Questions tagged [floating-point]

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

Filter by
Sorted by
Tagged with
0 votes
1 answer
34 views

Absolute difference between largest IEEE754 number and its predecesor

In simple precision format, the largest possible positive number is $A = 0 ~~~ 11111110 ~~~ 111\ldots 111$ Its predecessor is $B = 0 ~~~ 11111110 ~~~ 111 \ldots 110$ But what is the absolute ...
lafinur's user avatar
  • 181
2 votes
1 answer
51 views

Comparison of different algorithms for summing floating point numbers

I am exploring several approaches to summing floating point values, such as: Naive summation, for comparison Summing sorted values summing with numpy, again for comparison Kahan's algorithm Pairwise ...
Olumide's user avatar
  • 153
1 vote
2 answers
191 views

Convert a rational number to a floating-point number exactly

We have two integers, $n$ and $d$. They are coprime (the only positive integer that is a divisor of both of them is $1$). They may be implemented as something that fits in a machine register, or they ...
user2373145's user avatar
2 votes
2 answers
175 views

Multiplication of subnormal and normal numbers under IEEE 754

As far as I understand, when doing this operation, we first need to identify the subnormal value, normalise it, adjust the exponent, and then multiply the significands. Wouldn't it be advantageous to ...
pabloabur's user avatar
3 votes
2 answers
216 views

Floating-point modular multiplication algorithm

Is there a well-known algorithm for modular multiplication of floating-point numbers? I would like to multiply some large angle in single precision (6-7 significant digits) and wrap it back to 360 ...
phil5's user avatar
  • 33
1 vote
1 answer
59 views

FFT of logarithmic input data

Is there a reasonably accurate method of computing an FFT of logarithmically-represented input data (with a sign bit, that is $±2^{\text{double-precision value}}$)? The naive method (convert to linear ...
TLW's user avatar
  • 1,404
1 vote
1 answer
29 views

Floating-point rounding - bit patterns of values that are halfway between two possible results

I am working through the book Computer Systems: A Programmer's Perspective. The authors explain that round-to-even rounding can be applied for values that are halfway between two possible results. For ...
cmplx96's user avatar
  • 113
0 votes
0 answers
242 views

Why XMM register width is 128-bit while double precision floating point is 64-bit?

As far as I know, XMM is used to store floating point. But Highest width floating point according IEEE754 standard is double precision (64-bit). But why XMM register width is 128-bit. Is another 64-...
Muhammad Ikhwan Perwira's user avatar
0 votes
1 answer
39 views

How much larger is the next representable value if 2^59 is stored in a double?

This is an exam question I couldn't solve If I store 2^59 as double, that would give me 1 * 2^58. Is the answer just 2? I.e. next value is 2^60??
Rubus's user avatar
  • 121
2 votes
0 answers
50 views

Best way to constrain a complex number to being within the unit circle?

What is the best way of implementing the following function, $$f(x) = \frac{x}{\max(1, |x|)},$$ where $x$ is complex, using a Cartesian representation of $x$ with IEEE 754 floating point ...
sircolinton's user avatar
3 votes
0 answers
316 views

What are the use cases for the IEEE 754 inexact flag?

The IEEE 754 standard for floating point numbers defines a flag that is set when a result from floating point calculation isn't exact, i.e. has to be rounded. What algorithms are there that utilize ...
QuantumWiz's user avatar
4 votes
3 answers
2k views

Is significand same as mantissa in IEEE754?

I'm trying to understand IEEE 754 floating point. when I try convert 0.3 from decimal to binary with online calculator, it said the significand value was ...
Muhammad Ikhwan Perwira's user avatar
0 votes
1 answer
38 views

How does CPU determine Reserved Exponent cases?

Using IEEE 754 algorithm i assume, that it can be implemented in a branchless way. But how does CPU determine special cases (Reserved Exponent values): Exponent Significand is 11111111 000000000... ...
uptoyou's user avatar
  • 103
1 vote
1 answer
102 views

What does it mean unambiguously that a number is value 0 up to numerical precision?

I was reading that a quantity $x$ is $0$ upt to numerical precision. What does this statement formally mean -- especially in the context of numerical methods or real computers. I looked up in google ...
Charlie Parker's user avatar
1 vote
0 answers
32 views

Standard for representing a float scaled to a particular range?

TL;DR Is there a "standard" way to represent a float scaled to a particular range, such that we get maximum precision for the given bit depth, within that range? I'll start with my general ...
hazymat's user avatar
  • 111
0 votes
2 answers
70 views

(Numerical Analysis) What is the largest double float represented for the gamma function and $n!$

Consider that \begin{align} \Gamma(n+1) = n! \end{align} for any integers. I then got the following two questions: What is the largest value of $n$ for which $Γ(n+1)$ and $n!$ can be exactly ...
Jens Kramer's user avatar
3 votes
1 answer
82 views

Bisecting Intervals of floating point numbers containing 0 and infinity fairly

It is seldom considered that floating points are not evenly distributed in the real number line. I've been working with interval arithmetic and noticed when bisecting $[a,b]$ on the real number line ...
worldsmithhelper's user avatar
1 vote
0 answers
247 views

Can Radix Sort be modified for signed ints and/or floats?

