all_close_f.cpp

//*****************************************************************************
// Copyright 2017-2019 Intel Corporation
//
// 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 <algorithm>
#include <bitset>
#include <cmath>
#include <limits>
#include <sstream>

#include "gtest/gtest.h"

#include "ngraph/ngraph.hpp"
#include "util/all_close_f.hpp"

using namespace std;
using namespace ngraph;

union FloatUnion {
    FloatUnion() { i = 0; }
    FloatUnion(float val) { f = val; }
    FloatUnion(uint32_t val) { i = val; }
    float f;
    uint32_t i;
};

union DoubleUnion {
    DoubleUnion() { i = 0; }
    DoubleUnion(double val) { d = val; }
    DoubleUnion(uint64_t val) { i = val; }
    double d;
    uint64_t i;
};

string float_to_bits(float f)
{
    FloatUnion fu{f};
    stringstream ss;
    ss << bitset<32>(fu.i);
    string unformatted = ss.str();
    string formatted;
    formatted.reserve(41);
    // Sign
    formatted.push_back(unformatted[0]);
    formatted.append("  ");
    // Exponent
    formatted.append(unformatted, 1, 8);
    formatted.append("  ");
    // Mantissa
    formatted.append(unformatted, 9, 3);
    for (int i = 12; i < 32; i += 4)
    {
        formatted.push_back(' ');
        formatted.append(unformatted, i, 4);
    }
    return formatted;
}

string double_to_bits(double d)
{
    DoubleUnion du{d};
    stringstream ss;
    ss << bitset<64>(du.i);
    string unformatted = ss.str();
    string formatted;
    formatted.reserve(80);
    // Sign
    formatted.push_back(unformatted[0]);
    formatted.append("  ");
    // Exponent
    formatted.append(unformatted, 1, 11);
    formatted.push_back(' ');
    // Mantissa
    for (int i = 12; i < 64; i += 4)
    {
        formatted.push_back(' ');
        formatted.append(unformatted, i, 4);
    }
    return formatted;
}

float bits_to_float(const string& s)
{
    string unformatted = s;
    unformatted.erase(remove_if(unformatted.begin(), unformatted.end(), ::isspace),
                      unformatted.end());

    if (unformatted.size() != 32)
    {
        throw ngraph_error("Input length must be 32");
    }
    bitset<32> bs(unformatted);
    FloatUnion fu;
    fu.i = static_cast<uint32_t>(bs.to_ulong());
    return fu.f;
}

double bits_to_double(const string& s)
{
    string unformatted = s;
    unformatted.erase(remove_if(unformatted.begin(), unformatted.end(), ::isspace),
                      unformatted.end());

    if (unformatted.size() != 64)
    {
        throw ngraph_error("Input length must be 64");
    }
    bitset<64> bs(unformatted);
    DoubleUnion du;
    du.i = static_cast<uint64_t>(bs.to_ullong());
    return du.d;
}

class all_close_f_param_test : public testing::TestWithParam<::std::tuple<float, int>>
{
protected:
    all_close_f_param_test()
        : upper_bound(FLT_MAX)
        , lower_bound(-FLT_MAX)
        , past_upper_bound(FLT_MAX)
        , past_lower_bound(-FLT_MAX)
    {
        std::tie(expected, tolerance_bits) = GetParam();
    }
    void SetUp() override
    {
        constexpr int mantissa_bits = 24;
        uint32_t expected_as_int = FloatUnion(expected).i;

        // Turn on targeted bit
        // e.g. for float with 24 bit mantissa, 2 bit accuracy, and hard-coded 8 bit exponent_bits
        // tolerance_bit_shift = 32 -           (1 +  8 + (24 -     1         ) - 2             )
        //                       float_length    sign exp  mantissa implicit 1    tolerance_bits
        uint32_t tolerance_bit_shift = 32 - (1 + 8 + (mantissa_bits - 1) - tolerance_bits);
        uint32_t targeted_bit = (1u << tolerance_bit_shift);

        if (expected > 0.f)
        {
            uint32_t upper_bound_as_int = expected_as_int + targeted_bit;
            upper_bound = FloatUnion(upper_bound_as_int).f;
            past_upper_bound = FloatUnion(upper_bound_as_int + 1).f;

            uint32_t lower_bound_as_int = expected_as_int - targeted_bit;
            lower_bound = FloatUnion(lower_bound_as_int).f;
            past_lower_bound = FloatUnion(lower_bound_as_int - 1).f;
        }
        else if (expected < 0.f)
        {
            // Same logic/math as above, but reversed variable name order
            uint32_t lower_bound_as_int = expected_as_int + targeted_bit;
            lower_bound = FloatUnion(lower_bound_as_int).f;
            past_lower_bound = FloatUnion(lower_bound_as_int + 1).f;

            uint32_t upper_bound_as_int = expected_as_int - targeted_bit;
            upper_bound = FloatUnion(upper_bound_as_int).f;
            past_upper_bound = FloatUnion(upper_bound_as_int - 1).f;
        }
        else // (expected == 0.f) || (expected == -0.f)
        {
            // Special handling of 0 / -0 which get same bounds
            uint32_t upper_bound_as_int = targeted_bit;
            upper_bound = FloatUnion(upper_bound_as_int).f;
            uint32_t past_upper_bound_as_int = upper_bound_as_int + 1;
            past_upper_bound = FloatUnion(past_upper_bound_as_int).f;

            lower_bound = FloatUnion(upper_bound_as_int | 0x80000000).f;
            past_lower_bound = FloatUnion(past_upper_bound_as_int | 0x80000000).f;
        }
    }

    float expected;
    int tolerance_bits;
    float upper_bound;
    float lower_bound;
    float past_upper_bound;
    float past_lower_bound;
};

