av1/encoder/x86/ml_sse3.c - aom - Git at Google

 /*
  * Copyright (c) 2018, Alliance for Open Media. All rights reserved
  *
  * This source code is subject to the terms of the BSD 2 Clause License and
  * the Alliance for Open Media Patent License 1.0. If the BSD 2 Clause License
  * was not distributed with this source code in the LICENSE file, you can
  * obtain it at www.aomedia.org/license/software. If the Alliance for Open
  * Media Patent License 1.0 was not distributed with this source code in the
  * PATENTS file, you can obtain it at www.aomedia.org/license/patent.
  */

 #include <stdbool.h>
 #include <assert.h>

 #include "config/av1_rtcd.h"
 #include "av1/encoder/ml.h"
 #include "av1/encoder/x86/ml_sse3.h"

 // In order to avoid the high-latency of swapping between FPU and SIMD
 // operations, we keep the result in a 128-bit register even though we only
 // care about a single value.
 static void nn_propagate_8to1(const float *const inputs,
                               const float *const weights,
                               __m128 *const output) {
   const __m128 inputs_h = _mm_loadu_ps(&inputs[4]);
   const __m128 inputs_l = _mm_loadu_ps(inputs);

   const __m128 weights_h = _mm_loadu_ps(&weights[4]);
   const __m128 weights_l = _mm_loadu_ps(weights);

   const __m128 mul_h = _mm_mul_ps(inputs_h, weights_h);
   const __m128 mul_l = _mm_mul_ps(inputs_l, weights_l);
   // [7 6 5 4] [3 2 1 0] (weight and input indices)

   const __m128 vadd = _mm_add_ps(mul_l, mul_h);
   // [7+3 6+2 5+1 4+0]
   const __m128 hadd1 = _mm_hadd_ps(vadd, vadd);
   // [7+6+3+2 5+4+1+0 7+6+3+2 5+4+1+0]
   const __m128 hadd2 = _mm_hadd_ps(hadd1, hadd1);
   // [7+6+5+4+3+2+1+0 7+6+5+4+3+2+1+0 7+6+5+4+3+2+1+0 7+6+5+4+3+2+1+0]
   *output = _mm_add_ps(*output, hadd2);
 }

 void av1_nn_propagate_4to1_sse3(const float *const inputs,
                                 const float *const weights,
                                 __m128 *const output) {
   const __m128 inputs128 = _mm_loadu_ps(inputs);

   const __m128 weights128 = _mm_loadu_ps(weights);

   const __m128 mul = _mm_mul_ps(inputs128, weights128);
   // [3 2 1 0] (weight and input indices)

   const __m128 hadd1 = _mm_hadd_ps(mul, mul);
   // [3+2 1+0 3+2 1+0]
   const __m128 hadd2 = _mm_hadd_ps(hadd1, hadd1);
   // [3+2+1+0 3+2+1+0 3+2+1+0 3+2+1+0]
   *output = _mm_add_ps(*output, hadd2);
 }

 void av1_nn_propagate_4to4_sse3(const float *const inputs,
                                 const float *const weights,
                                 __m128 *const outputs, const int num_inputs) {
   const __m128 inputs128 = _mm_loadu_ps(inputs);

   __m128 hadd[2];
   for (int i = 0; i < 2; i++) {  // For each pair of outputs
     const __m128 weight0 = _mm_loadu_ps(&weights[2 * i * num_inputs]);
     const __m128 mul0 = _mm_mul_ps(weight0, inputs128);
     const __m128 weight1 = _mm_loadu_ps(&weights[(2 * i + 1) * num_inputs]);
     const __m128 mul1 = _mm_mul_ps(weight1, inputs128);
     hadd[i] = _mm_hadd_ps(mul0, mul1);
   }
   // hadd[0] = [7+6 5+4 3+2 1+0] (weight indices)
   // hadd[1] = [15+14 13+12 11+10 9+8]

   const __m128 hh = _mm_hadd_ps(hadd[0], hadd[1]);
   // [15+14+13+12 11+10+9+8 7+6+5+4 3+2+1+0]

