| /* |
| * Copyright (c) 2017-2022 Arm Limited. |
| * |
| * SPDX-License-Identifier: MIT |
| * |
| * Permission is hereby granted, free of charge, to any person obtaining a copy |
| * of this software and associated documentation files (the "Software"), to |
| * deal in the Software without restriction, including without limitation the |
| * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or |
| * sell copies of the Software, and to permit persons to whom the Software is |
| * furnished to do so, subject to the following conditions: |
| * |
| * The above copyright notice and this permission notice shall be included in all |
| * copies or substantial portions of the Software. |
| * |
| * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR |
| * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, |
| * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE |
| * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER |
| * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, |
| * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE |
| * SOFTWARE. |
| */ |
| #include "arm_compute/core/utils/quantization/AsymmHelpers.h" |
| #include "arm_compute/core/Helpers.h" |
| #include "support/ToolchainSupport.h" |
| |
| #include <cmath> |
| #include <limits> |
| #include <numeric> |
| |
| namespace arm_compute |
| { |
| namespace quantization |
| { |
| constexpr int64_t fixed_point_one_Q0 = (1LL << 31); |
| constexpr float epsilon = 0.00001f; |
| |
| Status calculate_quantized_multiplier(float multiplier, int32_t *quant_multiplier, int32_t *shift, bool ignore_epsilon) |
| { |
| if(multiplier >= 1.f) |
| { |
| Status status = calculate_quantized_multiplier_greater_than_one(multiplier, quant_multiplier, shift); |
| *shift *= -1; |
| return status; |
| } |
| else |
| { |
| return calculate_quantized_multiplier_less_than_one(multiplier, quant_multiplier, shift, ignore_epsilon); |
| } |
| } |
| |
| Status calculate_quantized_multiplier_less_than_one(float multiplier, |
| int32_t *quant_multiplier, |
| int32_t *right_shift, |
| bool ignore_epsilon) |
| { |
| const float internal_epsilon = ignore_epsilon ? 0.0f : epsilon; |
| |
| ARM_COMPUTE_RETURN_ERROR_ON(quant_multiplier == nullptr); |
| ARM_COMPUTE_RETURN_ERROR_ON(right_shift == nullptr); |
| ARM_COMPUTE_RETURN_ERROR_ON(multiplier < -internal_epsilon); |
| ARM_COMPUTE_RETURN_ERROR_ON(multiplier > 1.0f + internal_epsilon); |
| |
| int shift_exp = 0; |
| const double q = std::frexp(multiplier, &shift_exp); |
| *right_shift = -1 * shift_exp; |
| auto q_fixed = static_cast<int64_t>(support::cpp11::round(q * fixed_point_one_Q0)); |
| ARM_COMPUTE_RETURN_ERROR_ON(q_fixed > fixed_point_one_Q0); |
| if(q_fixed == fixed_point_one_Q0) |
| { |
| q_fixed /= 2; |
| --*right_shift; |
| } |
| |
| if(ignore_epsilon && *right_shift > 31) |
| { |
| *right_shift = 0; |
| q_fixed = 0; |
| } |
| |
| ARM_COMPUTE_RETURN_ERROR_ON(*right_shift < 0); |
| ARM_COMPUTE_RETURN_ERROR_ON(q_fixed > std::numeric_limits<int32_t>::max()); |
| *quant_multiplier = static_cast<int32_t>(q_fixed); |
| |
| return Status{}; |
| } |
| |
| Status calculate_quantized_multiplier_greater_than_one(float multiplier, |
| int32_t *quantized_multiplier, |
| int32_t *left_shift) |
| { |
| ARM_COMPUTE_RETURN_ERROR_ON(quantized_multiplier == nullptr); |
| ARM_COMPUTE_RETURN_ERROR_ON(left_shift == nullptr); |
| ARM_COMPUTE_RETURN_ERROR_ON(multiplier < 1.f); |
| |
| int shift_exp = 0; |
| const double q = std::frexp(multiplier, &shift_exp); |
| *left_shift = shift_exp; |
| auto q_fixed = static_cast<int64_t>(support::cpp11::round(q * fixed_point_one_Q0)); |
| ARM_COMPUTE_RETURN_ERROR_ON(q_fixed > fixed_point_one_Q0); |
| if(q_fixed == fixed_point_one_Q0) |
| { |
| q_fixed /= 2; |
| ++*left_shift; |
| } |
| ARM_COMPUTE_RETURN_ERROR_ON(*left_shift < 0); |
| ARM_COMPUTE_RETURN_ERROR_ON(q_fixed > std::numeric_limits<int32_t>::max()); |
| *quantized_multiplier = static_cast<int32_t>(q_fixed); |
| |
| return Status{}; |
| } |
| |
| arm_compute::Status calculate_quantized_multipliers(const QuantizationInfo &iq_info, |