TEST_P(all_close_f_param_test, test_boundaries)
{
    if (std::getenv("NGRAPH_GTEST_INFO") != nullptr)
    {
        // Print short string documenting which test is being run
        std::cout << "[   INFO   ] Test params: (" << expected << ", " << tolerance_bits << ")\n";
    }

    // Format verbose info to only print out in case of test failure
    stringstream ss;
    ss << "Testing target of: " << expected << " (" << float_to_bits(expected) << ")\n";
    ss << "Matching to targets with: " << tolerance_bits << " tolerance_bits\n";
    ss << "upper_bound: " << upper_bound << " (" << float_to_bits(upper_bound) << ")\n";
    ss << "lower_bound: " << lower_bound << " (" << float_to_bits(lower_bound) << ")\n";
    ss << "past_upper_bound: " << past_upper_bound << " (" << float_to_bits(past_upper_bound)
       << ")\n";
    ss << "past_lower_bound: " << past_lower_bound << " (" << float_to_bits(past_lower_bound)
       << ")\n";

    EXPECT_TRUE(test::close_f(expected, upper_bound, tolerance_bits)) << ss.str();
    EXPECT_TRUE(
        test::all_close_f(vector<float>({expected}), vector<float>({upper_bound}), tolerance_bits))
        << ss.str();
    EXPECT_TRUE(test::close_f(expected, lower_bound, tolerance_bits)) << ss.str();
    EXPECT_TRUE(
        test::all_close_f(vector<float>({expected}), vector<float>({lower_bound}), tolerance_bits))
        << ss.str();
    EXPECT_FALSE(test::close_f(expected, past_upper_bound, tolerance_bits)) << ss.str();
    EXPECT_FALSE(test::all_close_f(
        vector<float>({expected}), vector<float>({past_upper_bound}), tolerance_bits))
        << ss.str();
    EXPECT_FALSE(test::close_f(expected, past_lower_bound, tolerance_bits)) << ss.str();
    EXPECT_FALSE(test::all_close_f(
        vector<float>({expected}), vector<float>({past_lower_bound}), tolerance_bits))
        << ss.str();
}

INSTANTIATE_TEST_CASE_P(test_simple_floats_with_range_of_precisions,
                        all_close_f_param_test,
                        testing::Combine(testing::Values(0.f,
                                                         -0.f,
                                                         1.f,
                                                         -1.f,
                                                         10.f,
                                                         -10.f,
                                                         0.75f,
                                                         -0.75f,
                                                         0.5f,
                                                         -0.5f,
                                                         0.25f,
                                                         -0.25f,
                                                         0.125f,
                                                         -0.125f),
                                         testing::Range(0, 5)), );

class all_close_f_double_param_test : public testing::TestWithParam<::std::tuple<double, int>>
{
protected:
    all_close_f_double_param_test()
        : upper_bound(DBL_MAX)
        , lower_bound(-DBL_MAX)
        , past_upper_bound(DBL_MAX)
        , past_lower_bound(-DBL_MAX)
    {
        std::tie(expected, tolerance_bits) = GetParam();
    }
    void SetUp() override
    {
        constexpr int mantissa_bits = 53;
        uint64_t expected_as_int = DoubleUnion(expected).i;
        // Turn on targeted bit
        // e.g. for double with 52 bit mantissa, 2 bit accuracy, and hard-coded 11 bit exponent_bits
        // tolerance_bit_shift = 64 -           (1 +  11 + (52 -     1         ) - 2             )
        //                       double_length   sign exp   mantissa implicit 1    tolerance_bits
        uint64_t tolerance_bit_shift = 64 - (1 + 11 + (mantissa_bits - 1) - tolerance_bits);
        uint64_t targeted_bit = (1ull << tolerance_bit_shift);

        if (expected > 0.)
        {
            uint64_t upper_bound_as_int = expected_as_int + targeted_bit;
            upper_bound = DoubleUnion(upper_bound_as_int).d;
            past_upper_bound = DoubleUnion(upper_bound_as_int + 1).d;

            uint64_t lower_bound_as_int = expected_as_int - targeted_bit;
            lower_bound = DoubleUnion(lower_bound_as_int).d;
            past_lower_bound = DoubleUnion(lower_bound_as_int - 1).d;
        }
        else if (expected < 0.)
        {
            // Same logic/math as above, but reversed variable name order
            uint64_t lower_bound_as_int = expected_as_int + targeted_bit;
            lower_bound = DoubleUnion(lower_bound_as_int).d;
            past_lower_bound = DoubleUnion(lower_bound_as_int + 1).d;

            uint64_t upper_bound_as_int = expected_as_int - targeted_bit;
            upper_bound = DoubleUnion(upper_bound_as_int).d;
            past_upper_bound = DoubleUnion(upper_bound_as_int - 1).d;
        }
        else // (expected == 0.) || (expected == -0.)
        {
            // Special handling of 0 / -0 which get same bounds
            uint64_t upper_bound_as_int = targeted_bit;
            upper_bound = DoubleUnion(upper_bound_as_int).d;
            uint64_t past_upper_bound_as_int = upper_bound_as_int + 1;
            past_upper_bound = DoubleUnion(past_upper_bound_as_int).d;

            lower_bound = DoubleUnion(upper_bound_as_int | 0x8000000000000000).d;
            past_lower_bound = DoubleUnion(past_upper_bound_as_int | 0x8000000000000000).d;
        }
    }

    double expected;
    int tolerance_bits;
    double upper_bound;
    double lower_bound;
    double past_upper_bound;
    double past_lower_bound;
};

