MathTest.cpp revision 373ebc634573364c27b1ebd35bb537ef1285cba4 
1
2/*
3 * Copyright 2011 Google Inc.
4 *
5 * Use of this source code is governed by a BSD-style license that can be
6 * found in the LICENSE file.
7 */
8#include "Test.h"
9#include "SkFloatBits.h"
10#include "SkFloatingPoint.h"
11#include "SkMathPriv.h"
12#include "SkPoint.h"
13#include "SkRandom.h"
14#include "SkColorPriv.h"
15
16static float sk_fsel(float pred, float result_ge, float result_lt) {
17    return pred >= 0 ? result_ge : result_lt;
18}
19
20static float fast_floor(float x) {
21//    float big = sk_fsel(x, 0x1.0p+23, -0x1.0p+23);
22    float big = sk_fsel(x, (float)(1 << 23), -(float)(1 << 23));
23    return (float)(x + big) - big;
24}
25
26static float std_floor(float x) {
27    return sk_float_floor(x);
28}
29
30static void test_floor_value(skiatest::Reporter* reporter, float value) {
31    float fast = fast_floor(value);
32    float std = std_floor(value);
33    REPORTER_ASSERT(reporter, std == fast);
34//    SkDebugf("value[%1.9f] std[%g] fast[%g] equal[%d]\n",
35//             value, std, fast, std == fast);
36}
37
38static void test_floor(skiatest::Reporter* reporter) {
39    static const float gVals[] = {
40        0, 1, 1.1f, 1.01f, 1.001f, 1.0001f, 1.00001f, 1.000001f, 1.0000001f
41    };
42
43    for (size_t i = 0; i < SK_ARRAY_COUNT(gVals); ++i) {
44        test_floor_value(reporter, gVals[i]);
45//        test_floor_value(reporter, -gVals[i]);
46    }
47}
48
49///////////////////////////////////////////////////////////////////////////////
50
51static float float_blend(int src, int dst, float unit) {
52    return dst + (src - dst) * unit;
53}
54
55static int blend31(int src, int dst, int a31) {
56    return dst + ((src - dst) * a31 * 2114 >> 16);
57    //    return dst + ((src - dst) * a31 * 33 >> 10);
58}
59
60static int blend31_slow(int src, int dst, int a31) {
61    int prod = src * a31 + (31 - a31) * dst + 16;
62    prod = (prod + (prod >> 5)) >> 5;
63    return prod;
64}
65
66static int blend31_round(int src, int dst, int a31) {
67    int prod = (src - dst) * a31 + 16;
68    prod = (prod + (prod >> 5)) >> 5;
69    return dst + prod;
70}
71
72static int blend31_old(int src, int dst, int a31) {
73    a31 += a31 >> 4;
74    return dst + ((src - dst) * a31 >> 5);
75}
76
77// suppress unused code warning
78static int (*blend_functions[])(int, int, int) = {
79    blend31,
80    blend31_slow,
81    blend31_round,
82    blend31_old
83};
84
85static void test_blend31() {
86    int failed = 0;
87    int death = 0;
88    if (false) { // avoid bit rot, suppress warning
89        failed = (*blend_functions[0])(0,0,0);
90    }
91    for (int src = 0; src <= 255; src++) {
92        for (int dst = 0; dst <= 255; dst++) {
93            for (int a = 0; a <= 31; a++) {
94//                int r0 = blend31(src, dst, a);
95//                int r0 = blend31_round(src, dst, a);
96//                int r0 = blend31_old(src, dst, a);
97                int r0 = blend31_slow(src, dst, a);
98
99                float f = float_blend(src, dst, a / 31.f);
100                int r1 = (int)f;
101                int r2 = SkScalarRoundToInt(SkFloatToScalar(f));
102
103                if (r0 != r1 && r0 != r2) {
104                    printf("src:%d dst:%d a:%d result:%d float:%g\n",
105                                 src, dst, a, r0, f);
