/*
* Copyright (C) 2006-2008 The Android Open Source Project
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
#include "SkMath.h"
#include "SkCordic.h"
#include "SkFloatBits.h"
#include "SkFloatingPoint.h"
#include "Sk64.h"
#include "SkScalar.h"
#ifdef SK_SCALAR_IS_FLOAT
const uint32_t gIEEENotANumber = 0x7FFFFFFF;
const uint32_t gIEEEInfinity = 0x7F800000;
#endif
#define sub_shift(zeros, x, n) \
zeros -= n; \
x >>= n
int SkCLZ_portable(uint32_t x) {
if (x == 0) {
return 32;
}
#ifdef SK_CPU_HAS_CONDITIONAL_INSTR
int zeros = 31;
if (x & 0xFFFF0000) {
sub_shift(zeros, x, 16);
}
if (x & 0xFF00) {
sub_shift(zeros, x, 8);
}
if (x & 0xF0) {
sub_shift(zeros, x, 4);
}
if (x & 0xC) {
sub_shift(zeros, x, 2);
}
if (x & 0x2) {
sub_shift(zeros, x, 1);
}
#else
int zeros = ((x >> 16) - 1) >> 31 << 4;
x <<= zeros;
int nonzero = ((x >> 24) - 1) >> 31 << 3;
zeros += nonzero;
x <<= nonzero;
nonzero = ((x >> 28) - 1) >> 31 << 2;
zeros += nonzero;
x <<= nonzero;
nonzero = ((x >> 30) - 1) >> 31 << 1;
zeros += nonzero;
x <<= nonzero;
zeros += (~x) >> 31;
#endif
return zeros;
}
int32_t SkMulDiv(int32_t numer1, int32_t numer2, int32_t denom) {
SkASSERT(denom);
Sk64 tmp;
tmp.setMul(numer1, numer2);
tmp.div(denom, Sk64::kTrunc_DivOption);
return tmp.get32();
}
int32_t SkMulShift(int32_t a, int32_t b, unsigned shift) {
int sign = SkExtractSign(a ^ b);
if (shift > 63) {
return sign;
}
a = SkAbs32(a);
b = SkAbs32(b);
uint32_t ah = a >> 16;
uint32_t al = a & 0xFFFF;
uint32_t bh = b >> 16;
uint32_t bl = b & 0xFFFF;
uint32_t A = ah * bh;
uint32_t B = ah * bl + al * bh;
uint32_t C = al * bl;
/* [ A ]
[ B ]
[ C ]
*/
uint32_t lo = C + (B << 16);
int32_t hi = A + (B >> 16) + (lo < C);
if (sign < 0) {
hi = -hi - Sk32ToBool(lo);
lo = 0 - lo;
}
if (shift == 0) {
#ifdef SK_DEBUGx
SkASSERT(((int32_t)lo >> 31) == hi);
#endif
return lo;
} else if (shift >= 32) {
return hi >> (shift - 32);
} else {
#ifdef SK_DEBUGx
int32_t tmp = hi >> shift;
SkASSERT(tmp == 0 || tmp == -1);
#endif
// we want (hi << (32 - shift)) | (lo >> shift) but rounded
int roundBit = (lo >> (shift - 1)) & 1;
return ((hi << (32 - shift)) | (lo >> shift)) + roundBit;
}
}
SkFixed SkFixedMul_portable(SkFixed a, SkFixed b) {
#if 0
Sk64 tmp;
tmp.setMul(a, b);
tmp.shiftRight(16);
return tmp.fLo;
#elif defined(SkLONGLONG)
return (SkLONGLONG)a * b >> 16;
#else
int sa = SkExtractSign(a);
int sb = SkExtractSign(b);
// now make them positive
a = SkApplySign(a, sa);
b = SkApplySign(b, sb);
uint32_t ah = a >> 16;
uint32_t al = a & 0xFFFF;
uint32_t bh = b >> 16;
uint32_t bl = b & 0xFFFF;
uint32_t R = ah * b + al * bh + (al * bl >> 16);
return SkApplySign(R, sa ^ sb);
#endif
}
SkFract SkFractMul_portable(SkFract a, SkFract b) {
#if 0
Sk64 tmp;
tmp.setMul(a, b);
return tmp.getFract();
#elif defined(SkLONGLONG)
return (SkLONGLONG)a * b >> 30;
