tests/MathTest.cpp

/*
 * Copyright 2011 Google Inc.
 *
 * Use of this source code is governed by a BSD-style license that can be
 * found in the LICENSE file.
 */

#include "float.h"

#include "SkColorPriv.h"
#include "SkEndian.h"
#include "SkFixed.h"
#include "SkFloatBits.h"
#include "SkFloatingPoint.h"
#include "SkHalf.h"
#include "SkMathPriv.h"
#include "SkPoint.h"
#include "SkRandom.h"
#include "Test.h"

static void test_clz(skiatest::Reporter* reporter) {
    REPORTER_ASSERT(reporter, 32 == SkCLZ(0));
    REPORTER_ASSERT(reporter, 31 == SkCLZ(1));
    REPORTER_ASSERT(reporter, 1 == SkCLZ(1 << 30));
    REPORTER_ASSERT(reporter, 0 == SkCLZ(~0U));

    SkRandom rand;
    for (int i = 0; i < 1000; ++i) {
        uint32_t mask = rand.nextU();
        // need to get some zeros for testing, but in some obscure way so the
        // compiler won't "see" that, and work-around calling the functions.
        mask >>= (mask & 31);
        int intri = SkCLZ(mask);
        int porta = SkCLZ_portable(mask);
        REPORTER_ASSERT(reporter, intri == porta);
    }
}

///////////////////////////////////////////////////////////////////////////////

static float sk_fsel(float pred, float result_ge, float result_lt) {
    return pred >= 0 ? result_ge : result_lt;
}

static float fast_floor(float x) {
//    float big = sk_fsel(x, 0x1.0p+23, -0x1.0p+23);
    float big = sk_fsel(x, (float)(1 << 23), -(float)(1 << 23));
    return (float)(x + big) - big;
}

static float std_floor(float x) {
    return sk_float_floor(x);
}

static void test_floor_value(skiatest::Reporter* reporter, float value) {
    float fast = fast_floor(value);
    float std = std_floor(value);
    if (std != fast) {
        ERRORF(reporter, "fast_floor(%.9g) == %.9g != %.9g == std_floor(%.9g)",
               value, fast, std, value);
    }
}

static void test_floor(skiatest::Reporter* reporter) {
    static const float gVals[] = {
        0, 1, 1.1f, 1.01f, 1.001f, 1.0001f, 1.00001f, 1.000001f, 1.0000001f
    };

    for (size_t i = 0; i < SK_ARRAY_COUNT(gVals); ++i) {
        test_floor_value(reporter, gVals[i]);
//        test_floor_value(reporter, -gVals[i]);
    }
}

///////////////////////////////////////////////////////////////////////////////

// test that SkMul16ShiftRound and SkMulDiv255Round return the same result
static void test_muldivround(skiatest::Reporter* reporter) {
#if 0
    // this "complete" test is too slow, so we test a random sampling of it

    for (int a = 0; a <= 32767; ++a) {
        for (int b = 0; b <= 32767; ++b) {
            unsigned prod0 = SkMul16ShiftRound(a, b, 8);
            unsigned prod1 = SkMulDiv255Round(a, b);
            SkASSERT(prod0 == prod1);
        }
    }
#endif

    SkRandom rand;
    for (int i = 0; i < 10000; ++i) {
        unsigned a = rand.nextU() & 0x7FFF;
        unsigned b = rand.nextU() & 0x7FFF;

        unsigned prod0 = SkMul16ShiftRound(a, b, 8);
        unsigned prod1 = SkMulDiv255Round(a, b);

        REPORTER_ASSERT(reporter, prod0 == prod1);
    }
}

static float float_blend(int src, int dst, float unit) {
    return dst + (src - dst) * unit;
}

static int blend31(int src, int dst, int a31) {
    return dst + ((src - dst) * a31 * 2114 >> 16);
    //    return dst + ((src - dst) * a31 * 33 >> 10);
}

static int blend31_slow(int src, int dst, int a31) {
    int prod = src * a31 + (31 - a31) * dst + 16;
    prod = (prod + (prod >> 5)) >> 5;
    return prod;
}

static int blend31_round(int src, int dst, int a31) {
    int prod = (src - dst) * a31 + 16;
    prod = (prod + (prod >> 5)) >> 5;
    return dst + prod;
}

static int blend31_old(int src, int dst, int a31) {
    a31 += a31 >> 4;
    return dst + ((src - dst) * a31 >> 5);
}