TEST_P(all_close_f_double_param_test, test_boundaries)
{
    if (std::getenv("NGRAPH_GTEST_INFO") != nullptr)
    {
        // Print short string documenting which test is being run
        std::cout << "[   INFO   ] Test params: (" << expected << ", " << tolerance_bits << ")\n";
    }

    // Format verbose info to only print out in case of test failure

    stringstream ss;
    ss << "Testing target of: " << expected << " (" << double_to_bits(expected) << ")\n";
    ss << "Matching to targets with: " << tolerance_bits << " tolerance_bits\n";
    ss << "upper_bound: " << upper_bound << " (" << double_to_bits(upper_bound) << ")\n";
    ss << "lower_bound: " << lower_bound << " (" << double_to_bits(lower_bound) << ")\n";
    ss << "past_upper_bound: " << past_upper_bound << " (" << double_to_bits(past_upper_bound)
       << ")\n";
    ss << "past_lower_bound: " << past_lower_bound << " (" << double_to_bits(past_lower_bound)
       << ")\n";

    EXPECT_TRUE(test::close_f(expected, upper_bound, tolerance_bits)) << ss.str();
    EXPECT_TRUE(test::all_close_f(
        vector<double>({expected}), vector<double>({upper_bound}), tolerance_bits))
        << ss.str();
    EXPECT_TRUE(test::close_f(expected, lower_bound, tolerance_bits)) << ss.str();
    EXPECT_TRUE(test::all_close_f(
        vector<double>({expected}), vector<double>({lower_bound}), tolerance_bits))
        << ss.str();
    EXPECT_FALSE(test::close_f(expected, past_upper_bound, tolerance_bits)) << ss.str();
    EXPECT_FALSE(test::all_close_f(
        vector<double>({expected}), vector<double>({past_upper_bound}), tolerance_bits))
        << ss.str();
    EXPECT_FALSE(test::close_f(expected, past_lower_bound, tolerance_bits)) << ss.str();
    EXPECT_FALSE(test::all_close_f(
        vector<double>({expected}), vector<double>({past_lower_bound}), tolerance_bits))
        << ss.str();
}

INSTANTIATE_TEST_CASE_P(
    test_simple_doubles_with_range_of_precisions,
    all_close_f_double_param_test,
    testing::Combine(
        testing::Values(
            0., -0., 1., -1., 10., -10., 0.75, -0.75, 0.5, -0.5, 0.25, -0.25, 0.125, -0.125),
        testing::Range(0, 17)), );

// Test the exact bounds near +0.f
//
// With tolerance_bits = 18
// (equivalent to testing bfloat precision with 2 bits tolerance)
//
//                           Targeted bit
//                           |
//                           v
//                   2 3 4 5 6    (error allowed in 6th bit or later, w/ implicit leading bit)
// s e e e e e e e e m m m m m m m m m m m m m m m m m m m m m m m
//                =>|      8      |    (8 w/ implicit leading bit)
//                           ^
//                           |  2 |<=
//
// [Upper bound]
//                           Add 1 at this bit
//                           |
//                           v
// 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
// +                         1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
// ---------------------------------------------------------------
// 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
//
// [Lower bound]
//                           Minus 1 at this bit
//                           |
//                           v
// 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
// -                         1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
// ---------------------------------------------------------------
// 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
//
// Convert to 2's compliment
// 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
//
// Mask the sign bit
// 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
TEST(all_close_f, mantissa_8_near_0)
{
    constexpr int tolerance_bits = (FLOAT_MANTISSA_BITS - BFLOAT_MANTISSA_BITS + 2);

    // 0.f, the ground-truth value
    float expected = bits_to_float("0  00000000  000 0000 0000 0000 0000 0000");
    float computed;

    // ~3.67342E-40, the exact upper bound
    computed = bits_to_float("0  00000000  000 0100 0000 0000 0000 0000");
    EXPECT_TRUE(test::close_f(expected, computed, tolerance_bits));
    EXPECT_TRUE(
        test::all_close_f(vector<float>({expected}), vector<float>({computed}), tolerance_bits));

    // ~3.67343E-40, the next representable number bigger than upper bound
    computed = bits_to_float("0  00000000  000 0100 0000 0000 0000 0001");
    EXPECT_FALSE(test::close_f(expected, computed, tolerance_bits));
    EXPECT_FALSE(
        test::all_close_f(vector<float>({expected}), vector<float>({computed}), tolerance_bits));

    // ~-3.67342E-40, the exact lower bound
    computed = bits_to_float("1  00000000  000 0100 0000 0000 0000 0000");
    EXPECT_TRUE(test::close_f(expected, computed, tolerance_bits));
    EXPECT_TRUE(
        test::all_close_f(vector<float>({expected}), vector<float>({computed}), tolerance_bits));

    // ~-3.67343E-40, the next representable number smaller than lower bound
    computed = bits_to_float("1  00000000  000 0100 0000 0000 0000 0001");
    EXPECT_FALSE(test::close_f(expected, computed, tolerance_bits));
    EXPECT_FALSE(
        test::all_close_f(vector<float>({expected}), vector<float>({computed}), tolerance_bits));
}