#else
int sa = SkExtractSign(a);
int sb = SkExtractSign(b);
// now make them positive
a = SkApplySign(a, sa);
b = SkApplySign(b, sb);
uint32_t ah = a >> 16;
uint32_t al = a & 0xFFFF;
uint32_t bh = b >> 16;
uint32_t bl = b & 0xFFFF;
uint32_t A = ah * bh;
uint32_t B = ah * bl + al * bh;
uint32_t C = al * bl;
/* [ A ]
[ B ]
[ C ]
*/
uint32_t Lo = C + (B << 16);
uint32_t Hi = A + (B >>16) + (Lo < C);
SkASSERT((Hi >> 29) == 0); // else overflow
int32_t R = (Hi << 2) + (Lo >> 30);
return SkApplySign(R, sa ^ sb);
#endif
}
int SkFixedMulCommon(SkFixed a, int b, int bias) {
// this function only works if b is 16bits
SkASSERT(b == (int16_t)b);
SkASSERT(b >= 0);
int sa = SkExtractSign(a);
a = SkApplySign(a, sa);
uint32_t ah = a >> 16;
uint32_t al = a & 0xFFFF;
uint32_t R = ah * b + ((al * b + bias) >> 16);
return SkApplySign(R, sa);
}
#ifdef SK_DEBUGx
#define TEST_FASTINVERT
#endif
SkFixed SkFixedFastInvert(SkFixed x) {
/* Adapted (stolen) from gglRecip()
*/
if (x == SK_Fixed1) {
return SK_Fixed1;
}
int sign = SkExtractSign(x);
uint32_t a = SkApplySign(x, sign);
if (a <= 2) {
return SkApplySign(SK_MaxS32, sign);
}
#ifdef TEST_FASTINVERT
SkFixed orig = a;
uint32_t slow = SkFixedDiv(SK_Fixed1, a);
#endif
// normalize a
int lz = SkCLZ(a);
a = a << lz >> 16;
// compute 1/a approximation (0.5 <= a < 1.0)
uint32_t r = 0x17400 - a; // (2.90625 (~2.914) - 2*a) >> 1
// Newton-Raphson iteration:
// x = r*(2 - a*r) = ((r/2)*(1 - a*r/2))*4
r = ( (0x10000 - ((a*r)>>16)) * r ) >> 15;
r = ( (0x10000 - ((a*r)>>16)) * r ) >> (30 - lz);
#ifdef TEST_FASTINVERT
SkDebugf("SkFixedFastInvert(%x %g) = %x %g Slow[%x %g]\n",
orig, orig/65536.,
r, r/65536.,
slow, slow/65536.);
#endif
return SkApplySign(r, sign);
}
///////////////////////////////////////////////////////////////////////////////
#define DIVBITS_ITER(n) \
case n: \
if ((numer = (numer << 1) - denom) >= 0) \
result |= 1 << (n - 1); else numer += denom
int32_t SkDivBits(int32_t numer, int32_t denom, int shift_bias) {
SkASSERT(denom != 0);
if (numer == 0) {
return 0;
}
// make numer and denom positive, and sign hold the resulting sign
int32_t sign = SkExtractSign(numer ^ denom);
numer = SkAbs32(numer);
denom = SkAbs32(denom);
int nbits = SkCLZ(numer) - 1;
int dbits = SkCLZ(denom) - 1;
int bits = shift_bias - nbits + dbits;
if (bits < 0) { // answer will underflow
return 0;
}
if (bits > 31) { // answer will overflow
return SkApplySign(SK_MaxS32, sign);
}
denom <<= dbits;
numer <<= nbits;
SkFixed result = 0;
// do the first one
if ((numer -= denom) >= 0) {
result = 1;
} else {
numer += denom;
}
// Now fall into our switch statement if there are more bits to compute
if (bits > 0) {
// make room for the rest of the answer bits
result <<= bits;
switch (bits) {
DIVBITS_ITER(31); DIVBITS_ITER(30); DIVBITS_ITER(29);