106                    failed += 1;
107                }
108                if (r0 > 255) {
109                    death += 1;
110                    printf("death src:%d dst:%d a:%d result:%d float:%g\n",
111                           src, dst, a, r0, f);
112                }
113            }
114        }
115    }
116    SkDebugf("---- failed %d death %d\n", failed, death);
117}
118
119static void test_blend(skiatest::Reporter* reporter) {
120    for (int src = 0; src <= 255; src++) {
121        for (int dst = 0; dst <= 255; dst++) {
122            for (int a = 0; a <= 255; a++) {
123                int r0 = SkAlphaBlend255(src, dst, a);
124                float f1 = float_blend(src, dst, a / 255.f);
125                int r1 = SkScalarRoundToInt(SkFloatToScalar(f1));
126
127                if (r0 != r1) {
128                    float diff = sk_float_abs(f1 - r1);
129                    diff = sk_float_abs(diff - 0.5f);
130                    if (diff > (1 / 255.f)) {
131#ifdef SK_DEBUG
132                        SkDebugf("src:%d dst:%d a:%d result:%d float:%g\n",
133                                 src, dst, a, r0, f1);
134#endif
135                        REPORTER_ASSERT(reporter, false);
136                    }
137                }
138            }
139        }
140    }
141}
142
143#if defined(SkLONGLONG)
144static int symmetric_fixmul(int a, int b) {
145    int sa = SkExtractSign(a);
146    int sb = SkExtractSign(b);
147
148    a = SkApplySign(a, sa);
149    b = SkApplySign(b, sb);
150
151#if 1
152    int c = (int)(((SkLONGLONG)a * b) >> 16);
153
154    return SkApplySign(c, sa ^ sb);
155#else
156    SkLONGLONG ab = (SkLONGLONG)a * b;
157    if (sa ^ sb) {
158        ab = -ab;
159    }
160    return ab >> 16;
161#endif
162}
163#endif
164
165static void check_length(skiatest::Reporter* reporter,
166                         const SkPoint& p, SkScalar targetLen) {
167    float x = SkScalarToFloat(p.fX);
168    float y = SkScalarToFloat(p.fY);
169    float len = sk_float_sqrt(x*x + y*y);
170
171    len /= SkScalarToFloat(targetLen);
172
173    REPORTER_ASSERT(reporter, len > 0.999f && len < 1.001f);
174}
175
176static float nextFloat(SkRandom& rand) {
177    SkFloatIntUnion data;
178    data.fSignBitInt = rand.nextU();
179    return data.fFloat;
180}
181
182/*  returns true if a == b as resulting from (int)x. Since it is undefined
183 what to do if the float exceeds 2^32-1, we check for that explicitly.
184 */
185static bool equal_float_native_skia(float x, uint32_t ni, uint32_t si) {
186    if (!(x == x)) {    // NAN
187        return ((int32_t)si) == SK_MaxS32 || ((int32_t)si) == SK_MinS32;
188    }
189    // for out of range, C is undefined, but skia always should return NaN32
190    if (x > SK_MaxS32) {
191        return ((int32_t)si) == SK_MaxS32;
192    }
193    if (x < -SK_MaxS32) {
194        return ((int32_t)si) == SK_MinS32;
195    }
196    return si == ni;
197}
198
199static void assert_float_equal(skiatest::Reporter* reporter, const char op[],
200                               float x, uint32_t ni, uint32_t si) {
201    if (!equal_float_native_skia(x, ni, si)) {
202        SkString desc;
203        uint32_t xi = SkFloat2Bits(x);
204        desc.printf("%s float %g bits %x native %x skia %x\n", op, x, xi, ni, si);
205        reporter->reportFailed(desc);
206    }
207}
208
209static void test_float_cast(skiatest::Reporter* reporter, float x) {
