random number generator code

Random Number Generator: How Do Computers Generate Random Numbers?

People have been using random numbers for millennia, so the concept isn't new. From the lottery in ancient Babylon, to roulette tables in Monte Carlo, to dice games in Vegas, the goal is to leave the end result up to random chance.

But gambling aside, randomness has many uses in science, statistics, cryptography and more. Yet using dice, coins, or similar media as a random device has its limitations.

Because of the mechanical nature of these techniques, generating large quantities of random numbers requires great deal of time and work. Thanks to human ingenuity, we have more powerful tools and methods at our disposal.

Methods for generating random numbers

True random numbers.

Let's consider two principal methods used to generate random numbers. The first method is based on a physical process, and harvests the source of randomness from some physical phenomenon that is expected to be random .

Such a phenomenon takes place outside of the computer. It is measured and adjusted for possible biases due to the measurement process. Examples include radioactive decay, the photoelectric effect, cosmic background radiation, atmospheric noise (which we will use in this article), and more.

Thus, random numbers generated based on such randomness are said to be " true " random numbers.

Technically, the hardware part consists of a device that converts energy from one form to another (for example, radiation to an electrical signal), an amplifier, and an analog-to-digital converter to turn the output into a digital number.

What are Pseudorandom Numbers?

As an alternative to "true" random numbers, the second method of generating random numbers involves computational algorithms that can produce apparently random results.

Why apparently random? Because the end results obtained are in fact completely determined by an initial value also known as the seed value or key . Therefore, if you knew the key value and how the algorithm works, you could reproduce these seemingly random results.

Random number generators of this type are frequently called Pseudorandom number generators and, as a result, output Pseudorandom Numbers.

Even though this type of generator typically doesn't gather any data from sources of naturally occurring randomness, such gathering of keys can be made possible when needed.

Let's compare some aspects of true random number generators or TRNG s and pseudorandom number generators or PRNG s.

PRNGs are faster than TRNGs. Because of their deterministic nature, they are useful when you need to replay a sequence of random events. This helps a great deal in code testing, for example.

On the other hand, TRNGs are not periodic and work better in security sensitive roles such as encryption.

A period is the number of iterations a PRNG goes through before it starts repeating itself. Thus, all other things being equal, a PRNG with a longer period would take more computer resources to predict and crack.

Example Algorithm for Pseudo-Random Number Generator

A computer executes code that is based on a set of rules to be followed. For PRNGs in general, those rules revolve around the following:

• Accept some initial input number, that is a seed or key.
• Apply that seed in a sequence of mathematical operations to generate the result. That result is the random number.
• Use that resulting random number as the seed for the next iteration.
• Repeat the process to emulate randomness.

Now let's look at an example.

The Linear Congruential Generator

This generator produces a series of pseudorandom numbers. Given an initial seed X 0 and integer parameters a as the multiplier, b as the increment, and m as the modulus, the generator is defined by the linear relation: X n ≡ (aX n-1 + b)mod m . Or using more programming friendly syntax: X n = (a * X n-1 + b) % m .

Each of these members have to satisfy the following conditions:

• m > 0 (the modulus is positive),
• 0 < a < m (the multiplier is positive but less than the modulus),
• 0 ≤ b < m (the increment is non negative but less than the modulus), and
• 0 ≤ X 0 < m (the seed is non negative but less than the modulus).

Let's create a JavaScript function that takes the initial values as arguments and returns an array of random numbers of a given length:

The Linear Congruential Generator is one of the oldest and best-known PRNG algorithms.

As for random number generator algorithms that are executable by computers, they date back as early as the 1940s and 50s (the Middle-square method and Lehmer generator , for example) and continue to be written today ( Xoroshiro128+ , Squares RNG , and more).

A Sample Random Number Generator

When I decided to write this article about embedding a random number generator within a web page, I had a choice to make.

I could've used JavaScript's Math.random() function as the base and generate output in pseudorandom numbers like I have in earlier articles (see Multiplication Chart - Code Your Own Times Table ).

But this article itself is about generating random numbers. So I decided to learn how to gather "true" randomness based data and share my discovery with you.

So below is the "true" Random Number Generator. Set the parameters and hit Generate.

The code fetches data from one of the APIs, courtesy of Random.org . This online resource has a plethora of useful, customizable tools and comes with excellent documentation to go with it.

The randomness comes from atmospheric noise. I was able to use asynchronous functions. That is a huge benefit going forward. The core function looks like this:

The parameters it takes allow a user to customize random number output. For example, min and max allow you to set lower and upper limits on generated output. And base determines if the output is printed as binary, decimal or hexadecimal.

Again, I chose this configuration but there are many more available at the source .

When you click the Generate button, the handleGenerate() function is called. It in turn invokes the getRandom() asynchronous function, manages error handling, and outputs results:

The rest of the code deals with HTML structure, appearance, and styling.

The code is ready to be embedded and used within this web page. I separated it into component parts and supplied it with detailed comments. It can easily be modified. You can also modify the functionality and styles as your needs require.

This is the link to the GitHub repo of the complete code: https://github.com/sandroarobeli/random-generator

The fascination with the world of Mathematics provides a great service in my journey of becoming a successful developer. I am excited about the idea of helping others acquire high quality resources.

If you read this far, thank the author to show them you care. Say Thanks

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random — Generate pseudo-random numbers ¶

Source code: Lib/random.py

This module implements pseudo-random number generators for various distributions.

For integers, there is uniform selection from a range. For sequences, there is uniform selection of a random element, a function to generate a random permutation of a list in-place, and a function for random sampling without replacement.

On the real line, there are functions to compute uniform, normal (Gaussian), lognormal, negative exponential, gamma, and beta distributions. For generating distributions of angles, the von Mises distribution is available.

Almost all module functions depend on the basic function random() , which generates a random float uniformly in the half-open range 0.0 <= X < 1.0 . Python uses the Mersenne Twister as the core generator. It produces 53-bit precision floats and has a period of 2**19937-1. The underlying implementation in C is both fast and threadsafe. The Mersenne Twister is one of the most extensively tested random number generators in existence. However, being completely deterministic, it is not suitable for all purposes, and is completely unsuitable for cryptographic purposes.

The functions supplied by this module are actually bound methods of a hidden instance of the random.Random class. You can instantiate your own instances of Random to get generators that don’t share state.

Class Random can also be subclassed if you want to use a different basic generator of your own devising: in that case, override the random() , seed() , getstate() , and setstate() methods. Optionally, a new generator can supply a getrandbits() method — this allows randrange() to produce selections over an arbitrarily large range.

The random module also provides the SystemRandom class which uses the system function os.urandom() to generate random numbers from sources provided by the operating system.

The pseudo-random generators of this module should not be used for security purposes. For security or cryptographic uses, see the secrets module.

M. Matsumoto and T. Nishimura, “Mersenne Twister: A 623-dimensionally equidistributed uniform pseudorandom number generator”, ACM Transactions on Modeling and Computer Simulation Vol. 8, No. 1, January pp.3–30 1998.

Complementary-Multiply-with-Carry recipe for a compatible alternative random number generator with a long period and comparatively simple update operations.

Bookkeeping functions ¶

Initialize the random number generator.

If a is omitted or None , the current system time is used. If randomness sources are provided by the operating system, they are used instead of the system time (see the os.urandom() function for details on availability).

If a is an int, it is used directly.

