1 files changed, 400 insertions, 0 deletions
diff --git a/chromium/third_party/skia/experimental/Intersection/CubeRoot.cpp b/chromium/third_party/skia/experimental/Intersection/CubeRoot.cpp
new file mode 100644
index 00000000000..5f785a0358a
--- /dev/null
+++ b/chromium/third_party/skia/experimental/Intersection/CubeRoot.cpp
@@ -0,0 +1,400 @@
+/*
+ * Copyright 2012 Google Inc.
+ *
+ * Use of this source code is governed by a BSD-style license that can be
+ * found in the LICENSE file.
+ */
+// http://metamerist.com/cbrt/CubeRoot.cpp
+//
+
+#include <math.h>
+#include "CubicUtilities.h"
+
+#define TEST_ALTERNATIVES 0
+#if TEST_ALTERNATIVES
+typedef float  (*cuberootfnf) (float);
+typedef double (*cuberootfnd) (double);
+
+// estimate bits of precision (32-bit float case)
+inline int bits_of_precision(float a, float b)
+{
+    const double kd = 1.0 / log(2.0);
+
+    if (a==b)
+        return 23;
+
+    const double kdmin = pow(2.0, -23.0);
+
+    double d = fabs(a-b);
+    if (d < kdmin)
+        return 23;
+
+    return int(-log(d)*kd);
+}
+
+// estiamte bits of precision (64-bit double case)
+inline int bits_of_precision(double a, double b)
+{
+    const double kd = 1.0 / log(2.0);
+
+    if (a==b)
+        return 52;
+
+    const double kdmin = pow(2.0, -52.0);
+
+    double d = fabs(a-b);
+    if (d < kdmin)
+        return 52;
+
+    return int(-log(d)*kd);
+}
+
+// cube root via x^(1/3)
+static float pow_cbrtf(float x)
+{
+    return (float) pow(x, 1.0f/3.0f);
+}
+
+// cube root via x^(1/3)
+static double pow_cbrtd(double x)
+{
+    return pow(x, 1.0/3.0);
+}
+
+// cube root approximation using bit hack for 32-bit float
+static  float cbrt_5f(float f)
+{
+    unsigned int* p = (unsigned int *) &f;
+    *p = *p/3 + 709921077;
+    return f;
+}
+#endif
+
+// cube root approximation using bit hack for 64-bit float
+// adapted from Kahan's cbrt
+static  double cbrt_5d(double d)
+{
+    const unsigned int B1 = 715094163;
+    double t = 0.0;
+    unsigned int* pt = (unsigned int*) &t;
+    unsigned int* px = (unsigned int*) &d;
+    pt[1]=px[1]/3+B1;
+    return t;
+}
+
+#if TEST_ALTERNATIVES
+// cube root approximation using bit hack for 64-bit float
+// adapted from Kahan's cbrt
+#if 0
+static  double quint_5d(double d)
+{
+    return sqrt(sqrt(d));
+
+    const unsigned int B1 = 71509416*5/3;
+    double t = 0.0;
+    unsigned int* pt = (unsigned int*) &t;
+    unsigned int* px = (unsigned int*) &d;
+    pt[1]=px[1]/5+B1;
+    return t;
+}
+#endif
+
+// iterative cube root approximation using Halley's method (float)
+static  float cbrta_halleyf(const float a, const float R)
+{
+    const float a3 = a*a*a;
+    const float b= a * (a3 + R + R) / (a3 + a3 + R);
+    return b;
+}
+#endif
+
+// iterative cube root approximation using Halley's method (double)
+static  double cbrta_halleyd(const double a, const double R)
+{
+    const double a3 = a*a*a;
+    const double b= a * (a3 + R + R) / (a3 + a3 + R);
+    return b;
+}
+
+#if TEST_ALTERNATIVES
+// iterative cube root approximation using Newton's method (float)
+static  float cbrta_newtonf(const float a, const float x)
+{
+//    return (1.0 / 3.0) * ((a + a) + x / (a * a));
+    return a - (1.0f / 3.0f) * (a - x / (a*a));
+}
+
+// iterative cube root approximation using Newton's method (double)
+static  double cbrta_newtond(const double a, const double x)
+{
+    return (1.0/3.0) * (x / (a*a) + 2*a);
