Rational representation

Buggy, partly due to integer overflows, partly due to moronic bugs that have yet to be determined.

diff --git a/src/Makefile b/src/Makefile
index 6dbb2e1..8ff6370 100644 (file)
--- a/src/Makefile
+++ b/src/Makefile
@@ -69,7 +69,7 @@ $(BIN) : $(LINKOBJ) ../obj/$(MAIN)
 
 -include $(DEPS)
 
-../obj/%.o : %.cpp
+../obj/%.o : %.cpp main.h
        @mkdir -p $(dir $@)
        $(CXX) $(CFLAGS) $(DEF) -c -MMD -o $@ $<
 

diff --git a/src/arbint.cpp b/src/arbint.cpp
new file mode 100644 (file)
index 0000000..ccde0dd
--- /dev/null
+++ b/src/arbint.cpp
@@ -0,0 +1,52 @@
+#include "arbint.h"
+#include <algorithm>
+#include <cstring>
+using namespace std;
+
+/*
+static bool addc(uint32_t a, uint32_t b, uint32_t * r)
+{
+       volatile uint32_t carry = false;
+       volatile uint32_t result = a + b;
+       asm volatile
+       (
+               "jc 1f;"
+               "mov $0, %%eax;"
+               "1:"
+               : "=a" (carry)
+       );
+       *r = result;    
+       return (carry == 1);
+}
+*/
+
+namespace IPDF
+{
+
+Arbint::Arbint(int64_t i) : m_words(2), m_sign(false)
+{
+       m_sign = i < 0;
+       memcpy(m_words.data(), &i, sizeof(int64_t));
+}
+
+string Arbint::Str() const
+{
+       string s("");
+       for (unsigned i = 0; i < m_words.size(); ++i)
+       {
+               uint32_t w = m_words[i];
+               do
+               {
+                       uint32_t q = w % 10;
+                       w /= 10;
+                       s += ('0' + q);
+               }
+               while (w > 0);
+               if (i+1 < m_words.size()) s += ",";     
+       }
+       if (m_sign) s += '-';
+       reverse(s.begin(), s.end());
+       return s;
+}
+
+}

diff --git a/src/arbint.h b/src/arbint.h
new file mode 100644 (file)
index 0000000..d90a43b
--- /dev/null
+++ b/src/arbint.h
@@ -0,0 +1,26 @@
+#ifndef _ARBINT_H
+#define _ARBINT_H
+
+#include <vector>
+
+namespace IPDF
+{
+       class Arbint
+       {
+               public:
+                       Arbint(int64_t i);
+                       ~Arbint() {}
+                       Arbint(const Arbint & cpy);
+
+                       std::string Str() const;
+               
+               private:                
+                       std::vector<uint32_t> m_words;
+                       bool m_sign;
+                       
+                       
+                       
+       };      
+}
+
+#endif //_ARBINT_H

diff --git a/src/main.cpp b/src/main.cpp
index c14a586..8ead652 100644 (file)
--- a/src/main.cpp
+++ b/src/main.cpp
@@ -90,11 +90,15 @@ int main(int argc, char ** argv)
                
                for(int x = 0; x < 8; ++x)
                {
+                       
                        for (int y = 0; y < 8; ++y)
                        {
                                //doc.Add(static_cast<IPDF::ObjectType>((x^y)%3), Rect(0.2+x-4.0,0.2+y-4.0,0.6,0.6));
-                               doc.Add(BEZIER, Rect(0.2+x-4.0, 0.2+y-4.0, 0.6,0.6), (x^y)%3);
+                               //doc.Add(BEZIER, Rect(0.2+x-4.0, 0.2+y-4.0, 0.6,0.6), (x^y)%3);
                        }
+                       
+                       //doc.Add(RECT_OUTLINE, Rect(0.1,0.1,0.8,0.8), 0);
+                       doc.Add(BEZIER, Rect(0,0,1,1), 0);
                }
                
