Release calc version 2.12.6.5

Fixed a man page warning about ./myfile where the leading dot
was mistook for an nroff macro.  Thanks goes to David Haller
<dnh at opensuse dot org> for providing the patch.

Improved gen_v1(h,n) in lucas.cal for cases where h is not a
multiple of 3. Optimized the search for v(1) when h is a
multiple of 3.

Fixed a Makefile problem, reported by Doug Hays <doughays6 at gmail
dot com>, where if a macOS user set BINDIR, LIBDIR, CALC_SHAREDIR
or INCDIR in the top section, their values will be overwritten by
the Darwin specific section.

.gitignore

@@ -0,0 +1,100 @@
+# files and directories created during the building of calc and other Makefile actions
+#
+# NOTE: While many of these might be part of a released calc tarball, they are
+#	not consider development source.  Some other file(s) and/or programs
+#	generate these files.
+#
+.dynamic
+.hsrc
+Makefile.simple
+NOTES
+align32.h
+args.h
+cal/.all
+calc
+calc.1
+calc.usage
+calcerr.c
+calcerr.h
+conf.h
+cscript/.all
+cscript/4dsphere
+cscript/README
+cscript/fproduct
+cscript/mersenne
+cscript/piforever
+cscript/plus
+cscript/powerterm
+cscript/simple
+cscript/square
+custom/.all
+custom/Makefile.simple
+custom/libcustcalc*
+endian
+endian_calc.h
+fposval.h
+have_const.h
+have_fpos.h
+have_fpos_pos.h
+have_getpgid.h
+have_getprid.h
+have_getsid.h
+have_gettime.h
+have_memmv.h
+have_newstr.h
+have_offscl.h
+have_posscl.h
+have_rusage.h
+have_stdlib.h
+have_stdvs
+have_strdup.h
+have_string.h
+have_times.h
+have_uid_t.h
+have_unistd.h
+have_unused.h
+have_urandom.h
+have_ustat.h
+help/.all
+help/COPYING
+help/COPYING-LGPL
+help/binding
+help/bindings
+help/bug
+help/bugs
+help/builtin
+help/change
+help/changes
+help/copy
+help/cscript
+help/custom_cal
+help/errorcode
+help/errorcodes
+help/full
+help/funclist
+help/funclist.c
+help/libcalc
+help/man
+help/new_custom
+help/resource
+help/type
+help/usage
+libcalc*
+libcustcalc*
+longbits
+longbits.h
+sample_many
+sample_rand
+terminal.h
+ver_calc
+
+# other commonly excluded patterns
+#
+*~
+*.BAK
+core*
+.DS_Store
+*.dSYM/
+*.[oa]
+.*.swp
+*,v

BUGS

@@ -32,16 +32,25 @@ If you have tried all of the above and things still are not right,
 then it may be time to send in a bug report.  You can send bug
 and bug fixes reports to:
 
-    calc-bugs at asthe dot com
+	calc-bug-report at asthe dot com
 
-    [[ NOTE: Replace 'at' with @, 'dot' is with . and remove the spaces ]]
+	NOTE: Remove spaces and replace 'at' with @, 'dot' with .
-    [[ NOTE: The EMail address uses 'asthe', the web site URL uses 'isthe' ]]
 
-Your subject must contain the words:
+    This replaces the old calc-bugs at asthe dot com address.
+
+    To be sure we see your EMail reporting a calc bug, please use the
+    following phase in your EMail Subject line:
 
 	calc bug report
 
-You may have additional words in your subject line.
+    That phrase in your subject line will help ensure your request
+    will get past our anti-spam filters.  You may have additional
+    words in your subject line.
+
+    However, you may find it more helpful to simply subscribe
+    to the calc-tester mailing list (see below) and then to
+    send your report to that mailing list as a wider set calc
+    testers may be able to help you.
 
 When you send your report, please include the following information:
 
@@ -68,23 +77,18 @@ of a context diff patch).
 
 Known bugs:
 
+    The output of the alg_config.cal resource file is bogus.
+    We would welcome a replacement for this code.
+
     We are sure some more bugs exist.  When you find them, please let
     us know!  See the above for details on how to report and were to
     EMail your bug reports and hopefully patches to fix them.
 
 =-=
 
-Problems that have known work-a-rounds:
-
-    * There is a bug in gcc v4.1.0 that causes calc to fail the regression
-      test.  The work-a-round is to compile with gcc v4.1.1 or later.  This
-      problems was observed on Fedora 5.
-
-=-=
-
 mis-features in calc:
 
-    Some problems are not bugs but rarther mis-features / things that could
+    Some problems are not bugs but rather mis-features / things that could
     work better.  The following is a list of mis-features that should be
     addressed and improved someday.
 
@@ -129,7 +133,34 @@ mis-features in calc:
 
       will not.
 
-## Copyright (C) 1999-2007  Landon Curt Noll
+=-=
+
+To subscribe to the calc-tester mailing list, visit the following URL:
+
+	http://www.isthe.com/chongo/tech/comp/calc/calc-tester.html
+
+    This is a low volume moderated mailing list.
+
+    This mailing list replaces calc-tester at asthe dot com list.
+
+    If you need a human to help you with your mailing list subscription,
+    please send EMail to our special:
+
+	calc-tester-maillist-help at asthe dot com
+
+	NOTE: Remove spaces and replace 'at' with @, 'dot' with .
+
+    address.  To be sure we see your EMail asking for help with your
+    mailing list subscription, please use the following phase in your
+    EMail Subject line:
+
+	calc tester mailing list help
+
+    That phrase in your subject line will help ensure your
+    request will get past our anti-spam filters.  You may have
+    additional words in your subject line.
+
+## Copyright (C) 1999-2014  Landon Curt Noll
 ##
 ## Calc is open software; you can redistribute it and/or modify it under
 ## the terms of the version 2.1 of the GNU Lesser General Public License
@@ -145,10 +176,6 @@ mis-features in calc:
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## @(#) $Revision: 30.1 $
-## @(#) $Id: BUGS,v 30.1 2007/03/16 11:09:46 chongo Exp $
-## @(#) $Source: /usr/local/src/bin/calc/RCS/BUGS,v $
-##
 ## Under source code control:	1994/03/18 14:06:13
 ## File existed as early as:	1994
 ##

CHANGES

@@ -1,17 +1,516 @@
-The following are the changes from calc version 2.12.4.6 to date:
+The following are the changes from calc version 2.12.6.5 to date:
+
+    Fixed warning about undefined operations involving the qlink(q)
+    macro by deplacing that macro with an inline-function.  Thanks goes
+    to David Haller <dnh at opensuse dot org> for this fix.
+
+    NOTE for Windows 10 users: Pavel Nemec <pane at seznam dot cz>
+    reported that calc version 2.12.6.4 has been successfully
+    compiled, installed and running on Windows 10.  See README.WINDOWS
+    for more details.
+
+
+The following are the changes from calc version 2.12.6.1 to 2.12.6.3:
+
+    Improved gen_v1(h,n) in lucas.cal to use an even faster search method.
+
+    Improved are checking in lucas.cal.  In particular both h and n must be
+    integers >= 1.  In the case of both rodseth_xhn(x, h, n) and gen_v1(h, n)
+    h must be odd.
+
+    Fixed an C code indenting issue that was reported by Thomas Walter
+    <th dot walter42 at gmx dot de> in zfunc.c.
+
+    Fixed a man page warning about ./myfile where the leading dot
+    was mistook for an nroff macro.  Thanks goes to David Haller
+    <dnh at opensuse dot org> for providing the patch.
+
+    Improved gen_v1(h,n) in lucas.cal for cases where h is not a
+    multiple of 3. Optimized the search for v(1) when h is a
+    multiple of 3.
+
+    Fixed a Makefile problem, reported by Doug Hays <doughays6 at gmail
+    dot com>, where if a macOS user set BINDIR, LIBDIR, CALC_SHAREDIR
+    or INCDIR in the top section, their values will be overwritten by
+    the Darwin specific section.
+
+
+The following are the changes from calc version 2.12.6.0 to 2.12.6.0:
+
+    Added the makefile variable ${COMMON_ADD} that will add flags
+    to all compile and link commands. The ${COMMON_ADD} flags are
+    appended to both ${COMMON_CFLAGS} and ${COMMON_LDFLAGS}.  This
+    facility is available to nearly all platforms except those with
+    very old make commands that do not understand the += operator.
+
+    Example on macOS (Darwin), one may invoke clang's -fsanitize
+    facility by:
+
+	make clobber all \
+	  COMMON_ADD='-fsanitize=undefined -fsanitize=address'
+
+    Another example.  To force C warnings to be treated as errors:
+
+	make COMMON_ADD='-Werror'
+
+    Created a GitHub repository for calc:
+
+	https://github.com/lcn2/calc
+
+    NOTE: The calc GitHub repository represents the an active
+	  development stream.  While an effort will be made to keep
+	  the master branch of the calc GitHub repository in working
+	  order, that tree may be unstable.  Those wishing for more
+	  reliable releases use releases found at calc mirror sites:
+
+	    http://www.isthe.com/chongo/tech/comp/calc/calc-mirror.html
+
+    IMPORTANT NOTE:
+
+	On 2017 June 05, the calc GitHub history was re-written.
+	Anyone who was tracking the calc "pre-release" on GitHub prior
+	to version 2.12.6.0 should do a:
+
+	    git reset --hard origin/master
+	    git cleanup -f
+
+	Or you may just want to start over:
+
+	    rm -rf calc
+	    git clone https://github.com/lcn2/calc.git
+
+	Sorry about that.  The previous GitHub repository was an useful
+	experiment.  Based on what we learned, we decided to rebuild it.
+
+    Renamed README to README.FIRST.  Added README.md for the
+    GitHub repository.
+
+    Fixed reading from standard input (stdin) when -p is given on
+    the command line.  This now prints hello:
+
+	echo hello | calc -p 'stdin = files(0); print fgetline(stdin);'
+
+    Added more debugging related to stdin when bit 4 of calc_debug
+    is set (e.g., running calc with -D16).
+
+    Updated the calc(1) man page and 'help file' to explain about
+    reading from standard input (stdin).
+
+    Added some clarifying remarks for 'help ptest' explaining that
+    the ptest builtin can return 1 is some cases where the test
+    value is a pseudoprime.
+
+    Removed duplicate copyright comments from the help/builtin that
+    is built.
+
+    Fixed a number of typos in the CHANGES file.
+
+The following are the changes from calc version 2.12.5.4 to 2.12.5.6:
+
+    Recompile to match current RHEL7.2 libc and friends.
+
+    Added fix by Alexandre Fedotov <fedotov at mail dot desy dot de>
+    to prepend ${T} in front of the CALCPATH path components
+    ${CALC_SHAREDIR} and ${CUSTOMDIR}.  Add ${T} in front of ${HELPDIR}
+    and ${CUSTONHELPDIR} when making conf.h.
+
+    Improved the jacobi help page.
+
+    Rewrote gen_v1() in the lucas.cal resource file using the method
+    based on a paper:
+
+ 	"A note on primality tests for N = h*2^n-1", by Oystein J. Rodseth,
+	Department of Mathematics, University of Bergen, BIT Numerical
+	Mathematics. 34 (3): pp 451-454.
+
+	http://folk.uib.no/nmaoy/papers/luc.pdf
+
+    The improved gen_v1() function is capable of returning a value
+    for all valid values of h and n.  As a result, the trial tables
+    used by gen_v1() have been changed to a short list of values
+    to try, in order ot likelyhood of success, before doing an
+    exhaustive search for a v1 value to return.
+
+    Removed lucas_tbl.cal calc resource file.  This file was made
+    obsolete by the above rewrite of the lucas.cal resource file.
+    This file will be removed from the local cal directory and
+    from CALC_SHAREDIR during a 'make install', 'make clobber',
+    and 'make uninstall'.
+
+    Renamed gen_u0() to gen_u2() in lucas.cal.  Provided a gen_u0()
+    stub function that calls gen_u2() for backward compatibility.
+
+    The old gen_v1() method used by the Amdahl 6 group has been
+    renamed legacy_gen_v1() in lucas.cal.  This function is no
+    longer used by the lucas(h, n) function to test the primality of
+    h*2^n-1.  It is preserved in lucas.cal for historical purposes.
+
+    The 'make clobber' rule will attempt to remove all files that
+    start with libcalc and start with libcustcalc.
+
+    The 'man' command is now an alias for the 'help' command.
+
+    Fixed extra /'s that were put into CALCPATH because of ${T}.
+    Fixed extra /'s that were compiled into HELPDIR and CUSTOMHELPDIR.
+
+    The fix in 2.12.5.4 to to prepend ${T} in front of the CALCPATH
+    path components ${CALC_SHAREDIR} and ${CUSTOMDIR} broke the
+    calc rpm build process.  The check-buildroot tool discovered
+    that the BUILDROOT directory had been improperly put into various
+    paths and binaries.  This has been fixed in 2.12.5.5.
+
+    Fixed a crash that showed up on macOS (Darwin) that was reported
+    by Richard Outerbridge <outer at interlog dot com> and
+    fixed by Stuart Henderson <stu at spacehopper dot org>.
+    Thanks goes to both!
+
+
+The following are the changes from calc version 2.12.5.3 to 2.12.5.3:
+
+    Calc version 2.12.5.2 for macOS (Darwin) users, code to installed
+    calc under /opt/calc.  Moreover the CHANGES file did not mention
+    /opt/calc.  Sorry about that!.
+
+    A much better tree for macOS (Darwin) users would have been
+    to install cal under /opt/calc.  This release ONLY changes the
+    macOS (Darwin) install tree to /usr/local.
+
+    macOS (Darwin) users who installed calc version 2.12.5.2
+    should, after installing version 2.12.5.3:
+
+    	rm -rf /opt/calc
+
+
+The following are the changes from calc version 2.12.5.1 to 2.12.5.2:
+
+    NOTE: calc version 2.12.5.2, for macOS (Darwin) users,
+    	  installed under /opt/calc.  We neglected to mention this
+	  AND /usr/local would have been a better choice.  Sorry!
+	  Fixed in calc version 2.12.5.3.
+
+    Removed rules and makefile variables associated with shortened
+    calc version numbers of less than 4 levels.
+
+    Under OS X (Darwin), if /usr/include is missing, warnings
+    are issued to help the user use xcode-select --install
+    so that one may properly compile C code.
+
+    Lowered REDC levels:
+
+	#define MAXREDC 256	/* number of entries in REDC cache */
+
+	#define SQ_ALG2 28	/* size for alternative squaring */
+	    config("sq2") == 28		/* was 3388 */
+	#define MUL_ALG2 28	/* size for alternative multiply */
+	    config("mul2") == 28	/* was 1780 */
+	#define POW_ALG2 20	/* size for using REDC for powers */
+	    config("pow2") == 20	/* was 176 */
+	#define REDC_ALG2 25	/* size for using alternative REDC */
+	    config("redc2") == 25	/* was 220 */
+
+    The alg_config.cal script appears to be not correctly finding the
+    best REDC values.  While it has been improved, alg_config.cal still
+    seems to be suspect on how it attempts to find the best values.
+
+    Fixed an intro help file mistake found by Roger Hardiman
+    <roger at rjh dot org dot uk>.
+
+
+The following are the changes from calc version 2.12.5.0 to 2.12.5.1:
+
+    Calc has a new calc-tester mailing list.  This list is for those
+    who are using/testing calc.  We also use this list to announce
+    new versions of calc.  To subscribe to the calc-tester mailing
+    list, visit the following URL:
+
+	    http://www.isthe.com/chongo/tech/comp/calc/calc-tester.html
+
+	This is a low volume moderated mailing list.
+
+	This mailing list replaces calc-tester at asthe dot com list.
+
+	If you need a human to help you with your mailing list subscription,
+	please send Email to our special:
+
+	    calc-tester-maillist-help at asthe dot com
+
+	address.  To be sure we see your Email asking for help with your
+	mailing list subscription, please use the following phase in your
+	Email Subject line:
+
+	    calc tester mailing list help
+
+	That phrase in your subject line will help ensure your
+	request will get past our anti-spam filters.  You may have
+	additional words in your subject line.
+
+    There is a new calc bug report Email address:
+
+	    calc-bug-report at asthe dot com
+
+	This replaces the old calc-bugs at asthe dot com address.
+
+	To be sure we see your Email reporting a calc bug, please use the
+	following phase in your Email Subject line:
+
+	    calc bug report
+
+	That phrase in your subject line will help ensure your
+	request will get past our anti-spam filters.  You may have
+	additional words in your subject line.
+
+	However, you may find it more helpful to simply subscribe
+	to the calc-tester mailing list (see above) and then to
+	send your report to that mailing list as a wider set calc
+	testers may be able to help you.
+
+    The following makefile rules that were related to printing the
+    upper values of the calc version, rules that were made obsolete
+    in calc version 2.12.4.14, have been removed:
+
+	calc_vers calc_ver calc_ve
+	vers ver ve
+
+    Noted that the hash() builtin function, internally known as
+    quickhash (used for internal objects such as the associative
+    arrays as well as other internal processes) uses the deprecated
+    32-bit FNV-0 hash.  The use of this deprecated hash is sufficient
+    for calc internal purposes.  Use of FNV-1a is recommended for
+    a general non-cryptographic quick hash.
+
+
+The following are the changes from calc version 2.12.4.14 to 2.12.5.0:
+
+    For Apple OS X / Darwin target:
+
+    	MACOSX_DEPLOYMENT_TARGET is no longer defined
+	using clang compiler
+
+	By default, -install-name is used when forming shared libs.
+	To force -install-name to not be used, set SET_INSTALL_NAME=no.
+
+    The have_stdvs.c test uses <stdlib.h> and fixed va_start() test call
+    that didn't use last arg.
+
+    Fixed math_fmt (printf) in value.c where a LEN (SB32) be printed as %d.
+
+    Fixed a significant bug where that resulted in an incorrect
+    complex number comparison.  Thanks goes to David Binderman
+    <dcb314 at hotmail dot com> for identifying the subtle typo!
+
+    Make minor fixes to the make depend rule.
+
+    Fixed places were calc defined a reserved identifier that
+    begin with either __ or _[A-Z].  For example, __FILE_H__ has
+    been replaced with INCLUDE_FILE_H.
+
+    Fixed the addall3 example in the script help file.  Thanks for this
+    fix goes to Igor Furlan <igor dot furlan at gmail dot com>.
+
+    We made important fixes to the calc command line history:
+
+	Fixed a bug in the command line history where calc would sometimes
+	crash.  There was code that used memcpy() instead of memmove()
+	that could corrupt the command line history when entering a
+	into into history that was similar to a previous entry.  Thanks
+	goes to Einar Lielmanis <einars at spicausis dot lv> for first
+	identifying this mistake.
+
+	The calc command line history code, in general was not robust.
+	We made use a patch from Mathias Buhr <napcode at users dot sf
+	dot net>, that while it uses a bit more memory: is much more
+	flexible, readable and robust.  This patch replaced the improper
+	use of memcpy() (see above) with better code.  Thanks!
+
+    The alg_config.cal calc resource file has been reworked to produce
+    better diagnostics while attempting to determine the ideal values
+    for mul2, sq2, and pow2.  However, it has been shown that this
+    code is not correct.  Suggestions for a replacement are welcome!
+
+   	calc -u 'read alg_config; config("user_debug", 2),; best_mul2();'
+   	calc -u 'read alg_config; config("user_debug", 2),; best_sq2();'
+   	calc -u 'read alg_config; config("user_debug", 2),; best_pow2();'
+
+    Fixed a number of pedantic compiler warnings.
+
+    Removed -W and -Wno-comment from the the CCWARN makefile variable.
+
+    Removed no_implicit.arg makefile rule.  Removed HAVE_NO_IMPLICIT
+    makefile variable.  Removed no_implicit.c source file.
+
+    Added WNO_IMPLICT makefile variable to hold the compiler flag
+    -Wno-implicit for use on selective compile lines.
+
+    Added WNO_ERROR_LONG_LONG makefile variable to hold the compiler flag
+    -Wno-error=long-long for use on selective compile lines.
+
+    Added WNO_LONG_LONG makefile variable to hold the compiler flag
+    -Wno-long-long for use on selective compile lines.
+
+    The makefile variable ${MKDIR_ARG} has been replaced with just -p.
+
+    Minor fixes were made to the calc.spec.in file.
+
+    The target rpm architecture changed from i686 to x86_64.  For those
+    who do not run machine with x86_64, we continue to release a src
+    rpm. For those without the ability to process an rpm, we will always
+    to release src tarball.
+
+    When building the libcalc and libcustcalc shared  libraries,
+    ONLY the .so and .so.${VERSION} files are created.  The .so is
+    a symlink to the .so.${VERSION} file.  Here ${VERSION} is the
+    full "w.x.y.z" calc version.
+
+
+The following are the changes from calc version 2.12.4.11 to 2.12.4.13:
+
+    Fixed many typos in comments of the Makefile thanks to the review
+    work of Michael Somos.
+
+    Fixed typo in "help sysinfo".
+
+    The Makefile rule, debug, is now more verbose and prints more information
+    about the calc compiled constants.
+
+    Added a more of calc resource files by
+    Christoph Zurnieden <czurnieden at gmx dot de> including:
+
+    infinities.cal - handle infinities symbolically, a little helper file
+    intnum.cal - implementation of tanh sinh and Gauss-Legendre quadrature
+    smallfactors.cal - find the factors of a number < 2^32
+    strings.cal - implementation of isascii() and isblank()
+
+    Reformatted some calc resource files.  Cleanup in comment the headers
+    of some calc resource files.
+
+    Minor formatting changes to a few help files.
+
+    No need to be special picky about the test8900.cal calc resource file.
+
+    Added a number of ctype-like builtins:
+
+    isalnum - whether character is alpha-numeric
+    isalpha - whether character is alphabetic
+    iscntrl - whether character is a control character
+    isdigit - whether character is a digit character
+    isgraph - whether character is a graphical character
+    islower - whether character is lower case
+    isprint - whether character is a printable
+    ispunct - whether character is a punctuation
+    isspace - whether character is a space character
+    isupper - whether character is upper case
+    isxdigit - whether character a hexadecimal digit
+    strcasecmp - compare two strings, case independent
+    strncasecmp - compare two strings up to n characters, case independent
+    strtolower - transform an ASCII string to lower case
+    strtoupper - transform an ASCII string to upper case
+
+    For details on these new builtins, see their help messages.
+    Thanks goes to Inge Zurnieden <inge dot zurnieden at gmx dot de> for
+    these new builtins.
+
+    Calc source code is now picky v2.3 clean using:
+
+	picky -s -v file file2 ..
+
+    With the exception of:
+
+	help/errorcodes.sed
+	cal/set8700.line
+
+    Due to the long lines in those files, we use:
+
+	picky -w -s -v help/errorcodes.sed cal/set8700.line
+
+    For more information about the picky tool, see:
+
+	http://cis.csuohio.edu/~somos/picky.html
+
+    Removed functions from strings.cal that have been replaced by
+    the new ctype-like builtin functions.
+
+    Fixed cal/Makefile to include missing intnum.cal file.
+
+    Added detail_help_list make target to cal/Makefile.
+
+    The detaillist make target in help/Makefile is now
+    called detail_help_list.
+
+    Removed requirement of gen_u0(h, n, v1) in lucas.cal that h
+    be odd.  While still lucas(h, n) converts even h into an odd h
+    internally by incrementing n, gen_u0(h, n, v1) will output even
+    when h is even.
+
+
+The following are the changes from calc version 2.12.4.6 to version 2.12.4.10:
 
