TAOCP 4.2.4: Distribution of Floating Point Numbers
Section 4.2.4 exercises: 17/20 solved.
Section 4.2.4. Distribution of Floating Point Numbers
Exercises from TAOCP Volume 2 Section 4.2.4: 17/20 solved.
| # | Rating | Category | Status | Time |
|---|---|---|---|---|
| 1 | [13] | simple | verified | 7m34s |
| 2 | [22] | medium | solved | 52s |
| 3 | [15] | simple | verified | 1m49s |
| 4 | [M18] | math-medium | verified | 1m42s |
| 5 | ▶ [M20] | math-medium | solved | 7m53s |
| 6 | [25] | medium | solved | 9m53s |
| 7 | [HM28] | hm-hard | verified | 4m07s |
| 8 | [HM23] | hm-medium | solved | 3m45s |
| 9 | [HM25] | hm-medium | verified | 2m05s |
| 10 | ▶ [HM28] | hm-hard | verified | 3m58s |
| 11 | [M15] | math-simple | verified | 3m09s |
| 12 | [HM25] | hm-medium | solved | 3m07s |
| 13 | ▶ [M20] | math-medium | - | - |
| 14 | ▶ [HM30] | hm-hard | - | - |
| 15 | [HM28] | hm-hard | verified | 2m07s |
| 16 | [HM28] | hm-hard | verified | 1m54s |
| 17 | ▶ [HM25] | hm-medium | verified | 1m35s |
| 18 | [HM30] | hm-hard | - | - |
| 19 | [HM25] | hm-medium | verified | 1m28s |
| 20 | [HM40] | hm-project | solved | 9m43s |
TAOCP 4.2.4 Exercise 1
Write the normalized decimal floating point numbers in Knuth's form u=f_u10^{e_u},\qquad v=f_v10^{e_v}, where
TAOCP 4.2.4 Exercise 2
Let $u$ and $v$ be normalized floating point numbers, and let the double-precision operations $\oplus$, $\ominus$, and $\otimes$ denote addition, subtraction, and multiplication carried out in the ext...
TAOCP 4.2.4 Exercise 3
Let a normalized positive floating decimal number be written as $10^v \cdot f$, where $v$ is an integer exponent and $f \in [1,10)$ is the fraction part.
TAOCP 4.2.4 Exercise 4
An antilogarithm table is indexed by values of $\log_{10} x$.
TAOCP 4.2.4 Exercise 5
Let $U$ be a random variable uniformly distributed on the interval $[0,1)$.
TAOCP 4.2.4 Exercise 6
Let $f$ be the normalized fraction part of a positive radix-16 floating point number.
TAOCP 4.2.4 Exercise 7
We are asked to show that no single distribution function $F(u)$ exists that satisfies equation (5) for **all integers $b \ge 2$** simultaneously and for all $r$ in the interval $1 \le r \le b$.
TAOCP 4.2.4 Exercise 8
Something went wrong.
TAOCP 4.2.4 Exercise 9
Let the averaging operator of Eq.
TAOCP 4.2.4 Exercise 10
The exercise as quoted cannot be solved rigorously from the information provided.
TAOCP 4.2.4 Exercise 11
Let $V=1/U$.
TAOCP 4.2.4 Exercise 12
Let $U$ and $V$ be independent, normalized, positive floating point numbers with fraction parts distributed according to the density functions $f(x)$ and $g(y)$, defined on the interval $[1/b, 1)$.
TAOCP 4.2.4 Exercise 15
Let $U$ and $V$ be independently distributed, normalized, positive floating point numbers in base $b = 10$, with exponents distributed according to probabilities $p_0, p_1, p_2, \ldots$, as in exercis...
TAOCP 4.2.4 Exercise 16
Let ${P_1(n)}_{n \ge 1}$ be a sequence taking values 0 or 1.
TAOCP 4.2.4 Exercise 17
Let A_k=\{n\ge 1:(\log_{10} n)\bmod 1<r\}, where $0\le r\le 1$.