   *outputs = _mm_add_ps(*outputs, hh);
 }

 void av1_nn_propagate_4to8_sse3(const float *const inputs,
                                 const float *const weights, __m128 *const out_h,
                                 __m128 *const out_l, const int num_inputs) {
   const __m128 inputs128 = _mm_loadu_ps(inputs);

   __m128 hadd[4];
   for (int i = 0; i < 4; i++) {  // For each pair of outputs
     const __m128 weight0 = _mm_loadu_ps(&weights[2 * i * num_inputs]);
     const __m128 weight1 = _mm_loadu_ps(&weights[(2 * i + 1) * num_inputs]);
     const __m128 mul0 = _mm_mul_ps(inputs128, weight0);
     const __m128 mul1 = _mm_mul_ps(inputs128, weight1);
     hadd[i] = _mm_hadd_ps(mul0, mul1);
   }
   // hadd[0] = [7+6 5+4 3+2 1+0] (weight indices)
   // hadd[1] = [15+14 13+12 11+10 9+8]
   // hadd[2] = [23+22 21+20 19+18 17+16]
   // hadd[3] = [31+30 29+28 27+26 25+24]

   const __m128 hh0 = _mm_hadd_ps(hadd[0], hadd[1]);
   // [15+14+13+12 11+10+9+8 7+6+5+4 3+2+1+0]
   const __m128 hh1 = _mm_hadd_ps(hadd[2], hadd[3]);
   // [31+30+29+28 27+26+25+24 23+22+21+20 19+18+17+16]

   *out_h = _mm_add_ps(*out_h, hh1);
   *out_l = _mm_add_ps(*out_l, hh0);
 }

 static void nn_propagate_8to4(const float *const inputs,
                               const float *const weights, __m128 *const outputs,
                               const int num_inputs) {
   const __m128 inputs_h = _mm_loadu_ps(inputs + 4);
   const __m128 inputs_l = _mm_loadu_ps(inputs);
   // [7 6 5 4] [3 2 1 0] (input indices)

   __m128 add[4];
   for (int i = 0; i < 4; i++) {  // For each output:
     const __m128 weight_h = _mm_loadu_ps(&weights[i * num_inputs + 4]);
     const __m128 weight_l = _mm_loadu_ps(&weights[i * num_inputs]);
     const __m128 mul_h = _mm_mul_ps(inputs_h, weight_h);
     const __m128 mul_l = _mm_mul_ps(inputs_l, weight_l);
     add[i] = _mm_add_ps(mul_l, mul_h);
   }
   // add[0] = [7+3 6+2 5+1 4+0]
   // add[1] = [15+11 14+10 13+9 12+8]
   // add[2] = [23+19 22+18 21+17 20+16]
   // add[3] = [31+27 30+26 29+25 28+24]

   const __m128 hadd_h = _mm_hadd_ps(add[2], add[3]);
   // [31+30+27+26 29+28+25+24 23+22+19+18 21+20+17+16]
   const __m128 hadd_l = _mm_hadd_ps(add[0], add[1]);
   // [15+14+11+10 13+12+9+8 7+6+3+2 5+4+1+0]

   const __m128 haddhadd = _mm_hadd_ps(hadd_l, hadd_h);
   // [31+30+29+28+27+26+25+24 23+22+21+20+19+18+17+16
   //  15+14+13+12+11+10+9+8 7+6+5+4+3+2+1+0]

   *outputs = _mm_add_ps(*outputs, haddhadd);
 }

 static void nn_activate8(__m128 *out_h, __m128 *out_l) {
   const __m128 zero = _mm_setzero_ps();
   *out_h = _mm_max_ps(*out_h, zero);
   *out_l = _mm_max_ps(*out_l, zero);
 }

 static void nn_activate4(__m128 *x) { *x = _mm_max_ps(*x, _mm_setzero_ps()); }

 // Calculate prediction based on the given input features and neural net config.
 // Assume there are no more than NN_MAX_NODES_PER_LAYER nodes in each hidden
 // layer.
 void av1_nn_predict_sse3(const float *input_nodes,
                          const NN_CONFIG *const nn_config, int reduce_prec,
                          float *const output) {
   float buf[2][NN_MAX_NODES_PER_LAYER];
   int buf_index = 0;
   int num_inputs = nn_config->num_inputs;

