path: root/src/core/SkMath.cpp

/*
 * 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 "SkFloatBits.h"
#include "SkFloatingPoint.h"
#include "SkScalar.h"

const uint32_t gIEEENotANumber = 0x7FFFFFFF;
const uint32_t gIEEEInfinity = 0x7F800000;
const uint32_t gIEEENegativeInfinity = 0xFF800000;

#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;
}

SkFixed SkFixedMul_portable(SkFixed a, SkFixed b) {
#if defined(SkLONGLONG)
    return static_cast<SkFixed>((int64_t)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
}

///////////////////////////////////////////////////////////////////////////////

#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);
}

/* 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;
}

///////////////////////////////////////////////////////////////////////////////

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;
}

#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;
}