DIVBITS_ITER(28); DIVBITS_ITER(27); DIVBITS_ITER(26);
DIVBITS_ITER(25); DIVBITS_ITER(24); DIVBITS_ITER(23);
DIVBITS_ITER(22); DIVBITS_ITER(21); DIVBITS_ITER(20);
DIVBITS_ITER(19); DIVBITS_ITER(18); DIVBITS_ITER(17);
DIVBITS_ITER(16); DIVBITS_ITER(15); DIVBITS_ITER(14);
DIVBITS_ITER(13); DIVBITS_ITER(12); DIVBITS_ITER(11);
DIVBITS_ITER(10); DIVBITS_ITER( 9); DIVBITS_ITER( 8);
DIVBITS_ITER( 7); DIVBITS_ITER( 6); DIVBITS_ITER( 5);
DIVBITS_ITER( 4); DIVBITS_ITER( 3); DIVBITS_ITER( 2);
// we merge these last two together, makes GCC make better ARM
default:
DIVBITS_ITER( 1);
}
}
if (result < 0) {
result = SK_MaxS32;
}
return SkApplySign(result, sign);
}
/* mod(float numer, float denom) seems to always return the sign
of the numer, so that's what we do too
*/
SkFixed SkFixedMod(SkFixed numer, SkFixed denom) {
int sn = SkExtractSign(numer);
int sd = SkExtractSign(denom);
numer = SkApplySign(numer, sn);
denom = SkApplySign(denom, sd);
if (numer < denom) {
return SkApplySign(numer, sn);
} else if (numer == denom) {
return 0;
} else {
SkFixed div = SkFixedDiv(numer, denom);
return SkApplySign(SkFixedMul(denom, div & 0xFFFF), sn);
}
}
/* www.worldserver.com/turk/computergraphics/FixedSqrt.pdf
*/
int32_t SkSqrtBits(int32_t x, int count) {
SkASSERT(x >= 0 && count > 0 && (unsigned)count <= 30);
uint32_t root = 0;
uint32_t remHi = 0;
uint32_t remLo = x;
do {
root <<= 1;
remHi = (remHi<<2) | (remLo>>30);
remLo <<= 2;
uint32_t testDiv = (root << 1) + 1;
if (remHi >= testDiv) {
remHi -= testDiv;
root++;
}
} while (--count >= 0);
return root;
}
int32_t SkCubeRootBits(int32_t value, int bits) {
SkASSERT(bits > 0);
int sign = SkExtractSign(value);
value = SkApplySign(value, sign);
uint32_t root = 0;
uint32_t curr = (uint32_t)value >> 30;
value <<= 2;
do {
root <<= 1;
uint32_t guess = root * root + root;
guess = (guess << 1) + guess; // guess *= 3
if (guess < curr) {
curr -= guess + 1;
root |= 1;
}
curr = (curr << 3) | ((uint32_t)value >> 29);
value <<= 3;
} while (--bits);
return SkApplySign(root, sign);
}
SkFixed SkFixedMean(SkFixed a, SkFixed b) {
Sk64 tmp;
tmp.setMul(a, b);
return tmp.getSqrt();
}
///////////////////////////////////////////////////////////////////////////////
#ifdef SK_SCALAR_IS_FLOAT
float SkScalarSinCos(float radians, float* cosValue) {
float sinValue = sk_float_sin(radians);
if (cosValue) {
*cosValue = sk_float_cos(radians);
if (SkScalarNearlyZero(*cosValue)) {
*cosValue = 0;
}
}
if (SkScalarNearlyZero(sinValue)) {
sinValue = 0;
}
return sinValue;
}
#endif
#define INTERP_SINTABLE
#define BUILD_TABLE_AT_RUNTIMEx
#define kTableSize 256
#ifdef BUILD_TABLE_AT_RUNTIME
static uint16_t gSkSinTable[kTableSize];
static void build_sintable(uint16_t table[]) {
for (int i = 0; i < kTableSize; i++) {
double rad = i * 3.141592653589793 / (2*kTableSize);