   // Hidden layers, except the final iteration is the output layer.
   for (int layer = 0; layer <= nn_config->num_hidden_layers; layer++) {
     const float *layer_weights = nn_config->weights[layer];
     const float *layer_bias = nn_config->bias[layer];
     bool output_layer = (layer == nn_config->num_hidden_layers);
     float *const output_nodes = output_layer ? output : &buf[buf_index][0];
     const int num_outputs = output_layer ? nn_config->num_outputs
                                          : nn_config->num_hidden_nodes[layer];

     if (num_inputs % 4 == 0 && num_outputs % 8 == 0) {
       for (int out = 0; out < num_outputs; out += 8) {
         __m128 out_h = _mm_loadu_ps(&layer_bias[out + 4]);
         __m128 out_l = _mm_loadu_ps(&layer_bias[out]);
         for (int in = 0; in < num_inputs; in += 4) {
           av1_nn_propagate_4to8_sse3(&input_nodes[in],
                                      &layer_weights[out * num_inputs + in],
                                      &out_h, &out_l, num_inputs);
         }
         if (!output_layer) nn_activate8(&out_h, &out_l);
         _mm_storeu_ps(&output_nodes[out + 4], out_h);
         _mm_storeu_ps(&output_nodes[out], out_l);
       }
     } else if (num_inputs % 8 == 0 && num_outputs % 4 == 0) {
       for (int out = 0; out < num_outputs; out += 4) {
         __m128 outputs = _mm_loadu_ps(&layer_bias[out]);
         for (int in = 0; in < num_inputs; in += 8) {
           nn_propagate_8to4(&input_nodes[in],
                             &layer_weights[out * num_inputs + in], &outputs,
                             num_inputs);
         }
         if (!output_layer) nn_activate4(&outputs);
         _mm_storeu_ps(&output_nodes[out], outputs);
       }
     } else if (num_inputs % 4 == 0 && num_outputs % 4 == 0) {
       for (int out = 0; out < num_outputs; out += 4) {
         __m128 outputs = _mm_loadu_ps(&layer_bias[out]);
         for (int in = 0; in < num_inputs; in += 4) {
           av1_nn_propagate_4to4_sse3(&input_nodes[in],
                                      &layer_weights[out * num_inputs + in],
                                      &outputs, num_inputs);
         }
         if (!output_layer) nn_activate4(&outputs);
         _mm_storeu_ps(&output_nodes[out], outputs);
       }
     } else if (num_inputs % 8 == 0) {
       for (int out = 0; out < num_outputs; out++) {
         __m128 total = _mm_load1_ps(&layer_bias[out]);
         for (int in = 0; in < num_inputs; in += 8) {
           nn_propagate_8to1(&input_nodes[in],
                             &layer_weights[out * num_inputs + in], &total);
         }
         if (!output_layer) nn_activate4(&total);
         output_nodes[out] = _mm_cvtss_f32(total);
       }
     } else if (num_inputs % 4 == 0) {
       for (int out = 0; out < num_outputs; out++) {
         __m128 total = _mm_load1_ps(&layer_bias[out]);
         for (int in = 0; in < num_inputs; in += 4) {
           av1_nn_propagate_4to1_sse3(
               &input_nodes[in], &layer_weights[out * num_inputs + in], &total);
         }
         if (!output_layer) nn_activate4(&total);
         output_nodes[out] = _mm_cvtss_f32(total);
       }
     } else {
       // Use SSE instructions for scalar operations to avoid the latency of
       // swapping between SIMD and FPU modes.
       for (int out = 0; out < num_outputs; out++) {
         __m128 total = _mm_load1_ps(&layer_bias[out]);
         for (int in_node = 0; in_node < num_inputs; in_node++) {
           __m128 input = _mm_load1_ps(&input_nodes[in_node]);
           __m128 weight =
               _mm_load1_ps(&layer_weights[num_inputs * out + in_node]);
           total = _mm_add_ps(total, _mm_mul_ps(input, weight));
         }
         if (!output_layer) nn_activate4(&total);
         output_nodes[out] = _mm_cvtss_f32(total);
       }
     }
     input_nodes = output_nodes;
     num_inputs = num_outputs;
     buf_index = 1 - buf_index;
   }
   if (reduce_prec) av1_nn_output_prec_reduce(output, nn_config->num_outputs);
 }