// Test the exact bounds near -0.f
//
// With tolerance_bits = 18
// (equivalent to testing bfloat precision with 2 bits tolerance)
//
//                           Targeted bit
//                           |
//                           v
//                   2 3 4 5 6    (error allowed in 6th bit or later, w/ implicit leading bit)
// s e e e e e e e e m m m m m m m m m m m m m m m m m m m m m m m
//                =>|      8      |    (8 w/ implicit leading bit)
//                           ^
//                           |  2 |<=
//
// [Upper bound]
//                           Minus 1 at this bit
//                           |
//                           v
// 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
// -                         1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
// ---------------------------------------------------------------
// 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
//
// Convert to 2's compliment
// 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
//
// Mask off sign bit
// 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
//
// [Lower bound]
//                           Add 1 at this bit
//                           |
//                           v
// 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
// +                         1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
// ---------------------------------------------------------------
// 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
TEST(all_close_f, mantissa_8_near_n0)
{
    constexpr int tolerance_bits = (FLOAT_MANTISSA_BITS - BFLOAT_MANTISSA_BITS + 2);

    // 0.f, the ground-truth value
    float expected = bits_to_float("1  00000000  000 0000 0000 0000 0000 0000");
    float computed;

    // ~3.67342E-40, the exact upper bound
    computed = bits_to_float("0  00000000  000 0100 0000 0000 0000 0000");
    EXPECT_TRUE(test::close_f(expected, computed, tolerance_bits));
    EXPECT_TRUE(
        test::all_close_f(vector<float>({expected}), vector<float>({computed}), tolerance_bits));

    // ~3.67343E-40, the next representable number bigger than upper bound
    computed = bits_to_float("0  00000000  000 0100 0000 0000 0000 0001");
    EXPECT_FALSE(test::close_f(expected, computed, tolerance_bits));
    EXPECT_FALSE(
        test::all_close_f(vector<float>({expected}), vector<float>({computed}), tolerance_bits));

    // ~-3.67342E-40, the exact lower bound
    computed = bits_to_float("1  00000000  000 0100 0000 0000 0000 0000");
    EXPECT_TRUE(test::close_f(expected, computed, tolerance_bits));
    EXPECT_TRUE(
        test::all_close_f(vector<float>({expected}), vector<float>({computed}), tolerance_bits));

    // ~-3.67343E-40, the next representable number smaller than lower bound
    computed = bits_to_float("1  00000000  000 0100 0000 0000 0000 0001");
    EXPECT_FALSE(test::close_f(expected, computed, tolerance_bits));
    EXPECT_FALSE(
        test::all_close_f(vector<float>({expected}), vector<float>({computed}), tolerance_bits));
}

// Test the exact bounds near 1.f
//
// With tolerance_bits = 18
// (equivalent to testing bfloat precision with 2 bits tolerance)
//
//                           Targeted bit
//                           |
//                           v
//                   2 3 4 5 6    (error allowed in 6th bit or later, w/ implicit leading bit)
// s e e e e e e e e m m m m m m m m m m m m m m m m m m m m m m m
//                =>|      8      |    (8 w/ implicit leading bit)
//                           ^
//                           |  2 |<=
//
// [Upper bound]
//                           Add 1 at this bit to get upper bound
//                           |
//                           v
// 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
// +                         1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
// ---------------------------------------------------------------
// 0 0 1 1 1 1 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
//
// [Lower bound]
//                           Minus 1 at this bit to get lower bound
//                           |
//                           v
// 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
// -                         1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
// ---------------------------------------------------------------
// 0 0 1 1 1 1 1 1 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
TEST(all_close_f, mantissa_8_near_1)
{
    constexpr int tolerance_bits = (FLOAT_MANTISSA_BITS - BFLOAT_MANTISSA_BITS + 2);

    // 1.f, the ground-truth value
    float expected = bits_to_float("0  01111111  000 0000 0000 0000 0000 0000");
    float computed;

    // 1.03125f, the exact upper bound
    computed = bits_to_float("0  01111111  000 0100 0000 0000 0000 0000");
    EXPECT_TRUE(test::close_f(expected, computed, tolerance_bits));
    EXPECT_TRUE(
        test::all_close_f(vector<float>({expected}), vector<float>({computed}), tolerance_bits));

    // 1.031250119f, the next representable number bigger than upper bound
    computed = bits_to_float("0  01111111  000 0100 0000 0000 0000 0001");
    EXPECT_FALSE(test::close_f(expected, computed, tolerance_bits));
    EXPECT_FALSE(
        test::all_close_f(vector<float>({expected}), vector<float>({computed}), tolerance_bits));

    // 0.984375f, the exact lower bound
    computed = bits_to_float("0  01111110  111 1100 0000 0000 0000 0000");
    EXPECT_TRUE(test::close_f(expected, computed, tolerance_bits));
    EXPECT_TRUE(
        test::all_close_f(vector<float>({expected}), vector<float>({computed}), tolerance_bits));

    // 0.9843749404f, the next representable number smaller than lower bound
    computed = bits_to_float("0  01111110  111 1011 1111 1111 1111 1111");
    EXPECT_FALSE(test::close_f(expected, computed, tolerance_bits));
    EXPECT_FALSE(
        test::all_close_f(vector<float>({expected}), vector<float>({computed}), tolerance_bits));
}

// Test the exact bounds near -1.f
//
// With tolerance_bits = 18
// (equivalent to testing bfloat precision with 2 bits tolerance)
//
//                           Targeted bit
//                           |
//                           v
//                   2 3 4 5 6    (error allowed in 6th bit or later, w/ implicit leading bit)
// s e e e e e e e e m m m m m m m m m m m m m m m m m m m m m m m
//                =>|      8      |    (8 w/ implicit leading bit)
//                           ^
//                           |  2 |<=
//
// [Upper bound]
//                           Minus 1 at this bit
//                           |
//                           v
// 1 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
// -                         1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
// ---------------------------------------------------------------
// 1 0 1 1 1 1 1 1 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
//
// [Lower bound]
//                           Add 1 at this bit
//                           |
//                           v
// 1 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
// +                         1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
// ---------------------------------------------------------------
// 1 0 1 1 1 1 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
TEST(all_close_f, mantissa_8_near_n1)
{
    constexpr int tolerance_bits = (FLOAT_MANTISSA_BITS - BFLOAT_MANTISSA_BITS + 2);