With version 2 (the default), a str , bytes , or bytearray object gets converted to an int and all of its bits are used.

With version 1 (provided for reproducing random sequences from older versions of Python), the algorithm for str and bytes generates a narrower range of seeds.

Changed in version 3.2: Moved to the version 2 scheme which uses all of the bits in a string seed.

Changed in version 3.11: The seed must be one of the following types: NoneType , int , float , str , bytes , or bytearray .

Return an object capturing the current internal state of the generator. This object can be passed to setstate() to restore the state.

state should have been obtained from a previous call to getstate() , and setstate() restores the internal state of the generator to what it was at the time getstate() was called.

Functions for bytes ¶

Generate n random bytes.

This method should not be used for generating security tokens. Use secrets.token_bytes() instead.

New in version 3.9.

Functions for integers ¶

Return a randomly selected element from range(start, stop, step) .

This is roughly equivalent to choice(range(start, stop, step)) but supports arbitrarily large ranges and is optimized for common cases.

The positional argument pattern matches the range() function.

Keyword arguments should not be used because they can be interpreted in unexpected ways. For example randrange(start=100) is interpreted as randrange(0, 100, 1) .

Changed in version 3.2: randrange() is more sophisticated about producing equally distributed values. Formerly it used a style like int(random()*n) which could produce slightly uneven distributions.

Changed in version 3.12: Automatic conversion of non-integer types is no longer supported. Calls such as randrange(10.0) and randrange(Fraction(10, 1)) now raise a TypeError .

Return a random integer N such that a <= N <= b . Alias for randrange(a, b+1) .

Returns a non-negative Python integer with k random bits. This method is supplied with the Mersenne Twister generator and some other generators may also provide it as an optional part of the API. When available, getrandbits() enables randrange() to handle arbitrarily large ranges.

Changed in version 3.9: This method now accepts zero for k .

Functions for sequences ¶

Return a random element from the non-empty sequence seq . If seq is empty, raises IndexError .

Return a k sized list of elements chosen from the population with replacement. If the population is empty, raises IndexError .

If a weights sequence is specified, selections are made according to the relative weights. Alternatively, if a cum_weights sequence is given, the selections are made according to the cumulative weights (perhaps computed using itertools.accumulate() ). For example, the relative weights [10, 5, 30, 5] are equivalent to the cumulative weights [10, 15, 45, 50] . Internally, the relative weights are converted to cumulative weights before making selections, so supplying the cumulative weights saves work.

If neither weights nor cum_weights are specified, selections are made with equal probability. If a weights sequence is supplied, it must be the same length as the population sequence. It is a TypeError to specify both weights and cum_weights .

The weights or cum_weights can use any numeric type that interoperates with the float values returned by random() (that includes integers, floats, and fractions but excludes decimals). Weights are assumed to be non-negative and finite. A ValueError is raised if all weights are zero.

For a given seed, the choices() function with equal weighting typically produces a different sequence than repeated calls to choice() . The algorithm used by choices() uses floating point arithmetic for internal consistency and speed. The algorithm used by choice() defaults to integer arithmetic with repeated selections to avoid small biases from round-off error.

New in version 3.6.

Changed in version 3.9: Raises a ValueError if all weights are zero.

Shuffle the sequence x in place.

To shuffle an immutable sequence and return a new shuffled list, use sample(x, k=len(x)) instead.

Note that even for small len(x) , the total number of permutations of x can quickly grow larger than the period of most random number generators. This implies that most permutations of a long sequence can never be generated. For example, a sequence of length 2080 is the largest that can fit within the period of the Mersenne Twister random number generator.

Deprecated since version 3.9, removed in version 3.11: The optional parameter random .

Return a k length list of unique elements chosen from the population sequence. Used for random sampling without replacement.

Returns a new list containing elements from the population while leaving the original population unchanged. The resulting list is in selection order so that all sub-slices will also be valid random samples. This allows raffle winners (the sample) to be partitioned into grand prize and second place winners (the subslices).

Members of the population need not be hashable or unique. If the population contains repeats, then each occurrence is a possible selection in the sample.

Repeated elements can be specified one at a time or with the optional keyword-only counts parameter. For example, sample(['red', 'blue'], counts=[4, 2], k=5) is equivalent to sample(['red', 'red', 'red', 'red', 'blue', 'blue'], k=5) .

To choose a sample from a range of integers, use a range() object as an argument. This is especially fast and space efficient for sampling from a large population: sample(range(10000000), k=60) .

If the sample size is larger than the population size, a ValueError is raised.

Changed in version 3.9: Added the counts parameter.

Changed in version 3.11: The population must be a sequence. Automatic conversion of sets to lists is no longer supported.

Discrete distributions ¶

The following function generates a discrete distribution.

Binomial distribution . Return the number of successes for n independent trials with the probability of success in each trial being p :

Mathematically equivalent to:

The number of trials n should be a non-negative integer. The probability of success p should be between 0.0 <= p <= 1.0 . The result is an integer in the range 0 <= X <= n .

New in version 3.12.

Real-valued distributions ¶

The following functions generate specific real-valued distributions. Function parameters are named after the corresponding variables in the distribution’s equation, as used in common mathematical practice; most of these equations can be found in any statistics text.

Return the next random floating point number in the range 0.0 <= X < 1.0

Return a random floating point number N such that a <= N <= b for a <= b and b <= N <= a for b < a .

The end-point value b may or may not be included in the range depending on floating-point rounding in the equation a + (b-a) * random() .

Return a random floating point number N such that low <= N <= high and with the specified mode between those bounds. The low and high bounds default to zero and one. The mode argument defaults to the midpoint between the bounds, giving a symmetric distribution.

Beta distribution. Conditions on the parameters are alpha > 0 and beta > 0 . Returned values range between 0 and 1.

Exponential distribution. lambd is 1.0 divided by the desired mean. It should be nonzero. (The parameter would be called “lambda”, but that is a reserved word in Python.) Returned values range from 0 to positive infinity if lambd is positive, and from negative infinity to 0 if lambd is negative.

Changed in version 3.12: Added the default value for lambd .

Gamma distribution. ( Not the gamma function!) The shape and scale parameters, alpha and beta , must have positive values. (Calling conventions vary and some sources define ‘beta’ as the inverse of the scale).

The probability distribution function is:

Normal distribution, also called the Gaussian distribution. mu is the mean, and sigma is the standard deviation. This is slightly faster than the normalvariate() function defined below.

Multithreading note: When two threads call this function simultaneously, it is possible that they will receive the same return value. This can be avoided in three ways. 1) Have each thread use a different instance of the random number generator. 2) Put locks around all calls. 3) Use the slower, but thread-safe normalvariate() function instead.

Changed in version 3.11: mu and sigma now have default arguments.

Log normal distribution. If you take the natural logarithm of this distribution, you’ll get a normal distribution with mean mu and standard deviation sigma . mu can have any value, and sigma must be greater than zero.

Normal distribution. mu is the mean, and sigma is the standard deviation.

mu is the mean angle, expressed in radians between 0 and 2* pi , and kappa is the concentration parameter, which must be greater than or equal to zero. If kappa is equal to zero, this distribution reduces to a uniform random angle over the range 0 to 2* pi .

Pareto distribution. alpha is the shape parameter.

Weibull distribution. alpha is the scale parameter and beta is the shape parameter.

