sulix fixed the quad trees and I forgot about `git stash` again.
#Makefile
ARCH := $(shell uname -m)
# TODO: stb_truetype doesn't compile with some of these warnings.
-CXX = g++ -std=gnu++0x -g -Wall -Werror -Wshadow -pedantic -rdynamic
+CXX = g++ -std=c++11 -g -Wall -Werror -Wshadow -pedantic -rdynamic
MAIN = main.o
OBJ = log.o real.o bezier.o document.o objectrenderer.o view.o screen.o graphicsbuffer.o framebuffer.o shaderprogram.o stb_truetype.o gl_core44.o path.o paranoidnumber.o quadtree.o
#include <sstream>
#include <fenv.h>
#include "log.h"
+#include <cassert>
#include <iostream>
using namespace std;
{
int64_t ParanoidNumber::g_count = 0;
-ParanoidNumber::ParanoidNumber(const char * str) : m_value(0), m_op(ADD), m_next_term(NULL), m_next_factor(NULL)
+
+ParanoidNumber::~ParanoidNumber()
+{
+ g_count--;
+ for (int i = 0; i < NOP; ++i)
+ {
+ for (auto n : m_next[i])
+ delete n;
+ }
+}
+
+ParanoidNumber::ParanoidNumber(const char * str) : m_value(0), m_cached_result(0)
{
+ Construct();
int dp = 0;
int end = 0;
while (str[dp] != '\0' && str[dp] != '.')
}
while (str[end] != '\0')
++end;
-
ParanoidNumber m(1);
for (int i = dp-1; i >= 0; --i)
{
ParanoidNumber b(str[i]-'0');
b*=m;
- //Debug("m is %s", m.Str().c_str());
- //Debug("Add %s", b.Str().c_str());
this->operator+=(b);
- //Debug("Now at %s", Str().c_str());
m*=10;
}
ParanoidNumber n(1);
{
n/=10;
ParanoidNumber b(str[i]-'0');
- //Debug("%s * %s", b.Str().c_str(), n.Str().c_str());
b*=n;
- //Debug("b -> %s", b.Str().c_str());
- //Debug("Add %s", b.Str().c_str());
this->operator+=(b);
- //Debug("Now at %s", Str().c_str());
-
}
- //Debug("Constructed {%s} from %s (%f)", Str().c_str(), str, ToDouble());
}
ParanoidNumber & ParanoidNumber::operator=(const ParanoidNumber & a)
{
- //TODO: Optimise
- delete m_next_term;
- delete m_next_factor;
- m_op = a.m_op;
- if (a.m_next_term != NULL)
- {
- m_next_term = new ParanoidNumber(*(a.m_next_term));
- }
- if (a.m_next_factor != NULL)
+ m_value = a.m_value;
+ m_cached_result = a.m_cached_result;
+ for (int i = 0; i < NOP; ++i)
{
- m_next_factor = new ParanoidNumber(*(a.m_next_factor));
- }
- return *this;
-}
-
-ParanoidNumber & ParanoidNumber::operator+=(const ParanoidNumber & a)
-{
- if (m_next_factor == NULL && a.Floating())
- {
- if (ParanoidOp<digit_t>(m_value, a.m_value, ADD))
+ for (unsigned j = 0; j < m_next[i].size() && j < a.m_next[i].size(); ++j)
{
- Simplify();
- return *this;
- }
- }
- ParanoidNumber * nt = m_next_term;
- ParanoidNumber * nf = m_next_factor;
-
- ParanoidNumber ca(a);
- if (m_next_factor != NULL)
- {
- if (m_next_factor->m_op == MULTIPLY)
- ca /= (*m_next_factor);
- else
- ca *= (*m_next_factor);
-
- if (ca.Floating())
- {
- m_next_factor = NULL;
- m_next_term = NULL;
- operator+=(ca);
- m_next_factor = nf;
- m_next_term = nt;
- Simplify();
- return *this;
+ m_next[i][j]->operator=(*(a.m_next[i][j]));
}
- }
-
- m_next_term = new ParanoidNumber(a, ADD);
- ParanoidNumber * t = m_next_term;
- while (t->m_next_term != NULL)
- t = t->m_next_term;
- t->m_next_term = nt;
- //Debug("Simplify {%s} after add", Str().c_str());
- Simplify();
- return *this;
-}
-
-ParanoidNumber & ParanoidNumber::operator-=(const ParanoidNumber & a)
-{
- // this = v + t + (a)
- // -> v + (a) + t
- if (m_next_factor == NULL && a.Floating())
- {
- if (ParanoidOp<digit_t>(m_value, a.m_value, ADD))
+ for (unsigned j = a.m_next[i].size(); j < m_next[i].size(); ++j)
{
- Simplify();
- return *this;
+ delete m_next[i][j];
}
- }
-
- ParanoidNumber * nt = m_next_term;
- ParanoidNumber * nf = m_next_factor;
-
- ParanoidNumber ca(a, SUBTRACT);
- if (m_next_factor != NULL)
- {
- if (m_next_factor->m_op == MULTIPLY)
- ca /= (*m_next_factor);
- else
- ca *= (*m_next_factor);
-
- if (ca.Floating())
- {
- m_next_factor = NULL;
- m_next_term = NULL;
- operator-=(ca);
- m_next_factor = nf;
- m_next_term = nt;
- Simplify();
- return *this;
- }
-
- }
-
- m_next_term = new ParanoidNumber(a,SUBTRACT);
- ParanoidNumber * t = m_next_term;
- while (t->m_next_term != NULL)
- {
- t->m_op = SUBTRACT;
- t = t->m_next_term;
- }
- t->m_op = SUBTRACT;
- //Debug("next term {%s}", m_next_term->Str().c_str());
- t->m_next_term = nt;
- //Debug("Simplify {%s} after sub", Str().c_str());