     Updated RPM build process to remove use of deprecated flags.
 
-    Applied a number of fixes calc.spec file.
+    Applied a number of fixes to calc.spec and rpm.mk file.
+    See calc.spec.in for details.  Changed rpm release to 2.1.
 
-    Changed rpm release to 2.1.
+    Set MACOSX_DEPLOYMENT_TARGET=10.8 as we upgraded all of
+    our development Mac OS X to 10.8.
+
+    Libraries are chmod-ed as 0644 to allow for building rpms
+    without root.
+
+    Silenced annoying warning about unused variable 'intp'
+    while compiling endian.c under some circumstances.
+
+    Fixed typo in redeclaration warnings.  Thanks to
+    Christoph Zurnieden <czurnieden at gmx dot de> for this report.
+
+    Added a number of calc resource files by
+    Christoph Zurnieden <czurnieden at gmx dot de> including:
+
+    bernpoly.cal - Computes the nth Bernoulli polynomial at z for any n,z
+    brentsolve.cal - root-finder implemented with the Brent-Dekker trick
+    factorial.cal - product of the positive integers
+    factorial2.cal - variety of integer functions quasi-related to factorial
+    lambertw.cal - Computes Lambert's W-function at "z" at branch "branch"
+    lnseries.cal - Calculates a series of natural logarithms at 1,2,3,4...n
+    specialfunctions.cal - Calculates the value of the beta function
+    statistics.cal - a wide variety of statistical functions
+    toomcook.cal - Multiply by way of the Toom-Cook algorithm
+    zeta2.cal - Calculate the value of the Hurwitz Zeta function
+
+    Fixed a makefile bug that prevented the those new calc resource
+    files from being installed.
+
+    Improved the formatting of the output from:
+
+	help resource
+
+    We replaced COPYING-LGPL with the version that is found at
+    http://www.gnu.org/licenses/lgpl-2.1.txt because that version
+    contains some whitespace formatting cleanup.  Otherwise the
+    license is the same.
+
+    We fixed a number of places where "the the" was used
+    when just "the" should be used.
+
+	NOTE: Fixes to grammar, spelling and minor formatting
+	      problems are welcome.  Please send us your patches!
+
+    With the exception of 3 source files, we became "picky" about
+    line lengths and other issues reported by the picky tool:
+
+    	cal/test8900.cal
+	cal/set8700.line
+	help/errorcodes.sed
+
+    The above 3 files now pass picky -w (OK except for line length).
+    For more information about the picky tool, see:
+
+	http://cis.csuohio.edu/~somos/picky.html
 
 
 The following are the changes from calc version 2.12.4.3 to 2.12.4.5:
 
     Added gvec.cal resource script.
 
-    Added calc-symlink make rule to setup symlinks from stardard locations
+    Added calc-symlink make rule to setup symlinks from standard locations
     into a tree specified by a non-empty ${T} makefile variable.  Added
     calc-unsymlink to remove any symlinks that may have been created by
     the calc-symlink rule.
@@ -31,7 +530,7 @@ The following are the changes from calc version 2.12.4.0 to 2.12.4.2:
     Fixed a documentation bug for the sgn() builtin.
 
     Added the 1<<8/2 evaluation example to "help unexpected".  That
-    expression evalutes to 128, not 16 as some C programmers might expect.
+    expression evaluates to 128, not 16 as some C programmers might expect.
 
     Fixed a bug in solve.cal where high was not returned in some situations.
 
@@ -43,7 +542,7 @@ The following are the changes from calc version 2.12.4.0 to 2.12.4.2:
 
     The Makefile used in the source rpm (calc-*.src.rpm) no longer uses
     the -Werror compile flag.  This is to help those distributions with
-    compilers that make produce (hopefully) complination warnings.
+    compilers that make produce (hopefully) compilation warnings.
     NOTE: For testing and calc build purposes will recommend and will
     continue to use the -Werror flag.
 
@@ -57,7 +556,7 @@ The following are the changes from calc version 2.12.4.0 to 2.12.4.2:
 
     one may build a calc binary that is easier to debug.
 
-    Fixed a bug where an certains typos (e.g., calling an unknown
+    Fixed a bug where an certain typos (e.g., calling an unknown
     function) would previously cause calc to exit.
 
     Updated the COPYING file to reflect the new filenames associated
@@ -78,7 +577,7 @@ The following are the changes from calc version 2.12.4.0 to 2.12.4.2:
     Added dms.cal and hms.cal resource files.  The dms.cal is a more
     functional version of deg.cal.  It is a superset except that increment
     and decrement is on the arc second level.  The hms.cal is for
-    24-hour cycle instread of the 360 degree cycle of dms.cal.
+    24-hour cycle instead of the 360 degree cycle of dms.cal.
 
     Changed deg.cal object name from dms to deg so that the more functional
     dms.cal can own the dms object name.
@@ -86,7 +585,7 @@ The following are the changes from calc version 2.12.4.0 to 2.12.4.2:
     Updated 'help obj' to reflect changes to 'show objfunctions' and
     resource file example list since 1999.
 
-    Fixed problem where CALC_BYTE_ORDER refering to CALC_BIG_ENDIAN
+    Fixed problem where CALC_BYTE_ORDER referring to CALC_BIG_ENDIAN
     and CALC_LITTLE_ENDIAN instead of BIG_ENDIAN and LITTLE_ENDIAN.
 
 
@@ -98,7 +597,7 @@ The following are the changes from calc version 2.12.3.0 to 2.12.3.3:
 
     Calc versions will always be of the form x.y.z.w even when the
     MINOR_PATCH (w) is 0.  Thus, 2.12.3.0 will be printed as 2.12.3.0
-    instread of just 2.12.3.
+    instead of just 2.12.3.
 
     Added MINGW32_NT-5.0 compile target based on a patch from
     Brian L. Angus (angus at eng dot utah dot edu).
@@ -112,7 +611,7 @@ The following are the changes from calc version 2.12.3.0 to 2.12.3.3:
 
     The ${CALC_INCDIR}/custom is no longer being removed at install time
     if it is empty.  Now when ${ALLOW_CUSTOM} make variable is empty,
-    an empty ${CALC_INCDIR}/custom may be left hehind.
+    an empty ${CALC_INCDIR}/custom may be left behind.
 
     Fixed a problem where a "make clobber" would remove custom/Makefile
     and fail to rebuilt it.
@@ -182,7 +681,7 @@ The following are the changes from calc version 2.12.1.1 to 2.12.2.2:
     Fixed the wording for the -i flag in the calc man page.
 
     Added some notes to the help/unexpected file regarding calc
-    and interactice shells.
+    and interactive shells.
 
     Fixed bug where a FILEPOS was copied FPOS_POS_BITS octets instead of
     FPOS_POS_LEN octets.
@@ -206,7 +705,7 @@ The following are the changes from calc version 2.12.1.1 to 2.12.2.2:
     operate over a half closed interval.  The help/rand and help/random
     refer to  the top of the interval as "beyond" instead of "max".
 
-    Releaseing source tar balls using bzip2 instead of with gzip.  So
+    Releasing source tar balls using bzip2 instead of with gzip.  So
     what was calc-something.tar.gz is now calc-something.tar.bz2.
     To "uncompress" use:
 
@@ -345,7 +844,7 @@ The following are the changes from calc version 2.12.1.10 to 2.12.2:
 
 	      	calc-contrib at asthe dot com
 
-	      EMail address an "ifeq ($(target),YOUR_TARGET_NAME)"
+	      Email address an "ifeq ($(target),YOUR_TARGET_NAME)"
 	      ... "endif" set of lines from the Makefile so that
 	      we can consider them for the next release.
 
@@ -478,7 +977,7 @@ The following are the changes from calc version 2.12.1.10 to 2.12.2:
 	2.5 ^ 2.718i            3.13145i ^ 0.30103i
 
     Fixed typos in the calc man page thanks to a Debian bug report
-    by A. Costa <agcosta at gis dot .net> that wsa kindly forwarded
+    by A. Costa <agcosta at gis dot .net> that was kindly forwarded
     to us by Martin Buck <m at rtin-buck dot de>.
 
 
@@ -1099,7 +1598,7 @@ The following are the changes from calc version 2.11.10 to 2.11.10:
     and ${L64_FORMAT}.  Removed longlong.c and longlong.h.  The use
     of HAVE_LONGLONG=0 was problematic.  The lack of complaints about
     the HAVE_LONGLONG=0 shows that the 'long long' type is wide spread
-    enough warrent not trying to support compilers without 'long long'.
+    enough to warrant not trying to support compilers without 'long long'.
 
     Removed the SVAL and SHVAL macros from zrand.c, zrand.h, and zmath.h
     as they were causing too many broken C pre-processors and C checkers
@@ -1113,7 +1612,7 @@ The following are the changes from calc version 2.11.10 to 2.11.10:
     could test calc.  Best wishes to the former BSDI folk and thanks
     for breaking important ground in the Open Source Movement!
 
-    Fixed several typos found in the documentation and buildin
+    Fixed several typos found in the documentation and builtin
     function output by C Smith <smichr at hotmail dot com>.
 
     Fixed -d so that:
@@ -1161,8 +1660,7 @@ The following are the changes from calc version 2.11.10 to 2.11.10:
 The following are the changes from calc version 2.11.9 to 2.11.9.3:
 
     Fixed calc man page examples to move -f to the end of the line.
-    Thanks goes to Michael Somos <somos at grail dot cba dot csuohio
+    Thanks goes to Michael Somos for pointing this out.
-    dot edu> for pointing this out.
 
     Linux and gcc now compiled with -Wall -W -Wno-comment.
 
@@ -1486,7 +1984,7 @@ The following are the changes from calc version 2.11.5t4.1 to 2.11.5t4.4:
     version string.
 
     Added subject requirements for the calc-tester-request and
-    calc-bugs-mail EMail aliases.  See:
+    calc-bugs-mail Email aliases.  See:
 
     	http://www.isthe.com/chongo/tech/comp/calc/email.html
 
@@ -1514,7 +2012,7 @@ The following are the changes from calc version 2.11.5t4.1 to 2.11.5t4.4:
     (kawamura at mlb.co.jp) for the bug report and patch!
 
     Fixed headers on fproduct.calc powerterm.calc 4dsphere.calc so
-    that they are correcly changed on installation.
+    that they are correctly changed on installation.
 
     Added ${GREP} Makefile variable.
 
@@ -1798,7 +2296,7 @@ The following are the changes from calc version 2.11.4t1 to 2.11.4t2:
     function.  It remains for backward compatibility.
 
     The Makefile now builds have_fpos_pos.h to determine if the
-    a non-scalar FILEPOS has a __pos stucture element.  If it does,
+    a non-scalar FILEPOS has a __pos structure element.  If it does,
     the FILEPOS_BITS is taken to be the size of just the __pos element.
 
     Misc fixes related to non-scalar (e.g., structure) FILEPOS.  Fixed
@@ -2063,8 +2561,8 @@ The following are the changes from calc version 2.11.2t0 to 2.11.2t1.0:
     Fixed a bug whereby help files are not displayed correctly on
     systems such as NetBSD 1.4.1.  Thanks to a fix from Jakob Naumann.
 
-    Changed EMail addresses to use asthe.com.  Changed URLs to use
+    Changed Email addresses to use asthe.com.  Changed URLs to use
-    www.isthe.com.  NOTE: The EMail address uses 'asthe' and the web
+    www.isthe.com.  NOTE: The Email address uses 'asthe' and the web
     site URL uses 'isthe'.
 
     Using calc-bugs at asthe dot com for calc bug reports,
@@ -2072,7 +2570,7 @@ The following are the changes from calc version 2.11.2t0 to 2.11.2t1.0:
     calc-tester-request at asthe dot com for requests to join calc-tester and
     calc-tester at asthe dot com for the calc tester mailing list.
 
-    Replaced explicit EMail addresses found this file with the <user at
+    Replaced explicit Email addresses found this file with the <user at
     site dot domain> notation to reduce the potential for those folks
     to be spammed.
 
@@ -2117,7 +2615,7 @@ The following are the changes from calc version 2.11.1 to 2.11.1t2.2:
     Cleaned up help display system.  Help file lines that begin with
     '##' are not displayed.
 
-    Calc source and documentation now uses the the these terms:
+    Calc source and documentation now uses these terms:
 
 	*.cal files	calc resource file
 	*.a files	calc binary link library
@@ -2155,7 +2653,7 @@ The following are the changes from calc version 2.11.0t10 to 2.11.0t11:
     Fixed whitespace to make the best use of 8 character tabs.
 
     Fixed some bugs relating to '// and %' in combination with some
-    of the the rounding modes based on a patch from Ernest Bowen
+    of the rounding modes based on a patch from Ernest Bowen
     <ernie at turing dot une dot edu dot au>.
 
     A patch from Klaus Alexander Seistrup <klaus at seistrup dot dk>, when
@@ -2349,7 +2847,7 @@ The following are the changes from calc version 2.11.0t10 to 2.11.0t11:
 
 	Where ``/usr/local/bin/calc'' is the path to the calc binary.
 	Additional -options may be added to the line, but it MUST
-	start with -S.	For example, the the executable file ``plus''
+	start with -S.	For example, the executable file ``plus''
 	contain the following:
 
 	    #!/usr/local/bin/calc -S -e
@@ -2548,7 +3046,7 @@ The following are the changes from calc version 2.11.0t8.9.1 to 2.11.0t9.4.5:
     by Prentice-Hall (UK) Ltd., 1990.)	The piforever() function prints
     digits of pi for as long as your memory and system uptime allows.  :-)
 
-    Fixed the URLs found thruout the source and documentation which did
+    Fixed the URLs found throughout the source and documentation which did
     not and in /, but should for performance and server load reasons.
 
