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1 /*
2  * Copyright (C) 2017 The Android Open Source Project
3  *
4  * Licensed under the Apache License, Version 2.0 (the "License");
5  * you may not use this file except in compliance with the License.
6  * You may obtain a copy of the License at
7  *
8  *      http://www.apache.org/licenses/LICENSE-2.0
9  *
10  * Unless required by applicable law or agreed to in writing, software
11  * distributed under the License is distributed on an "AS IS" BASIS,
12  * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
13  * See the License for the specific language governing permissions and
14  * limitations under the License.
15  */
16 
17 #include "QuantizedLSTM.h"
18 
19 #include "CpuExecutor.h"
20 #include "CpuOperationUtils.h"
21 
22 #include "Tracing.h"
23 
24 #include "public/gemmlowp.h"
25 #include "tensorflow/lite/kernels/internal/reference/legacy_reference_ops.h"
26 
27 namespace android {
28 namespace nn {
29 
30 namespace {
31 
32 template <typename T>
GetBuffer(RunTimeOperandInfo * operand)33 inline T* GetBuffer(RunTimeOperandInfo* operand) {
34     return reinterpret_cast<T*>(operand->buffer);
35 }
36 
37 template <typename T>
GetBuffer(const RunTimeOperandInfo * operand)38 inline const T* GetBuffer(const RunTimeOperandInfo* operand) {
39     return reinterpret_cast<const T*>(operand->buffer);
40 }
41 
42 using tflite::Dims;
43 
44 // The function below is taken from TF Lite implementation in order to decouple
45 // NN API from TF Lite dependency. Original function, with a description of its
46 // parameters and types can be found by this link:
47 // https://github.com/tensorflow/tensorflow/blob/0d697e5fc4c05c699eea0764364104ea500ccc68/tensorflow/contrib/lite/kernels/internal/reference/reference_ops.h#L1926
48 //
49 // clang-format off
50 template <int StateIntegerBits>
quantizedLstmStep(const uint8_t * input_data_uint8,const Dims<4> & input_dims,const uint8_t * prev_activ_data_uint8,const Dims<4> & prev_activ_dims,const uint8_t * weights_data_uint8,const Dims<4> & weights_dims,const int32_t * bias_data_int32,const Dims<4> & bias_dims,const int16_t * prevCellState_data_int16,const Dims<4> & prevCellState_dims,int16_t * output_state_data_int16,const Dims<4> & output_state_dims,uint8_t * output_activ_data_uint8,const Dims<4> & output_activ_dims,uint8_t * concat_temp_data_uint8,const Dims<4> & concat_temp_dims,int16_t * activ_temp_data_int16,const Dims<4> & activ_temp_dims,int32_t weights_zero_point,int32_t accum_multiplier,int accum_shift)51 void quantizedLstmStep(const uint8_t* input_data_uint8, const Dims<4>& input_dims,
52                        const uint8_t* prev_activ_data_uint8,
53                        const Dims<4>& prev_activ_dims, const uint8_t* weights_data_uint8,
54                        const Dims<4>& weights_dims, const int32_t* bias_data_int32,
55                        const Dims<4>& bias_dims, const int16_t* prevCellState_data_int16,
56                        const Dims<4>& prevCellState_dims, int16_t* output_state_data_int16,
57                        const Dims<4>& output_state_dims, uint8_t* output_activ_data_uint8,
58                        const Dims<4>& output_activ_dims, uint8_t* concat_temp_data_uint8,
59                        const Dims<4>& concat_temp_dims, int16_t* activ_temp_data_int16,
60                        const Dims<4>& activ_temp_dims, int32_t weights_zero_point,
61                        int32_t accum_multiplier, int accum_shift) {
62   // Gather dimensions information, and perform consistency checks.
