| Title: | Accurate Floating Point Sums and Products |
| Version: | 0.7 |
| Description: | Most of the time floating point arithmetic does approximately the right thing. When adding sums or having products of numbers that greatly differ in magnitude, the floating point arithmetic may be incorrect. This package implements the Kahan (1965) sum <doi:10.1145/363707.363723>, Neumaier (1974) sum <doi:10.1002/zamm.19740540106>, pairwise-sum (adapted from 'NumPy', See Castaldo (2008) <doi:10.1137/070679946> for a discussion of accuracy), and arbitrary precision sum (adapted from the fsum in 'Python' ; Shewchuk (1997) https://people.eecs.berkeley.edu/~jrs/papers/robustr.pdf). In addition, products are changed to long double precision for accuracy, or changed into a log-sum for accuracy. |
| Depends: | R (≥ 3.2) |
| License: | GPL-2 | GPL-3 [expanded from: GPL (≥ 2)] |
| Encoding: | UTF-8 |
| RoxygenNote: | 7.3.2 |
| Suggests: | testthat |
| BugReports: | https://github.com/nlmixr2/PreciseSums/issues/ |
| URL: | https://github.com/nlmixr2/PreciseSums |
| NeedsCompilation: | yes |
| Packaged: | 2024-09-17 21:52:49 UTC; matt |
| Author: | Matthew Fidler [aut, cre, cph], Raymond Hettinger [cph, aut], Jonathan Shewchuk [cph, aut], Julian Taylor [cph, aut], Nathaniel Smith [cph, aut], NumPy Team [cph], Python Team [cph] |
| Maintainer: | Matthew Fidler <matthew.fidler@gmail.com> |
| Repository: | CRAN |
| Date/Publication: | 2024-09-17 22:20:12 UTC |
Get the function pointers to link in C
Description
This allows the user to use the C functions in their own C/C++ packages without binary linking to PreciseSums.
Usage
.preciseSumsPtr()
Value
list of function pointers
Author(s)
Matthew L. Fidler
Examples
.preciseSumsPtr()
Return an accurate floating point sum of values
Description
This method avoids loss of precision by tracking multiple intermediate partial sums. Based on python's math.fsum
Usage
fsum(numbers)
Arguments
numbers |
A vector of numbers to sum. |
Value
Sum of numbers without loss of precision
The algorithm's accuracy depends on IEEE-754 arithmetic guarantees and the typical case where the rounding mode is half-even. On some non-Windows builds, the underlying C library uses extended precision addition and may occasionally double-round an intermediate sum causing it to be off in its least significant bit.
Author(s)
Matthew Fidler (R implementation), Raymond Hettinger, Jonathan Shewchuk, Python Team
References
https://docs.python.org/2/library/math.html https://github.com/python/cpython/blob/a0ce375e10b50f7606cb86b072fed7d8cd574fe7/Modules/mathmodule.c
Shewchuk, JR. (1996) Adaptive Precision Floating-Point Arithmetic and Fast Robust Geometric Predicates. http://www-2.cs.cmu.edu/afs/cs/project/quake/public/papers/robust-arithmetic.ps
Examples
sum(c(1,1e100,1,-1e100)) ## Should be 2, gives 0
fsum(c(1,1e100,1,-1e100)) ## Gives 2.
Using the Kahan method, take a more accurate sum
Description
Using the Kahan method, take a more accurate sum
Usage
kahanSum(numbers)
Arguments
numbers |
A vector of numbers to sum. |
Value
Sum of numbers
References
https://en.wikipedia.org/wiki/Kahan_summation_algorithm
Examples
sum(c(1,1e100,1,-1e100)) ## Should be 2, gives 0
kahanSum(c(1,1e100,1,-1e100)) ## Not accurate enough for the correct result. (still = 0)
Using the Neumaier method, take a more accurate sum
Description
Using the Neumaier method, take a more accurate sum
Usage
neumaierSum(numbers)
Arguments
numbers |
A vector of numbers to sum. |
Value
Sum of numbers, a bit more accurate than kahanSum
References
https://en.wikipedia.org/wiki/Kahan_summation_algorithm
Examples
sum(c(1,1e100,1,-1e100)) ## Should be 2, gives 0
neumaierSum(c(1,1e100,1,-1e100)) ## Gives 2
Return an accurate floating point sum of values
Description
This was taken by NumPy and adapted for use here. It is more accurate than a standard sum, but still has numerical issues. Its main benefit is that it is about the same amount of time as a standard time with the added accuracy.
Usage
pairwiseSum(numbers)
Arguments
numbers |
A vector of numbers to sum. |
Value
A sum of numbers with a rounding error of O(lg n) instead of O(n).
Author(s)
Matthew Fidler (R implementation), Julian Taylor, Nathaniel J Smith, and NumPy team. #' @examples sum(c(1,1e100,1,-1e100)) ## Should be 2, gives 0 pairwiseSum(c(1,1e100,1,-1e100)) ## Should be 2, still 0
References
https://github.com/numpy/numpy/pull/3685
Using PreciceSums's default method, take a product
Description
Using PreciceSums's default method, take a product
Usage
psProd(numbers)
Arguments
numbers |
A vector of numbers to sum. |
Value
Product of numbers
Choose the type of product to use in PreciceSums. These are used in the
PreciceSums prod blocks
Description
Choose the type of product to use in PreciceSums. These are used in the
PreciceSums prod blocks
Usage
psSetProd(type = c("long double", "double", "logify"))
Arguments
type |
Product to use for
|
Value
nothing
Author(s)
Matthew L. Fidler
Choose the type of sums to use for PreciceSums.
Description
Choose the types of sums to use in PreciceSums. These are used in the
PreciceSums sum blocks and the psSum function
Usage
psSetSum(type = c("pairwise", "fsum", "kahan", "neumaier", "klein", "c"))
Arguments
type |
Sum type to use for
|
Value
nothing
Author(s)
Matthew L. Fidler
Using PreciceSums's default method, take a sum
Description
Using PreciceSums's default method, take a sum
Usage
psSum(numbers)
Arguments
numbers |
A vector of numbers to sum. |
Value
Sum of numbers