// suppress unused code warning
static int (*blend_functions[])(int, int, int) = {
    blend31,
    blend31_slow,
    blend31_round,
    blend31_old
};

static void test_blend31() {
    int failed = 0;
    int death = 0;
    if (false) { // avoid bit rot, suppress warning
        failed = (*blend_functions[0])(0,0,0);
    }
    for (int src = 0; src <= 255; src++) {
        for (int dst = 0; dst <= 255; dst++) {
            for (int a = 0; a <= 31; a++) {
//                int r0 = blend31(src, dst, a);
//                int r0 = blend31_round(src, dst, a);
//                int r0 = blend31_old(src, dst, a);
                int r0 = blend31_slow(src, dst, a);

                float f = float_blend(src, dst, a / 31.f);
                int r1 = (int)f;
                int r2 = SkScalarRoundToInt(f);

                if (r0 != r1 && r0 != r2) {
                    SkDebugf("src:%d dst:%d a:%d result:%d float:%g\n",
                                 src,   dst, a,        r0,      f);
                    failed += 1;
                }
                if (r0 > 255) {
                    death += 1;
                    SkDebugf("death src:%d dst:%d a:%d result:%d float:%g\n",
                                        src,   dst, a,        r0,      f);
                }
            }
        }
    }
    SkDebugf("---- failed %d death %d\n", failed, death);
}

static void test_blend(skiatest::Reporter* reporter) {
    for (int src = 0; src <= 255; src++) {
        for (int dst = 0; dst <= 255; dst++) {
            for (int a = 0; a <= 255; a++) {
                int r0 = SkAlphaBlend255(src, dst, a);
                float f1 = float_blend(src, dst, a / 255.f);
                int r1 = SkScalarRoundToInt(f1);

                if (r0 != r1) {
                    float diff = sk_float_abs(f1 - r1);
                    diff = sk_float_abs(diff - 0.5f);
                    if (diff > (1 / 255.f)) {
                        ERRORF(reporter, "src:%d dst:%d a:%d "
                               "result:%d float:%g\n", src, dst, a, r0, f1);
                    }
                }
            }
        }
    }
}

static void check_length(skiatest::Reporter* reporter,
                         const SkPoint& p, SkScalar targetLen) {
    float x = SkScalarToFloat(p.fX);
    float y = SkScalarToFloat(p.fY);
    float len = sk_float_sqrt(x*x + y*y);

    len /= SkScalarToFloat(targetLen);

    REPORTER_ASSERT(reporter, len > 0.999f && len < 1.001f);
}

static float nextFloat(SkRandom& rand) {
    SkFloatIntUnion data;
    data.fSignBitInt = rand.nextU();
    return data.fFloat;
}

/*  returns true if a == b as resulting from (int)x. Since it is undefined
 what to do if the float exceeds 2^32-1, we check for that explicitly.
 */
static bool equal_float_native_skia(float x, int32_t ni, int32_t si) {
    // When the float is out of integer range (NaN, above, below),
    // the C cast is undefined, but Skia's methods should have clamped.
    if (!(x == x)) {    // NaN
        return si == SK_MaxS32 || si == SK_MinS32;
    }
    if (x > SK_MaxS32) {
        return si == SK_MaxS32;
    }
    if (x < SK_MinS32) {
        return si == SK_MinS32;
    }
    return si == ni;
}

static void assert_float_equal(skiatest::Reporter* reporter, const char op[],
                               float x, int32_t ni, int32_t si) {
    if (!equal_float_native_skia(x, ni, si)) {
        ERRORF(reporter, "%s float %g bits %x native %x skia %x\n",
               op, x, SkFloat2Bits(x), ni, si);
    }
}

static void test_float_floor(skiatest::Reporter* reporter, float x) {
    int ix = (int)floor(x);
    int iix = SkFloatToIntFloor(x);
    assert_float_equal(reporter, "floor", x, ix, iix);
}

static void test_float_round(skiatest::Reporter* reporter, float x) {
    double xx = x + 0.5;    // need intermediate double to avoid temp loss
    int ix = (int)floor(xx);
    int iix = SkFloatToIntRound(x);
    assert_float_equal(reporter, "round", x, ix, iix);
}