    // -1.f, the ground-truth value
    float expected = bits_to_float("1  01111111  000 0000 0000 0000 0000 0000");
    float computed;

    // -0.984375f, the exact upper bound
    computed = bits_to_float("1  01111110  111 1100 0000 0000 0000 0000");
    EXPECT_TRUE(test::close_f(expected, computed, tolerance_bits));
    EXPECT_TRUE(
        test::all_close_f(vector<float>({expected}), vector<float>({computed}), tolerance_bits));

    // -0.984374940395355224609375f, the next representable number bigger than upper bound
    computed = bits_to_float("1  01111110  111 1011 1111 1111 1111 1111");
    EXPECT_FALSE(test::close_f(expected, computed, tolerance_bits));
    EXPECT_FALSE(
        test::all_close_f(vector<float>({expected}), vector<float>({computed}), tolerance_bits));

    // -1.03125f, the exact lower bound
    computed = bits_to_float("1  01111111  000 0100 0000 0000 0000 0000");
    EXPECT_TRUE(test::close_f(expected, computed, tolerance_bits));
    EXPECT_TRUE(
        test::all_close_f(vector<float>({expected}), vector<float>({computed}), tolerance_bits));

    // -1.03125011920928955078125f, the next representable number smaller than lower bound
    computed = bits_to_float("1  01111111  000 0100 0000 0000 0000 0001");
    EXPECT_FALSE(test::close_f(expected, computed, tolerance_bits));
    EXPECT_FALSE(
        test::all_close_f(vector<float>({expected}), vector<float>({computed}), tolerance_bits));
}

// For intuitive understanding of tightness of bounds in decimal
// Test bounds near 0, 1, 10, 100, 1000 with tolerance_bits = 18
//
//                           Targeted bit
//                           |
//                           v
//                   2 3 4 5 6    (error allowed in 6th bit or later, w/ implicit leading bit)
// s e e e e e e e e m m m m m m m m m m m m m m m m m m m m m m m
//                =>|      8      |    (8 w/ implicit leading bit)
//                           ^
//                           |  2 |<=
TEST(all_close_f, mantissa_8_near_0_1_10_100_1000)
{
    constexpr int tolerance_bits = (FLOAT_MANTISSA_BITS - BFLOAT_MANTISSA_BITS + 2);

    float expected;
    float upper_bound;
    float bigger_than_upper_bound;
    float lower_bound;
    float smaller_than_lower_bound;

    // Bounds around 0: 0 +- 3.67e-40
    expected = 0.f;             // 0  00000000  000 0000 0000 0000 0000 0000
    upper_bound = 3.67342e-40f; // 0  00000000  000 0100 0000 0000 0000 0000, approximated
    bigger_than_upper_bound =
        3.67343e-40f;            // 0  00000000  000 0100 0000 0000 0000 0001, approximated
    lower_bound = -3.67342e-40f; // 1  00000000  000 0100 0000 0000 0000 0000, approximated
    smaller_than_lower_bound =
        3.67343e-40f; // 1  00000000  000 0100 0000 0000 0000 0001, approximated
    EXPECT_TRUE(test::close_f(expected, upper_bound, tolerance_bits));
    EXPECT_TRUE(
        test::all_close_f(vector<float>({expected}), vector<float>({upper_bound}), tolerance_bits));
    EXPECT_FALSE(test::close_f(expected, bigger_than_upper_bound, tolerance_bits));
    EXPECT_FALSE(test::all_close_f(
        vector<float>({expected}), vector<float>({bigger_than_upper_bound}), tolerance_bits));
    EXPECT_TRUE(test::close_f(expected, lower_bound, tolerance_bits));
    EXPECT_TRUE(
        test::all_close_f(vector<float>({expected}), vector<float>({lower_bound}), tolerance_bits));
    EXPECT_FALSE(test::close_f(expected, smaller_than_lower_bound, tolerance_bits));
    EXPECT_FALSE(test::all_close_f(
        vector<float>({expected}), vector<float>({smaller_than_lower_bound}), tolerance_bits));

    // Bounds around 1: 1 +- 0.03
    expected = 1.f;                           // 0  01111111  000 0000 0000 0000 0000 0000
    upper_bound = 1.03125f;                   // 0  01111111  000 0100 0000 0000 0000 0000
    bigger_than_upper_bound = 1.031250119f;   // 0  01111111  000 0100 0000 0000 0000 0001
    lower_bound = 0.984375f;                  // 0  01111110  111 1100 0000 0000 0000 0000
    smaller_than_lower_bound = 0.9843749404f; // 0  01111110  111 1011 1111 1111 1111 1111
    EXPECT_TRUE(test::close_f(expected, upper_bound, tolerance_bits));
    EXPECT_TRUE(
        test::all_close_f(vector<float>({expected}), vector<float>({upper_bound}), tolerance_bits));
    EXPECT_FALSE(test::close_f(expected, bigger_than_upper_bound, tolerance_bits));
    EXPECT_FALSE(test::all_close_f(
        vector<float>({expected}), vector<float>({bigger_than_upper_bound}), tolerance_bits));
    EXPECT_TRUE(test::close_f(expected, lower_bound, tolerance_bits));
    EXPECT_TRUE(
        test::all_close_f(vector<float>({expected}), vector<float>({lower_bound}), tolerance_bits));
    EXPECT_FALSE(test::close_f(expected, smaller_than_lower_bound, tolerance_bits));
    EXPECT_FALSE(test::all_close_f(
        vector<float>({expected}), vector<float>({smaller_than_lower_bound}), tolerance_bits));

