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Diffstat (limited to 'src/core/SkMath.cpp')
| -rw-r--r-- | src/core/SkMath.cpp | 938 |
1 files changed, 938 insertions, 0 deletions
diff --git a/src/core/SkMath.cpp b/src/core/SkMath.cpp new file mode 100644 index 0000000..e0babeb --- /dev/null +++ b/src/core/SkMath.cpp @@ -0,0 +1,938 @@ +/* + * 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 static_cast<SkFixed>((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 static_cast<SkFract>((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" + +#if defined(SkLONGLONG) && defined(SK_SUPPORT_UNITTEST) +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) { +#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); + + SkASSERT(len > 0.999f && len < 1.001f); +#endif +} +#endif + +#if defined(SK_CAN_USE_FLOAT) && defined(SK_SUPPORT_UNITTEST) + +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 + +#ifdef SK_SUPPORT_UNITTEST +static void test_muldiv255() { +#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); + + SkASSERT(iround == round); + SkASSERT(itrunc == trunc); + + SkASSERT(itrunc <= iround); + SkASSERT(iround <= a); + SkASSERT(iround <= b); + } + } +#endif +} +#endif + +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 |