 // Based on N. N. Schraudolph. A Fast, Compact Approximation of the Exponential
 // Function. Neural Computation, 11(4):853–862, 1999.
 static AOM_INLINE __m128 approx_exp(__m128 y) {
 #define A ((1 << 23) / 0.69314718056f)  // (1 << 23) / ln(2)
 #define B \
   127  // Offset for the exponent according to IEEE floating point standard.
 #define C 60801  // Magic number controls the accuracy of approximation
   const __m128 multiplier = _mm_set1_ps(A);
   const __m128i offset = _mm_set1_epi32(B * (1 << 23) - C);

   y = _mm_mul_ps(y, multiplier);
   y = _mm_castsi128_ps(_mm_add_epi32(_mm_cvtps_epi32(y), offset));
   return y;
 #undef A
 #undef B
 #undef C
 }

 static AOM_INLINE __m128 reduce_max(__m128 reg) {
   __m128 tmp_reg;

   tmp_reg = _mm_shuffle_ps(reg, reg, 0x4e);  // 01 00 11 10
   reg = _mm_max_ps(reg, tmp_reg);

   tmp_reg = _mm_shuffle_ps(reg, reg, 0xb1);  // 10 11 00 01
   reg = _mm_max_ps(reg, tmp_reg);

   return reg;
 }

 static AOM_INLINE __m128 reduce_sum(__m128 reg) {
   __m128 tmp_reg;

   tmp_reg = _mm_shuffle_ps(reg, reg, 0x4e);  // 01 00 11 10
   reg = _mm_add_ps(reg, tmp_reg);

   tmp_reg = _mm_shuffle_ps(reg, reg, 0xb1);  // 10 11 00 01
   reg = _mm_add_ps(reg, tmp_reg);

   return reg;
 }

 void av1_nn_fast_softmax_16_sse3(const float *input, float *output) {
   // Clips at -10 to avoid underflowing
   const __m128 clipper = _mm_set1_ps(-10.0f);

   // Load in 16 values
   __m128 in_0 = _mm_loadu_ps(&input[0]);
   __m128 in_1 = _mm_loadu_ps(&input[4]);
   __m128 in_2 = _mm_loadu_ps(&input[8]);
   __m128 in_3 = _mm_loadu_ps(&input[12]);

   // Get the max
   __m128 max_0 = _mm_max_ps(in_0, in_1);
   __m128 max_1 = _mm_max_ps(in_2, in_3);

   max_0 = _mm_max_ps(max_0, max_1);
   max_0 = reduce_max(max_0);

   // Subtract the max off and clip
   in_0 = _mm_sub_ps(in_0, max_0);
   in_1 = _mm_sub_ps(in_1, max_0);
   in_2 = _mm_sub_ps(in_2, max_0);
   in_3 = _mm_sub_ps(in_3, max_0);

   in_0 = _mm_max_ps(in_0, clipper);
   in_1 = _mm_max_ps(in_1, clipper);
   in_2 = _mm_max_ps(in_2, clipper);
   in_3 = _mm_max_ps(in_3, clipper);

   // Exponentiate and compute the denominator
   __m128 sum = in_0 = approx_exp(in_0);
   in_1 = approx_exp(in_1);
   sum = _mm_add_ps(sum, in_1);
   in_2 = approx_exp(in_2);
   sum = _mm_add_ps(sum, in_2);
   in_3 = approx_exp(in_3);
   sum = _mm_add_ps(sum, in_3);
   sum = reduce_sum(sum);

   // Divide to get the probability
   in_0 = _mm_div_ps(in_0, sum);
   in_1 = _mm_div_ps(in_1, sum);
   in_2 = _mm_div_ps(in_2, sum);
   in_3 = _mm_div_ps(in_3, sum);