210    int ix = (int)x;
211    int iix = SkFloatToIntCast(x);
212    assert_float_equal(reporter, "cast", x, ix, iix);
213}
214
215static void test_float_floor(skiatest::Reporter* reporter, float x) {
216    int ix = (int)floor(x);
217    int iix = SkFloatToIntFloor(x);
218    assert_float_equal(reporter, "floor", x, ix, iix);
219}
220
221static void test_float_round(skiatest::Reporter* reporter, float x) {
222    double xx = x + 0.5;    // need intermediate double to avoid temp loss
223    int ix = (int)floor(xx);
224    int iix = SkFloatToIntRound(x);
225    assert_float_equal(reporter, "round", x, ix, iix);
226}
227
228static void test_float_ceil(skiatest::Reporter* reporter, float x) {
229    int ix = (int)ceil(x);
230    int iix = SkFloatToIntCeil(x);
231    assert_float_equal(reporter, "ceil", x, ix, iix);
232}
233
234static void test_float_conversions(skiatest::Reporter* reporter, float x) {
235    test_float_cast(reporter, x);
236    test_float_floor(reporter, x);
237    test_float_round(reporter, x);
238    test_float_ceil(reporter, x);
239}
240
241static void test_int2float(skiatest::Reporter* reporter, int ival) {
242    float x0 = (float)ival;
243    float x1 = SkIntToFloatCast(ival);
244    float x2 = SkIntToFloatCast_NoOverflowCheck(ival);
245    REPORTER_ASSERT(reporter, x0 == x1);
246    REPORTER_ASSERT(reporter, x0 == x2);
247}
248
249static void unittest_fastfloat(skiatest::Reporter* reporter) {
250    SkRandom rand;
251    size_t i;
252
253    static const float gFloats[] = {
254        0.f, 1.f, 0.5f, 0.499999f, 0.5000001f, 1.f/3,
255        0.000000001f, 1000000000.f,     // doesn't overflow
256        0.0000000001f, 10000000000.f    // does overflow
257    };
258    for (i = 0; i < SK_ARRAY_COUNT(gFloats); i++) {
259        test_float_conversions(reporter, gFloats[i]);
260        test_float_conversions(reporter, -gFloats[i]);
261    }
262
263    for (int outer = 0; outer < 100; outer++) {
264        rand.setSeed(outer);
265        for (i = 0; i < 100000; i++) {
266            float x = nextFloat(rand);
267            test_float_conversions(reporter, x);
268        }
269
270        test_int2float(reporter, 0);
271        test_int2float(reporter, 1);
272        test_int2float(reporter, -1);
273        for (i = 0; i < 100000; i++) {
274            // for now only test ints that are 24bits or less, since we don't
275            // round (down) large ints the same as IEEE...
276            int ival = rand.nextU() & 0xFFFFFF;
277            test_int2float(reporter, ival);
278            test_int2float(reporter, -ival);
279        }
280    }
281}
282
283#ifdef SK_SCALAR_IS_FLOAT
284static float make_zero() {
285    return sk_float_sin(0);
286}
287#endif
288
289static void unittest_isfinite(skiatest::Reporter* reporter) {
290#ifdef SK_SCALAR_IS_FLOAT
291    float nan = sk_float_asin(2);
292    float inf = 1.0f / make_zero();
293    float big = 3.40282e+038f;
294
295    REPORTER_ASSERT(reporter, !SkScalarIsNaN(inf));
296    REPORTER_ASSERT(reporter, !SkScalarIsNaN(-inf));
297    REPORTER_ASSERT(reporter, !SkScalarIsFinite(inf));
298    REPORTER_ASSERT(reporter, !SkScalarIsFinite(-inf));
299#else
300    SkFixed nan = SK_FixedNaN;
301    SkFixed big = SK_FixedMax;
302#endif
303
304    REPORTER_ASSERT(reporter,  SkScalarIsNaN(nan));
305    REPORTER_ASSERT(reporter, !SkScalarIsNaN(big));