static void test_float_ceil(skiatest::Reporter* reporter, float x) {
    int ix = (int)ceil(x);
    int iix = SkFloatToIntCeil(x);
    assert_float_equal(reporter, "ceil", x, ix, iix);
}

static void test_float_conversions(skiatest::Reporter* reporter, float x) {
    test_float_floor(reporter, x);
    test_float_round(reporter, x);
    test_float_ceil(reporter, x);
}

static void unittest_fastfloat(skiatest::Reporter* reporter) {
    SkRandom rand;
    size_t i;

    static const float gFloats[] = {
        0.f/0.f, -0.f/0.f, 1.f/0.f, -1.f/0.f,
        0.f, 1.f, 0.5f, 0.499999f, 0.5000001f, 1.f/3,
        0.000000001f, 1000000000.f,     // doesn't overflow
        0.0000000001f, 10000000000.f    // does overflow
    };
    for (i = 0; i < SK_ARRAY_COUNT(gFloats); i++) {
        test_float_conversions(reporter, gFloats[i]);
        test_float_conversions(reporter, -gFloats[i]);
    }

    for (int outer = 0; outer < 100; outer++) {
        rand.setSeed(outer);
        for (i = 0; i < 100000; i++) {
            float x = nextFloat(rand);
            test_float_conversions(reporter, x);
        }
    }
}

static float make_zero() {
    return sk_float_sin(0);
}

static void unittest_isfinite(skiatest::Reporter* reporter) {
    float nan = sk_float_asin(2);
    float inf = 1.0f / make_zero();
    float big = 3.40282e+038f;

    REPORTER_ASSERT(reporter, !SkScalarIsNaN(inf));
    REPORTER_ASSERT(reporter, !SkScalarIsNaN(-inf));
    REPORTER_ASSERT(reporter, !SkScalarIsFinite(inf));
    REPORTER_ASSERT(reporter, !SkScalarIsFinite(-inf));

    REPORTER_ASSERT(reporter,  SkScalarIsNaN(nan));
    REPORTER_ASSERT(reporter, !SkScalarIsNaN(big));
    REPORTER_ASSERT(reporter, !SkScalarIsNaN(-big));
    REPORTER_ASSERT(reporter, !SkScalarIsNaN(0));

    REPORTER_ASSERT(reporter, !SkScalarIsFinite(nan));
    REPORTER_ASSERT(reporter,  SkScalarIsFinite(big));
    REPORTER_ASSERT(reporter,  SkScalarIsFinite(-big));
    REPORTER_ASSERT(reporter,  SkScalarIsFinite(0));
}

static void unittest_half(skiatest::Reporter* reporter) {
    static const float gFloats[] = {
        0.f, 1.f, 0.5f, 0.499999f, 0.5000001f, 1.f/3,
        -0.f, -1.f, -0.5f, -0.499999f, -0.5000001f, -1.f/3
    };

    for (size_t i = 0; i < SK_ARRAY_COUNT(gFloats); ++i) {
        SkHalf h = SkFloatToHalf(gFloats[i]);
        float f = SkHalfToFloat(h);
        REPORTER_ASSERT(reporter, SkScalarNearlyEqual(f, gFloats[i]));
    }

    // check some special values
    union FloatUnion {
        uint32_t fU;
        float    fF;
    };

    static const FloatUnion largestPositiveHalf = { ((142 << 23) | (1023 << 13)) };
    SkHalf h = SkFloatToHalf(largestPositiveHalf.fF);
    float f = SkHalfToFloat(h);
    REPORTER_ASSERT(reporter, SkScalarNearlyEqual(f, largestPositiveHalf.fF));

    static const FloatUnion largestNegativeHalf = { (1u << 31) | (142u << 23) | (1023u << 13) };
    h = SkFloatToHalf(largestNegativeHalf.fF);
    f = SkHalfToFloat(h);
    REPORTER_ASSERT(reporter, SkScalarNearlyEqual(f, largestNegativeHalf.fF));

    static const FloatUnion smallestPositiveHalf = { 102 << 23 };
    h = SkFloatToHalf(smallestPositiveHalf.fF);
    f = SkHalfToFloat(h);
    REPORTER_ASSERT(reporter, SkScalarNearlyEqual(f, smallestPositiveHalf.fF));

