Lesson plan
RANDU
of 100,000 values generated with RANDU. Each point represents 3 consecutive pseudorandom values. It is clearly seen that the points fall in 15 two-dimensional planes. RANDU is an obsolete method for generating random numbers used primarily in the 1960s and 1970s. It is a linear congruential generator (LCG) of the Park–Miller type defined by the recurrence : V_{j+1} = 65539 \cdot V_j \bmod 2^{31} with the initial seed number V_0 as an odd number. It generates pseudorandom integers V_j which are uniformly distributed in the interval , but in practical applications are often mapped into pseudorandom rationals X_j in the interval , by the formula : X_j = \frac{V_j}{2^{31}}. IBM's RANDU is widely considered to be one of the most ill-conceived random number generators ever designed, and was described as "truly horrible" by Donald Knuth. It fails the spectral test badly for dimensions greater than 2, as shown below. The reason for choosing these particular values for the multiplier and modulus had been that with a 32-bit-integer word size, the arithmetic of mod 2 31 and 65539 = 2^{16} + 3 calculations could be done quickly, using bitwise operators in hardware, but the values were chosen for computational convenience, not statistical quality.
Article summary
of 100,000 values generated with RANDU. Each point represents 3 consecutive pseudorandom values. It is clearly seen that the points fall in 15 two-dimensional planes. RANDU is an obsolete method for generating random numbers used primarily in the 1960s and 1970s. It is a linear congruential generator (LCG) of the Park–Miller type defined by the recurrence : V_{j+1} = 65539 \cdot V_j \bmod 2^{31} with the initial seed number V_0 as an odd number. It generates pseudorandom integers V_j which are uniformly distributed in the interval , but in practical applications are often mapped into pseudorandom rationals X_j in the interval , by the formula : X_j = \frac{V_j}{2^{31}}. IBM's RANDU is widely considered to be one of the most ill-conceived random number generators ever designed, and was described as "truly horrible" by Donald Knuth. It fails the spectral test badly for dimensions greater than 2, as shown below. The reason for choosing these particular values for the multiplier and modulus had been that with a 32-bit-integer word size, the arithmetic of mod 2 31 and 65539 = 2^{16} + 3 calculations could be done quickly, using bitwise operators in hardware, but the values were chosen for computational convenience, not statistical quality.
Key claims
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Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
Bibliography
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Key claims and bibliography are generated from the same tracked claims and sources as the article page.