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Question about the floating point system

I started to read Numerical analysis by Walter Gautschi. On the page $ 3 $, the author presents the floating point number system as follows: a floating point number is a representable number as
start {equation}
pm (.b _ {- 1} b _ {- 2} … b _ {- t}) _ 2 cdot 2 ^ { pm (c_ {s-1} c_ {s-2} .. . c_0.) _2} tag {1}
end {equation}

or $ s, t $ is fixed. We refer to this digital system as $ mathbb {R} (s, t) $.

Then Walter says that a number $ x in mathbb {R} (s, t) $ is normalized if $ b _ {- 1} = 1 $, and that we $ "$assume all numbers $ mathbb {R} (s, t) $ are standardized $ "$.

My question: Consider considering the number
$$ x = + (. 00100) cdot 2 ^ {- (111.)} $$
Is this number an element of $ mathbb {R} (5, 3) $? By definition, I mean yes. But when the author says $ "$we assume that all numbers $ mathbb {R} (s, t) $ are standardized,$ "$ I don't know if it implicitly redefines $ mathbb {R} (s, t) $ be form numbers $ (1) $ with the Additional requirement that $ b _ {- 1} = 1 $. If we try to impose this requirement on $ x $, I believe $ x $ would go out to
$$ x = + (. 10000) cdot 2 ^ {- 1001} $$
who should not be part of $ mathbb {R} (5, 3) $

I am a major mathematician taking my first numerical analysis. I have no previous experience in computer science or digital math.

opengl – the floating table of the c ++ vector binds glBufferData

std::vector BoneW(300000);  

for (int i = 0; i < indicess.size(); i++){

    glm::vec4 indices_vertex = glm::vec4(verticess(indicess(i)), 1.0f);
    verticesSkinned.push_back(glm::vec3(indices_vertex(0), indices_vertex(1), indices_vertex(2)));
    for(int ii = 0; ii <= 21; ii++){


// weights
glBindBuffer(GL_ARRAY_BUFFER, VBO2);
glBufferData(GL_ARRAY_BUFFER, BoneW.size() * sizeof(GLfloat), &BoneW(0), GL_DYNAMIC_DRAW);
glVertexAttribPointer(1, 1, GL_FLOAT, GL_FALSE, 3 * sizeof(float), ((void*)(sizeof(float)*1)));

How should glBufferData fields be?

Vertex Share Code

layout (location = 0) in vec3 aPos;
layout (location = 1) in float aWeight(23);

position += BoneTransforms(0) * vec4(aPos.x, aPos.y, aPos.z, 1.0f) * aWeight(0);
position += BoneTransforms(1) * vec4(aPos.x, aPos.y, aPos.z, 1.0f) * aWeight(1);
position += BoneTransforms(2) * vec4(aPos.x, aPos.y, aPos.z, 1.0f) * aWeight(2);

I want to shred the bone with the weight range?
glBufferData import vertex shader problem: S

Floating point and relative error

On the course notes, the following was written:

"In floating point, the relative error is independent of the" size "of the number"

floating point – Use float not double in Java methods and constructors

I'm trying to use the float type inside builders and methods like the following code. Unfortunately, my code says that float is not of compatible type in constructors and methods in code.

import java.util.Scanner;

public class Box {
    float width,height,length;

    Box(float w,float h, float l){
        width = w;
        height = h;
        length = l;

    float getWidth(){
        return width;
    float getHeight(){
        return height;

    float getLength(){
        return length;

    void setWidth(float w){
        width= w;
    void setHeight(float h){
        width= h;
    void setLength(float l){
        width= l;
    float getArea(){
        return width*length;
    float getVolume(){
        return width*height*length;

    public static void main(String() args) {

        Scanner in = new Scanner(;
        Box b1 = new Box();

        System.out.print("Enter length: ");
        float a= in.nextFloat();

        System.out.print("Enter Width: ");
        float b= in.nextFloat();

        System.out.print("Enter Height: ");
        float c= in.nextFloat();      


        float area=b1.getArea();
        float vol =b1.getVolume();
        System.out.println("Area of Box 1: " + area+ "nVolume of Box 1: " + vol);


animation – The FadeTransition () widget is animated only once in floating?

class pin extends StatefulWidget {
_PinState createState() => _PinState();

class _PinState extends State with TickerProviderStateMixin {
AnimationController _controller;
Animation _animation;
bool error = false;

void initState() {
  this._controller = AnimationController(
      duration: const Duration(milliseconds: 1000), vsync: this);
  this._animation =
      Tween(begin: 0.0, end: 1.0).animate(CurvedAnimation(
    parent: _controller,
    curve: Curves.easeIn,

Widget build(BuildContext context) {
  if(this.error) {
    this.error = false;
  return Container(
    child: if (this.error)
            child: FadeTransition(
              opacity: _animation,
              child: Column(
                children: (
                    padding: const EdgeInsets.all(8.0),
                    child: Image.asset("assets/images/sad_face.png"),

In the code above FadeTransition() The widget is animated at the first launch of the application.
and the visibility of FadeTransition() is tipped by the error variable.
but when next time FadeTransition() the widget is visible is not it animated?

what's missing, when we rock FadeTransition() the widget must be animated whenever it appears!

How can I prevent the conversion of floating / decimal numbers to text in Google Sheets? (IOS)

I have a cell with the value 2.2 that is displayed as text. I can not convert the text value format to a number.

Screenshot 1 shows that the cell format is a number
Screenshot 1

Screenshot 2 shows that using the standard formula, the cell value type is text
Screen capture

type info formula:

I am currently using Google Sheets v1.2019.46202 on iOS 13.1.3.

mobile application – Notification of toast over content or floating

I'm working on a mobile app and I'm trying to understand how to view recoverable and unrecoverable errors in the context of a list. If a list of items is extracted in the initial request and that a subsequent page load fails, how to inform the user of the error? Toast Notification maybe?

In the current implementation, the toast notification appears at the top of the screen, lowering the content. I'm not sure this is the best approach and I wonder if I should let the toast float at the top. Thoughts?

enter the description of the image here

Mantisa and party exponents floating point numbers

what is the mantissa and exponent part of 502.4 and 23.6 and how can I perform an arithmetic operation on these floating point numbers. kindly somebody please explain

Floating Point – How to Calculate the Exponential Integral?

(I'm not sure this is the right forum.)

I write a program that uses the first count function. Right now, I'm using x/log(x)but I want to move on to something more specific. A better approximation is the logarithmic integral function (actually, its Eulerian variant), which can be computed from the exponential integral. Now, how can I calculate the exponential integral? I am working on an Intel macOS system using Swift in order to use the various advanced floating point functions provided by Apple's system libraries if needed.