306    REPORTER_ASSERT(reporter, !SkScalarIsNaN(-big));
307    REPORTER_ASSERT(reporter, !SkScalarIsNaN(0));
308
309    REPORTER_ASSERT(reporter, !SkScalarIsFinite(nan));
310    REPORTER_ASSERT(reporter,  SkScalarIsFinite(big));
311    REPORTER_ASSERT(reporter,  SkScalarIsFinite(-big));
312    REPORTER_ASSERT(reporter,  SkScalarIsFinite(0));
313}
314
315static void test_muldiv255(skiatest::Reporter* reporter) {
316    for (int a = 0; a <= 255; a++) {
317        for (int b = 0; b <= 255; b++) {
318            int ab = a * b;
319            float s = ab / 255.0f;
320            int round = (int)floorf(s + 0.5f);
321            int trunc = (int)floorf(s);
322
323            int iround = SkMulDiv255Round(a, b);
324            int itrunc = SkMulDiv255Trunc(a, b);
325
326            REPORTER_ASSERT(reporter, iround == round);
327            REPORTER_ASSERT(reporter, itrunc == trunc);
328
329            REPORTER_ASSERT(reporter, itrunc <= iround);
330            REPORTER_ASSERT(reporter, iround <= a);
331            REPORTER_ASSERT(reporter, iround <= b);
332        }
333    }
334}
335
336static void test_muldiv255ceiling(skiatest::Reporter* reporter) {
337    for (int c = 0; c <= 255; c++) {
338        for (int a = 0; a <= 255; a++) {
339            int product = (c * a + 255);
340            int expected_ceiling = (product + (product >> 8)) >> 8;
341            int webkit_ceiling = (c * a + 254) / 255;
342            REPORTER_ASSERT(reporter, expected_ceiling == webkit_ceiling);
343            int skia_ceiling = SkMulDiv255Ceiling(c, a);
344            REPORTER_ASSERT(reporter, skia_ceiling == webkit_ceiling);
345        }
346    }
347}
348
349static void test_copysign(skiatest::Reporter* reporter) {
350    static const int32_t gTriples[] = {
351        // x, y, expected result
352        0, 0, 0,
353        0, 1, 0,
354        0, -1, 0,
355        1, 0, 1,
356        1, 1, 1,
357        1, -1, -1,
358        -1, 0, 1,
359        -1, 1, 1,
360        -1, -1, -1,
361    };
362    for (size_t i = 0; i < SK_ARRAY_COUNT(gTriples); i += 3) {
363        REPORTER_ASSERT(reporter,
364                        SkCopySign32(gTriples[i], gTriples[i+1]) == gTriples[i+2]);
365        float x = (float)gTriples[i];
366        float y = (float)gTriples[i+1];
367        float expected = (float)gTriples[i+2];
368        REPORTER_ASSERT(reporter, sk_float_copysign(x, y) == expected);
369    }
370
371    SkRandom rand;
372    for (int j = 0; j < 1000; j++) {
373        int ix = rand.nextS();
374        REPORTER_ASSERT(reporter, SkCopySign32(ix, ix) == ix);
375        REPORTER_ASSERT(reporter, SkCopySign32(ix, -ix) == -ix);
376        REPORTER_ASSERT(reporter, SkCopySign32(-ix, ix) == ix);
377        REPORTER_ASSERT(reporter, SkCopySign32(-ix, -ix) == -ix);
378
379        SkScalar sx = rand.nextSScalar1();
380        REPORTER_ASSERT(reporter, SkScalarCopySign(sx, sx) == sx);
381        REPORTER_ASSERT(reporter, SkScalarCopySign(sx, -sx) == -sx);
382        REPORTER_ASSERT(reporter, SkScalarCopySign(-sx, sx) == sx);
383        REPORTER_ASSERT(reporter, SkScalarCopySign(-sx, -sx) == -sx);
384    }
385}
386
387static void TestMath(skiatest::Reporter* reporter) {
388    int         i;
389    int32_t     x;
390    SkRandom    rand;
391
392    // these should assert
393#if 0
394    SkToS8(128);
395    SkToS8(-129);
396    SkToU8(256);