- Simplify();
- return *this;
-}
-
-ParanoidNumber & ParanoidNumber::operator*=(const ParanoidNumber & a)
-{
-
- //if (m_value == 0)
- // return *this;
- //Debug("{%s} *= {%s}", Str().c_str(), a.Str().c_str());
- // this = (vf + t) * (a)
- if (a.Floating() && ParanoidOp<digit_t>(m_value, a.m_value, MULTIPLY))
- {
- if (m_next_term != NULL)
- m_next_term->operator*=(a);
- Simplify();
- return *this;
- }
-
- ParanoidNumber * t = this;
- while (t->m_next_factor != NULL)
- t = t->m_next_factor;
- t->m_next_factor = new ParanoidNumber(a, MULTIPLY);
-
- if (m_next_term != NULL)
- m_next_term->operator*=(a);
-
- //Debug("Simplify {%s}", Str().c_str());
- Simplify();
- //Debug("Simplified to {%s}", Str().c_str());
- return *this;
-}
-
-
-ParanoidNumber & ParanoidNumber::operator/=(const ParanoidNumber & a)
-{
-
-
-
- if (a.Floating() && ParanoidOp<digit_t>(m_value, a.m_value, DIVIDE))
- {
- if (m_next_term != NULL)
- m_next_term->operator/=(a);
- Simplify();
- return *this;
- }
-
- //Debug("Called %s /= %s", Str().c_str(), a.Str().c_str());
- // this = (vf + t) * (a)
- ParanoidNumber * t = this;
- while (t->m_next_factor != NULL)
- {
- t = t->m_next_factor;
- }
- t->m_next_factor = new ParanoidNumber(a, DIVIDE);
-
- if (m_next_term != NULL)
- m_next_term->operator/=(a);
-
- Simplify();
+ m_next[i].resize(a.m_next[i].size());
+ }
return *this;
}
-
-void ParanoidNumber::SimplifyTerms()
-{
-
- //Debug("Simplify {%s}", Str().c_str());
- if (m_next_term == NULL)
- {
- //Debug("No terms!");
- return;
- }
-
- for (ParanoidNumber * a = this; a != NULL; a = a->m_next_term)
- {
- ParanoidNumber * b = a->m_next_term;
- if (a->m_next_factor != NULL && !a->m_next_factor->Floating())
- {
- continue;
- }
-
- ParanoidNumber * bprev = a;
- while (b != NULL)
- {
- //Debug("Simplify factors of %s", b->Str().c_str());
- b->SimplifyFactors();
- if (b->m_next_factor != NULL && !b->m_next_factor->Floating())
- {
- bprev = b;
- b = b->m_next_term;
- continue;
- }
-
- bool simplify = false;
- if (a->m_next_factor != NULL || b->m_next_factor != NULL)
- {
- digit_t aa(a->Head<digit_t>());
- digit_t ab = (a->m_next_factor != NULL) ? a->m_next_factor->Head<digit_t>() : 1;
- digit_t bc(b->Head<digit_t>());
- digit_t bd = (b->m_next_factor != NULL) ? b->m_next_factor->Head<digit_t>() : 1;
- Optype aop = (a->m_next_factor != NULL) ? a->m_next_factor->m_op : DIVIDE;
- Optype cop = (b->m_next_factor != NULL) ? b->m_next_factor->m_op : DIVIDE;
- simplify = CombineTerms<digit_t>(aa, aop, ab, bc, cop, bd);
- if (simplify)
- {
- a->m_value = aa;
- if (a->m_next_factor != NULL)
- a->m_next_factor->m_value = ab;
- else if (ab != 1)
- {
- a->m_next_factor = b->m_next_factor;
- b->m_next_factor = NULL;
- a->m_next_factor->m_value = ab;
- }
- }
- }
- else
- {
- simplify = ParanoidOp<digit_t>(a->m_value, b->Head<digit_t>(), ADD);
- }
- if (simplify)
- {
- bprev->m_next_term = b->m_next_term;
- b->m_next_term = NULL;
- delete b;
- b = bprev;
- }
-
- bprev = b;
- b = b->m_next_term;
- }
- }
-}
-
-void ParanoidNumber::SimplifyFactors()
-{
-
- //Debug("Simplify {%s}", Str().c_str());
- if (m_next_factor == NULL)
- {
- //Debug("No factors!");
- return;
- }
-
- for (ParanoidNumber * a = this; a != NULL; a = a->m_next_factor)
- {
- if ((a->m_op != ADD || a->m_op != SUBTRACT) && a->m_next_term != NULL)
- continue;
-
- ParanoidNumber * bprev = a;
- ParanoidNumber * b = a->m_next_factor;
- while (b != NULL)
- {
- b->SimplifyTerms();
- if (b->m_next_term != NULL)
- {
- bprev = b;
- b = b->m_next_factor;
- continue;
- }
-
- Optype op = b->m_op;
- if (a->m_op == DIVIDE)
- {
- op = (b->m_op == DIVIDE) ? MULTIPLY : DIVIDE;
- }
-
- if (ParanoidOp<digit_t>(a->m_value, b->m_value, op))
- {
-
- bprev->m_next_factor = b->m_next_factor;
- b->m_next_factor = NULL;
- delete b;
- b = bprev;
- }
- bprev = b;
- b = b->m_next_factor;
- }
- }
-}
-
-void ParanoidNumber::Simplify()
-{
- SimplifyFactors();
- SimplifyTerms();
-}
-
string ParanoidNumber::Str() const
{
string result("");
stringstream s;
s << (double)m_value;
-
- if (m_next_factor != NULL)
+ result += s.str();
+ for (auto mul : m_next[MULTIPLY])
{
- result += s.str();
- result += OpChar(m_next_factor->m_op);
