August 2008
Intermediate to advanced
368 pages
7h 54m
English
Content preview from F# for Scientists![Values i of the type int, called machine-precision integers, are an exact representation of a consecutive subset of the set of integers i ϵ [I... u] C Z where I and u are given by min_int and max_int, respectively.](/api/v2/epubs/urn:orm:book:9780470242117/files/figs/0401.png)
Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
O’Reilly covers everything we've got, with content to help us build a world-class technology community, upgrade the capabilities and competencies of our teams, and improve overall team performance as well as their engagement.I wanted to learn C and C++, but it didn't click for me until I picked up an O'Reilly book. When I went on the O’Reilly platform, I was astonished to find all the books there, plus live events and sandboxes so you could play around with the technology.I’ve been on the O’Reilly platform for more than eight years. I use a couple of learning platforms, but I'm on O'Reilly more than anybody else. When you're there, you start learning. I'm never disappointed.I'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do.
Chapter 4. NUMERICAL ANALYSIS
Computers can only perform finite computations. Consequently, computers only make use of finite precision representations of numbers. This has several important implications in the context of scientific computation.
This chapter provides an overview of the representations and properties of values of types int and float, used to represent members of the sets Z and R, respectively. Practical examples demonstrating the robust use of floating-point arithmetic are then given. Finally, some other forms of arithmetic are discussed.
NUMBER REPRESENTATION
In this section, we shall introduce the representation of integer and floating-point numbers before outlining some properties of these representations.
Machine-precision integers
Positive integers are represented by several, least-significant binary digits (bits). For example, the number 1 is represented by the bits ... 00001 and the number 11 is represented by the bits ... 01011. Negative integers are represented in twoscomplement format. For example, the number −1 is represented by the bits ... 11111 and the number −11 is represented by the bits ... 10101.
Figure 4.1. Values i of the type int, called machine-precision integers, are an exact representation of a consecutive subset of the set of integers i ϵ [I... u] C Z where I and u are given by min_int and max_int, respectively.
Consequently, the representation of ...
Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.
Read now
Unlock full access
More than 5,000 organizations count on O’Reilly
O’Reilly covers everything we've got, with content to help us build a world-class technology community, upgrade the capabilities and competencies of our teams, and improve overall team performance as well as their engagement.Julian F.
I wanted to learn C and C++, but it didn't click for me until I picked up an O'Reilly book. When I went on the O’Reilly platform, I was astonished to find all the books there, plus live events and sandboxes so you could play around with the technology.Addison B.
I’ve been on the O’Reilly platform for more than eight years. I use a couple of learning platforms, but I'm on O'Reilly more than anybody else. When you're there, you start learning. I'm never disappointed.Amir M.
I'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do.