src/core/utils/quantization/AsymmHelpers.cpp

/*
 * Copyright (c) 2017-2021 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
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 * 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);
    if(std::fabs(0.0f - multiplier) < internal_epsilon)
    {
        *quant_multiplier = 0;
        *right_shift      = 0;
        return Status{};
    }

    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;
    bool    is_positive_or_zero = a == 0 || b == 0 || (std::signbit(a) == std::signbit(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