path: root/chapters/ewise_binary.adoc

//
// This confidential and proprietary software may be used only as
// authorised by a licensing agreement from ARM Limited
// (C) COPYRIGHT 2020-2021 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.

=== Elementwise Binary Operators

==== ADD

Elementwise addition of input1 and input2.
Axis of size 1 will be broadcast, as necessary. Rank of input tensors must match.

*Arguments:*

|===
|Argument|Type|Name|Shape|Description

|Input|in_t*|input1|shape1|Input tensor
|Input|in_t*|input2|shape2|Input tensor with the same rank as input1
|Output|in_t*|output|shape|Output tensor with broadcast shape if necessary
|===

*Operation Function:*

[source,c]
----
for_each (index in shape) {
    index1 = apply_broadcast(shape, shape1, index)
    index2 = apply_broadcast(shape, shape2, index)
    in_t value1 = tensor_read<in_t>(input1, shape1, index1)
    in_t value2 = tensor_read<in_t>(input2, shape2, index2)
    in_t acc = apply_add<in_t>(value1, value2)
    tensor_write<in_t>(output, shape, index, acc)
}
----

*Supported Data Types:*

|===
|Profile|Mode|in_t

|Any|signed 32|int32
|MI, MT|float|float
|===

==== ARITHMETIC_RIGHT_SHIFT

Elementwise arithmetic right shift of input1 by the amount specified in input2.
Axis of size 1 will be broadcast, as necessary. Rank of input tensors must match.

*Arguments:*

|===
|Argument|Type|Name|Shape|Description

|Input|in_t*|input1|shape1|Input tensor
|Input|in_t*|input2|shape2|Input tensor with the same rank as input1
|Input|bool |round |- | If true then the shift is rounded
|Output|in_t*|output|shape|Output tensor with broadcast shape if necessary
|===

*Operation Function:*

[source,c]
----
for_each (index in shape) {
    index1 = apply_broadcast(shape, shape1, index)
    index2 = apply_broadcast(shape, shape2, index)
    in_t value1 = tensor_read<in_t>(input1, shape1, index1)
    in_t value2 = tensor_read<in_t>(input2, shape2, index2)
    assert(0 <= value2 && value2 <= 31)
    in_t acc = value1 >> value2
    if (round==true && value2>0 && (value1>>(value2-1))&1!=0) {
        acc = acc + 1;
    }
    acc = apply_clip(acc, minimum<in_t>, maximum<in_t>)
    tensor_write<in_t>(output, shape, index, acc)
}
----

*Supported Data Types:*

|===
|Profile|Mode|in_t

|Any|signed 8|int8
|Any|signed 16|int16
|Any|signed 32|int32
|===

==== BITWISE_AND

Elementwise bitwise AND of input1 and input2.
Axis of size 1 will be broadcast as necessary. Rank of input tensors must match.

*Arguments:*

|===
|Argument|Type|Name|Shape|Description

|Input|in_t*|input1|shape1|Input tensor
|Input|in_t*|input2|shape2|Input tensor with the same rank as input1
|Output|in_t*|output|shape|Output tensor of same type as the input tensors, with broadcast shape if necessary
|===

*Operation Function:*

[source,c]
----
for_each (index in shape) {
    index1 = apply_broadcast(shape, shape1, index)
    index2 = apply_broadcast(shape, shape2, index)
    in_t value1 = tensor_read<in_t>(input1, shape1, index1)
    in_t value2 = tensor_read<in_t>(input2, shape2, index2)
    in_t acc = value1 & value2
    tensor_write<in_t>(output, shape, index, acc)
}
----

*Supported Data Types:*

|===
|Profile|Mode|in_t

|Any|signed 8|int8
|Any|signed 16|int16
|Any|signed 32|int32
|===

==== BITWISE_OR

Elementwise bitwise OR of input1 and input2.
Axis of size 1 will be broadcast as necessary. Rank of input tensors must match.

*Arguments:*

|===
|Argument|Type|Name|Shape|Description

|Input|in_t*|input1|shape1|Input tensor
|Input|in_t*|input2|shape2|Input tensor with the same rank as input1
|Output|in_t*|output|shape|Output tensor with broadcast shape if necessary
|===

*Operation Function:*

[source,c]
----
for_each (index in shape) {
    index1 = apply_broadcast(shape, shape1, index)
    index2 = apply_broadcast(shape, shape2, index)
    in_t value1 = tensor_read<in_t>(input1, shape1, index1)
    in_t value2 = tensor_read<in_t>(input2, shape2, index2)
    in_t acc = value1 | value2
    tensor_write<in_t>(output, shape, index, acc)
}
----

*Supported Data Types:*

|===
|Profile|Mode|in_t

|Any|signed 8|int8
|Any|signed 16|int16
|Any|signed 32|int32
|===

==== BITWISE_XOR

Elementwise bitwise XOR of input1 and input2.
Axis of size 1 will be broadcast as necessary. Rank of input tensors must match.