    static const FloatUnion overflowHalf = { ((143 << 23) | (1023 << 13)) };
    h = SkFloatToHalf(overflowHalf.fF);
    f = SkHalfToFloat(h);
    REPORTER_ASSERT(reporter, !SkScalarIsFinite(f) );

    static const FloatUnion underflowHalf = { 101 << 23 };
    h = SkFloatToHalf(underflowHalf.fF);
    f = SkHalfToFloat(h);
    REPORTER_ASSERT(reporter, f == 0.0f );

    static const FloatUnion inf32 = { 255 << 23 };
    h = SkFloatToHalf(inf32.fF);
    f = SkHalfToFloat(h);
    REPORTER_ASSERT(reporter, !SkScalarIsFinite(f) );

    static const FloatUnion nan32 = { 255 << 23 | 1 };
    h = SkFloatToHalf(nan32.fF);
    f = SkHalfToFloat(h);
    REPORTER_ASSERT(reporter, SkScalarIsNaN(f) );

}

template <typename RSqrtFn>
static void test_rsqrt(skiatest::Reporter* reporter, RSqrtFn rsqrt) {
    const float maxRelativeError = 6.50196699e-4f;

    // test close to 0 up to 1
    float input = 0.000001f;
    for (int i = 0; i < 1000; ++i) {
        float exact = 1.0f/sk_float_sqrt(input);
        float estimate = rsqrt(input);
        float relativeError = sk_float_abs(exact - estimate)/exact;
        REPORTER_ASSERT(reporter, relativeError <= maxRelativeError);
        input += 0.001f;
    }

    // test 1 to ~100
    input = 1.0f;
    for (int i = 0; i < 1000; ++i) {
        float exact = 1.0f/sk_float_sqrt(input);
        float estimate = rsqrt(input);
        float relativeError = sk_float_abs(exact - estimate)/exact;
        REPORTER_ASSERT(reporter, relativeError <= maxRelativeError);
        input += 0.01f;
    }

    // test some big numbers
    input = 1000000.0f;
    for (int i = 0; i < 100; ++i) {
        float exact = 1.0f/sk_float_sqrt(input);
        float estimate = rsqrt(input);
        float relativeError = sk_float_abs(exact - estimate)/exact;
        REPORTER_ASSERT(reporter, relativeError <= maxRelativeError);
        input += 754326.f;
    }
}

static void test_muldiv255(skiatest::Reporter* reporter) {
    for (int a = 0; a <= 255; a++) {
        for (int b = 0; b <= 255; b++) {
            int ab = a * b;
            float s = ab / 255.0f;
            int round = (int)floorf(s + 0.5f);
            int trunc = (int)floorf(s);

            int iround = SkMulDiv255Round(a, b);
            int itrunc = SkMulDiv255Trunc(a, b);

            REPORTER_ASSERT(reporter, iround == round);
            REPORTER_ASSERT(reporter, itrunc == trunc);

            REPORTER_ASSERT(reporter, itrunc <= iround);
            REPORTER_ASSERT(reporter, iround <= a);
            REPORTER_ASSERT(reporter, iround <= b);
        }
    }
}

static void test_muldiv255ceiling(skiatest::Reporter* reporter) {
    for (int c = 0; c <= 255; c++) {
        for (int a = 0; a <= 255; a++) {
            int product = (c * a + 255);
            int expected_ceiling = (product + (product >> 8)) >> 8;
            int webkit_ceiling = (c * a + 254) / 255;
            REPORTER_ASSERT(reporter, expected_ceiling == webkit_ceiling);
            int skia_ceiling = SkMulDiv255Ceiling(c, a);
            REPORTER_ASSERT(reporter, skia_ceiling == webkit_ceiling);
        }
    }
}

static void test_copysign(skiatest::Reporter* reporter) {
    static const int32_t gTriples[] = {
        // x, y, expected result
        0, 0, 0,
        0, 1, 0,
        0, -1, 0,
        1, 0, 1,
        1, 1, 1,
        1, -1, -1,
        -1, 0, 1,
        -1, 1, 1,
        -1, -1, -1,
    };
    for (size_t i = 0; i < SK_ARRAY_COUNT(gTriples); i += 3) {
        REPORTER_ASSERT(reporter,
                        SkCopySign32(gTriples[i], gTriples[i+1]) == gTriples[i+2]);
        float x = (float)gTriples[i];
        float y = (float)gTriples[i+1];
        float expected = (float)gTriples[i+2];
        REPORTER_ASSERT(reporter, sk_float_copysign(x, y) == expected);
    }