     Cleaned up and improved handling of "mat" and "obj".  The comma in:
@@ -2627,7 +3125,7 @@ The following are the changes from calc version 2.11.0t8.9.1 to 2.11.0t9.4.5:
     and investigated by Michel van der List <vanderlistmj at sbphrd dot com>.
 
     Made an effort to ensure that the v_subtype of VALUES are initialized
-    to V_NOSUBTYPE thruout the source code.
+    to V_NOSUBTYPE through out the source code.
 
     Established a separate calc-bugs address from the calc-tester
     mailing list.  Using anti-spam address forms in order to try and
@@ -2660,7 +3158,7 @@ The following are the changes from calc version 2.11.0t8 to 2.11.0t8.9:
     If $CALCRC has more than one file as in file1:file2 and an error
     occurs in file1, then calc -c will not read file2.
 
-    Fixed some of the old EMail addresses found in calc documentation.
+    Fixed some of the old Email addresses found in calc documentation.
 
     Added HAVE_USTAT, HAVE_GETSID, HAVE_GETPGID, HAVE_GETTIME, HAVE_GETPRID
     and HAVE_URANDOM symbols to the Makefile.  These symbols, along with
@@ -3118,7 +3616,7 @@ The following are the changes from calc version 2.11.0t1 to 2.11.0t6.3:
     A patch from Ernest Bowen <ernie at turing dot une dot edu dot au> now
     defines special meaning to the first 2 bits of config("lib_debug"):
 
-	bit 0 set => messages printed when inputisterminal
+	bit 0 set => messages printed when input is from a terminal
 	bit 1 set => messages printed when reading from a file
 
     The lib/regress.cal regression suite does:
@@ -4067,7 +4565,7 @@ The following are the changes from calc version 2.10.3t5.28 to 2.10.3t5.33:
     long Mersenne factorizations.  The default reporting loop
     is now 10000 cycles.
 
-    SGI Mips r10k compile set is speced for IRIX6.5 with v7.2
+    SGI Mips r10k compile set is specified for IRIX6.5 with v7.2
     compilers.	A note for pre-IRIX6.5 and/or pre-v7.2 compilers
     is given in the compile set.
 
@@ -4328,7 +4826,7 @@ The following are the changes from calc version 2.10.3t5.1 to 2.10.3t5.10:
     surprises that C programmers may encounter.
 
     Updated the 'help', 'intro' and 'overview' to reflect the
-    full list of non-builtin function help files.  Reorered the
+    full list of non-builtin function help files.  Reordered the
     'full' help file.
 
     The blkalloc() builtin has been renamed blk().
@@ -4812,7 +5310,7 @@ The following are the changes from calc version 2.10.3t0 to 2.10.3t2:
 
 	global variable: to the end of the session with calc
 
-	static within a function definition: to the the first of:
+	static within a function definition: to the first of:
 
 	    an end of a global, static or local declaration (including
 	    initialization code) with the same identifier
@@ -4910,7 +5408,7 @@ The following are the changes from calc version 2.10.3t0 to 2.10.3t2:
 
 	global a, b, mat A, B[2] = {3,4}, C[2] = {4,5}, obj point P = {5,6}, Q
 
-    Fixed some bugs related to global and static scoping.  See the the
+    Fixed some bugs related to global and static scoping.  See the
     5200 regress test and lib/test5200.cal for details.
 
     Optimized opcode generator so that functions defined using '=' do not
@@ -5279,7 +5777,7 @@ The following are the changes from calc version 2.10.2t4 to 2.10.2t24:
 
      The regression test suite output has been changed so that it will
      output the same information regardless of CPU performance.	 In
-     particular, cpu times of certain tests are not printed.  This allows
+     particular, CPU times of certain tests are not printed.  This allows
      one to compare the regression output of two different systems easier.
 
      A matrix or object declaration is now considered an expression
@@ -5407,7 +5905,7 @@ The following are the changes from calc version 2.10.2t4 to 2.10.2t24:
 	 ILDFLAGS are flags given to ${CC} for linking .o files
 		  for intermediate progs
 
-	 CC is how the the C compiler is invoked
+	 CC is how the C compiler is invoked
 
     Added more tests to regress.cal.
 
@@ -5602,11 +6100,11 @@ The following are the changes from calc version 2.10.2t1 to 2.10.2t3:
 	    y = fgetstr(f);	/* returns "Curt" */
 	    z = fgetstr(f);	/* returns "Noll" */
 
-    The builtin fgetfield() returns the next field of non-whitepsace
+    The builtin fgetfield() returns the next field of non-whitespace
     characters.
 
     The builtins scan(), fscan(), strscan() read tokens (fields of
-    non-whitepsace characters) and evaluates them.  Thus:
+    non-whitespace characters) and evaluates them.  Thus:
 
 	global a,b,c;
 	strscan("2+3  4^2\n c=a+b", a, b, 0);
@@ -5632,7 +6130,7 @@ The following are the changes from calc version 2.10.2t1 to 2.10.2t3:
     Some systems has a libc symbolic qadd() that conflicted with calc's
     qadd function.  To avoid this, qadd() has been renamed to qqadd().
 
-    The calc error codes are produced from the the calcerr.tbl file.
+    The calc error codes are produced from the calcerr.tbl file.
     Instead of changing #defines in value.h, one can not edit calcerr.tbl.
     The Makefile builds calcerr.h from this file.
 
@@ -5885,7 +6383,7 @@ The following are the changes from calc version 2.10.1t11 to 2.10.1t19:
 	config("all", "newstd")
 
     Renamed config.h (configuration file built during the make) to conf.h.
-    Added a new config.h to contain info on thw V_CONFIG type.
+    Added a new config.h to contain info on the V_CONFIG type.
 
     Fixed some ANSI C compile warnings.
 
@@ -6175,7 +6673,7 @@ The following are the changes from calc version 2.9.3t11 to 2.10.0t12:
 	LDFLAGS are flags given to ${CC} for linking .o files
 	ILDFLAGS are given to ${CC} for linking .o's for intermediate progs
 
-	CC is how the the C compiler is invoked
+	CC is how the C compiler is invoked
 
     The syntax error:
 
@@ -6450,7 +6948,7 @@ The following are the changes from calc version 2.9.3t8 to 2.9.3t9.2:
     the rand() builtin does not match the additive 55 / shuffle
     generators from the old cryrand.cal file.
 
-    Added Makfile support for building BSD/386 releases.
+    Added Makefile support for building BSD/386 releases.
 
     The cmp() builtin can now compare complex values.
 
@@ -6501,10 +6999,10 @@ The following are the changes from calc version 2.9.3t8 to 2.9.3t9.2:
     which is built from have_const.c will determine if we can or should
     use const.	See the Makefile for details.
 
-    Some systems do not have uid_t.  The file have_uid_t.h, which is
+    Some systems do not have uid_t.  The file have_uid_t.h, which
-    built from have_uid_t.c will determine if we can or should depend
+    is built from have_uid_t.c will determine if we can or should
-    on uid_t being typefed by the system include files.	 See the Makefile
+    depend on uid_t being typedefed by the system include files.
-    for details.
+    See the Makefile for details.
 
     Some systems do not have memcpy(), memset() and strchr().  The
     file have_newstr.h, which is built from have_newstr.c will
@@ -6810,7 +7308,7 @@ Following is a list of visible changes to calc from version 1.24.7 to 1.26.1:
 
     A small bug in the library file regress.cal was fixed.
 
-## Copyright (C) 2001  Landon Curt Noll
+## Copyright (C) 2001-2017  Landon Curt Noll
 ##
 ## Calc is open software; you can redistribute it and/or modify it under
 ## the terms of the version 2.1 of the GNU Lesser General Public License
@@ -6826,10 +7324,6 @@ Following is a list of visible changes to calc from version 1.24.7 to 1.26.1:
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## @(#) $Revision: 30.24 $
-## @(#) $Id: CHANGES,v 30.24 2013/05/05 08:31:08 chongo Exp $
-## @(#) $Source: /usr/local/src/bin/calc/RCS/CHANGES,v $
-##
 ## Under source code control:	1993/06/02 18:12:57
 ## File existed as early as:	1989
 ##

COPYING

@@ -6,17 +6,13 @@ This file is Copyrighted
 
     This file is covered under the following Copyright:
 
-	Copyright (C) 1999-2008  Landon Curt Noll
+	Copyright (C) 1999-2014  Landon Curt Noll
 	All rights reserved.
 
 	Everyone is permitted to copy and distribute verbatim copies
 	of this license document, but changing it is not allowed.
 
-    # @(#) $Revision: 30.2 $
+-=-
-    # @(#) $Id: COPYING,v 30.2 2008/10/24 10:46:52 chongo Exp $
-    # @(#) $Source: /usr/local/src/bin/calc/RCS/COPYING,v $
-
-=-=
 
 Calc is covered by the GNU Lesser General Public License
 --------------------------------------------------------
@@ -53,47 +49,64 @@ Calc is covered by the GNU Lesser General Public License
 	    Boston, MA  02110-1301
 	    USA
 
-    The contact addresses for calc is as follows:
+    To subscribe to the calc-tester mailing list, visit the following URL:
 
-	Web:	http://www.isthe.com/chongo/tech/comp/calc/email.html
+	    http://www.isthe.com/chongo/tech/comp/calc/calc-tester.html
 
-    To join the low volume calc mailing list.  Send a EMail message to:
+	This is a low volume moderated mailing list.
 
-	calc-tester-request at asthe dot com
+	This mailing list replaces calc-tester at asthe dot com list.
 
-    Your subject must contain the words:
+	If you need a human to help you with your mailing list subscription,
+	please send EMail to our special:
 
-	calc mailing list subscription
+	    calc-tester-maillist-help at asthe dot com
 
-    You may have additional words in your subject line.
+	    NOTE: Remove spaces and replace 'at' with @, 'dot' with .
 
-    Your message body (not the subject) should consist of:
+	address.  To be sure we see your EMail asking for help with your
+	mailing list subscription, please use the following phase in your
+	EMail Subject line:
 
-	 subscribe calc-tester address
+	    calc tester mailing list help
-	 end
-	 name your_full_name
 
-    where ``address'' is your EMail address and ``your_full_name'' is
+	That phrase in your subject line will help ensure your
-    your full name.
+	request will get past our anti-spam filters.  You may have
+	additional words in your subject line.
 
-    Feel free to follow the name line with additional EMail text as desired.
+-=-
-
-=-=
 
     Calc bug reports and calc bug fixes should be sent to:
 
-	calc-bugs at asthe dot com
+	    calc-bug-report at asthe dot com
 
-    [[ NOTE: Replace 'at' with @, 'dot' is with . and remove the spaces ]]
+	    NOTE: Remove spaces and replace 'at' with @, 'dot' with .
-    [[ NOTE: The EMail address uses 'asthe' and the web site URL uses 'isthe' ]]
 
-    Your subject must contain the words:
+	This replaces the old calc-bugs at asthe dot com address.
+
+	To be sure we see your EMail reporting a calc bug, please use the
+	following phase in your EMail Subject line:
 
 	    calc bug report
 
-    You may have additional words in your subject line.
+	That phrase in your subject line will help ensure your
+	request will get past our anti-spam filters.  You may have
+	additional words in your subject line.
 
-=-=
+	However, you may find it more helpful to simply subscribe
+	to the calc-tester mailing list (see above) and then to
+	send your report to that mailing list as a wider set calc
+	testers may be able to help you.
+
+-=-
+
+    The calc web site is located at:
+
+	http://www.isthe.com/chongo/tech/comp/calc/
+
+    NOTE: The EMail address uses 'asthe', while the web site uses 'isthe'.
+
+-=-
 
 Calc's relationship to the GNU Lesser General Public License
 ------------------------------------------------------------
@@ -149,7 +162,7 @@ Calc's relationship to the GNU Lesser General Public License
      except for the exception files explicitly listed in the ``Calc
      copyrights and exception files'' section below.
 
-=-=
+-=-
 
 Calc copyrights and exception files
 -----------------------------------
@@ -165,6 +178,7 @@ Calc copyrights and exception files
 	Copyright (C) year  Ernest Bowen and Landon Curt Noll
 	Copyright (C) year  Ernest Bowen
 	Copyright (C) year  Petteri Kettunen and Landon Curt Noll
+	Copyright (C) year  Christoph Zurnieden
 
     These files are not covered under one of the Copyrights listed above:
 
@@ -188,7 +202,7 @@ Calc copyrights and exception files
     And because one may freely distribute the LGPL covered files, the
     entire calc source may be freely used and distributed.
 
-=-=
+-=-
 
 General Copyleft and License info
 ---------------------------------
@@ -202,7 +216,7 @@ General Copyleft and License info
 	http://www.gnu.org/copyleft/lesser.html
 	http://www.gnu.org/copyleft/lesser.txt
 
-=-=
+-=-
 
 Why calc did not use the GNU General Public License
 ---------------------------------------------------

COPYING-LGPL

@@ -2,7 +2,7 @@
                        Version 2.1, February 1999
 
  Copyright (C) 1991, 1999 Free Software Foundation, Inc.
-     51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA
+ 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
  Everyone is permitted to copy and distribute verbatim copies
  of this license document, but changing it is not allowed.
 
@@ -485,7 +485,8 @@ convey the exclusion of warranty; and each file should have at least the
 
     You should have received a copy of the GNU Lesser General Public
     License along with this library; if not, write to the Free Software
-    Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA
+    Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301
+    USA
 
 Also add information on how to contact you by electronic and paper mail.
 
@@ -500,5 +501,3 @@ necessary.  Here is a sample; alter the names:
   Ty Coon, President of Vice
 
 That's all there is to it!
-
-

HOWTO.INSTALL

@@ -185,8 +185,8 @@ Installing calc from the bzip2-ed tarball in 4 easy steps:
 
 	make install
 
-We suggest that you might want to read the README file and look at
+We suggest that you might want to read the README.FIRST file and look at
-the calc help subsystem.  See the README file for details.
+the calc help subsystem.  See also the README.md file.
 
 ## Copyright (C) 1999-2007  Landon Curt Noll
 ##
@@ -204,10 +204,6 @@ the calc help subsystem.  See the README file for details.
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## @(#) $Revision: 30.6 $
-## @(#) $Id: HOWTO.INSTALL,v 30.6 2007/10/16 12:22:22 chongo Exp $
-## @(#) $Source: /usr/local/src/bin/calc/RCS/HOWTO.INSTALL,v $
-##
 ## Under source code control:	1999/09/27 20:48:44
 ## File existed as early as:	1999
 ##

LIBRARY

@@ -638,10 +638,6 @@ need call libcalc_call_me_last() only once.
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## @(#) $Revision: 30.1 $
-## @(#) $Id: LIBRARY,v 30.1 2007/03/16 11:09:46 chongo Exp $
-## @(#) $Source: /usr/local/src/bin/calc/RCS/LIBRARY,v $
-##
 ## Under source code control:	1993/07/30 19:44:49
 ## File existed as early as:	1993
 ##

README.FIRST

@@ -73,52 +73,64 @@ for a wish/todo list.  Code contributions are welcome.
 
 =-=
 
-To join the calc-tester mailing list.  Send an EMail message to:
+To subscribe to the calc-tester mailing list, visit the following URL:
 
-    calc-tester-request at asthe dot com
+	http://www.isthe.com/chongo/tech/comp/calc/calc-tester.html
 
-    [[ NOTE: Replace 'at' with @, 'dot' is with . and remove the spaces ]]
+    This is a low volume moderated mailing list.
-    [[ NOTE: The EMail address uses 'asthe' and the web site URL uses 'isthe' ]]
 
-Your subject must contain the words:
+    This mailing list replaces calc-tester at asthe dot com list.
 
-    calc mailing list subscription
+    If you need a human to help you with your mailing list subscription,
+    please send EMail to our special:
 
-You may have additional words in your subject line.
+	calc-tester-maillist-help at asthe dot com
 
-Your message body (not the subject) should consist of:
+	NOTE: Remove spaces and replace 'at' with @, 'dot' with .
 
-     subscribe calc-tester address
+    address.  To be sure we see your EMail asking for help with your
-     end
+    mailing list subscription, please use the following phase in your
-     name your_full_name
+    EMail Subject line:
 
-where ``address'' is your EMail address and ``your_full_name'' is
+	calc tester mailing list help
-your full name.
 
-Feel free to follow the name line with additional EMail text as desired.
+    That phrase in your subject line will help ensure your
+    request will get past our anti-spam filters.  You may have
+    additional words in your subject line.
 
-=-=
+-=-
 
-Send Calc bug and bug fixes to:
+Calc bug reports and calc bug fixes should be sent to:
 
-    calc-bugs at asthe dot com
+	calc-bug-report at asthe dot com
 
-    [[ NOTE: Replace 'at' with @, 'dot' is with . and remove the spaces ]]
+	NOTE: Remove spaces and replace 'at' with @, 'dot' with .
-    [[ NOTE: The EMail address uses 'asthe' and the web site URL uses 'isthe' ]]
 
-but see the BUGS file first.
+    This replaces the old calc-bugs at asthe dot com address.
 
-Your subject must contain the words:
+    To be sure we see your EMail reporting a calc bug, please use the
+    following phase in your EMail Subject line:
 
 	calc bug report
 
-You may have additional words in your subject line.
+    That phrase in your subject line will help ensure your
+    request will get past our anti-spam filters.  You may have
+    additional words in your subject line.
+
+    However, you may find it more helpful to simply subscribe
+    to the calc-tester mailing list (see above) and then to
+    send your report to that mailing list as a wider set calc
+    testers may be able to help you.
+
+-=-
 
 The calc web site is located at:
 
     http://www.isthe.com/chongo/tech/comp/calc/
 
-## Copyright (C) 1999  Landon Curt Noll
+NOTE: The EMail address uses 'asthe', while the web site uses 'isthe'.
+
+## Copyright (C) 1999,2014,2017  Landon Curt Noll
 ##
 ## Calc is open software; you can redistribute it and/or modify it under
 ## the terms of the version 2.1 of the GNU Lesser General Public License
@@ -134,10 +146,6 @@ The calc web site is located at:
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## @(#) $Revision: 30.1 $
-## @(#) $Id: README,v 30.1 2007/03/16 11:09:46 chongo Exp $
-## @(#) $Source: /usr/local/src/bin/calc/RCS/README,v $
-##
 ## Under source code control:	1995/10/25 05:27:59
 ## File existed as early as:	1995
 ##

README.WINDOWS

@@ -10,6 +10,21 @@ NOTE: The main developers do not have access to a Windoz based platform.
       Of course you are welcome to send us any patches that fix your
       Windoz build environment.
 
