I understand how equivalence testing works.
How is it the same or different from boundary value testing?
Equivalence Class Testing
EC Testing is when you have a number of test items (e.g. values) that you want to test but because of cost (time/money) you do not have time to test them all. Therefore you group the test item into class where all items in each class are suppose to behave exactly the same. The theory is that you only need to test one of each item to make sure the system works.
Example 1
Children under 2 ride the bus for free. Young people pay $10, Adults $15 and Senior Citizen pay $5.
Classes:
Price:0 -> Age:0-1
Price:10 -> Age:2-14
Price:15 -> Age:15-64
Price:5 -> Age:65-infinity
Example 2 (more than one parameter)
Cellphones K80, J64 and J54 run Java 5. K90 and J99 run Java 6. But there are two possible browsers FireFox and Opera, J models run FF and K models run O.
Classes:
Browser:FF, Java:5 -> Phones:J64,J54
Browser:FF, Java:6 -> Phones:J99
Browser:O, Java:5 -> Phones:K80
Browser:O, Java:6 -> Phones:K90
Dangers Of Equivalence Class Testing
There is a danger of using EC Testing that is rarely mentioned in the testing books but is very important to remember.
Just because two items/values are suppose to be in the same class and behave the same, does not mean they DO behave the same.
That means that just because you test one value in the class that ALL values in the class behave the same. Real world example of mine is with cell phones that all had a certain Java Platform. They were suppose to all work the same but they didn't in reality. So testing just one value in a class is good, but not good enough. EC Testing is a good tool, but it's not fool proof and be careful with it. If test cases are cheap and fast (like automation), test more, or why not test them all!
Boundary Value Testing
BV Testing is when you decide to test the values on the edge of each Class you have identified. The theory is that most defects is around the edges of a class.
Example
Classes:
Price:0 -> Age:0-1 ( Boundary values 0, 1)
Price:10 -> Age:2-14 ( Boundary values 2, 14)
Price:15 -> Age:15-64 ( Boundary values 15, 64)
Price:5 -> Age:65-infinity ( Boundary values 65)
Critique of Boundary Value Testing
1) I, and other test professionals I have taken courses from, are not convinced that most defects are hidden around the edges of each class. And I have never seen any studies that proves this to be the case.
2) The fact that you need to use BV Testing proves that EC Testing is flawed since you test more than one value of each class.
3) It's easy to use when using values like integers. But what is a boundary value of class of phones models or browsers versions?
Hidden Boundary Value Testing
The boundary values of a class is often based on the specification of how the system should work. This is all good and well but most systems contain boundaries that are not explained in any spec and you will need to look for yourself. E.g. 'How many characters can I put into the test field before the system fails and breaks.','How big can the data file become before it so slow to read it gets annoying'.
Real world examples
- Pasting one million characters into a text area in FireFox 3.5 on win 7 crashes it
- ReCaptcha has a limit of 16003 characters, does your system handle the 413 that it passes back to it if somebody puts 16004+ characters in field. Or does it break
Summary
EC Testing and BV Testing are great tools and you should use them but they are not perfect and don't expect to find all defects using them. Use your know-how about the system and your intelligence and intuition to try more items and looks for other ways it could fail. And look for the hidden boundaries!
Boundary value analysis simply means to select values near the boundaries of the classes. So you are still dividing the input domain according to the classes then instead of selecting values from the middle of the class use values from the boundaries.
For example, if the input condition is a range from 20 to 70 then you have three classes of input
less than 20
between 20 and 70
more than 70
then for boundary value analysis select input = 19, 20, 21, 69, 70, 71. This type of analysis picks up errors on the boundaries.
The Equivalence testing needs to be supplemented with the Boundary value testing.
For example for equivalent testing of a function that takes values between 1 and 12
(say months of a year) the partitions would be:
values less than 1 (0,-1,-2), invalid partition
values between 1-12, valid partition
values greater than 12,invalid partition
For equivalence testing it is enough to pick one value as test input from each of these partition classes. That would mean tests with value of -2,6, and 15 would be considered enough to test behavior of the function. But these values doesn't catch Off-by-one error which can occur quite often.
With the boundary value testing the test inputs would be : -1,0,1,11,12,13 (at the boundaries), which would catch off-by-one errors.
I see both these testing methods to be a complement of each other.
Boundary value analysis is part or subset of equivalence partitioning. In boundary values analysis, instead of some random value, only values in the boundary are selected.
Boundary value analysis overcome the drawback of the Equivalance class partitioning. If a fix length is g9iven for eg. Mobile number (10 digit.)