    SkRandom rand;
    for (int j = 0; j < 1000; j++) {
        int ix = rand.nextS();
        REPORTER_ASSERT(reporter, SkCopySign32(ix, ix) == ix);
        REPORTER_ASSERT(reporter, SkCopySign32(ix, -ix) == -ix);
        REPORTER_ASSERT(reporter, SkCopySign32(-ix, ix) == ix);
        REPORTER_ASSERT(reporter, SkCopySign32(-ix, -ix) == -ix);

        SkScalar sx = rand.nextSScalar1();
        REPORTER_ASSERT(reporter, SkScalarCopySign(sx, sx) == sx);
        REPORTER_ASSERT(reporter, SkScalarCopySign(sx, -sx) == -sx);
        REPORTER_ASSERT(reporter, SkScalarCopySign(-sx, sx) == sx);
        REPORTER_ASSERT(reporter, SkScalarCopySign(-sx, -sx) == -sx);
    }
}

DEF_TEST(Math, reporter) {
    int         i;
    SkRandom    rand;

    // these should assert
#if 0
    SkToS8(128);
    SkToS8(-129);
    SkToU8(256);
    SkToU8(-5);

    SkToS16(32768);
    SkToS16(-32769);
    SkToU16(65536);
    SkToU16(-5);

    if (sizeof(size_t) > 4) {
        SkToS32(4*1024*1024);
        SkToS32(-4*1024*1024);
        SkToU32(5*1024*1024);
        SkToU32(-5);
    }
#endif

    test_muldiv255(reporter);
    test_muldiv255ceiling(reporter);
    test_copysign(reporter);

    {
        SkScalar x = SK_ScalarNaN;
        REPORTER_ASSERT(reporter, SkScalarIsNaN(x));
    }

    for (i = 0; i < 1000; i++) {
        int value = rand.nextS16();
        int max = rand.nextU16();

        int clamp = SkClampMax(value, max);
        int clamp2 = value < 0 ? 0 : (value > max ? max : value);
        REPORTER_ASSERT(reporter, clamp == clamp2);
    }

    for (i = 0; i < 10000; i++) {
        SkPoint p;

        // These random values are being treated as 32-bit-patterns, not as
        // ints; calling SkIntToScalar() here produces crashes.
        p.setLength((SkScalar) rand.nextS(),
                    (SkScalar) rand.nextS(),
                    SK_Scalar1);
        check_length(reporter, p, SK_Scalar1);
        p.setLength((SkScalar) (rand.nextS() >> 13),
                    (SkScalar) (rand.nextS() >> 13),
                    SK_Scalar1);
        check_length(reporter, p, SK_Scalar1);
    }

    {
        SkFixed result = SkFixedDiv(100, 100);
        REPORTER_ASSERT(reporter, result == SK_Fixed1);
        result = SkFixedDiv(1, SK_Fixed1);
        REPORTER_ASSERT(reporter, result == 1);
        result = SkFixedDiv(10 - 1, SK_Fixed1 * 3);
        REPORTER_ASSERT(reporter, result == 3);
    }

    unittest_fastfloat(reporter);
    unittest_isfinite(reporter);
    unittest_half(reporter);
    test_rsqrt(reporter, sk_float_rsqrt);
    test_rsqrt(reporter, sk_float_rsqrt_portable);

    for (i = 0; i < 10000; i++) {
        SkFixed numer = rand.nextS();
        SkFixed denom = rand.nextS();
        SkFixed result = SkFixedDiv(numer, denom);
        int64_t check = SkLeftShift((int64_t)numer, 16) / denom;

        (void)SkCLZ(numer);
        (void)SkCLZ(denom);

        REPORTER_ASSERT(reporter, result != (SkFixed)SK_NaN32);
        if (check > SK_MaxS32) {
            check = SK_MaxS32;
        } else if (check < -SK_MaxS32) {
            check = SK_MinS32;
        }
        if (result != (int32_t)check) {
            ERRORF(reporter, "\nFixed Divide: %8x / %8x -> %8x %8x\n", numer, denom, result, check);
        }
        REPORTER_ASSERT(reporter, result == (int32_t)check);
    }

    test_blend(reporter);

    if (false) test_floor(reporter);