+
+=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
+=-= compiling with Windows Subsystem for Linux (WSL) =-Cygwin =-=
+=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
+
+It has been reported that calc version 2.12.6.4 has been successfully
+compiled, installed and running on Windows 10 on 2018 Jan 21.
+
+We were told:
+
+  "The Windows Subsystem for Linux (WSL) is a new Windows 10 feature that
+   enables you to run native Linux command-line tools directly on Windows"
+
+   https://docs.microsoft.com/cs-cz/windows/wsl/about
+
 =-=-=-=-=-=-=-=-=-=-=-=-=-=-=
 =-= compiling with Cygwin =-=
 =-=-=-=-=-=-=-=-=-=-=-=-=-=-=
@@ -142,10 +157,6 @@ the above Makefile list, follow the recommendation in the Makefile.
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## @(#) $Revision: 30.2 $
-## @(#) $Id: README.WINDOWS,v 30.2 2009/03/14 02:29:31 chongo Exp $
-## @(#) $Source: /usr/local/src/bin/calc/RCS/README.WINDOWS,v $
-##
 ## Under source code control:	2001/02/25 14:00:05
 ## File existed as early as:	2001
 ##

README.md

@@ -0,0 +1,260 @@
+# What is calc?
+
+Calc is an interactive calculator which provides for easy large
+Otherwise, it enters interactive mode.  In this mode, it accepts
+commands one at a time, processes them, and displays the answers.
+In the simplest case, commands are simply expressions which are
+evaluated.  For example, the following line can be input:
+
+```sh
+3 * (4 + 1)
+```
+
+and the calculator will print:
+
+```sh
+15
+```
+
+Calc as the usual collection of arithmetic operators +, -, /, * as
+well as ^ (exponentiation), % (modulus) and // (integer divide).
+For example:
+
+```sh
+3 * 19^43 - 1
+```
+
+will produce:
+
+```sh
+29075426613099201338473141505176993450849249622191102976
+```
+
+Notice that calc values can be very large.  For example:
+
+```sh
+2^23209-1
+```
+
+will print:
+
+```sh
+402874115778988778181873329071 ... many digits ... 3779264511
+```
+
+The special '.' symbol (called dot), represents the result of the
+last command expression, if any.  This is of great use when a series
+of partial results are calculated, or when the output mode is changed
+and the last result needs to be redisplayed.  For example, the above
+result can be modified by typing:
+
+```sh
+. % (2^127-1)
+```
+
+and the calculator will print:
+
+```sh
+47385033654019111249345128555354223304
+```
+
+For more complex calculations, variables can be used to save the
+intermediate results.  For example, the result of adding 7 to the
+previous result can be saved by typing:
+
+```sh
+curds = 15
+whey = 7 + 2*curds
+```
+
+Functions can be used in expressions.  There are a great number of
+pre-defined functions.  For example, the following will calculate
+the factorial of the value of 'whey':
+
+```sh
+fact(whey)
+```
+
+and the calculator prints:
+
+```sh
+13763753091226345046315979581580902400000000
+```
+
+The calculator also knows about complex numbers, so that typing:
+
+```sh
+(2+3i) * (4-3i)
+cos(.)
+```
+
+will print:
+
+```sh
+17+6i
+-55.50474777265624667147+193.9265235748927986537i
+```
+
+The calculator can calculate transcendental functions, and accept and
+display numbers in real or exponential format. For example, typing:
+
+```sh
+config("display", 70),
+epsilon(1e-70),
+sin(1)
+```
+
+prints:
+
+```sh
+0.8414709848078965066525023216302989996225630607983710656727517099919104
+```
+
+Calc can output values in terms of fractions, octal or hexadecimal.
+For example:
+
+```sh
+config("mode", "fraction"),
+(17/19)^23
+print
+base(16),
+(19/17)^29
+print
+log(79.3i)
+```
+
+ will print:
+
+```sh
+19967568900859523802559065713/257829627945307727248226067259
+
+0x9201e65bdbb801eaf403f657efcf863/0x5cd2e2a01291ffd73bee6aa7dcf7d1
+
+0x17b5164ac24ee836bf/0xc7b7a8e3ef5fcf752+0x883eaf5adadd26be3/0xc7b7a8e3ef5fcf752i
+```
+
+All numbers are represented as fractions with arbitrarily large
+numerators and denominators which are always reduced to lowest terms.
+Real or exponential format numbers can be input and are converted
+to the equivalent fraction.  Hex, binary, or octal numbers can be
+input by using numbers with leading '0x', '0b' or '0' characters.
+Complex numbers can be input using a trailing 'i', as in '2+3i'.
+Strings and characters are input by using single or double quotes.
+
+Commands are statements in a C-like language, where each input
+line is treated as the body of a procedure.  Thus the command
+line can contain variable declarations, expressions, labels,
+conditional tests, and loops.  Assignments to any variable name
+will automatically define that name as a global variable.  The
+other important thing to know is that all non-assignment expressions
+which are evaluated are automatically printed.  Thus, you can evaluate
+an expression's value by simply typing it in.
+
+Many useful built-in mathematical functions are available.  Use the:
+
+```sh
+help builtin
+```
+
+command to list them.
+
+You can also define your own functions by using the 'define' keyword,
+followed by a function declaration very similar to C.
+
+```sh
+define f2(n)
+{
+	local ans;
+
+	ans = 1;
+	while (n > 1)
+		ans *= (n -= 2);
+	return ans;
+}
+```
+
+Thus the input:
+
+```sh
+f2(79)
+```
+
+will produce:
+
+```sh
+1009847364737869270905302433221592504062302663202724609375
+```
+
+Functions which only need to return a simple expression can be defined
+using an equals sign, as in the example:
+
+```sh
+define sc(a,b) = a^3 + b^3
+```
+
+Thus the input:
+
+```sh
+sc(31, 61)
+```
+
+will produce:
+
+```sh
+256772
+```
+
+Variables in functions can be defined as either 'global', 'local',
+or 'static'.  Global variables are common to all functions and the
+command line, whereas local variables are unique to each function
+level, and are destroyed when the function returns.  Static variables
+are scoped within single input files, or within functions, and are
+never destroyed.  Variables are not typed at definition time, but
+dynamically change as they are used.
+
+For more information about the calc language and features, try:
+
+```sh
+help overview
+```
+
+Calc has a help command that will produce information about
+every builtin function, command as well as a number of other
+aspects of calc usage.  Try the command:
+
+```sh
+help help
+```
+
+for and overview of the help system.  The command:
+
+```sh
+help builtin
+```
+
+provides information on built-in mathematical functions, whereas:
+
+```sh
+help asinh
+```
+
+will provides information a specific function.  The following
+help files:
+
+```sh
+help command
+help define
+help operator
+help statement
+help variable
+```
+
+provide a good overview of the calc language.  If you are familiar
+with C, you should also try:
+
+```sh
+help unexpected
+```
+
+It contains information about differences between C and calc
+that may surprize C programmers.

addop.c

@@ -19,10 +19,6 @@
  * received a copy with calc; if not, write to Free Software Foundation, Inc.
  * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
  *
- * @(#) $Revision: 30.1 $
- * @(#) $Id: addop.c,v 30.1 2007/03/16 11:09:46 chongo Exp $
- * @(#) $Source: /usr/local/src/bin/calc/RCS/addop.c,v $
- *
  * Under source code control:	1990/02/15 01:48:10
  * File existed as early as:	before 1990
  *

align32.c

@@ -17,10 +17,6 @@
  * received a copy with calc; if not, write to Free Software Foundation, Inc.
  * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
  *
- * @(#) $Revision: 30.1 $
- * @(#) $Id: align32.c,v 30.1 2007/03/16 11:09:46 chongo Exp $
- * @(#) $Source: /usr/local/src/bin/calc/RCS/align32.c,v $
- *
  * Under source code control:	1995/11/23 05:18:06
  * File existed as early as:	1995
  *

alloc.h

@@ -1,7 +1,7 @@
 /*
  * alloc - storage allocation and storage debug macros
  *
- * Copyright (C) 1999-2007  David I. Bell
+ * Copyright (C) 1999-2007,2014  David I. Bell
  *
  * Calc is open software; you can redistribute it and/or modify it under
  * the terms of the version 2.1 of the GNU Lesser General Public License
@@ -17,10 +17,6 @@
  * received a copy with calc; if not, write to Free Software Foundation, Inc.
  * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
  *
- * @(#) $Revision: 30.2 $
- * @(#) $Id: alloc.h,v 30.2 2008/04/15 21:17:57 chongo Exp $
- * @(#) $Source: /usr/local/src/bin/calc/RCS/alloc.h,v $
- *
  * Under source code control:	1990/02/15 01:48:29
  * File existed as early as:	before 1990
  *
@@ -28,8 +24,8 @@
  */
 
 
-#if !defined(__ALLOC_H__)
+#if !defined(INCLUDE_ALLOC_H)
-#define __ALLOC_H__
+#define INCLUDE_ALLOC_H
 
 
 #if defined(CALC_SRC)	/* if we are building from the calc source tree */
@@ -53,7 +49,8 @@
 # if defined(HAVE_NEWSTR)
 E_FUNC void *memcpy();
 E_FUNC void *memset();
-#if defined(FORCE_STDC) || (defined(__STDC__) && __STDC__ != 0) || defined(__cplusplus)
+#if defined(FORCE_STDC) || \
+   (defined(__STDC__) && __STDC__ != 0) || defined(__cplusplus)
 E_FUNC size_t strlen();
 #  else
 E_FUNC long strlen();
@@ -82,7 +79,8 @@ E_FUNC int strcmp();
 
 #if !defined(HAVE_MEMMOVE)
 # undef MEMMOVE_SIZE_T
-#if defined(FORCE_STDC) || (defined(__STDC__) && __STDC__ != 0) || defined(__cplusplus)
+#if defined(FORCE_STDC) || \
+   (defined(__STDC__) && __STDC__ != 0) || defined(__cplusplus)
 #  define MEMMOVE_SIZE_T size_t
 # else
 #  define MEMMOVE_SIZE_T long
@@ -90,4 +88,4 @@ E_FUNC int strcmp();
 E_FUNC void *memmove(void *s1, CONST void *s2, MEMMOVE_SIZE_T n);
 #endif
 
-#endif /* !__ALLOC_H__ */
+#endif /* !INCLUDE_ALLOC_H */

assocfunc.c

@@ -17,10 +17,6 @@
  * received a copy with calc; if not, write to Free Software Foundation, Inc.
  * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
  *
- * @(#) $Revision: 30.1 $
- * @(#) $Id: assocfunc.c,v 30.1 2007/03/16 11:09:46 chongo Exp $
- * @(#) $Source: /usr/local/src/bin/calc/RCS/assocfunc.c,v $
- *
  * Under source code control:	1993/07/20 23:04:27
  * File existed as early as:	1993
  *
@@ -83,7 +79,7 @@ associndex(ASSOC *ap, BOOL create, long dim, VALUE *indices)
 	 * so that we can first select the correct hash chain, and
 	 * also so we can quickly compare each element for a match.
 	 */
-	hash = FNV1_32_BASIS;
+	hash = QUICKHASH_BASIS;
 	for (i = 0; i < dim; i++)
 		hash = hashvalue(&indices[i], hash);
 
@@ -332,7 +328,8 @@ assoccopy(ASSOC *oldap)
 			oldep = oldep->e_next) {
 			ep = (ASSOCELEM *) malloc(ELEMSIZE(oldep->e_dim));
 			if (ep == NULL) {
-				math_error("Cannot allocate association element");
+				math_error("Cannot allocate "
+					   "association element");
 				/*NOTREACHED*/
 			}
 			ep->e_dim = oldep->e_dim;
@@ -340,7 +337,8 @@ assoccopy(ASSOC *oldap)
 			ep->e_value.v_type = V_NULL;
 			ep->e_value.v_subtype = V_NOSUBTYPE;
 			for (i = 0; i < ep->e_dim; i++)
-				copyvalue(&oldep->e_indices[i], &ep->e_indices[i]);
+				copyvalue(&oldep->e_indices[i],
+					  &ep->e_indices[i]);
 			copyvalue(&oldep->e_value, &ep->e_value);
 			listhead = &ap->a_table[ep->e_hash % ap->a_size];
 			ep->e_next = *listhead;

blkcpy.c

@@ -19,10 +19,6 @@
  * received a copy with calc; if not, write to Free Software Foundation, Inc.
  * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
  *
- * @(#) $Revision: 30.1 $
- * @(#) $Id: blkcpy.c,v 30.1 2007/03/16 11:09:46 chongo Exp $
- * @(#) $Source: /usr/local/src/bin/calc/RCS/blkcpy.c,v $
- *
  * Under source code control:	1997/04/18 20:41:26
  * File existed as early as:	1997
  *
@@ -374,7 +370,8 @@ copyblk2mat(BLOCK *blk, long ssi, long num, MATRIX *dmat, long dsi)
  * copymat2blk - copy matrix to block
  */
 int
-copymat2blk(MATRIX *smat, long ssi, long num, BLOCK *dblk, long dsi, BOOL noreloc)
+copymat2blk(MATRIX *smat, long ssi, long num, BLOCK *dblk, long dsi,
+	    BOOL noreloc)
 {
 	long i;
 	long newlen;
@@ -720,7 +717,8 @@ copystr2file(STRING *str, long ssi, long num, FILEID id, long dsi)
  * copyblk2blk - copy block to block
  */
 int
-copyblk2blk(BLOCK *sblk, long ssi, long num, BLOCK *dblk, long dsi, BOOL noreloc)
+copyblk2blk(BLOCK *sblk, long ssi, long num, BLOCK *dblk, long dsi,
+	    BOOL noreloc)
 {
 	long	newlen;
 	long	newsize;
@@ -762,7 +760,8 @@ copyblk2blk(BLOCK *sblk, long ssi, long num, BLOCK *dblk, long dsi, BOOL noreloc
  * copystr2blk - copy string to block
  */
 int
-copystr2blk(STRING *str, long ssi, long num, BLOCK *dblk, long dsi, BOOL noreloc)
+copystr2blk(STRING *str, long ssi, long num, BLOCK *dblk, long dsi,
+	    BOOL noreloc)
 {
 	long	len;
 	long	newlen;
@@ -982,7 +981,8 @@ memmove(void *s1, CONST void *s2, MEMMOVE_SIZE_T n)
  * copynum2blk - copy number numerator to block
  */
 int
-copynum2blk(NUMBER *snum, long ssi, long num, BLOCK *dblk, long dsi, BOOL noreloc)
+copynum2blk(NUMBER *snum, long ssi, long num, BLOCK *dblk, long dsi,
+	    BOOL noreloc)
 {
 	size_t	newlen;
 	size_t	newsize;
@@ -1033,7 +1033,8 @@ copynum2blk(NUMBER *snum, long ssi, long num, BLOCK *dblk, long dsi, BOOL norelo
  * copyblk2num - copy block to number
  */
 int
-copyblk2num(BLOCK *sblk, long ssi, long num, NUMBER *dnum, long dsi, NUMBER **res)
+copyblk2num(BLOCK *sblk, long ssi, long num, NUMBER *dnum, long dsi,
+	    NUMBER **res)
 {
 	size_t	newlen;
 	NUMBER *ret;		/* cloned and modified numerator */

blkcpy.h

@@ -1,7 +1,7 @@
 /*
  * blkcpy - general values and related routines used by the calculator
  *
- * Copyright (C) 1999-2007  Landon Curt Noll and Ernest Bowen
+ * Copyright (C) 1999-2007,2014  Landon Curt Noll and Ernest Bowen
  *
  * Primary author:  Landon Curt Noll
  *
@@ -19,10 +19,6 @@
  * received a copy with calc; if not, write to Free Software Foundation, Inc.
  * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
  *
- * @(#) $Revision: 30.1 $
- * @(#) $Id: blkcpy.h,v 30.1 2007/03/16 11:09:46 chongo Exp $
- * @(#) $Source: /usr/local/src/bin/calc/RCS/blkcpy.h,v $
- *
  * Under source code control:	1997/04/18 20:41:25
  * File existed as early as:	1997
  *
@@ -30,8 +26,8 @@
  */
 
 
-#if !defined(__BLKCPY_H__)
+#if !defined(INCLUDE_BLKCPY_H)
-#define __BLKCPY_H__
+#define INCLUDE_BLKCPY_H
 
 /*
  * the main copy gateway function
@@ -59,4 +55,4 @@ E_FUNC int copystr2blk(STRING *, long, long, BLOCK *, long, BOOL);
 E_FUNC int copystr2file(STRING *, long, long, FILEID, long);
 E_FUNC int copystr2str(STRING *, long, long, STRING *, long);
 
-#endif /* !__BLKCPY_H__ */
+#endif /* !INCLUDE_BLKCPY_H */

block.c

@@ -19,10 +19,6 @@
  * received a copy with calc; if not, write to Free Software Foundation, Inc.
  * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
  *
- * @(#) $Revision: 30.1 $
- * @(#) $Id: block.c,v 30.1 2007/03/16 11:09:46 chongo Exp $
- * @(#) $Source: /usr/local/src/bin/calc/RCS/block.c,v $
- *
  * Under source code control:	1997/02/27 00:29:40
  * File existed as early as:	1997
  *

block.h

@@ -1,7 +1,7 @@
 /*
  * block - fixed, dynamic, fifo and circular memory blocks
  *
- * Copyright (C) 1999-2007  Landon Curt Noll and Ernest Bowen
+ * Copyright (C) 1999-2007,2014  Landon Curt Noll and Ernest Bowen
  *
  * Primary author:  Landon Curt Noll
  *
@@ -19,10 +19,6 @@
  * received a copy with calc; if not, write to Free Software Foundation, Inc.
  * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
  *
- * @(#) $Revision: 30.1 $
- * @(#) $Id: block.h,v 30.1 2007/03/16 11:09:46 chongo Exp $
- * @(#) $Source: /usr/local/src/bin/calc/RCS/block.h,v $
- *
  * Under source code control:	1997/02/21 05:03:39
  * File existed as early as:	1997
  *
@@ -31,8 +27,8 @@
  */
 
 
-#if !defined(__BLOCK_H__)
+#if !defined(INCLUDE_BLOCK_H)
-#define __BLOCK_H__
+#define INCLUDE_BLOCK_H
 