The lower boundary in this case is - digit - 1 (ie. 10 - 1 =9)
The upper boundary in this case is - digit +1 (ie 10 + 1 =11)
Now we can perform test for the 9 and 11
Dynamic Testing Types –
Specification Based testing
A. Equivalance Partitioning
A1. Boundary value analysis
A2. Decision Tables
A3. Use case Testing
A4. State Transition testing
Structural Based testing
A. Test Coverage
B. Code coverage
C. Statement coverage
D. Decision coverage
Experience Based Testing
A. Error testing
B. Exploratory Testing
Equivalance Partitioning – It is a technique where tester divide the test conditions into groups and sets. System should handle them equivalently hence called equivalence classes. To test one condition from each partition will work to assume all condition will work in that partition.
EX >> Check addition of the single digit values. i.e. values between 0 and 9.
Values less than -9, i.e. -10,-11, …. (Invalid partition)
Values less than 0, i.e. -1,-2, …. till -9 (Valid Partition)
Values between 0-9 i.e. 0,1 …. till 9 (Valid Partition)
Values greater than 9, i.e. 10,11 (Invalid partition)
Testing the addition for any two values of each partition is enough.
Boundary value testing – It is based on testing at the boundaries between partition.
EX >> Consider below combination.
Addition of -9 and -10,
Addition of -10 and -11
Addition of 0 and -1
Addition of 0 and 1
Addition of 9 and 10
Addition of 11 and 10
Related
I work in theoretical physics, and I have come upon a problem that requires the minimization of a particular Hamiltonian operator for a system of 8 particles, with one non-linear constraint. Due to the complexity of the system, I cannot define the entire Hamiltonian "in one go", nor the constraint. By this I mean that the quantity I am searching for is defined recurrently, depending on complex summations over quantities calculated for systems of 7 particles, which in turn depend on quantities calculated for systems of 6, and so on, until it reaches a one or two-particle system, for which said quantities are given as initial values, dependent on the elements of a column vector (the argument/minization parameters). The constraint itself is also of this form, requiring the "overlap" between the states of 8 particles to be exactly 1. (I.E. the state be normalized) I have been thinking of a way to use fmincon for this, but I've come up short, since my function has an implicit dependence on the parameters, and I can't write the whole thing explicitly. For a better understanding, here is some of the code:
for m=3:npairs+1
for n=3:npairs+1
for i=1:nsps
for j=1:nsps
overlap(m,n)=overlap(m,n)+x(i)*x(j)*(delta(i,j)*(overlap(m-1,n-1)-N(m-1,n-1,i))+p0p(m-1,n-1,j,i));
p(m,n,i)=(n-1)*x(i)*overlap(m,n-1)-(n-2)*(n-1)*x(i)*x(i)*((m-1)*x(i)*overlap(m-1,n-1)-(m-2)*(m-1)*x(i)*x(i)*p(m-1,n-1,i));
N(m,n,i)=2*(n-1)*x(i)*p(n-1,m,i);
p0p(m,n,i,j)=(m-1)*(n-1)*x(i)*x(j)*overlap(m-1,n-1)-(m-1)*(n-1)*(m-2)*x(i)*x(i)*x(j)*p(m-2,n-1,i)-(m-1)*(n-1)*(n-2)*x(i)*x(j)*x(j)*p0(m-1,n-2,j)-(m-1)*(n-1)*(m-2)*(n-2)*x(i)*x(i)*x(j)*x(j)*(delta(i,j)*(overlap(m-2,n-2)-N(m-2,n-2,i))+p0p(m-2,n-2,j,i));
endfor
endfor
endfor
endfor
function [E]=H(x)
E=summation over all i and j of N and p0p for m=n=8 %not actual code
endfunction
overlap(9,9)=1 %constraint
It's hard to give a specific answer, but I would advise the following to get you started.
First, note that, the inner two steps of the nest loop can be vectorised, since i and j always appear as indices (whereas m and n make backreferences, so they cannot be vectorised). So your 4-level loop can be reduced to a 2-level loop containing 4 functions operating over i-by-j matrices.
Second, note that the whole construct can be expressed as a recursive function. If you have suitable base cases for m = 0, n = 0, you can iteratively obtain all i,j matrices for all cases up to m=9,n=9. In particular, you can try to 'memoize' the early steps, and plug them into higher steps, rather than rely on actual recursion.
