Beyond the Floating Point Computations - What’s New, What’s Useful?
summary
Covers IEEE 754 limits and practical alternatives with concrete numbers: binary16 (half) shows epsilon ≈ 9e-4 and max ≈ 65 000 but often lacks hardware support; zfp lossy compression achieves up to 16× size reduction and an example gives 73% compression with MSE ≈ 0.063 on values in −123..123 while preserving visual fidelity; introduces posit (Gustafson) with tapered accuracy, no NaNs, mandated fused ops and a 12-bit posit example that shrinks storage by 62.5% while keeping area calculation error near 1%.
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chapters (28)
- 0:00Introduction
- 1:00The Plan
- 3:09Computations
- 4:52In practice
- 6:37Subsection brief intro
- 7:25Background
- 8:29Why do we need a standard
- 9:45The proposed standard
- 10:52Floating point formats
- 16:38Rounding
- 21:05Examples
- 24:17Threshold
- 25:40Improvements
- 28:22Example
- 31:44Numerical Limits
- 36:05Floating Point Compression
- 39:14How it works
- 41:09Characteristics
- 42:07Compression modes
- 42:32Limitations
- 43:11ZFP
- 46:36Tensor Decomposition
- 47:24ItripleE
- 49:37I3 Standard
- 50:41I3 754
- 51:58Arranging beats
- 55:42Interpolation
- 58:30Software
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