63   const int outer_size =
64       MatchingFlatSizeSkipDim(input_dims, 0, prev_activ_dims, prevCellState_dims,
65                               output_state_dims, output_activ_dims);
66   TFLITE_CHECK_EQ(ArraySize(weights_dims, 2), 1);
67   TFLITE_CHECK_EQ(ArraySize(weights_dims, 3), 1);
68   const int input_depth = ArraySize(input_dims, 0);
69   const int prev_activ_depth = ArraySize(prev_activ_dims, 0);
70   const int total_input_depth = prev_activ_depth + input_depth;
71   TFLITE_CHECK_EQ(ArraySize(weights_dims, 0), total_input_depth);
72   TFLITE_CHECK_EQ(MatchingArraySize(bias_dims, 1, bias_dims, 2, bias_dims, 3),
73                   1);
74   const int intern_activ_depth =
75       MatchingArraySize(weights_dims, 1, bias_dims, 0);
76   TFLITE_CHECK_EQ(intern_activ_depth % 4, 0);
77   const int output_depth =
78       MatchingArraySize(prevCellState_dims, 0, prev_activ_dims, 0,
79                         output_state_dims, 0, output_activ_dims, 0);
80   TFLITE_CHECK_EQ(output_depth, intern_activ_depth / 4);
81   const int fc_batches = FlatSizeSkipDim(activ_temp_dims, 0);
82   const int fc_output_depth =
83       MatchingArraySize(weights_dims, 1, activ_temp_dims, 0);
84   const int fc_accum_depth = ArraySize(weights_dims, 0);
85   TFLITE_CHECK_EQ(fc_output_depth, 4 * output_depth);
86 
87   // Depth-concatenate prev_activ and input data together.
88   uint8_t const* concat_input_arrays_data[2] = {input_data_uint8,
89                                                 prev_activ_data_uint8};
90   Dims<4> const* concat_input_arrays_dims[2] = {&input_dims, &prev_activ_dims};
91   tflite::reference_ops::Concatenation<tflite::FusedActivationFunctionType::kNone, uint8_t>(
92       0, concat_input_arrays_data, concat_input_arrays_dims, 2,
93       concat_temp_data_uint8, concat_temp_dims);
94 
95   // Implementation of the fully connected node inside the LSTM cell.
96   // The operands are 8-bit integers, the accumulators are internally 32bit
97   // integers, and the output is 16-bit fixed-point with 3 integer bits so
98   // the output range is [-2^3, 2^3] == [-8, 8]. The rationale for that
99   // is explained in the function comment above.
100   for (int b = 0; b < fc_batches; ++b) {
101     for (int out_c = 0; out_c < fc_output_depth; ++out_c) {
102       // Internal accumulation.
103       // Initialize accumulator with the bias-value.
104       int32_t accum = bias_data_int32[out_c];
105       // Accumulation loop.
106       for (int d = 0; d < fc_accum_depth; ++d) {
107         int16_t input_val = concat_temp_data_uint8[b * fc_accum_depth + d] - 128;
108         int16_t weights_val =
109             weights_data_uint8[out_c * fc_accum_depth + d] - weights_zero_point;
110         accum += input_val * weights_val;
111       }
112       // Down-scale the final int32 accumulator to the scale used by our
113       // (16-bit, using 3 integer bits) fixed-point format. The quantized
114       // multiplier and shift here have been pre-computed offline
115       // (e.g. by toco).
116       accum =
117           tflite::MultiplyByQuantizedMultiplier(accum, accum_multiplier, accum_shift);
118       // Saturate, cast to int16, and store to the temporary activations array.
119       accum = std::max(-32768, std::min(32767, accum));
120       activ_temp_data_int16[out_c + fc_output_depth * b] = accum;
121     }
122   }
123 
124   // Rest of the LSTM cell: tanh and logistic math functions, and some adds
125   // and muls, all done in 16-bit fixed-point.
126   for (int b = 0; b < outer_size; ++b) {
127     for (int c = 0; c < output_depth; ++c) {
128       // Define the fixed-point data types that we will use here. All use
129       // int16 as the underlying integer type i.e. all are 16-bit fixed-point.