Assuming you need to sum with the first two indeces fixed to 8 (if I understood correctly), you can easily do with Anonymous Functions
https://octave.org/doc/v6.1.0/Anonymous-Functions.html#Anonymous-Functions
# creating same data
A=ones(8,8,4,4);
B=2*ones(8,8,4,4);
# defining 2 versions of sums
f = #(A,B) [sum(sum(A(8,8,:,:))), sum(sum(B(8,8,:,:)))];
g = #(A,B) sum(sum(A(8,8,:,:)))+ sum(sum(B(8,8,:,:)));
E1=f(A,B)
E2=g(A,B)
the output will be:
octave:21> E1=f(A,B)
E1 =
16 32
octave:22> E2=g(A,B)
E2 = 48
Recently, I'm quite excited when reading about the idea of property based testing.
But I have 1 question that I still cannot find the answer anywhere:
How can property based testing ensures that it will test the corner cases every time?
To be more specific, let say I'm using ScalaCheck to test my division function:
def divide(a: Int, b: Int): Int
As the test cases will be generated randomly, how can I be sure that ScalaCheck will check the case where b = 0 every time?
Special cases are often properties of their own. If you try to write a single case that covers b = any integer, then all your properties will end up in one big and complicated test. But you can split the parameter space into multiple chunks e.g.:
b = positive integer
b = negative integer
b = 0
And check them separately.
Some PBT tools will always inject corner cases before generating random ones.
For example, jqwik (for Java) would try 0, 1, -1, Integer.MIN…VALUE and Integer.MAX…VALUE before any random values.
What is pairwise testing? Is this method preferred over equivalence classes and boundary value testing? Does pairwise testing require the use of automated test case generation software?
pairwise testing is a combinatorial method of software testing that, for each pair of input parameters to a system (typically, a software algorithm), tests all possible discrete combinations of those parameters.
Here is a more detailed example: http://www.tutorialspoint.com/software_testing_dictionary/pairwise_testing.htm
The rest of your question is similar to this Equivalence Class Testing vs. Boundary Value Testing
Equivalence Class Testing
EC Testing is when you have a number of test items (e.g. values) that you want to test but because of cost (time/money) you do not have time to test them all. Therefore you group the test item into class where all items in each class are suppose to behave exactly the same. The theory is that you only need to test one of each item to make sure the system works.
Example 1
Children under 2 ride the buss for free. Young people pay $10, Adults $15 and Senior Citizen pay $5.
Classes:
Price:0 -> Age:0-1
Price:10 -> Age:2-14
Price:15 -> Age:15-64
Price:5 -> Age:65-infinity
Example 2 (more than one parameter)
Cellphones K80, J64 and J54 run Java 5. K90 and J99 run Java 6. But there are two possible browsers FireFox and Opera, J models run FF and K models run O.
Classes:
Browser:FF, Java:5 -> Phones:J64,J54
Browser:FF, Java:6 -> Phones:J99
Browser:O, Java:5 -> Phones:K80
Browser:O, Java:6 -> Phones:K90
Dangers Of Equivalence Class Testing
There is a danger of using EC Testing that is rarely mentioned in the testing books but is very important to remember.
Just because two items/values are suppose to be in the same class and behave the same, does not mean they DO behave the same.
That means that just because you test one value in the class that ALL values in the class behave the same. Real world example of mine is with cell phones that all had a certain Java Platform. They were suppose to all work the same but they didn't in reality. So testing just one value in a class is good, but not good enough. EC Testing is a good tool, but it's not fool proof and be careful with it. If test cases are cheap and fast (like automation), test more, or why not test them all!
Boundary Value Testing
BV Testing is when you decide to test the values on the edge of each Class you have identified. The theory is that most defects is around the edges of a class.
Example
Classes:
Price:0 -> Age:0-1 ( Boundary values 0, 1)
Price:10 -> Age:2-14 ( Boundary values 2, 14)
Price:15 -> Age:15-64 ( Boundary values 15, 64)
Price:5 -> Age:65-infinity ( Boundary values 65)
Pairwise testing is the method to test the application for all possible inputs combination.
In market lot of Pairwise Testing Tools are available use below link as -
EX >> system has ten configuration parameters, and every configuration parameter has ten different values. To test that system behaves correctly with all the different configurations(around 10 billion combination) is not possible.
with the help of tool like (Allpairs, PICT etc) find a small set of test cases to satisfy that coverage standard.
The proposal of pairwise testing for above example is that it is enough to test for all the possible value combinations for any two of the ten variables.
All pairs or pairwise testing is simpler then you think. If you have 10 inputs and each input has 5 equivalence classes. You calculate the number of pair inputs which is the inputs - 1 summed. so 9+8+7+6+5+4+3+2+1 = 45. Then you take the equivalence classes^2 so 5^2 and you get 25. Then you multiply 25*45 = 1125 test cases.
