Questions tagged [floating-point]

Approximate representation of numbers as a fixed number of digits multiplied by a logarithmic scale.

32 questions
43 views

Convert $1.75\times10^{15}$ to IEEE-32 format?

$1.75\times10^{15}$ I know how to convert decimal to binary $(1.75)_{10}$ is equal to $(1.11)_2$ But to represent $10^{15}$ is the main problem for me. I can solve the question but this is the ...
29 views

89 views

Using a 16-bit 2,s Complement normalised floating-point representation; 10-bit fractional mantissa and a 6-bit integer exponent: express 2.171875

So far I know how to normalize when you are given, say: 1111010010 Mantissa, and 000100 exponent and are told that it's a positive number: ...
79 views

Computing the error bound of floating-point expression

How should I compute the maximum absolute and relative error of the following IEEE-754 floating-point expression? a.y + (x - a.x) * ((b.y - a.y) / (b.x - a.x)) ...
498 views

Convert between IEEE 754-2008 decimal64 and IEEE double precision floating point number

I need to know the algorithm for converting between IEEE 754-2008 decimal64 and IEEE 754-1985 double precision floating point number. I have been working on this for the past 2 days and I match the ...
83 views

What is the state of the algorithmic art for floating point arithmetic on complex numbers?

Most modern compilers and processors implement the IEEE 754 binary formats for floating point numbers. IEEE 754 guarantees that the addition, subtraction, multiplication, division, and square root ...
81 views

Representing Computations on Transcendental Numbers

Consider the set of transcendental numbers that are not compressible to a finite base-2 representation. How can I compute multiples (more generally, any algebraic computation) of one of these numbers,...
49 views

Stable and fast computation of the squared euclidean distance matrix

Let's say I want to compute the matrix $M$ of the squared euclidean distances between each pair of vectors $(x, y)$ belonging to two sets $X$ and $Y$ respectively. The sets of vectors $X$ and $Y$ have ...
27 views

Heuristic Consistency with float multiplications

I'm running A* search with a theoretically consistent heuristic. I'm doing a lot of float multiplications, and I'm not sure how best to ensure that my heuristic remains consistent down to the last ...
31 views

numeric stability of map reduce operations

I am building a small library for computing information retrieval metrics for classifiers (precision, recall, f1, accuracy, whatever). Typically each metric is built by calculating a single value for ...
199 views

Why mantissa and exponent are stored differently in a float?

As we know, in IEEE 754 standard, float number's exponent and mantissa are stored differently. While the exponent is stored as an unsigned number, taking advantage of the bias, the mantissa is in sign-...
58 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? ...
41 views

47 views

Why have only 15 bits been apportioned for the exponent in the 128-bit quad-precision datatype?

I look forward to the day we can start using quad-precision numbers, but was disappointed to see that in the specification, only 15 bits out of a whopping 128 were assigned to the exponent as shown by ...
187 views

Hi I have this simple question. When adding a positive number with a negative number, both of same exponent. Imagine that after complementing the negative we have something like this: 1.111 + 0.001 .....
20 views

How does normalised floating point binary work with two's complement?

I'm doing AQA a-level computer science, and the specification for which states that: Exam questions on floating point numbers will use a format in which both the normalised mantissa and exponent are ...
521 views

Understanding denormalized numbers in floating point representation

I am confused about how denormalized numbers work in floating point representation. I was referring to Stallings book and this article. The book initially explains floating point number format in ...
23 views

Numbers lying between single and double precision

The IEEE floating point number format is defined as $$s\underbrace{c_1\dots c_m}_\text{exponent}\underbrace{f_1\dots f_n}_\text{fraction}\text{ (*)}$$ with $s, c_i, f_j$ being either $1$ or $0$. The ...
21 views

IEEE-754 and machine numbers

I've been trying to wrap my head around machine numbers like the unit roundoff (u) and epsilon (e) in combination with the IEEE 754 standard. My textbook states some things that don't really make ...
35 views

Using half float to represent scaled short (int16), do I lose precision comparing to using double?

A device is generating 14-bit integer which is stored as int16 (short), a scaling process will then scale the data to value of order 10E-3. Does it then matter if I store these number with half float ...
55 views

Inverting an IEEE 754 double

While preparing for an exam I've come across this problem: Let $x$ be an IEEE 754 double precision number. Show that $$\texttt{fl}(x * \texttt{fl}(1/x))$$ has only 2 possible results ...
31 views

When do you know whether an exponent represents a movement of the decimal point to the left?

I'm learning about floating point numbers and I don't quite understand when one should interpret an exponent as moving the decimal point to the left. By book shows an example of converting -10.5 ...
97 views

How can a Number Represented without Normalization Technique?

Consider the following floating point Representation Mantissa is pure fraction in signed magnitude form . What is the representation of the binary number 1111.1111 $\times 2^{2}$ in hexadecimal ...
3k views

How do the Guard, sticky, and round bits work and affect floating point Representation?

I've got a test on this tomorrow, my instructor's lectures aren't up, and the notes are ambiguous... Anyhow, we've been covering floating point operations, specifically addition, and he mentioned ...
87 views

How to determine the range of a number represented in IEEE-754 format?

Given a format: say 12-bit floating point with sign bit, 5 - bit biased exponent and 6- bit significant with implied bit, how do i go about determining the range of ...
42 views

Logarithms using digit recurrence, how many bits to store in a LUT?

In a known method for approximating logarithms the following decomposition is adopted (assuming $x \in [1,2)$): $$log_2(x) = 1 + \sum_{j=1}^{+\infty} w_i log_2(1+2^{-j})$$ Where all the ...