double val = sin(rad);
int ival = (int)(val * SK_Fixed1);
table[i] = SkToU16(ival);
}
}
#else
#include "SkSinTable.h"
#endif
#define SK_Fract1024SizeOver2PI 0x28BE60 /* floatToFract(1024 / 2PI) */
#ifdef INTERP_SINTABLE
static SkFixed interp_table(const uint16_t table[], int index, int partial255) {
SkASSERT((unsigned)index < kTableSize);
SkASSERT((unsigned)partial255 <= 255);
SkFixed lower = table[index];
SkFixed upper = (index == kTableSize - 1) ? SK_Fixed1 : table[index + 1];
SkASSERT(lower < upper);
SkASSERT(lower >= 0);
SkASSERT(upper <= SK_Fixed1);
partial255 += (partial255 >> 7);
return lower + ((upper - lower) * partial255 >> 8);
}
#endif
SkFixed SkFixedSinCos(SkFixed radians, SkFixed* cosValuePtr) {
SkASSERT(SK_ARRAY_COUNT(gSkSinTable) == kTableSize);
#ifdef BUILD_TABLE_AT_RUNTIME
static bool gFirstTime = true;
if (gFirstTime) {
build_sintable(gSinTable);
gFirstTime = false;
}
#endif
// make radians positive
SkFixed sinValue, cosValue;
int32_t cosSign = 0;
int32_t sinSign = SkExtractSign(radians);
radians = SkApplySign(radians, sinSign);
// scale it to 0...1023 ...
#ifdef INTERP_SINTABLE
radians = SkMulDiv(radians, 2 * kTableSize * 256, SK_FixedPI);
int findex = radians & (kTableSize * 256 - 1);
int index = findex >> 8;
int partial = findex & 255;
sinValue = interp_table(gSkSinTable, index, partial);
findex = kTableSize * 256 - findex - 1;
index = findex >> 8;
partial = findex & 255;
cosValue = interp_table(gSkSinTable, index, partial);
int quad = ((unsigned)radians / (kTableSize * 256)) & 3;
#else
radians = SkMulDiv(radians, 2 * kTableSize, SK_FixedPI);
int index = radians & (kTableSize - 1);
if (index == 0) {
sinValue = 0;
cosValue = SK_Fixed1;
} else {
sinValue = gSkSinTable[index];
cosValue = gSkSinTable[kTableSize - index];
}
int quad = ((unsigned)radians / kTableSize) & 3;
#endif
if (quad & 1) {
SkTSwap<SkFixed>(sinValue, cosValue);
}
if (quad & 2) {
sinSign = ~sinSign;
}
if (((quad - 1) & 2) == 0) {
cosSign = ~cosSign;
}
// restore the sign for negative angles
sinValue = SkApplySign(sinValue, sinSign);
cosValue = SkApplySign(cosValue, cosSign);
#ifdef SK_DEBUG
if (1) {
SkFixed sin2 = SkFixedMul(sinValue, sinValue);
SkFixed cos2 = SkFixedMul(cosValue, cosValue);
int diff = cos2 + sin2 - SK_Fixed1;
SkASSERT(SkAbs32(diff) <= 7);
}
#endif
if (cosValuePtr) {
*cosValuePtr = cosValue;
}
return sinValue;
}
///////////////////////////////////////////////////////////////////////////////
SkFixed SkFixedTan(SkFixed radians) { return SkCordicTan(radians); }
SkFixed SkFixedASin(SkFixed x) { return SkCordicASin(x); }
SkFixed SkFixedACos(SkFixed x) { return SkCordicACos(x); }
SkFixed SkFixedATan2(SkFixed y, SkFixed x) { return SkCordicATan2(y, x); }
SkFixed SkFixedExp(SkFixed x) { return SkCordicExp(x); }
SkFixed SkFixedLog(SkFixed x) { return SkCordicLog(x); }
