path: root/chapters/tensor_ops.adoc

//
// This confidential and proprietary software may be used only as
// authorised by a licensing agreement from ARM Limited
// (C) COPYRIGHT 2020-2022 ARM Limited
// ALL RIGHTS RESERVED
// The entire notice above must be reproduced on all authorised
// copies and copies may only be made to the extent permitted
// by a licensing agreement from ARM Limited.

=== Tensor Operators

==== ARGMAX

This returns the index with the largest value across the given axis of the input tensor.

include::{generated}/operators/ARGMAX.adoc[]

[source,c++]
----
ERROR_IF(axis < 0 || axis >= rank(shape1) || rank(shape1) > 4);
if (axis == 0) {
    left_shape = [];
} else {
    left_shape = shape1[0:axis - 1];
}
if (axis == rank(shape1)-1) {
    right_shape = [];
} else {
    right_shape = shape1[axis+1:rank(shape1) - 1];
}
ERROR_IF(flatten(left_shape, right_shape) != shape);
for_each(left_index in left_shape) {
    for_each(right_index in right_shape) {
        in_t max_value = minimum_value<in_t>;
        out_t max_index = 0;
        for (i = 0; i < shape[axis]; i++) {
            dim_t index = flatten(left_index, [i], right_index);
            in_t value = tensor_read<in_t>(input, shape1, index);
            if (value > max_value) { max_value = value; max_index = i; }
        }
        dim_t index = flatten(left_index, right_index);
        tensor_write<out_t>(output, shape, index, max_index);
    }
}
----

==== AVG_POOL2D

This performs an average pooling over the given input tensor.
A sliding window of size given by <kernel size> is passed over the input tensor, with the mean value being placed in the output tensor.
When calculating the average, only the number of valid input tensor values, but not padding, are used to calculate the divisor.

include::{generated}/operators/AVG_POOL2D.adoc[]

[source,c++]
----
ERROR_IF(in_out_t != int8_t && input_zp != 0); // Zero point only for int8_t
ERROR_IF(in_out_t != int8_t && output_zp != 0); // Zero point only for int8_t
ERROR_IF(kernel_y < 1 || kernel_x < 1); // kernel size must be >= 1
ERROR_IF(stride_y < 1 || stride_x < 1);
ERROR_IF(pad_top < 0 || pad_bottom < 0 || pad_left < 0 || pad_right < 0);
// Padding must be less than kernel size to avoid
// a divide-by-zero.
ERROR_IF(pad_right >= kernel_x || pad_left >= kernel_x);
ERROR_IF(pad_top >= kernel_y || pad_bottom >= kernel_y);
ERROR_IF(OH != idiv_check(IH + pad_top + pad_bottom - kernel_y, stride_y) + 1);
ERROR_IF(OW != idiv_check(IW + pad_left + pad_right - kernel_x, stride_x) + 1);

for_each(0 <= n < N, 0 <= oy < OH, 0 <= ox < OW, 0 <= c < C ) {
    in_out_t output_val;
    acc_t acc = 0;
    int count = 0;
    index_t iy = oy * stride_y - pad_top;
    index_t ix = ox * stride_x - pad_left;
    for_each(0 <= ky < kernel_y, 0 <= kx < kernel_x) {
        index_t y = iy + ky;
        index_t x = ix + kx;
        // Only values from the input tensor are used to calculate the
        // average, padding does not count
        if (0 <= y < IH and 0 <= x < IW) {
            count++;
            acc_t value = tensor_read<in_out_t>(input, [N,IH,IW,C], [n,y,x,c]);
            value = value - input_zp;
            acc = apply_add<acc_t>(acc, value);
        }
    }
    if (is_float(in_out_t)) {
        output_val = acc / (float)count;
    } else {
        scale_t scale = reciprocal_scale(count);
        acc = apply_scale_32(acc, scale.multiplier, scale.shift, false);
        output_val = (in_out_t)apply_clip<acc_t>(acc + output_zp, minimum<in_out_t>, maximum<in_out_t>)
    }
    tensor_write<in_out_t>(output, [N,OH,OW,C], [n,oy,ox,c], output_val);
}
----