130       // They only differ by the number of integral vs. fractional bits,
131       // determining the range of values that they can represent.
132       //
133       // F0 uses 0 integer bits, range [-1, 1].
134       // This is the return type of math functions such as tanh, logistic,
135       // whose range is in [-1, 1].
136       using F0 = gemmlowp::FixedPoint<std::int16_t, 0>;
137       // F3 uses 3 integer bits, range [-8, 8].
138       // This is the range of the previous fully-connected node's output,
139       // which is our input here.
140       using F3 = gemmlowp::FixedPoint<std::int16_t, 3>;
141       // FS uses StateIntegerBits integer bits, range [-2^StateIntegerBits,
142       // 2^StateIntegerBits]. It's used to represent the internal state, whose
143       // number of integer bits is currently dictated by the model. See comment
144       // on the StateIntegerBits template parameter above.
145       using FS = gemmlowp::FixedPoint<std::int16_t, StateIntegerBits>;
146       // Implementation of input gate, using fixed-point logistic function.
147       F3 input_gate_input = F3::FromRaw(
148           activ_temp_data_int16[b * fc_output_depth + 0 * output_depth + c]);
149       F0 input_gate_output = gemmlowp::logistic(input_gate_input);
150       // Implementation of input modulation gate, using fixed-point tanh
151       // function.
152       F3 input_modulation_gate_input = F3::FromRaw(
153           activ_temp_data_int16[b * fc_output_depth + 1 * output_depth + c]);
154       F0 input_modulation_gate_output =
155           gemmlowp::tanh(input_modulation_gate_input);
156       // Implementation of forget gate, using fixed-point logistic function.
157       F3 forget_gate_input = F3::FromRaw(
158           activ_temp_data_int16[b * fc_output_depth + 2 * output_depth + c]);
159       F0 forget_gate_output = gemmlowp::logistic(forget_gate_input);
160       // Implementation of output gate, using fixed-point logistic function.
161       F3 output_gate_input = F3::FromRaw(
162           activ_temp_data_int16[b * fc_output_depth + 3 * output_depth + c]);
163       F0 output_gate_output = gemmlowp::logistic(output_gate_input);
164       // Implementation of internal multiplication nodes, still in fixed-point.
165       F0 input_times_input_modulation =
166           input_gate_output * input_modulation_gate_output;
167       FS prevCellState = FS::FromRaw(prevCellState_data_int16[b * output_depth + c]);
168       FS prevCellState_times_forget_state = forget_gate_output * prevCellState;
169       // Implementation of internal addition node, saturating.
170       FS new_state = gemmlowp::SaturatingAdd(
171           gemmlowp::Rescale<StateIntegerBits>(input_times_input_modulation),
172           prevCellState_times_forget_state);
173       // Implementation of last internal Tanh node, still in fixed-point.
174       // Since a Tanh fixed-point implementation is specialized for a given
175       // number or integer bits, and each specialization can have a substantial
176       // code size, and we already used above a Tanh on an input with 3 integer
177       // bits, and per the table in the above function comment there is no
178       // significant accuracy to be lost by clamping to [-8, +8] for a
179       // 3-integer-bits representation, let us just do that. This helps people
180       // porting this to targets where code footprint must be minimized.
181       F3 new_state_f3 = gemmlowp::Rescale<3>(new_state);
182       F0 output_activ_int16 = output_gate_output * gemmlowp::tanh(new_state_f3);
183       // Store the new internal state back to memory, as 16-bit integers.
184       // Note: here we store the original value with StateIntegerBits, not
185       // the rescaled 3-integer-bits value fed to tanh.
186       output_state_data_int16[b * output_depth + c] = new_state.raw();
187       // Down-scale the output activations to 8-bit integers, saturating,
188       // and store back to memory.
