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Questions tagged [floating-point]

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

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4answers
107 views

Float multiplication

While doing the multiplication 1.4*0.8 in a python program, I got the result as 1.1199999999999999. Why didn't I get ...
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2answers
45 views

Float type variable uncertainty

I developed an image processing software and I need to do a numerical analysis of it, considering the error propagation associated to its operations and the uncertainty of float type variables caused ...
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0answers
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 ...
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1answer
937 views

What is exponent of denormalized real in IEEE 754 floating point format?

I was reading this link. Here I noticed that, in table titles "Float Values (b = bias)", in exponent column, entry for denormalized reals is $00..00$, but in value column, the entry is $-b+1$. Why is ...
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1answer
142 views

Genetic Algorithm Getting Stuck on Certain Values

I'm attempting to teach myself something about genetic algorithms. I found a simple tutorial on it here, and it made enough sense that I was able implement the suggested example of generating a string ...
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1answer
43 views

How do proof assistants nowadays avoid floatpoint error?

I heard that Coq is using "Dedekind cut", but how's that related to floatpoint errors? Can we just use something like ...
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1answer
23 views

Exact Value of Denormalised number related to floating point numbers

I faced with the following issue: if the value of a floating point format number is in the range of underflow, it must be 0 or a denormal number.If the value is not 0 than what is the exact value of ...
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1answer
313 views

Why do floating point values have infinity?

Why do floating point values have infinity instead of just a higher exponent?
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1answer
38 views

Converting a 32-bit bit pattern into floating point number

In The Scientist and Engineer's Guide to Digital Signal Processing By Steven W. Smith, Ph.D. i have read something like that, Single precision or 32-bit floating point forms the floating point number,...
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1answer
886 views

How does conversion from fixed-point to floating-point happen?

I came across to the code that convert 32-bit signed fixed-point number (16.16) to a float and it looks like (pseudocode) floating = fixed / 65536.0 Could you ...
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1answer
40 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 an efficient algorithm exists to determine the ...
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0answers
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 ...
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1answer
121 views

how to convert any fraction to decimal

So for a project I am working on. I need to take a string representation of a floating point number, lets say "1.5" and do arithmetic on it with another floating point number. The catch is I cannot ...
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2answers
495 views

Convert a decimal floating-point number into a binary floating-point number

Let's say I have a decimal floating-point number, i.e. a mantissa and precision (negative exponent), both represented as integers. How do I convert this into a binary floating point number (of the ...
6
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1answer
363 views

Simple algorithm for IEEE-754 division on 8-bit CPU?

IEEE Std 754-2008 is the modern definition of Floating-Point Arithmetic. It requires that division (among other operations) performs as if it first produced an intermediate result correct to ...
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1answer
49 views

Compress 32 bit integer into a normalized float

and sorry if this is a duplicate of some sort, my poor technical vocabulary doesn't get me very far with google. I am trying to implement some well-known PRNG algorithms. For the time, the algorithm ...
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1answer
103 views

What are some of the practical applications of functions that extract the exponent and mantissa of a floating point number?

I'm talking about functions such as Python's math.frexp() : math.frexp(x) Return the mantissa and exponent of x as the pair (m, e). m is a float and e is an integer such that x == m * 2**e ...
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1answer
390 views

Neural Networks: Simulate the working of Dynamic Fixed Point representation of the weights on hardware

I am looking to implement a neural network on hardware using Verilog. I have completed and tested with floating point representation and a 20 bit fixed point representation. I want to further reduce ...
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0answers
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 ...
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0answers
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 ...
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2answers
916 views

How to estimate floating-point precision of function?

Let's say I have a function that consists solely of floating-point operations where the last operation rounds the computed value to a predefined number of digits. And I feed this function with a range ...
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2answers
1k views

What are the reasons for and against using normalized floating point?

Floating point number formats can be normalized or not, meaning that ‘normal’ floating point numbers have an implicit (hidden) leading bit 1 in the significand. For example, the binary IEEE 754 ...
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1answer
202 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 ...
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1answer
218 views

Why a separate ALU is needed, since any integer can be represented as floating point numbers?