Alternative Generator ¶

Class that implements the default pseudo-random number generator used by the random module.

Deprecated since version 3.9, removed in version 3.11: Formerly the seed could be any hashable object. Now it is limited to: NoneType , int , float , str , bytes , or bytearray .

Class that uses the os.urandom() function for generating random numbers from sources provided by the operating system. Not available on all systems. Does not rely on software state, and sequences are not reproducible. Accordingly, the seed() method has no effect and is ignored. The getstate() and setstate() methods raise NotImplementedError if called.

Notes on Reproducibility ¶

Sometimes it is useful to be able to reproduce the sequences given by a pseudo-random number generator. By reusing a seed value, the same sequence should be reproducible from run to run as long as multiple threads are not running.

Most of the random module’s algorithms and seeding functions are subject to change across Python versions, but two aspects are guaranteed not to change:

If a new seeding method is added, then a backward compatible seeder will be offered.

The generator’s random() method will continue to produce the same sequence when the compatible seeder is given the same seed.

Basic examples:

Simulations:

Example of statistical bootstrapping using resampling with replacement to estimate a confidence interval for the mean of a sample:

Example of a resampling permutation test to determine the statistical significance or p-value of an observed difference between the effects of a drug versus a placebo:

Simulation of arrival times and service deliveries for a multiserver queue:

Statistics for Hackers a video tutorial by Jake Vanderplas on statistical analysis using just a few fundamental concepts including simulation, sampling, shuffling, and cross-validation.

Economics Simulation a simulation of a marketplace by Peter Norvig that shows effective use of many of the tools and distributions provided by this module (gauss, uniform, sample, betavariate, choice, triangular, and randrange).

A Concrete Introduction to Probability (using Python) a tutorial by Peter Norvig covering the basics of probability theory, how to write simulations, and how to perform data analysis using Python.

These recipes show how to efficiently make random selections from the combinatoric iterators in the itertools module:

The default random() returns multiples of 2⁻⁵³ in the range 0.0 ≤ x < 1.0 . All such numbers are evenly spaced and are exactly representable as Python floats. However, many other representable floats in that interval are not possible selections. For example, 0.05954861408025609 isn’t an integer multiple of 2⁻⁵³.

The following recipe takes a different approach. All floats in the interval are possible selections. The mantissa comes from a uniform distribution of integers in the range 2⁵² ≤ mantissa < 2⁵³ . The exponent comes from a geometric distribution where exponents smaller than -53 occur half as often as the next larger exponent.

All real valued distributions in the class will use the new method:

The recipe is conceptually equivalent to an algorithm that chooses from all the multiples of 2⁻¹⁰⁷⁴ in the range 0.0 ≤ x < 1.0 . All such numbers are evenly spaced, but most have to be rounded down to the nearest representable Python float. (The value 2⁻¹⁰⁷⁴ is the smallest positive unnormalized float and is equal to math.ulp(0.0) .)

Generating Pseudo-random Floating-Point Values a paper by Allen B. Downey describing ways to generate more fine-grained floats than normally generated by random() .

Table of Contents

• Bookkeeping functions
• Functions for bytes
• Functions for integers
• Functions for sequences
• Discrete distributions
• Real-valued distributions
• Alternative Generator
• Notes on Reproducibility

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fractions — Rational numbers

statistics — Mathematical statistics functions

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How to Generate a Random Number in Python

The aim of a programmer while creating a program is to ensure that the program stands the test for any random input. The program should correctly process the input and accurately calculate the output for any arbitrary data. A programmer must test the program for a wide range of information and amend the code accordingly to achieve this ambition.

But how do you choose a random number from the infinite possibilities available to you? Even if you have got a set of numbers, how do you change it into an efficient program? Are there any in-built functions to achieve this? Well, the answer is Yes!

Python offers a large number of modules and functions to use random data. This article will guide you to include these functions in your code and provide code snippets for your convenience. We’ll keep our range limited to {1,10} but remember, you can use these methods and programming syntax for any range you prefer. Let’s get started!

Python library used: Anaconda Distribution (Jupyter notebook)

List Of Functions Available To Generate Random Numbers:

• random.randint() function
• random.randrange() function
• random.sample() function
• random.uniform() function
• numpy.random.randint() function
• numpy.random.uniform() function
• numpy.random.choice() function
• secrets.randbelow() function

Using the ‘ random.randint() ’ function :

random.randint() function is a part of the random module. The randint() function returns an integer value(of course, random!) between the starting and ending point entered in the function. This function is inclusive of both the endpoints entered.

We can write the code as follows:

The output of this program is as follows:

The function returns the number 5 as a random output. Note that here we have generated only a single random number. You can also create a list of random numbers. The code for generating a list of random numbers is as shown below:

The output is also shown in the code snippet given above. For loop can be used to generate a list.

Using the ‘ random.randrange() ’ function :

This function is similar to the randint() function. This function includes the step parameter and excludes the upper limit entered in the function. The step parameter is optional and is used to exclude a particular value in the given range. The default value of this parameter is 1.

The code given here prints the single random value as well as the list of random values.

The output is shown below:

As we can see here, the first line gives a single-digit output, whereas the following line gives a list of values. 

Using the ‘ random.sample() ’ function :

We use the sample() function to create a list that has the length of our choice. Also, it returns a list that has no repeated values.

Note that the syntax of this function uses the range() parameter to obtain the desired starting and ending values. Moreover, to generate a single-digit output, we have to enter ‘1’ as the list length beside the range() parameter. 

The output we obtain is as follows:

Using the ‘ random.uniform() ’ function :

We use the uniform() function to find floating-point numbers between the given range. This function is inclusive of both the endpoints of the given range.

The syntax of this code is the same as those mentioned for previous functions.

The output of this code is a floating-point number.

To obtain the output as an integer, we can specially typecast the uniform() function.

Typecasting the function gives integer output.

Using the ‘ numpy.random.randint() ’ function :

The numpy module also has the sub-module random .  We can use the numpy module when we want to generate a large number of numbers. This module stores the output in an array of the desired size.

The randint() method is used similarly as in the random module. 

The syntax for this module is as follows:

In the output of this code, we will obtain an array of random numbers.

As you can see, an array of size six is generated.

Using the ‘ numpy.random.uniform() ’ function :

The numpy module also has the uniform() function to generate an array of floating-point numbers.

Using the ‘ numpy.random.choice() ’ function :

This function is used to obtain random numbers when we already have a list of numbers, and we have to choose a random number from that specific list. This function also stores the output in an array.

We can write the input of this function as follows:

Notice the arbitrary order of numbers in the user-entered list.

Let's see what the output of the given code is:

Using the ‘ secrets.randbelow() ’ function :

The secrets module is the most secure method to generate random numbers and finds excellent use in cryptography. One application of this module is to create strong, secure random passwords, tokens etc.

The randbelow() function is inclusive of both the limits entered in the function.

The syntax of this module is as follows:

Conclusion 

The use of random test cases is immense in programming. The built-in functions of several programming languages make it easier for us- the programmers to execute millions of arbitrary test cases and develop an efficient and accurate program. Python also offers a module for application in cryptography, as we have seen above. This module is beneficial if we want to create user-secure platforms. We hope this article helped you in learning the basics of random number generation.  

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Python Program to Generate a Random Number

To understand this example, you should have the knowledge of the following Python programming topics:

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To generate random number in Python, randint() function is used. This function is defined in random module .