A few months ago I learned about the magic that allows radix sort to run in O(n) time and space. Most tutorials on radix sort say it is useful for very large ...
Adam Hoelscher's user avatar
0 votes
1 answer
50 views

IEEE 754 conversion

I'm trying to convert 3.2 into IEEE 754 format. We find that $(3)_2=11$ and we also find that $0.2*2=0.4 -0$ $0.4*2=0.8 -0$ $0.8*2=1.6 -1$ $0.6*2=1.2 -1$ and this cycle repeats so $.2=00110011...$ ...
Iwan5050's user avatar
  • 135
4 votes
0 answers
106 views

Uniformly random decimal numbers

Due to finite precision of number representations, we face situations like: In: 0.1+0.1+0.1==0.3 Out: False (on my ...
Matthieu Latapy's user avatar
1 vote
0 answers
45 views

(Branchless) Bitonic Sorting Network for a Set of Floating Point Numbers

In the past I've implemented a branchless Bitonic Sorting Network on a gpu using CUDA, for integers. I am facing a related problem: In my Order Independent Transparency implementation, I would like to ...
Vectorizer's user avatar
0 votes
1 answer
57 views

How can vector angle comparison between lattice points be done without using floating-points? (Convex Hull)

Let's say I have a point $(x_0, y_0)$, and some other points $(x_1, y_1), (x_2, y_2) ... (x_n, y_n)$, such that all of them are lattice points; all have integer coordinates. Let's further assume that ...
Christopher Miller's user avatar
1 vote
2 answers
730 views

How many Integers can be represent in Double-Precision floating-point form

How to calculate the number of Integers that can be represent in Double-Precision floating-point form?
0xAlon's user avatar
  • 15
1 vote
1 answer
312 views

Prove every number in double precision 32-bit floating-point format can be represented in 64-bit format

Theorem: Prove every number in double precision 32-bit floating-point format can be represented in double precision 64-bit floating point-format. 64-bit format: Attempt: Let $ b = b_0 ,...,b_{31} $ ...
flamel12's user avatar
  • 233
1 vote
1 answer
45 views

Why does floating point become less accurate as the powers of 2 increase?

https://fabiensanglard.net/floating_point_visually_explained/ I was reading this article where the exponent and the mantissa are explained as the window and offset respectively. As the gap between ...
Neel Sandell's user avatar
0 votes
0 answers
123 views

Is there a way to convert FLOPS to bit operation per second

My problem is the following: I have $N$ inner products to compute in parallel every second. Each of the vectors in those inner product is composed of $7$ bits. I want to know for which $N$ it starts ...
Marco Fellous-Asiani's user avatar
2 votes
1 answer
203 views

Unit conversion - Better to divide by an integer or multiply by a double?

I currently have a long timestamp measured in units of 100ns elapsed since January 1st, 1900. I need to convert it to milliseconds. I have the choice of either ...
Bassinator's user avatar
1 vote
2 answers
875 views

Half precision floating point question -- smallest non-zero number

There's a floating point question that popped up and I'm confused about the solution. It states that IEEE 754-2008 introduces half precision, which is a binary floating-point representation that uses ...
Manny's user avatar
  • 13
1 vote
1 answer
483 views

Floating Point Arithmetic with 3 bits mantissa

Find all values of $ x ∈ R $ such that x + 1 = 1 in floating point arithmetic with 3 bits mantissa. How do we represent number 1 in floating point arithmetic with 3 bits mantissa I wonder? After that, ...
Hung Do's user avatar
  • 13
3 votes
2 answers
172 views

Python versus Matlab on the quantity 1/0

Python and Matlab seem to disagree on the division by 0. Python: ...
pluton's user avatar
  • 133
1 vote
3 answers
4k views

Negative Numbers in 32 bit Floating Point IEEE Numbers

So I understand the logic behind converting positive decimal numbers to IEEE 32 bit floating numbers but I'm not completely sure behind the negative one's. If for example we have a decimal number say -...
idkrlly's user avatar
  • 13
1 vote
2 answers
336 views

Adding two numbers in base 2(floating point) vs Multiplying two numbers in base 2(floating point)

Is it true that adding two numbers in base 2 is more complex than multiplying them? If so can someone please explain why this is the case?
Roy Fischer's user avatar
1 vote
2 answers
149 views

Prove that $1^\text{nan} = 1.00$

I know that for most computation involve nan (not a number) the result is a nan itself except for some cases. For example, $1^{\text{nan}} = 1.00$ which proven by mathematicians to be true. I tried to ...
Monther's user avatar
  • 120
2 votes
2 answers
27 views

Floating point bitwise comparator. If f1 and f2 are floating point numbers with the following properties can we always say f1 > f2?

Recall floating-point representation: Suppose $f$ is a floating-point number then we can express f as, If $f$ is normal: $$(-1)^{s}\cdot2^{e-127}(1 + \sum\limits_{k=1}^{23} b_{23-k}\cdot 2^{-k})$$ If $...
VilePoison's user avatar
0 votes
0 answers
103 views

Convert $8.75×10^{6}$ to IEEE-32 format?

