How do we code Randomness ?

• Generates random numbers from a physical process capable of producing entropy (in other words, the device always has access to a physical entropy source)
• Nature provides ample phenomena that generate low-level, statistically random "noise" signals, including thermal and shot noise, jitter and metastability of electronic circuits, Brownian motion, atmospheric noise, radioactive decay.
  
• Services/Devices: USBs, Quantum RNGs, Free Running Oscillators (FROs)

• Utilizes a deterministic algorithm to generate a sequence of numbers whose properties approximate the properties of sequences of random numbers.
• The PRNG-generated sequence is not truly random, because it is completely determined by an initial value, called the PRNG's seed (which may include truly random values).
• Important in practice for their speed in number generation and their reproducibility.

The generator is defined by the recurrence relation:

Python Code

From Javascript's v8 engine official source code:

static inline void XorShift128(uint64_t* state0, uint64_t* state1) {
    uint64_t s1 = *state0;
    uint64_t s0 = *state1;
    *state0 = s0;
    s1 ^= s1 << 23;
    s1 ^= s1 >> 17;
    s1 ^= s0;
    s1 ^= s0 >> 26;
    *state1 = s1;
  }

1. Javascript
   • Math.Random() implementation depends on engine (browser).
   • v8 engine uses xorshift128+
2. Python
   • CPython uses the Mersenne Twister as the core generator. It produces 53-bit precision floats and has a period of 2**19937-1.
3. Java
   • Uses a modified linear congruential formula.

   public synchronized void setSeed(long seed) {
   this.seed = (seed ^ 0x5DEECE66DL) & ((1L << 48) - 1);
   haveNextNextGaussian = false;
   }
   
   protected synchronized int next(int bits) {
   seed = (seed * 0x5DEECE66DL + 0xBL) & ((1L << 48) - 1);
   return (int) (seed >>> (48 - bits));
   }

4. C++

RNGs can be tested against statistical test suites:

1. Dieharder
2. TestU01
3. PracRand