    // disable for now
    if (false) test_blend31();  // avoid bit rot, suppress warning

    test_muldivround(reporter);
    test_clz(reporter);
}

template <typename T> struct PairRec {
    T   fYin;
    T   fYang;
};

DEF_TEST(TestEndian, reporter) {
    static const PairRec<uint16_t> g16[] = {
        { 0x0,      0x0     },
        { 0xFFFF,   0xFFFF  },
        { 0x1122,   0x2211  },
    };
    static const PairRec<uint32_t> g32[] = {
        { 0x0,          0x0         },
        { 0xFFFFFFFF,   0xFFFFFFFF  },
        { 0x11223344,   0x44332211  },
    };
    static const PairRec<uint64_t> g64[] = {
        { 0x0,      0x0                             },
        { 0xFFFFFFFFFFFFFFFFULL,  0xFFFFFFFFFFFFFFFFULL  },
        { 0x1122334455667788ULL,  0x8877665544332211ULL  },
    };

    REPORTER_ASSERT(reporter, 0x1122 == SkTEndianSwap16<0x2211>::value);
    REPORTER_ASSERT(reporter, 0x11223344 == SkTEndianSwap32<0x44332211>::value);
    REPORTER_ASSERT(reporter, 0x1122334455667788ULL == SkTEndianSwap64<0x8877665544332211ULL>::value);

    for (size_t i = 0; i < SK_ARRAY_COUNT(g16); ++i) {
        REPORTER_ASSERT(reporter, g16[i].fYang == SkEndianSwap16(g16[i].fYin));
    }
    for (size_t i = 0; i < SK_ARRAY_COUNT(g32); ++i) {
        REPORTER_ASSERT(reporter, g32[i].fYang == SkEndianSwap32(g32[i].fYin));
    }
    for (size_t i = 0; i < SK_ARRAY_COUNT(g64); ++i) {
        REPORTER_ASSERT(reporter, g64[i].fYang == SkEndianSwap64(g64[i].fYin));
    }
}

template <typename T>
static void test_divmod(skiatest::Reporter* r) {
    const struct {
        T numer;
        T denom;
    } kEdgeCases[] = {
        {(T)17, (T)17},
        {(T)17, (T)4},
        {(T)0,  (T)17},
        // For unsigned T these negatives are just some large numbers.  Doesn't hurt to test them.
        {(T)-17, (T)-17},
        {(T)-17, (T)4},
        {(T)17,  (T)-4},
        {(T)-17, (T)-4},
    };

    for (size_t i = 0; i < SK_ARRAY_COUNT(kEdgeCases); i++) {
        const T numer = kEdgeCases[i].numer;
        const T denom = kEdgeCases[i].denom;
        T div, mod;
        SkTDivMod(numer, denom, &div, &mod);
        REPORTER_ASSERT(r, numer/denom == div);
        REPORTER_ASSERT(r, numer%denom == mod);
    }

    SkRandom rand;
    for (size_t i = 0; i < 10000; i++) {
        const T numer = (T)rand.nextS();
        T denom = 0;
        while (0 == denom) {
            denom = (T)rand.nextS();
        }
        T div, mod;
        SkTDivMod(numer, denom, &div, &mod);
        REPORTER_ASSERT(r, numer/denom == div);
        REPORTER_ASSERT(r, numer%denom == mod);
    }
}

DEF_TEST(divmod_u8, r) {
    test_divmod<uint8_t>(r);
}

DEF_TEST(divmod_u16, r) {
    test_divmod<uint16_t>(r);
}

DEF_TEST(divmod_u32, r) {
    test_divmod<uint32_t>(r);
}

DEF_TEST(divmod_u64, r) {
    test_divmod<uint64_t>(r);
}

DEF_TEST(divmod_s8, r) {
    test_divmod<int8_t>(r);
}

DEF_TEST(divmod_s16, r) {
    test_divmod<int16_t>(r);
}

DEF_TEST(divmod_s32, r) {
    test_divmod<int32_t>(r);
}

DEF_TEST(divmod_s64, r) {
    test_divmod<int64_t>(r);
}