189       int16_t rescaled_output_activ =
190           gemmlowp::RoundingDivideByPOT(output_activ_int16.raw(), 8);
191       int16_t clamped_output_activ =
192           std::max<int16_t>(-128, std::min<int16_t>(127, rescaled_output_activ));
193       output_activ_data_uint8[b * output_depth + c] =
194           128 + clamped_output_activ;
195     }
196   }
197 }
198 // clang-format on
199 
200 // The function assigns a 2D matrix to a submatrix of the weights at a given row
201 // and column offsets.
assignWeightsSubmatrix(const RunTimeOperandInfo * submatrix,const int32_t offset_row,const int32_t offset_column,const std::vector<uint32_t> & weightsDims,uint8_t * weights)202 void assignWeightsSubmatrix(const RunTimeOperandInfo* submatrix, const int32_t offset_row,
203                             const int32_t offset_column, const std::vector<uint32_t>& weightsDims,
204                             uint8_t* weights) {
205     const uint8_t* submatrixValues = GetBuffer<uint8_t>(submatrix);
206     const std::vector<uint32_t> submatrixDims = submatrix->shape().dimensions;
207     for (uint32_t i = 0; i < submatrixDims[0] * submatrixDims[1]; ++i) {
208         const uint32_t row = i / submatrixDims[1];
209         const uint32_t column = i % submatrixDims[1];
210         weights[(row + offset_row) * weightsDims[1] + column + offset_column] = submatrixValues[i];
211     }
212 }
213 
214 }  // namespace
215 
QuantizedLSTMCell(const Operation & operation,std::vector<RunTimeOperandInfo> & operands)216 QuantizedLSTMCell::QuantizedLSTMCell(const Operation& operation,
217                                      std::vector<RunTimeOperandInfo>& operands) {
218     input_ = GetInput(operation, operands, kInputTensor);
219 
220     inputToInputWeights_ = GetInput(operation, operands, kInputToInputWeightsTensor);
221     inputToForgetWeights_ = GetInput(operation, operands, kInputToForgetWeightsTensor);
222     inputToCellWeights_ = GetInput(operation, operands, kInputToCellWeightsTensor);
223     inputToOutputWeights_ = GetInput(operation, operands, kInputToOutputWeightsTensor);
224 
225     recurrentToInputWeights_ = GetInput(operation, operands, kRecurrentToInputWeightsTensor);
226     recurrentToForgetWeights_ = GetInput(operation, operands, kRecurrentToForgetWeightsTensor);
227     recurrentToCellWeights_ = GetInput(operation, operands, kRecurrentToCellWeightsTensor);
228     recurrentToOutputWeights_ = GetInput(operation, operands, kRecurrentToOutputWeightsTensor);
229 
230     inputGateBias_ = GetInput(operation, operands, kInputGateBiasTensor);
231     forgetGateBias_ = GetInput(operation, operands, kForgetGateBiasTensor);
232     cellGateBias_ = GetInput(operation, operands, kCellGateBiasTensor);
233     outputGateBias_ = GetInput(operation, operands, kOutputGateBiasTensor);
234 
235     prevCellState_ = GetInput(operation, operands, kPrevCellStateTensor);
236     prevOutput_ = GetInput(operation, operands, kPrevOutputTensor);
237 
238     cellStateOut_ = GetOutput(operation, operands, kCellStateOutTensor);
239     output_ = GetOutput(operation, operands, kOutputTensor);
240 }
241 
prepare(const Operation & operation,std::vector<RunTimeOperandInfo> & operands,Shape * cellStateOutShape,Shape * outputShape)242 bool QuantizedLSTMCell::prepare(const Operation& operation,
243                                 std::vector<RunTimeOperandInfo>& operands, Shape* cellStateOutShape,
244                                 Shape* outputShape) {
