Archive: forth/complex

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complex number word sets

complex.fs	06May11 18:52:58EDT	23K	A revision of Julian V. Noble's complex arithmetic lexicon, with OpenMath principal expressions for inverse functions. Included in the FSL as Algorithm #60.
complex-kahan.fs	12Dec10 16:53:15EST	34K	Another revision that uses William Kahan's extended accuracy algorithms.
complex-kahan.log	12Dec10 16:52:50EST	5.8K	Change log for complex-kahan.fs.
complex.seq	19Feb03 14:42:46EST	7.8K	The basic complex arithmetic lexicon from the Forth Scientific Library.
zabs.seq	19Feb03 14:42:50EST	6.2K	A subset of complex.seq modified for testing zabs with the celefunt port in zabs.fs below.

tests

complex-test.fs complex-test-xf.fs	24Dec10 07:44:57EST 06May11 18:49:14EDT	27K 28K	Formal correctness tests for complex.fs, complex-kahan.fs, and pfe's COMPLEX-EXT environment. Here complex-test uses ttester.fs, and is included as an auxiliary file in the FSL, while complex-test-xf uses ttester-xf and supporting files in ttester-xf.zip.
complex-ieee-test.fs complex-ieee-test-xf.fs	30Nov10 18:05:30EST 12Dec10 17:05:29EST	28K 29K	Additional tests for IEEE 754 signed zero, signed infinity, and NaN properties of the complex functions, including the evaluation of functions having principal branches on either side of their cuts, by using appropriate real or imaginary, signed zero arguments. Here complex-ieee-test uses ttester.fs, while complex-ieee-test-xf uses ztester, and ttester-xf and supporting files in ttester-xf.zip.
ztester.fs ztester-test.fs	06Dec10 14:50:34EST 10Dec10 11:00:18EST	9.3K 11K	Tester for complex numbers on the fp stack, and tests for itself. The tester requires a complex number library such as complex.fs, complex-kahan.fs, and pfe's COMPLEX-EXT environment, plus ttester-xf; and the tests require ttester-xf and supporting files in ttester-xf.zip.
lagroots-test.fs lagroots.zip	30Nov10 16:05:36EST 02Dec10 12:50:04EST	14K 33K	Tests using ttester-xf for Julian Noble's Forth Scientific Library Algorithm 61, the Laguerre algorithm for complex polynomial roots. The .zip file includes the algorithm, tests, and all files necessary to run them.
ftester-old.fs	07Nov10 10:03:09EST	5.8K	Obsolete, functionality absorbed into ttester.

ports of celefunt tests

The following complex function accuracy tests are ported from W. J. Cody's celefunt Fortran package. They all require machar.fs and ren.fs from the next section, and all but zabs.fs require zfunstat.fs as well. In the style of the JVN lexicon, we call the port zelefunt.

These are not intended as models of Forth code; they are fairly literal translations from Fortran, aimed at allowing exact comparison of the Fortran and Forth results. This especially applies to the random number generator ren.fs. Cody asserts that its algorithm is good enough for this purpose, while acknowledging its crudeness.

zabs.fs	19Jan05 17:40:37EST	8.9K
zexp.fs	19Jan05 17:41:05EST	5.7K
zln.fs	19Jan05 17:41:16EST	4.5K
zpow.fs	19Jan05 17:41:30EST	5.6K
zsincos.fs	19Jan05 17:42:53EST	7.1K
zsqrt.fs	19Jan05 17:41:59EST	4.1K
zabs-results.txt	19Jan05 17:40:42EST	3.1K
zexp-results.txt	19Jan05 17:40:57EST	7.8K
zln-results.txt	19Jan05 17:41:11EST	6.8K
zpow-results.txt	19Jan05 17:41:25EST	6.8K
zsincos-results.txt	19Jan05 17:41:45EST	6.7K
zsqrt-results.txt	19Jan05 17:41:55EST	3.8K

ports of celefunt subprograms

machar.fs	09Mar05 08:44:50EST	15K
ren.fs	04Dec04 10:17:52EST	1.6K
zfunstat.fs	19Jan05 17:40:06EST	13K

Borda's mouthpiece

William Kahan uses Borda's mouthpiece as an example where the proper treatment of signed zero makes a dramatic difference. See the plots in his article on The Baleful Effect of Computer Benchmarks. The files below verify correctness for the same example with any of complex.fs, complex-kahan.fs, or the pfe primitive port of the complex lexicon, and incorrectness with a g77 version of Fortran.

borda.html	04Feb05 15:13:00EST	2.5K	The plots.
borda.pdf	11Jan09 09:56:54EST	45K	The plots as pdf.
borda.fs	11Jan09 08:58:32EST	6.7K	ANSForth source for the plot data.
borda.tar.gz	11Jan09 09:57:30EST	51K	An archive containing the above two files, Fortran source, and the LaTeX/PSTricks source for borda.pdf, with the UPDL license.

links

• Online book: Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Information by M. Abramowitz and I. Stegun.
• ACM article, preprint: "According to Abramowitz and Stegun" or arcoth needn't be uncouth by Robert M. Corless, David J. Jeffrey, Stephen M. Watt, and James H. Davenport.
• The OpenMath standard home page. The two content dictionaries that include the complex inverse functions are transc1 and transc3.
• William Kahan's home page. Unfortunately his standard-setting article is not online: "Branch Cuts for Complex Elementary Functions", The State of the Art in Numerical Analysis, A. Iserles and M. J. D. Powell, eds., Clarendon Press, Oxford, 1987, pp. 165-211. There is, however, an augmented and superceding version in three pieces here: slits02.pdf, slits34.pdf, and slits56.pdf.
• James Davenport's home page.
• Treatment of the inverse functions in Mathematica.
• ACM article: Algorithm 714; CELEFUNT: a portable test package for complex elementary functions by W. J. Cody.
• John von Neumann lecture: The Baleful Effect of Computer Languages and Benchmarks upon Applied Mathematics, Physics and Chemistry by William Kahan. A longer version of the article mentioned under Borda's mouthpiece.

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