TAOCP 3.6: Summary

Section 3.6 exercises: 15/15 solved.

15 items

Section 3.6. Summary

Exercises from TAOCP Volume 2 Section 3.6: 15/15 solved.

# Rating Category Status Time
1 [21] medium verified 6m45s
2 ▶ [15] simple verified 1m27s
3 [14] simple verified 1m31s
4 [25] medium verified 1m18s
5 [28] hard verified 1m18s
6 ▶ [**] verified 1m13s
7 ▶ [**] verified 3m59s
8 [**] verified 2m17s
9 [**] verified 4m48s
10 [**] solved 3m49s
11 [**] verified 1m19s
12 ▶ [**] verified 1m04s
13 [**] verified 2m17s
14 ▶ [**] solved 1m52s
15 [**] verified 2m28s
Practice › Mathematics › TAOCP › TAOCP Vol 2: Seminumerical Algorithms › TAOCP 3.6: Summary ›

TAOCP 3.6 Exercise 1

We are asked to write a MIX subroutine, callable by JMP RAND1 with entry condition
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TAOCP 3.6 Exercise 2

Lady Lovelace's statement concerns the relation between a machine and the instructions that govern its behavior.
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TAOCP 3.6 Exercise 3

We simulate a game of craps as described, using the standard linear congruential generator from Section 3.
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TAOCP 3.6 Exercise 4

We are asked to simulate dice rolls, shuffle a deck of cards, play a common game to a winning outcome, and display results in a way consistent with a particular random number generator.
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TAOCP 3.6 Exercise 5

Let us formalize the problem in terms of computational probability and sequence generation.
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TAOCP 3.6 Exercise 6

This exercise is not a mathematical problem but a practical programming assignment.
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TAOCP 3.6 Exercise 7

Y_n=\left\lfloor \frac{X_n}{2^{10}}\right\rfloor,\qquad X_n=2^{10}Y_n+Z_n,\qquad 0\le Z_n<2^{10}.
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TAOCP 3.6 Exercise 8

A good test is to choose parameters $a$, $c$, $m$, and a seed $X_0$, then compute a short sequence of values independently from the defining recurrence X_{n+1}=(aX_n+c)\bmod m.
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TAOCP 3.6 Exercise 9

We consider the random-number generator `run_array` after initialization by `run_start(s)`.
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TAOCP 3.6 Exercise 10

We are asked to convert the C routines `run_array` and `run_start` to FORTRAN 77 subroutines that generate exactly the same sequences of numbers.
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TAOCP 3.6 Exercise 11

Let the modulus be $MM=2^{52},$ and replace all arithmetic modulo $2^{30}$ by arithmetic modulo $2^{52}$.
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TAOCP 3.6 Exercise 12

A lagged Fibonacci generator of the type recommended in Section 3.
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TAOCP 3.6 Exercise 13

**Exercise 3.
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TAOCP 3.6 Exercise 14

The phenomenon occurs because the sequence $\langle X_n \rangle$ defined by $X_n = (X_{n-37} + X_{n-100}) \bmod 2$ is a linear recurrence modulo 2, which generates a purely periodic sequence of period...
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TAOCP 3.6 Exercise 15

The generator must advance through _all_ $1009$ values in each block, returning the first $100$ and discarding the remaining $909$.
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