245     auto input = GetInput(operation, operands, kInputTensor);
246     NN_RET_CHECK_EQ(NumDimensions(input), 2);
247     NN_RET_CHECK_EQ(input->scale, 1. / 128.0);
248     NN_RET_CHECK_EQ(input->zeroPoint, 128);
249     const uint32_t numBatches = SizeOfDimension(input, 0);
250     const uint32_t inputSize = SizeOfDimension(input, 1);
251 
252     auto prevOutput = GetInput(operation, operands, kPrevOutputTensor);
253     NN_RET_CHECK_EQ(NumDimensions(prevOutput), 2);
254     NN_RET_CHECK_EQ(SizeOfDimension(prevOutput, 0), numBatches);
255     NN_RET_CHECK_EQ(prevOutput->scale, 1. / 128.0);
256     NN_RET_CHECK_EQ(prevOutput->zeroPoint, 128);
257     const uint32_t outputSize = SizeOfDimension(prevOutput, 1);
258 
259     auto inputToInputWeights = GetInput(operation, operands, kInputToInputWeightsTensor);
260     const float weightsScale = inputToInputWeights->scale;
261     NN_RET_CHECK(weightsScale != 0);
262     const float weightsZeroPoint = inputToInputWeights->zeroPoint;
263 
264     auto checkWeightsShape = [&](const RunTimeOperandInfo* weights, uint32_t columns) -> bool {
265         NN_RET_CHECK_EQ(NumDimensions(weights), 2);
266         NN_RET_CHECK_EQ(SizeOfDimension(weights, 0), outputSize);
267         NN_RET_CHECK_EQ(SizeOfDimension(weights, 1), columns);
268         NN_RET_CHECK_EQ(weights->scale, weightsScale);
269         NN_RET_CHECK_EQ(weights->zeroPoint, weightsZeroPoint);
270         return true;
271     };
272 
273     auto inputToForgetWeights = GetInput(operation, operands, kInputToForgetWeightsTensor);
274     auto inputToCellWeights = GetInput(operation, operands, kInputToCellWeightsTensor);
275     auto inputToOutputWeights = GetInput(operation, operands, kInputToOutputWeightsTensor);
276     NN_RET_CHECK(checkWeightsShape(inputToInputWeights, inputSize));
277     NN_RET_CHECK(checkWeightsShape(inputToForgetWeights, inputSize));
278     NN_RET_CHECK(checkWeightsShape(inputToCellWeights, inputSize));
279     NN_RET_CHECK(checkWeightsShape(inputToOutputWeights, inputSize));
280 
281     auto recurrentToInputWeights = GetInput(operation, operands, kRecurrentToInputWeightsTensor);
282     auto recurrentToForgetWeights = GetInput(operation, operands, kRecurrentToForgetWeightsTensor);
283     auto recurrentToCellWeights = GetInput(operation, operands, kRecurrentToCellWeightsTensor);
284     auto recurrentToOutputWeights = GetInput(operation, operands, kRecurrentToOutputWeightsTensor);
285     NN_RET_CHECK(checkWeightsShape(recurrentToInputWeights, outputSize));
286     NN_RET_CHECK(checkWeightsShape(recurrentToForgetWeights, outputSize));
287     NN_RET_CHECK(checkWeightsShape(recurrentToCellWeights, outputSize));
288     NN_RET_CHECK(checkWeightsShape(recurrentToOutputWeights, outputSize));
289 
290     auto inputGateBias = GetInput(operation, operands, kInputGateBiasTensor);
291     const float biasScale = inputGateBias->scale;
292     NN_RET_CHECK_EQ(biasScale, weightsScale / 128.0);
293     const float biasZeroPoint = inputGateBias->zeroPoint;
294     NN_RET_CHECK_EQ(biasZeroPoint, 0);
295 
296     auto checkBiasShape = [&](const RunTimeOperandInfo* bias) -> bool {
297         NN_RET_CHECK_EQ(NumDimensions(bias), 1);
298         NN_RET_CHECK_EQ(SizeOfDimension(bias, 0), outputSize);
299         NN_RET_CHECK_EQ(bias->scale, biasScale);
300         NN_RET_CHECK_EQ(bias->zeroPoint, biasZeroPoint);
301         return true;
302     };
303 
