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skia2/tests/MathTest.cpp
jvanverth 936799204b Add float-to-half (binary16) conversion functions. 
Based on code by Fabian Giesen at
https://fgiesen.wordpress.com/2012/03/28/half-to-float-done-quic/.

These will be needed for creating binary16 textures from floating point data.

BUG=skia:3103

Review URL: https://codereview.chromium.org/760753003
2014-11-26 13:15:59 -08:00

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/*
* 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 "SkColorPriv.h"
#include "SkEndian.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);
REPORTER_ASSERT(reporter, std == fast);
// SkDebugf("value[%1.9f] std[%g] fast[%g] equal[%d]\n",
// value, std, fast, std == fast);
}
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)) {
#ifdef SK_DEBUG
SkDebugf("src:%d dst:%d a:%d result:%d float:%g\n",
src, dst, a, r0, f1);
#endif
REPORTER_ASSERT(reporter, false);
}
}
}
}
}
}
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, uint32_t ni, uint32_t si) {
if (!(x == x)) { // NAN
return ((int32_t)si) == SK_MaxS32 || ((int32_t)si) == SK_MinS32;
}
// for out of range, C is undefined, but skia always should return NaN32
if (x > SK_MaxS32) {
return ((int32_t)si) == SK_MaxS32;
}
if (x < -SK_MaxS32) {
return ((int32_t)si) == SK_MinS32;
}
return si == ni;
}
static void assert_float_equal(skiatest::Reporter* reporter, const char op[],
float x, uint32_t ni, uint32_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_cast(skiatest::Reporter* reporter, float x) {
int ix = (int)x;
int iix = SkFloatToIntCast(x);
assert_float_equal(reporter, "cast", x, ix, iix);
}
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_cast(reporter, x);
test_float_floor(reporter, x);
test_float_round(reporter, x);
test_float_ceil(reporter, x);
}
static void test_int2float(skiatest::Reporter* reporter, int ival) {
float x0 = (float)ival;
float x1 = SkIntToFloatCast(ival);
REPORTER_ASSERT(reporter, x0 == x1);
}
static void unittest_fastfloat(skiatest::Reporter* reporter) {
SkRandom rand;
size_t i;
static const float gFloats[] = {
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);
}
test_int2float(reporter, 0);
test_int2float(reporter, 1);
test_int2float(reporter, -1);
for (i = 0; i < 100000; i++) {
// for now only test ints that are 24bits or less, since we don't
// round (down) large ints the same as IEEE...
int ival = rand.nextU() & 0xFFFFFF;
test_int2float(reporter, ival);
test_int2float(reporter, -ival);
}
}
}
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) );
}
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);
}
unittest_fastfloat(reporter);
unittest_isfinite(reporter);
unittest_half(reporter);
for (i = 0; i < 10000; i++) {
SkFixed numer = rand.nextS();
SkFixed denom = rand.nextS();
SkFixed result = SkFixedDiv(numer, denom);
int64_t check = ((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;
}
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);
}
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