#Demystifying Floating Point John Farrier, CPPCon 2015

Slides and Source Code from "Demystifying Floating Point Numbers" given at CPPCon 2015.

##Notes

• IEEE Single Format - 1 sign, 8 exponent, 23 fraction
• IEEE Double Format - 1 sign, 11 exponent, 52 fraction
• Has several rounding options (Java only permits "Round to Nearest")
• Do not test for equality
• Order of operations matters
• The relative magnitudes of numbers involved in a computataion matters
• Prefer to multiply, add, and subtract - divide only when necessary
• Avoid elementary functions i.e. logarithmic, exponential, trigonometric, hyperbolic

##General Online References

• A Logarithm Too Clever by Half
• Anatomy of a floating point number
• Comparing Floating Point Numbers
• Demystifying Floating Point
• Don't Store That in a Float
• Five Tips for Floating Point Programming
• Floating Point Comparison
• Floating Point Determinisim
• Floating point number representation
• Floating Point Operations and Streaming SIMD Extensions
• Floating Point Representation
• Floating Point
• IEEE 754 Converter
• IEEE floating-point exceptions in C++
• Is floating point math deterministic?
• Is Your Model Susceptible to Floating-Point Errors?
• Lecture Notes on the Status of IEEE 754, Kahan, October 1, 1997
• Mathematics in Video Games
• Miscalculating Area and Angles of a Needle-like Triangle
• Visualizing Floats
• We Really Don't Know How To Compute!
• What Every Computer Scientist Should Know About Floating-Point Arithmetic

##General Offline References

• Hacker's Delight, (Warren)
• Handbook of Floating-Point Arithmetic (Muller, Brisebarre)
• Numerical Computing with IEEE Floating Point Arithmetic (Overton)

##Compiler Specific Information ###Visual Studio Microsoft Visual C++ Floating-Point Optimization https://msdn.microsoft.com/library/aa289157.aspx

####Compiler Flags

• /fp:[precise | except[-] | fast | strict ]

####Pragmas

• float_control( value,setting [push] | push | pop )
• fenv_access [ON | OFF]
• fp_contract [ON | OFF]

###GCC Math_Optimization_Flags Semantics of Floating Point Math in GCC https://gcc.gnu.org/wiki/FloatingPointMath https://gcc.gnu.org/wiki/Math_Optimization_Flags

####Compiler Flags

• -ffinite-math-only
• -fno-rounding-math
• -fno-signaling-nans
• -fno-signed-zeros
• -fnotrapping-math
• -frounding-math
• -fsignaling-nans
• -funsafe-math-optimizations
• -funsafe-math-optimizations