MathTest.cpp revision ed673310e2551e64d8196f7776d7d4c92085f8c2 
1#include "Test.h"
2#include "SkPoint.h"
3#include "SkRandom.h"
4
5#if defined(SkLONGLONG)
6static int symmetric_fixmul(int a, int b) {
7    int sa = SkExtractSign(a);
8    int sb = SkExtractSign(b);
9
10    a = SkApplySign(a, sa);
11    b = SkApplySign(b, sb);
12
13#if 1
14    int c = (int)(((SkLONGLONG)a * b) >> 16);
15
16    return SkApplySign(c, sa ^ sb);
17#else
18    SkLONGLONG ab = (SkLONGLONG)a * b;
19    if (sa ^ sb) {
20        ab = -ab;
21    }
22    return ab >> 16;
23#endif
24}
25#endif
26
27static void check_length(skiatest::Reporter* reporter,
28                         const SkPoint& p, SkScalar targetLen) {
29#ifdef SK_CAN_USE_FLOAT
30    float x = SkScalarToFloat(p.fX);
31    float y = SkScalarToFloat(p.fY);
32    float len = sk_float_sqrt(x*x + y*y);
33
34    len /= SkScalarToFloat(targetLen);
35
36    REPORTER_ASSERT(reporter, len > 0.999f && len < 1.001f);
37#endif
38}
39
40#if defined(SK_CAN_USE_FLOAT)
41
42static float nextFloat(SkRandom& rand) {
43    SkFloatIntUnion data;
44    data.fSignBitInt = rand.nextU();
45    return data.fFloat;
46}
47
48/*  returns true if a == b as resulting from (int)x. Since it is undefined
49 what to do if the float exceeds 2^32-1, we check for that explicitly.
50 */
51static bool equal_float_native_skia(float x, uint32_t ni, uint32_t si) {
52    if (!(x == x)) {    // NAN
53        return si == SK_MaxS32 || si == SK_MinS32;
54    }
55    // for out of range, C is undefined, but skia always should return NaN32
56    if (x > SK_MaxS32) {
57        return si == SK_MaxS32;
58    }
59    if (x < -SK_MaxS32) {
60        return si == SK_MinS32;
61    }
62    return si == ni;
63}
64
65static void assert_float_equal(skiatest::Reporter* reporter, const char op[],
66                               float x, uint32_t ni, uint32_t si) {
67    if (!equal_float_native_skia(x, ni, si)) {
68        SkString desc;
69        desc.printf("%s float %g bits %x native %x skia %x\n", op, x, ni, si);
70        reporter->reportFailed(desc);
71    }
72}
73
74static void test_float_cast(skiatest::Reporter* reporter, float x) {
75    int ix = (int)x;
76    int iix = SkFloatToIntCast(x);
77    assert_float_equal(reporter, "cast", x, ix, iix);
78}
79
80static void test_float_floor(skiatest::Reporter* reporter, float x) {
81    int ix = (int)floor(x);
82    int iix = SkFloatToIntFloor(x);
83    assert_float_equal(reporter, "floor", x, ix, iix);
84}
85
86static void test_float_round(skiatest::Reporter* reporter, float x) {
87    double xx = x + 0.5;    // need intermediate double to avoid temp loss
88    int ix = (int)floor(xx);
89    int iix = SkFloatToIntRound(x);
90    assert_float_equal(reporter, "round", x, ix, iix);
91}
92
93static void test_float_ceil(skiatest::Reporter* reporter, float x) {
94    int ix = (int)ceil(x);
95    int iix = SkFloatToIntCeil(x);
96    assert_float_equal(reporter, "ceil", x, ix, iix);
97}
98
99static void test_float_conversions(skiatest::Reporter* reporter, float x) {
100    test_float_cast(reporter, x);
101    test_float_floor(reporter, x);
102    test_float_round(reporter, x);
103    test_float_ceil(reporter, x);
104}