 
 /*
@@ -222,4 +218,4 @@ E_FUNC int countnblocks(void);
 E_FUNC void shownblocks(void);
 
 
-#endif /* !__BLOCK_H__ */
+#endif /* !INCLUDE_BLOCK_H */

byteswap.c

@@ -17,10 +17,6 @@
  * received a copy with calc; if not, write to Free Software Foundation, Inc.
  * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
  *
- * @(#) $Revision: 30.1 $
- * @(#) $Id: byteswap.c,v 30.1 2007/03/16 11:09:46 chongo Exp $
- * @(#) $Source: /usr/local/src/bin/calc/RCS/byteswap.c,v $
- *
  * Under source code control:	1995/10/11 04:44:01
  * File existed as early as:	1995
  *
@@ -102,7 +98,8 @@ swap_b8_in_ZVALUE(ZVALUE *dest, ZVALUE *src, BOOL all)
 		 */
 		dest = malloc(sizeof(ZVALUE));
 		if (dest == NULL) {
-			math_error("swap_b8_in_ZVALUE: swap_b8_in_ZVALUE: Not enough memory");
+			math_error("swap_b8_in_ZVALUE: swap_b8_in_ZVALUE: "
+				    "Not enough memory");
 			/*NOTREACHED*/
 		}
 

byteswap.h

@@ -1,7 +1,7 @@
 /*
  * byteswap - byte swapping macros
  *
- * Copyright (C) 1999  Landon Curt Noll
+ * Copyright (C) 1999,2014  Landon Curt Noll
  *
  * Calc is open software; you can redistribute it and/or modify it under
  * the terms of the version 2.1 of the GNU Lesser General Public License
@@ -17,10 +17,6 @@
  * received a copy with calc; if not, write to Free Software Foundation, Inc.
  * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
  *
- * @(#) $Revision: 30.1 $
- * @(#) $Id: byteswap.h,v 30.1 2007/03/16 11:09:46 chongo Exp $
- * @(#) $Source: /usr/local/src/bin/calc/RCS/byteswap.h,v $
- *
  * Under source code control:	1995/10/11 04:44:01
  * File existed as early as:	1995
  *
@@ -29,8 +25,8 @@
  */
 
 
-#if !defined(__BYTESWAP_H__)
+#if !defined(INCLUDE_BYTESWAP_H)
-#define __BYTESWAP_H__
+#define INCLUDE_BYTESWAP_H
 
 
 #if defined(CALC_SRC)	/* if we are building from the calc source tree */
@@ -178,4 +174,4 @@
 #endif /* LONG_BITS == 64 */
 
 
-#endif /* !__BYTESWAP_H__ */
+#endif /* !INCLUDE_BYTESWAP_H */

cal/Makefile

@@ -2,7 +2,7 @@
 #
 # cal - makefile for calc standard resource files
 #
-# Copyright (C) 1999-2006  Landon Curt Noll
+# Copyright (C) 1999-2006,2017  Landon Curt Noll
 #
 # Calc is open software; you can redistribute it and/or modify it under
 # the terms of the version 2.1 of the GNU Lesser General Public License
@@ -18,10 +18,6 @@
 # received a copy with calc; if not, write to Free Software Foundation, Inc.
 # 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 #
-# @(#) $Revision: 30.5 $
-# @(#) $Id: Makefile,v 30.5 2011/05/23 22:50:18 chongo Exp $
-# @(#) $Source: /usr/local/src/bin/calc/cal/RCS/Makefile,v $
-#
 # Under source code control:	1991/07/21 05:00:54
 # File existed as early as:	1991
 #
@@ -179,22 +175,41 @@ MV= mv
 CO= co
 TRUE= true
 TOUCH= touch
+SED= sed
+SORT= sort
+FMT= fmt
 
 # The calc files to install
 #
-CALC_FILES= README bigprime.cal deg.cal ellip.cal lucas.cal lucas_chk.cal \
+# This list is prodiced by the detaillist rule when no WARNINGS are detected.
-	lucas_tbl.cal mersenne.cal mod.cal pell.cal pi.cal pix.cal \
+#
-	pollard.cal poly.cal psqrt.cal quat.cal regress.cal solve.cal \
+# Please use:
-	sumsq.cal surd.cal unitfrac.cal varargs.cal chrem.cal mfactor.cal \
+#
-	bindings randmprime.cal test1700.cal randrun.cal linear.cal \
+#	make calc_files_list
-	randbitrun.cal bernoulli.cal test2300.cal test2600.cal \
+#
-	test2700.cal test3100.cal test3300.cal test3400.cal prompt.cal \
+# to keep this list in nice sorted order and to check that these
-	test3500.cal seedrandom.cal test4000.cal test4100.cal test4600.cal \
+# deailed help files are under RCS control.
-	beer.cal hello.cal test5100.cal test5200.cal randombitrun.cal \
+#
-	randomrun.cal repeat.cal xx_print.cal natnumset.cal qtime.cal \
+CALC_FILES= README alg_config.cal beer.cal bernoulli.cal \
-	test8400.cal test8500.cal test8600.cal chi.cal intfile.cal screen.cal \
+	bernpoly.cal bigprime.cal bindings brentsolve.cal chi.cal chrem.cal \
-	dotest.cal set8700.cal set8700.line alg_config.cal sumtimes.cal \
+	constants.cal deg.cal dms.cal dotest.cal ellip.cal factorial.cal \
-	dms.cal hms.cal gvec.cal
+	factorial2.cal gvec.cal hello.cal hms.cal infinities.cal \
+	intfile.cal intnum.cal lambertw.cal linear.cal lnseries.cal \
+	lucas.cal lucas_chk.cal mersenne.cal mfactor.cal \
+	mod.cal natnumset.cal pell.cal pi.cal pix.cal pollard.cal poly.cal \
+	prompt.cal psqrt.cal qtime.cal quat.cal randbitrun.cal randmprime.cal \
+	randombitrun.cal randomrun.cal randrun.cal regress.cal repeat.cal \
+	screen.cal seedrandom.cal set8700.cal set8700.line smallfactors.cal \
+	solve.cal specialfunctions.cal statistics.cal strings.cal sumsq.cal \
+	sumtimes.cal surd.cal test1700.cal test2300.cal test2600.cal \
+	test2700.cal test3100.cal test3300.cal test3400.cal test3500.cal \
+	test4000.cal test4100.cal test4600.cal test5100.cal test5200.cal \
+	test8400.cal test8500.cal test8600.cal test8900.cal toomcook.cal \
+	unitfrac.cal varargs.cal xx_print.cal zeta2.cal
+
+# These calc files are now obsolete and are removed by the install rule.
+#
+DEAD_CALC_FILES= lucas_tbl.cal
 
 # These files are found (but not built) in the distribution
 #
@@ -242,6 +257,27 @@ calcliblist:
 	    fi; \
 	done
 
+# These next rule help form the ${CALC_FILES} makefile variables above.
+#
+calc_files_list:
+	${Q} -(find .  -mindepth 1 -maxdepth 1 -type f -name '*.cal' -print | \
+	   while read i; do \
+		if [ X"$$i" != X"/dev/null" ]; then \
+		    if [ ! -f RCS/$$i,v ]; then \
+			echo "WARNING: $$i not under RCS control" 1>&2; \
+		    else \
+			echo $$i; \
+		    fi; \
+		fi; \
+	done; \
+	echo '--first_line--'; \
+	echo README; \
+	echo set8700.line; \
+	echo bindings) | \
+	    ${SED} -e 's:^\./::' | LANG=C ${SORT} | ${FMT} -70 | \
+	    ${SED} -e '1s/--first_line--/CALC_FILES=/' -e '2,$$s/^/	/' \
+		   -e 's/$$/ \\/' -e '$$s/ \\$$//'
+
 ##
 #
 # rpm rules
@@ -265,6 +301,23 @@ clean:
 
 clobber: clean
 	${RM} -f .all
+	-${Q} if [ -e .DS_Store ]; then \
+	    echo ${RM} -rf .DS_Store; \
+	    ${RM} -rf .DS_Store; \
+	fi
+	-${Q} for i in ${DEAD_CALC_FILES} /dev/null; do \
+	    if [ "$$i" = "/dev/null" ]; then \
+		continue; \
+	    fi; \
+	    if [ -e "${T}${CALC_SHAREDIR}/$$i" ]; then \
+		echo "${RM} -f ${T}${CALC_SHAREDIR}/$$i"; \
+		${RM} -f ${T}${CALC_SHAREDIR}/$$i; \
+	    fi; \
+	    if [ -e "./$$i" ]; then \
+		echo "${RM} -f ./$$i"; \
+		${RM} -f ./$$i; \
+	    fi; \
+	done
 
 # install everything
 #
@@ -272,8 +325,8 @@ clobber: clean
 #
 install: all
 	-${Q} if [ ! -d ${T}${CALC_SHAREDIR} ]; then \
-	    echo ${MKDIR} ${T}${CALC_SHAREDIR}; \
+	    echo ${MKDIR} -p ${T}${CALC_SHAREDIR}; \
-	    ${MKDIR} ${T}${CALC_SHAREDIR}; \
+	    ${MKDIR} -p ${T}${CALC_SHAREDIR}; \
 	    if [ ! -d "${T}${CALC_SHAREDIR}" ]; then \
 		echo ${MKDIR} -p "${T}${CALC_SHAREDIR}"; \
 		${MKDIR} -p "${T}${CALC_SHAREDIR}"; \
@@ -293,16 +346,42 @@ install: all
 		${RM} -f ${T}${CALC_SHAREDIR}/$$i.new; \
 		${CP} -f $$i ${T}${CALC_SHAREDIR}/$$i.new; \
 		${CHMOD} 0444 ${T}${CALC_SHAREDIR}/$$i.new; \
-		${MV} -f ${T}${CALC_SHAREDIR}/$$i.new ${T}${CALC_SHAREDIR}/$$i; \
+		${MV} -f ${T}${CALC_SHAREDIR}/$$i.new ${T}${CALC_SHAREDIR}/$$i;\
 		echo "installed ${T}${CALC_SHAREDIR}/$$i"; \
 	    fi; \
 	done
+	${Q} for i in ${DEAD_CALC_FILES} /dev/null; do \
+	    if [ "$$i" = "/dev/null" ]; then \
+		continue; \
+	    fi; \
+	    if [ -e "${T}${CALC_SHAREDIR}/$$i" ]; then \
+		echo "${RM} -f ${T}${CALC_SHAREDIR}/$$i"; \
+		${RM} -f ${T}${CALC_SHAREDIR}/$$i; \
+	    fi; \
+	    if [ -e "./$$i" ]; then \
+		echo "${RM} -f ./$$i"; \
+		${RM} -f ./$$i; \
+	    fi; \
+	done
 
 # Try to remove everything that was installed
 #
 # NOTE: Keep the uninstall rule in reverse order to the install rule
 #
 uninstall:
+	- ${Q} for i in ${DEAD_CALC_FILES} /dev/null; do \
+	    if [ "$$i" = "/dev/null" ]; then \
+		continue; \
+	    fi; \
+	    if [ -e "${T}${CALC_SHAREDIR}/$$i" ]; then \
+		echo "${RM} -f ${T}${CALC_SHAREDIR}/$$i"; \
+		${RM} -f ${T}${CALC_SHAREDIR}/$$i; \
+	    fi; \
+	    if [ -e "./$$i" ]; then \
+		echo "${RM} -f ./$$i"; \
+		${RM} -f ./$$i; \
+	    fi; \
+	done
 	-${Q} for i in ${CALC_FILES} /dev/null; do \
 	    if [ "$$i" = "/dev/null" ]; then \
 		continue; \

cal/alg_config.cal

@@ -1,7 +1,7 @@
 /*
  * alg_config - help determine optimal values for algorithm levels
  *
- * Copyright (C) 2006  Landon Curt Noll
+ * Copyright (C) 2006,2014  Landon Curt Noll
  *
  * Calc is open software; you can redistribute it and/or modify it under
  * the terms of the version 2.1 of the GNU Lesser General Public License
@@ -17,10 +17,6 @@
  * received a copy with calc; if not, write to Free Software Foundation, Inc.
  * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
  *
- * @(#) $Revision: 30.1 $
- * @(#) $Id: alg_config.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/bin/calc/cal/RCS/alg_config.cal,v $
- *
  * Under source code control:	2006/06/07 14:10:11
  * File existed as early as:	2006
  *
@@ -28,8 +24,37 @@
  * Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
  */
 
+static test_time;	/* try for this many seconds in loop test */
 
-global test_time;	/* try for this many seconds in loop test */
+
+/*
+ * close_to_one - set to 1 if the ratio is close enough to 1
+ *
+ * given:
+ *	ratio	the ratio of time between two algorithms
+ *
+ * retuns:
+ *	1	When ratio is near 1.0
+ *	0	otherwise
+ *
+ * We consider the range [0.995, 1.005] to be close enough to 1 to be call unity
+ * because of the precision of the CPU timing.
+ */
+define close_to_one(ratio)
+{
+    /* firewall */
+    if (!isreal(ratio)) {
+	quit "close: 1st arg: must be a real number";
+    }
+
+    /* check if the ratio is far from unity */
+    if ((ratio < 0.995) || (ratio > 1.005)) {
+	return 0;
+    }
+
+    /* we are close to unity */
+    return 1;
+}
 
 
 /*
@@ -80,7 +105,8 @@ define mul_loop(repeat, x)
     len = sizeof((*x)[0]) / baseb_bytes;
     for (i=1; i < 4; ++i) {
 	if ((sizeof((*x)[i]) / baseb_bytes) != len) {
-	    quit "mul_loop: 2nd arg matrix elements are not of equal BASEB-bit word length";
+	    quit "mul_loop: 2nd arg matrix elements are not of "
+	         "equal BASEB-bit word length";
 	}
     }
 
@@ -142,7 +168,7 @@ define mul_loop(repeat, x)
  *	len	length in BASEB-bit words to multiply
  *
  * return:
- *	ratio of (1st / 2nd) algorithm rate
+ *	ratio of (1st / 2nd) algorithm rate.
  *
  * When want to determine a rate to a precision of 1 part in 1000.
  * Most systems today return CPU time to at least 10 msec precision.
@@ -165,6 +191,7 @@ define mul_ratio(len)
     local tover;		/* est of time for loop overhead */
     local alg1_rate;		/* loop rate of 1st algorithm */
     local alg2_rate;		/* loop rate of 2nd algorithm */
+    local ret;			/* return ratio, or 1.0 */
     local i;
 
     /*
@@ -217,12 +244,12 @@ define mul_ratio(len)
      * determine the 1st algorithm rate
      */
     loops = max(1, ceil(loops * test_time / tlen));
-    if (loops < 8) {
+    if (loops < 16) {
 	if (config("user_debug") > 1) {
-	    printf("    we must expand loop test time to more than %d secs\n",
+	    printf("    we must expand alg1 loop test time to about %d secs\n",
-		ceil(test_time * (8 / loops)));
+		ceil(test_time * (16 / loops)));
 	}
-	loops = 8;
+	loops = 16;
     }
     if (config("user_debug") > 3) {
 	printf("\t    will try alg1 %d loops\n", loops);
@@ -263,12 +290,12 @@ define mul_ratio(len)
      * determine the 2nd algorithm rate
      */
     loops = max(1, ceil(loops * test_time / tlen));
-    if (loops < 8) {
+    if (loops < 16) {
 	if (config("user_debug") > 1) {
-	    printf("    we must expand loop test time to more than %d secs\n",
+	    printf("    we must expand alg2 loop test time to about %d secs\n",
-		ceil(test_time * (8 / loops)));
+		ceil(test_time * (16 / loops)));
 	}
-	loops = 8;
+	loops = 16;
     }
     tlen = mul_loop(loops, &x);
     if (config("user_debug") > 3) {
@@ -297,7 +324,12 @@ define mul_ratio(len)
     /*
      * return alg1 / alg2 rate ratio
      */
-    return (alg1_rate / alg2_rate);
+    ret = alg1_rate / alg2_rate;
+    if (config("user_debug") > 2) {
+	printf("\tprecise ratio is: %.f mul_ratio will return: %.3f\n",
+		alg1_rate / alg2_rate, ret);
+    }
+    return ret;
 }
 
 
@@ -319,30 +351,40 @@ define best_mul2()
 {
     local ratio;	/* previously calculated alg1/alg2 ratio */
     local low;		/* low loop value tested */
-    local high;		/* low loop value tested */
+    local high;		/* high loop value tested */
+    local mid;		/* between low and high */
+    local best_val;	/* value found with ratio closest to unity */
+    local best_ratio;	/* cloest ratio found to unity */
     local expand;	/* how fast to expand the length */
 
     /*
      * setup
      */
-    test_time = 15.0;
+    printf("WARNING: This tool may not be computing the correct best value\n");
-    if (config("user_debug") > 0) {
+    test_time = 5.0;
-	printf("will start with loop test time of %d secs\n", test_time);
+    printf("The best_mul2() function will take a LONG time to run!\n");
+    printf("It is important that best_mul2() run on an othwewise idle host!\n");
+    if (config("user_debug") <= 0) {
+	printf("To monitor progress, set user_debug to 2: "
+	       "config(\"user_debug\", 2)\n");
     }
+    printf("Starting with loop test time of %d secs\n", test_time);
 
     /*
      * firewall - must have a >1 ratio for the initial length
      */
-    high = 16;
+    high = 8;
+    best_val = high;
     if (config("user_debug") > 0) {
 	printf("testing multiply alg1/alg2 ratio for len = %d\n", high);
     }
     ratio = mul_ratio(high);
+    best_ratio = ratio;
     if (config("user_debug") > 1) {
-	printf("    multiply alg1/alg2 ratio = %.3f\n", ratio);
+	printf("    multiply alg1/alg2 ratio = %.6f\n", ratio);
     }
-    if (ratio <= 1.0) {
+    if (ratio < 1.0) {
-	quit "best_mul2: tests imply config(\"mul2\") should be < 4";
+	quit "best_mul2: tests imply mul2 should be < 16, which seems bogus";
     }
 