///////////////////////////////////////////////////////////////////////////////
///////////////////////////////////////////////////////////////////////////////
#ifdef SK_DEBUG
#include "SkRandom.h"
#ifdef 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
#include "SkPoint.h"
#ifdef SK_SUPPORT_UNITTEST
static void check_length(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);
SkASSERT(len > 0.999f && len < 1.001f);
}
#endif
#ifdef 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(const char op[], float x, uint32_t ni,
uint32_t si) {
if (!equal_float_native_skia(x, ni, si)) {
SkDebugf("-- %s float %g bits %x native %x skia %x\n", op, x, ni, si);
SkASSERT(!"oops");
}
}
static void test_float_cast(float x) {
int ix = (int)x;
int iix = SkFloatToIntCast(x);
assert_float_equal("cast", x, ix, iix);
}
static void test_float_floor(float x) {
int ix = (int)floor(x);
int iix = SkFloatToIntFloor(x);
assert_float_equal("floor", x, ix, iix);
}
static void test_float_round(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("round", x, ix, iix);
}
static void test_float_ceil(float x) {
int ix = (int)ceil(x);
int iix = SkFloatToIntCeil(x);
assert_float_equal("ceil", x, ix, iix);
}
static void test_float_conversions(float x) {
test_float_cast(x);
test_float_floor(x);
test_float_round(x);
test_float_ceil(x);
}
static void test_int2float(int ival) {
float x0 = (float)ival;
float x1 = SkIntToFloatCast(ival);
float x2 = SkIntToFloatCast_NoOverflowCheck(ival);
SkASSERT(x0 == x1);
SkASSERT(x0 == x2);
}
static void unittest_fastfloat() {
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++) {
// SkDebugf("---- test floats %g %d\n", gFloats[i], (int)gFloats[i]);
test_float_conversions(gFloats[i]);
test_float_conversions(-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(x);
}
test_int2float(0);
test_int2float(1);
test_int2float(-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(ival);
test_int2float(-ival);
}
}
}
#endif
static void test_muldiv255() {
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);
SkASSERT(iround == round);
SkASSERT(itrunc == trunc);
SkASSERT(itrunc <= iround);
SkASSERT(iround <= a);
SkASSERT(iround <= b);
}
}
}
void SkMath::UnitTest() {
#ifdef SK_SUPPORT_UNITTEST
int i;
int32_t x;
SkRandom rand;
SkToS8(127); SkToS8(-128); SkToU8(255);
SkToS16(32767); SkToS16(-32768); SkToU16(65535);
SkToS32(2*1024*1024); SkToS32(-2*1024*1024); SkToU32(4*1024*1024);
SkCordic_UnitTest();
// 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();
#ifdef SK_DEBUG
{
SkScalar x = SK_ScalarNaN;
SkASSERT(SkScalarIsNaN(x));
}
#endif
for (i = 1; i <= 10; i++) {
x = SkCubeRootBits(i*i*i, 11);
SkASSERT(x == i);
}
x = SkFixedSqrt(SK_Fixed1);
SkASSERT(x == SK_Fixed1);
x = SkFixedSqrt(SK_Fixed1/4);
SkASSERT(x == SK_Fixed1/2);