| const QuantizationInfo &wq_info, |
| const QuantizationInfo &oq_info, |
| GEMMLowpOutputStageInfo &stage_info) |
| { |
| ARM_COMPUTE_RETURN_ERROR_ON(iq_info.scale().empty()); |
| ARM_COMPUTE_RETURN_ERROR_ON(wq_info.scale().empty()); |
| ARM_COMPUTE_RETURN_ERROR_ON(oq_info.scale().empty()); |
| |
| const unsigned int size = wq_info.scale().size(); |
| |
| auto &quant_multipliers = stage_info.gemmlowp_multipliers; |
| auto &quant_shifts = stage_info.gemmlowp_shifts; |
| quant_multipliers.resize(size); |
| quant_shifts.resize(size); |
| |
| const auto &w_scales = wq_info.scale(); |
| const float i_scale = iq_info.scale().at(0); |
| const float o_scale = oq_info.scale().at(0); |
| |
| for(unsigned int i = 0; i < size; ++i) |
| { |
| const float multiplier = i_scale * w_scales[i] / o_scale; |
| int32_t quant_multiplier = 0; |
| int32_t quant_shift = 0; |
| ARM_COMPUTE_RETURN_ON_ERROR(calculate_quantized_multiplier(multiplier, &quant_multiplier, &quant_shift)); |
| quant_multipliers[i] = quant_multiplier; |
| quant_shifts[i] = quant_shift; |
| } |
| |
| // Legacy part |
| stage_info.gemmlowp_shift = quant_shifts[0]; |
| stage_info.gemmlowp_multiplier = quant_multipliers[0]; |
| |
| return Status{}; |
| } |
| |
| std::pair<int, int> get_min_max_values_from_quantized_data_type(DataType data_type) |
| { |
| int min_quant_val = 0; |
| int max_quant_val = 0; |
| switch(data_type) |
| { |
| case DataType::QASYMM8: |
| min_quant_val = std::numeric_limits<uint8_t>::min(); |
| max_quant_val = std::numeric_limits<uint8_t>::max(); |
| break; |
| case DataType::QSYMM8: |
| case DataType::QASYMM8_SIGNED: |
| min_quant_val = std::numeric_limits<int8_t>::min(); |
| max_quant_val = std::numeric_limits<int8_t>::max(); |
| break; |
| case DataType::QASYMM16: |
| min_quant_val = std::numeric_limits<uint16_t>::min(); |
| max_quant_val = std::numeric_limits<uint16_t>::max(); |
| break; |
| case DataType::QSYMM16: |
| min_quant_val = std::numeric_limits<int16_t>::min(); |
| max_quant_val = std::numeric_limits<int16_t>::max(); |
| break; |
| default: |
| ARM_COMPUTE_ERROR("Unsupported data type"); |
| } |
| return std::make_pair(min_quant_val, max_quant_val); |
| } |
| void compute_quantized_multipliers_and_shifts(const ITensorInfo *input, |
| const ITensorInfo *weights, |
| const ITensorInfo *output, |
| int32_t *output_multipliers_ptr, |
| int32_t *output_shifts_ptr) |
| { |
| const UniformQuantizationInfo iq_info = input->quantization_info().uniform(); |
| const QuantizationInfo wq_info = weights->quantization_info(); |
| const UniformQuantizationInfo oq_info = output->quantization_info().uniform(); |
| |
| const unsigned int num_filters = wq_info.scale().size(); |
| |
| for(unsigned int i = 0; i < num_filters; ++i) |
| { |
| int32_t output_multiplier = 0; |
| int32_t output_shift = 0; |
| const float multiplier = iq_info.scale * wq_info.scale()[i] / oq_info.scale; |
| calculate_quantized_multiplier(multiplier, &output_multiplier, &output_shift); |
| |
| output_multipliers_ptr[i] = output_multiplier; |
| output_shifts_ptr[i] = output_shift; |
| } |
| } |
| |
| int32_t saturating_rounding_doubling_highmul(int32_t a, int32_t b) |
| { |
| bool overflow = a == b && a == std::numeric_limits<int32_t>::min(); |
| int64_t a_64(a); |
| int64_t b_64(b); |
| int64_t ab_64 = a_64 * b_64; |
| const bool is_positive_or_zero = |
| a == 0 || b == 0 || |
| (std::signbit(static_cast<double>(a)) == std::signbit(static_cast<double>(b))); |
| int32_t nudge = is_positive_or_zero ? (1 << 30) : (1 - (1 << 30)); |
| int32_t ab_x2_high32 = static_cast<int32_t>((ab_64 + nudge) / (1ll << 31)); |
| return overflow ? std::numeric_limits<int32_t>::max() : ab_x2_high32; |
| } |
| |
| inline int32_t rounding_divide_by_pow2(int32_t x, int exponent) |
| { |
| const int32_t mask = (1 << exponent) - 1; |
| const int32_t threshold = (mask >> 1) + (x < 0 ? 1 : 0); |
| return (x >> exponent) + ((x & mask) > threshold ? 1 : 0); |
| } |
| |
| int32_t multiply_by_quantized_multiplier(int32_t input, int32_t qmul, int32_t shift) |
