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Multi precision arithmetic applications 

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Program Information

Name: Multi precision arithmetic applications 
Domain: Numerical program
Functionality: an application with arithmetics carried out in software as IEEE 754 standard to achieve higher precision and accuracy than hardware based environment 
Input: $i, j \in R$: i, j and k are three numbers 
Output: $k \in R$ 

Reference

Metamorphic Relations to Improve the Test Accuracy of Multi Precision Arithmetic Software Applications https://dx.doi.org/10.1109/ICACCI.2014.6968586 

MR Information

MR1------

Description:
Property: If $i, j$ and $k$ are three numbers, $\forall{i,j,k}\in N$ and multiplication result of (i ,j) is k then i, j, k has to satisfy $i * j = k \Leftrightarrow (i*j)*x = k*x$, $\forall\{(i, j, k)\in N\ and\ (i, j, k) \in Q\}$ 
Source input: $i,j$ $\forall{i,j,k}\in N\ and\ (i,j,k)\in Q$ 
Source output: $k$ 
Follow-up input: $(i*j)*x$ 
Follow-up output: $k*x$ 
Input relation: $i*j=k$ 
Output relation: $(i*j)*x=k*x$ 
Pattern: symmetry 

MR2------

Description:
Property: If $i, j$ and $k$ are three numbers, $\forall{i,j,k}\in N$ and multiplication result of (i ,j) is k then i, j, k has to satisfy $i * j = k \Leftrightarrow k/j=i \cap k/i=j$, $\forall\{(i, j, k)\in N\ and\ (i, j, k) \in Q\}$ 
Source input:   
Source output: $k$ 
Follow-up input: $(i*j)*x$ 
Follow-up output: $k*x$ 
Input relation: $i*j=k$ 
Output relation: $k/j=i$ && $k/i=j$ 
Pattern: symmetry 

MR3------

Description:
Property: If $i, j$ and $k$ are three numbers, $\forall{i,j,k}\in N$ and multiplication result of (i ,j) is k then i, j, k has to satisfy $i * j = k \Leftrightarrow ((i*j/n)+(i*j/n))=(k/2)*n$, $\forall\{(i, j, k, n)\in N\}$ 
Source input: $i,j$ $\forall(i,j,k,n)\in N$ 
Source output: $k$ 
Follow-up input: $(i*j/n) +(i*j/n)$ 
Follow-up output: $(k/2)*n$ 
Input relation: $i*j=k$ 
Output relation: $((i*j/n) +(i*j/n)) = (k/2)*n$ 
Pattern: symmetry 

MR4------

Description:
Property: If $i, j$ and $k$ are three numbers, $\forall{i,j,k}\in N$ and multiplication result of (i ,j) is k then i, j, k has to satisfy $i * j = k \Leftrightarrow (i + 1)*(j – 1) = ( i * j)- i + j - 1 = k - (i + 1 – j)$ 
Source input: $i,j$
Source output: $k$ 
Follow-up input: $(i + 1)*(j – 1)$,  $(i * j)- i + j - 1$ 
Follow-up output: $k-(i+1–j)$ 
Input relation: $i*j=k$ 
Output relation: $(i + 1)*(j – 1) = ( i * j)- i + j - 1 = k - (i + 1 – j)$ 
Pattern: symmetry 

MR5------

Description:
Property: If i, j and k are three numbers ${i, j, k \in R }$ and multiplication result of (i ,j) is k then i, j, k has to satisfy $i / j = k\Leftrightarrow (i/j)*x = k*x \in\{ (i, j, k) \in N$ and $(i, j, k) \in Q \}$ 
Source input: $i,j$ 
Source output: $k$ 
Follow-up input: $(i/j)*x$ 
Follow-up output: $k*x$ 
Input relation: $i/j=k$ 
Output relation: $(i/j)*x = k*x\in (i, j, k) \in N and (i, j, k) \in Q$ 
Pattern: symmetry 

MR6------

Description:
Property: If i, j and k are three numbers ${i, j, k \in R }$ and multiplication result of (i ,j) is k then i, j, k has to satisfy $i/j=k\Leftrightarrow k*j=i\ \&\&\ i/k = j \in\{ (i, j, k) \in N$ and $(i, j, k) \in Q \}$ 
Source input: $i,j$ 
Source output: $k$ 
Follow-up input: $k*j$,$i/k$ 
Follow-up output: $i,j$ 
Input relation: $i/j=k$ 
Output relation: $k*j= i$ && $i/k = j \in\ {(i, j, k) \in N\ and\ (i, j, k) \in Q}$ 
Pattern: symmetry 

MR7------

Description:
Property: If i, j and k are three numbers ${i, j, k \in R }$ and multiplication result of (i ,j) is k then i, j, k has to satisfy $i/j=k\Leftrightarrow (((i/j)*n) +((i/j)*n))= (k*2)/n \in \{(i,j,k,n)\in N\}$ 
Source input: $i,j$ 
Source output: $k$ 
Follow-up input: $(((i/j)*n) +((i/j)*n))$ 
Follow-up output: $(k*2)/n$ 
Input relation: $i/j=k$ 
Output relation: $(k*2)/n \in {(i, j, k, n) \in N }$ 
Pattern: symmetry 
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