From: Sam Moore <matches@ucc.asn.au>
Date: Tue, 16 Sep 2014 10:43:39 +0000 (+0800)
Subject: Slightly better results
X-Git-Url: https://git.ucc.asn.au/?a=commitdiff_plain;h=0f3a7a9d2c6cc19852fae8ed048dcd1089d33250;p=ipdf%2Fcode.git

Slightly better results

Assuming we can trust Wolfram's Giant Ego, err, I mean Wolfram Alpha, to give exact results,
it is generally giving a better result than doubles.

Try simplifying the "a/b + c/d" cases next?

Also at the moment "(a + b)*c" does not simplify to "a*c + b*c" even if
a*c is exact.

Have to be careful because sometimes making the representation more exact
ends up making the conversion back to double have a bigger error.
---

diff --git a/src/paranoidnumber.cpp b/src/paranoidnumber.cpp
index 4769c46..b45c71e 100644
--- a/src/paranoidnumber.cpp
+++ b/src/paranoidnumber.cpp
@@ -22,7 +22,7 @@ ParanoidNumber::~ParanoidNumber()
 	}
 }
 
-ParanoidNumber::ParanoidNumber(const char * str) : m_value(0)
+ParanoidNumber::ParanoidNumber(const char * str) : m_value(0), m_cached_result(0)
 {
 	Construct();
 	int dp = 0;
@@ -55,6 +55,7 @@ ParanoidNumber::ParanoidNumber(const char * str) : m_value(0)
 ParanoidNumber & ParanoidNumber::operator=(const ParanoidNumber & a)
 {
 	m_value = a.m_value;
+	m_cached_result = a.m_cached_result;
 	for (int i = 0; i < NOP; ++i)
 	{
 		for (unsigned j = 0; j < m_next[i].size() && j < a.m_next[i].size(); ++j)
@@ -198,6 +199,8 @@ bool TrustingOp<int8_t>(int8_t & a, const int8_t & b, Optype op)
 ParanoidNumber & ParanoidNumber::operator+=(const ParanoidNumber & a)
 {
 	delete Operation(new ParanoidNumber(a), ADD);
+	Simplify(ADD);
+	Simplify(SUBTRACT);
 	return *this;
 }
 
@@ -205,6 +208,8 @@ ParanoidNumber & ParanoidNumber::operator+=(const ParanoidNumber & a)
 ParanoidNumber & ParanoidNumber::operator-=(const ParanoidNumber & a)
 {
 	delete Operation(new ParanoidNumber(a), SUBTRACT);
+	//Simplify(SUBTRACT);
+	//Simplify(ADD);
 	return *this;
 }
 
@@ -224,7 +229,7 @@ ParanoidNumber & ParanoidNumber::operator/=(const ParanoidNumber & a)
 // 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;
@@ -246,7 +251,8 @@ ParanoidNumber * ParanoidNumber::OperationTerm(ParanoidNumber * b, Optype op, Pa
 		
 
 	
-	if (NoFactors() && b->NoFactors())
+	if ((NoFactors() && b->NoFactors())
+		|| (GetFactors() == b->GetFactors()))
 	{
 		if (ParanoidOp<digit_t>(m_value, b->m_value, op))
 		{
@@ -265,7 +271,6 @@ ParanoidNumber * ParanoidNumber::OperationTerm(ParanoidNumber * b, Optype op, Pa
 		}
 	}
 
-
 	
 	
 	bool parent = (merge_point == NULL);
@@ -309,7 +314,8 @@ ParanoidNumber * ParanoidNumber::OperationTerm(ParanoidNumber * b, Optype op, Pa
 	
 	if (parent)
 	{
-		merge->m_next[*merge_op].push_back(b);
+		//merge->m_next[*merge_op].push_back(b);
+		m_next[op].push_back(b);
 	}
 	else
 	{
@@ -324,7 +330,7 @@ ParanoidNumber * ParanoidNumber::OperationTerm(ParanoidNumber * b, Optype op, Pa
 