     /*
@@ -355,7 +397,7 @@ define best_mul2()
 	 * We will multiplicatively expand our test level until
 	 * the ratio drops below 1.0.
 	 */
-	expand = ((ratio >= 3.5) ? 16 : 2^round(ratio));
+	expand = 2;
 	low = high;
 	high *= expand;
 	if (config("user_debug") > 1) {
@@ -367,19 +409,63 @@ define best_mul2()
 	 * determine the alg1/alg2 test ratio for this new length
 	 */
 	if (high >= 2^31) {
-	    quit "best_mul2: tests imply config(\"mul2\") should be >= 2^31";
+	    quit "best_mul2: test implies mul2 >= 2^31, which seems bogus";
 	}
 	if (config("user_debug") > 0) {
 	    printf("testing multiply alg1/alg2 ratio for len = %d\n", high);
 	}
 	ratio = mul_ratio(high);
+	if (abs(ratio - 1.0) < abs(best_ratio - 1.0)) {
+	    best_val = high;
+	    best_ratio = ratio;
 	    if (config("user_debug") > 1) {
-	    printf("    multiply alg1/alg2 ratio = %.3f\n", ratio);
+		printf("    len %d has a new cloest ratio to unity: %.6f\n",
+		       best_val, best_ratio);
 	    }
-    } while (ratio >= 1.0);
+	}
+	if (config("user_debug") > 1) {
+	    printf("    multiply alg1/alg2 ratio = %.6f\n", ratio);
+	}
+    } while (ratio > 1.0);
+
+    /*
+     * If we previously expanded more than by a factor of 2, then
+     * we may have jumped over the crossover point.  So now
+     * drop down powers of two until the ratio is again >= 1.0
+     */
+    if (expand > 2) {
+	do {
+
+	    /*
+	     * contract by 2
+	     */
+	    high /= 2;
+	    low = high / 2;
 	    if (config("user_debug") > 0) {
-	printf("alg1/alg2 ratio now < 1.0, starting binary search between %d and %d\n",
+		printf("retesting multiply alg1/alg2 ratio for len = %d\n",
-	    low, high);
+		       high);
+	    }
+	    ratio = mul_ratio(high);
+	    if (abs(ratio - 1.0) < abs(best_ratio - 1.0)) {
+		best_val = high;
+		best_ratio = ratio;
+		if (config("user_debug") > 1) {
+		    printf("    len %d has a new cloest ratio to unity: %.6f\n",
+			   best_val, best_ratio);
+		}
+	    }
+	    if (config("user_debug") > 1) {
+		printf("    multiply alg1/alg2 ratio = %.6f\n", ratio);
+	    }
+
+	} while (ratio <= 1.0);
+
+	/* now that the ratio flipped again, use the previous range */
+	low = high;
+	high = high * 2;
+    }
+    if (config("user_debug") > 0) {
+	printf("Starting binary search between %d and %d\n", low, high);
     }
 
     /*
@@ -388,30 +474,54 @@ define best_mul2()
     while (low+1 < high) {
 
     	/* try the mid-point */
+	mid = int((low+high)/2);
 	if (config("user_debug") > 0) {
-	    printf("testing multiply alg1/alg2 ratio for len = %d\n",
+	    printf("testing multiply alg1/alg2 ratio for len = %d\n", mid);
-	    	int((low+high)/2));
 	}
-	ratio = mul_ratio(int((low+high)/2));
+	ratio = mul_ratio(mid);
+	if (abs(ratio - 1.0) < abs(best_ratio - 1.0)) {
+	    best_val = mid;
+	    best_ratio = ratio;
 	    if (config("user_debug") > 1) {
-	    printf("    multiply alg1/alg2 ratio = %.3f\n", ratio);
+		printf("    len %d has a new cloest ratio to unity: %.6f\n",
+		       best_val, best_ratio);
+	    }
+	}
+	if (config("user_debug") > 1) {
+	    printf("    len %d multiply alg1/alg2 ratio = %.6f\n", mid, ratio);
+	}
+
+	/* stop search if near unity */
+	if (close_to_one(ratio)) {
+	    low = mid;
+	    high = mid;
+	    if (config("user_debug") > 0) {
+	    	printf("\twe are close enough to unity ratio at: %d\n", mid);
+	    }
+	    break;
 	}
 
 	/* bump lower range up if we went over */
-	if (ratio >= 1.0) {
+	if (ratio > 1.0) {
 	    if (config("user_debug") > 2) {
 	    	printf("\tmove low from %d up to %d\n",
-		    low, int((low+high)/2));
+		    low, mid);
 	    }
-	    low = int((low+high)/2);
+	    low = mid;
 
 	/* drop higher range down if we went under */
 	} else {
 	    if (config("user_debug") > 2) {
 	    	printf("\tmove high from %d down to %d\n",
-		     high, int((low+high)/2));
+		     high, mid);
 	    }
-	    high = int((low+high)/2);
+	    high = mid;
+	}
+
+	/* report on test loop progress */
+	if (config("user_debug") > 1) {
+	    printf("\tsetting low: %d high: %d diff: %d\n",
+	    	   low, high, high-low);
 	}
     }
 
@@ -419,10 +529,15 @@ define best_mul2()
      * return on the suggested config("mul2") value
      */
     if (config("user_debug") > 0) {
-	printf("best value of config(\"mul2\") is %d\n",
+	printf("Best value for multiply is near %d\n", best_val);
-	    (ratio >= 1.0) ? high : low);
+	printf("Best multiply alg1/alg2 ratio is: %.6f\n", best_ratio);
+	printf("We suggest placing this line in your .calcrc:\n");
+	printf("config(\"mul2\", %d),;\n", best_val);
+	printf("WARNING: It is believed that the output "
+	       "of this resource file is bogus!\n");
+	printf("WARNING: You may NOT wish to follow the above suggeston.\n");
     }
-    return ((ratio >= 1.0) ? high : low);
+    return mid;
 }
 
 
@@ -472,7 +587,8 @@ define sq_loop(repeat, x)
     len = sizeof((*x)[0]) / baseb_bytes;
     for (i=1; i < 4; ++i) {
 	if ((sizeof((*x)[i]) / baseb_bytes) != len) {
-	    quit "sq_loop: 2nd arg matrix elements are not of equal BASEB-bit word length";
+	    quit "sq_loop: 2nd arg matrix elements are not of equal "
+	         "BASEB-bit word length";
 	}
     }
 
@@ -559,6 +675,7 @@ define sq_ratio(len)
     local tover;		/* est of time for loop overhead */
     local alg1_rate;		/* loop rate of 1st algorithm */
     local alg2_rate;		/* loop rate of 2nd algorithm */
+    local ret;			/* return ratio, or 1.0 */
     local i;
 
     /*
@@ -611,12 +728,12 @@ define sq_ratio(len)
      * determine the 1st algorithm rate
      */
     loops = max(1, ceil(loops * test_time / tlen));
-    if (loops < 8) {
+    if (loops < 16) {
 	if (config("user_debug") > 1) {
-	    printf("    we must expand loop test time to more than %d secs\n",
+	    printf("    we must expand alg1 loop test time to about %d secs\n",
-		ceil(test_time * (8 / loops)));
+		ceil(test_time * (16 / loops)));
 	}
-	loops = 8;
+	loops = 16;
     }
     tlen = sq_loop(loops, &x);
     if (config("user_debug") > 3) {
@@ -654,12 +771,12 @@ define sq_ratio(len)
      * determine the 2nd algorithm rate
      */
     loops = max(1, ceil(loops * test_time / tlen));
-    if (loops < 8) {
+    if (loops < 16) {
 	if (config("user_debug") > 1) {
-	    printf("    we must expand loop test time to more than %d secs\n",
+	    printf("    we must expand alg2 loop test time to about %d secs\n",
-		ceil(test_time * (8 / loops)));
+		ceil(test_time * (16 / loops)));
 	}
-	loops = 8;
+	loops = 16;
     }
     tlen = sq_loop(loops, &x);
     if (config("user_debug") > 3) {
@@ -688,7 +805,12 @@ define sq_ratio(len)
     /*
      * return alg1 / alg2 rate ratio
      */
-    return (alg1_rate / alg2_rate);
+    ret = alg1_rate / alg2_rate;
+    if (config("user_debug") > 2) {
+	printf("\tprecise ratio is: %.f sq_ratio will return: %.3f\n",
+		alg1_rate / alg2_rate, ret);
+    }
+    return ret;
 }
 
 
@@ -710,30 +832,40 @@ define best_sq2()
 {
     local ratio;	/* previously calculated alg1/alg2 ratio */
     local low;		/* low loop value tested */
-    local high;		/* low loop value tested */
+    local high;		/* high loop value tested */
+    local mid;		/* between low and high */
+    local best_val;	/* value found with ratio closest to unity */
+    local best_ratio;	/* cloest ratio found to unity */
     local expand;	/* how fast to expand the length */
 
     /*
      * setup
      */
-    test_time = 15.0;
+    printf("WARNING: This tool may not be computing the correct best value\n");
-    if (config("user_debug") > 0) {
+    test_time = 5.0;
-	printf("will start with loop test time of %d secs\n", test_time);
+    printf("The best_sq2() function will take a LONG time to run!\n");
+    printf("It is important that best_sq2() run on an othwewise idle host!\n");
+    if (config("user_debug") <= 0) {
+	printf("To monitor progress, set user_debug to 2: "
+	       "config(\"user_debug\", 2)\n");
     }
+    printf("Starting with loop test time of %d secs\n", test_time);
 
     /*
      * firewall - must have a >1 ratio for the initial length
      */
-    high = 16;
+    high = 8;
+    best_val = high;
     if (config("user_debug") > 0) {
 	printf("testing square alg1/alg2 ratio for len = %d\n", high);
     }
     ratio = sq_ratio(high);
+    best_ratio = ratio;
     if (config("user_debug") > 1) {
 	printf("    square alg1/alg2 ratio = %.3f\n", ratio);
     }
-    if (ratio <= 1.0) {
+    if (ratio < 1.0) {
-	quit "best_sq2: tests imply config(\"sq2\") should be < 4";
+	quit "best_sq2: test implies sq2 < 16, which seems bogus";
     }
 
     /*
@@ -746,7 +878,7 @@ define best_sq2()
 	 * We will multiplicatively expand our test level until
 	 * the ratio drops below 1.0.
 	 */
-	expand = ((ratio >= 3.5) ? 16 : 2^round(ratio));
+	expand = 2;
 	low = high;
 	high *= expand;
 	if (config("user_debug") > 1) {
@@ -758,19 +890,63 @@ define best_sq2()
 	 * determine the alg1/alg2 test ratio for this new length
 	 */
 	if (high >= 2^31) {
-	    quit "best_sq2: tests imply config(\"sq2\") should be >= 2^31";
+	    quit "best_sq2: tests imply sq2 >= 2^31, which seems bogus";
 	}
 	if (config("user_debug") > 0) {
 	    printf("testing square alg1/alg2 ratio for len = %d\n", high);
 	}
 	ratio = sq_ratio(high);
+	if (abs(ratio - 1.0) < abs(best_ratio - 1.0)) {
+	    best_val = high;
+	    best_ratio = ratio;
+	    if (config("user_debug") > 1) {
+		printf("    len %d has a new cloest ratio to unity: %.6f\n",
+		       best_val, best_ratio);
+	    }
+	}
 	if (config("user_debug") > 1) {
 	    printf("    square alg1/alg2 ratio = %.3f\n", ratio);
 	}
-    } while (ratio >= 1.0);
+    } while (ratio > 1.0);
+
+    /*
+     * If we previously expanded more than by a factor of 2, then
+     * we may have jumped over the crossover point.  So now
+     * drop down powers of two until the ratio is again >= 1.0
+     */
+    if (expand > 2) {
+	do {
+
+	    /*
+	     * contract by 2
+	     */
+	    high /= 2;
+	    low = high / 2;
 	    if (config("user_debug") > 0) {
-	printf("alg1/alg2 ratio now < 1.0, starting binary search between %d and %d\n",
+		printf("retesting multiply alg1/alg2 ratio for len = %d\n",
-	    low, high);
+		       high);
+	    }
+	    ratio = mul_ratio(high);
+	    if (abs(ratio - 1.0) < abs(best_ratio - 1.0)) {
+		best_val = high;
+		best_ratio = ratio;
+		if (config("user_debug") > 1) {
+		    printf("    len %d has a new cloest ratio to unity: %.6f\n",
+			   best_val, best_ratio);
+		}
+	    }
+	    if (config("user_debug") > 1) {
+		printf("    multiply alg1/alg2 ratio = %.6f\n", ratio);
+	    }
+
+	} while (ratio <= 1.0);
+
+	/* now that the ratio flipped again, use the previous range */
+	low = high;
+	high = high * 2;
+    }
+    if (config("user_debug") > 0) {
+	printf("Starting binary search between %d and %d\n", low, high);
     }
 
     /*
@@ -779,41 +955,71 @@ define best_sq2()
     while (low+1 < high) {
 
     	/* try the mid-point */
+	mid = int((low+high)/2);
 	if (config("user_debug") > 0) {
-	    printf("testing square alg1/alg2 ratio for len = %d\n",
+	    printf("testing square alg1/alg2 ratio for len = %d\n", mid);
-	    	int((low+high)/2));
 	}
-	ratio = sq_ratio(int((low+high)/2));
+	ratio = sq_ratio(mid);
+	if (abs(ratio - 1.0) < abs(best_ratio - 1.0)) {
+	    best_val = mid;
+	    best_ratio = ratio;
 	    if (config("user_debug") > 1) {
-	    printf("    square alg1/alg2 ratio = %.3f\n", ratio);
+		printf("    len %d has a new cloest ratio to unity: %.6f\n",
+		       best_val, best_ratio);
+	    }
+	}
+	if (config("user_debug") > 1) {
+	    printf("    len %d square alg1/alg2 ratio = %.6f\n", mid, ratio);
+	}
+
+	/* stop search if near unity */
+	if (close_to_one(ratio)) {
+	    low = mid;
+	    high = mid;
+	    if (config("user_debug") > 0) {
+	    	printf("\twe are close enough to unity ratio at: %d\n", mid);
+	    }
+	    break;
 	}
 
 	/* bump lower range up if we went over */
-	if (ratio >= 1.0) {
+	if (ratio > 1.0) {
 	    if (config("user_debug") > 2) {
 	    	printf("\tmove low from %d up to %d\n",
-		    low, int((low+high)/2));
+		    low, mid);
 	    }
-	    low = int((low+high)/2);
+	    low = mid;
 
 	/* drop higher range down if we went under */
 	} else {
 	    if (config("user_debug") > 2) {
 	    	printf("\tmove high from %d down to %d\n",
-		     high, int((low+high)/2));
+		     high, mid);
 	    }
-	    high = int((low+high)/2);
+	    high = mid;
+	}
+
+	/* report on test loop progress */
+	if (config("user_debug") > 1) {
+	    printf("\tsetting low: %d high: %d diff: %d\n",
+	    	   low, high, high-low);
 	}
     }
 
     /*
      * return on the suggested config("sq2") value
      */
+    mid = int((low+high)/2);
     if (config("user_debug") > 0) {
-	printf("best value of config(\"sq2\") is %d\n",
+	printf("Best value for square is near %d\n", best_val);
-	    (ratio >= 1.0) ? high : low);
+	printf("Best square alg1/alg2 ratio is: %.6f\n", best_ratio);
+	printf("We suggest placing this line in your .calcrc:\n");
+	printf("config(\"sq2\", %d),;\n", best_val);
+	printf("WARNING: It is believed that the output "
+	       "of this resource file is bogus!\n");
+	printf("WARNING: You may NOT wish to follow the above suggeston.\n");
     }
-    return ((ratio >= 1.0) ? high : low);
+    return mid;
 }
 
 
@@ -866,7 +1072,8 @@ define pow_loop(repeat, x, ex)
     len = sizeof((*x)[0]) / baseb_bytes;
     for (i=1; i < 4; ++i) {
 	if ((sizeof((*x)[i]) / baseb_bytes) != len) {
-	    quit "pow_loop: 2nd arg matrix elements are not of equal BASEB-bit word length";
+	    quit "pow_loop: 2nd arg matrix elements are not of "
+	         "equal BASEB-bit word length";
 	}
     }
     if (!isint(ex) || ex < 3) {
@@ -963,6 +1170,7 @@ define pow_ratio(len)
     local alg1_rate;		/* loop rate of 1st algorithm */
     local alg2_rate;		/* loop rate of 2nd algorithm */
     local ex;			/* exponent to use in pow_loop() */
+    local ret;			/* return ratio, or 1.0 */
     local i;
 
     /*
@@ -985,7 +1193,7 @@ define pow_ratio(len)
     /*
      * setup
      */
-    ex = 5;
+    ex = 7;
 
     /*
      * initialize x, the values we will pmod
@@ -1021,12 +1229,12 @@ define pow_ratio(len)
      * determine the 1st algorithm rate
      */
     loops = max(1, ceil(loops * test_time / tlen));
-    if (loops < 8) {
+    if (loops < 16) {
 	if (config("user_debug") > 1) {
-	    printf("    we must expand loop test time to more than %d secs\n",
+	    printf("    we must expand alg1 loop test time to about %d secs\n",
-		ceil(test_time * (8 / loops)));
+		ceil(test_time * (16 / loops)));
 	}
-	loops = 8;
+	loops = 16;
     }
     tlen = pow_loop(loops, &x, ex);
     if (config("user_debug") > 3) {
@@ -1065,12 +1273,12 @@ define pow_ratio(len)
      * determine the 2nd algorithm rate
      */
     loops = max(1, ceil(loops * test_time / tlen));
-    if (loops < 8) {
+    if (loops < 16) {
 	if (config("user_debug") > 1) {
-	    printf("    we must expand loop test time to more than %d secs\n",
+	    printf("    we must expand alg2 loop test time to about %d secs\n",
-		ceil(test_time * (8 / loops)));
+		ceil(test_time * (16 / loops)));
 	}
-	loops = 8;
+	loops = 16;
     }
     tlen = pow_loop(loops, &x, ex);
     if (config("user_debug") > 3) {
@@ -1099,7 +1307,12 @@ define pow_ratio(len)
     /*
      * return alg1 / alg2 rate ratio
      */
-    return (alg1_rate / alg2_rate);
+    ret = alg1_rate / alg2_rate;
+    if (config("user_debug") > 2) {
+	printf("\tprecise ratio is: %.f pow_ratio will return: %.3f\n",
+		alg1_rate / alg2_rate, ret);
+    }
+    return ret;
 }
 
 
@@ -1121,17 +1334,25 @@ define best_pow2()
 {
     local ratio;	/* previously calculated alg1/alg2 ratio */
     local low;		/* low loop value tested */
-    local high;		/* low loop value tested */
+    local high;		/* high loop value tested */
+    local mid;		/* between low and high */
+    local best_val;	/* value found with ratio closest to unity */
+    local best_ratio;	/* cloest ratio found to unity */
     local expand;	/* how fast to expand the length */
     local looped;	/* 1 ==> we have expanded lengths before */
 