*Arguments:*

|===
|Argument|Type|Name|Shape|Description

|Input|in_t*|input1|shape1|Input tensor
|Input|in_t*|input2|shape2|Input tensor with the same rank as input1
|Output|in_t*|output|shape|Output tensor with broadcast shape if necessary
|===

*Operation Function:*

[source,c]
----
for_each (index in shape) {
    index1 = apply_broadcast(shape, shape1, index)
    index2 = apply_broadcast(shape, shape2, index)
    in_t value1 = tensor_read<in_t>(input1, shape1, index1)
    in_t value2 = tensor_read<in_t>(input2, shape2, index2)
    in_t acc = value1 ^ value2
    tensor_write<in_t>(output, shape, index, acc)
}
----

*Supported Data Types:*

|===
|Profile|Mode|in_t

|Any|signed 8|int8
|Any|signed 16|int16
|Any|signed 32|int32
|===

==== LOGICAL_AND

Elementwise logical AND of input1 and input2.
Axis of size 1 will be broadcast, as necessary. Rank of input tensors must match.

*Arguments:*

|===
|Argument|Type|Name|Shape|Description

|Input|in_t*|input1|shape1|Input tensor
|Input|in_t*|input2|shape2|Input tensor with the same rank as input1
|Output|in_t*|output|shape|Output tensor with broadcast shape if necessary
|===

*Quantization Parameters:*

None

*Operation Function:*

[source,c]
----
for_each (index in shape) {
    index1 = apply_broadcast(shape, shape1, index)
    index2 = apply_broadcast(shape, shape2, index)
    in_t value1 = tensor_read<in_t>(input1, shape1, index1)
    in_t value2 = tensor_read<in_t>(input2, shape2, index2)
    in_t acc = value1 && value2
    tensor_write<in_t>(output, shape, index, acc)
}
----

*Supported Data Types:*

|===
|Profile|Mode|in_t

|Any|Bool|Bool
|===

==== LOGICAL_LEFT_SHIFT

Elementwise left shift of input1 and input2.
Axis of size 1 will be broadcast, as necessary. Rank of input tensors must match.

*Arguments:*

|===
|Argument|Type|Name|Shape|Description

|Input|in_t*|input1|shape1|Input tensor
|Input|in_t*|input2|shape2|Input tensor with the same rank as input1
|Output|in_t*|output|shape|Output tensor with broadcast shape if necessary
|===

*Operation Function:*

[source,c]
----
for_each (index in shape) {
    index1 = apply_broadcast(shape, shape1, index)
    index2 = apply_broadcast(shape, shape2, index)
    in_t value1 = tensor_read<in_t>(input1, shape1, index1)
    in_t value2 = tensor_read<in_t>(input2, shape2, index2)
    assert(0 <= value2 && value2 <= 31)
    in_t acc = value1 << value2
    tensor_write<in_t>(output, shape, index, acc)
}
----

*Supported Data Types:*

|===
|Profile|Mode|in_t

|Any|signed 8|int8
|Any|signed 16|int16
|Any|signed 32|int32
|===

==== LOGICAL_RIGHT_SHIFT

Elementwise logical right shift of input1 by the amount specified in input2.
Axis of size 1 will be broadcast, as necessary. Rank of input tensors must match.

*Arguments:*

|===
|Argument|Type|Name|Shape|Description

|Input|in_t*|input1|shape1|Input tensor
|Input|in_t*|input2|shape2|Input tensor with the same rank as input1
|Output|in_t*|output|shape|Output tensor with broadcast shape if necessary
|===

*Operation Function:*

[source,c]
----
for_each (index in shape) {
    index1 = apply_broadcast(shape, shape1, index)
    index2 = apply_broadcast(shape, shape2, index)
    in_t value1 = tensor_read<in_t>(input1, shape1, index1)
    in_t value2 = tensor_read<in_t>(input2, shape2, index2)
    assert(0 <= value2 && value2 <= 31)
    in_t acc = (unsigned in_t)value1 >> value2
    tensor_write<in_t>(output, shape, index, acc)
}
----

*Supported Data Types:*

|===
|Profile|Mode|in_t

|Any|signed 8|int8
|Any|signed 16|int16
|Any|signed 32|int32
|===

==== LOGICAL_OR

Elementwise logical OR of input1 and input2.
Axis of size 1 will be broadcast as necessary. Rank of input tensors must match.