- if (m_next_factor->m_next_term != NULL)
- result += "(" + m_next_factor->Str() + ")";
+ result += "*";
+ if (!mul->Floating())
+ result += "(" + mul->Str() + ")";
else
- result += m_next_factor->Str();
+ result += mul->Str();
}
- else
+ for (auto div : m_next[DIVIDE])
+ {
+ result += "/";
+ if (!div->Floating())
+ result += "(" + div->Str() + ")";
+ else
+ result += div->Str();
+ }
+
+ for (auto add : m_next[ADD])
{
- result += s.str();
+ result += "+";
+ if (!add->Floating())
+ result += "(" + add->Str() + ")";
+ else
+ result += add->Str();
}
-
- if (m_next_term != NULL)
+ for (auto sub : m_next[SUBTRACT])
{
- result += " ";
- result += OpChar(m_next_term->m_op);
- result += m_next_term->Str();
+ result += "-";
+ if (!sub->Floating())
+ result += "(" + sub->Str() + ")";
+ else
+ result += sub->Str();
}
+
+
return result;
}
case DIVIDE:
a /= b;
break;
+ case NOP:
+ break;
}
return !fetestexcept(FE_ALL_EXCEPT);
}
case DIVIDE:
a /= b;
break;
+ case NOP:
+ break;
}
return !fetestexcept(FE_ALL_EXCEPT);
}
exact = (b != 0 && sa > b && sa % b == 0);
sa /= b;
break;
+ case NOP:
+ break;
}
a = (int8_t)(sa);
return exact;
}
+
+ParanoidNumber & ParanoidNumber::operator+=(const ParanoidNumber & a)
+{
+ delete Operation(new ParanoidNumber(a), ADD);
+ Simplify(ADD);
+ Simplify(SUBTRACT);
+ return *this;
+}
+
+
+ParanoidNumber & ParanoidNumber::operator-=(const ParanoidNumber & a)
+{
+ delete Operation(new ParanoidNumber(a), SUBTRACT);
+ //Simplify(SUBTRACT);
+ //Simplify(ADD);
+ return *this;
+}
+
+ParanoidNumber & ParanoidNumber::operator*=(const ParanoidNumber & a)
+{
+ delete Operation(new ParanoidNumber(a), MULTIPLY);
+ return *this;
+}
+
+
+ParanoidNumber & ParanoidNumber::operator/=(const ParanoidNumber & a)
+{
+ delete Operation(new ParanoidNumber(a), DIVIDE);
+ return *this;
+}
+
+// a + b
+ParanoidNumber * ParanoidNumber::OperationTerm(ParanoidNumber * b, Optype op, ParanoidNumber ** merge_point, Optype * merge_op)
+{
+ m_cached_result = nan("");
+ if (Floating() && m_value == 0) // 0 + b = b
+ {
+ m_value = b->m_value;
+ if (op == SUBTRACT)
+ {
+ m_value = -m_value;
+ swap(b->m_next[ADD], b->m_next[SUBTRACT]);
+ }
+
+ for (int i = 0; i < NOP; ++i)
+ {
+ m_next[i] = b->m_next[i];
+ b->m_next[i].clear();
+ }
+ return b;
+ }
+ if (b->Floating() && b->m_value == 0) // a + 0 = a
+ return b;
+
+
+
+ if ((NoFactors() && b->NoFactors())
+ || (GetFactors() == b->GetFactors()))
+ {
+ if (ParanoidOp<digit_t>(m_value, b->m_value, op))
+ {
+ Optype addop = (op == ADD) ? ADD : SUBTRACT;
+ for (auto add : b->m_next[ADD])
+ {
+ delete OperationTerm(add, addop);
+ }
+ Optype subop = (op == ADD) ? SUBTRACT : ADD;
+ for (auto sub : b->m_next[SUBTRACT])
+ delete OperationTerm(sub, subop);
+
+ b->m_next[ADD].clear();
+ b->m_next[SUBTRACT].clear();
+ return b;
+ }
+ }
+
+
+
+ bool parent = (merge_point == NULL);
+ ParanoidNumber * merge = this;
+ Optype mop = op;
+ assert(mop != NOP); // silence compiler warning
+ if (parent)
+ {
+ merge_point = &merge;
+ merge_op = &mop;
+ }
+ else
+ {
+ merge = *merge_point;
+ mop = *merge_op;
+ }
+
+ Optype invop = InverseOp(op); // inverse of p
+ Optype fwd = op;
+ Optype rev = invop;
+ if (op == SUBTRACT)
+ {
+ fwd = ADD;
+ rev = SUBTRACT;
+ }
+
+ for (auto prev : m_next[invop])
+ {
+ if (prev->OperationTerm(b, rev, merge_point, merge_op) == b)
+ return b;
+
+ }
+ for (auto next : m_next[op])
+ {
+ if (next->OperationTerm(b, fwd, merge_point, merge_op) == b)
+ return b;
+ }
+
+
+
+
+ if (parent)
+ {
+ //merge->m_next[*merge_op].push_back(b);
+ m_next[op].push_back(b);
+ }
+ else
+ {
+ if (m_next[op].size() == 0)
+ {
+ *merge_point = this;
+ *merge_op = op;
+ }
+ }
+ return NULL;
+}
+
+ParanoidNumber * ParanoidNumber::OperationFactor(ParanoidNumber * b, Optype op, ParanoidNumber ** merge_point, Optype * merge_op)
+{
+ m_cached_result = nan("");
+ if (Floating() && m_value == 0)
+ {
+ return b;
+ }
+
+ if (Floating() && m_value == 1 && op == MULTIPLY)
+ {
+ m_value = b->m_value;
+ for (int i = 0; i < NOP; ++i)
+ {
+ for (auto n : m_next[i])
+ delete n;
+ m_next[i].clear();
+ swap(m_next[i], b->m_next[i]);
+ }
+ return b;
+ }
+ if (b->Floating() && b->m_value == 1)
+ return b;
+
+
+
+ if (NoTerms() && b->NoTerms())
+ {
