#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)
{
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)
{
- 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);}
-
-
-
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 operator<(const ParanoidNumber & a) const {return ToDouble() < a.ToDouble();}
bool operator<=(const ParanoidNumber & a) const {return this->operator<(a) || this->operator==(a);}
}
std::string Str() const;
- static char OpChar(Optype op)
+
+ ParanoidNumber * CopyTerms()
+ {
+ ParanoidNumber * copy = new ParanoidNumber(*this);
+ copy->m_value = 0;
+ copy->Simplify(ADD);
+ copy->Simplify(SUBTRACT);
+ return copy;
+ }
+
+ ParanoidNumber * CopyFactors()
{
- static char opch[] = {'+','-','*','/'};
- return opch[(int)op];
+ 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];
+
+ int m_size;
};
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)
+ T value(m_value);
+ for (auto mul : m_next[MULTIPLY])
{
- value += a->Head<T>() * a->MultiplyFactors<T>();
+ value *= mul->Digit();
}
- 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->Digit();
}
+ for (auto add : m_next[ADD])
+ value += add->Digit();
+ for (auto sub : m_next[SUBTRACT])
+ value -= sub->Digit();
return value;
}
-
-
-template <class T>
-T ParanoidNumber::Convert() const
-{
- return Head<T>() * MultiplyFactors<T>() + AddTerms<T>();
-}
-
-
-
}
#endif //_PARANOIDNUMBER_H