remove prototype pathops code

experimental/Intersection/CubeRoot.cpp

Index: experimental/Intersection/CubeRoot.cpp
diff --git a/experimental/Intersection/CubeRoot.cpp b/experimental/Intersection/CubeRoot.cpp
deleted file mode 100644
index 5f785a0358a96942dcd84a3c3845d53e7f6d3afb..0000000000000000000000000000000000000000
--- a/experimental/Intersection/CubeRoot.cpp
+++ /dev/null
@@ -1,400 +0,0 @@
-/*
- * 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