+ if (ParanoidOp<digit_t>(m_value, b->m_value, op))
+ {
+ Optype mulop = (op == MULTIPLY) ? MULTIPLY : DIVIDE;
+ for (auto mul : b->m_next[MULTIPLY])
+ {
+ delete OperationFactor(mul, mulop);
+ }
+ Optype divop = (op == MULTIPLY) ? DIVIDE : MULTIPLY;
+ for (auto div : b->m_next[DIVIDE])
+ delete OperationFactor(div, divop);
+
+ b->m_next[DIVIDE].clear();
+ b->m_next[MULTIPLY].clear();
+
+
+
+ return b;
+ }
+ }
+
+
+ bool parent = (merge_point == NULL);
+ ParanoidNumber * merge = this;
+ Optype mop = op;
+ if (parent)
+ {
+ merge_point = &merge;
+ merge_op = &mop;
+ }
+ else
+ {
+ merge = *merge_point;
+ mop = *merge_op;
+ }
+
+ Optype invop = InverseOp(op); // inverse of p
+ Optype fwd = op;
+ Optype rev = invop;
+ if (op == DIVIDE)
+ {
+ fwd = MULTIPLY;
+ rev = DIVIDE;
+ }
+
+ ParanoidNumber * cpy_b = NULL;
+
+ if (m_next[ADD].size() > 0 || m_next[SUBTRACT].size() > 0)
+ {
+ cpy_b = new ParanoidNumber(*b);
+ }
+
+ for (auto prev : m_next[invop])
+ {
+ if (prev->OperationFactor(b, rev, merge_point, merge_op) == b)
+ {
+ for (auto add : m_next[ADD])
+ delete add->OperationFactor(new ParanoidNumber(*cpy_b), op);
+ for (auto sub : m_next[SUBTRACT])
+ delete sub->OperationFactor(new ParanoidNumber(*cpy_b), op);
+
+ delete cpy_b;
+ return b;
+ }
+ }
+ for (auto next : m_next[op])
+ {
+ if (next->OperationFactor(b, fwd, merge_point, merge_op) == b)
+ {
+ for (auto add : m_next[ADD])
+ delete add->OperationFactor(new ParanoidNumber(*cpy_b), op);
+ for (auto sub : m_next[SUBTRACT])
+ delete sub->OperationFactor(new ParanoidNumber(*cpy_b), op);
+ delete cpy_b;
+ return b;
+ }
+ }
+
+ if (parent)
+ {
+ m_next[op].push_back(b);
+ for (auto add : m_next[ADD])
+ delete add->OperationFactor(new ParanoidNumber(*cpy_b), op);
+ for (auto sub : m_next[SUBTRACT])
+ delete sub->OperationFactor(new ParanoidNumber(*cpy_b), op);
+ }
+ return NULL;
+}
+
+
+
+/**
+ * Performs the operation on a with argument b (a += b, a -= b, a *= b, a /= b)
+ * @returns b if b can safely be deleted
+ * @returns NULL if b has been merged with a
+ * append indicates that b should be merged
+ */
+ParanoidNumber * ParanoidNumber::Operation(ParanoidNumber * b, Optype op, ParanoidNumber ** merge_point, Optype * merge_op)
+{
+
+ if (b == NULL)
+ return NULL;
+
+
+ if (op == SUBTRACT || op == ADD)
+ return OperationTerm(b, op, merge_point, merge_op);
+ if (op == MULTIPLY || op == DIVIDE)
+ return OperationFactor(b, op, merge_point, merge_op);
+ return b;
+}
+
+
+
+string ParanoidNumber::PStr() const
+{
+ stringstream s;
+ for (int i = 0; i < NOP; ++i)
+ {
+ Optype f = Optype(i);
+ s << this;
+ for (auto n : m_next[f])
+ {
+ s << OpChar(f) << n->PStr();
+ }
+ }
+ return s.str();
+}
+
+bool ParanoidNumber::Simplify(Optype op)
+{
+ vector<ParanoidNumber*> next(0);
+ swap(m_next[op], next);
+ for (auto n : next)
+ {
+ delete Operation(n, op);
+ }
+ return (next.size() > m_next[op].size());
+}
+
+bool ParanoidNumber::FullSimplify()
+{
+ bool result = false;
+ result |= Simplify(MULTIPLY);
+ result |= Simplify(DIVIDE);
+ result |= Simplify(ADD);
+ result |= Simplify(SUBTRACT);
+ return result;
+}
+
+
+ParanoidNumber::digit_t ParanoidNumber::Digit()
+{
+ if (!isnan(m_cached_result))
+ return m_cached_result;
+ m_cached_result = m_value;
+ for (auto mul : m_next[MULTIPLY])
+ {
+ m_cached_result *= mul->Digit();
+ }
+ for (auto div : m_next[DIVIDE])
+ {
+ m_cached_result /= div->Digit();
+ }
+ for (auto add : m_next[ADD])
+ m_cached_result += add->Digit();
+ for (auto sub : m_next[SUBTRACT])
+ m_cached_result -= sub->Digit();
+ return m_cached_result;
+
+}
+
+ParanoidNumber::digit_t ParanoidNumber::GetFactors()
+{
+ digit_t value = 1;
+ for (auto mul : m_next[MULTIPLY])
+ value *= mul->Digit();
+ for (auto div : m_next[DIVIDE])
+ value /= div->Digit();
+ return value;
+}
+
+
+ParanoidNumber::digit_t ParanoidNumber::GetTerms()
+{
+ digit_t value = 0;
+ for (auto add : m_next[ADD])
+ value += add->Digit();
+ for (auto sub : m_next[SUBTRACT])
+ value -= sub->Digit();
+ return value;
+}
+
+
}
#include <string>
#include "log.h"
#include <fenv.h>
+#include <vector>
+#include <cmath>
#define PARANOID_DIGIT_T float // we could theoretically replace this with a template
// but let's not do that...