    // Bounds around 10: 10 +- 0.25
    expected = 10.f;                                    // 0  10000010  010 0000 0000 0000 0000 0000
    upper_bound = 10.25f;                               // 0  10000010  010 0100 0000 0000 0000 0000
    bigger_than_upper_bound = 10.25000095367431640625f; // 0  10000010  010 0100 0000 0000 0000 0001
    lower_bound = 9.75f;                                // 0  10000010  001 1100 0000 0000 0000 0000
    smaller_than_lower_bound = 9.74999904632568359375f; // 0  10000010  001 1011 1111 1111 1111 1111
    EXPECT_TRUE(test::close_f(expected, upper_bound, tolerance_bits));
    EXPECT_TRUE(
        test::all_close_f(vector<float>({expected}), vector<float>({upper_bound}), tolerance_bits));
    EXPECT_FALSE(test::close_f(expected, bigger_than_upper_bound, tolerance_bits));
    EXPECT_FALSE(test::all_close_f(
        vector<float>({expected}), vector<float>({bigger_than_upper_bound}), tolerance_bits));
    EXPECT_TRUE(test::close_f(expected, lower_bound, tolerance_bits));
    EXPECT_TRUE(
        test::all_close_f(vector<float>({expected}), vector<float>({lower_bound}), tolerance_bits));
    EXPECT_FALSE(test::close_f(expected, smaller_than_lower_bound, tolerance_bits));
    EXPECT_FALSE(test::all_close_f(
        vector<float>({expected}), vector<float>({smaller_than_lower_bound}), tolerance_bits));

    // Bounds around 100: 100 +- 2
    expected = 100.f;                                 // 0  10000101  100 1000 0000 0000 0000 0000
    upper_bound = 102.f;                              // 0  10000101  100 1100 0000 0000 0000 0000
    bigger_than_upper_bound = 102.00000762939453125f; // 0  10000101  100 1100 0000 0000 0000 0001
    lower_bound = 98.0f;                              // 0  10000101  100 0100 0000 0000 0000 0000
    smaller_than_lower_bound = 97.99999237060546875f; // 0  10000101  100 0011 1111 1111 1111 1111
    EXPECT_TRUE(test::close_f(expected, upper_bound, tolerance_bits));
    EXPECT_TRUE(
        test::all_close_f(vector<float>({expected}), vector<float>({upper_bound}), tolerance_bits));
    EXPECT_FALSE(test::close_f(expected, bigger_than_upper_bound, tolerance_bits));
    EXPECT_FALSE(test::all_close_f(
        vector<float>({expected}), vector<float>({bigger_than_upper_bound}), tolerance_bits));
    EXPECT_TRUE(test::close_f(expected, lower_bound, tolerance_bits));
    EXPECT_TRUE(
        test::all_close_f(vector<float>({expected}), vector<float>({lower_bound}), tolerance_bits));
    EXPECT_FALSE(test::close_f(expected, smaller_than_lower_bound, tolerance_bits));
    EXPECT_FALSE(test::all_close_f(
        vector<float>({expected}), vector<float>({smaller_than_lower_bound}), tolerance_bits));

    // Bounds around 1000: 1000 +- 16
    expected = 1000.f;                              // 0  10001000  111 1010 0000 0000 0000 0000
    upper_bound = 1016.f;                           // 0  10001000  111 1110 0000 0000 0000 0000
    bigger_than_upper_bound = 1016.00006103515625f; // 0  10001000  111 1110 0000 0000 0000 0001
    lower_bound = 984.0f;                           // 0  10001000  111 0110 0000 0000 0000 0000
    smaller_than_lower_bound = 983.99993896484375f; // 0  10001000  111 0101 1111 1111 1111 1111
    EXPECT_TRUE(test::close_f(expected, upper_bound, tolerance_bits));
    EXPECT_TRUE(
        test::all_close_f(vector<float>({expected}), vector<float>({upper_bound}), tolerance_bits));
    EXPECT_FALSE(test::close_f(expected, bigger_than_upper_bound, tolerance_bits));
    EXPECT_FALSE(test::all_close_f(
        vector<float>({expected}), vector<float>({bigger_than_upper_bound}), tolerance_bits));
    EXPECT_TRUE(test::close_f(expected, lower_bound, tolerance_bits));
    EXPECT_TRUE(
        test::all_close_f(vector<float>({expected}), vector<float>({lower_bound}), tolerance_bits));
    EXPECT_FALSE(test::close_f(expected, smaller_than_lower_bound, tolerance_bits));
    EXPECT_FALSE(test::all_close_f(
        vector<float>({expected}), vector<float>({smaller_than_lower_bound}), tolerance_bits));
}

// For intuitive understanding of tightness of bounds in decimal
// Test bounds near 0, 1, 10, 100, 1000 with tolerance_bits = 2
//
//                                                           Targeted bit
//                                                           |
//            (22 bits must match, w/ implicit leading bit)  v
//                   2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2
// s e e e e e e e e m m m m m m m m m m m m m m m m m m m m m m m
//                =>|        24 (w/ implicit leading bit)         |
//                                                           ^
//                                                           | 2  |<=
TEST(all_close_f, mantissa_24_near_0_1_10_100_1000)
{
    constexpr int tolerance_bits = 2;

    float expected;
    float upper_bound;
    float bigger_than_upper_bound;
    float lower_bound;
    float smaller_than_lower_bound;