        }

diff --git a/src/main.h b/src/main.h
index 65eabb6..dcd85fb 100644 (file)
--- a/src/main.h
+++ b/src/main.h
@@ -57,7 +57,11 @@ inline void MainLoop(Document & doc, const Rect & bounds = Rect(0,0,1,1), const
                }
                if (buttons)
                {
-                       view.Translate(Real(oldx-x)/Real(scr.ViewportWidth()), Real(oldy-y)/Real(scr.ViewportHeight()));
+                       #if REAL == REAL_RATIONAL
+                               view.Translate(Real(oldx, scr.ViewportWidth()) -Real(x,scr.ViewportWidth()), Real(oldy, scr.ViewportHeight()) - Real(y,scr.ViewportHeight()));
+                       #else                   
+                               view.Translate(Real(oldx-x)/Real(scr.ViewportWidth()), Real(oldy-y)/Real(scr.ViewportHeight()));
+                       #endif
                }
                else
                {
@@ -69,7 +73,12 @@ inline void MainLoop(Document & doc, const Rect & bounds = Rect(0,0,1,1), const
                
                if (wheel)
                {
-                       view.ScaleAroundPoint(Real(x)/Real(scr.ViewportWidth()),Real(y)/Real(scr.ViewportHeight()), expf(-wheel/20.f));
+                       #if REAL == REAL_RATIONAL
+                               view.ScaleAroundPoint(Real(x,scr.ViewportWidth()), Real(y,scr.ViewportHeight()), Real(100-5*wheel, 100));
+                       #else
+                               view.ScaleAroundPoint(Real(x)/Real(scr.ViewportWidth()),Real(y)/Real(scr.ViewportHeight()), Real(expf(-wheel/20.f)));
+                       #endif
+               
                }
        }
        );
@@ -83,7 +92,7 @@ inline void MainLoop(Document & doc, const Rect & bounds = Rect(0,0,1,1), const
        clock_gettime(CLOCK_MONOTONIC_RAW, &real_clock_start);
        real_clock_now = real_clock_start;
        double frames = 0;
-       double data_rate = -1; // period between data output to stdout (if <= 0 there will be no output)
+       double data_rate = 1; // period between data output to stdout (if <= 0 there will be no output)
        uint64_t data_points = 0;
        setbuf(stdout, NULL);
        while (scr.PumpEvents())
@@ -114,6 +123,7 @@ inline void MainLoop(Document & doc, const Rect & bounds = Rect(0,0,1,1), const
                scr.DebugFontPrintF("[GPU] Render took %lf ms (%lf FPS) (total %lf s, avg FPS %lf)\n", gpu_frame*1e3, 1.0/gpu_frame, total_gpu_time, frames/total_gpu_time);
                scr.DebugFontPrintF("[REALTIME] Render+Present+Cruft took %lf ms (%lf FPS) (total %lf s, avg FPS %lf)\n", real_frame*1e3, 1.0/real_frame, total_real_time,frames/total_real_time);
                scr.DebugFontPrintF("View bounds: %s\n", view.GetBounds().Str().c_str());
+               scr.DebugFontPrintF("type of Real == %s\n", g_real_name[REAL]);
 
                if (view.UsingGPUTransform())
                {

diff --git a/src/objectrenderer.cpp b/src/objectrenderer.cpp
index 755df98..13d17b2 100644 (file)
--- a/src/objectrenderer.cpp
+++ b/src/objectrenderer.cpp
@@ -228,7 +228,7 @@ void BezierRenderer::RenderUsingCPU(const Objects & objects, const View & view,
                for (unsigned j = 1; j <= 100; ++j)
                {
                        control.Evaluate(x[j % 2],y[j % 2], Real(0.01)*j);                      
-                       ObjectRenderer::RenderLineOnCPU((int64_t)x[0],(int64_t)y[0], (int64_t)x[1],(int64_t)y[1], target);
+                       ObjectRenderer::RenderLineOnCPU((int64_t)Double(x[0]),(int64_t)Double(y[0]), (int64_t)Double(x[1]),(int64_t)Double(y[1]), target);
                }
                
                /*
@@ -261,9 +261,9 @@ void BezierRenderer::PrepareBezierGPUBuffer(const Objects& objects)
        for (auto bez : objects.beziers)
        {
                GPUBezierCoeffs coeffs = {
-                       (float)bez.x0, (float)bez.y0,
-                       (float)bez.x1 - (float)bez.x0, (float)bez.y1 - (float)bez.y0,
-                       (float)bez.x2 - (float)bez.x0, (float)bez.y2 - (float)bez.y0
+                       Float(bez.x0), Float(bez.y0),
+                       Float(bez.x1 - bez.x0), Float(bez.y1 - bez.y0),
+                       Float(bez.x2 - bez.x0), Float(bez.y2 - bez.y0)
                        };
                builder.Add(coeffs);
        }

diff --git a/src/objectrenderer.h b/src/objectrenderer.h
index 4ebb66a..6f29add 100644 (file)
--- a/src/objectrenderer.h
+++ b/src/objectrenderer.h
@@ -50,7 +50,7 @@ namespace IPDF
                        struct PixelBounds
                        {
                                int64_t x; int64_t y; int64_t w; int64_t h;
-                               PixelBounds(const Rect & bounds) : x(bounds.x), y(bounds.y), w(bounds.w), h(bounds.h) {}
+                               PixelBounds(const Rect & bounds) : x(Double(bounds.x)), y(Double(bounds.y)), w(Double(bounds.w)), h(Double(bounds.h)) {}
                        };
 
