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Calculate with error-free, faithful, and compensated transforms and extended signficands.
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README.md

AccurateArithmetic.jl

Floating point math with error-free, faithful, and compensated transforms.


 

These arithmetic functions calculate results with extended precision significands.
They are used as building blocks for extended precision floating point types.

Exports

The exported functions that are named with the postfixes _2, _3 &etc are functions that return 2 values or 3 values (respectively). The exported functions that are named with the postfix _ are functions that return the same number of values as it is given arguments. These are easier to use where the number of components to an extended precision value may vary. And they are more succinct where that is useful.

The functions add_hilo_acc and sub_hilo_acc expect their arguments in order of decreasing magnitude. This is an unchecked precondition.

function n args in n values out transformation
add_ 2,3,4,5 n args in two_sum
add_2 2,3,4,5 2 two_sum
add_3 3,4,5 3 two_sum
add_4 4,5 4 two_sum
add_5 5 5 two_sum
add_hilo_ 2,3,4,5 n args in two_sum
add_hilo_2 2,3,4,5 2 quick_two_sum
add_hilo_3 3,4,5 3 quick_two_sum
add_hilo_4 4,5 4 quick_two_sum
add_hilo_5 5 5 quick_two_sum
sub_ 2,3 n args in two_diff
sub_2 2,3 2 two_diff
sub_3 3 3 two_diff
sub_hilo_ 2,3 n args in quick_two_diff
sub_hilo_2 2,3 2 quick_two_diff
sub_hilo_3 3 3 quick_two_diff
mul_ 2,3 n args in two_prod_fma
mul_2 2,3 2 two_prod_fma
mul_3 3 3 two_prod_fma
sqrt_ 1 2 faithful sqrt
inv_ 1 2 faithful divide
dvi_ 2 2 faithful divide
sqrt_2 1 2 faithful sqrt
inv_2 1 2 faithful divide
dvi_2 2 2 faithful divide
  • note that divide is abbreviated dvi (to distinguish it from div)

 

function mapping
sqr_2 hi(x^2), lo(x^2)
cub_2 hi(x^3), lo(x^3)
fma_ hi(fma), mid(fma), lo(fma)
fms_ hi(fms), mid(fms), lo(fms)
sum_ error-free compensated

 


this package is under development
repository created on 2018-01-26
tests pass on 2018-01-27
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