==== CONV2D

Performs a 2D convolution over the given tensor input, using the weight tensor.

include::{generated}/operators/CONV2D.adoc[]

[source,c++]
----
ERROR_IF(in_t != int8_t && input_zp != 0); // Zero point only for int8_t
ERROR_IF(weight_t != int8_t && weight_zp != 0);
ERROR_IF(pad_top < 0 || pad_bottom < 0 || pad_left < 0 || pad_right < 0);
ERROR_IF(stride_y < 1 || stride_x < 1);
ERROR_IF(dilation_y < 1 || dilation_x < 1);
ERROR_IF(OH != idiv_check(IH - 1 + pad_top + pad_bottom - (KH - 1) * dilation_y, stride_y) + 1);
ERROR_IF(OW != idiv_check(IW - 1 + pad_left + pad_right - (KW - 1) * dilation_x, stride_x) + 1);

pad = flatten([0,0], pad, [0,0]);
for_each(0 <= n < N, 0 <= oy < OH, 0 <= ox < OW; 0 <= oc < OC) {
    out_t acc = 0;
    index_t iy = oy * stride_y - pad_top;
    index_t ix = ox * stride_x - pad_left;
    for_each(0 <= ky < KH, 0 <= kx < KW, 0 <= ic < IC) {
        index_t y = iy + ky * dilation_y;
        index_t x = ix + kx * dilation_x;
        if (0 <= y < IH && 0 <= x < IW) {
            out_t value  = tensor_read<in_t>(input, [N,IH,IW,IC], [n,y,x,ic]);
            out_t weight = tensor_read<weight_t>(weight, [OC,KH,KW,IC], [oc,ky,kx,ic]);
            value  = value - input_zp;
            weight = weight - weight_zp;
            acc = apply_add<out_t>(acc, value * weight);
        }
    }
    acc = apply_add<out_t>(acc, bias[oc]);
    tensor_write<out_t>(output, [N,OH,OW,OC], [n,oy,ox,oc], acc);
}
----

==== CONV3D

Performs a 3D convolution over the given input tensor.

include::{generated}/operators/CONV3D.adoc[]

[source,c++]
----
ERROR_IF(in_t != int8_t && input_zp != 0); // Zero point only for int8_t
ERROR_IF(weight_t != int8_t && weight_zp != 0);
ERROR_IF(pad_d0 < 0 || pad_d1 < 0 || pad_top < 0 || pad_bottom < 0 || pad_left < 0 || pad_right < 0);
ERROR_IF(stride_d < 1 || stride_y < 1 || stride_x < 1);
ERROR_IF(dilation_d < 1 || dilation_y < 1 || dilation_x < 1);
ERROR_IF(OD != idiv_check(ID - 1 + pad_d0 + pad_d1      - (KD - 1) * dilation_d, stride_d) + 1);
ERROR_IF(OH != idiv_check(IH - 1 + pad_top + pad_bottom - (KH - 1) * dilation_y, stride_y) + 1);
ERROR_IF(OW != idiv_check(IW - 1 + pad_left + pad_right - (KW - 1) * dilation_x, stride_x) + 1);

pad = flatten([0,0], pad, [0,0]);
for_each(0 <= n < N, 0 <= od < OD, 0 <= oy < OH, 0 <= ox < OW; 0 <= oc < OC) {
    out_t acc = 0;
    index_t id = od * stride_d - pad_d0;
    index_t iy = oy * stride_y - pad_top;
    index_t ix = ox * stride_x - pad_left;
    for_each(0 <= kd < KD, 0 <= ky < KH, 0 <= kx < KW, 0 <= ic < IC) {
        index_t d = id + kd * dilation_d;
        index_t y = iy + ky * dilation_y;
        index_t x = ix + kx * dilation_x;
        if (0 <= x < IW && 0 <= y < IH && 0 <= d < ID) {
            out_t value  = tensor_read<in_t>(input, [N,ID,IH,IW,IC], [n,d,y,x,ic]);
            out_t weight = tensor_read<weight_t>(weight,[OC,KD,KH,KW,IC],[oc,kd,ky,kx,ic]);
            value  = value - input_zp;
            weight = weight - weight_zp;
            acc = apply_add<out_t>(acc, value * weight);
        }
    }
    acc = apply_add<out_t>(acc, bias[oc]);
    tensor_write<out_t>(output, [N,OD,OH,OW,OC], [n,od,oy,ox,oc], acc);
}
----

