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// Copyright 2021 Google LLC
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
#include "sparse_matmul/numerics/fast_transcendentals.h"
namespace csrblocksparse {
// Maximum desired precision of the output.
static constexpr int kMaxMantissaBits = 14;
// Returns (and builds if not done yet) a static data table that implements
// tanh on fixed32 input, returning another fixed32 with the given number of
// mantissa bits (which is assumed to be less than the input mantissa bits).
// NOTE that this function is intended to be used only with fixed16 outputs that
// are sign-extended to 32 bits for convenience, and will return a nullptr
// if asked for more than |kMaxMantissaBits| of precision in the output table.
const int32_t* TanhTable(int num_mantissa_bits_out) {
if (num_mantissa_bits_out > kMaxMantissaBits) return nullptr;
// Static data dynamically created and never destructed.
static const int32_t* tanh_luts[kMaxMantissaBits];
if (tanh_luts[num_mantissa_bits_out - 1] == nullptr) {
// Total bits is number each side of the binary point.
int tanh_lut_bits = num_mantissa_bits_out + kNumTanhExpBits;
// Offset is the number of negative numbers represented.
int tanh_offset = 1 << tanh_lut_bits;
// Size is double the offset plus one more for zero.
int tanh_size = tanh_offset * 2 + 1;
// Conversion between int and float.
float float_factor = static_cast<float>(1 << num_mantissa_bits_out);
int* tanh_lut = new int[tanh_size];
// Initialize the table.
for (int i = 0; i < tanh_size; ++i) {
float x = (i - tanh_offset) / float_factor;
tanh_lut[i] = static_cast<int>(std::round(tanhf(x) * float_factor));
}
tanh_luts[num_mantissa_bits_out - 1] = tanh_lut;
}
return tanh_luts[num_mantissa_bits_out - 1];
}
// As TanhTable, but for Sigmoid.
const int32_t* SigmoidTable(int num_mantissa_bits_out) {
if (num_mantissa_bits_out > kMaxMantissaBits) return nullptr;
// Static data dynamically created and never destructed.
static const int32_t* sigmoid_luts[kMaxMantissaBits];
if (sigmoid_luts[num_mantissa_bits_out - 1] == nullptr) {
// Total bits is number each side of the binary point minus one for the fact
// that the gradient never exceeds 1/4. (Could probably use -2.)
int sigmoid_lut_bits =
num_mantissa_bits_out + kNumSigmoidExpBits - kNumExtraSigmoidShiftBits;
// Offset is the number of negative numbers represented.
int sigmoid_offset = 1 << sigmoid_lut_bits;
// Size is double the offset plus one more for zero.
int sigmoid_size = sigmoid_offset * 2 + 1;
// Conversion between int and float.
float float_factor = static_cast<float>(1 << num_mantissa_bits_out);
int* sigmoid_lut = new int[sigmoid_size];
// Initialize the table.
for (int i = 0; i < sigmoid_size; ++i) {
constexpr int kSigmoidFactor = 1 << kNumExtraSigmoidShiftBits;
float x = ((i - sigmoid_offset) * kSigmoidFactor) / float_factor;
float sigmoid = 1.0f / (1.0f + expf(-x));
sigmoid_lut[i] = static_cast<int>(std::round(sigmoid * float_factor));
}
sigmoid_luts[num_mantissa_bits_out - 1] = sigmoid_lut;
}
return sigmoid_luts[num_mantissa_bits_out - 1];
}
} // namespace csrblocksparse
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