    // Bounds around 0: 0 +- 5.6e-45
    expected = 0.f;
    upper_bound = bits_to_float("0  00000000  000 0000 0000 0000 0000 0100");
    bigger_than_upper_bound = bits_to_float("0  00000000  000 0000 0000 0000 0000 0101");
    lower_bound = bits_to_float("1  00000000  000 0000 0000 0000 0000 0100");
    smaller_than_lower_bound = bits_to_float("1  00000000  000 0000 0000 0000 0000 0101");
    EXPECT_TRUE(test::close_f(expected, upper_bound, tolerance_bits));
    EXPECT_TRUE(
        test::all_close_f(vector<float>({expected}), vector<float>({upper_bound}), tolerance_bits));
    EXPECT_FALSE(test::close_f(expected, bigger_than_upper_bound, tolerance_bits));
    EXPECT_FALSE(test::all_close_f(
        vector<float>({expected}), vector<float>({bigger_than_upper_bound}), tolerance_bits));
    EXPECT_TRUE(test::close_f(expected, lower_bound, tolerance_bits));
    EXPECT_TRUE(
        test::all_close_f(vector<float>({expected}), vector<float>({lower_bound}), tolerance_bits));
    EXPECT_FALSE(test::close_f(expected, smaller_than_lower_bound, tolerance_bits));
    EXPECT_FALSE(test::all_close_f(
        vector<float>({expected}), vector<float>({smaller_than_lower_bound}), tolerance_bits));

    // Bounds around 1: 1 +- 4.77e-7
    expected = 1.f;
    upper_bound = bits_to_float("0  01111111  000 0000 0000 0000 0000 0100");
    bigger_than_upper_bound = bits_to_float("0  01111111  000 0000 0000 0000 0000 0101");
    lower_bound = bits_to_float("0  01111110  111 1111 1111 1111 1111 1100");
    smaller_than_lower_bound = bits_to_float("0  01111110  111 1111 1111 1111 1111 1011");
    EXPECT_TRUE(test::close_f(expected, upper_bound, tolerance_bits));
    EXPECT_TRUE(
        test::all_close_f(vector<float>({expected}), vector<float>({upper_bound}), tolerance_bits));
    EXPECT_FALSE(test::close_f(expected, bigger_than_upper_bound, tolerance_bits));
    EXPECT_FALSE(test::all_close_f(
        vector<float>({expected}), vector<float>({bigger_than_upper_bound}), tolerance_bits));
    EXPECT_TRUE(test::close_f(expected, lower_bound, tolerance_bits));
    EXPECT_TRUE(
        test::all_close_f(vector<float>({expected}), vector<float>({lower_bound}), tolerance_bits));
    EXPECT_FALSE(test::close_f(expected, smaller_than_lower_bound, tolerance_bits));
    EXPECT_FALSE(test::all_close_f(
        vector<float>({expected}), vector<float>({smaller_than_lower_bound}), tolerance_bits));

    // Bounds around 10: 10 +- 3.81e-6
    expected = 10.f;
    upper_bound = bits_to_float("0  10000010  010 0000 0000 0000 0000 0100");
    bigger_than_upper_bound = bits_to_float("0  10000010  010 0000 0000 0000 0000 0101");
    lower_bound = bits_to_float("0  10000010  001 1111 1111 1111 1111 1100");
    smaller_than_lower_bound = bits_to_float("0  10000010  001 1111 1111 1111 1111 1011");
    EXPECT_TRUE(test::close_f(expected, upper_bound, tolerance_bits));
    EXPECT_TRUE(
        test::all_close_f(vector<float>({expected}), vector<float>({upper_bound}), tolerance_bits));
    EXPECT_FALSE(test::close_f(expected, bigger_than_upper_bound, tolerance_bits));
    EXPECT_FALSE(test::all_close_f(
        vector<float>({expected}), vector<float>({bigger_than_upper_bound}), tolerance_bits));
    EXPECT_TRUE(test::close_f(expected, lower_bound, tolerance_bits));
    EXPECT_TRUE(
        test::all_close_f(vector<float>({expected}), vector<float>({lower_bound}), tolerance_bits));
    EXPECT_FALSE(test::close_f(expected, smaller_than_lower_bound, tolerance_bits));
    EXPECT_FALSE(test::all_close_f(
        vector<float>({expected}), vector<float>({smaller_than_lower_bound}), tolerance_bits));

    // Bounds around 100: 100 +- 3.05e-5
    expected = 100.f;
    upper_bound = bits_to_float("0  10000101  100 1000 0000 0000 0000 0100");
    bigger_than_upper_bound = bits_to_float("0  10000101  100 1000 0000 0000 0000 0101");
    lower_bound = bits_to_float("0  10000101  100 0111 1111 1111 1111 1100");
    smaller_than_lower_bound = bits_to_float("0  10000101  100 0111 1111 1111 1111 1011");
    EXPECT_TRUE(test::close_f(expected, upper_bound, tolerance_bits));
    EXPECT_TRUE(
        test::all_close_f(vector<float>({expected}), vector<float>({upper_bound}), tolerance_bits));
    EXPECT_FALSE(test::close_f(expected, bigger_than_upper_bound, tolerance_bits));
    EXPECT_FALSE(test::all_close_f(
        vector<float>({expected}), vector<float>({bigger_than_upper_bound}), tolerance_bits));
    EXPECT_TRUE(test::close_f(expected, lower_bound, tolerance_bits));
    EXPECT_TRUE(
        test::all_close_f(vector<float>({expected}), vector<float>({lower_bound}), tolerance_bits));
    EXPECT_FALSE(test::close_f(expected, smaller_than_lower_bound, tolerance_bits));
    EXPECT_FALSE(test::all_close_f(
        vector<float>({expected}), vector<float>({smaller_than_lower_bound}), tolerance_bits));