Most of the operations in computer are using floating point arithmetic.Put it simply why a Floating Point Unit alone is not sufficient? Can we do away with ALU?Is FP operations are resource intensive ...
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2answers
696 views

Is the exponent in floating point numbers signed or unsigned

This may be sound like a stupid question, because, of course, it can be negative and, as Wikipedia states: A numeric variable is signed if it can represent both positive and negative numbers, and ...
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1answer
144 views

-4 as floating point

How would one represent the number -4 as an 8-bit normalised, 2's complement, floating point, with 4 bits dedicated to the exponent? As a normal 4-bit 2's complement number, it would be represented ...
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0answers
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-...
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0answers
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 ...
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2answers
172 views

What is meant by “uneven spacing” on number line when dealing with floating point numbers in computers?

I read some examples online on this subject, but none of them really gave an explanation. When I visualize the number line all I can see is evenly spaced numbers, I'm not grasping the notation of "...
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3answers
730 views

Comparing floating-point numbers as integers

In the article http://floating-point-gui.de/errors/comparison/, a method for comparing floating-point numbers is suggested: There is an alternative to heaping conceptual complexity onto such an ...
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1answer
188 views

NaN simple precision IEEE 754 [closed]

How many words exist in the format of the simple precision IEEE 754 standard to represent the NaN value?
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0answers
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 ...
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4answers
2k views

Inequality caused by float inaccuracy

At least in Java, if I write this code: float a = 1000.0F; float b = 0.00004F; float c = a + b + b; float d = b + b + a; boolean e = c == d; the value of $e$ ...
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1answer
2k views

MSB and LSB in floating point number

What is MSB and LSB in significant of a floating point number? If I have a significant for example 0011010000 (half-precision) but 1. bit is implicit what is MSB: 0 or 1? In this case LSB is 0, ...
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0answers
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 ...
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2answers
704 views

Floating Point Systems - Rounding Error in Taylor series

I have a question about rounding error. I have created a function to approximate exp(x) by summing the terms of its taylor series until the sum stops changing. (That is, 1 + x + x^2/2! ...). This ...
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1answer
738 views

How to add two numbers in IEE754 half precision format?

i'm trying to understand how to add two numbers in IEE754 half precision format , i haven't found a good reference/tutorial on this , so i've tried to follow the 32 bit floating point addition ...
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0answers
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 ...
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0answers
317 views

Are floats abstract data types?

Source:https://en.wikipedia.org/wiki/Abstract_data_type Can we say that float data types (or all primitive data types or only integer) are abstract data types?
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1answer
43 views

Formal notations of equivalencence between floating point expressions

In an informal context, most programmers might call these two expressions "equal" and no one would be mislead: (a + b) + c a + (b + c) For floating point numbers,...
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2answers
348 views

Find the duplicates in a list of floating point numbers

I receive a list of real numbers ( float ) between $0$ and $1$. The list has length $N+1$ and I need to find two numbers on the list which are $\le \frac{1}{N}$ ...
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1answer
93 views

What factors influence machine epsilon?

I was wondering what factors effect a machine's epsilon value. I was thinking about how modern computers can calculate expressions to higher accuracy then their predecessors, but what hardware and ...
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1answer
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 ...
3
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3answers
491 views

Whether assigning of single precision IEEE754 float to double is reversible?

Using the IEEE754 standard, let's assign single precision variable s to double precision variable d and then assign d to single precision variable s'. Is this operation is reversible (lossless) for ...
2
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1answer
1k views

How to work out if an IEEE 754 floating point number is normalized?

How do I tell whether a particular IEEE 754 floating point number is a normalized floating point number? Is there some way to recognize an IEEE 754 normalized floating point number?
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0answers
52 views

Dual Signed Kahan Summation

NOTE: This is for a project I'm working on for fun, NOT production code. So I'm working on a pet project that involves reading data in from a sensor and summing it up. The values are mostly ...
1
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1answer
893 views

half precision floating point multiplication

A = 0 10011 0011110111 B = 1 00011 0010011000 exponent is 15, mantissa is 10 bits and first bit is implicit. Can somebody please tell me the final answer cause I am having trouble figuring ...
7
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1answer
123 views

Difference between ways to compare floating-point numbers

There seems to be many approaches to judge whether two floating-point numbers are identical. Here are some examples I've found: ...
2
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1answer
122 views

Approximate a float using a minimal fraction

This sounds like it's probably a well-known problem, but I haven't been able to find references to it by searching. Given a floating point value $x$ and an error range $\varepsilon$, how can I ...
10
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1answer
577 views

Implementation of Naive Bayes

I am implementing a Naive Bayes algorithm for text categorization with Laplacian smoothing. The problem I am having is that the probability approaches zero because I am multiplying many small ...