| /* |
| * Copyright 2008 The Android Open Source Project |
| * |
| * Use of this source code is governed by a BSD-style license that can be |
| * found in the LICENSE file. |
| */ |
| |
| #include "SkMathPriv.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; |
| const uint32_t gIEEENegativeInfinity = 0xFF800000; |
| #endif |
| |
| #define sub_shift(zeros, x, n) \ |
| zeros -= n; \ |
| x >>= n |
| |
| int SkCLZ_portable(uint32_t x) { |
| if (x == 0) { |
| return 32; |
| } |
| |
| 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); |
| } |
| |
| 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); } |
