Why does the Math.random function return a double in the range [0, 1), instead of other intervals in Java?

By On Sunday, December 27th, 2020 Categories : Question & Answer

Why does the Math.random function return a double in the range [0, 1), instead of other intervals in Java?. Are You sir and mam has this kind of query?, If do then plz check the tips below:

Generating numbers between 0 and 1 allows you to scale directly to other ranges. If you need the range 0 to 256, simply multiply the result by 256. So from a practical standpoint, the range [0,1) is the most convenient.

Why is one end open and the other not? Because this is how numbers work in a given base. Consider a base 10 number. You can always represent [math]0[/math] regardless of digits – [math]0[/math], [math]00[/math], [math]000[/math], [math]0000[/math], etc. always comes down to the same. However, given a number of digits, the maximum is always one bit away from a “nice” number – with 4 digits, you can reach [math]9999[/math], but [math]10000[/math] would require an additional digit and actually push the maximum to [math]99999[/math].

Similarly, when encoding a floating point number, you would add all digits after point – [math]0.XXXXX[/math]. To get the 1.0000, you would have to waste an additional digit just for looking nice. It cannot be used for other values, as 1.0001 would be out of range, for example. So, culling 1.0000 is the most efficient.

Aside from this, there isn’t really an algorithmic advantage for creating random numbers. With IEEE 754 floats (what basically everybody is using), a float is encoded as separate sign, exponent and fraction. This is translated to a number as

[math](-1)^signcdot(1+fraction)cdot 2^exponent[/math]

Note the 1+fraction part – floats naturally describe the range [math][1,2)[/math] which is simply shifted by factors of 2. Thus, the range [math][0,1)[/math] is actually composed of many uniform ranges as [math][0.5,1)+[0.25,0.5)+[0.125,0.25)…[/math].

This makes it impossible to fix the exponent and just vary the fraction, since that would only create [math][0.5,1)[/math] or [math][0.25,0.5)[/math] or [math][0.125,0.25)[/math] etc. Each range also doubles precision compared to its predecessor. This means you can’t just randomly pick an exponent/range and fraction – this would create the same number of values in each range, which gives you an exponential distribution. Consider a reduced precision creating only the ranges [math][0.5,1)+[0.25,0.5)+[0.125,0.25)[/math] and picking 300 numbers – 100 would be in the first range >0.5, but 200 would be in the later two ranges <0.5.

I don’t know how Java actually creates random numbers, but the Python source code shows how they do it. Basically they create an integer in the range of [0, MAX_FLOAT) and just divide that by MAX_FLOAT again.

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