namespace IPDF
{
- typedef enum {ADD, SUBTRACT, MULTIPLY, DIVIDE} Optype;
+ typedef enum {ADD, SUBTRACT, MULTIPLY, DIVIDE, NOP} Optype;
+ inline Optype InverseOp(Optype op)
+ {
+ return ((op == ADD) ? SUBTRACT :
+ (op == SUBTRACT) ? ADD :
+ (op == MULTIPLY) ? DIVIDE :
+ (op == DIVIDE) ? MULTIPLY :
+ (op == NOP) ? NOP : NOP);
+ }
+
+
+ inline char OpChar(int op)
+ {
+ static char opch[] = {'+','-','*','/'};
+ return (op < NOP && op >= 0) ? opch[op] : '?';
+ }
+
/** Performs an operation, returning if the result was exact **/
// NOTE: DIFFERENT to ParanoidOp (although that wraps to this...)
}
return false;
}
-
-
template <> bool TrustingOp<float>(float & a, const float & b, Optype op);
template <> bool TrustingOp<double>(double & a, const double & b, Optype op);
template <> bool TrustingOp<int8_t>(int8_t & a, const int8_t & b, Optype op);
- // Attempt to comine two terms: a*b + c*d or a/b + c/d
- template <class T> bool CombineTerms(T & aa, Optype aop, T & bb, T & cc, Optype cop, T & dd)
- {
- T a(aa); T b(bb); T c(cc); T d(dd);
- if (aop == MULTIPLY && cop == MULTIPLY) // a*b + c*d
- {
-
- if ((ParanoidOp<T>(c, b, DIVIDE) || ParanoidOp(d, b, DIVIDE))
- && TrustingOp<T>(c, d, MULTIPLY) && TrustingOp<T>(a,c,ADD)
- && TrustingOp<T>(a, b, MULTIPLY)) // (a + (cd)/b) * b
- {
- aa = a;
- bb = 1;
- cc = 1;
- dd = 1;
- return true;
- }
- if ((ParanoidOp<T>(a, d, DIVIDE) || ParanoidOp(b, d, DIVIDE))
- && TrustingOp<T>(a, b, MULTIPLY) && TrustingOp<T>(a,c,ADD)
- && TrustingOp<T>(a, d, MULTIPLY)) // ((ab)/d + c)*d
- {
- aa = a;
- bb = 1;
- cc = 1;
- dd = 1;
- return true;
- }
- return false;
- }
- else if (aop == DIVIDE && cop == DIVIDE)
- {
-
-
- if (TrustingOp<T>(a, d, MULTIPLY) && TrustingOp<T>(c, b, MULTIPLY)
- && TrustingOp<T>(a, c, ADD) && TrustingOp<T>(b, d, MULTIPLY))
- {
- cc = 1;
- dd = 1;
- if (ParanoidOp<T>(a, b, DIVIDE))
- {
- aa = a;
- bb = 1;
- return true;
- }
- aa = a;
- bb = b;
- return true;
- }
- return false;
- }
- return false;
- }
-
+ /**
+ * A ParanoidNumber
+ * Idea: Perform regular floating point arithmetic but rearrange operations to only ever use exact results
+ * Memory Usage: O(all of it)
+ * CPU Usage: O(all of it)
+ * Accuracy: O(gives better result for 0.3+0.3+0.3, gives same result for everything else, or worse result)
+ *
+ * The ParanoidNumber basically stores 4 linked lists which can be split into two "dimensions"
+ * 1. Terms to ADD and terms to SUBTRACT
+ * 2. Factors to MULTIPLY and DIVIDE
+ * Because ADD and SUBTRACT are inverse operations and MULTIPLY and DIVIDE are inverse operations
+ * See paranoidnumber.cpp and the ParanoidNumber::Operation function
+ */
class ParanoidNumber
{
public:
typedef PARANOID_DIGIT_T digit_t;
- ParanoidNumber(digit_t value=0, Optype type = ADD) : m_value(value), m_op(type), m_next_term(NULL), m_next_factor(NULL)
+ ParanoidNumber(digit_t value=0) : m_value(value), m_cached_result(value)
{
Construct();
}
- ParanoidNumber(const ParanoidNumber & cpy) : m_value(cpy.m_value), m_op(cpy.m_op), m_next_term(NULL), m_next_factor(NULL)
+ ParanoidNumber(const ParanoidNumber & cpy) : m_value(cpy.m_value), m_cached_result(cpy.m_cached_result)
{
- if (cpy.m_next_term != NULL)
- {
- m_next_term = new ParanoidNumber(*(cpy.m_next_term));
- }
- if (cpy.m_next_factor != NULL)
+ Construct();
+ for (int i = 0; i < NOP; ++i)
{
- m_next_factor = new ParanoidNumber(*(cpy.m_next_factor));
+ for (auto next : cpy.m_next[i])
+ m_next[i].push_back(new ParanoidNumber(*next));
}
- Construct();
- }
-
- ParanoidNumber(const ParanoidNumber & cpy, Optype type) : ParanoidNumber(cpy)
- {
- m_op = type;
}
ParanoidNumber(const char * str);
- ParanoidNumber(const std::string & str) : ParanoidNumber(str.c_str()) {Construct();}