105
106static void test_int2float(skiatest::Reporter* reporter, int ival) {
107    float x0 = (float)ival;
108    float x1 = SkIntToFloatCast(ival);
109    float x2 = SkIntToFloatCast_NoOverflowCheck(ival);
110    REPORTER_ASSERT(reporter, x0 == x1);
111    REPORTER_ASSERT(reporter, x0 == x2);
112}
113
114static void unittest_fastfloat(skiatest::Reporter* reporter) {
115    SkRandom rand;
116    size_t i;
117
118    static const float gFloats[] = {
119        0.f, 1.f, 0.5f, 0.499999f, 0.5000001f, 1.f/3,
120        0.000000001f, 1000000000.f,     // doesn't overflow
121        0.0000000001f, 10000000000.f    // does overflow
122    };
123    for (i = 0; i < SK_ARRAY_COUNT(gFloats); i++) {
124        //        SkDebugf("---- test floats %g %d\n", gFloats[i], (int)gFloats[i]);
125        test_float_conversions(reporter, gFloats[i]);
126        test_float_conversions(reporter, -gFloats[i]);
127    }
128
129    for (int outer = 0; outer < 100; outer++) {
130        rand.setSeed(outer);
131        for (i = 0; i < 100000; i++) {
132            float x = nextFloat(rand);
133            test_float_conversions(reporter, x);
134        }
135
136        test_int2float(reporter, 0);
137        test_int2float(reporter, 1);
138        test_int2float(reporter, -1);
139        for (i = 0; i < 100000; i++) {
140            // for now only test ints that are 24bits or less, since we don't
141            // round (down) large ints the same as IEEE...
142            int ival = rand.nextU() & 0xFFFFFF;
143            test_int2float(reporter, ival);
144            test_int2float(reporter, -ival);
145        }
146    }
147}
148
149#endif
150
151static void test_muldiv255(skiatest::Reporter* reporter) {
152#ifdef SK_CAN_USE_FLOAT
153    for (int a = 0; a <= 255; a++) {
154        for (int b = 0; b <= 255; b++) {
155            int ab = a * b;
156            float s = ab / 255.0f;
157            int round = (int)floorf(s + 0.5f);
158            int trunc = (int)floorf(s);
159
160            int iround = SkMulDiv255Round(a, b);
161            int itrunc = SkMulDiv255Trunc(a, b);
162
163            REPORTER_ASSERT(reporter, iround == round);
164            REPORTER_ASSERT(reporter, itrunc == trunc);
165
166            REPORTER_ASSERT(reporter, itrunc <= iround);
167            REPORTER_ASSERT(reporter, iround <= a);
168            REPORTER_ASSERT(reporter, iround <= b);
169        }
170    }
171#endif
172}
173
174static void TestMath(skiatest::Reporter* reporter) {
175    int         i;
176    int32_t     x;
177    SkRandom    rand;
178
179    // these should not assert
180    SkToS8(127);    SkToS8(-128);       SkToU8(255);
181    SkToS16(32767); SkToS16(-32768);    SkToU16(65535);
182    SkToS32(2*1024*1024);   SkToS32(-2*1024*1024);  SkToU32(4*1024*1024);
183
184    // these should assert
185#if 0
186    SkToS8(128);
187    SkToS8(-129);
188    SkToU8(256);
189    SkToU8(-5);
190
191    SkToS16(32768);
192    SkToS16(-32769);
193    SkToU16(65536);
194    SkToU16(-5);
195
196    if (sizeof(size_t) > 4) {
197        SkToS32(4*1024*1024);
198        SkToS32(-4*1024*1024);
199        SkToU32(5*1024*1024);
200        SkToU32(-5);
201    }
202#endif
203