   _mm_storeu_ps(&output[0], in_0);
   _mm_storeu_ps(&output[4], in_1);
   _mm_storeu_ps(&output[8], in_2);
   _mm_storeu_ps(&output[12], in_3);
 }
	/*
	* Copyright (c) 2018, Alliance for Open Media. All rights reserved
	*
	* This source code is subject to the terms of the BSD 2 Clause License and
	* the Alliance for Open Media Patent License 1.0. If the BSD 2 Clause License
	* was not distributed with this source code in the LICENSE file, you can
	* obtain it at www.aomedia.org/license/software. If the Alliance for Open
	* Media Patent License 1.0 was not distributed with this source code in the
	* PATENTS file, you can obtain it at www.aomedia.org/license/patent.
	*/

	#include <stdbool.h>
	#include <assert.h>

	#include "config/av1_rtcd.h"
	#include "av1/encoder/ml.h"
	#include "av1/encoder/x86/ml_sse3.h"

	// In order to avoid the high-latency of swapping between FPU and SIMD
	// operations, we keep the result in a 128-bit register even though we only
	// care about a single value.
	static void nn_propagate_8to1(const float *const inputs,
	const float *const weights,
	__m128 *const output) {
	const __m128 inputs_h = _mm_loadu_ps(&inputs[4]);
	const __m128 inputs_l = _mm_loadu_ps(inputs);

	const __m128 weights_h = _mm_loadu_ps(&weights[4]);
	const __m128 weights_l = _mm_loadu_ps(weights);

	const __m128 mul_h = _mm_mul_ps(inputs_h, weights_h);
	const __m128 mul_l = _mm_mul_ps(inputs_l, weights_l);
	// [7 6 5 4] [3 2 1 0] (weight and input indices)

	const __m128 vadd = _mm_add_ps(mul_l, mul_h);
	// [7+3 6+2 5+1 4+0]
	const __m128 hadd1 = _mm_hadd_ps(vadd, vadd);
	// [7+6+3+2 5+4+1+0 7+6+3+2 5+4+1+0]
	const __m128 hadd2 = _mm_hadd_ps(hadd1, hadd1);
	// [7+6+5+4+3+2+1+0 7+6+5+4+3+2+1+0 7+6+5+4+3+2+1+0 7+6+5+4+3+2+1+0]
	output = _mm_add_ps(output, hadd2);
	}

	void av1_nn_propagate_4to1_sse3(const float *const inputs,
	const float *const weights,
	__m128 *const output) {
	const __m128 inputs128 = _mm_loadu_ps(inputs);

	const __m128 weights128 = _mm_loadu_ps(weights);

	const __m128 mul = _mm_mul_ps(inputs128, weights128);
	// [3 2 1 0] (weight and input indices)

	const __m128 hadd1 = _mm_hadd_ps(mul, mul);
	// [3+2 1+0 3+2 1+0]
	const __m128 hadd2 = _mm_hadd_ps(hadd1, hadd1);
	// [3+2+1+0 3+2+1+0 3+2+1+0 3+2+1+0]
	output = _mm_add_ps(output, hadd2);
	}

	void av1_nn_propagate_4to4_sse3(const float *const inputs,
	const float *const weights,
	__m128 *const outputs, const int num_inputs) {
	const __m128 inputs128 = _mm_loadu_ps(inputs);

	__m128 hadd[2];
	for (int i = 0; i < 2; i++) { // For each pair of outputs
	const __m128 weight0 = _mm_loadu_ps(&weights[2 * i * num_inputs]);
	const __m128 mul0 = _mm_mul_ps(weight0, inputs128);
	const __m128 weight1 = _mm_loadu_ps(&weights[(2 * i + 1) * num_inputs]);
	const __m128 mul1 = _mm_mul_ps(weight1, inputs128);
	hadd[i] = _mm_hadd_ps(mul0, mul1);
	}
	// hadd[0] = [7+6 5+4 3+2 1+0] (weight indices)
	// hadd[1] = [15+14 13+12 11+10 9+8]

	const __m128 hh = _mm_hadd_ps(hadd[0], hadd[1]);
	// [15+14+13+12 11+10+9+8 7+6+5+4 3+2+1+0]

	outputs = _mm_add_ps(outputs, hh);
	}

	void av1_nn_propagate_4to8_sse3(const float *const inputs,
	const float const weights, __m128 const out_h,
	__m128 *const out_l, const int num_inputs) {
	const __m128 inputs128 = _mm_loadu_ps(inputs);

