7(result_shape, &result_params, result_data);
aimath_q7_default_tensor_add_different_shift(&a, &b, &result);
print_aitensor(&result);
aimath_q7_default_tensor_add_different_shift
void aimath_q7_default_tensor_add_different_shift(const aitensor_t *a, const aitensor_t *b, aitensor_t *result)
Performs an element wise addition of Q7 tensors a and b with different shifts.

Parameters

  *a | Q7 tensor a (N-D tensor)
  *b | Q7 tensor b (N-D tensor)
  *result | Resulting Q7 tensor of the element wise addition (N-D tensor)

## ◆ aimath_q7_default_tensor_add_same_shift()

void aimath_q7_default_tensor_add_same_shift | ( | const aitensor_t * | a,
|  | const aitensor_t * | b,
|  | aitensor_t * | result
| ) |  |

Performs an element wise addition of Q7 tensors a and b with same shifts.

\[ result = a + b \]

The tensors a, b and result must have the same shift. If a, b and result have the different shifts, use aimath_q7_default_tensor_add_different_shift() instead.

Example:

uint16_t a_shape[2] = {2, 3};
aimath_q7_params_t a_params = {1, 0}; // {shift, zero point}
int8_t a_data[2*3] = { 2, -4, 6,
-8, 10, -12};
aitensor_t a = AITENSOR_2D_Q7(a_shape, &a_params, a_data);
uint16_t b_shape[2] = {2, 3};
aimath_q7_params_t b_params = {1, 0}; // {shift, zero point}
int8_t b_data[2*3] = { 2, -4, 6,
-8, 10, -12};
aitensor_t b = AITENSOR_2D_Q7(b_shape, &b_params, b_data);
uint16_t result_shape[2] = {2, 3};
aimath_q7_params_t result_params = {1, 0}; // {shift, zero point}
int8_t result_data[2*3];
aitensor_t result = AITENSOR_2D_Q7(result_shape, &result_params, result_data);
aimath_q7_default_tensor_add_same_shift(&a, &b, &result);
print_aitensor(&result);
aimath_q7_default_tensor_add_same_shift
void aimath_q7_default_tensor_add_same_shift(const aitensor_t *a, const aitensor_t *b, aitensor_t *result)
Performs an element wise addition of Q7 tensors a and b with same shifts.

Parameters

  *a | Q7 tensor a (N-D tensor)
  *b | Q7 tensor b (N-D tensor)
  *result | Resulting Q7 tensor of the element wise addition (N-D tensor)

## ◆ aimath_q7_default_tensor_sub_different_shift()

void aimath_q7_default_tensor_sub_different_shift | ( | const aitensor_t * | a,
|  | const aitensor_t * | b,
|  | aitensor_t * | result
| ) |  |

Performs an element wise addition of Q7 tensors a and b with different shifts.

\[ result = a - b \]

The tensors a, b and result can have different shifts. The function will rescale the tensors internally to perform the subtraction. If a, b and result have the same shift, use aimath_q7_default_tensor_sub_same_shift() instead because it is more efficient.

Example:

uint16_t a_shape[2] = {2, 3};
aimath_q7_params_t a_params = {1, 0}; // {shift, zero point}
int8_t a_data[2*3] = { 2, -4, 6,
-8, 10, -12};
aitensor_t a = AITENSOR_2D_Q7(a_shape, &a_params, a_data);
uint16_t b_shape[2] = {2, 3};
aimath_q7_params_t b_params = {2, 0}; // {shift, zero point}
int8_t b_data[2*3] = { 4, 8, 12,
16, 20, 24};
aitensor_t b = AITENSOR_2D_Q7(b_shape, &b_params, b_data);
uint16_t result_shape[2] = {2, 3};
aimath_q7_params_t result_params = {0, 0}; // {shift, zero point}
int8_t result_data[2*3];
aitensor_t result = AITENSOR_2D_Q7(result_shape, &result_params, result_data);
aimath_q7_default_tensor_sub_different_shift(&a, &b, &result);
print_aitensor(&result);
aimath_q7_default_tensor_sub_different_shift
void aimath_q7_default_tensor_sub_different_shift(const aitensor_t *a, const aitensor_t *b, aitensor_t *result)
Performs an element wise addition of Q7 tensors a and b with different shifts.