397    SkToU8(-5);
398
399    SkToS16(32768);
400    SkToS16(-32769);
401    SkToU16(65536);
402    SkToU16(-5);
403
404    if (sizeof(size_t) > 4) {
405        SkToS32(4*1024*1024);
406        SkToS32(-4*1024*1024);
407        SkToU32(5*1024*1024);
408        SkToU32(-5);
409    }
410#endif
411
412    test_muldiv255(reporter);
413    test_muldiv255ceiling(reporter);
414    test_copysign(reporter);
415
416    {
417        SkScalar x = SK_ScalarNaN;
418        REPORTER_ASSERT(reporter, SkScalarIsNaN(x));
419    }
420
421    for (i = 1; i <= 10; i++) {
422        x = SkCubeRootBits(i*i*i, 11);
423        REPORTER_ASSERT(reporter, x == i);
424    }
425
426    x = SkFixedSqrt(SK_Fixed1);
427    REPORTER_ASSERT(reporter, x == SK_Fixed1);
428    x = SkFixedSqrt(SK_Fixed1/4);
429    REPORTER_ASSERT(reporter, x == SK_Fixed1/2);
430    x = SkFixedSqrt(SK_Fixed1*4);
431    REPORTER_ASSERT(reporter, x == SK_Fixed1*2);
432
433    x = SkFractSqrt(SK_Fract1);
434    REPORTER_ASSERT(reporter, x == SK_Fract1);
435    x = SkFractSqrt(SK_Fract1/4);
436    REPORTER_ASSERT(reporter, x == SK_Fract1/2);
437    x = SkFractSqrt(SK_Fract1/16);
438    REPORTER_ASSERT(reporter, x == SK_Fract1/4);
439
440    for (i = 1; i < 100; i++) {
441        x = SkFixedSqrt(SK_Fixed1 * i * i);
442        REPORTER_ASSERT(reporter, x == SK_Fixed1 * i);
443    }
444
445    for (i = 0; i < 1000; i++) {
446        int value = rand.nextS16();
447        int max = rand.nextU16();
448
449        int clamp = SkClampMax(value, max);
450        int clamp2 = value < 0 ? 0 : (value > max ? max : value);
451        REPORTER_ASSERT(reporter, clamp == clamp2);
452    }
453
454    for (i = 0; i < 10000; i++) {
455        SkPoint p;
456
457        // These random values are being treated as 32-bit-patterns, not as
458        // ints; calling SkIntToScalar() here produces crashes.
459        p.setLength((SkScalar) rand.nextS(),
460                    (SkScalar) rand.nextS(),
461                    SK_Scalar1);
462        check_length(reporter, p, SK_Scalar1);
463        p.setLength((SkScalar) (rand.nextS() >> 13),
464                    (SkScalar) (rand.nextS() >> 13),
465                    SK_Scalar1);
466        check_length(reporter, p, SK_Scalar1);
467    }
468
469    {
470        SkFixed result = SkFixedDiv(100, 100);
471        REPORTER_ASSERT(reporter, result == SK_Fixed1);
472        result = SkFixedDiv(1, SK_Fixed1);
473        REPORTER_ASSERT(reporter, result == 1);
474    }
475
476    unittest_fastfloat(reporter);
477    unittest_isfinite(reporter);
478
479#ifdef SkLONGLONG
480    for (i = 0; i < 10000; i++) {
481        SkFixed numer = rand.nextS();
482        SkFixed denom = rand.nextS();
483        SkFixed result = SkFixedDiv(numer, denom);
484        SkLONGLONG check = ((SkLONGLONG)numer << 16) / denom;
485
486        (void)SkCLZ(numer);
487        (void)SkCLZ(denom);
488
489        REPORTER_ASSERT(reporter, result != (SkFixed)SK_NaN32);
490        if (check > SK_MaxS32) {
491            check = SK_MaxS32;
492        } else if (check < -SK_MaxS32) {
493            check = SK_MinS32;
494        }
495        REPORTER_ASSERT(reporter, result == (int32_t)check);
496
497        result = SkFractDiv(numer, denom);
498        check = ((SkLONGLONG)numer << 30) / denom;
499
500        REPORTER_ASSERT(reporter, result != (SkFixed)SK_NaN32);
501        if (check > SK_MaxS32) {