+ ParanoidNumber(const std::string & str) : ParanoidNumber(str.c_str()) {}
+
+ virtual ~ParanoidNumber();
- virtual ~ParanoidNumber()
+ inline void Construct()
{
- if (m_next_term != NULL)
- delete m_next_term;
- if (m_next_factor != NULL)
- delete m_next_factor;
- g_count--;
+ g_count++;
}
- inline void Construct() {g_count++;}
-
template <class T> T Convert() const;
- template <class T> T AddTerms() const;
- template <class T> T MultiplyFactors() const;
- template <class T> T Head() const {return (m_op == SUBTRACT) ? T(-m_value) : T(m_value);}
-
+ digit_t GetFactors();
+ digit_t GetTerms();
+
+ double ToDouble() {return (double)Digit();}
+ digit_t Digit();
-
- double ToDouble() const {return Convert<double>();}
- float ToFloat() const {return Convert<float>();}
- digit_t Digit() const {return Convert<digit_t>();}
-
- bool Floating() const {return (m_next_term == NULL && m_next_factor == NULL);}
+ bool Floating() const
+ {
+ return NoFactors() && NoTerms();
+ }
bool Sunken() const {return !Floating();} // I could not resist...
+ bool NoFactors() const {return (m_next[MULTIPLY].size() == 0 && m_next[DIVIDE].size() == 0);}
+ bool NoTerms() const {return (m_next[ADD].size() == 0 && m_next[SUBTRACT].size() == 0);}
+
ParanoidNumber & operator+=(const ParanoidNumber & a);
ParanoidNumber & operator-=(const ParanoidNumber & a);
ParanoidNumber & operator*=(const ParanoidNumber & a);
ParanoidNumber & operator/=(const ParanoidNumber & a);
ParanoidNumber & operator=(const ParanoidNumber & a);
+ ParanoidNumber * OperationTerm(ParanoidNumber * b, Optype op, ParanoidNumber ** merge_point = NULL, Optype * mop = NULL);
+ ParanoidNumber * OperationFactor(ParanoidNumber * b, Optype op, ParanoidNumber ** merge_point = NULL, Optype * mop = NULL);
+ ParanoidNumber * TrivialOp(ParanoidNumber * b, Optype op);
+ ParanoidNumber * Operation(ParanoidNumber * b, Optype op, ParanoidNumber ** merge_point = NULL, Optype * mop = NULL);
+ bool Simplify(Optype op);
+ bool FullSimplify();
- bool operator<(const ParanoidNumber & a) const {return ToDouble() < a.ToDouble();}
- bool operator<=(const ParanoidNumber & a) const {return this->operator<(a) || this->operator==(a);}
- bool operator>(const ParanoidNumber & a) const {return !(this->operator<=(a));}
- bool operator>=(const ParanoidNumber & a) const {return !(this->operator<(a));}
- bool operator==(const ParanoidNumber & a) const {return ToDouble() == a.ToDouble();}
- bool operator!=(const ParanoidNumber & a) const {return !(this->operator==(a));}
+ bool operator<(ParanoidNumber & a) {return ToDouble() < a.ToDouble();}
+ bool operator<=(ParanoidNumber & a) {return this->operator<(a) || this->operator==(a);}
+ bool operator>(ParanoidNumber & a) {return !(this->operator<=(a));}
+ bool operator>=(ParanoidNumber & a) {return !(this->operator<(a));}
+ bool operator==(ParanoidNumber & a) {return ToDouble() == a.ToDouble();}
+ bool operator!=(ParanoidNumber & a) {return !(this->operator==(a));}
ParanoidNumber operator+(const ParanoidNumber & a) const
{
}
std::string Str() const;
- static char OpChar(Optype op)
+
+ ParanoidNumber * CopyTerms()
{
- static char opch[] = {'+','-','*','/'};
- return opch[(int)op];
+ ParanoidNumber * copy = new ParanoidNumber(*this);
+ copy->m_value = 0;
+ copy->Simplify(ADD);
+ copy->Simplify(SUBTRACT);
+ return copy;
}
-
+
+ ParanoidNumber * CopyFactors()
+ {
+ ParanoidNumber * copy = new ParanoidNumber(*this);
+ copy->m_value = 1;
+ copy->Simplify(MULTIPLY);
+ copy->Simplify(DIVIDE);
+ return copy;
+ }
+
+
static int64_t Paranoia() {return g_count;}
+
+ std::string PStr() const;
private:
static int64_t g_count;
digit_t m_value;
Optype m_op;
- ParanoidNumber * m_next_term;
- ParanoidNumber * m_next_factor;
+ std::vector<ParanoidNumber*> m_next[4];
