#include "Test.h"
#include "SkPoint.h"
#include "SkRandom.h"
#if defined(SkLONGLONG)
static int symmetric_fixmul(int a, int b) {
int sa = SkExtractSign(a);
int sb = SkExtractSign(b);
a = SkApplySign(a, sa);
b = SkApplySign(b, sb);
#if 1
int c = (int)(((SkLONGLONG)a * b) >> 16);
return SkApplySign(c, sa ^ sb);
#else
SkLONGLONG ab = (SkLONGLONG)a * b;
if (sa ^ sb) {
ab = -ab;
}
return ab >> 16;
#endif
}
#endif
static void check_length(skiatest::Reporter* reporter,
const SkPoint& p, SkScalar targetLen) {
#ifdef SK_CAN_USE_FLOAT
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);
#endif
}
#if defined(SK_CAN_USE_FLOAT)
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 si == SK_MaxS32 || si == SK_MinS32;
}
// for out of range, C is undefined, but skia always should return NaN32
if (x > SK_MaxS32) {
return si == SK_MaxS32;
}
if (x < -SK_MaxS32) {
return 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)) {
SkString desc;
desc.printf("%s float %g bits %x native %x skia %x\n", op, x, ni, si);
reporter->reportFailed(desc);
}
}
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);
float x2 = SkIntToFloatCast_NoOverflowCheck(ival);
REPORTER_ASSERT(reporter, x0 == x1);
REPORTER_ASSERT(reporter, x0 == x2);
}
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);
}
}
}
#endif
static void test_muldiv255(skiatest::Reporter* reporter) {
#ifdef SK_CAN_USE_FLOAT
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);
}
}
#endif
}
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]);
#ifdef SK_CAN_USE_FLOAT
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);
#endif
}
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);
}
}
static void TestMath(skiatest::Reporter* reporter) {
int i;
int32_t x;
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_copysign(reporter);
{
SkScalar x = SK_ScalarNaN;
REPORTER_ASSERT(reporter, SkScalarIsNaN(x));
}
for (i = 1; i <= 10; i++) {
x = SkCubeRootBits(i*i*i, 11);
REPORTER_ASSERT(reporter, x == i);
}
x = SkFixedSqrt(SK_Fixed1);
REPORTER_ASSERT(reporter, x == SK_Fixed1);
x = SkFixedSqrt(SK_Fixed1/4);
REPORTER_ASSERT(reporter, x == SK_Fixed1/2);
x = SkFixedSqrt(SK_Fixed1*4);
REPORTER_ASSERT(reporter, x == SK_Fixed1*2);
x = SkFractSqrt(SK_Fract1);
REPORTER_ASSERT(reporter, x == SK_Fract1);
x = SkFractSqrt(SK_Fract1/4);
REPORTER_ASSERT(reporter, x == SK_Fract1/2);
x = SkFractSqrt(SK_Fract1/16);
REPORTER_ASSERT(reporter, x == SK_Fract1/4);
for (i = 1; i < 100; i++) {
x = SkFixedSqrt(SK_Fixed1 * i * i);
REPORTER_ASSERT(reporter, x == SK_Fixed1 * i);
}
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;
p.setLength(rand.nextS(), rand.nextS(), SK_Scalar1);
check_length(reporter, p, SK_Scalar1);
p.setLength(rand.nextS() >> 13, 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);
}
#ifdef SK_CAN_USE_FLOAT
unittest_fastfloat(reporter);
#endif
#ifdef SkLONGLONG
for (i = 0; i < 10000; i++) {
SkFixed numer = rand.nextS();
SkFixed denom = rand.nextS();
SkFixed result = SkFixedDiv(numer, denom);
SkLONGLONG check = ((SkLONGLONG)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);
result = SkFractDiv(numer, denom);
check = ((SkLONGLONG)numer << 30) / 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);
// make them <= 2^24, so we don't overflow in fixmul
numer = numer << 8 >> 8;
denom = denom << 8 >> 8;
result = SkFixedMul(numer, denom);
SkFixed r2 = symmetric_fixmul(numer, denom);
// SkASSERT(result == r2);
result = SkFixedMul(numer, numer);
r2 = SkFixedSquare(numer);
REPORTER_ASSERT(reporter, result == r2);
#ifdef SK_CAN_USE_FLOAT
if (numer >= 0 && denom >= 0) {
SkFixed mean = SkFixedMean(numer, denom);
float prod = SkFixedToFloat(numer) * SkFixedToFloat(denom);
float fm = sk_float_sqrt(sk_float_abs(prod));
SkFixed mean2 = SkFloatToFixed(fm);
int diff = SkAbs32(mean - mean2);
REPORTER_ASSERT(reporter, diff <= 1);
}
{
SkFixed mod = SkFixedMod(numer, denom);
float n = SkFixedToFloat(numer);
float d = SkFixedToFloat(denom);
float m = sk_float_mod(n, d);
// ensure the same sign
REPORTER_ASSERT(reporter, mod == 0 || (mod < 0) == (m < 0));
int diff = SkAbs32(mod - SkFloatToFixed(m));
REPORTER_ASSERT(reporter, (diff >> 7) == 0);
}
#endif
}
#endif
#ifdef SK_CAN_USE_FLOAT
for (i = 0; i < 10000; i++) {
SkFract x = rand.nextU() >> 1;
double xx = (double)x / SK_Fract1;
SkFract xr = SkFractSqrt(x);
SkFract check = SkFloatToFract(sqrt(xx));
REPORTER_ASSERT(reporter, xr == check ||
xr == check-1 ||
xr == check+1);
xr = SkFixedSqrt(x);
xx = (double)x / SK_Fixed1;
check = SkFloatToFixed(sqrt(xx));
REPORTER_ASSERT(reporter, xr == check || xr == check-1);
xr = SkSqrt32(x);
xx = (double)x;
check = (int32_t)sqrt(xx);
REPORTER_ASSERT(reporter, xr == check || xr == check-1);
}
#endif
#if !defined(SK_SCALAR_IS_FLOAT) && defined(SK_CAN_USE_FLOAT)
{
SkFixed s, c;
s = SkFixedSinCos(0, &c);
REPORTER_ASSERT(reporter, s == 0);
REPORTER_ASSERT(reporter, c == SK_Fixed1);
}
int maxDiff = 0;
for (i = 0; i < 1000; i++) {
SkFixed rads = rand.nextS() >> 10;
double frads = SkFixedToFloat(rads);
SkFixed s, c;
s = SkScalarSinCos(rads, &c);
double fs = sin(frads);
double fc = cos(frads);
SkFixed is = SkFloatToFixed(fs);
SkFixed ic = SkFloatToFixed(fc);
maxDiff = SkMax32(maxDiff, SkAbs32(is - s));
maxDiff = SkMax32(maxDiff, SkAbs32(ic - c));
}
SkDebugf("SinCos: maximum error = %d\n", maxDiff);
#endif
}
#include "TestClassDef.h"
DEFINE_TESTCLASS("Math", MathTestClass, TestMath)