This is the floating-point-contractions Reference Manual, generated automatically by Declt version 4.0 beta 2 "William Riker" on Wed Mar 15 06:03:46 2023 GMT+0.
The main system appears first, followed by any subsystem dependency.
floating-point-contractions
Numerically stable contractions of floating-point operations.
Paul M. Rodriguez <pmr@ruricolist.com>
MIT
package.lisp
(file).
floating-point-contractions.lisp
(file).
Files are sorted by type and then listed depth-first from the systems components trees.
floating-point-contractions/floating-point-contractions.asd
floating-point-contractions/package.lisp
floating-point-contractions/floating-point-contractions.lisp
floating-point-contractions/floating-point-contractions.asd
floating-point-contractions
(system).
floating-point-contractions/package.lisp
floating-point-contractions
(system).
floating-point-contractions/floating-point-contractions.lisp
package.lisp
(file).
floating-point-contractions
(system).
sq
(function).
Packages are listed by definition order.
floating-point-contractions
common-lisp
.
sq
(function).
Definitions are sorted by export status, category, package, and then by lexicographic order.
Compute (- (exp x) 1) stably even when X is near zero.
Compute (/ (- (exp x) 1) x) stably even when X is near zero.
Compute (a^z)-1 stably even when A is close to 1 or Z is close to zero.
Compute the hypotenuse of X and Y without danger of floating-point overflow or underflow.
Binary logarithm.
Decimal logarithm.
Natural logarithm.
Compute (log (+ 1 x)) stably even when X is near zero.
Compute (/ (log (+ 1 x)) x) stably even when X is near zero.
Accurately compute log(1+exp(x)) even when A is near zero.
Compute (log (- 1 x)) stably even when X is near zero.
Compute log(1-exp(x)) stably even when A is near zero.
This is sometimes known as the E_3, the third Einstein function.
See Mächler 2008 for notes on accurate calculation.
https://cran.r-project.org/web/packages/Rmpfr/vignettes/log1mexp-note.pdf
Compute log(2-exp(x)) stably even when X is near zero.
Compute log(exp(a)-1) stably even when A is small.
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