204    test_muldiv255(reporter);
205
206    {
207        SkScalar x = SK_ScalarNaN;
208        REPORTER_ASSERT(reporter, SkScalarIsNaN(x));
209    }
210
211    for (i = 1; i <= 10; i++) {
212        x = SkCubeRootBits(i*i*i, 11);
213        REPORTER_ASSERT(reporter, x == i);
214    }
215
216    REPORTER_ASSERT(reporter, !"test the reporter");
217
218    x = SkFixedSqrt(SK_Fixed1);
219    REPORTER_ASSERT(reporter, x == SK_Fixed1);
220    x = SkFixedSqrt(SK_Fixed1/4);
221    REPORTER_ASSERT(reporter, x == SK_Fixed1/2);
222    x = SkFixedSqrt(SK_Fixed1*4);
223    REPORTER_ASSERT(reporter, x == SK_Fixed1*2);
224
225    x = SkFractSqrt(SK_Fract1);
226    REPORTER_ASSERT(reporter, x == SK_Fract1);
227    x = SkFractSqrt(SK_Fract1/4);
228    REPORTER_ASSERT(reporter, x == SK_Fract1/2);
229    x = SkFractSqrt(SK_Fract1/16);
230    REPORTER_ASSERT(reporter, x == SK_Fract1/4);
231
232    for (i = 1; i < 100; i++) {
233        x = SkFixedSqrt(SK_Fixed1 * i * i);
234        REPORTER_ASSERT(reporter, x == SK_Fixed1 * i);
235    }
236
237    for (i = 0; i < 1000; i++) {
238        int value = rand.nextS16();
239        int max = rand.nextU16();
240
241        int clamp = SkClampMax(value, max);
242        int clamp2 = value < 0 ? 0 : (value > max ? max : value);
243        REPORTER_ASSERT(reporter, clamp == clamp2);
244    }
245
246    for (i = 0; i < 100000; i++) {
247        SkPoint p;
248
249        p.setLength(rand.nextS(), rand.nextS(), SK_Scalar1);
250        check_length(reporter, p, SK_Scalar1);
251        p.setLength(rand.nextS() >> 13, rand.nextS() >> 13, SK_Scalar1);
252        check_length(reporter, p, SK_Scalar1);
253    }
254
255    {
256        SkFixed result = SkFixedDiv(100, 100);
257        REPORTER_ASSERT(reporter, result == SK_Fixed1);
258        result = SkFixedDiv(1, SK_Fixed1);
259        REPORTER_ASSERT(reporter, result == 1);
260    }
261
262#ifdef SK_CAN_USE_FLOAT
263    unittest_fastfloat(reporter);
264#endif
265
266#ifdef SkLONGLONG
267    for (i = 0; i < 100000; i++) {
268        SkFixed numer = rand.nextS();
269        SkFixed denom = rand.nextS();
270        SkFixed result = SkFixedDiv(numer, denom);
271        SkLONGLONG check = ((SkLONGLONG)numer << 16) / denom;
272
273        (void)SkCLZ(numer);
274        (void)SkCLZ(denom);
275
276        REPORTER_ASSERT(reporter, result != (SkFixed)SK_NaN32);
277        if (check > SK_MaxS32) {
278            check = SK_MaxS32;
279        } else if (check < -SK_MaxS32) {
280            check = SK_MinS32;
281        }
282        REPORTER_ASSERT(reporter, result == (int32_t)check);
283
284        result = SkFractDiv(numer, denom);
285        check = ((SkLONGLONG)numer << 30) / denom;
286
287        REPORTER_ASSERT(reporter, result != (SkFixed)SK_NaN32);
288        if (check > SK_MaxS32) {
289            check = SK_MaxS32;
290        } else if (check < -SK_MaxS32) {
291            check = SK_MinS32;
292        }
293        REPORTER_ASSERT(reporter, result == (int32_t)check);
294
295        // make them <= 2^24, so we don't overflow in fixmul
296        numer = numer << 8 >> 8;
297        denom = denom << 8 >> 8;
298
299        result = SkFixedMul(numer, denom);
300        SkFixed r2 = symmetric_fixmul(numer, denom);