	__m128 hadd[4];
	for (int i = 0; i < 4; i++) { // For each pair of outputs
	const __m128 weight0 = _mm_loadu_ps(&weights[2 * i * num_inputs]);
	const __m128 weight1 = _mm_loadu_ps(&weights[(2 * i + 1) * num_inputs]);
	const __m128 mul0 = _mm_mul_ps(inputs128, weight0);
	const __m128 mul1 = _mm_mul_ps(inputs128, weight1);
	hadd[i] = _mm_hadd_ps(mul0, mul1);
	}
	// hadd[0] = [7+6 5+4 3+2 1+0] (weight indices)
	// hadd[1] = [15+14 13+12 11+10 9+8]
	// hadd[2] = [23+22 21+20 19+18 17+16]
	// hadd[3] = [31+30 29+28 27+26 25+24]

	const __m128 hh0 = _mm_hadd_ps(hadd[0], hadd[1]);
	// [15+14+13+12 11+10+9+8 7+6+5+4 3+2+1+0]
	const __m128 hh1 = _mm_hadd_ps(hadd[2], hadd[3]);
	// [31+30+29+28 27+26+25+24 23+22+21+20 19+18+17+16]

	out_h = _mm_add_ps(out_h, hh1);
	out_l = _mm_add_ps(out_l, hh0);
	}

	static void nn_propagate_8to4(const float *const inputs,
	const float const weights, __m128 const outputs,
	const int num_inputs) {
	const __m128 inputs_h = _mm_loadu_ps(inputs + 4);
	const __m128 inputs_l = _mm_loadu_ps(inputs);
	// [7 6 5 4] [3 2 1 0] (input indices)

	__m128 add[4];
	for (int i = 0; i < 4; i++) { // For each output:
	const __m128 weight_h = _mm_loadu_ps(&weights[i * num_inputs + 4]);
	const __m128 weight_l = _mm_loadu_ps(&weights[i * num_inputs]);
	const __m128 mul_h = _mm_mul_ps(inputs_h, weight_h);
	const __m128 mul_l = _mm_mul_ps(inputs_l, weight_l);
	add[i] = _mm_add_ps(mul_l, mul_h);
	}
	// add[0] = [7+3 6+2 5+1 4+0]
	// add[1] = [15+11 14+10 13+9 12+8]
	// add[2] = [23+19 22+18 21+17 20+16]
	// add[3] = [31+27 30+26 29+25 28+24]

	const __m128 hadd_h = _mm_hadd_ps(add[2], add[3]);
	// [31+30+27+26 29+28+25+24 23+22+19+18 21+20+17+16]
	const __m128 hadd_l = _mm_hadd_ps(add[0], add[1]);
	// [15+14+11+10 13+12+9+8 7+6+3+2 5+4+1+0]

	const __m128 haddhadd = _mm_hadd_ps(hadd_l, hadd_h);
	// [31+30+29+28+27+26+25+24 23+22+21+20+19+18+17+16
	// 15+14+13+12+11+10+9+8 7+6+5+4+3+2+1+0]

	outputs = _mm_add_ps(outputs, haddhadd);
	}

	static void nn_activate8(__m128 out_h, __m128 out_l) {
	const __m128 zero = _mm_setzero_ps();
	out_h = _mm_max_ps(out_h, zero);
	out_l = _mm_max_ps(out_l, zero);
	}

	static void nn_activate4(__m128 x) { x = _mm_max_ps(*x, _mm_setzero_ps()); }

	// Calculate prediction based on the given input features and neural net config.
	// Assume there are no more than NN_MAX_NODES_PER_LAYER nodes in each hidden
	// layer.
	void av1_nn_predict_sse3(const float *input_nodes,
	const NN_CONFIG *const nn_config, int reduce_prec,
	float *const output) {
	float buf[2][NN_MAX_NODES_PER_LAYER];
	int buf_index = 0;
	int num_inputs = nn_config->num_inputs;