+ digit_t m_cached_result;
+ bool m_cache_valid;
};
+
+
+
template <class T>
-T ParanoidNumber::AddTerms() const
+T ParanoidNumber::Convert() const
{
- T value(0);
- for (ParanoidNumber * a = m_next_term; a != NULL; a = a->m_next_term)
+ if (!isnan(m_cached_result))
+ return (T)m_cached_result;
+ T value(m_value);
+ for (auto mul : m_next[MULTIPLY])
{
- value += a->Head<T>() * a->MultiplyFactors<T>();
+ value *= mul->Convert<T>();
}
- return value;
-}
-
-template <class T>
-T ParanoidNumber::MultiplyFactors() const
-{
- T value(1);
- for (ParanoidNumber * a = m_next_factor; a != NULL; a = a->m_next_factor)
+ for (auto div : m_next[DIVIDE])
{
- if (a->m_op == DIVIDE)
- value /= (a->Head<T>() + a->AddTerms<T>());
- else
- value *= (a->Head<T>() + a->AddTerms<T>());
+ value /= div->Convert<T>();
}
+ for (auto add : m_next[ADD])
+ value += add->Convert<T>();
+ for (auto sub : m_next[SUBTRACT])
+ value -= sub->Convert<T>();
return value;
}
-template <class T>
-T ParanoidNumber::Convert() const
-{
- return Head<T>() * MultiplyFactors<T>() + AddTerms<T>();
-}
-
-
-
}
#endif //_PARANOIDNUMBER_H
float fa = da;
while (cin.good())
{
+ Debug("a is {%s} \"%.40lf\"", a.Str().c_str(), a.ToDouble());
char op;
cin >> op;
token = "";
token += c;
c = cin.get();
}
- Debug("String is %s", token.c_str());
+
+ //Debug("String is \"%s\"", token.c_str());
float fb = strtof(token.c_str(), NULL);
double db = strtod(token.c_str(), NULL);
ParanoidNumber b(token.c_str());
- Debug("b is {%s} %lf", b.Str().c_str(), b.ToDouble());
+
+ Debug("b is {%s} \"%lf\"", b.Str().c_str(), b.ToDouble());
+ Debug("db is %lf", db);
switch (op)
{
case '+':
break;
}
- Debug("a is: %s", a.Str().c_str());
- Debug("a as double: %.40f\n", a.ToDouble());
- Debug("a as float: %.40f\n", a.ToFloat());
- Debug("a as int64_t: %ld\n", a.Convert<int64_t>());
- Debug("floats give: %.40f\n", fa);
- Debug("double gives: %.40f\n", da);
+ Debug("a is: {%s}", a.Str().c_str());
+ Debug("a as double: %.40lf", a.ToDouble());
+ //Debug("a as float: %.40f", a.ToFloat());
+ //Debug("a as int64_t: %ld", a.Convert<int64_t>());
+ //Debug("floats give: %.40f", fa);
+ Debug("double gives: %.40lf", da);
}
using namespace std;
using namespace IPDF;
-string RandomNumberAsString(int max_digits = 12)
+string RandomNumberAsString(int max_digits = 3)
{
string result("");
int digits = 1+(rand() % max_digits);
return result;
}
-bool CloseEnough(double d, ParanoidNumber & p)
+bool CloseEnough(long double d, ParanoidNumber & p, long double eps = 1e-6)
{
- double pd = p.ToDouble();
+ long double pd = p.Convert<long double>();
if (d == 0)
- return fabs(pd) <= 1e-6;
- return fabs((fabs(pd - d) / d)) <= 1e-6;
+ return fabs(pd) <= eps;
+ return fabs((fabs(pd - d) / d)) <= eps;
+}
+
+void TestOp(ParanoidNumber & p, double & d, Optype op, const double amount)
+{
+ string p0str(p.Str());
+ double p0 = p.ToDouble();
+ switch (op)
+ {
+ case ADD:
+ p += amount;
+ d += amount;
+ break;
+ case SUBTRACT:
+ p -= amount;
+ d -= amount;
+ break;
+ case MULTIPLY:
+ p *= amount;
+ d *= amount;
+ break;
+ case DIVIDE:
+ p /= amount;
+ d /= amount;
+ break;
+ default:
+ break;
+ }
+ if (!CloseEnough(d, p))
+ {
+ Debug("%lf %c= %lf failed", p0, OpChar(op), amount);
+ Debug("%lf vs %lf", p.ToDouble(), d);
+ Debug("Before: {%s}\n", p0str.c_str());
+ Debug("After: {%s}\n", p.Str().c_str());
+ Fatal(":-(");
+ }
+
+}
+
+void TestAddSubIntegers(int max=100)
+{
+ Debug("Test add/sub integers 0 -> %i", max);
+ ParanoidNumber p;
+ double d(0);
+ for (int a = 0; a < max; ++a)
+ {
+ TestOp(p, d, ADD, a);
+ for (int b = 0; b < max; ++b)
+ {
+ TestOp(p, d, SUBTRACT, b);
+ }
+ for (int b = 0; b < max; ++b)
+ {
+ TestOp(p, d, ADD, b);
+ }
+ }
+ for (int a = 0; a < max; ++a)