                        static Rect CPURenderBounds(const Rect & bounds, const View & view, const CPURenderTarget & target);

diff --git a/src/rational.h b/src/rational.h
new file mode 100644 (file)
index 0000000..b3709ad
--- /dev/null
+++ b/src/rational.h
@@ -0,0 +1,177 @@
+#ifndef _RATIONAL_H
+#define _RATIONAL_H
+
+/**
+ * A really shoddy implementation of Rational numbers
+ */
+
+#include "common.h"
+#include <cmath>
+#include <cassert>
+
+namespace IPDF
+{
+
+/** Greatest Common Divisor - Euclid's algorithm **/
+
+template <class T>
+T gcd(const T & a, const T & b)
+{
+       if (a == 1 || a == 0) return 1;
+       if (b == 0) return a;
+       if (b == a) return a;
+       
+       if (a > b) return gcd(a-b,b);
+       return gcd(a, b-a);
+}
+
+/*
+template <class T>
+T gcd(const T & p, const T & q)
+{
+       Debug("p/q = %
+       T g(1);
+       T big(p);
+       T small(q);
+       if (p < q)
+       {
+               big = q;
+               small = p;
+       }
+       if (small == 0)
+               return g;
+       while ((g = big % small) > 0)
+       {
+               big = small;
+               small = g;
+       }
+       return small;
+}       
+*/
+template <class T = int64_t>
+struct Rational
+{
+       /** Construct from a double.**/
+       Rational(double d = 0) : P(d*1e3), Q(1e3) // Possibly the worst thing ever...
+       {
+               Simplify();
+               //CheckAccuracy(d, "Construct from double");
+       }
+
+       Rational(const T & _P, const T & _Q) : P(_P), Q(_Q)
+       {
+               Simplify();
+       }
+
+       Rational(const Rational & cpy) : P(cpy.P), Q(cpy.Q)
+       {
+               Simplify();
+       }
+
+       void Simplify()
+       {
+               if (Q < 0) 
+               {
+                       P = (P < 0) ? -P : P;
+                       Q = -Q;
+               }
+
+               T g = gcd(llabs(P),llabs(Q));
+               P /= g;
+               Q /= g;
+       }
+
+       bool operator==(const Rational & r)  const
+       {
+               if (P == r.P && Q == r.Q) return true;
+               return ToDouble() == r.ToDouble();
+       }
+
+
+       bool operator<(const Rational & r) const {return (P*r.Q < r.P * Q);}
+       bool operator>(const Rational & r) const {return !(*this < r);}
+       bool operator<=(const Rational & r) const {return *this == r || *this < r;}
+       bool operator>=(const Rational & r) const {return *this == r || *this > r;}
+       bool operator!=(const Rational & r) const {return !(*this == r);}
+
+
+
+       /*
+       Rational operator+(const Rational & r) const 
+       {
+               Rational result = (r.P == 0) ? Rational(P,Q) : Rational(P*r.Q + r.P*Q, Q*r.Q);
+               result.CheckAccuracy(ToDouble() + r.ToDouble(),"+");
+               return result;
+       }
+       Rational operator-(const Rational & r) const 
+       {
+               Rational result = (r.P == 0) ? Rational(P,Q) : Rational(P*r.Q - r.P*Q, Q*r.Q);
+               result.CheckAccuracy(ToDouble() - r.ToDouble(),"-");
+               return result;
+       }
+       */
+       Rational operator*(const Rational & r) const 
+       {
+               Rational result(P * r.P, Q * r.Q);
+               if (!result.CheckAccuracy(ToDouble() * r.ToDouble(),"*"))
+               {
+                       Debug("This is %s (%f) and r is %s (%f)", Str().c_str(), ToDouble(), r.Str().c_str(), r.ToDouble());
+               }
+               return result;
+       }
+       Rational operator/(const Rational & r) const 
+       {
+               Rational result = (r.P == 0) ? Rational(P,Q) : Rational(P*r.Q + r.P*Q, Q*r.Q);
+               if (!result.CheckAccuracy(ToDouble() / r.ToDouble(),"*"))
+               {
+                       Debug("This is %s (%f) and r is %s (%f)", Str().c_str(), ToDouble(), r.Str().c_str(), r.ToDouble());
+               }
+               return result;
+       }       
+
+       Rational operator+(const Rational & r) const {return Rational(ToDouble()+r.ToDouble());}
+       Rational operator-(const Rational & r) const {return Rational(ToDouble()-r.ToDouble());}
+       //Rational operator*(const Rational & r) const {return Rational(ToDouble()*r.ToDouble());}
+       //Rational operator/(const Rational & r) const {return Rational(ToDouble()/r.ToDouble());}
+
+       Rational & operator=(const Rational & r) {P = r.P; Q = r.Q; return *this;}
+       Rational & operator+=(const Rational & r) {this->operator=(*this+r); return *this;}
+       Rational & operator-=(const Rational & r) {this->operator=(*this-r); return *this;}
+       Rational & operator*=(const Rational & r) {this->operator=(*this*r); return *this;}
+       Rational & operator/=(const Rational & r) {this->operator=(*this/r); return *this;}
+
+       double ToDouble() const {return (double)(P) / (double)(Q);}
+       bool CheckAccuracy(double d, const char * msg, double threshold = 1e-6) const
+       {
+               double result = fabs(ToDouble() - d) / d;
+               if (result > threshold)
+               {
+                       Warn("(%s) : Rational %s (%f) is not close enough at representing %f (%f vs %f)", msg, Str().c_str(), ToDouble(), d, result, threshold);
+                       return false;
+               }
+               return true;
+       }
+       std::string Str() const
+       {
+               std::stringstream s;
+               s << (int64_t)P << "/" << (int64_t)Q;
+               return s.str();
+       }
+       
+       T P;
+       T Q;
+};
+
+inline Rational<int64_t> pow(const Rational<int64_t> & a, const Rational<int64_t> & b)
+{
+       //TODO:Implement properly
+       int64_t P = std::pow((double)a.P, b.ToDouble());
+       int64_t Q = std::pow((double)a.Q, b.ToDouble());
+       return Rational<int64_t>(P, Q);
+}
+
+
+}
+
+#endif //_RATIONAL_H
+

