/* * 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 "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); }