+ {
+ TestOp(p, d, SUBTRACT, a);
+ for (int b = 0; b < max; ++b)
+ {
+ TestOp(p, d, ADD, b);
+ }
+ for (int b = 0; b < max; ++b)
+ {
+ TestOp(p, d, SUBTRACT, b);
+ }
+ }
+ Debug("PN Yields: %.40lf", p.ToDouble());
+ Debug("Doubles Yield: %.40lf", d);
+ Debug("Complete!");
+
+}
+
+void TestMulDivIntegers(int max=50)
+{
+ Debug("Test mul/div integers 1 -> %i", max);
+ ParanoidNumber p(1.0);
+ double d(1.0);
+ for (int a = 1; a < max; ++a)
+ {
+ TestOp(p, d, MULTIPLY, a);
+ for (int b = 1; b < max; ++b)
+ {
+ TestOp(p, d, DIVIDE, b);
+ }
+ for (int b = 1; b < max; ++b)
+ {
+ TestOp(p, d, MULTIPLY, b);
+ }
+ }
+ for (int a = 1; a < max; ++a)
+ {
+ TestOp(p, d, DIVIDE, a);
+ for (int b = 1; b < max; ++b)
+ {
+ TestOp(p, d, MULTIPLY, b);
+ }
+ for (int b = 1; b < max; ++b)
+ {
+ TestOp(p, d, DIVIDE, b);
+ }
+ }
+ Debug("PN Yields: %.40lf", p.ToDouble());
+ Debug("Doubles Yield: %.40lf", d);
+ Debug("Complete!");
+
+}
+
+void TestRandomisedOps(int test_cases = 1000, int ops_per_case = 1, int max_digits = 4)
+{
+ Debug("Test %i*%i randomised ops (max digits = %i)", test_cases, ops_per_case, max_digits);
+ long double eps = 1e-2; //* (1e4*ops_per_case);
+ for (int i = 0; i < test_cases; ++i)
+ {
+ string s = RandomNumberAsString(max_digits);
+ ParanoidNumber a(s);
+
+ double da(a.ToDouble());
+ for (int j = 1; j <= ops_per_case; ++j)
+ {
+ double da2(a.ToDouble());
+ s = RandomNumberAsString(max_digits);
+ ParanoidNumber b(s);
+ double db(b.ToDouble());
+
+
+
+ Optype op = Optype(rand() % 4);
+
+ ParanoidNumber a_before(a);
+
+
+ switch (op)
+ {
+ case ADD:
+ a += b;
+ da += db;
+ da2 += db;
+ break;
+ case SUBTRACT:
+ a -= b;
+ da -= db;
+ da2 -= db;
+ break;
+ case MULTIPLY:
+ a *= b;
+ da *= db;
+ da2 *= db;
+ break;
+ case DIVIDE:
+ if (db == 0)
+ {
+ --i;
+ }
+ else
+ {
+ a /= b;
+ da /= db;
+ da2 /= db;
+ }
+ break;
+ case NOP:
+ break;
+ }
+ if (!CloseEnough(da2, a, eps))
+ {
+ Error("{%s} %c= {%s}", a_before.Str().c_str(), OpChar(op), b.Str().c_str());
+ Error("{%s}", a.Str().c_str());
+ Error("double Yields: %.40lf", da);
+ Error("PN Yields: %.40lf", a.ToDouble());
+ Fatal("Failed on case %i", i*ops_per_case + j-1);
+ }
+ }
+ if (!CloseEnough(da, a, eps))
+ {
+ Warn("double Yields: %.40lf", da);
+ Warn("PN Yields: %.40lf", a.ToDouble());
+ }
+ }
+ Debug("Complete!");
+
}
#define TEST_CASES 1000
int main(int argc, char ** argv)
{
- srand(time(NULL));
+ TestAddSubIntegers();
+ TestMulDivIntegers();
+ for (int i = 1; i <= 100; ++i)
+ TestRandomisedOps(1000, i);
+ return 0;
+ srand(0);//time(NULL)); //always test off same set
string number(RandomNumberAsString());
ParanoidNumber a(number);
+
float fa = strtof(number.c_str(), NULL);
double da = strtod(number.c_str(), NULL);
double diff = 0;
long double lda = strtold(number.c_str(), NULL);
-
+ Debug("a is %s", a.Str().c_str());
if (fabs(a.ToDouble() - da) > 1e-6)
{
Error("double %lf, pn %lf {%s}", da, a.ToDouble(), a.Str().c_str());
Fatal("Didn't construct correctly off %s", number.c_str());
+
}
char opch[] = {'+','-','*','/'};
break;
}
diff = 100.0*(fabs(a.ToDouble() - da) / da);
- if (!CloseEnough(da, a))
+ if (!CloseEnough(lda, a))
{
Error("Op %i: ParanoidNumber probably doesn't work", i);
Error("Operation: %lf %c %lf", oldda, opch[op], db);
Error("As PN: %lf %c %lf", olda.ToDouble(), opch[op], b.ToDouble());
+ Error("PN String before: %s", olda.Str().c_str());
Error("PN String: %s", a.Str().c_str());
- Error("Diff is %.40lf", diff);
Error("LONG double gives %.40llf", lda);
- Fatal("%.40lf, expected aboout %.40lf", a.ToDouble(), da);
+ Fatal("%.40llf, expected aboout %.40llf", a.Convert<long double>(), lda);
}
git.ucc.asn.au / ipdf / code.git / commitdiff
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