+}
+
+// cube root approximation using 1 iteration of Halley's method (double)
+static double halley_cbrt1d(double d)
+{
+    double a = cbrt_5d(d);
+    return cbrta_halleyd(a, d);
+}
+
+// cube root approximation using 1 iteration of Halley's method (float)
+static float halley_cbrt1f(float d)
+{
+    float a = cbrt_5f(d);
+    return cbrta_halleyf(a, d);
+}
+
+// cube root approximation using 2 iterations of Halley's method (double)
+static double halley_cbrt2d(double d)
+{
+    double a = cbrt_5d(d);
+    a = cbrta_halleyd(a, d);
+    return cbrta_halleyd(a, d);
+}
+#endif
+
+// cube root approximation using 3 iterations of Halley's method (double)
+static double halley_cbrt3d(double d)
+{
+    double a = cbrt_5d(d);
+    a = cbrta_halleyd(a, d);
+    a = cbrta_halleyd(a, d);
+    return cbrta_halleyd(a, d);
+}
+
+#if TEST_ALTERNATIVES
+// cube root approximation using 2 iterations of Halley's method (float)
+static float halley_cbrt2f(float d)
+{
+    float a = cbrt_5f(d);
+    a = cbrta_halleyf(a, d);
+    return cbrta_halleyf(a, d);
+}
+
+// cube root approximation using 1 iteration of Newton's method (double)
+static double newton_cbrt1d(double d)
+{
+    double a = cbrt_5d(d);
+    return cbrta_newtond(a, d);
+}
+
+// cube root approximation using 2 iterations of Newton's method (double)
+static double newton_cbrt2d(double d)
+{
+    double a = cbrt_5d(d);
+    a = cbrta_newtond(a, d);
+    return cbrta_newtond(a, d);
+}
+
+// cube root approximation using 3 iterations of Newton's method (double)
+static double newton_cbrt3d(double d)
+{
+    double a = cbrt_5d(d);
+    a = cbrta_newtond(a, d);
+    a = cbrta_newtond(a, d);
+    return cbrta_newtond(a, d);
+}
+
+// cube root approximation using 4 iterations of Newton's method (double)
+static double newton_cbrt4d(double d)
+{
+    double a = cbrt_5d(d);
+    a = cbrta_newtond(a, d);
+    a = cbrta_newtond(a, d);
+    a = cbrta_newtond(a, d);
+    return cbrta_newtond(a, d);
+}
+
+// cube root approximation using 2 iterations of Newton's method (float)
+static float newton_cbrt1f(float d)
+{
+    float a = cbrt_5f(d);
+    return cbrta_newtonf(a, d);
+}
+
+// cube root approximation using 2 iterations of Newton's method (float)
+static float newton_cbrt2f(float d)
+{
+    float a = cbrt_5f(d);
+    a = cbrta_newtonf(a, d);
+    return cbrta_newtonf(a, d);
+}
+
+// cube root approximation using 3 iterations of Newton's method (float)
+static float newton_cbrt3f(float d)
+{
+    float a = cbrt_5f(d);
+    a = cbrta_newtonf(a, d);
+    a = cbrta_newtonf(a, d);
+    return cbrta_newtonf(a, d);
+}
+
+// cube root approximation using 4 iterations of Newton's method (float)
+static float newton_cbrt4f(float d)
+{
+    float a = cbrt_5f(d);
+    a = cbrta_newtonf(a, d);
+    a = cbrta_newtonf(a, d);
+    a = cbrta_newtonf(a, d);
+    return cbrta_newtonf(a, d);
+}
+
+static double TestCubeRootf(const char* szName, cuberootfnf cbrt, double rA, double rB, int rN)
+{
+    const int N = rN;
+
+    float dd = float((rB-rA) / N);
+
+    // calculate 1M numbers
+    int i=0;
+    float d = (float) rA;
+
+    double s = 0.0;
+
+    for(d=(float) rA, i=0; i<N; i++, d += dd)
+    {
+        s += cbrt(d);
+    }
+
+    double bits = 0.0;
+    double worstx=0.0;
+    double worsty=0.0;
+    int minbits=64;
+
+    for(d=(float) rA, i=0; i<N; i++, d += dd)
+    {
+        float a = cbrt((float) d);