diff --git a/src/rationalrange.data b/src/rationalrange.data
new file mode 100644 (file)
index 0000000..a40e4ad
--- /dev/null
+++ b/src/rationalrange.data
@@ -0,0 +1,10000 @@
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+2997049798.043630      2997049798.043630       0.000000        1717309534279   573
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diff --git a/src/real.cpp b/src/real.cpp
index bda6102..70c6530 100644 (file)
--- a/src/real.cpp
+++ b/src/real.cpp
@@ -7,7 +7,8 @@ namespace IPDF
                "single",
                "double",
                "long double",
-               "single [fast2sum]"
+               "single [fast2sum]", //TODO REMOVE DOESN'T DO ANYTHING USEFUL
+               "Rational<int64_t>"
        };
 
 }

diff --git a/src/real.h b/src/real.h
index 00eff9c..ab90384 100644 (file)
--- a/src/real.h
+++ b/src/real.h
@@ -3,10 +3,12 @@
 
 #include "common.h"
 
+
 #define REAL_SINGLE 0
 #define REAL_DOUBLE 1
 #define REAL_LONG_DOUBLE 2
-#define REAL_SINGLE_FAST2SUM 3
+#define REAL_SINGLE_FAST2SUM 3 //TODO: Remove, is FITH
+#define REAL_RATIONAL 4
 
 #ifndef REAL
        #error "REAL was not defined!"
@@ -16,6 +18,10 @@
        #include "real_fast2sum.h"
 #endif //REAL
 