Source Code

Note that we may get different output because this program generates random number in range 0 and 9. The syntax of this function is:

This returns a number N in the inclusive range [a,b] , meaning a <= N <= b , where the endpoints are included in the range.

Sorry about that.

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Using Random Numbers

The randomNumber() block can be used to generate random numbers in your programs. The parameters set the minimum and maximum value that could be generated. You can use this block anywhere that you could write a number.

This example is like a die that could randomly generate any number from 1 to 6

Drawing and Random Numbers

You can use randomNumber() as a parameter in drawing commands to make random drawings. With the following command, your program might generate different drawings each time it's run.

Multiple Random Numbers

If you use randomNumber() multiple times in your program it will generate new random numbers every time. You can think of each randomNumber() like a new roll of a die.

Found a bug in the documentation? Let us know at [email protected]

Random Number Generator

This version of the generator creates a random integer. It can deal with very large integers up to a few thousand digits.

Comprehensive Version

This version of the generator can create one or many random integers or decimals. It can deal with very large numbers with up to 999 digits of precision.

A random number is a number chosen from a pool of limited or unlimited numbers that has no discernible pattern for prediction. The pool of numbers is almost always independent from each other. However, the pool of numbers may follow a specific distribution. For example, the height of the students in a school tends to follow a normal distribution around the median height. If the height of a student is picked at random, the picked number has a higher chance to be closer to the median height than being classified as very tall or very short. The random number generators above assume that the numbers generated are independent of each other, and will be evenly spread across the whole range of possible values.

A random number generator, like the ones above, is a device that can generate one or many random numbers within a defined scope. Random number generators can be hardware based or pseudo-random number generators. Hardware based random-number generators can involve the use of a dice, a coin for flipping, or many other devices.

A pseudo-random number generator is an algorithm for generating a sequence of numbers whose properties approximate the properties of sequences of random numbers. Computer based random number generators are almost always pseudo-random number generators. Yet, the numbers generated by pseudo-random number generators are not truly random. Likewise, our generators above are also pseudo-random number generators. The random numbers generated are sufficient for most applications yet they should not be used for cryptographic purposes. True random numbers are based on physical phenomena such as atmospheric noise, thermal noise, and other quantum phenomena. Methods that generate true random numbers also involve compensating for potential biases caused by the measurement process.

JS Tutorial

Js versions, js functions, js html dom, js browser bom, js web apis, js vs jquery, js graphics, js examples, js references, javascript random, math.random().

Math.random() returns a random number between 0 (inclusive),  and 1 (exclusive):

Math.random() always returns a number lower than 1.

JavaScript Random Integers

Math.random() used with Math.floor() can be used to return random integers.

There is no such thing as JavaScript integers.

We are talking about numbers with no decimals here.

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A Proper Random Function

As you can see from the examples above, it might be a good idea to create a proper random function to use for all random integer purposes.

This JavaScript function always returns a random number between min (included) and max (excluded):

This JavaScript function always returns a random number between min and max (both included):

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Rnd function

• 8 contributors

Returns a Single containing a pseudo-random number.

Rnd [ ( Number ) ]

The optional Number argument is a Single or any valid numeric expression .

Return values

The Rnd function returns a value less than 1 but greater than or equal to zero.

The value of Number determines how Rnd generates a pseudo-random number:

For any given initial seed, the same number sequence is generated because each successive call to the Rnd function uses the previous number as a seed for the next number in the sequence.

Before calling Rnd , use the Randomize statement without an argument to initialize the random-number generator with a seed based on the system timer.

To produce random integers in a given range, use this formula:

Here, upperbound is the highest number in the range, and lowerbound is the lowest number in the range.

To repeat sequences of random numbers, call Rnd with a negative argument immediately before using Randomize with a numeric argument. Using Randomize with the same value for Number does not repeat the previous sequence.

This example uses the Rnd function to generate a random integer value from 1 to 6.

• Functions (Visual Basic for Applications)

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Additional resources

Random number generator (included)

The task is to:

Note: the task is not to create an RNG, but to report on the languages in-built RNG that would be the most likely RNG used.

The main types of pseudo-random number generator ( PRNG ) that are in use are the Linear Congruential Generator ( LCG ), and the Generalized Feedback Shift Register ( GFSR ), (of which the Mersenne twister generator is a subclass). The last main type is where the output of one of the previous ones (typically a Mersenne twister) is fed through a cryptographic hash function to maximize unpredictability of individual bits.

Note that neither LCGs nor GFSRs should be used for the most demanding applications (cryptography) without additional steps.

11l uses a linear congruential generator accessed via the built-in random module .

The default random number generator in 8th is a cryptographically strong one using Fortuna , which is seeded from the system's entropy provider. An additional random generator (which is considerably faster) is a PCG , though it is not cryptographically strong.

• ActionScript

In both Actionscript 2 and 3, the type of pseudorandom number generator is implementation-defined. This number generator is accessed through the Math.random() function, which returns a double greater than or equal to 0 and less than 1. [1] [2] In Actionscript 2, the global random() function returns an integer greater than or equal to 0 and less than the given argument, but it is deprecated and not recommended. [3]

The Ada standard defines Random Number Generation in Annex A.5.2. There are two kinds of RNGs, Ada.Numerics.Float_Random for floating point values from 0.0 to 1.0, and Ada.Numerics.Discrete_Random for pseudo-random values of enumeration types (including integer types). It provides facilities to initialize the generator and to save it's state.

The standard requires the implementation to uniformly distribute over the range of the result type.

The used algorithm is implementation defined. The standard says: "To enable the user to determine the suitability of the random number generators for the intended application, the implementation shall describe the algorithm used and shall give its period, if known exactly, or a lower bound on the period, if the exact period is unknown."

• Ada 95 RM - A.5.2 Random Number Generation
• Ada 2005 RM - A.5.2 Random Number Generation
• Ada 2012 RM - A.5.2 Random Number Generation

Details of the random number generator are in the Revised Reports sections: 10.2.1. and 10.5.1.

• 10.2. The standard prelude - 10.2.1. Environment enquiries
• 10.5. The particular preludes and postlude - 10.5.1. The particular preludes

Note the suitable "next random number" is suggested to be: ( a := ¢ the next pseudo-random ℒ integral value after 'a' from a uniformly distributed sequence on the interval [ℒ 0,ℒ maxint] ¢; ¢ the real value corresponding to 'a' according to some mapping of integral values [ℒ 0, ℒ max int] into real values [ℒ 0, ℒ 1) i.e., such that -0 <= x < 1 such that the sequence of real values so produced preserves the properties of pseudo-randomness and uniform distribution of the sequence of integral values ¢);

Algol68 supports random number generation for all precisions available for the specific implementation. The prefix ℒ real indicates all the available precisions. eg short short real , short real , real , long real , long long real etc

For an ASCII implementation and for long real precision these routines would appears as:

The built-in random is based on Nim's random number generator and, thus, in turn based on xoroshiro128+ (xor/rotate/shift/rotate), see here .

The built-in command Random generates a pseudo-random number using Mersenne Twister "MT19937" (see documentation).

The built-in command "rand" generates a pseudo-random uniform distributed random variable. More information is available from the documentation of gawk .

It is important that the RNG is seeded with the funtions "srand", otherwise, the same random number is produced.

