One Polynomial Approximation to Produce Correctly Rounded Results of an Elementa
summary
Claims a single polynomial, found by solving linear programs over rounding intervals, yields correctly rounded elementary-function results across multiple precisions and modes by generating it for n+2 bits using the round-to-odd mode. Prototype RLIBM prototype implements a 32-bit float library that is correctly rounded for all five IEEE rounding modes and for >160 FP formats (10–32 bits, up to 23 mantissa bits), identifies singleton intervals (special cases), and reports speedups (≈1.1–1.9×) over mainstream and correctly rounded libraries.
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chapters (16)
- 0:00Intro
- 0:32Elementary Functions
- 1:56What Is This Paper About
- 3:30What is a Correctly Rounded Result?
- 4:14The RLIBM Project
- 6:04A Naive Solution
- 6:45Double Rounding Is The Enemy
- 8:03Round-to-Odd Rounding Mode
- 9:19How Does Round-to-Odd Work?
- 9:45Correctly Rounded Results with Round-to-Odd
- 10:08The RLIBM Approach for Multiple Representations
- 10:44Handling Singleton Intervals
- 12:46Prototypes And Experimental Evaluation
- 13:25RLIBM-ALL Functions Are Correct
- 14:39RLIBM-ALL Functions Are Fast
- 17:00Conclusion
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