     /*
      * setup
      */
-    test_time = 15.0;
+    printf("WARNING: This tool may not be computing the correct best value\n");
-    if (config("user_debug") > 0) {
+    test_time = 60.0;
-	printf("will start with loop test time of %d secs\n", test_time);
+    printf("The best_pow2() function will take a LONG time to run!\n");
+    printf("It is important that best_pow2() run on an othwewise idle host!\n");
+    if (config("user_debug") <= 0) {
+	printf("To monitor progress, set user_debug to 2: "
+	       "config(\"user_debug\", 2)\n");
     }
+    printf("Starting with loop test time of %d secs\n", test_time);
 
     /*
      * firewall - must have a >1.02 ratio for the initial length
@@ -1142,16 +1363,27 @@ define best_pow2()
      */
     low = 4;
     high = 4;
+    best_val = high;
+    best_ratio = 1e10;	/* not a real value */
     do {
 	high *= 4;
 	if (config("user_debug") > 0) {
 	    printf("testing pmod alg1/alg2 ratio for len = %d\n", high);
 	}
 	ratio = pow_ratio(high);
+	if (abs(ratio - 1.0) < abs(best_ratio - 1.0)) {
+	    best_val = high;
+	    best_ratio = ratio;
+	    if (config("user_debug") > 1) {
+		printf("    len %d has a new cloest ratio to unity: %.6f\n",
+		       best_val, best_ratio);
+	    }
+	}
 	if (config("user_debug") > 1) {
 	    printf("    pmod alg1/alg2 ratio = %.3f\n", ratio);
 	    if (ratio > 1.0 && ratio <= 1.02) {
-	    printf("    while alg1 is slightly better than alg2, it is not clearly better\n");
+	    printf("    while alg1 is slightly better than alg2, "
+	    	   "it is not clearly better\n");
 	    }
 	}
     } while (ratio <= 1.02);
@@ -1193,20 +1425,27 @@ define best_pow2()
 	 * determine the alg1/alg2 test ratio for this new length
 	 */
 	if (high >= 2^31) {
-	    quit "best_pow2: tests imply config(\"pow2\") should be >= 2^31";
+	    quit "best_pow2: test implies pow2 >= 2^31, which seems bogus";
 	}
 	if (config("user_debug") > 0) {
 	    printf("testing pmod alg1/alg2 ratio for len = %d\n", high);
 	}
 	ratio = pow_ratio(high);
+	if (abs(ratio - 1.0) < abs(best_ratio - 1.0)) {
+	    best_val = high;
+	    best_ratio = ratio;
 	    if (config("user_debug") > 1) {
-	    printf("    pmod alg1/alg2 ratio = %.3f\n", ratio);
+		printf("    len %d has a new cloest ratio to unity: %.6f\n",
+		       best_val, best_ratio);
+	    }
+	}
+	if (config("user_debug") > 1) {
+	    printf("    pmod alg1/alg2 ratio = %.6f\n", ratio);
 	}
 	looped = 1;
-    } while (ratio >= 1.0);
+    } while (ratio > 1.0);
     if (config("user_debug") > 0) {
-	printf("alg1/alg2 ratio now < 1.0, starting binary search between %d and %d\n",
+	printf("Starting binary search between %d and %d\n", low, high);
-	    low, high);
     }
 
     /*
@@ -1215,39 +1454,69 @@ define best_pow2()
     while (low+1 < high) {
 
     	/* try the mid-point */
+	mid = int((low+high)/2);
 	if (config("user_debug") > 0) {
-	    printf("testing pmod alg1/alg2 ratio for len = %d\n",
+	    printf("testing pow2 alg1/alg2 ratio for len = %d\n", mid);
-	    	int((low+high)/2));
 	}
-	ratio = pow_ratio(int((low+high)/2));
+	ratio = pow_ratio(mid);
+	if (abs(ratio - 1.0) < abs(best_ratio - 1.0)) {
+	    best_val = mid;
+	    best_ratio = ratio;
 	    if (config("user_debug") > 1) {
-	    printf("    pmod alg1/alg2 ratio = %.3f\n", ratio);
+		printf("    len %d has a new cloest ratio to unity: %.6f\n",
+		       best_val, best_ratio);
+	    }
+	}
+	if (config("user_debug") > 1) {
+	    printf("    len %d pmod alg1/alg2 ratio = %.6f\n", mid, ratio);
+	}
+
+	/* stop search if near unity */
+	if (close_to_one(ratio)) {
+	    low = mid;
+	    high = mid;
+	    if (config("user_debug") > 0) {
+	    	printf("\twe are close enough to unity ratio at: %d\n", mid);
+	    }
+	    break;
 	}
 
 	/* bump lower range up if we went over */
-	if (ratio >= 1.0) {
+	if (ratio > 1.0) {
 	    if (config("user_debug") > 2) {
 	    	printf("\tmove low from %d up to %d\n",
-		    low, int((low+high)/2));
+		    low, mid);
 	    }
-	    low = int((low+high)/2);
+	    low = mid;
 
 	/* drop higher range down if we went under */
 	} else {
 	    if (config("user_debug") > 2) {
 	    	printf("\tmove high from %d down to %d\n",
-		     high, int((low+high)/2));
+		     high, mid);
 	    }
-	    high = int((low+high)/2);
+	    high = mid;
+	}
+
+	/* report on test loop progress */
+	if (config("user_debug") > 1) {
+	    printf("\tsetting low: %d high: %d diff: %d\n",
+	    	   low, high, high-low);
 	}
     }
 
     /*
      * return on the suggested config("pow2") value
      */
+    mid = int((low+high)/2);
     if (config("user_debug") > 0) {
-	printf("best value of config(\"pow2\") is %d\n",
+	printf("Best value for pmod is near %d\n", best_val);
-	    (ratio >= 1.0) ? high : low);
+	printf("Best pmod alg1/alg2 ratio is: %.6f\n", best_ratio);
+	printf("We suggest placing this line in your .calcrc:\n");
+	printf("config(\"pow2\", %d),;\n", best_val);
+	printf("WARNING: It is believed that the output "
+	       "of this resource file is bogus!\n");
+	printf("WARNING: You may NOT wish to follow the above suggeston.\n");
     }
-    return ((ratio >= 1.0) ? high : low);
+    return mid;
 }

cal/beer.cal

@@ -17,10 +17,6 @@
  * received a copy with calc; if not, write to Free Software Foundation, Inc.
  * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
  *
- * @(#) $Revision: 30.1 $
- * @(#) $Id: beer.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/bin/calc/cal/RCS/beer.cal,v $
- *
  * Under source code control:	1996/11/13 13:21:05
  * File existed as early as:	1996
  *

cal/bernoulli.cal

@@ -17,10 +17,6 @@
  * received a copy with calc; if not, write to Free Software Foundation, Inc.
  * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
  *
- * @(#) $Revision: 30.1 $
- * @(#) $Id: bernoulli.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/bin/calc/cal/RCS/bernoulli.cal,v $
- *
  * Under source code control:	1991/09/30 11:18:41
  * File existed as early as:	1991
  *

cal/bernpoly.cal

@@ -0,0 +1,55 @@
+/*
+ * bernpoly - Bernoully polynomials B_n(z) for arbitrary n,z..
+ *
+ * Copyright (C) 2013 Christoph Zurnieden
+ *
+ * Calc is open software; you can redistribute it and/or modify it under
+ * the terms of the version 2.1 of the GNU Lesser General Public License
+ * as published by the Free Software Foundation.
+ *
+ * Calc is distributed in the hope that it will be useful, but WITHOUT
+ * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+ * or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
+ * Public License for more details.
+ *
+ * A copy of version 2.1 of the GNU Lesser General Public License is
+ * distributed with calc under the filename COPYING-LGPL.  You should have
+ * received a copy with calc; if not, write to Free Software Foundation, Inc.
+ * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
+ *
+ * Under source code control:	2013/08/11 01:31:28
+ * File existed as early as:	2013
+ */
+
+
+static resource_debug_level;
+resource_debug_level = config("resource_debug", 0);
+
+
+read -once zeta2
+
+
+/* Idea by Don Zagier */
+define bernpoly(n,z){
+  local h s c k;
+  if(isint(n) && n>=0){
+    h=0;s=0;c=-1;
+    for(k=1;k<=n+1;k++){
+      c*=1-(n+2)/k;
+      s+=z^n;
+      z++;
+      h+=c*s/k;
+    }
+    return h;
+  }
+  else return -n*hurwitzzeta(1-n,z);
+}
+
+
+/*
+ * restore internal function from resource debugging
+ */
+config("resource_debug", resource_debug_level),;
+if (config("resource_debug") & 3) {
+    print "bernpoly(n,z)";
+}

cal/bigprime.cal

@@ -17,10 +17,6 @@
  * received a copy with calc; if not, write to Free Software Foundation, Inc.
  * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
  *
- * @(#) $Revision: 30.1 $
- * @(#) $Id: bigprime.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/bin/calc/cal/RCS/bigprime.cal,v $
- *
  * Under source code control:	1991/05/22 21:56:32
  * File existed as early as:	1991
  *

cal/bindings

@@ -16,10 +16,6 @@
 # received a copy with calc; if not, write to Free Software Foundation, Inc.
 # 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 #
-# @(#) $Revision: 30.1 $
-# @(#) $Id: bindings,v 30.1 2007/03/16 11:09:54 chongo Exp $
-# @(#) $Source: /usr/local/src/bin/calc/cal/RCS/bindings,v $
-#
 # Under source code control:	1993/05/02 20:09:19
 # File existed as early as:	1993
 #

cal/brentsolve.cal

@@ -0,0 +1,254 @@
+/*
+ * brentsolve - Root finding with the Brent-Dekker trick
+ *
+ * Copyright (C) 2013 Christoph Zurnieden
+ *
+ * Calc is open software; you can redistribute it and/or modify it under
+ * the terms of the version 2.1 of the GNU Lesser General Public License
+ * as published by the Free Software Foundation.
+ *
+ * Calc is distributed in the hope that it will be useful, but WITHOUT
+ * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+ * or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
+ * Public License for more details.
+ *
+ * A copy of version 2.1 of the GNU Lesser General Public License is
+ * distributed with calc under the filename COPYING-LGPL.  You should have
+ * received a copy with calc; if not, write to Free Software Foundation, Inc.
+ * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
+ *
+ * Under source code control:	2013/08/11 01:31:28
+ * File existed as early as:	2013
+ */
+
+
+static resource_debug_level;
+resource_debug_level = config("resource_debug", 0);
+
+
+/*
+  A short explanation is at http://en.wikipedia.org/wiki/Brent%27s_method
+  I tried to follow the description at wikipedia as much as possible to make
+  the slight changes I did more visible.
+  You may give http://people.sc.fsu.edu/~jburkardt/cpp_src/brent/brent.html a
+  short glimpse (Brent's originl Fortran77 versions and some translations of
+  it).
+*/
+
+static true = 1;
+static false = 0;
+define brentsolve(low, high,eps){
+  local a b c d fa fb fc fa2 fb2 fc2 s fs  tmp tmp2  mflag i places;
+  a = low;
+  b = high;
+  c = 0;
+
+  if(isnull(eps))
+    eps = epsilon(epsilon()*1e-3);
+  places = highbit(1 + int( 1/epsilon() ) ) + 1;
+
+  d = 1/eps;
+
+  fa = f(a);
+  fb = f(b);
+
+  fc = 0;
+  s = 0;
+  fs = 0;
+
+  if(fa * fb >= 0){
+    if(fa < fb){
+      epsilon(eps);
+      return a;
+    }
+    else{
+      epsilon(eps);
+      return b;
+    }
+  }
+
+  if(abs(fa) < abs(fb)){
+    tmp = a; a = b; b = tmp;
+    tmp = fa; fa = fb; fb = tmp;
+  }
+
+  c = a;
+  fc = fa;
+  mflag = 1;
+  i = 0;
+
+  while(!(fb==0) && (abs(a-b) > eps)){
+    if((fa != fc) && (fb != fc)){
+      /* Inverse quadratic interpolation*/
+      fc2 = fc^2;
+      fa2 = fa^2;
+      s = bround(((fb^2*((fc*a)-(c*fa)))+(fb*((c*fa2)-(fc2*a)))+(b*((fc2*fa)
+                    -(fc*fa2))))/((fc - fb)*(fa - fb)*(fc - fa)),places++);
+    }
+    else{
+      /* Secant Rule*/
+      s =bround( b - fb * (b - a) / (fb - fa),places++);
+    }
+    tmp2 = (3 * a + b) / 4;
+    if( (!( ((s > tmp2) && (s < b))||((s < tmp2) && (s > b))))
+        || (mflag && (abs(s - b) >= (abs(b - c) / 2)))
+        || (!mflag && (abs(s - b) >= (abs(c - d) / 2)))) {
+      s = (a + b) / 2;
+      mflag = true;
+    }
+    else{
+      if( (mflag && (abs(b - c) < eps))
+          || (!mflag && (abs(c - d) < eps))) {
+        s = (a + b) / 2;
+        mflag = true;
+      }
+      else
+        mflag = false;
+    }
+    fs = f(s);
+    c = b;
+    fc = fb;
+    if (fa * fs < 0){
+      b = s;
+      fb = fs;
+    }
+    else {
+      a = s;
+      fa = fs;
+    }
+
+    if (abs(fa) < abs(fb)){
+      tmp = a; a = b; b = tmp;
+      tmp = fa; fa = fb; fb = tmp;
+    }
+    i++;
+    if (i > 1000){
+      epsilon(eps);
+      return newerror("brentsolve: does not converge");
+    }
+  }
+  epsilon(eps);
+  return b;
+}
+
+/*
+  A variation of the solver to accept functions named differently from "f". The
+  code should explain it.
+*/
+define brentsolve2(low, high,which,eps){
+  local a b c d fa fb fc fa2 fb2 fc2 s fs  tmp tmp2  mflag i places;
+  a = low;
+  b = high;
+  c = 0;
+
+  switch(param(0)){
+    case 0:
+    case 1: return newerror("brentsolve2: not enough argments");
+    case 2: eps = epsilon(epsilon()*1e-2);
+            which = 0;break;
+    case 3: eps = epsilon(epsilon()*1e-2);break;
+    default: break;
+  };
+  places = highbit(1 + int(1/epsilon())) + 1;
+
+  d = 1/eps;
+
+  switch(which){
+    case 1:  fa = __CZ__invbeta(a);
+             fb = __CZ__invbeta(b); break;
+    case 2:  fa = __CZ__invincgamma(a);
+             fb = __CZ__invincgamma(b); break;
+
+    default: fa = f(a);fb = f(b);   break;
+  };
+
+  fc = 0;
+  s = 0;
+  fs = 0;
+
+  if(fa * fb >= 0){
+    if(fa < fb)
+      return a;
+    else
+      return b;
+  }
+
+  if(abs(fa) < abs(fb)){
+    tmp = a; a = b; b = tmp;
+    tmp = fa; fa = fb; fb = tmp;
+  }
+
+  c = a;
+  fc = fa;
+  mflag = 1;
+  i = 0;
+
+  while(!(fb==0) && (abs(a-b) > eps)){
+
+    if((fa != fc) && (fb != fc)){
+      /* Inverse quadratic interpolation*/
+      fc2 = fc^2;
+      fa2 = fa^2;
+      s = bround(((fb^2*((fc*a)-(c*fa)))+(fb*((c*fa2)-(fc2*a)))+(b*((fc2*fa)
+                    -(fc*fa2))))/((fc - fb)*(fa - fb)*(fc - fa)),places);
+      places++;
+    }
+    else{
+      /* Secant Rule*/
+      s =bround( b - fb * (b - a) / (fb - fa),places);
+      places++;
+    }
+    tmp2 = (3 * a + b) / 4;
+    if( (!( ((s > tmp2) && (s < b))||((s < tmp2) && (s > b))))
+        || (mflag && (abs(s - b) >= (abs(b - c) / 2)))
+        || (!mflag && (abs(s - b) >= (abs(c - d) / 2)))) {
+      s = (a + b) / 2;
+      mflag = true;
+    }
+    else{
+      if( (mflag && (abs(b - c) < eps))
+          || (!mflag && (abs(c - d) < eps))) {
+        s = (a + b) / 2;
+        mflag = true;
+      }
+      else
+        mflag = false;
+    }
+    switch(which){
+      case 1:  fs = __CZ__invbeta(s); break;
+      case 2:  fs = __CZ__invincgamma(s); break;
+
+      default: fs = f(s);             break;
+    };
+    c = b;
+    fc = fb;
+    if (fa * fs < 0){
+      b = s;
+      fb = fs;
+    }
+    else {
+      a = s;
+      fa = fs;
+    }
+
+    if (abs(fa) < abs(fb)){
+      tmp = a; a = b; b = tmp;
+      tmp = fa; fa = fb; fb = tmp;
+    }
+    i++;
+    if (i > 1000){
+      return newerror("brentsolve2: does not converge");
+    }
+  }
+  return b;
+}
+
+
+/*
+ * restore internal function from resource debugging
+ */
+config("resource_debug", resource_debug_level),;
+if (config("resource_debug") & 3) {
+    print "brentsolve(low, high,eps)";
+    print "brentsolve2(low, high,which,eps)";
+}

cal/chi.cal

@@ -17,10 +17,6 @@
  * received a copy with calc; if not, write to Free Software Foundation, Inc.
  * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
  *
- * @(#) $Revision: 30.1 $
- * @(#) $Id: chi.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/bin/calc/cal/RCS/chi.cal,v $
- *
  * Under source code control:	2001/03/27 14:10:11
  * File existed as early as:	2001
  *

cal/chrem.cal

@@ -19,10 +19,6 @@
  * received a copy with calc; if not, write to Free Software Foundation, Inc.
  * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
  *
- * @(#) $Revision: 30.1 $
- * @(#) $Id: chrem.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/bin/calc/cal/RCS/chrem.cal,v $
- *
  * Under source code control:	1992/09/26 01:00:47
  * File existed as early as:	1992
  *