+        float b = (float) pow((double) d, 1.0/3.0);
+
+        int bc = bits_of_precision(a, b);
+        bits += bc;
+
+        if (b > 1.0e-6)
+        {
+            if (bc < minbits)
+            {
+                minbits = bc;
+                worstx = d;
+                worsty = a;
+            }
+        }
+    }
+
+    bits /= N;
+
+    printf(" %3d mbp  %6.3f abp\n", minbits, bits);
+
+    return s;
+}
+
+
+static double TestCubeRootd(const char* szName, cuberootfnd cbrt, double rA, double rB, int rN)
+{
+    const int N = rN;
+
+    double dd = (rB-rA) / N;
+
+    int i=0;
+
+    double s = 0.0;
+    double d = 0.0;
+
+    for(d=rA, i=0; i<N; i++, d += dd)
+    {
+        s += cbrt(d);
+    }
+
+
+    double bits = 0.0;
+    double worstx = 0.0;
+    double worsty = 0.0;
+    int minbits = 64;
+    for(d=rA, i=0; i<N; i++, d += dd)
+    {
+        double a = cbrt(d);
+        double b = pow(d, 1.0/3.0);
+
+        int bc = bits_of_precision(a, b); // min(53, count_matching_bitsd(a, b) - 12);
+        bits += bc;
+
+        if (b > 1.0e-6)
+        {
+            if (bc < minbits)
+            {
+                bits_of_precision(a, b);
+                minbits = bc;
+                worstx = d;
+                worsty = a;
+            }
+        }
+    }
+
+    bits /= N;
+
+    printf(" %3d mbp  %6.3f abp\n", minbits, bits);
+
+    return s;
+}
+
+static int _tmain()
+{
+    // a million uniform steps through the range from 0.0 to 1.0
+    // (doing uniform steps in the log scale would be better)
+    double a = 0.0;
+    double b = 1.0;
+    int n = 1000000;
+
+    printf("32-bit float tests\n");
+    printf("----------------------------------------\n");
+    TestCubeRootf("cbrt_5f", cbrt_5f, a, b, n);
+    TestCubeRootf("pow", pow_cbrtf, a, b, n);
+    TestCubeRootf("halley x 1", halley_cbrt1f, a, b, n);
+    TestCubeRootf("halley x 2", halley_cbrt2f, a, b, n);
+    TestCubeRootf("newton x 1", newton_cbrt1f, a, b, n);
+    TestCubeRootf("newton x 2", newton_cbrt2f, a, b, n);
+    TestCubeRootf("newton x 3", newton_cbrt3f, a, b, n);
+    TestCubeRootf("newton x 4", newton_cbrt4f, a, b, n);
+    printf("\n\n");
+
+    printf("64-bit double tests\n");
+    printf("----------------------------------------\n");
+    TestCubeRootd("cbrt_5d", cbrt_5d, a, b, n);
+    TestCubeRootd("pow", pow_cbrtd, a, b, n);
+    TestCubeRootd("halley x 1", halley_cbrt1d, a, b, n);
+    TestCubeRootd("halley x 2", halley_cbrt2d, a, b, n);
+    TestCubeRootd("halley x 3", halley_cbrt3d, a, b, n);
+    TestCubeRootd("newton x 1", newton_cbrt1d, a, b, n);
+    TestCubeRootd("newton x 2", newton_cbrt2d, a, b, n);
+    TestCubeRootd("newton x 3", newton_cbrt3d, a, b, n);
+    TestCubeRootd("newton x 4", newton_cbrt4d, a, b, n);
+    printf("\n\n");
+
+    return 0;
+}
+#endif
+
+double cube_root(double x) {
+    if (approximately_zero_cubed(x)) {
+        return 0;
+    }
+    double result = halley_cbrt3d(fabs(x));
+    if (x < 0) {
+        result = -result;
+    }
+    return result;
+}
+
+#if TEST_ALTERNATIVES
+// http://bytes.com/topic/c/answers/754588-tips-find-cube-root-program-using-c
+/* cube root */
+int icbrt(int n) {
+    int t=0, x=(n+2)/3; /* works for n=0 and n>=1 */
+    for(; t!=x;) {
+        int x3=x*x*x;
+        t=x;
+        x*=(2*n + x3);
+        x/=(2*x3 + n);
+    }
+    return x ; /* always(?) equal to floor(n^(1/3)) */
+}
+#endif