1 Computing with Numbers
1.2 Representing the Real Numbers
1.3 Properties of Number Formats
1.5 Decoupling Precision from Magnitude
2 Numbers in Floating Point
2.1 Extending the Real Numbers
2.2 Binary Scientific Notation
2.3 Floating Point Bit Layouts
2.7 Other Floating-Point Formats
3 Sources of Error
3.1 Rounding and Rounding Modes
3.3 The Inexact (IX) Exception
3.4 Invalid Operations (IO) and Division by Zero (DZ)
3.5 Overflow (OF) and Underflow (UF)
3.6 Exceptions and Rounding in Processors
4 The Basic Arithmetic Operations
4.1 Multiplication
4.2 Division
4.4 Square Root
4.6 The Algebra of Floating Point
5 Comparing Floating-Point Numbers
5.4 Setting Epsilon
5.8 Interactions between Comparisons
6 Conversion to and from Floating Point
6.2 Narrowing and Widening Formats
6.3 Integer to Float Conversion
6.4 Float to Integer Conversion
6.5 String to Float
6.6 Float to String
6.7 Exactness of Decimals in Floating Point
6.8 Bit Casting Floating-Point Numbers
7 Numerical Operations
7.1 Remainder and Modulus Operations
7.2 Exponentials and Logarithms
7.3 Powers and Roots
8 Bitwise Manipulations
8.3 Iterators
8.4 NaN Boxing
9 Working with Error in Floating Point
9.2 Changes of Units
9.5 Error Analysis
9.6 Avoiding Invalid Operations
9.7 Fast Math Compiler Options
10 Function Approximation
10.1 Accuracy of Approximations
10.2 Polynomial Approximations
10.3 Newton-Raphson and Iterative Methods
10.4 Lookup Tables and Interpolation
10.5 Comparison of Math Libraries
10.6 Floating Point Bit Hacks
11 Geometry in Floating Point
11.2 Splines
11.3 B´ezier Curves and Surfaces
11.4 B-Splines and NURBS
11.5 Faraway Objects and Floating Point
11.6 Intersection Finding and Collision Detection
11.7 The Gilbert-Johnson-Keerthi Algorithm
12 Numerical Integration
12.1 Simulation Accuracy and Error
12.2 Euler Integration
12.3 Adding Energy Conservation to Euler
12.4 Leapfrog Integration and Velocity Verlet
12.5 Predictor-Corrector Methods
12.6 Runge-Kutta Methods
12.7 Direct Calculation of Trajectories
Biography
Nima Badizadegan is an engineer who works at the intersection of computer systems and mathematics. His past experience includes work at Google and on Wall Street, as well as being a consultant and startup founder. Badizadegan has several publications in the fields of simulation and computer arithmetic and is the inventor of over 10 patents. He is a member of the IEEE and ACM and contributes to the IEEE 754 floating point standard. He is the author of the popular technical blog Speculative Branches (https://specbranch.com), where he writes about computer systems, software engineering, and math.
