Demystifying Floating Point
summary
Explains how IEEE floats are stored (sign/exponent/mantissa), demonstrates epsilon and relative error (pi shows ~2.8e-8 relative error), and details guard/round/sticky bits and rounding modes. Shows unstable algorithms: naive time-accumulation by adding small deltas drifts into tenths of a second over minutes, while a fixed-frame counter or integer ticks (fixed‑point) keeps correct time. Uses Google Test and code on GitHub, recommends compiler warnings, FP exceptions, FMA/SSE where available, and preferring stable algorithms or doubles for precision.
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chapters (13)
- 0:00Introduction to floating point
- 2:52Floating point standards
- 6:23Floating point representation
- 10:44Precision and significant digits
- 14:07Floating point errors
- 16:42Rounding and rounding modes
- 21:16Stable algorithms for precision
- 24:31Floating point in simulations
- 30:32Mathematical identities and compiler assumptions
- 32:21Floating point exceptions
- 33:47Compiler warnings and optimizations
- 35:35Floating point tricks and testing
- 37:19Q&A session
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