	// Hidden layers, except the final iteration is the output layer.
	for (int layer = 0; layer <= nn_config->num_hidden_layers; layer++) {
	const float *layer_weights = nn_config->weights[layer];
	const float *layer_bias = nn_config->bias[layer];
	bool output_layer = (layer == nn_config->num_hidden_layers);
	float *const output_nodes = output_layer ? output : &buf[buf_index][0];
	const int num_outputs = output_layer ? nn_config->num_outputs
	: nn_config->num_hidden_nodes[layer];

	if (num_inputs % 4 == 0 && num_outputs % 8 == 0) {
	for (int out = 0; out < num_outputs; out += 8) {
	__m128 out_h = _mm_loadu_ps(&layer_bias[out + 4]);
	__m128 out_l = _mm_loadu_ps(&layer_bias[out]);
	for (int in = 0; in < num_inputs; in += 4) {
	av1_nn_propagate_4to8_sse3(&input_nodes[in],
	&layer_weights[out * num_inputs + in],
	&out_h, &out_l, num_inputs);
	}
	if (!output_layer) nn_activate8(&out_h, &out_l);
	_mm_storeu_ps(&output_nodes[out + 4], out_h);
	_mm_storeu_ps(&output_nodes[out], out_l);
	}
	} else if (num_inputs % 8 == 0 && num_outputs % 4 == 0) {
	for (int out = 0; out < num_outputs; out += 4) {
	__m128 outputs = _mm_loadu_ps(&layer_bias[out]);
	for (int in = 0; in < num_inputs; in += 8) {
	nn_propagate_8to4(&input_nodes[in],
	&layer_weights[out * num_inputs + in], &outputs,
	num_inputs);
	}
	if (!output_layer) nn_activate4(&outputs);
	_mm_storeu_ps(&output_nodes[out], outputs);
	}
	} else if (num_inputs % 4 == 0 && num_outputs % 4 == 0) {
	for (int out = 0; out < num_outputs; out += 4) {
	__m128 outputs = _mm_loadu_ps(&layer_bias[out]);
	for (int in = 0; in < num_inputs; in += 4) {
	av1_nn_propagate_4to4_sse3(&input_nodes[in],
	&layer_weights[out * num_inputs + in],
	&outputs, num_inputs);
	}
	if (!output_layer) nn_activate4(&outputs);
	_mm_storeu_ps(&output_nodes[out], outputs);
	}
	} else if (num_inputs % 8 == 0) {
	for (int out = 0; out < num_outputs; out++) {
	__m128 total = _mm_load1_ps(&layer_bias[out]);
	for (int in = 0; in < num_inputs; in += 8) {
	nn_propagate_8to1(&input_nodes[in],
	&layer_weights[out * num_inputs + in], &total);
	}
	if (!output_layer) nn_activate4(&total);
	output_nodes[out] = _mm_cvtss_f32(total);
	}
	} else if (num_inputs % 4 == 0) {
	for (int out = 0; out < num_outputs; out++) {
	__m128 total = _mm_load1_ps(&layer_bias[out]);
	for (int in = 0; in < num_inputs; in += 4) {
	av1_nn_propagate_4to1_sse3(
	&input_nodes[in], &layer_weights[out * num_inputs + in], &total);
	}
	if (!output_layer) nn_activate4(&total);
	output_nodes[out] = _mm_cvtss_f32(total);
	}
	} else {
	// Use SSE instructions for scalar operations to avoid the latency of
	// swapping between SIMD and FPU modes.
	for (int out = 0; out < num_outputs; out++) {
	__m128 total = _mm_load1_ps(&layer_bias[out]);
	for (int in_node = 0; in_node < num_inputs; in_node++) {
	__m128 input = _mm_load1_ps(&input_nodes[in_node]);
	__m128 weight =
	_mm_load1_ps(&layer_weights[num_inputs * out + in_node]);
	total = _mm_add_ps(total, _mm_mul_ps(input, weight));
	}
	if (!output_layer) nn_activate4(&total);
	output_nodes[out] = _mm_cvtss_f32(total);
	}
	}
	input_nodes = output_nodes;
	num_inputs = num_outputs;
	buf_index = 1 - buf_index;
	}
	if (reduce_prec) av1_nn_output_prec_reduce(output, nn_config->num_outputs);
	}