304     auto forgetGateBias = GetInput(operation, operands, kForgetGateBiasTensor);
305     auto cellGateBias = GetInput(operation, operands, kCellGateBiasTensor);
306     auto outputGateBias = GetInput(operation, operands, kOutputGateBiasTensor);
307     NN_RET_CHECK(checkBiasShape(inputGateBias));
308     NN_RET_CHECK(checkBiasShape(forgetGateBias));
309     NN_RET_CHECK(checkBiasShape(cellGateBias));
310     NN_RET_CHECK(checkBiasShape(outputGateBias));
311 
312     auto prevCellState = GetInput(operation, operands, kPrevCellStateTensor);
313     NN_CHECK_EQ(NumDimensions(prevCellState), 2);
314     NN_CHECK_EQ(SizeOfDimension(prevCellState, 0), numBatches);
315     NN_CHECK_EQ(SizeOfDimension(prevCellState, 1), outputSize);
316     NN_CHECK_EQ(prevCellState->zeroPoint, 0);
317     // Cell state range for quantized LSTM is a function of StateIntegerBits and
318     // can be calculated as:
319     // [-2^StateIntegerBits, 2^StateIntegerBits * 32767/32768].
320     // Therefore, for a fixed StateIntegerBits parameter, cell state scale is
321     // equal to 2^StateIntegerBits * 2^(-15) = 2^(StateIntegerBits - 15) and
322     // therefore:
323     // StateIntegerBits = log2(cell state scale) + 15
324     int stateScaleLog2Rounded;
325     NN_CHECK(tflite::CheckedLog2(prevCellState->scale, &stateScaleLog2Rounded));
326     const int stateIntegerBits = 15 + stateScaleLog2Rounded;
327     // We only support StateIntegerBits == 4
328     NN_CHECK(stateIntegerBits == 4);
329 
330     *cellStateOutShape = prevCellState->shape();
331     *outputShape = prevOutput->shape();
332     return true;
333 }
334 
335 // The function contatenates 8 input weight matrices into one. Resulting matrix
336 // has a shape [4 * outputSize, outputSize + inputSize]. The matrix is
337 // constructed as follows:
338 // +-----------------------------------+
339 // | recurrentToInput  | inputToInput  |
340 // |-------------------+---------------|
341 // | recurrentToCell   | inputToCell   |
342 // |-------------------+---------------|
343 // | recurrentToForget | inputToForget |
344 // |-------------------+---------------|
345 // | recurrentToOutput | inputToOutput |
346 // +-----------------------------------+
concatenateWeights(const std::vector<uint32_t> & weightsDims,uint8_t * weights)347 void QuantizedLSTMCell::concatenateWeights(const std::vector<uint32_t>& weightsDims,
348                                            uint8_t* weights) {
349     const int outputSize = SizeOfDimension(inputToInputWeights_, 0);
350 
351     assignWeightsSubmatrix(inputToInputWeights_, 0 * outputSize, outputSize, weightsDims, weights);
352     assignWeightsSubmatrix(inputToCellWeights_, 1 * outputSize, outputSize, weightsDims, weights);
353     assignWeightsSubmatrix(inputToForgetWeights_, 2 * outputSize, outputSize, weightsDims, weights);
354     assignWeightsSubmatrix(inputToOutputWeights_, 3 * outputSize, outputSize, weightsDims, weights);
355     assignWeightsSubmatrix(recurrentToInputWeights_, 0 * outputSize, 0, weightsDims, weights);
356     assignWeightsSubmatrix(recurrentToCellWeights_, 1 * outputSize, 0, weightsDims, weights);
357     assignWeightsSubmatrix(recurrentToForgetWeights_, 2 * outputSize, 0, weightsDims, weights);
358     assignWeightsSubmatrix(recurrentToOutputWeights_, 3 * outputSize, 0, weightsDims, weights);
359 }
360 
361 // The function concatenate four bias vectors of shape [outputSize] into one
362 // vector of shape [4 * outputSize].
