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This is the floating-point-contractions Reference Manual, generated automatically by Declt version 4.0 beta 2 "William Riker" on Mon Aug 15 04:33:49 2022 GMT+0.
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This system provides some numerically stable, contracted versions of common but unstable floating-point operations. | Export | (AKA) | Computes | |----------+----------+-----------------| | log1+ | log1p | log (1 + x) | | log1- | log1m | log (1 - x) | | log1+/x | | (log (1 + x))/x | | exp-1 | expm1 | exp(x) - 1 | | exp-1/x | | (exp(x)-1)/x | | expt-1 | powm1 | (x^y)-1 | | log1-exp | log1mexp | log(1 - exp(x)) | | log1+exp | log1pexp | log(1 + exp(x)) | | log2-exp | log2mexp | log(2 - exp(x)) | | logexp-1 | logexpm1 | log(exp(a) -1) | | hypot | | sqrt(x^2 + y^2) |
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The main system appears first, followed by any subsystem dependency.
Numerically stable contractions of floating-point operations.
Paul M. Rodriguez <pmr@ruricolist.com>
MIT
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Files are sorted by type and then listed depth-first from the systems components trees.
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floating-point-contractions (system).
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floating-point-contractions (system).
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package.lisp (file).
floating-point-contractions (system).
sq (function).
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Packages are listed by definition order.
common-lisp.
sq (function).
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Definitions are sorted by export status, category, package, and then by lexicographic order.
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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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