I hope this helps.
i am currenty studying BDD, but i have a different doubt, can you tell me if the following is right or not:
1) Feature = it means "the problem" isn't it?
2) Scenario = the way (the beahaviour) to resolve the feature
I find very difficult to find the "given when then" sentences.
In this problem for example:
As a student
I would like / i want to calculate the rectangle perimeters if i have 2 number
Or the circle area if i have one
So i don't make mistake with the computation
I wrote down the scenario, is that correct?
Given 1 number
Or 2 number
When i have 1 positive number
Or 2 positive number
Then calculate the area
Or the Perimeters
About the terminology:
1) feature is not a "problem". It would rather be a solution.
In software programming, a feature is a something that your program does to solve a problem.
A feature could be the ability to compute the area of a rectangle.
2) a scenario is a description of the usage of your feature. Like an example.
Like a test case, but usually in a more human-readable form.
3) a story (in Agile terminology, in which BDD stands) is a way to describe the a need/problem.
Your problem ("as a student...") is presented as a story.
This story will lead to a new feature in your soft.
This new feature will be tested by scenarios.
About your scenarios.
Yours are not correct.
There is no way to know that if you have 1 nb you should compute an area.
You should have several scenarios, like
Given I send the number 2
When I launch the computation
Then I get the result 12,56
Given I send the number 2 and 3
When I launch the computation
Then I get the result 10
Given I send the number -4
When I launch the computation
Then I get the result error
Given I send the number 1 3 7
When I launch the computation
Then I get the result error
This question already has answers here:
Closed 10 years ago.
Possible Duplicate:
Most efficient implementation of a large number class
Suppose I needed to calculate 2^150000. Obviously that number is going to exceed the size of an int, float, or double. How can I make a data type that allows normal math functions but exceeds the basic number types?
If this is a "depends which language you use" kind of deal. I will say C#.
See
Most efficient implementation of a large number class
for some leads.
If C# is not cast in stone, and you want something that just works out of the box, then there are several options. The one I know best is Python, but I think that languages like Scheme and Ruby support large numbers, too.
Python: 2**150000. Prints the result after about 1 second.
If you want free mathematics software, look at Maxima or Sage.
You might also consider using Frink, which is a language with the native capability of dealing with measurement units.
It computes 2^150000 without difficulty, deals with fractions (e.g. 1/3+2/5 --> 11/15), computes 3 meters + 2 inch --> 3.0508 m and is a full programming language.
Frink - Copyright 2000-2008 Alan Eliasen, eliasen#mindspring.com
http://futureboy.us/frinkdocs/
Several languages have built in support for arbitrary large numbers. You could use Mathematica, for example. I tried your example in Mathematica, and the result has 45,155 digits. I tried the same example with bc on a Unix machine. bc supports extended precision, but not that extended; it bombed on the example.
Lisp is your friend. Default biginteger numbers.
I find it very frustrating to use a language without arbitrarily large numbers: it seems nonsensical to be able to use ordinary operators like addition on most numbers, but to have to switch to method calls on a BigInt instance simply because of its size.
A whole bunch of languages have more complete numeric towers, and seamlessly coerce when needed; e.g., Allegro Common Lisp evaluates and prints all 45,155 digits of (expt 2 150000) in 1ms.
cl-user(2): (time (expt 2 150000))
; cpu time (non-gc) 0 msec user, 0 msec system
; cpu time (gc) 0 msec user, 0 msec system
; cpu time (total) 0 msec user, 0 msec system
; real time 1 msec
; space allocation:
; 2 cons cells, 18,784 other bytes, 0 static bytes
There is a product in C called calc which is an arbitrary precision calculator. I used it once when working as a researcher and found it fairly straightforward to use...
http://sourceforge.net/projects/calc/
It can be programmed for difficult or long calculations and can accept arguments from the command line. In interactive mode, it accepts one command at a time, and displays the answer.
Ordinarily the commands are simply expressions such as:
3 * (4 + 1)
and calc will print:
15
Calc does the arithmetic operators +, -, /, * as well as ^ (exponentiation), % (modulus) and // (integer divide).
For example:
3 * 19 ^ 43 - 1
will produce:
29075426613099201338473141505176993450849249622191102976
Calc values can be VERY large. For example:
2 ^ 23209 - 1
will print:
402874115778988778181873329071 ... loads of digits ... 3779264511
Hope this helps...
I don't know C# but I do know the Ruby programming language has the BigDemical class that seems to allow numbers of unlimited size.
Python has a bignum library. If you need to implement a bignum library in another language you can at least use the Python one as reference for validating your work. Note that bignums have a few implementation gotchas that aren't immediately obvious if you don't know what you're looking for.