TAOCP 4.2.1: Single-Precision Calculations
Section 4.2.1 exercises: 19/19 solved.
Section 4.2.1. Single-Precision Calculations
Exercises from TAOCP Volume 2 Section 4.2.1: 19/19 solved.
| # | Rating | Category | Status | Time |
|---|---|---|---|---|
| 1 | [10] | simple | verified | 1m14s |
| 2 | [12] | simple | verified | 3m18s |
| 3 | [11] | simple | solved | 4m45s |
| 4 | ▶ [16] | medium | verified | 4m30s |
| 5 | [24] | medium | verified | 5m01s |
| 6 | [20] | medium | verified | 1m41s |
| 7 | [27] | hard | verified | 9m56s |
| 8 | [20] | medium | solved | 1m39s |
| 9 | [M24] | math-medium | solved | 12m04s |
| 10 | [12] | simple | solved | 1m41s |
| 11 | ▶ [M20] | math-medium | verified | 2m26s |
| 12 | [M35] | math-hard | solved | 6m17s |
| 13 | [30] | hard | verified | 2m15s |
| 14 | [25] | medium | solved | 7m39s |
| 15 | ▶ [28] | hard | verified | 1m41s |
| 16 | [HM21] | hm-medium | verified | 2m02s |
| 17 | [40] | project | verified | 1m41s |
| 18 | [25] | medium | verified | 2m28s |
| 19 | [24] | medium | verified | 7m09s |
TAOCP 4.2.1 Exercise 1
Using the values given in §3, h \approx 6.
TAOCP 4.2.1 Exercise 2
A base $b$, excess $q$, $p$-digit floating point number has the form \pm f\,b^{\,e-q}, where the exponent satisfies
TAOCP 4.2.1 Exercise 3
In normalized binary floating-point arithmetic, every nonzero number is represented in the form x=\pm(0.
TAOCP 4.2.1 Exercise 4
We apply Algorithm A with base $b=10$ and precision $p=8$.
TAOCP 4.2.1 Exercise 5
Let the quantity actually stored for exponent $e$ be denoted by $F_e$.
TAOCP 4.2.1 Exercise 6
The question asks for the sign of register A when a floating point addition produces the value zero.
TAOCP 4.2.1 Exercise 7
Balanced ternary uses radix $b=3$ and digits \bar 1=-1,\qquad 0,\qquad 1.
TAOCP 4.2.1 Exercise 8
Let the floating decimal numbers have $p=8$ digits in the fraction, and let normalized numbers satisfy $\frac1{10}\le |f|<1,$ unless the number is zero.
TAOCP 4.2.1 Exercise 9
We are asked to construct positive eight-digit floating decimal numbers $a,b,c,d,y$ with exponent range $-50 \le e < 50$ such that \frac{(a \otimes y) \oplus b}{(c \otimes y) \oplus d} \approx \frac{2...
TAOCP 4.2.1 Exercise 10
Let the floating point numbers have base $10$ and $p=8$ digits.
TAOCP 4.2.1 Exercise 11
We are asked to give an example of normalized, excess-50, eight-digit floating decimal numbers $u$ and $v$ such that multiplication produces a rounding overflow.
TAOCP 4.2.1 Exercise 12
Let u=(e_u,f_u), \qquad v=(e_v,f_v) be normalized floating point numbers in radix $b$, with $p$-digit fractions.
TAOCP 4.2.1 Exercise 13
Let $\beta=10$, let the precision be $p$, and let the floating point operations be rounded to the nearest representable number, as in Algorithm N.
TAOCP 4.2.1 Exercise 14
A MIX floating-point number has the form x = s\,(0.
TAOCP 4.2.1 Exercise 15
We are to design a MIX subroutine that computes u \pmod 1 = u-\lfloor u\rfloor, returning the result rounded to the nearest normalized floating point number.
TAOCP 4.2.1 Exercise 16
We wish to compute the real and imaginary parts of $\frac{a + b i}{c + d i}$ without forming $c^2 + d^2$, which may overflow even if $|c|$ or $|d|$ is near the largest representable floating point num...
TAOCP 4.2.1 Exercise 17
A floating point number is represented by a single word containing a fraction and exponent.
TAOCP 4.2.1 Exercise 18
We are asked to define a rounding rule for a 36-bit binary machine using two's complement representation for negative floating point numbers, in which the combination of normalization and rounding can...
TAOCP 4.2.1 Exercise 19
We analyze the actual MIX **FADD** subroutine in **Program A**, which adds two floating-point numbers $u=(e_u,f_u)$ and $v=(e_v,f_v)$ in the MIX computer with **word size $w=5$ bytes** and fraction le...