There is a similar question already asked on this site but does not have an answer as to how the 10x was converted into 2y. I know how to convert 8.75 or 875 into IEEE representation. But what about ...
callmeanythingyouwant's user avatar
1 vote
1 answer
465 views

What is the machine epsilon and number of mantissa bits for TI-83?

I am trying to determine how many bits the TI-83 Plus uses to store floating point numbers. I am using the algorithm for approximating the machine epsilon given in "Numerical Mathematics and ...
irowe's user avatar
  • 113
1 vote
0 answers
51 views

How close are current computer technologies in terms of energy efficiency to the Landauer Limit?

I'm trying to figure out how close (in orders of magnitude) current computer technologies are in terms of energy efficiency to the Landauer Limit. However, I'm finding (seemingly) conflicting ...
andrewzian's user avatar
1 vote
3 answers
143 views

How to determine the set of real numbers corresponding to a given floating point number?

Let's say we consider IEEE 754 double precision floating-point numbers, and we use RNTE - Round To Nearest, Ties to Even - rounding. I know that the RNTE rounding works this way: given two consecutive ...
Fabio Nardelli's user avatar
4 votes
1 answer
570 views

Logic behind choosing the exponent bias as $2^7 -1$ instead of $2^7$ in $32$ bits IEEE-754 floating point representation

The $\text{IEEE-754}$ uses $32$ bits to represent single precision floating point numbers. The partitions of the register are as follows: ...
Abhishek Ghosh's user avatar
0 votes
0 answers
38 views

What is the currently know fastest algorithms to convert each individual Java primitive and Number types to a Char Array/String

What is the currently know fastest algorithms to convert each individual Java primitive and Number types to a Char Array/String number representation while ...
Suminda Sirinath S. Dharmasena's user avatar
2 votes
1 answer
8k views

How to represent zero as floating point number?

For the floating-point number, we have the form $\pm d_0.d_1d_2···d_{P-1}\times\beta^E$ $\pm$ --------------------------- sign $d_0.d_1d_2···d_{p-1}$ --------- significant $\beta$ --------------------...
user8314628's user avatar
0 votes
0 answers
41 views

Are floating-point numbers normalised by computers or humans?

I keep seeing posts and articles about how to normalise a floating-point number, why that's done and how such a number is represented in binary. But no one seems to mention who/what the normalisation ...
DeadManProp's user avatar
-1 votes
3 answers
650 views

How are bitwise operators used in normalisation of floating-point numbers?

After having spent a significant amount of time googling this topic, I am still struggling to confidently answer the following question: ...
DeadManProp's user avatar
1 vote
1 answer
953 views

Converting Decimal Numbers between 0 and 1 to Binary

I've been playing around with a program I wrote that converts decimal numbers to binary numbers and i've noticed that eventually, after applying the algorithm (multiply by 2, subtract 1 if greater ...
wasabiwaffles's user avatar
1 vote
2 answers
49 views

Floating-point oblivious way to compute multiset numbers

I have to compute $R = \left(\!\!{n + 1\choose k}\!\!\right)$, which happens to be: $$ R = \left(\!\!{n+1\choose k }\!\!\right) = \binom{n+k}{k} = \frac{(n + k)!}{n!k!} = \frac{(n+1)(n+2)\cdots(n+k)}{...
ABu's user avatar
  • 457
2 votes
2 answers
83 views

Validity of Algorithm for Testing Two Floating Point Numbers

This question is related to the epsilon- (or delta- if you prefer) test for floating point equality. But my question is not how to do it. Instead I have a related algorithm for testing equality, and I ...
Jack Straub's user avatar
0 votes
0 answers
43 views

New way of representing floating point

I want to create a new way of representing floating point. In standard IEEE floating point, we have 1 bit to represent sign, 8 bits to represent exponential and 23 bits to represent significand. In ...
errorcodemonkey's user avatar
0 votes
2 answers
217 views

IEEE 754 addition wrong result floating point numbers

I want to add two IEEE 754 numbers. I followed the steps to add two 754 numbers. However the result it not correct. Number 1: S:0 E:01111111 M:11111111111111111111111 Number 2: S:0 E:01111111 M:...
otto's user avatar
  • 101
0 votes
2 answers
80 views

Cancellation of inequalities in floating point arithmetic

In finite precision floating point arithmetic the associative property of addition is not satisfied. This is, it is not always the case that $$(a+b)+c=a+(b+c)$$ Even $a=(a+b)-b$ is not always true. To ...
plop's user avatar
  • 549
0 votes
1 answer
60 views

How does value decompression work for Facebook's Gorilla in the case where count of leading zeroes is not stored

I am referring to this paper: http://www.vldb.org/pvldb/vol8/p1816-teller.pdf My question is regarding section 4.1.2 where it says: When XOR is non-zero, calculate the number of leading and ...
Alvin's user avatar
  • 101

1
2 3 4 5