grab from latest android

git-svn-id: http://skia.googlecode.com/svn/trunk@27 2bbb7eff-a529-9590-31e7-b0007b416f81

1 files changed, 932 insertions, 0 deletions

diff --git a/src/core/SkMath.cpp b/src/core/SkMath.cpp
new file mode 100644
index 0000000000..c627d9b336
--- /dev/null
+++ b/src/core/SkMath.cpp
@@ -0,0 +1,932 @@
+/*
+ * 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