Example usage: see #UNIX_Shell

The RND function generates a pseudo random number greater than or equal to zero, but less than one. The implementation is machine specific based on contents of the ROM and there is no fixed algorithm.

Windows batch files can use the %RANDOM% pseudo-variable which returns a pseudo-random number between 0 and 32767. Behind the scenes this is just a call to the C runtime's rand() function which uses an LCG in this case:

The RND function uses a 33-bit maximal-length Linear Feedback Shift Register (LFSR), with 32-bits being used to provide the result. Hence the sequence length is 2^33-1, during which the value zero is returned once and all non-zero 32-bit values are each returned twice.

The ? instruction usually uses the random number generator in the interpreter's language. The original interpreter is written in C and uses rand().

Standard C has rand(). Some implementations of C have other sources of random numbers, along with rand().

The C standard specifies the interface to the rand() and srand() functions in <stdlib.h>.

• void srand(unsigned int seed) begins a new sequence of pseudorandom integers.
• RAND_MAX must be at least 32767.

The same seed to srand() reproduces the same sequence. The default seed is 1, when a program calls rand() without calling srand(); so srand(1) reproduces the default sequence. ( n1124.pdf )

There are no requirements as to the algorithm to be used for generating the random numbers. All versions of rand() return integers that are uniformly distributed in the interval from 0 to RAND_MAX, but some algorithms have problems in their randomness. For example, the cycle might be too short, or the probabilities might not be independent.

Many popular C libraries implement rand() with a linear congruential generator . The specific multiplier and constant varies by implementation, as does which subset of bits within the result is returned as the random number. These rand() functions should not be used where a good quality random number generator is required.

FreeBSD switched to a different formula, but NetBSD and OpenBSD stayed with this formula. ( NetBSD rand.c , OpenBSD rand.c )

If the C compiler uses BSD rand(), then this program has only two possible outputs.

• At even seconds: heads, tails, heads, tails, heads, tails, heads, tails, heads, tails.
• At odd seconds: tails, heads, tails, heads, tails, heads, tails, heads, tails, heads.

The low bit manages a uniform distribution between heads and tails, but it has a period length of only 2: it can only flip a coin 2 times before it must repeat itself. Therefore it must alternate heads and tails. This is not a real coin, and these are not truly random flips.

In general, the low bits from BSD rand() are much less random than the high bits. This defect of BSD rand() is so famous that some programs ignore the low bits from rand().

Microsoft rand()

Microsoft sets RAND_MAX to 32767 and uses this linear congruential formula:

POSIX drand48()

POSIX adds the drand48() family to <stdlib.h>.

• void srand48(long seed) begins a new sequence.
• double drand48(void) returns a random double in [0.0, 1.0).
• long lrand48(void) returns a random long in [0, 2**31).
• long mrand48(void) returns a random long in [-2**31, 2**31).

This family uses a 48-bit linear congruential generator with this formula:

The .NET Random class says that it uses Knuth's subtractive random number generator algorithm. [4]

As part of the C++11 specification the language now includes various forms of random number generation.

While the default engine is implementation specific (ex, unspecified), the following Pseudo-random generators are available in the standard:

• Linear congruential (minstd_rand0, minstd_rand)
• Mersenne twister (mt19937, mt19937_64)
• Subtract with carry (ranlux24_base, ranlux48_base)
• Discard block (ranlux24, ranlux48)
• Shuffle order (knuth_b)

Additionally, the following distributions are supported:

• Uniform distributions: uniform_int_distribution, uniform_real_distribution
• Bernoulli distributions: bernoulli_distribution, geometric_distribution, binomial_distribution, negative_binomial_distribution
• Poisson distributions: poisson_distribution, gamma_distribution, exponential_distribution, weibull_distribution, extreme_value_distribution
• Normal distributions: normal_distribution, fisher_f_distribution, cauchy_distribution, lognormal_distribution, chi_squared_distribution, student_t_distribution
• Sampling distributions: discrete_distribution, piecewise_linear_distribution, piecewise_constant_distribution

Example of use:

When using the Random module , Chapel defaults to a Permuted Linear Congruential Random Number Generator .

CMake has a random string generator.

The current implementation (in cmStringCommand.cxx and cmSystemTools.cxx ) calls rand() and srand() from C . It picks random letters from the alphabet. The probability of each letter is near 1 ÷ length , but the implementation uses floating-point arithmetic to map RAND_MAX + 1 values onto length letters, so there is a small modulo bias when RAND_MAX + 1 is not a multiple of length .

CMake 2.6.x has bug #9851 ; two random strings might be equal because they use the same seed. CMake 2.8.0 fixes this bug by seeding the random generator only once, during the first call to string(RANDOM ...) .

CMake 2.8.5 tries a secure seed (CryptGenRandom or /dev/urandom) or falls back to high-resolution system time . Older versions seed the random generator with time(NULL) , the current time in seconds.

• Common Lisp

The easiest way to generate random numbers in Common Lisp is to use the built-in rand function after seeding the random number generator. For example, the first line seeds the random number generator and the second line generates a number from 0 to 9

Common Lisp: The Language, 2nd Ed. does not specify a specific random number generator algorithm, nor a way to use a user-specified seed.

From std.random:

The generators feature a number of well-known and well-documented methods of generating random numbers. An overall fast and reliable means to generate random numbers is the Mt19937 generator, which derives its name from " Mersenne Twister with a period of 2 to the power of 19937". In memory-constrained situations, linear congruential generators such as MinstdRand0 and MinstdRand might be useful. The standard library provides an alias Random for whichever generator it considers the most fit for the target environment.

According to Wikipedia , Delphi uses a Linear Congruential Generator.

Random functions:

Based on the values given in the wikipedia entry here is a Delphi compatible implementation for use in other pascal dialects.

DWScript currently uses a 64bit XorShift PRNG, which is a fast and light form of GFSR.

The standard implementation, vu , uses a Mersenne twister.

EchoLisp uses an ARC4 (or RCA4) implementation by David Bau, which replaces the JavaScript Math.random(). Thanks to him. [5] . Some examples :

ELENA 6.x :

Elixir does not come with its own module for random number generation. But you can use the appropriate Erlang functions instead. Some examples:

For further information, read the Erlang section.

Random number generator. The method is attributed to B.A. Wichmann and I.D.Hill, in 'An efficient and portable pseudo-random number generator', Journal of Applied Statistics. AS183. 1982. Also Byte March 1987.

The current algorithm is a modification of the version attributed to Richard A O'Keefe in the standard Prolog library.

Every time a random number is requested, a state is used to calculate it, and a new state produced. The state can either be implicit (kept in the process dictionary) or be an explicit argument and return value. In this implementation, the state (the type ran()) consists of a tuple of three integers.

It should be noted that this random number generator is not cryptographically strong. If a strong cryptographic random number generator is needed for example crypto:rand_bytes/1 could be used instead.

Seed with a fixed known value triplet A1, A2, A3:

Example with the running time:

Get a random float value between 0.0 and 1.0:

Get a random integer value between 1 and N (N is an integer >= 1):

• Euler Math Toolbox

Bays and Durham as describend in Knuth's book.