*Arguments:*

|===
|Argument|Type|Name|Shape|Description

|Input|in_t*|input1|shape1|Input tensor
|Input|in_t*|input2|shape2|Input tensor with the same rank as input1
|Output|in_t*|output|shape|Output tensor with broadcast shape if necessary
|===

*Operation Function:*

[source,c]
----
for_each (index in shape) {
    index1 = apply_broadcast(shape, shape1, index)
    index2 = apply_broadcast(shape, shape2, index)
    in_t value1 = tensor_read<in_t>(input1, shape1, index1)
    in_t value2 = tensor_read<in_t>(input2, shape2, index2)
    in_t acc = value1 || value2
    tensor_write<in_t>(output, shape, index, acc)
}
----

*Supported Data Types:*

|===
|Profile|Mode|in_t

|Any|Bool|Bool
|===

==== LOGICAL_XOR

Elementwise logical XOR of input1 and input2.
Axis of size 1 will be broadcast as necessary. Rank of input tensors must match.

*Arguments:*

|===
|Argument|Type|Name|Shape|Description

|Input|in_t*|input1|shape1|Input tensor from 1 to 4 dims
|Input|in_t*|input2|shape2|Input tensor with the same rank as input1
|Output|in_t*|output|shape|Output tensor of same type as the input tensors, with broadcast shape if necessary
|===

*Operation Function:*

[source,c]
----
for_each (index in shape) {
    index1 = apply_broadcast(shape, shape1, index)
    index2 = apply_broadcast(shape, shape2, index)
    in_t value1 = tensor_read<in_t>(input1, shape1, index1)
    in_t value2 = tensor_read<in_t>(input2, shape2, index2)
    in_t acc = value1 != value2
    tensor_write<in_t>(output, shape, index, acc)
}
----

*Supported Data Types:*

|===
|Profile|Mode|in_t

|Any|Bool|Bool
|===

==== MAXIMUM

Elementwise max of input1 and input2.
Axis of size 1 will be broadcast, as necessary. Rank of input tensors must match.

*Arguments:*

|===
|Argument|Type|Name|Shape|Description

|Input|in_t*|input1|shape1|Input tensor
|Input|in_t*|input2|shape2|Input tensor with the same rank as input1
|Output|in_t*|output|shape|Output tensor with broadcast shape if necessary
|===

*Operation Function:*

[source,c]
----
for_each (index in shape) {
    index1 = apply_broadcast(shape, shape1, index)
    index2 = apply_broadcast(shape, shape2, index)
    in_t value1 = tensor_read<in_t>(input1, shape1, index1)
    in_t value2 = tensor_read<in_t>(input2, shape2, index2)
    in_t acc = apply_max(value1, value2)
    tensor_write<in_t>(output, shape, index, acc)
}
----

*Supported Data Types:*

|===
|Profile|Mode|in_t

|Any|signed 32|int32
|MI, MT|float|float
|===

==== MINIMUM

Elementwise minimum of input1 and input2.
Axis of size 1 will be broadcast, as necessary. Rank of input tensors must match.

*Arguments:*

|===
|Argument|Type|Name|Shape|Description

|Input|in_t*|input1|shape1|Input tensor
|Input|in_t*|input2|shape2|Input tensor with the same rank as input1
|Output|in_t*|output|shape|Output tensor with broadcast shape if necessary
|===

*Operation Function:*

[source,c]
----
for_each (index in shape) {
    index1 = apply_broadcast(shape, shape1, index)
    index2 = apply_broadcast(shape, shape2, index)
    in_t value1 = tensor_read<in_t>(input1, shape1, index1)
    in_t value2 = tensor_read<in_t>(input2, shape2, index2)
    in_t acc = apply_min(value1, value2)
    tensor_write<in_t>(output, shape, index, acc)
}
----

*Supported Data Types:*

|===
|Profile|Mode|in_t

|Any|signed 32|int32
|MI, MT|float|float
|===

==== MUL

Elementwise multiplication (Hadamard product) of input1 and input2.
Axis of size 1 will be broadcast, as necessary. Rank of input tensors must match.

