FloatingPointTest.cpp

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/*
 * Copyright 2023 Google LLC
 *
 * Use of this source code is governed by a BSD-style license that can be
 * found in the LICENSE file.
 */
 
#include "include/private/base/SkAssert.h"
#include "include/private/base/SkFloatingPoint.h"
#include "src/base/SkUtils.h"
#include "tests/Test.h"
 
#include <array>
#include <cfloat>
#include <cmath>
#include <cstdint>
#include <cstring>
#include <limits>
 
DEF_TEST(DoubleNearlyZero, reporter) {
    REPORTER_ASSERT(reporter, sk_double_nearly_zero(0.));
    REPORTER_ASSERT(reporter, sk_double_nearly_zero(-0.));
    REPORTER_ASSERT(reporter, sk_double_nearly_zero(DBL_EPSILON));
    REPORTER_ASSERT(reporter, sk_double_nearly_zero(-DBL_EPSILON));
 
    double nearly = 1. / 20000000000LL;
    REPORTER_ASSERT(reporter, nearly != 0);
    REPORTER_ASSERT(reporter, sk_double_nearly_zero(nearly));
    REPORTER_ASSERT(reporter, sk_double_nearly_zero(-nearly));
 
    REPORTER_ASSERT(reporter, !sk_double_nearly_zero(FLT_EPSILON));
    REPORTER_ASSERT(reporter, !sk_double_nearly_zero(-FLT_EPSILON));
    REPORTER_ASSERT(reporter, !sk_double_nearly_zero(1));
    REPORTER_ASSERT(reporter, !sk_double_nearly_zero(-1));
    REPORTER_ASSERT(reporter, !sk_double_nearly_zero(INFINITY));
    REPORTER_ASSERT(reporter, !sk_double_nearly_zero(HUGE_VALF));
    REPORTER_ASSERT(reporter, !sk_double_nearly_zero(HUGE_VAL));
    REPORTER_ASSERT(reporter, !sk_double_nearly_zero(HUGE_VALL));
    REPORTER_ASSERT(reporter, !sk_double_nearly_zero(-INFINITY));
    REPORTER_ASSERT(reporter, !sk_double_nearly_zero(-HUGE_VALF));
    REPORTER_ASSERT(reporter, !sk_double_nearly_zero(-HUGE_VAL));
    REPORTER_ASSERT(reporter, !sk_double_nearly_zero(-HUGE_VALL));
    REPORTER_ASSERT(reporter, !sk_double_nearly_zero(NAN));
    REPORTER_ASSERT(reporter, !sk_double_nearly_zero(-NAN));
}
 
DEF_TEST(DoubleNearlyEqualUlps, reporter) {
    // Our tolerance is looser than DBL_EPSILON
    REPORTER_ASSERT(reporter, sk_doubles_nearly_equal_ulps(1., 1.));
    REPORTER_ASSERT(reporter, sk_doubles_nearly_equal_ulps(1., 1. - DBL_EPSILON));
    REPORTER_ASSERT(reporter, sk_doubles_nearly_equal_ulps(1., 1. + DBL_EPSILON));
    REPORTER_ASSERT(reporter, sk_doubles_nearly_equal_ulps(100.5, 100.5));
    REPORTER_ASSERT(reporter, sk_doubles_nearly_equal_ulps(100.5, 100.5 - DBL_EPSILON));
    REPORTER_ASSERT(reporter, sk_doubles_nearly_equal_ulps(100.5, 100.5 + DBL_EPSILON));
 
    // Our tolerance is tighter than FLT_EPSILON
    REPORTER_ASSERT(reporter, !sk_doubles_nearly_equal_ulps(1., 1. - FLT_EPSILON));
    REPORTER_ASSERT(reporter, !sk_doubles_nearly_equal_ulps(1., 1. + FLT_EPSILON));
    REPORTER_ASSERT(reporter, !sk_doubles_nearly_equal_ulps(100.5, 100.5 - FLT_EPSILON));
    REPORTER_ASSERT(reporter, !sk_doubles_nearly_equal_ulps(100.5, 100.5 + FLT_EPSILON));
    REPORTER_ASSERT(reporter, !sk_doubles_nearly_equal_ulps(0, 0.1));
    REPORTER_ASSERT(reporter, !sk_doubles_nearly_equal_ulps(FLT_EPSILON, 0));
 
    REPORTER_ASSERT(reporter, sk_doubles_nearly_equal_ulps(INFINITY, INFINITY));
    REPORTER_ASSERT(reporter, !sk_doubles_nearly_equal_ulps(INFINITY, 10));
    REPORTER_ASSERT(reporter, !sk_doubles_nearly_equal_ulps(10, INFINITY));
    REPORTER_ASSERT(reporter, !sk_doubles_nearly_equal_ulps(NAN, INFINITY));
 