The default RNG used when the random vocabulary is used, is the Mersenne twister algorithm [6] . But there are other RNGs available, including SFMT , the system RNG ( /dev/random on Unix) and Blum Blum Shub . It's also very easy to implement your own RNG and integrate it into the system. [7]

Fortran has intrinsic random_seed() and random_number() subroutines. Used algorithm of the pseudorandom number generator is compiler dependent (not specified in ISO Fortran Standard, see ISO/IEC 1539-1:2010 (E), 13.7.135 RANDOM NUMBER). For algorithm in GNU gfortran see https://gcc.gnu.org/onlinedocs/gfortran/RANDOM_005fNUMBER.html Note that with the GNU gfortran compiler program needs to call random_seed with a random PUT= argument to get a pseudorandom number otherwise the sequence always starts with the same number. Intel compiler ifort reinitializes the seed randomly without PUT argument to random value using the system date and time. Here we are seeding random_seed() with some number obtained from the Linux urandom device.

• Free Pascal

FreeBASIC has a Rnd() function which produces a pseudo-random double precision floating point number in the half-closed interval [0, 1) which can then be easily used to generate pseudo-random numbers (integral or decimal) within any range.

The sequence of pseudo-random numbers can either by seeded by a parameter to the Rnd function itself or to the Randomize statement and, if omitted, uses a seed based on the system timer.

However, a second parameter to the Randomize statement determines which of 5 different algorithms is used to generate the pseudo-random numbers:

1. Uses the C runtime library's rand() function (based on LCG) which differs depending on the platform but produces a low degree of randomness.

2. Uses a fast, platform independent, algorithm with 32 bit granularity and a reasonable degree of randomness. The basis of this algorithm is not specified in the language documentation.

3. Uses the Mersenne Twister algorithm (based on GFSR) which is platform independent, with 32 bit granularity and a high degree of randomness. This is good enough for most non-cryptographic purposes.

4. Uses a QBASIC compatible algorithm which is platform independent, with 24 bit granularity and a low degree of randomness.

5. Uses system features (Win32 Crypto API or /dev/urandom device on Linux) to generate pseudo-random numbers, with 32 bit granularity and a very high degree of randomness (cryptographic strength).

A parameter of 0 can also be used (and is the default if omitted) which uses algorithm 3 in the -lang fb dialect, 4 in the -lang qb dialect and 1 in the -lang fblite dialect.

• FutureBasic

This function returns a pseudo-random long integer uniformly distributed in the range 1 through expr. The expr parameter should be greater than 1, and must not exceed 65536. If the value returned is to be assigned to a 16-bit integer (randomInteger), expr should not exceed 32767. The actual sequence of numbers returned by rnd depends on the random number generator's "seed" value. (Note that rnd(1) always returns the value 1.)

This statement "seeds" the random number generator: this affects the sequence of values which are subsequently returned by the rnd function and the maybe function. The numbers returned by rnd and maybe are not truly random, but follow a "pseudo-random" sequence which is uniquely determined by the seed number (expr). If you use the same seed number on two different occasions, you'll get the same sequence of "random" numbers both times. When you execute random without any expr parameter, the system's current time is used to seed the random number generator.

Example: To get a random integer between two arbitrary limits min and max, use the following statement. (Note: max - min must be less than or equal to 65536.):

To get a random fraction, greater than or equal to zero and less than 1, use this statement:

To get a random long integer in the range 1 through 2,147,483,647, use this statement:

GAP may use two algorithms : MersenneTwister, or algorithm A in section 3.2.2 of TAOCP (which is the default). One may create several random sources in parallel, or a global one (based on the TAOCP algorithm).

One can get random elements from many objects, including lists

Go has two random number packages in the standard library and another package in the "subrepository."

• math/rand in the standard library provides general purpose random number support, implementing some sort of feedback shift register. (It uses a large array commented "feeback register" and has variables named "tap" and "feed.") Comments in the code attribute the algorithm to DP Mitchell and JA Reeds. A little more insight is in this issue in the Go issue tracker.
• crypto/rand , also in the standard library, says it "implements a cryptographically secure pseudorandom number generator." I think though it should say that it accesses a cryptographically secure pseudorandom number generator. It uses /dev/urandom on Unix-like systems and the CryptGenRandom API on Windows.
• x/exp/rand implements the Permuted Congruential Generator which is also described in the issue linked above.

Golfscript uses Ruby's Mersenne Twister algorithm

~rand produces a random integer between 0 and n-1, where n is a positive integer piped into the program

Same as Java.

The Haskell 98 report specifies an interface for pseudorandom number generation and requires that implementations be minimally statistically robust. It is silent, however, on the choice of algorithm.

Icon and Unicon

Icon and Unicon both use the same linear congruential random number generator x := (x * 1103515245 + 453816694) mod 2^31. Icon uses an initial seed value of 0 and Unicon randomizes the initial seed.

This LCRNG has a number of well documented quirks (see The Icon Analyst issues #26, 28, 38 ) relating to the choices of an even additive and a power of two modulus. This LCRNG produces two independent sequences of length 2^30 one of even numbers the other odd.

Inform's random functions are built on the random number generator exposed at runtime by the virtual machine, which is implementation-defined.

Io's Random object uses the Mersenne Twister algorithm.

By default J's ? primitive (Roll/Deal) uses the Mersenne twister algorithm, but can be set to use a number of other algorithms as detailed on the J Dictionary page for Roll/Deal .

Java's Random class uses a Linear congruential formula , as described in its documentation . The commonly used Math.random() uses a Random object under the hood.

The only built-in random number generation facility is Math.random() , which returns a floating-point number greater than or equal to 0 and less than 1, with approximately uniform distribution. The standard (ECMA-262) does not specify what algorithm is to be used.

Julia's built-in random-number generation functions , rand() etcetera, use the Mersenne Twister algorithm.

As mentioned in the Java entry, the java.util.Random class uses a linear congruential formula and is not therefore cryptographically secure. However, there is also a derived class, java.security.SecureRandom, which can be used for cryptographic purposes

Lua's math.random() is an interface to the C rand() function provided by the OS libc; its implementation varies by platform.

• M2000 Interpreter

M2000 uses Wichmann-Hill Pseudo Random Number Generator

Mathematica / Wolfram Language

Mathematica 7, by default, uses an Extended Cellular Automaton method ("ExtendedCA") to generate random numbers. The main PRNG functions are RandomReal[] and RandomInteger[] You can specify alternative generation methods including the Mersenne Twister and a Linear Congruential Generator (the default earlier versions). Information about random number generation is provided at Mathematica .

MATLAB uses the Mersenne Twister as its default random number generator. Information about how the "rand()" function is utilized is given at MathWorks .

Maxima uses a Lisp implementation of the Mersenne Twister. See ? random for help, or file share/maxima/5.28.0-2/src/rand-mt19937.lisp for the source code.

There are also random generators for several distributions in package distrib  :

• random_bernoulli
• random_beta
• random_binomial
• random_cauchy
• random_chi2
• random_continuous_uniform
• random_discrete_uniform
• random_gamma
• random_general_finite_discrete
• random_geometric
• random_gumbel
• random_hypergeometric
• random_laplace
• random_logistic
• random_lognormal
• random_negative_binomial
• random_noncentral_chi2
• random_noncentral_student_t
• random_normal
• random_pareto
• random_poisson
• random_rayleigh
• random_student_t
• random_weibull

Note: the package distrib also has functions starting with pdf , cdf , quantile , mean , var , std , skewness or kurtosis instead of random , except the Cauchy distribution, which does not have moments .

The Random interface in Modula-3 states that it uses "an additive generator based on Knuth's Algorithm 3.2.2A".