Parameters

  *a | Q7 tensor a (N-D tensor)
  *b | Q7 tensor b (N-D tensor)
  *result | Resulting Q7 tensor of the element wise subtraction (N-D tensor)

## ◆ aimath_q7_default_tensor_sub_same_shift()

void aimath_q7_default_tensor_sub_same_shift | ( | const aitensor_t * | a,
|  | const aitensor_t * | b,
|  | aitensor_t * | result
| ) |  |

Performs an element wise subtraction of Q7 tensors a and b with same shifts.

\[ result = a - b \]

The tensors a, b and result must have the same shift. If a, b and result have the different shifts, use aimath_q7_default_tensor_sub_different_shift() instead.

Example:

uint16_t a_shape[2] = {2, 3};
aimath_q7_params_t a_params = {1, 0}; // {shift, zero point}
int8_t a_data[2*3] = { 2, -4, 6,
-8, 10, -12};
aitensor_t a = AITENSOR_2D_Q7(a_shape, &a_params, a_data);
uint16_t b_shape[2] = {2, 3};
aimath_q7_params_t b_params = {1, 0}; // {shift, zero point}
int8_t b_data[2*3] = { 2, 4, 6,
8, 10, 12};
aitensor_t b = AITENSOR_2D_Q7(b_shape, &b_params, b_data);
uint16_t result_shape[2] = {2, 3};
aimath_q7_params_t result_params = {1, 0}; // {shift, zero point}
int8_t result_data[2*3];
aitensor_t result = AITENSOR_2D_Q7(result_shape, &result_params, result_data);
aimath_q7_default_tensor_sub_same_shift(&a, &b, &result);
print_aitensor(&result);
aimath_q7_default_tensor_sub_same_shift
void aimath_q7_default_tensor_sub_same_shift(const aitensor_t *a, const aitensor_t *b, aitensor_t *result)
Performs an element wise subtraction of Q7 tensors a and b with same shifts.

Parameters

  *a | Q7 tensor a (N-D tensor)
  *b | Q7 tensor b (N-D tensor)
  *result | Resulting Q7 tensor of the element wise subtraction (N-D tensor)

## ◆ aimath_q7_default_transpose_matrix()

void aimath_q7_default_transpose_matrix | ( | aitensor_t * | x | ) |

Transpose a Q7 tensor.

\[ x \leftarrow x^T \]

Example:

uint16_t x_shape[2] = {2, 3};
aimath_q7_params_t x_params = {1, 0}; // {shift, zero point}
int8_t x_data[2*3] = { 2, -4, 6,
-8, 10, -12};
aitensor_t x = AITENSOR_2D_Q7(x_shape, &x_params, x_data);
aimath_q7_default_transpose_matrix(&x);
print_aitensor(&x);
aimath_q7_default_transpose_matrix
void aimath_q7_default_transpose_matrix(aitensor_t *x)
Transpose a Q7 tensor.

Parameters

  *x | Q7 tensor to be transposed (2D tensor)

## ◆ aimath_q7_default_transpose_vector()

void aimath_q7_default_transpose_vector | ( | aitensor_t * | vector | ) |

Transposes a Q7 vector.

The given tensor must be a vector (2D tensor of shape [1 x N] or [N x 1]).

\[ vector \leftarrow vector^T \]

Example:

uint16_t vector_shape[2] = {1, 3};
aimath_q7_params_t vector_params = {1, 0}; // {shift, zero point}
int8_t vector_data[2*3] = { 2, -4, 6};
aitensor_t vector = AITENSOR_2D_Q7(vector_shape, &vector_params, vector_data);
aimath_q7_default_transpose_vector(&vector);
print_aitensor(&vector);
aimath_q7_default_transpose_vector
void aimath_q7_default_transpose_vector(aitensor_t *vector)
Transposes a Q7 vector.

Parameters

  *vector | Q7 vector (2D tensor of shape [1 x N] or [N x 1])

## ◆ aimath_q7_default_zero_tensor()

void aimath_q7_default_zero_tensor | ( | aitensor_t * | tensor | ) |

Fills a Q7 tensor with zeros.

\[ tensor_{i} = 0 \]

The function sets all tensor elements to the zero_point given in the tensor parameters.

Example:

uint16_t tensor_shape[2] = {2, 3};
aimath_q7_params_t tensor_params = {1, 0}; // {shift, zero point}
int8_t tensor_data[2*3] = { 2, -4, 6,
-8, 10, -12};
aitensor_t tensor = AITENSOR_2D_Q7(tensor_shape, &tensor_params, tensor_data);
aimath_q7_default_zero_tensor(&tensor);
print_aitensor(&tensor);
aimath_q7_default_zero_tensor
void aimath_q7_default_zero_tensor(aitensor_t *tensor)
Fills a Q7 tensor with zeros.

Parameters

  *tensor | Q7 tensor to set to zero (N-D tensor)