Binary arithmetic | Floating point types

Quadruple-precision floating-point format

In computing, quadruple precision (or quad precision) is a binary floating point–based computer number format that occupies 16 bytes (128 bits) with precision at least twice the 53-bit double precision. This 128-bit quadruple precision is designed not only for applications requiring results in higher than double precision, but also, as a primary function, to allow the computation of double precision results more reliably and accurately by minimising overflow and round-off errors in intermediate calculations and scratch variables. William Kahan, primary architect of the original IEEE-754 floating point standard noted, "For now the 10-byte Extended format is a tolerable compromise between the value of extra-precise arithmetic and the price of implementing it to run fast; very soon two more bytes of precision will become tolerable, and ultimately a 16-byte format ... That kind of gradual evolution towards wider precision was already in view when IEEE Standard 754 for Floating-Point Arithmetic was framed." In IEEE 754-2008 the 128-bit base-2 format is officially referred to as binary128. (Wikipedia).

Quadruple-precision floating-point format
Video thumbnail

Binary 4 – Floating Point Binary Fractions 1

This is the fourth in a series of videos about the binary number system which is fundamental to the operation of a digital electronic computer. In particular, this video covers the representation of real numbers using floating point binary notation. It begins with a description of standard

From playlist Binary

Video thumbnail

Binary 5 – Floating Point Range versus Precision

This is the fifth in a series of videos about the binary number system which is fundamental to the operation of a digital electronic computer. In particular, this video elaborates on the representation of real numbers using floating point binary notation. It explains how the relative allo

From playlist Binary

Video thumbnail

IEEE 754 Standard for Floating Point Binary Arithmetic

This computer science video describes the IEEE 754 standard for floating point binary. The layouts of single precision, double precision and quadruple precision floating point binary numbers are described, including the sign bit, the biased exponent and the mantissa. Examples of how to con

From playlist Binary

Video thumbnail

Binary 8 – Floating Point Binary Subtraction

This is the eighth in a series of videos about the binary number system which is fundamental to the operation of a digital electronic computer. In particular, this video covers subtraction of floating point binary numbers for a given sized mantissa and exponent, both in two’s complement.

From playlist Binary

Video thumbnail

Binary 7 – Floating Point Binary Addition

This is the seventh in a series of videos about the binary number system which is fundamental to the operation of a digital electronic computer. In particular, this video covers adding together floating point binary numbers for a given sized mantissa and exponent, both in two’s complement.

From playlist Binary

Video thumbnail

12/05/2019, Nicolas Brisebarre

Nicolas Brisebarre, École Normale Supérieure de Lyon Title: Correct rounding of transcendental functions: an approach via Euclidean lattices and approximation theory Abstract: On a computer, real numbers are usually represented by a finite set of numbers called floating-point numbers. Wh

From playlist Fall 2019 Symbolic-Numeric Computing Seminar

Video thumbnail

Everything You Need to Know About JPEG - Episode 6 Part 2: Inverse DCT

In this series you will learn all of the in-depth details of the complex and sophisticated JPEG image compression format In this episode, we learn all about performing the Inverse Discrete Cosine Transform, to transform DCT coefficient matrices into YCbCr color matrices, and how to optimi

From playlist Fourier

Video thumbnail

How to subtract a larger decimal from a smaller decimal

👉 You will learn how to add and subtract numbers in decimal form. When adding and subtracting decimals it is very important to align the decimal points and use zero as space holders. Then you will apply the operations just like we do in multi-digit operations but keep track of the decima

From playlist Decimals

Video thumbnail

Learn how to subtract a larger decimal from a smaller decimal

👉 You will learn how to add and subtract numbers in decimal form. When adding and subtracting decimals it is very important to align the decimal points and use zero as space holders. Then you will apply the operations just like we do in multi-digit operations but keep track of the decima

From playlist Decimals

Video thumbnail

Emil Saucan (7/29/22): Discrete Morse Theory, Persistent Homology and Forman-Ricci Curvature

Abstract: It was observed experimentally that Persistent Homology of networks and hypernetworks schemes based on Forman's discrete Morse Theory and on the 1-dimensional version of Forman's Ricci curvature not only both perform well, but they also produce practically identical results. We s

From playlist Applied Geometry for Data Sciences 2022

Video thumbnail

Adding three digit decimals

👉 You will learn how to add and subtract numbers in decimal form. When adding and subtracting decimals it is very important to align the decimal points and use zero as space holders. Then you will apply the operations just like we do in multi-digit operations but keep track of the decima

From playlist Decimals

Video thumbnail

Floating Point Representation

Floating Point Representation

From playlist Scientific Computing

Video thumbnail

Overview Surveys - Nikhil Padmanabhan

Nikhil Padmanabhan - September 24, 2015 The interpretation of low-redshift galaxy surveys is more complicated than the interpretation of CMB temperature anisotropies. First, the matter distribution evolves nonlinearly at low redshift, limiting the use of perturbative methods. Secondly, we

From playlist Unbiased Cosmology from Biased Tracers

Video thumbnail

Urs Lang (2/3/23): Combinatorial dimension and higher-rank hyperbolicity

Dress characterized metric spaces of combinatorial dimension at most n in terms of a 2(n+1)-point inequality. We investigate a relaxed version of this inequality, which in the case n = 1 reduces to Gromov's quadruple definition of δ-hyperbolicity and which we experimentally call (n,δ)-hype

From playlist Vietoris-Rips Seminar

Video thumbnail

Dynamo onset as a first-order transition by Rahul Pandit

GdR Dynamo 2015 PROGRAM LINK: www.icts.res.in/program/GDR2015 DATES : 01 Jun, 2015 - 12 Jun, 2015 VENUE : ICTS-TIFR, IISc campus, Bangalore DESCRIPTION : Dynamo or self-induced magnetic field generation in nature and laboratory is a very important area of research in physics, astrop

From playlist GdR Dynamo 2015

Video thumbnail

Decimal Notation: Writing Decimals in Words

This video explains how to write numbers in decimal notation in words. http://mathispower4u.com

From playlist Introduction to Decimals

Related pages

IEEE 754 | Hexadecimal | Offset binary | Significand | MATLAB | Long double | Primitive data type | IBM hexadecimal floating-point | IEEE 754-2008 | Extended precision | POWER9 | Exponent bias | Double-precision floating-point format | Arbitrary-precision arithmetic | Sign bit | Unit in the last place | Infinity | NaN | Round-off error | Computer number format | Boost (C++ libraries) | ISO/IEC 10967