*Arguments:*

|===
|Argument|Type|Name|Shape|Description

|Input|in_t*|input1|shape1|Input tensor
|Input|in_t*|input2|shape2|Input tensor with the same rank as input1
|Input (MT profile) Attribute (BI/MI profiles)|uint6_t|shift|-|Result right shift (int32 data type only)
|Output|out_t*|output|shape|Output tensor with broadcast shape if necessary
|===

*Operation Function:*

[source,c]
----
assert(in_t==int32_t || shift==0);
for_each (index in shape) {
    index1 = apply_broadcast(shape, shape1, index)
    index2 = apply_broadcast(shape, shape2, index)
    in_t value1 = tensor_read<in_t>(input1, shape1, index1)
    in_t value2 = tensor_read<in_t>(input2, shape2, index2)
    if (shift>0) {
        out_t acc = apply_scale_32(value1, value2, shift)
    } else {
        out_t acc = value1 * value2;  // low 32-bits of result for int32_t
    }
    tensor_write<out_t>(output, shape, index, acc)
}
----

*Supported Data Types:*
|===
|Profile|Mode|in_t|out_t

|Any|signed 8|int8|int32
|Any|signed 16|int16|int32
|Any|signed 32|int32|int32
|MI, MT|float|float|float
|===

==== POW

Elementwise input1 value raised to the power of input2.
Axis of size 1 will be broadcast, as necessary. Rank of input tensors must match.

*Arguments:*

|===
|Argument|Type|Name|Shape|Description

|Input|in_t*|input1|shape1|Input tensor from 1 to 4 dims
|Input|in_t*|input2|shape2|Input tensor with the same rank as input1
|Output|in_t*|output|shape|Output tensor of same type as the input tensors, with broadcast shape if necessary
|===

*Quantization Parameters:*

Only supported with floating point values.

*Supported Data Types:*

|===
|Profile|Mode|in_t

|MI, MT|float|float
|===

==== SUB

Elementwise subtraction of input1 and input2.
Axis of size 1 will be broadcast as necessary. Rank of input tensors must match.

*Arguments:*

|===
|Argument|Type|Name|Shape|Description

|Input|in_t*|input1|shape1|Input tensor
|Input|in_t*|input2|shape2|Input tensor with the same rank as input1
|Output|in_t*|output|shape|Output tensor with broadcast shape if necessary
|===

*Operation Function:*

[source,c]
----
for_each (index in shape) {
    index1 = apply_broadcast(shape, shape1, index)
    index2 = apply_broadcast(shape, shape2, index)
    in_t value1 = tensor_read<in_t>(input1, shape1, index1)
    in_t value2 = tensor_read<in_t>(input2, shape2, index2)
    in_t acc = apply_sub<out_t>(value1, value2);
    tensor_write<in_t>(output, shape, index, acc)
}
----

*Supported Data Types:*

|===
|Profile|Mode|in_t

|Any|signed 32|int32
|MI, MT|float|float
|===

====   TABLE

Interpolated table lookup operation. The int16 input is treated as a fixed-point 9.7 value. The high 9 bits are used to index into the table. The fractional 7 bits are used to interpolate based on table[index] and table[index+1]. The TABLE operator returns a 16.7 interpolated value which can then be input to the RESCALE operator to scale to the required output data type. Note that table has 513 values to handle table[index+1] when index=511.

An int8_t to int8_t table lookup can be constructed in TOSA as follows:

* Use RESCALE (in_t=int8, out_t=int16, input_zp=0, scale=1<<14, shift=7) to perform a shift left of 7 and convert to int16
* Use the TABLE operator to produce a fixed point 16.7 result. The lower 7 bits will be zero and only the central 256 table entries will be used.
* Use RESCALE (in_t=int32, out_t=int8, scale=1<<14, shift=28) to scale the output to int8_t range (or alternate scale as required)
* Note that this TOSA sequence can be implemented in software as a 256 entry 8-bit lookup table.

An int16_t to int16_t table lookup can be constructed in TOSA as follows:

* Use the TABLE operator to produce a fixed point 16.7 interpolated result
* Use RESCALE (in_t=int32, out_t=int16, scale=1<<14, shift=21) to scale the output to int16_t range (or alternate scale as required)

*Arguments:*

|===
|Argument|Type|Name|Shape|Description

|Input|in_t*|Input|shape|Input tensor
|Input|table_t*|table|[513]|Lookup table tensor
|Output|out_t*|output|shape|Output tensor
|===

*Quantization Parameters:*

None

*Operation Function:*

[source,c]
----
assert(rank(shape)<=4)
for_each (index in shape) {
    in_t value = tensor_read<in_t>(input, shape, index)
    out_t acc = apply_lookup(table, value)
    tensor_write<out_t>(output, shape, index, acc)
}
----

*Supported Data Types:*

|===
|Profile|Mode|in_t|table_t|out_t

|Any|signed 16|int16|int16|int32
|===