    REPORTER_ASSERT(reporter, !sk_doubles_nearly_equal_ulps(INFINITY, -INFINITY));
    REPORTER_ASSERT(reporter, !sk_doubles_nearly_equal_ulps(-INFINITY, INFINITY));
    REPORTER_ASSERT(reporter, sk_doubles_nearly_equal_ulps(-INFINITY, -INFINITY));
 
    // Test values upto the edge of infinity.
    const double biggest = std::numeric_limits<double>::max();
    auto almostBiggest = [&](int n) {
        double almostBiggest = biggest;
        for (int i = 0; i < n; ++i) {
            almostBiggest = std::nextafter(almostBiggest, -INFINITY);
        }
        return almostBiggest;
    };
    const double nextBiggest = almostBiggest(1);
    REPORTER_ASSERT(reporter, sk_doubles_nearly_equal_ulps(biggest, nextBiggest));
    REPORTER_ASSERT(reporter, sk_doubles_nearly_equal_ulps(biggest, almostBiggest(16)));
    REPORTER_ASSERT(reporter, !sk_doubles_nearly_equal_ulps(biggest, almostBiggest(17)));
 
    // One ulp less would be infinity.
    const uint64_t smallestNANPattern =
            0b0'11111111111'0000000000000000000000000000000000000000000000000001;
    double smallestNAN;
    memcpy(&smallestNAN, &smallestNANPattern, sizeof(double));
    SkASSERT(std::isnan(smallestNAN));
    SkASSERT(biggest != nextBiggest);
 
    // Sanity check.
    REPORTER_ASSERT(reporter, !sk_doubles_nearly_equal_ulps(smallestNAN, NAN));
 
    // Make sure to return false along the edge of infinity.
    REPORTER_ASSERT(reporter, !sk_doubles_nearly_equal_ulps(INFINITY, biggest));
    REPORTER_ASSERT(reporter, !sk_doubles_nearly_equal_ulps(smallestNAN, biggest));
    REPORTER_ASSERT(reporter, !sk_doubles_nearly_equal_ulps(smallestNAN, INFINITY));
 
    const double smallest = std::numeric_limits<double>::denorm_min();
    REPORTER_ASSERT(reporter, !sk_doubles_nearly_equal_ulps(NAN, NAN));
    REPORTER_ASSERT(reporter, sk_doubles_nearly_equal_ulps(smallest, 0));
    REPORTER_ASSERT(reporter, sk_doubles_nearly_equal_ulps(smallest, -smallest));
    REPORTER_ASSERT(reporter, sk_doubles_nearly_equal_ulps(8*smallest, -8*smallest));
    REPORTER_ASSERT(reporter, !sk_doubles_nearly_equal_ulps(8*smallest, -9*smallest));
}
 
DEF_TEST(BitCastDoubleRoundTrip, reporter) {
    std::array<double, 5>  testCases = {0.0, 1.0, -13.0, 1.234567890123456, -543210.987654321};
 
    for (size_t i = 0; i < testCases.size(); i++) {
        double input = testCases[i];
        uint64_t bits = sk_bit_cast<uint64_t>(input);
        double output = sk_bit_cast<double>(bits);
        REPORTER_ASSERT(reporter, input == output, "%.16f is not exactly %.16f", input, output);
    }
 
    {
        uint64_t bits = sk_bit_cast<uint64_t>((double) NAN);
        double output = sk_bit_cast<double>(bits);
        REPORTER_ASSERT(reporter, std::isnan(output), "%.16f is not nan", output);
    }
    {
        uint64_t bits = sk_bit_cast<uint64_t>((double) INFINITY);
        double output = sk_bit_cast<double>(bits);
        REPORTER_ASSERT(reporter, !SkIsFinite(output), "%.16f is not infinity", output);
    }
}
 
DEF_TEST(FMA, reporter) {
    // 0b0'01111111111'00'0000000000'0000000000'0000000010'0000000000'0000000000
    double over1 = 1+4.656612873e-10;
 
    // 0b0'01111111110'11'1111111111'1111111111'1111111100'0000000000'0000000000
    double under1 = 1-4.656612873e-10;
 
    // Precision loss
    //                         -------------- becomes 1; extra bits are rounded off.
    double x = std::fma(1, -1, over1 * under1);
 
    // Precision maintained
    //                  ------------- becomes 1 - 2^-62; extra bits are maintained
    double y = std::fma(over1, under1, -1);
 
    REPORTER_ASSERT(reporter, x == 0);
    REPORTER_ASSERT(reporter, y == -exp2(-62));
}
 
DEF_TEST(Midpoint, reporter) {
    const float smallest = std::numeric_limits<float>::denorm_min();
    REPORTER_ASSERT(reporter, sk_float_midpoint(smallest, smallest) == smallest);
    REPORTER_ASSERT(reporter, sk_float_midpoint(smallest, -smallest) == 0);
 
    const float biggest = std::numeric_limits<float>::max();
    REPORTER_ASSERT(reporter, sk_float_midpoint(biggest, biggest) == biggest);
    REPORTER_ASSERT(reporter, sk_float_midpoint(biggest, -biggest) == 0);
 
}