+#if REAL == REAL_RATIONAL
+       #include "rational.h"
+#endif //REAL
+
 namespace IPDF
 {      
        extern const char * g_real_name[];
@@ -28,8 +34,13 @@ namespace IPDF
        typedef long double Real;
 #elif REAL == REAL_SINGLE_FAST2SUM
        typedef RealF2S<float> Real;
-       inline float Float(Real r) {return r.m_value;}
-               
+       inline float Float(const Real & r) {return r.m_value;}
+       inline double Double(const Real & r) {return r.m_value;}
+#elif REAL == REAL_RATIONAL
+
+       typedef Rational<int64_t> Real;
+       inline float Float(const Real & r) {return (float)r.ToDouble();}
+       inline double Double(const Real & r) {return r.ToDouble();}
 #else
        #error "Type of Real unspecified."
 #endif //REAL
@@ -37,9 +48,12 @@ namespace IPDF
        // Allow us to call Float on the primative types
        // Useful so I can template some things that could be either (a more complicated) Real or a primitive type
        // Mostly in the testers.
-       inline float Float(float f) {return f;}
-       inline double Float(double f) {return f;}
-       inline double Float(long double f) {return double(f);}
+       inline float Float(float f) {return (float)f;}
+       inline float Float(double f) {return (float)f;}
+       inline float Float(long double f) {return (float)(f);}
+       inline double Double(float f) {return (double)f;}
+       inline double Double(double f) {return (double)f;}
+       inline double Double(long double f) {return (double)(f);}
 }
 
 #endif //_REAL_H

diff --git a/src/tests/arb.cpp b/src/tests/arb.cpp
new file mode 100644 (file)
index 0000000..29c6325
--- /dev/null
+++ b/src/tests/arb.cpp
@@ -0,0 +1,14 @@
+#include <cstdlib>
+#include <cstdio>
+#include <iostream>
+
+#include "arbint.cpp"
+
+using namespace std;
+using namespace IPDF;
+
+int main(int argc, char ** argv)
+{
+       Arbint a(4294967296L);
+       printf("%s\n", a.Str().c_str());
+}

diff --git a/src/tests/asm.cpp b/src/tests/asm.cpp
new file mode 100644 (file)
index 0000000..aa17b3b
--- /dev/null
+++ b/src/tests/asm.cpp
@@ -0,0 +1,17 @@
+#include <cstdlib>
+#include <cstdio>
+#include <iostream>
+
+using namespace std;
+
+
+
+int main(int argc, char ** argv)
+{
+       uint32_t a = 4294967295;
+       uint32_t b = 0;
+       uint32_t r = 0;
+       bool c = addc(a, b, &r);
+       printf("%u + %u = %u (%u)\n", a, b, r, (uint32_t)c);
+       
+}

diff --git a/src/tests/rationalrange.cpp b/src/tests/rationalrange.cpp
new file mode 100644 (file)
index 0000000..0c16973
--- /dev/null
+++ b/src/tests/rationalrange.cpp
@@ -0,0 +1,37 @@
+#include "main.h"
+#include "rational.h"
+#include <cassert>
+#include <list>
+
+using namespace std;
+using namespace IPDF;
+
+int main(int argc, char ** argv)
+{
+       typedef uint64_t Uint;
+       typedef pair<pair<Uint, Uint>, Rational<Uint> > RatPear;
+
+       for (int i = 0; i < (int)(1e4); ++i)
+       {
+               double test = double(rand() % (int)(1e12)) * double(rand() % (int)(1e12)) / double(rand() % (int)1e12);
+               Rational<Uint> r(test);
+               printf("%f\t%f\t%f\t%lu\t%lu\n", test, r.ToDouble(), fabs(r.ToDouble() - test), r.P, r.Q);
+       }
+
+#if 0
+       list<RatPear> space;
+       for (Uint p = 0; p < 128; ++p)
+       {
+               for (Uint q = 0; q < 128; ++q)
+               {
+                       space.push_back(RatPear(pair<Uint, Uint>(p,q), Rational<Uint>(p,q)));
+               }
+       }
+       space.sort([=](const RatPear & a, const RatPear & b){return a.second < b.second;});
+       for (auto i = space.begin(); i != space.end(); ++i)
+       {
+               if (i->second.Q != 0)
+                       printf("%li\t%li\t%li\t%li\t%f\n", i->first.first, i->first.second, i->second.P, i->second.Q, i->second.ToDouble());
+       }
+#endif
+}

diff --git a/src/view.cpp b/src/view.cpp
index af1980a..2d9d0b3 100644 (file)
--- a/src/view.cpp
+++ b/src/view.cpp
@@ -88,7 +88,7 @@ void View::ScaleAroundPoint(Real x, Real y, Real scale_amount)
        m_bounds.y = y - top;
        m_bounds.w *= scale_amount;
        m_bounds.h *= scale_amount;
-       Debug("View Bounds => %s", m_bounds.Str().c_str());
+       //Debug("Scale at {%s, %s} by %s View Bounds => %s", x.Str().c_str(), y.Str().c_str(), scale_amount.Str().c_str(), m_bounds.Str().c_str());
        if (!m_use_gpu_transform)
                m_buffer_dirty = true;
        m_bounds_dirty = true;