---
title: "Domain-to-range ratio"
chunk: 1/1
source: "https://en.wikipedia.org/wiki/Domain-to-range_ratio"
category: "reference"
tags: "science, encyclopedia"
date_saved: "2026-05-05T12:04:48.191214+00:00"
instance: "kb-cron"
---

The domain-to-range ratio (DRR) is a ratio which describes how the number of outputs corresponds to the number of inputs of a given logical function or software component. The domain-to-range ratio is a mathematical ratio of cardinality between the set of the function's possible inputs (the domain) and the set of possible outputs (the range). For a function defined on a domain, 
  
    
      
        D
      
    
    {\displaystyle D}
  
, and a range, 
  
    
      
        R
      
    
    {\displaystyle R}
  
, the domain-to-range ratio is given as:
  
    
      
        D
        R
        R
        =
        
          
            
              
                |
              
              D
              
                |
              
            
            
              
                |
              
              R
              
                |
              
            
          
        
      
    
    {\displaystyle DRR={\frac {|D|}{|R|}}}
  
It can be used to measure the risk of missing potential errors when testing the range of outputs alone.


== Example ==
Consider the function isEven() below, which checks the parity of an unsigned short number 
  
    
      
        x
      
    
    {\displaystyle x}
  
, any value between 
  
    
      
        0
      
    
    {\displaystyle 0}
  
 and 
  
    
      
        65
        ,
        536
      
    
    {\displaystyle 65,536}
  
, and yields a boolean value which corresponds to whether 
  
    
      
        x
      
    
    {\displaystyle x}
  
 is even or odd. This solution takes advantage of the fact that integer division in programming typically rounds towards zero. 

Because 
  
    
      
        x
      
    
    {\displaystyle x}
  
 can be any value from 
  
    
      
        0
      
    
    {\displaystyle 0}
  
 to 
  
    
      
        65
        ,
        535
      
    
    {\displaystyle 65,535}
  
, the function's domain has a cardinality of 
  
    
      
        65
        ,
        536
      
    
    {\displaystyle 65,536}
  
. The function yields 
  
    
      
        0
      
    
    {\displaystyle 0}
  
, if 
  
    
      
        x
      
    
    {\displaystyle x}
  
 is even, or 
  
    
      
        1
      
    
    {\displaystyle 1}
  
, if 
  
    
      
        x
      
    
    {\displaystyle x}
  
 is odd. This is expressed as the range 
  
    
      
        {
        0
        ;
        1
        }
      
    
    {\displaystyle \{0;1\}}
  
, which has a cardinality of 
  
    
      
        2
      
    
    {\displaystyle 2}
  
. Therefore, the domain-to-range ratio of isEven() is given by:
  
    
      
        D
        R
        R
        =
        
          
            
              65
              ,
              536
            
            2
          
        
        =
        32
        ,
        768
      
    
    {\displaystyle DRR={65,536 \over 2}=32,768}
  
Here, the domain-to-range ratio indicates that this function would require a comparatively large number of tests to find errors. If a test program attempts every possible value of 
  
    
      
        x
      
    
    {\displaystyle x}
  
 in order from 
  
    
      
        0
      
    
    {\displaystyle 0}
  
 to 
  
    
      
        65
        ,
        535
      
    
    {\displaystyle 65,535}
  
, the program would have to perform 
  
    
      
        32
        ,
        768
      
    
    {\displaystyle 32,768}
  
 tests for each of the two possible outputs in order to find errors or edge cases. Because errors in functions with a high domain-to-range ratio are difficult to identify via manual testing or methods which reduce the number of tested inputs, such as orthogonal array testing or all-pairs testing, more computationally complex techniques may be used, such as fuzzing or static program analysis, to find errors.


== See also ==
Software testing
Formal verification


== References ==