x = SkFixedSqrt(SK_Fixed1*4);
SkASSERT(x == SK_Fixed1*2);
x = SkFractSqrt(SK_Fract1);
SkASSERT(x == SK_Fract1);
x = SkFractSqrt(SK_Fract1/4);
SkASSERT(x == SK_Fract1/2);
x = SkFractSqrt(SK_Fract1/16);
SkASSERT(x == SK_Fract1/4);
for (i = 1; i < 100; i++) {
x = SkFixedSqrt(SK_Fixed1 * i * i);
SkASSERT(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);
SkASSERT(clamp == clamp2);
}
for (i = 0; i < 100000; i++) {
SkPoint p;
p.setLength(rand.nextS(), rand.nextS(), SK_Scalar1);
check_length(p, SK_Scalar1);
p.setLength(rand.nextS() >> 13, rand.nextS() >> 13, SK_Scalar1);
check_length(p, SK_Scalar1);
}
{
SkFixed result = SkFixedDiv(100, 100);
SkASSERT(result == SK_Fixed1);
result = SkFixedDiv(1, SK_Fixed1);
SkASSERT(result == 1);
}
#ifdef SK_CAN_USE_FLOAT
unittest_fastfloat();
#endif
#ifdef SkLONGLONG
for (i = 0; i < 100000; 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);
SkASSERT(result != (SkFixed)SK_NaN32);
if (check > SK_MaxS32) {
check = SK_MaxS32;
} else if (check < -SK_MaxS32) {
check = SK_MinS32;
}
SkASSERT(result == (int32_t)check);
result = SkFractDiv(numer, denom);
check = ((SkLONGLONG)numer << 30) / denom;
SkASSERT(result != (SkFixed)SK_NaN32);
if (check > SK_MaxS32) {
check = SK_MaxS32;
} else if (check < -SK_MaxS32) {
check = SK_MinS32;
}
SkASSERT(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);
SkASSERT(result == r2);
#ifdef SK_CAN_USE_FLOAT
if (numer >= 0 && denom >= 0) {
SkFixed mean = SkFixedMean(numer, denom);
float fm = sk_float_sqrt(sk_float_abs(SkFixedToFloat(numer) * SkFixedToFloat(denom)));
SkFixed mean2 = SkFloatToFixed(fm);
int diff = SkAbs32(mean - mean2);
SkASSERT(diff <= 1);
}
{
SkFixed mod = SkFixedMod(numer, denom);
float n = SkFixedToFloat(numer);
float d = SkFixedToFloat(denom);
float m = sk_float_mod(n, d);
#if 0
SkDebugf("%g mod %g = %g [%g]\n",
SkFixedToFloat(numer), SkFixedToFloat(denom),
SkFixedToFloat(mod), m);
#endif
SkASSERT(mod == 0 || (mod < 0) == (m < 0)); // ensure the same sign
int diff = SkAbs32(mod - SkFloatToFixed(m));
SkASSERT((diff >> 7) == 0);
}
#endif
}
#endif
#ifdef SK_CAN_USE_FLOAT
for (i = 0; i < 100000; i++) {
SkFract x = rand.nextU() >> 1;
double xx = (double)x / SK_Fract1;
SkFract xr = SkFractSqrt(x);
SkFract check = SkFloatToFract(sqrt(xx));
SkASSERT(xr == check || xr == check-1 || xr == check+1);
xr = SkFixedSqrt(x);
xx = (double)x / SK_Fixed1;
check = SkFloatToFixed(sqrt(xx));
SkASSERT(xr == check || xr == check-1);
xr = SkSqrt32(x);
xx = (double)x;
check = (int32_t)sqrt(xx);
SkASSERT(xr == check || xr == check-1);
}
#endif
#if !defined(SK_SCALAR_IS_FLOAT) && defined(SK_CAN_USE_FLOAT)
{
SkFixed s, c;
s = SkFixedSinCos(0, &c);
SkASSERT(s == 0);
SkASSERT(c == SK_Fixed1);
}
int maxDiff = 0;
for (i = 0; i < 10000; 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
#endif
}
#endif