concatenateBiases(uint32_t outputSize,int32_t * bias)363 void QuantizedLSTMCell::concatenateBiases(uint32_t outputSize, int32_t* bias) {
364     memcpy(bias + 0 * outputSize, GetBuffer<int32_t>(inputGateBias_), sizeof(int32_t) * outputSize);
365     memcpy(bias + 1 * outputSize, GetBuffer<int32_t>(cellGateBias_), sizeof(int32_t) * outputSize);
366     memcpy(bias + 2 * outputSize, GetBuffer<int32_t>(forgetGateBias_),
367            sizeof(int32_t) * outputSize);
368     memcpy(bias + 3 * outputSize, GetBuffer<int32_t>(outputGateBias_),
369            sizeof(int32_t) * outputSize);
370 }
371 
eval()372 bool QuantizedLSTMCell::eval() {
373     NNTRACE_COMP("QuantizedLSTM::eval");
374 
375     Shape weightsShape;
376     weightsShape.dimensions = {4 * SizeOfDimension(prevOutput_, 1),
377                                SizeOfDimension(input_, 1) + SizeOfDimension(prevOutput_, 1)};
378     std::vector<uint8_t> weights(getNumberOfElements(weightsShape));
379     concatenateWeights(weightsShape.dimensions, weights.data());
380 
381     Shape biasShape;
382     biasShape.dimensions = {getSizeOfDimension(weightsShape, 0)};
383     std::vector<int32_t> bias(getNumberOfElements(biasShape));
384     concatenateBiases(SizeOfDimension(prevOutput_, 1), bias.data());
385 
386     Shape concatTempShape;
387     concatTempShape.dimensions = {SizeOfDimension(input_, 0), getSizeOfDimension(weightsShape, 1)};
388 
389     Shape activationTempShape;
390     activationTempShape.dimensions = {SizeOfDimension(input_, 0),
391                                       getSizeOfDimension(weightsShape, 0)};
392 
393     std::vector<uint8_t> concatTemp(getNumberOfElements(concatTempShape));
394     std::vector<int16_t> activationTemp(getNumberOfElements(activationTempShape));
395 
396     // From https://arxiv.org/pdf/1712.05877, for a fully-connected layer,
397     // accumulator multiplier is equal to:
398     // (input scale) * (weights scale) / (fully-connected output scale)
399     // In our case fully-connected output scale is fixed and equal to
400     // 2^(-12) (See LSTMCell definition in TF Lite for more details on that).
401     // But bias scale is set to (input scale) * (weights scale) (also from the
402     // paper), so we can multiply it to an inverse of the fc-output scale to get
403     // the multiplier value:
404     double realAccumMultiplier = 4096 * inputGateBias_->scale;
405     int32_t accumMultiplier;
406     int accumShift;
407     tflite::QuantizeMultiplier(realAccumMultiplier, &accumMultiplier, &accumShift);
408     quantizedLstmStep<4>(
409             // Inputs.
410             GetBuffer<const uint8_t>(input_), convertShapeToDims(input_->shape()),
411             GetBuffer<const uint8_t>(prevOutput_), convertShapeToDims(prevOutput_->shape()),
412             weights.data(), convertShapeToDims(weightsShape), bias.data(),
413             convertShapeToDims(biasShape), GetBuffer<const int16_t>(prevCellState_),
414             convertShapeToDims(prevCellState_->shape()),
415             // Outputs.
416             GetBuffer<int16_t>(cellStateOut_), convertShapeToDims(cellStateOut_->shape()),
417             GetBuffer<uint8_t>(output_), convertShapeToDims(output_->shape()), concatTemp.data(),
418             convertShapeToDims(concatTempShape), activationTemp.data(),
419             convertShapeToDims(activationTempShape), inputToInputWeights_->zeroPoint,
420             accumMultiplier, accumShift);
421     return true;
422 }
423 
424 }  // namespace nn
425 }  // namespace android
426