==== DEPTHWISE_CONV2D

Performs 2D convolutions separately over each channel of the given tensor input, using the weight tensor.

include::{generated}/operators/DEPTHWISE_CONV2D.adoc[]

[source,c++]
----
ERROR_IF(in_t != int8_t && input_zp != 0); // Zero point only for int8_t
ERROR_IF(weight_t != int8_t && weight_zp != 0);
ERROR_IF(pad_top < 0 || pad_bottom < 0 || pad_left < 0 || pad_right < 0);
ERROR_IF(stride_y < 1 || stride_x < 1);
ERROR_IF(dilation_y < 1 || dilation_x < 1);
ERROR_IF(OH != idiv_check(IH - 1 + pad_top + pad_bottom - (KH - 1) * dilation_y, stride_y) + 1);
ERROR_IF(OW != idiv_check(IW - 1 + pad_left + pad_right - (KW - 1) * dilation_x, stride_x) + 1);

pad = flatten([0,0], pad, [0,0]);
for_each(0 <= n < N, 0 <= oy < OH, 0 <= ox < OW; 0 <= c < C, 0 <= m < M) {
    out_t acc = 0;
    index_t iy = oy * stride_y - pad_top;
    index_t ix = ox * stride_x - pad_left;
    for_each(0 <= ky < KH, 0 <= kx < KW) {
        index_t y = iy + ky * dilation_y;
        index_t x = ix + kx * dilation_x;
        if (0 <= y < IH && 0 <= x < IW) {
            out_t value  = tensor_read<in_t>(input, [N,IH,IW,C], [n,y,x,c]);
            out_t weight = tensor_read<weight_t>(weight, [KH,KW,C,M], [ky,kx,c,m]);
            value  = value - input_zp;
            weight = weight - weight_zp;
            acc = apply_add<out_t>(acc, value * weight);
        }
    }
    acc = apply_add<out_t>(acc, bias[(c * M) + m]);
    tensor_write<out_t>(output, [N,OH,OW,C * M], [n,oy,ox,c * M + m], acc);
}
----

==== FFT2D

Performs a batched complex 2D Fast Fourier Transform over the input.
The complex input values are constructed from the corresponding values in the input_real and input_imag tensors.
The resulting values in the output are split into the output_real and output_imag tensors.
No normalization is applied on either the forward or inverse versions of the operation.

// output[h][w] = \sum_{m=0}^{H-1}\sum_{n=0}^{W-1}input[m][n] * \exp\left(-2\pi i\left(\frac{mh}{H} + \frac{nw}{W}\right)\right)

.Calculation for the forward FFT2D calculation (inverse=false)
image::forward_fft2d.svg["forward FFT definition", align="center"]

// output[h][w] = \sum_{m=0}^{H-1}\sum_{n=0}^{W-1}input[m][n] * \exp\left(2\pi i\left(\frac{mh}{H} + \frac{nw}{W}\right)\right)

.Calculation for the inverse FFT2D calculation (inverse=true)
image::inverse_fft2d.svg["inverse FFT definition", align="center"]

include::{generated}/operators/FFT2D.adoc[]

