TAOCP Vol 2: Seminumerical Algorithms · Week 60
TAOCP 4.2.3 Double-Precision Calculations: reading guide
Building higher-precision floating arithmetic out of single-precision operations, with care for carries and rounding.
Time About 4 hours this week
Why it matters
The same idea powers double-double and quad-double libraries used when 64-bit floats are not enough.
Before you start
- 4.2.2 Accuracy of Floating Point Arithmetic
How to approach it
Read for the method. Skim MIX-heavy details. If you are curious, look up the two-sum trick, which is the modern building block.
Exercises
This is a light section. Skim the exercises, do the ones rated 10 or under in your head, and spend the spare time catching up on earlier exercises you skipped.