The Nanoquery Nanoquery.Util.Random class makes native calls to the java.util.Random class, which uses a Linear congruential formula .

Uses .Net Random class; so, as mentioned under C#, above, implements Knuth's subtractive random number generator algorithm. Random class documentation at MSDN .

As NetRexx runs in the JVM it simply leverages the Java library. See Java for details of the algorithms used.

There are two PRNGs provided in the standard library:

• random  : Based on xoroshiro128+ (xor/rotate/shift/rotate), see here .
• mersenne  : The Mersenne Twister.

OCaml provides a module called Random in its standard library. It used to be a "Linear feedback shift register" pseudo-random number generator (References: Robert Sedgewick, "Algorithms", Addison-Wesley). It is now (as of version 3.12.0) a "lagged-Fibonacci F(55, 24, +) with a modified addition function to enhance the mixing of bits." It passes the Diehard test suite.

As explained here (see rand function), Octave uses the "Mersenne Twister with a period of 2^19937-1".

Oz provides a binding to the C rand function as OS.rand .

See #Delphi and #Free Pascal .

Previous to Perl 5.20.0 (May 2014), Perl's rand function will try and call drand48 , random or rand from the C library stdlib.h in that order.

Beginning with Perl 5.20.0, a drand48() implementation is built into Perl and used on all platforms. The implementation is from FreeBSD and uses a 48-bit linear congruential generator with this formula:

Seeds for drand48 are 32-bit and the initial seed uses 4 bytes of data read from /dev/urandom if possible; a 32-bit mix of various system values otherwise.

Additionally, there are many PRNG's available as modules. Two good Mersenne Twister modules are Math::Random::MTwist and Math::Random::MT::Auto . Modules supporting other distributions can be found in Math::Random and Math::GSL::Randist among others. CSPRNGs include Bytes::Random::Secure , Math::Random::Secure , Math::Random::ISAAC , and many more.

The rand(n) routine returns an integer in the range 1 to n, and rnd() returns a floating point number between 0.0 and 1.0. In both cases the underlying algorithm is just about as trivial as it can be, certainly not suitable for serious cryptographic work. There are at least a couple of Mersenne twister components in the archive.

PHP has two random number generators: rand , which uses the underlying C library's rand function; and mt_rand , which uses the Mersenne twister algorithm.

PicoLisp uses a linear congruential generator in the built-in (rand) function, with a multiplier suggested in Knuth's "Seminumerical Algorithms". See the documentation .

Values produced by IBM Visualage PL/I compiler built-in random number generator are uniformly distributed between 0 and 1 [0 <= random < 1]

It uses a multiplicative congruential method:

Oracle Database has two packages that can be used for random numbers generation.

DBMS_RANDOM

The DBMS_RANDOM package provides a built-in random number generator. This package is not intended for cryptography. It will automatically initialize with the date, user ID, and process ID if no explicit initialization is performed. If this package is seeded twice with the same seed, then accessed in the same way, it will produce the same results in both cases.

DBMS_CRYPTO

The DBMS_CRYPTO package contains basic cryptographic functions and procedures. The DBMS_CRYPTO.RANDOMBYTES function returns a RAW value containing a cryptographically secure pseudo-random sequence of bytes, which can be used to generate random material for encryption keys. This function is based on the RSA X9.31 PRNG (Pseudo-Random Number Generator).

The Get-Random cmdlet (part of PowerShell 2) uses the .NET-supplied pseudo-random number generator which uses Knuth's subtractive method; see C# .

PureBasic has two random number generators, Random() and CryptRandom() . Random() uses a RANROT type W generator [8] . CryptRandom() uses a very strong PRNG that makes use of a cryptographic safe random number generator for its 'seed', and refreshes the seed if such data is available. The exact method used for CryptRandom() is uncertain.

Python uses the Mersenne twister algorithm accessed via the built-in random module .

Quackery uses the 64 bit variant of Bob Jenkins' public domain "A small noncryptographic PRNG", which can be found at burtleburtle.net .

In case the website does not endure, the C implementation provided is:

For uniform random numbers, R may use Wichmann-Hill, Marsaglia-multicarry, Super-Duper, Mersenne-Twister, or Knuth-TAOCP (both 1997 and 2002 versions), or a user-defined method. The default is Mersenne Twister.

R is able to generate random numbers from a variety of distributions, e.g.

• Chi-Squared
• Exponential
• Hypergeometric
• Multinomial
• Negative Binomial

See R help on Random number generation , or in the R system type

Racket's random number generator uses a 54-bit version of L’Ecuyer’s MRG32k3a algorithm [L'Ecuyer02], as specified in the docs . In addition, the "math" library has a bunch of additional random functions .

(formerly Perl 6) The implementation underlying the rand function is platform and VM dependent. The JVM backend uses that platform's SecureRandom class.

Rascal does not have its own arbitrary number generator, but uses the Java generator. Nonetheless, you can redefine the arbitrary number generator if needed. Rascal has the following functions connected to the random number generator:

The last function can be used to redefine the arbitrary number generator. This function is also used in the getOneFrom() functions.

The   random   BIF function is a pseudo-random number (non-negative integer) generator, with a range (spread) limited to   100,000   (but some REXX interpreters support a larger range, including negative numbers). The random numbers generated are not consistent between different REXX interpreters or even the same REXX interpreters executing on different hardware.

The random numbers may be repeatable by specifiying a   seed   for the   random   BIF:

Comparison of random BIF output for different REXX implementations using a deterministic seed .

outputs from various REXX interpreters:

Conclusion: It's not safe to transport a program that uses 'reproducable' use of random-bif (i.e. with a seed) from one environment/implementation to another :-(

Ruby's rand function currently uses the Mersenne twister algorithm, as described in its documentation .

Rust's rand crate offers several PRNGs. (It is also available via #![feature(rustc_private)] ). The offering includes some cryptographically secure PRNGs: ISAAC (both 32 and 64-bit variants) and ChaCha20 . StdRng is a wrapper of one of those efficient on the current platform. The crate also provides a weak PRNG: Xorshift128 . It passes diehard but fails TestU01, replacement is being considered . thread_rng returns a thread local StdRng initialized from the OS. Other PRNGs can be created from the OS or with thread_rng .

For any other PRNGs not provided, they merely have to implement the Rng trait.

Scala's scala.util.Random class uses a Linear congruential formula of the JVM run-time libary, as described in its documentation . An example can be found here:

Seed7 uses a linear congruential generator to compute pseudorandom numbers. Usually random number generators deliver a random value in a fixed range, The Seed7 function rand(low, high) delivers a random number in the requested range [low, high]. Seed7 overloads the rand functions for the types char, boolean, bigInteger , float and others.

Latest versions of Sidef use the Mersenne Twister algorithm to compute pseudorandom numbers, with different initial seeds (and implementations) for floating-points and integers.

Sparkling uses the built-in PRNG of whichever C library implementation the interpreter is compiled against. The Sparkling library functions random() and seed() map directly to the C standard library functions rand() and srand() with only one small difference: the return value of rand() is divided by RAND_MAX so that the generated number is between 0 and 1.

• Standard ML

The basis library does not include a random number generator.

SML/NJ provides the Rand and Random structures (with a description of the used algorithms in the documentation).

MLton additionally ships with MLtonRandom , which implements a simple LCG, taken from " Numerical Recipes in C ", page 284 ("An Even Quicker Generator").