[source,c++]
----
ERROR_IF(!power_of_two(H));
ERROR_IF(!power_of_two(W));

float sign_val = 1.0;

if (inverse) {
    sign_val = -1.0;
}

for_each(0 <= n < N, 0 <= oy < H, 0 <= ox < W) {
    in_out_t sum_real = 0.0;
    in_out_t sum_imag = 0.0;
    for_each(0 <= iy < H, 0 <= ix < W) {
        in_out_t val_real = tensor_read<in_out_t>(input_real, [N,H,W], [n,iy,ix]);
        in_out_t val_imag = tensor_read<in_out_t>(input_imag, [N,H,W], [n,iy,ix]);
        float_t a = sign_val * 2 * pi() * ((iy * oy) / H + (ix * ox) / W);
        sum_real += val_real * cos(a) + val_imag * sin(a);
        sum_imag += -val_real * sin(a) + val_imag * cos(a);
    }
    tensor_write<in_out_t>(output_real, [N,H,W], [n,oy,ox], sum_real);
    tensor_write<in_out_t>(output_imag, [N,H,W], [n,oy,ox], sum_imag);
}
----

==== FULLY_CONNECTED

Performs a fully connected network.

include::{generated}/operators/FULLY_CONNECTED.adoc[]

[source,c++]
----
ERROR_IF(in_t != int8_t && input_zp != 0); // Zero point only for int8_t
ERROR_IF(weight_t != int8_t && weight_zp != 0);
for_each(0 <= n < N, 0 <= oc < OC) {
    out_t acc = 0;
    for_each(0 <= ic < IC) {
        out_t value  = tensor_read<in_t>(input, [N,IC], [n,ic]);
        out_t weight = tensor_read<weight_t>(weight, [OC,IC], [oc,ic]);
        value  = value - input_zp;
        weight = weight - weight_zp;
        acc = apply_add<out_t>(acc, value * weight);
    }
    acc = apply_add<out_t>(acc, bias[oc]);
    tensor_write<out_t>(output, [N,OC], [n,oc], acc);
}
----

==== MATMUL

Performs two dimensional matrix multiplications. This allows both inputs to be activations, rather than reserving weights as an attribute in the FULLY_CONNECTED operator.

include::{generated}/operators/MATMUL.adoc[]

[source,c++]
----
ERROR_IF(in_t != int8_t && (A_zp != 0 || B_zp != 0)); // Zero point only for int8_t
for_each(0 <= n < N, 0 <= h < H, 0 <= w < W) {
    out_t acc = 0;
    for_each(0 <= c < C) {
        out_t value1 = tensor_read<in_t>(A, [N,H,C], [n,h,c]);
        out_t value2 = tensor_read<in_t>(B, [N,C,W], [n,c,w]);
        value1 = value1 - A_zp;
        value2 = value2 - B_zp;
        acc = apply_add<out_t>(acc, value1 * value2);
    }
    tensor_write<out_t>(output, [N,H,W], [n,h,w], acc);
}
----

==== MAX_POOL2D

This performs a max pooling over the given input tensor. A sliding window of size given by <kernel size> is passed over the input tensor, with the maximum value being placed in the output tensor.

include::{generated}/operators/MAX_POOL2D.adoc[]

[source,c++]
----
ERROR_IF(kernel_y < 1 || kernel_x < 1); // kernel size must be >= 1
ERROR_IF(stride_y < 1 || stride_x < 1);
ERROR_IF(pad_top < 0 || pad_bottom < 0 || pad_left < 0 || pad_right < 0);
// Padding must be less than kernel size, otherwise no
// input values will be used.
ERROR_IF(pad_right >= kernel_x || pad_left >= kernel_x);
ERROR_IF(pad_top >= kernel_y || pad_bottom >= kernel_y);
ERROR_IF(OH != idiv_check(IH + pad_top + pad_bottom - kernel_y, stride_y) + 1);
ERROR_IF(OW != idiv_check(IW + pad_left + pad_right - kernel_x, stride_x) + 1);

for_each(0 <= n < N, 0 <= oy < H, 0 <= ox < W, 0 <= c < C ) {
    in_out_t acc = minimum_value<in_out_t>;
    index_t iy = oy * stride_y - pad_top;
    index_t ix = ox * stride_x - pad_left;
    for_each( 0 <= ky < kernel_y, 0 <= kx < kernel_x ) {
        index_t y = iy + ky;
        index_t x = ix + kx;
        if (y >= 0 && y < IH && x >= 0 && x < IW) {
            in_out_t value = tensor_read<in_out_t>(input, [N,IH,IW,C], [n,y,x,c]);
            acc = apply_max(acc, value);
        }
    }
    tensor_write<in_out_t>(output, [N,OH,OW,C], [n,oy,ox,c], acc);
}
----