    // Bounds around 1000: 1000 +- 2.44e-4
    expected = 1000.f;
    upper_bound = bits_to_float("0  10001000  111 1010 0000 0000 0000 0100");
    bigger_than_upper_bound = bits_to_float("0  10001000  111 1010 0000 0000 0000 0101");
    lower_bound = bits_to_float("0  10001000  111 1001 1111 1111 1111 1100");
    smaller_than_lower_bound = bits_to_float("0  10001000  111 1001 1111 1111 1111 1011");
    EXPECT_TRUE(test::close_f(expected, upper_bound, tolerance_bits));
    EXPECT_TRUE(
        test::all_close_f(vector<float>({expected}), vector<float>({upper_bound}), tolerance_bits));
    EXPECT_FALSE(test::close_f(expected, bigger_than_upper_bound, tolerance_bits));
    EXPECT_FALSE(test::all_close_f(
        vector<float>({expected}), vector<float>({bigger_than_upper_bound}), tolerance_bits));
    EXPECT_TRUE(test::close_f(expected, lower_bound, tolerance_bits));
    EXPECT_TRUE(
        test::all_close_f(vector<float>({expected}), vector<float>({lower_bound}), tolerance_bits));
    EXPECT_FALSE(test::close_f(expected, smaller_than_lower_bound, tolerance_bits));
    EXPECT_FALSE(test::all_close_f(
        vector<float>({expected}), vector<float>({smaller_than_lower_bound}), tolerance_bits));
}

TEST(all_close_f, inf_nan)
{
    float zero = 0.f;
    float infinity = numeric_limits<float>::infinity();
    float neg_infinity = -numeric_limits<float>::infinity();
    float quiet_nan = numeric_limits<float>::quiet_NaN();
    float signaling_nan = numeric_limits<float>::signaling_NaN();

    EXPECT_FALSE(test::close_f(zero, infinity));
    EXPECT_FALSE(test::all_close_f(vector<float>({zero}), vector<float>({infinity})));
    EXPECT_FALSE(test::close_f(zero, neg_infinity));
    EXPECT_FALSE(test::all_close_f(vector<float>({zero}), vector<float>({neg_infinity})));
    EXPECT_FALSE(test::close_f(zero, quiet_nan));
    EXPECT_FALSE(test::all_close_f(vector<float>({zero}), vector<float>({quiet_nan})));
    EXPECT_FALSE(test::close_f(zero, signaling_nan));
    EXPECT_FALSE(test::all_close_f(vector<float>({zero}), vector<float>({signaling_nan})));

    EXPECT_FALSE(test::close_f(infinity, infinity));
    EXPECT_FALSE(test::all_close_f(vector<float>({infinity}), vector<float>({infinity})));
    EXPECT_FALSE(test::close_f(neg_infinity, neg_infinity));
    EXPECT_FALSE(test::all_close_f(vector<float>({neg_infinity}), vector<float>({neg_infinity})));
    EXPECT_FALSE(test::close_f(quiet_nan, quiet_nan));
    EXPECT_FALSE(test::all_close_f(vector<float>({quiet_nan}), vector<float>({quiet_nan})));
    EXPECT_FALSE(test::close_f(signaling_nan, signaling_nan));
    EXPECT_FALSE(test::all_close_f(vector<float>({signaling_nan}), vector<float>({signaling_nan})));
}

TEST(all_close_f, double_inf_nan)
{
    double zero = 0.f;
    double infinity = numeric_limits<double>::infinity();
    double neg_infinity = -numeric_limits<double>::infinity();
    double quiet_nan = numeric_limits<double>::quiet_NaN();
    double signaling_nan = numeric_limits<double>::signaling_NaN();

    EXPECT_FALSE(test::close_f(zero, infinity));
    EXPECT_FALSE(test::all_close_f(vector<double>({zero}), vector<double>({infinity})));
    EXPECT_FALSE(test::close_f(zero, neg_infinity));
    EXPECT_FALSE(test::all_close_f(vector<double>({zero}), vector<double>({neg_infinity})));
    EXPECT_FALSE(test::close_f(zero, quiet_nan));
    EXPECT_FALSE(test::all_close_f(vector<double>({zero}), vector<double>({quiet_nan})));
    EXPECT_FALSE(test::close_f(zero, signaling_nan));
    EXPECT_FALSE(test::all_close_f(vector<double>({zero}), vector<double>({signaling_nan})));

    EXPECT_FALSE(test::close_f(infinity, infinity));
    EXPECT_FALSE(test::all_close_f(vector<double>({infinity}), vector<double>({infinity})));
    EXPECT_FALSE(test::close_f(neg_infinity, neg_infinity));
    EXPECT_FALSE(test::all_close_f(vector<double>({neg_infinity}), vector<double>({neg_infinity})));
    EXPECT_FALSE(test::close_f(quiet_nan, quiet_nan));
    EXPECT_FALSE(test::all_close_f(vector<double>({quiet_nan}), vector<double>({quiet_nan})));
    EXPECT_FALSE(test::close_f(signaling_nan, signaling_nan));
    EXPECT_FALSE(
        test::all_close_f(vector<double>({signaling_nan}), vector<double>({signaling_nan})));
}