See set rng in Stata help. Stata uses the Mersenne Twister RNG by default, and may use the 32-bit KISS RNG for compatibility with versions earlier than Stata 14.

Tcl uses a linear congruential generator in it's built-in rand() function. This is seeded by default from the system time, and kept per-interpreter so different security contexts and different threads can't affect each other's generators (avoiding key deployment issues with the rand function from C 's math library).

Citations (from Tcl source code):

• S.K. Park & K.W. Miller, “ Random number generators: good ones are hard to find ,” Comm ACM 31(10):1192-1201, Oct 1988
• W.H. Press & S.A. Teukolsky, “ Portable random number generators ,” Computers in Physics 6(5):522-524, Sep/Oct 1992.
• TI-83 BASIC

TI-83 uses L'Ecuyer's algorithm to generate random numbers. See L'Ecuyer's algorithm . More explainations can be found in this paper .

Random function:

TXR 50 has a PRNG API, and uses a re-implementation of WELL 512 (avoiding contagion by the "contact authors for commercial uses" virus present in the reference implementation, which attacks BSD licenses). Mersenne Twister was a runner up. There is an object of type random-state, and a global variable *random-state* which holds the default random state. Programs can create random states which are snapshots of existing ones, or which are seeded using an integer value (which can be a bignum). The random function produces a random number modulo some integer value, which can have arbitrary precision. The random-fixnum function produces a non-heap-allocated positive integer with random bits.

All Bourne Shell clones have a very quick pseudo random number generator.

Rach time $RANDOM is referenced it changes it's value (with it's maximum value 32767).

Standard Ursa defines the ursa.util.random type for random number generators and gives objects of this type a standard interface, but leaves the choice of algorithm up to the implementor.

Cygnus/X Ursa is written in Java and makes calls to java.util.Random, which uses a Linear congruential formula .

Ursala uses the Mersenne twister algorithm as implemented by the Avram run time system for most purposes, except for arbitrary precision floating point random numbers, which are generated by the urandomb function from the mpfr library.

V (Vlang) has at least two random number modules (at the time this was typed), which are "rand" and "crypto.rand":

• https://modules.vlang.io/rand.html , in the standard library, provides two main ways in which users can generate pseudorandom numbers.
• https://modules.vlang.io/crypto.rand.html , also in the standard library, and returns an array of random bytes.

Wee Basic does not any built-in algorithms for random number generation. However, as can be seen in Random number generator (device)#Wee Basic , pseudo-random number generation can be accomplished by using a loop that quickly increases the number from 1 to 10 until any key is pressed.

Wren's Random class uses the Well equidistributed long-period linear PRNG (WELL512a) .

A 31-bit linear congruential generator is used based on an algorithm by Donald Knuth in his book "Art of Computer Programming" Vol 2, 3rd ed. p. 185. It passes all tests in the Diehard suite. The seed is initialized with the system timer count (at 046C) whenever a program starts. The seed can also be set within a program to give a repeatable sequence of (pseudo) random numbers. Calls to the random number intrinsic return values modulo the argument.

zkl uses the Xorshift ( http://en.wikipedia.org/wiki/Xorshift ) random number generator. It will also, on occasion, read from /dev/urandom.

• Z80 Assembly

This is a bit of a stretch, but the R register which handles memory refresh can be read from to obtain somewhat random numbers. It only ranges from 0 to 127 and is most likely to be very biased but this is as close to a built-in RNG as the language has.

• ZX Spectrum Basic

The manual is kind enough to detail how the whole thing works. Nobody is expected to do the maths here, although it has been disassembled online; in short, it's a modified Park-Miller (or Lehmer ) generator.

1. Test this rule:

Suppose you choose a random number between 1 and 872 and type

Then the next value of RND will be

2. (For mathematicians only.)

RND is approximately uniformly distributed over the range 0 to 1.

Number Generator

Random pin code generator.

Combinatorics

Here are some more predefined number generators.

• Random number 1 - 10 - quickly generate a random number between 1 and 10
• Random number 1 - 100 - quickly generate a random number between 1 and 100
• 100 Random numbers - generate a 100 random numbers between 1 and 1000
• Random Number Picker - lets you quickly pick 5 random lottery numbers
• Number list randomizer - randomize your own list of numbers. You can decide whether order matters and whether replacement is allowed
• RNG Combinations - Advanced - Looking for more numbers for research or other purposes? generate multiple sets of random numbers and customize them in various ways; multiple quick picks or lines, csv to generate comma-separated lists, decide if the numbers are unique, or whether the order of numbers in each set matters or not.
• Hex Code Generator - lets you generate random hexadecimal numbers and also shows html color
• HTML color codes - generate random html color combinations and pick the best
• Binary number generator - in case you need random binary numbers of any length
• Random integers - need negative numbers as well? Generate negative/positive random integers
• Lists of random numbers - generate large lists of random numbers unique (without replacement) or repeating (with replacement)
• Lists of numbers - generate large lists of numbers in sequence so you don't have to type them manually
• Random phone numbers - in case you need to pick a random 7 or 10 digit phone number
• Pin codes - generate random pin codes
• Credit card numbers - hmm.. wonder why you need this, perhaps for testing? Most credit card numbers are 16 digits, and this lets you generate 16 random digits.
• Number converter - Try number converter to convert from hex to rgb, decimal to binary and more
• Permutations and Combinations
• Random permutations and combinations of a range of numbers. Use these for research, lotteries, etc.
• ALL possible combinations of length N of a given range of numbers. Use this to generate all possible combinations (even millions of them)
• ALL possible combinations of length R from a list of N items (n Choose r or nCr). Use this to generate all possible combinations of a list of items.
• ALL possible permutations of length N of a given range of numbers. Use this to generate all possible permutations (even millions of them). Permutations are combinations in which order of the items matters such that 1,2,3 is not same as 1,3,2.
• ALL possible permutations (combinations where order of the items matters) of length R from a list of N items (nPr). Use this to generate all possible permutations of a list of items.

Magic Filters

Display font, add/roll dice, random numbers, number converters, number formats, number lists.

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Flutter – Make a Random Number Generator App

In Flutter we can create a random object using the Random() method to create a random number. We can use this concept to make an OTP that can be used for various authentication. In this article, we are going to Generate a 4-digit random pin in every click. A sample video is given below to get an idea about what we are going to do in this article.

Step By Step Implementation

Step 1: create a new project in android studio.

To set up Flutter Development on Android Studio please refer to Android Studio Setup for Flutter Development , and then create a new project in Android Studio please refer to Creating a Simple Application in Flutter .

Step 2: Import the Package

First of all import material.dart file.

Step 3: Execute the main Method

Here the execution of our app starts.

Step 4: Create MyApp Class

In this class we are going to implement the MaterialApp , here we are also set the Theme of our App.

Step 5: Create RandomNumberGenerator Class

In this class we are going to generate the 4 digit random number in every click and display it by the help of a TextView. This class contains a method named as generateRandomNumber() that is responsible for generating a 4 digit random number in every call. Comments are added for better understanding .

Here is the full Code of main.dart file:

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This is a basic number generator but with a twist. If a number as already been generated until every number from 1 to 100 has been generated.

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Random Codes

Use Generate Codes, the random code generator. All codes will be uniquely generated codes. Generate codes for discounts, coupons, unique ids and much more.

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