==== RFFT2D

Performs a batched 2D real-valued Fast Fourier Transform over the input where the input tensor consists of real values producing complex valued output.
The complex output values will be split into the output_real and output_imag tensor arguments.
RFFT2D takes advantage of Hermitian symmetry to only calculate the first half of the output.
Imaginary values with locations h=0,H/2 or w=0,W/2 are zero.

image::forward_fft2d.svg["forward FFT definition", align="center"]

include::{generated}/operators/RFFT2D.adoc[]

[source,c++]
----
ERROR_IF(!power_of_two(H));
ERROR_IF(!power_of_two(W));

for_each(0 <= n < N, 0 <= oy < H/2 + 1, 0 <= ox < W/2 + 1) {
    in_out_t sum_real = 0.0;
    in_out_t sum_imag = 0.0;
    for_each(0 <= iy < H, 0 <= ix < W) {
        in_out_t val_real = tensor_read<in_out_t>(input_real, [N,H,W], [n,iy,ix]);
        float_t a = 2 * pi() * ((iy * oy) / H + (ix * ox) / W);
        sum_real += val_real * cos(a);
        sum_imag += -val_real * sin(a);
    }
    tensor_write<in_out_t>(output_real, [N,H,W], [n,oy,ox], sum_real);
    tensor_write<in_out_t>(output_imag, [N,H,W], [n,oy,ox], sum_imag);
}
----

==== TRANSPOSE_CONV2D

Performs a 2D transposed convolution over the given tensor input, using the weights tensor.

include::{generated}/operators/TRANSPOSE_CONV2D.adoc[]

[source,c++]
----
ERROR_IF(in_t != int8_t  && input_zp != 0); // Zero point only allowed for int8_t
ERROR_IF(weight_t != int8_t && weight_zp != 0);
ERROR_IF(out_pad_top <= -KH || out_pad_bottom <= -KH);
ERROR_IF(out_pad_left <= -KW || out_pad_right <= -KW);
ERROR_IF(stride_y < 1 || stride_x < 1);
ERROR_IF(OH != (IH - 1) * stride_y + out_pad_top + out_pad_bottom + KH);
ERROR_IF(OW != (IW - 1) * stride_x + out_pad_left + out_pad_right + KW);

for_each(index in out_shape) {
    tensor_write<out_t>(output, [N,OH,OW,OC], index, bias[index[3]])
}
for_each(0 <= n < N, 0 <= iy < IH, 0 <= ix < IW, 0 <= oc < OC,
          0 <= ic < IC, 0 <= ky < KH,  0 <= kx < KW) {
    index_t oy = iy * stride_y + out_pad_top + ky;
    index_t ox = ix * stride_x + out_pad_left + kx;
    if (oy >= 0 && oy < OH && ox >= 0 && ox < OW) {
        out_t acc = tensor_read<out_t>(output, [N,OH,OW,OC], [n,oy,ox,oc]);
        out_t value = tensor_read<in_t>(input, [N,IH,IW,IC], [n,iy,ix,ic]);
        out_t weight = tensor_read<weight_t>(weight, [OC,KH,KW,IC], [oc,ky,kx,ic]);
        value = value - input_zp;
        weight = weight - weight_zp;
        acc = apply_add<out_t>(acc, value * weight);
        tensor_write<out_t>(output, [N,OH,OW,OC], [n,oy,ox,oc], acc);
    }
}
----