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This is the floating-point-contractions Reference Manual, generated automatically by Declt version 2.4 "Will Decker" on Wed Jun 20 11:47:10 2018 GMT+0.
• Introduction: | What floating-point-contractions is all about | |
• Systems: | The systems documentation | |
• Files: | The files documentation | |
• Packages: | The packages documentation | |
• Definitions: | The symbols documentation | |
• Indexes: | Concepts, functions, variables and data types |
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.
• The floating-point-contractions system: |
Paul M. Rodriguez <pmr@ruricolist.com>
MIT
Numerically stable contractions of floating-point operations.
Files are sorted by type and then listed depth-first from the systems components trees.
• Lisp files: |
• The floating-point-contractions.asd file: | ||
• The floating-point-contractions/package.lisp file: | ||
• The floating-point-contractions/floating-point-contractions.lisp file: |
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floating-point-contractions.asd
floating-point-contractions (system)
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floating-point-contractions (system)
package.lisp
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package.lisp (file)
floating-point-contractions (system)
floating-point-contractions.lisp
sq (function)
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Packages are listed by definition order.
• The floating-point-contractions package: |
package.lisp (file)
common-lisp
sq (function)
Definitions are sorted by export status, category, package, and then by lexicographic order.
• Exported definitions: | ||
• Internal definitions: |
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• Exported functions: |
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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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• Internal functions: |
Previous: Internal definitions, Up: Internal definitions [Contents][Index]
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• Concept index: | ||
• Function index: | ||
• Variable index: | ||
• Data type index: |
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Jump to: | F L |
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Jump to: | F L |
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Jump to: | E F H L S |
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Jump to: | E F H L S |
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Next: Data type index, Previous: Function index, Up: Indexes [Contents][Index]
Previous: Variable index, Up: Indexes [Contents][Index]
Jump to: | F P S |
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Jump to: | F P S |
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