 ParanoidNumber * ParanoidNumber::OperationFactor(ParanoidNumber * b, Optype op, ParanoidNumber ** merge_point, Optype * merge_op)
 {
-	
+	m_cached_result = nan("");
 	if (Floating() && m_value == 0)
 	{
 		return b;
@@ -344,6 +350,8 @@ ParanoidNumber * ParanoidNumber::OperationFactor(ParanoidNumber * b, Optype op,
 	}
 	if (b->Floating() && b->m_value == 1)
 		return b;
+	
+
 		
 	if (NoTerms() && b->NoTerms())
 	{
@@ -360,6 +368,9 @@ ParanoidNumber * ParanoidNumber::OperationFactor(ParanoidNumber * b, Optype op,
 				
 			b->m_next[DIVIDE].clear();
 			b->m_next[MULTIPLY].clear();
+			
+			
+			
 			return b;		
 		}
 	}
@@ -477,16 +488,63 @@ bool ParanoidNumber::Simplify(Optype op)
 	swap(m_next[op], next);
 	for (auto n : next)
 	{
-		ParanoidNumber * result = Operation(n, op);
-		if (result != NULL)
-			delete result;
-		else
-			m_next[op].push_back(n);
+		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;
+}
 
 
 }
diff --git a/src/paranoidnumber.h b/src/paranoidnumber.h
index e88cfe7..9e63a23 100644
--- a/src/paranoidnumber.h
+++ b/src/paranoidnumber.h
@@ -71,12 +71,12 @@ namespace IPDF
 		public:
 			typedef PARANOID_DIGIT_T digit_t;
 
-			ParanoidNumber(digit_t value=0) : m_value(value)
+			ParanoidNumber(digit_t value=0) : m_value(value), m_cached_result(value)
 			{
 				Construct();
 			}
 			
-			ParanoidNumber(const ParanoidNumber & cpy) : m_value(cpy.m_value)
+			ParanoidNumber(const ParanoidNumber & cpy) : m_value(cpy.m_value), m_cached_result(cpy.m_cached_result)
 			{
 				Construct();
 				for (int i = 0; i < NOP; ++i)
@@ -98,9 +98,12 @@ namespace IPDF
 			
 			
 			template <class T> T Convert() const;
+			digit_t GetFactors();
+			digit_t GetTerms();
+		
 
-			double ToDouble() const {return Convert<double>();}
-			digit_t Digit() const {return Convert<digit_t>();}
+			double ToDouble() {return (double)Digit();}
+			digit_t Digit();
 			
 			bool Floating() const 
 			{
@@ -122,14 +125,14 @@ namespace IPDF
 			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
 			{
@@ -176,7 +179,7 @@ namespace IPDF
 				return copy;
 			}
 
-		
+
 			static int64_t Paranoia() {return g_count;}
 			
 			std::string PStr() const;
@@ -191,29 +194,36 @@ namespace IPDF
 			digit_t m_value;
 			Optype m_op;
 			std::vector<ParanoidNumber*> m_next[4];
-			
-			int m_size;
+			digit_t m_cached_result;
+			bool m_cache_valid;
 	};
+	
+
+
 
 template <class T>
 T ParanoidNumber::Convert() const
 {
+	if (!isnan(m_cached_result))
+		return (T)m_cached_result;
 	T value(m_value);
 	for (auto mul : m_next[MULTIPLY])
 	{
-		value *= mul->Digit();
+		value *= mul->Convert<T>();
 	}
 	for (auto div : m_next[DIVIDE])
 	{
-		value /= div->Digit();
+		value /= div->Convert<T>();
 	}
 	for (auto add : m_next[ADD])
-		value += add->Digit();
+		value += add->Convert<T>();
 	for (auto sub : m_next[SUBTRACT])
-		value -= sub->Digit();
+		value -= sub->Convert<T>();
 	return value;
 }
 
+
+
 }
 
 #endif //_PARANOIDNUMBER_H
diff --git a/src/tests/paranoidtester.cpp b/src/tests/paranoidtester.cpp
index 1d4f26a..47969b9 100644
--- a/src/tests/paranoidtester.cpp
+++ b/src/tests/paranoidtester.cpp
@@ -148,7 +148,7 @@ void TestMulDivIntegers(int max=50)
 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-6; //* (1e4*ops_per_case);
+	long double eps = 1e-2; //* (1e4*ops_per_case);
 	for (int i = 0; i < test_cases; ++i)
 	{
 		string s = RandomNumberAsString(max_digits);