502            check = SK_MaxS32;
503        } else if (check < -SK_MaxS32) {
504            check = SK_MinS32;
505        }
506        REPORTER_ASSERT(reporter, result == (int32_t)check);
507
508        // make them <= 2^24, so we don't overflow in fixmul
509        numer = numer << 8 >> 8;
510        denom = denom << 8 >> 8;
511
512        result = SkFixedMul(numer, denom);
513        SkFixed r2 = symmetric_fixmul(numer, denom);
514        //        SkASSERT(result == r2);
515
516        result = SkFixedMul(numer, numer);
517        r2 = SkFixedSquare(numer);
518        REPORTER_ASSERT(reporter, result == r2);
519
520        if (numer >= 0 && denom >= 0) {
521            SkFixed mean = SkFixedMean(numer, denom);
522            float prod = SkFixedToFloat(numer) * SkFixedToFloat(denom);
523            float fm = sk_float_sqrt(sk_float_abs(prod));
524            SkFixed mean2 = SkFloatToFixed(fm);
525            int diff = SkAbs32(mean - mean2);
526            REPORTER_ASSERT(reporter, diff <= 1);
527        }
528
529        {
530            SkFixed mod = SkFixedMod(numer, denom);
531            float n = SkFixedToFloat(numer);
532            float d = SkFixedToFloat(denom);
533            float m = sk_float_mod(n, d);
534            // ensure the same sign
535            REPORTER_ASSERT(reporter, mod == 0 || (mod < 0) == (m < 0));
536            int diff = SkAbs32(mod - SkFloatToFixed(m));
537            REPORTER_ASSERT(reporter, (diff >> 7) == 0);
538        }
539    }
540#endif
541
542    for (i = 0; i < 10000; i++) {
543        SkFract x = rand.nextU() >> 1;
544        double xx = (double)x / SK_Fract1;
545        SkFract xr = SkFractSqrt(x);
546        SkFract check = SkFloatToFract(sqrt(xx));
547        REPORTER_ASSERT(reporter, xr == check ||
548                                  xr == check-1 ||
549                                  xr == check+1);
550
551        xr = SkFixedSqrt(x);
552        xx = (double)x / SK_Fixed1;
553        check = SkFloatToFixed(sqrt(xx));
554        REPORTER_ASSERT(reporter, xr == check || xr == check-1);
555
556        xr = SkSqrt32(x);
557        xx = (double)x;
558        check = (int32_t)sqrt(xx);
559        REPORTER_ASSERT(reporter, xr == check || xr == check-1);
560    }
561
562#if !defined(SK_SCALAR_IS_FLOAT)
563    {
564        SkFixed s, c;
565        s = SkFixedSinCos(0, &c);
566        REPORTER_ASSERT(reporter, s == 0);
567        REPORTER_ASSERT(reporter, c == SK_Fixed1);
568    }
569
570    int maxDiff = 0;
571    for (i = 0; i < 1000; i++) {
572        SkFixed rads = rand.nextS() >> 10;
573        double frads = SkFixedToFloat(rads);
574
575        SkFixed s, c;
576        s = SkScalarSinCos(rads, &c);
577
578        double fs = sin(frads);
579        double fc = cos(frads);
580
581        SkFixed is = SkFloatToFixed(fs);
582        SkFixed ic = SkFloatToFixed(fc);
583
584        maxDiff = SkMax32(maxDiff, SkAbs32(is - s));
585        maxDiff = SkMax32(maxDiff, SkAbs32(ic - c));
586    }
587    SkDebugf("SinCos: maximum error = %d\n", maxDiff);
588#endif
589
590#ifdef SK_SCALAR_IS_FLOAT
591    test_blend(reporter);
592#endif
593
594//    test_floor(reporter);
595
596    // disable for now
597    if (false) test_blend31();  // avoid bit rot, suppress warning
598}
599
600#include "TestClassDef.h"
601DEFINE_TESTCLASS("Math", MathTestClass, TestMath)
602