	// Based on N. N. Schraudolph. A Fast, Compact Approximation of the Exponential
	// Function. Neural Computation, 11(4):853–862, 1999.
	static AOM_INLINE __m128 approx_exp(__m128 y) {
	#define A ((1 << 23) / 0.69314718056f) // (1 << 23) / ln(2)
	#define B \
	127 // Offset for the exponent according to IEEE floating point standard.
	#define C 60801 // Magic number controls the accuracy of approximation
	const __m128 multiplier = _mm_set1_ps(A);
	const __m128i offset = _mm_set1_epi32(B * (1 << 23) - C);

	y = _mm_mul_ps(y, multiplier);
	y = _mm_castsi128_ps(_mm_add_epi32(_mm_cvtps_epi32(y), offset));
	return y;
	#undef A
	#undef B
	#undef C
	}

	static AOM_INLINE __m128 reduce_max(__m128 reg) {
	__m128 tmp_reg;

	tmp_reg = _mm_shuffle_ps(reg, reg, 0x4e); // 01 00 11 10
	reg = _mm_max_ps(reg, tmp_reg);

	tmp_reg = _mm_shuffle_ps(reg, reg, 0xb1); // 10 11 00 01
	reg = _mm_max_ps(reg, tmp_reg);

	return reg;
	}

	static AOM_INLINE __m128 reduce_sum(__m128 reg) {
	__m128 tmp_reg;

	tmp_reg = _mm_shuffle_ps(reg, reg, 0x4e); // 01 00 11 10
	reg = _mm_add_ps(reg, tmp_reg);

	tmp_reg = _mm_shuffle_ps(reg, reg, 0xb1); // 10 11 00 01
	reg = _mm_add_ps(reg, tmp_reg);

	return reg;
	}

	void av1_nn_fast_softmax_16_sse3(const float input, float output) {
	// Clips at -10 to avoid underflowing
	const __m128 clipper = _mm_set1_ps(-10.0f);

	// Load in 16 values
	__m128 in_0 = _mm_loadu_ps(&input[0]);
	__m128 in_1 = _mm_loadu_ps(&input[4]);
	__m128 in_2 = _mm_loadu_ps(&input[8]);
	__m128 in_3 = _mm_loadu_ps(&input[12]);

	// Get the max
	__m128 max_0 = _mm_max_ps(in_0, in_1);
	__m128 max_1 = _mm_max_ps(in_2, in_3);

	max_0 = _mm_max_ps(max_0, max_1);
	max_0 = reduce_max(max_0);

	// Subtract the max off and clip
	in_0 = _mm_sub_ps(in_0, max_0);
	in_1 = _mm_sub_ps(in_1, max_0);
	in_2 = _mm_sub_ps(in_2, max_0);
	in_3 = _mm_sub_ps(in_3, max_0);

	in_0 = _mm_max_ps(in_0, clipper);
	in_1 = _mm_max_ps(in_1, clipper);
	in_2 = _mm_max_ps(in_2, clipper);
	in_3 = _mm_max_ps(in_3, clipper);

	// Exponentiate and compute the denominator
	__m128 sum = in_0 = approx_exp(in_0);
	in_1 = approx_exp(in_1);
	sum = _mm_add_ps(sum, in_1);
	in_2 = approx_exp(in_2);
	sum = _mm_add_ps(sum, in_2);
	in_3 = approx_exp(in_3);
	sum = _mm_add_ps(sum, in_3);
	sum = reduce_sum(sum);

	// Divide to get the probability
	in_0 = _mm_div_ps(in_0, sum);
	in_1 = _mm_div_ps(in_1, sum);
	in_2 = _mm_div_ps(in_2, sum);
	in_3 = _mm_div_ps(in_3, sum);

	_mm_storeu_ps(&output[0], in_0);
	_mm_storeu_ps(&output[4], in_1);
	_mm_storeu_ps(&output[8], in_2);
	_mm_storeu_ps(&output[12], in_3);
	}