This package provides extended precision versions of Float64, Float32, Float16.
| type name | significand | exponent | ◊ | base type | significand | exponent |
|---|---|---|---|---|---|---|
Double64 | 106 bits | 11 bits | ◊ | Float64 | 53 bits | 11 bits |
Double32 | 48 bits | 8 bits | ◊ | Float32 | 24 bits | 8 bits |
Double16 | 22 bits | 5 bits | ◊ | Float16 | 11 bits | 5 bits |
Double64is a magnitude ordered, nonoverlapping pair of Float64s
Double32is a magnitude ordered, nonoverlapping pair of Float32s
Double16is a magnitude ordered, nonoverlapping pair of Float16s
- arithmetic (
+,-,*,/) is exact - elementary functions are quite accurate
- often better than C "double-double" libraries
For Double64 arguments within 0.0..2.0 except tan(x), cot(x) as they approach ±Inf
- expect the
abserrof elementary functions to be 1e-30 or less - expect the
relerrof elementary functions to be 1e-28 or less
When used with reasonably sized values, expect successive DoubleFloat ops to add no more than 10⋅𝘂² to the cumulative relative error (𝘂 is the relative rounding unit, usually 𝘂 = eps(x)/2). Relative error can accrue steadily. After 100,000 DoubleFloat ops with reasonably sized values, the relerr could approach 100,000 * 10⋅𝘂². In practice these functions are considerably more resiliant: our algorithms come frome seminal papers and extensive numeric investigation.
should you encounter a situation where either error grows strongly in one direction, please submit an issue