libdpf/test/tests/exact_steps_test.cpp

#include <gtest/gtest.h>
#include <tuple>

#include "grotto/exact_steps.hpp"

#include <cmath>
#include <cstdint>
#include <limits>

namespace
{

int ref_bit_width(std::uint16_t bits)
{
    if (bits == 0)
        return 0;
    return 32 - __builtin_clz(static_cast<unsigned>(bits));
}

int ref_countl_one(std::uint16_t bits)
{
    int n = 0;
    for (int b = 15; b >= 0; --b)
    {
        if (((bits >> b) & 1u) == 0)
            break;
        ++n;
    }
    return n;
}

std::uint16_t ref_bit_floor(std::uint16_t bits)
{
    if (bits == 0)
        return 0;
    return std::uint16_t{1} << (ref_bit_width(bits) - 1);
}

std::uint32_t ref_bit_ceil(std::uint16_t bits)
{
    if (bits <= 1)
        return 1;
    if ((bits & (bits - 1u)) == 0)
        return bits;
    return std::uint32_t{1} << ref_bit_width(bits);
}

int ref_ceil_log(std::int16_t raw, unsigned k, int group)
{
    const long double x = std::ldexp(static_cast<long double>(raw < 0 ? -raw : raw), -static_cast<int>(k));
    return static_cast<int>(std::ceil(std::log2(static_cast<double>(x)) / group - 1e-15));
}

int ref_logstar(std::int16_t raw, unsigned k)
{
    long double x = std::ldexp(static_cast<long double>(raw), -static_cast<int>(k));
    int n = 0;
    while (x > 1.0L)
    {
        x = std::log2(static_cast<double>(x));
        ++n;
        if (n > 8)
            break;
    }
    return n;
}

int ref_length(std::int16_t raw, unsigned k, int base)
{
    const long double x = std::ldexp(static_cast<long double>(raw < 0 ? -raw : raw), -static_cast<int>(k));
    const auto n = static_cast<std::int64_t>(std::floor(static_cast<double>(x)));
    if (n <= 0)
        return 1;
    int digits = 0;
    auto m = n;
    while (m > 0)
    {
        m /= base;
        ++digits;
    }
    return digits;
}

}  // namespace

TEST(ExactSteps, WordBitsMatchTheUnsignedPattern)
{
    for (int raw = -32768; raw <= 32767; ++raw)
    {
        const auto bits = static_cast<std::uint16_t>(raw);
        const auto value = static_cast<std::int64_t>(static_cast<std::int16_t>(raw));
        EXPECT_EQ(grotto::eval_bit_width<std::int16_t>(value, 0), ref_bit_width(bits));
        EXPECT_EQ(grotto::eval_countl_one<std::int16_t>(value, 0), ref_countl_one(bits));
        EXPECT_EQ(grotto::eval_has_single_bit<std::int16_t>(value, 0),
            ((bits != 0 && (bits & (bits - 1u)) == 0) ? 1 : 0));
        EXPECT_EQ(grotto::eval_bit_floor<std::int16_t>(value), ref_bit_floor(bits));
        EXPECT_EQ(grotto::eval_bit_ceil<std::int16_t>(value), ref_bit_ceil(bits));
    }
}

TEST(ExactSteps, IntegerLogsAndLogstar)
{
    for (unsigned k : {0u, 4u})
    {
        for (int raw = 1; raw <= 32767; raw += (k == 0 ? 17 : 3))
        {
            const auto value = static_cast<std::int64_t>(raw);
            EXPECT_EQ(grotto::eval_ilog16<std::int16_t>(value, k) >> k, ref_ceil_log(static_cast<std::int16_t>(raw), k, 4))
                << raw << " k=" << k;
            EXPECT_EQ(grotto::eval_ilog256<std::int16_t>(value, k) >> k, ref_ceil_log(static_cast<std::int16_t>(raw), k, 8))
                << raw;
            EXPECT_EQ(grotto::eval_logstar<std::int16_t>(value, k) >> k, ref_logstar(static_cast<std::int16_t>(raw), k))
                << raw;
        }
    }
    EXPECT_EQ(grotto::eval_ilog16<std::int16_t>(0, 0), grotto::ilog_of_zero);
    EXPECT_EQ(grotto::eval_logstar<std::int16_t>(-4, 0), grotto::ilog_of_zero);
    EXPECT_EQ(grotto::eval_logstar<std::int16_t>(1, 0), 0);
    EXPECT_EQ(grotto::eval_logstar<std::int16_t>(2, 0), 1);
    EXPECT_EQ(grotto::eval_logstar<std::int16_t>(4, 0), 2);
    EXPECT_EQ(grotto::eval_logstar<std::int16_t>(16, 0), 3);
}

TEST(ExactSteps, DecimalFloorCeilAndLengths)
{
    for (unsigned k : {0u, 4u})
    {
        for (int raw = -4000; raw <= 4000; raw += 3)
        {
            const long double x = std::ldexp(static_cast<long double>(raw), -static_cast<int>(k));
            const auto floor_raw = static_cast<std::int64_t>(std::floor(static_cast<double>(x)) * std::ldexp(1.0, static_cast<int>(k)));
            const auto ceil_raw = static_cast<std::int64_t>(std::ceil(static_cast<double>(x)) * std::ldexp(1.0, static_cast<int>(k)));
            EXPECT_EQ(grotto::eval_dec_floor(raw, k), floor_raw) << raw;
            EXPECT_EQ(grotto::eval_dec_ceil(raw, k), ceil_raw) << raw;
            const auto width = static_cast<std::int16_t>(raw);
            EXPECT_EQ(grotto::eval_dec_width(raw, k) >> k, ref_length(width, k, 10));
            EXPECT_EQ(grotto::eval_oct_width(raw, k) >> k, ref_length(width, k, 8));
            EXPECT_EQ(grotto::eval_b64_width(raw, k) >> k, ref_length(width, k, 64));
            const auto digits = std::llabs(static_cast<long long>(std::floor(std::fabs(static_cast<double>(x)))));
            EXPECT_EQ(grotto::eval_has_single_digit(raw, k) >> k, digits <= 9 ? 1 : 0);
        }
    }
}

TEST(ExactSteps, AngleScaleIsTheLinearFactor)
{
    const unsigned k = 16;
    const std::int64_t deg = 180ll << k;
    const auto rad = grotto::eval_deg2rad(deg, k);
    const long double want = 180.0L * 3.14159265358979323846L / 180.0L * std::ldexp(1.0L, k);
    EXPECT_LE(std::fabsl(static_cast<long double>(rad) - want), 64.0L);
    const auto back = grotto::eval_rad2deg(rad, k);
    EXPECT_LE(std::llabs(back - deg), 4096);
}

TEST(ExactSteps, StepLutAgreesWithTheScalarOnInt8)
{
    const auto lut = grotto::make_exact_step_lut<std::int8_t>(0, [](std::int64_t raw) {
        return grotto::eval_bit_width<std::int8_t>(raw, 0);
    });
    for (int raw = -128; raw <= 127; ++raw)
        EXPECT_EQ(lut(static_cast<std::int8_t>(raw)), grotto::eval_bit_width<std::int8_t>(raw, 0));
    EXPECT_THROW(grotto::make_exact_step_lut<std::int32_t>(0, [](std::int64_t) { return 0; }), std::invalid_argument);
}