Questions tagged [rounding]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
2
votes
1answer
67 views

Integrality gap and LP-rounding

I have a doubt about integrality gap. If I know that there is no integrality gap for a given problem, i.e.: $$\frac{\mathrm{OPT}(\mathrm{ILP})}{\mathrm{OPT}(\mathrm{LP})} = 1 \text{ (right?)},$$ ...
0
votes
0answers
56 views

Doubt on integrality gap and LP relaxation

I have an exercise that tells me that, given a problem P (of which now I omit the description) there is no integrality gap between LP and ILP formulation of this problem, and for every fractional LP-...
1
vote
1answer
19 views

Rounding of $2-10^{20}$ in IEEE double precision

How do we get the rounding of $2-10^{20}$ in IEEE double precision? The textbook says it is $-10^{20}$, but I do not know why. I think my textbook only explains the rule for rounding mantissa.
1
vote
0answers
42 views

An LP with two covering constraints - how to round

I came across an LP with two covering problems, and I wonder how to find a good approximation. For the relevant part of the LP: We have a set $E$ , for each $e\in E$ we have a corresponding set $Y_{e}\...
1
vote
2answers
62 views

Increased rounding relative error when subtracting

I'm reading the book "Lessons in Scientific Computing" by Schoerghofer and it says: If x and y are real numbers of the same sign, their sum x + y has an absolute error that adds the two ...
3
votes
0answers
45 views

Compile-time error control vs. interval arithmetic?

I use interval arithmetic for reliable computing. Now, a procedure coded in a good implementation of interval arithmetic takes perhaps about eight times as much as the same procedure carried out ...
1
vote
1answer
57 views

Shortest decimal expansion within binary interval

Consider an interval $[x-2^n,x+2^n]$ defined by a binary float $x$ and a power of two $2^n$ typically much smaller than $x$. I would like to know whether an efficient algorithm exists to determine the ...
2
votes
1answer
228 views

Are IEEE floating point numbers intervals or point values?

The context is IEEE 754-2008 floating point number systems. The systems defined by the standard comprise, as far as I understand it, a bit-level representation and a set of guarantees on the precision ...
1
vote
1answer
155 views

Rounding logarithm to next integer — Potential function

The problem is IV-3 of this pdf: potential function. Defining a potential function as $\Phi(i) = 2i - 2^{\lfloor{\log_2i}\rfloor+1} + 1$ The solution states that if $i$ is not an exact power of $2$,...
3
votes
2answers
4k views

Why can't we round results of linear programming to get integer programming?

If linear programming suggests that we need $2.5$ trucks to deliver goods, why can't we round up and say $3$ trucks are needed? If linear programming suggests we can afford only $3.7$ workers, then ...
0
votes
2answers
326 views

Why are transcendental functions of large numbers inaccurate on computers?

For instance, why is it hard to accurately compute sin(1e99)? I suspect it has something to do with rounding error.
2
votes
0answers
60 views

Normalised Floating Point System

I have a floating point number system and I have a number for which I need to calculate the exact relative error after rounding. The number is clearly an overflow. Does anyone know what I should do? ...
1
vote
1answer
142 views

floating point rounding (1/x)*x

I'm trying to figure out what the smallest positive integer x such that the floating point expression round(round(1/x)*x) is not equal to 1 in single precision. I have that the answer is 41, but when ...
3
votes
1answer
18k views

Normalizing the mantissa in floating point representation

How to represent $0.148 * 2^{14}$ in normalized floating point arithmetic with the format 1 - Sign bit 7 - Exponent in Excess-64 form 8 - Mantissa $(0.148)_{10} =...
0
votes
1answer
625 views

In a 32-bit floating number with normalized mantissa and excess-64 exponent base 16, the number $16^{-65}$ denotes

In a 32-bit floating number with normalized mantissa and excess-64 exponent base 16, the number $16^{-65}$ denotes Floating point overflow. Negative floating point overflow. All 0's in the exponent ...
13
votes
1answer
430 views

Floating point rounding

Can an IEEE-754 floating point number < 1 (i.e. generated with a random number generator which generates a number >= 0.0 and < 1.0) ever be multiplied by some integer (in floating point form) to ...