#include <cfloat>
#include <map>
#include <string>
+#include "log.h"
+#include <fenv.h>
+
+#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, 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 Optype AdjacentOp(Optype op)
+ {
+ return ((op == ADD) ? MULTIPLY :
+ (op == SUBTRACT) ? DIVIDE :
+ (op == MULTIPLY) ? ADD :
+ (op == DIVIDE) ? SUBTRACT :
+ (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...)
+ template <class T> bool TrustingOp(T & a, const T & b, Optype op);
+
+ /** Performs an operation _only_ if the result would be exact **/
+ template <class T> bool ParanoidOp(T & a, const T & b, Optype op)
+ {
+ T cpy(a);
+ if (TrustingOp<T>(cpy, b, op))
+ {
+ a = cpy;
+ return true;
+ }
+ 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);
+
+ /**
+ * 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 enum {ADD, SUBTRACT, MULTIPLY, DIVIDE} Optype;
-
- ParanoidNumber(float value=0, Optype type = ADD) : m_value(value), m_op(type), m_next(NULL)
+ typedef PARANOID_DIGIT_T digit_t;
+
+ 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(NULL)
+ ParanoidNumber(const ParanoidNumber & cpy) : m_value(cpy.m_value)
{
- if (cpy.m_next != NULL)
+ Construct();
+ for (int i = 0; i < NOP; ++i)
{
- m_next = new ParanoidNumber(*(cpy.m_next));
+ if (cpy.m_next[i] != NULL)
+ m_next[i] = new ParanoidNumber(*(cpy.m_next[i]));
}
}
- ParanoidNumber(const ParanoidNumber & cpy, Optype type) : ParanoidNumber(cpy)
+ ParanoidNumber(const char * str);
+ ParanoidNumber(const std::string & str) : ParanoidNumber(str.c_str()) {Construct();}
+
+ virtual ~ParanoidNumber();
+
+ inline void Construct()
{
- m_op = type;
+ for (int i = 0; i < NOP; ++i)
+ m_next[i] = NULL;
+ g_count++;
}
- ParanoidNumber(const char * str);
- virtual ~ParanoidNumber()
+ template <class T> T Convert() const;
+ template <class T> T AddTerms(T value = T(0)) const;
+ template <class T> T MultiplyFactors(T value = T(1)) 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
{
- if (m_next != NULL)
- delete m_next;
+ for (int i = 0; i < NOP; ++i)
+ {
+ if (m_next[i] != NULL)
+ return false;
+ }
+ return true;
}
+ bool Sunken() const {return !Floating();} // I could not resist...
-
- double ToDouble() const;
+ bool Pure(Optype op) const
+ {
+ if (op == ADD || op == SUBTRACT)
+ return (m_next[MULTIPLY] == NULL && m_next[DIVIDE] == NULL);
+ return (m_next[ADD] == NULL && m_next[SUBTRACT] == NULL);
+ }
ParanoidNumber & operator+=(const ParanoidNumber & a);
ParanoidNumber & operator-=(const ParanoidNumber & a);
ParanoidNumber & operator=(const ParanoidNumber & a);
+ ParanoidNumber * Operation(ParanoidNumber * b, Optype op, ParanoidNumber ** parent = 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);}
bool operator>(const ParanoidNumber & a) const {return !(this->operator<=(a));}
}
std::string Str() const;
+
+
+ static int64_t Paranoia() {return g_count;}
+
+ std::string PStr() const;
private:
+ static int64_t g_count;
void Simplify();
- ParanoidNumber * InsertAfter(ParanoidNumber * insert);
- ParanoidNumber * InsertAfter(float value, Optype op);
+ void SimplifyTerms();
+ void SimplifyFactors();
- float m_value;
+
+ digit_t m_value;
Optype m_op;
- ParanoidNumber * m_next;
+ ParanoidNumber * m_next[4]; // Next by Operation
+ };
-
-
+template <class T>
+T ParanoidNumber::AddTerms(T value) const
+{
+ ParanoidNumber * add = m_next[ADD];
+ ParanoidNumber * sub = m_next[SUBTRACT];
+ while (add != NULL && sub != NULL)
+ {
+ value += add->m_value * add->MultiplyFactors<T>();
+ value -= sub->m_value * sub->MultiplyFactors<T>();
+ add = add->m_next[ADD];
+ sub = sub->m_next[SUBTRACT];
+ }
+ while (add != NULL)
+ {
+ value += add->m_value * add->MultiplyFactors<T>();
+ add = add->m_next[ADD];
+ }
+ while (sub != NULL)
+ {
+ value -= sub->m_value * sub->MultiplyFactors<T>();
+ sub = sub->m_next[SUBTRACT];;
+ }
+ return value;
+}
+
+template <class T>
+T ParanoidNumber::MultiplyFactors(T value) const
+{
+ ParanoidNumber * mul = m_next[MULTIPLY];
+ ParanoidNumber * div = m_next[DIVIDE];
+ while (mul != NULL && div != NULL)
+ {
+ value *= (mul->m_value + mul->AddTerms<T>());
+ value /= (div->m_value + div->AddTerms<T>());
+ mul = mul->m_next[MULTIPLY];
+ div = div->m_next[DIVIDE];
+ }
+ while (mul != NULL)
+ {
+ value *= (mul->m_value + mul->AddTerms<T>());
+ mul = mul->m_next[MULTIPLY];
+ }
+ while (div != NULL)
+ {
+ value /= (div->m_value + div->AddTerms<T>());
+ div = div->m_next[DIVIDE];
+ }
+ return value;
+}
+
+
+
+template <class T>
+T ParanoidNumber::Convert() const
+{
+ return MultiplyFactors<T>(m_value) + AddTerms<T>(0);
+}
- };
}
git.ucc.asn.au / ipdf / code.git / blobdiff
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