| { |
| const auto left_shift = shift > 0 ? shift : 0; |
| const auto right_shift = shift > 0 ? 0 : -shift; |
| return rounding_divide_by_pow2(saturating_rounding_doubling_highmul(input * (1 << left_shift), qmul), right_shift); |
| } |
| |
| int32_t saturating_rounding_multiply_by_pow2(int32_t exponent, int32_t v) |
| { |
| if(exponent == 0) |
| { |
| return v; |
| } |
| else if(exponent < 0) |
| { |
| return rounding_divide_by_pow2(v, -exponent); |
| } |
| else |
| { |
| constexpr auto min = std::numeric_limits<int32_t>::min(); |
| constexpr auto max = std::numeric_limits<int32_t>::max(); |
| const auto width = sizeof(int32_t) * 8; |
| |
| const int32_t threshold = ((1 << (width - 1 - exponent)) - 1); |
| bool pos_mask = v > threshold; |
| bool neg_mask = v < -threshold; |
| int32_t result = v << exponent; |
| result = pos_mask ? max : result; |
| result = neg_mask ? min : result; |
| return result; |
| } |
| } |
| |
| void get_invsqrt_quantized_multiplier_exp(int32_t input, int32_t reverse_shift, int32_t &output_inv_sqrt, int32_t &output_shift) |
| { |
| ARM_COMPUTE_ERROR_ON(input < 0); |
| |
| if(input <= 1) |
| { |
| // dealing the inputs (0 and 1) separately to avoid overflow |
| output_inv_sqrt = std::numeric_limits<std::int32_t>::max(); |
| output_shift = 0; |
| return; |
| } |
| |
| // prepare input for fixed point operation and compute shift value |
| output_shift = 11; |
| while(input >= (1 << 29)) |
| { |
| input /= 4; |
| ++output_shift; |
| } |
| |
| const uint32_t max_left_shift_bits = __builtin_clz(static_cast<uint32_t>(input)) - 1; |
| const uint32_t max_left_shift_bits_pairs = max_left_shift_bits / 2; |
| const uint32_t left_shift_bit_pairs = max_left_shift_bits_pairs - 1; |
| output_shift -= left_shift_bit_pairs; |
| input <<= 2 * left_shift_bit_pairs; |
| |
| // Calculation in fixed point domain with 3 integer bits. |
| using FixedPointRawType = int32_t; |
| constexpr uint32_t fixedpoint_position = 3; |
| constexpr uint32_t fixedpoint_int_position = sizeof(FixedPointRawType) * 8 - 1 - fixedpoint_position; |
| using FixedPoint3 = FixedPointRawType; |
| using FixedPoint0 = FixedPointRawType; |
| |
| // fixed point representation of input divided by 2 and 1.5 for Newton-Raphson iteration |
| const FixedPoint3 fixedpoint_input = (input >> 1); |
| const FixedPoint3 fixedpoint_half_input = rounding_divide_by_pow2(fixedpoint_input, 1); |
| const FixedPoint3 fixedpoint_half_three = (0x1 << fixedpoint_int_position) + (0x1 << (fixedpoint_int_position - 1)); |
| |
| // initial guess (1) in fixed point representation |
| FixedPoint3 x = 0x1 << fixedpoint_int_position; |
| |
| // multiplication of two fixed point numbers, defined for readability |
| auto fixed_point_mul = [](FixedPointRawType a, FixedPointRawType b) -> FixedPointRawType |
| { |
| return saturating_rounding_doubling_highmul(a, b); |
| }; |
| |
| // rescaling of fixed point to have dst_bit integer bits, defined for readability |
| auto fixed_point_rescale = [](FixedPointRawType a, uint32_t src_bit, uint32_t dst_bit) -> FixedPointRawType |
| { |
| const uint32_t exponent = src_bit - dst_bit; |
| return saturating_rounding_multiply_by_pow2(exponent, a); |
| }; |
| |
| // 5 iterations of Newton-Raphson method for inverse square root - 1.5 * x_n = input/2 * (x_n)^3 |
| constexpr int32_t num_iteration = 5; |
| for(int32_t i = 0; i < num_iteration; ++i) |
| { |
| const auto x3 = fixed_point_rescale(fixed_point_mul(fixed_point_mul(x, x), x), 9, fixedpoint_position); |
| x = fixed_point_rescale(fixed_point_mul(fixedpoint_half_three, x) - fixed_point_mul(fixedpoint_half_input, x3), 6, fixedpoint_position); |
| } |
| |
| // fixed point representation of sqrt(1/2) |
| const FixedPoint0 fixedpoint_half_sqrt_2 = 1518500250; |
| x = fixed_point_mul(fixedpoint_half_sqrt_2, x); |
| output_inv_sqrt = x; |
| if(output_shift < 0) |
| { |
| output_inv_sqrt <<= -output_shift; |
| output_shift = 0; |
| } |
| // convert right shift to left shift |
| output_shift *= reverse_shift; |
| } |
| } // quantization |
| } // arm_compute |