301        //        SkASSERT(result == r2);
302
303        result = SkFixedMul(numer, numer);
304        r2 = SkFixedSquare(numer);
305        REPORTER_ASSERT(reporter, result == r2);
306
307#ifdef SK_CAN_USE_FLOAT
308        if (numer >= 0 && denom >= 0) {
309            SkFixed mean = SkFixedMean(numer, denom);
310            float fm = sk_float_sqrt(sk_float_abs(SkFixedToFloat(numer) * SkFixedToFloat(denom)));
311            SkFixed mean2 = SkFloatToFixed(fm);
312            int diff = SkAbs32(mean - mean2);
313            REPORTER_ASSERT(reporter, diff <= 1);
314        }
315
316        {
317            SkFixed mod = SkFixedMod(numer, denom);
318            float n = SkFixedToFloat(numer);
319            float d = SkFixedToFloat(denom);
320            float m = sk_float_mod(n, d);
321            REPORTER_ASSERT(reporter, mod == 0 || (mod < 0) == (m < 0)); // ensure the same sign
322            int diff = SkAbs32(mod - SkFloatToFixed(m));
323            REPORTER_ASSERT(reporter, (diff >> 7) == 0);
324        }
325#endif
326    }
327#endif
328
329#ifdef SK_CAN_USE_FLOAT
330    for (i = 0; i < 100000; i++) {
331        SkFract x = rand.nextU() >> 1;
332        double xx = (double)x / SK_Fract1;
333        SkFract xr = SkFractSqrt(x);
334        SkFract check = SkFloatToFract(sqrt(xx));
335        REPORTER_ASSERT(reporter, xr == check || xr == check-1 || xr == check+1);
336
337        xr = SkFixedSqrt(x);
338        xx = (double)x / SK_Fixed1;
339        check = SkFloatToFixed(sqrt(xx));
340        REPORTER_ASSERT(reporter, xr == check || xr == check-1);
341
342        xr = SkSqrt32(x);
343        xx = (double)x;
344        check = (int32_t)sqrt(xx);
345        REPORTER_ASSERT(reporter, xr == check || xr == check-1);
346    }
347#endif
348
349#if !defined(SK_SCALAR_IS_FLOAT) && defined(SK_CAN_USE_FLOAT)
350    {
351        SkFixed s, c;
352        s = SkFixedSinCos(0, &c);
353        REPORTER_ASSERT(reporter, s == 0);
354        REPORTER_ASSERT(reporter, c == SK_Fixed1);
355    }
356
357    int maxDiff = 0;
358    for (i = 0; i < 10000; i++) {
359        SkFixed rads = rand.nextS() >> 10;
360        double frads = SkFixedToFloat(rads);
361
362        SkFixed s, c;
363        s = SkScalarSinCos(rads, &c);
364
365        double fs = sin(frads);
366        double fc = cos(frads);
367
368        SkFixed is = SkFloatToFixed(fs);
369        SkFixed ic = SkFloatToFixed(fc);
370
371        maxDiff = SkMax32(maxDiff, SkAbs32(is - s));
372        maxDiff = SkMax32(maxDiff, SkAbs32(ic - c));
373    }
374    SkDebugf("SinCos: maximum error = %d\n", maxDiff);
375#endif
376}
377
378///////////////////////////////////////////////////////////////////////////////
379
380namespace skiatest {
381
382    class MathTest : public Test {
383    public:
384        static Test* Factory(void*) {
385            return SkNEW(MathTest);
386        }
387
388    protected:
389        virtual void onGetName(SkString* name) {
390            name->set("Math");
391        }
392
393        virtual void onRun(Reporter* reporter) {
394            TestMath(reporter);
395        }
396    };
397
398    static TestRegistry gReg(MathTest::Factory);
399}
400
401