cal/constants.cal

@@ -0,0 +1,100 @@
+/*
+ * constants - implementation of different constants to arbitrary precision
+ *
+ * Copyright (C) 2013 Christoph Zurnieden
+ *
+ * Calc is open software; you can redistribute it and/or modify it under
+ * the terms of the version 2.1 of the GNU Lesser General Public License
+ * as published by the Free Software Foundation.
+ *
+ * Calc is distributed in the hope that it will be useful, but WITHOUT
+ * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+ * or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
+ * Public License for more details.
+ *
+ * A copy of version 2.1 of the GNU Lesser General Public License is
+ * distributed with calc under the filename COPYING-LGPL.  You should have
+ * received a copy with calc; if not, write to Free Software Foundation, Inc.
+ * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
+ *
+ * Under source code control:	2013/08/11 01:31:28
+ * File existed as early as:	2013
+ */
+
+
+static resource_debug_level;
+resource_debug_level = config("resource_debug", 0);
+
+
+static __CZ__euler_mascheroni = 0;
+static __CZ__euler_mascheroni_prec = 0;
+
+
+define e(){
+  local k temp1 temp2 ret eps factor upperlimit prec;
+
+  prec = digits(1/epsilon());
+  if(__CZ__euler_mascheroni != 0 &&  __CZ__euler_mascheroni_prec >= prec)
+    return __CZ__euler_mascheroni;
+  if(prec<=20) return 2.718281828459045235360287471;
+  if(prec<=1800){
+    __CZ__euler_mascheroni = exp(1);
+    __CZ__euler_mascheroni_prec = prec;
+  }
+
+  eps=epsilon(1e-20);
+  factor = 1;
+  k = 0;
+  upperlimit = prec * ln(10);
+  while(k<upperlimit){
+    k += ln(factor);
+    factor++;
+  }
+  epsilon(eps);
+  temp1 = 0;
+  ret   = 1;
+  for(k=3;k<=factor;k++){
+    temp2 = temp1;
+    temp1 = ret;
+    ret =  (k-1) *(temp1 + temp2);
+  }
+
+  ret = inverse( ret * inverse(factorial(factor) ) ) ;
+  __CZ__euler_mascheroni = ret;
+  __CZ__euler_mascheroni_prec = prec;
+  return ret;
+}
+
+
+/* Lupas' series */
+static __CZ__catalan = 0;
+static __CZ__catalan_prec = 0;
+define G(){
+  local eps a s t n;
+  eps = epsilon(epsilon()*1e-10);
+  if(__CZ__catalan != 0 &&  __CZ__catalan >= log(1/eps))
+    return __CZ__catalan;
+  a = 1;
+  s = 0;
+  t = 1;
+  n = 1;
+  while(abs(t)> eps){
+    a *= 32 * n^3 * (2*n-1);
+    a /=((3-16*n+16*n^2)^2);
+    t = a * (-1)^(n-1) * (40*n^2-24*n+3) / (n^3 * (2*n-1));
+    s += t;
+    n += 1;
+  }
+  s = s/64;
+  __CZ__catalan = s;
+  __CZ__catalan_prec = log(1/eps);
+  epsilon(eps);
+  return s;
+}
+
+
+config("resource_debug", resource_debug_level),;
+if (config("resource_debug") & 3) {
+    print "e()";
+    print "G()";
+}

cal/deg.cal

@@ -17,10 +17,6 @@
  * received a copy with calc; if not, write to Free Software Foundation, Inc.
  * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
  *
- * @(#) $Revision: 30.2 $
- * @(#) $Id: deg.cal,v 30.2 2010/09/02 06:01:14 chongo Exp $
- * @(#) $Source: /usr/local/src/bin/calc/cal/RCS/deg.cal,v $
- *
  * Under source code control:	1990/02/15 01:50:33
  * File existed as early as:	before 1990
  *

cal/dms.cal

@@ -17,10 +17,6 @@
  * received a copy with calc; if not, write to Free Software Foundation, Inc.
  * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
  *
- * @(#) $Revision: 30.2 $
- * @(#) $Id: dms.cal,v 30.2 2010/09/02 06:14:16 chongo Exp $
- * @(#) $Source: /usr/local/src/bin/calc/cal/RCS/dms.cal,v $
- *
  * Under source code control:	1990/02/15 01:50:33
  * File existed as early as:	before 1990
  *

cal/dotest.cal

@@ -16,10 +16,6 @@
  * NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR  IN
  * CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
  *
- * @(#) $Revision: 30.2 $
- * @(#) $Id: dotest.cal,v 30.2 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/bin/calc/cal/RCS/dotest.cal,v $
- *
  * This file is not covered under version 2.1 of the GNU LGPL.
  *
  * Under source dotest_code control:	2006/03/08 05:54:09

cal/ellip.cal

@@ -17,10 +17,6 @@
  * received a copy with calc; if not, write to Free Software Foundation, Inc.
  * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
  *
- * @(#) $Revision: 30.1 $
- * @(#) $Id: ellip.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/bin/calc/cal/RCS/ellip.cal,v $
- *
  * Under source code control:	1990/02/15 01:50:33
  * File existed as early as:	before 1990
  *

cal/factorial.cal

@@ -0,0 +1,200 @@
+/*
+ * factorial - implementation of different algorithms for the factorial
+ *
+ * Copyright (C) 2013 Christoph Zurnieden
+ *
+ * Calc is open software; you can redistribute it and/or modify it under
+ * the terms of the version 2.1 of the GNU Lesser General Public License
+ * as published by the Free Software Foundation.
+ *
+ * Calc is distributed in the hope that it will be useful, but WITHOUT
+ * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+ * or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
+ * Public License for more details.
+ *
+ * A copy of version 2.1 of the GNU Lesser General Public License is
+ * distributed with calc under the filename COPYING-LGPL.  You should have
+ * received a copy with calc; if not, write to Free Software Foundation, Inc.
+ * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
+ *
+ * Under source code control:	2013/08/11 01:31:28
+ * File existed as early as:	2013
+ */
+
+
+/*
+ * hide internal function from resource debugging
+ */
+static resource_debug_level;
+resource_debug_level = config("resource_debug", 0);
+
+
+/*
+  get dependencies
+*/
+read -once toomcook;
+
+
+/* A simple list to keep things...uhm...simple?*/
+static __CZ__primelist = list();
+
+/* Helper for primorial: fill list with primes in range a,b */
+define __CZ__fill_prime_list(a,b)
+{
+  local k;
+  k=a;
+  if(isprime(k))k--;
+  while(1){
+    k = nextprime(k);
+    if(k > b) break;
+    append(__CZ__primelist,k );
+  }
+}
+
+/* Helper for factorial: how often prime p divides the factorial of n */
+define __CZ__prime_divisors(n,p)
+{
+    local q,m;
+    q = n;
+    m = 0;
+    if (p > n) return 0;
+    if (p > n/2) return 1;
+    while (q >= p) {
+        q  = q//p;
+        m += q;
+    }
+    return m;
+}
+
+/*
+  Wrapper. Please set cut-offs to own taste and hardware.
+*/
+define factorial(n){
+  local prime result shift prime_list k k1 k2 expo_list pix cut primorial;
+
+  result = 1;
+  prime  = 2;
+
+  if(!isint(n))  {
+    return newerror("factorial(n): n is not an integer"); ## or gamma(n)?
+  }
+  if(n < 0)      return newerror("factorial(n): n < 0");
+  if(n < 9000 && !isdefined("test8900"))   {
+    ## builtin is implemented with splitting but only with
+    ## Toom-Cook 2 (by Karatsuba (the father))
+    return n!;
+  }
+
+  shift = __CZ__prime_divisors(n,prime);
+  prime = 3;
+  cut = n//2;
+  pix   = pix(cut);
+  prime_list = mat[pix];
+  expo_list  = mat[pix];
+
+  k = 0;
+/*
+  Peter Borwein's algorithm
+
+  @Article{journals/jal/Borwein85,
+  author = {Borwein, Peter B.},
+  title  = {On the Complexity of Calculating Factorials.},
+  journal = {J. Algorithms},
+  year   = {1985},
+  number = {3},
+  url    = {http://dblp.uni-trier.de/db/journals/jal/jal6.html#Borwein85}
+*/
+
+  do {
+    prime_list[k]  = prime;
+    expo_list[k++] = __CZ__prime_divisors(n,prime);
+    prime          = nextprime(prime);
+  }while(prime <= cut);
+
+  /* size of the largest exponent in bits  */
+  k1 = highbit(expo_list[0]);
+  k2 = size(prime_list)-1;
+
+  for(;k1>=0;k1--){
+    /*
+       the cut-off for T-C-4 ist still to low, using T-C-3 here
+       TODO: check cutoffs
+     */
+    result = toomcook3square(result);
+    /*
+      almost all time is spend in this loop, so cutting of the
+      upper half of the primes makes sense
+    */
+    for(k=0; k<=k2; k++) {
+      if((expo_list[k] & (1 << k1)) != 0) {
+        result *= prime_list[k];
+      }
+    }
+
+  }
+  primorial = primorial( cut, n);
+  result *= primorial;
+  result <<= shift;
+  return result;
+}
+
+/*
+  Helper for primorial: do the product with binary splitting
+  TODO: do it without the intermediate list
+*/
+define __CZ__primorial__lowlevel( a, b ,p)
+{
+  local  c;
+  if( b == a) return p ;
+  if( b-a > 1){
+    c= (b + a) >> 1;
+    return  __CZ__primorial__lowlevel( a   , c , __CZ__primelist[a] )
+         *  __CZ__primorial__lowlevel( c+1 , b , __CZ__primelist[b] ) ;
+  }
+  return  __CZ__primelist[a] * __CZ__primelist[b];
+}
+
+/*
+   Primorial, Product of consecutive primes in range a,b
+
+  Originally meant to do primorials with a start different from 2, but
+  found out that this is faster at about a=1,b>=10^5 than the builtin
+  function pfact().  With the moderately small list a=1,b=10^6 (78498
+  primes) it is 3 times faster.  A quick look-up showed what was already
+  guessed: pfact() does it linearly.  (BTW: what is the time complexity
+  of the primorial with the naive algorithm?)
+*/
+define primorial(a,b)
+{
+  local C1 C2;
+  if(!isint(a)) return newerror("primorial(a,b): a is not an integer");
+  else if(!isint(b)) return newerror("primorial(a,b): b is not an integer");
+  else if(a < 0) return newerror("primorial(a,b): a < 0");
+  else if( b < 2 ) return newerror("primorial(a,b): b < 2");
+  else if( b < a) return newerror("primorial(a,b): b < a");
+  else{
+    /* last prime < 2^32 is also  max. prime for nextprime()*/
+    if(b >= 4294967291) return newerror("primorial(a,b): max. prime exceeded");
+    if(b ==  2) return 2;
+    /*
+      Can be extended by way of pfact(b)/pfact(floor(a-1/2)) for small a
+     */
+    if(a<=2 && b < 10^5) return pfact(b);
+    /* TODO: use pix() and a simple array (mat[])instead*/
+     __CZ__primelist = list();
+     __CZ__fill_prime_list(a,b);
+    C1 = size(__CZ__primelist)-1;
+    return __CZ__primorial__lowlevel( 0, C1,1)
+  }
+}
+
+
+/*
+ * restore internal function from resource debugging
+ * report important interface functions
+ */
+config("resource_debug", resource_debug_level),;
+if (config("resource_debug") & 3) {
+    print "factorial(n)";
+    print "primorial(a, b)";
+}

cal/factorial2.cal

@@ -0,0 +1,719 @@
+/*
+ * factorial2 - implementation of different factorial related functions
+ *
+ * Copyright (C) 2013 Christoph Zurnieden
+ *
+ * Calc is open software; you can redistribute it and/or modify it under
+ * the terms of the version 2.1 of the GNU Lesser General Public License
+ * as published by the Free Software Foundation.
+ *
+ * Calc is distributed in the hope that it will be useful, but WITHOUT
+ * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+ * or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
+ * Public License for more details.
+ *
+ * A copy of version 2.1 of the GNU Lesser General Public License is
+ * distributed with calc under the filename COPYING-LGPL.  You should have
+ * received a copy with calc; if not, write to Free Software Foundation, Inc.
+ * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
+ *
+ * Under source code control:	2013/08/11 01:31:28
+ * File existed as early as:	2013
+ */
+
+
+/*
+ * hide internal function from resource debugging
+ */
+static resource_debug_level;
+resource_debug_level = config("resource_debug", 0);
+
+
+/*
+  get dependencies
+*/
+read -once factorial toomcook specialfunctions;
+
+
+/*
+  Factorize a factorial and put the result in a 2-column matrix with pi(n) rows
+  mat[ primes , exponent ]
+  Result can be restricted to start at a prime different from 2 with the second
+  argument "start". That arguments gets taken at face value if it prime and
+  smaller than n, otherwise the next larger prime is taken if that prime is
+  smaller than n.
+*/
+
+define __CZ__factor_factorial(n,start){
+  local prime prime_list k pix stop;
+
+
+  if(!isint(n)) return
+    newerror("__CZ__factor_factorial(n,start): n is not integer");
+  if(n <  0)    return newerror("__CZ__factor_factorial(n,start): n < 0");
+  if(n == 1)    return newerror("__CZ__factor_factorial(n,start): n == 1");
+
+  if(start){
+    if(!isint(start) && start < 0 && start > n)
+      return newerror("__CZ__factor_factorial(n,start): value of "
+      		      "parameter 'start' out of range");
+    if(start == n && isprime(n)){
+      prime_list = mat[1 , 2];
+      prime_list[0,0] = n;
+      prime_list[0,1] = 1;
+    }
+    else if(!isprime(start) && nextprime(start) >n)
+      return newerror("__CZ__factor_factorial(n,start): value of parameter "
+      		      "'start' out of range");
+    else{
+      if(!isprime(start))  prime = nextprime(start);
+      else prime = start;
+    }
+  }
+  else
+    prime = 2;
+
+  pix   = pix(n);
+  if(start){
+    pix -= pix(prime) -1;
+  }
+  prime_list = mat[pix , 2];
+
+  k = 0;
+
+  do {
+    prime_list[k  ,0] = prime;
+    prime_list[k++,1] = __CZ__prime_divisors(n,prime);
+    prime          = nextprime(prime);
+  }while(prime <= n);
+
+  return prime_list;
+}
+
+/*
+
+  subtracts exponents of n_1! from exponents of n_2! with n_1<=n_2
+
+  Does not check for size or consecutiveness of the primes or a carry
+*/
+
+define __CZ__subtract_factored_factorials(matrix_2n,matrix_n){
+  local k ret len1,len2,tmp count p e;
+  len1 = size(matrix_n)/2;
+  len2 = size(matrix_2n)/2;
+  if(len2<len1){
+
+    swap(len1,len2);
+    tmp = matrix_n;
+    matrix_n = matrix_2n;
+    matrix_2n = tmp;
+  }
+  tmp = mat[len1,2];
+  k   = 0;
+
+  for(;k<len1;k++){
+     p = matrix_2n[k,0];
+     e = matrix_2n[k,1] - matrix_n[k,1];
+     if(e!=0){
+       tmp[count  ,0] = p;
+       tmp[count++,1] = e;
+     }
+  }
+  ret = mat[count + (len2-len1),2];
+  for(k=0;k<count;k++){
+     ret[k,0] = tmp[k,0];
+     ret[k,1] = tmp[k,1];
+  }
+
+  free(tmp);
+  for(k=len1;k<len2;k++){
+     ret[count,0] = matrix_2n[k,0];
+     ret[count++,1] = matrix_2n[k,1];
+  }
+  return ret;
+}
+
+/*
+
+  adds exponents of n_1! to exponents of n_2! with n_1<=n_2
+
+  Does not check for size or consecutiveness of the primes or a carry
+*/
+
+define __CZ__add_factored_factorials(matrix_2n,matrix_n){
+  local k ret len1,len2,tmp;
+  len1 = size(matrix_n)/2;
+  len2 = size(matrix_2n)/2;
+  if(len2<len1){
+    swap(len1,len2);
+    tmp = matrix_n;
+    matrix_n = matrix_2n;
+    matrix_2n = tmp;
+  }
+  ret = mat[len2,2];
+  k   = 0;
+  for(;k<len1;k++){
+     ret[k,0] = matrix_2n[k,0];
+     ret[k,1] = matrix_2n[k,1] + matrix_n[k,1];
+  }
+  for(;k<len2;k++){
+     ret[k,0] = matrix_2n[k,0];
+     ret[k,1] = matrix_2n[k,1];
+  }
+  return ret;
+}
+
+/*
+   Does not check if all exponents are positive
+
+
+                   timings
+                   this		  comb	    comb-this     rel. k/n
+;  benchmark_binomial(10,13)
+n=2^13 k=2^10 	 0.064004 	 0.016001	+ 	0.76923076923076923077
+n=2^13 k=2^11 	 0.064004 	 0.048003	+ 	0.84615384615384615385
+n=2^13 k=2^12 	 0.068004 	 0.124008	- 	0.92307692307692307692
+;  benchmark_binomial(10,15)
+n=2^15 k=2^10 	 0.216014 	 0.024001	+ 	0.66666666666666666667
+n=2^15 k=2^11 	 0.220014 	 0.064004	+ 	0.73333333333333333333
+n=2^15 k=2^12 	 0.228014 	 0.212014	+ 	0.8
+n=2^15 k=2^13 	 0.216013 	 0.664042	- 	0.86666666666666666667
+n=2^15 k=2^14 	 0.240015 	 1.868117	- 	0.93333333333333333333
+;  benchmark_binomial(11,15)
+n=2^15 k=2^11 	 0.216014 	 0.068004	+ 	0.73333333333333333333
+n=2^15 k=2^12 	 0.236015 	 0.212013	+ 	0.8
+n=2^15 k=2^13 	 0.216013 	 0.656041	- 	0.86666666666666666667
+n=2^15 k=2^14 	 0.244016 	 1.872117	- 	0.93333333333333333333
+;  benchmark_binomial(11,18)
+n=2^18 k=2^11 	 1.652103 	 0.100006	+ 	0.61111111111111111111
+n=2^18 k=2^12 	 1.608101 	 0.336021	+ 	0.66666666666666666667
+n=2^18 k=2^13 	 1.700106 	 1.140071	+ 	0.72222222222222222222
+n=2^18 k=2^14 	 1.756109 	 3.924245	- 	0.77777777777777777778
+n=2^18 k=2^15 	 2.036127 	 13.156822	- 	0.83333333333333333333
+n=2^18 k=2^16 	 2.172135 	 41.974624	- 	0.88888888888888888889
+n=2^18 k=2^17 	 2.528158 	 121.523594	- 	0.94444444444444444444
+;  benchmark_binomial(15,25)
+n=2^25 k=2^15 	 303.790985 	 38.266392	+ 	0.6
+;  benchmark_binomial(17,25)
+n=2^25 k=2^17 	 319.127944 	 529.025062	- 	0.68
+*/
+
+define benchmark_binomial(s,limit){
+  local ret k A B T1 T2 start end N K;
+    N = 2^(limit);
+  for(k=s;k<limit;k++){
+    K = 2^k;
+   start=usertime();A=binomial(N,K);end=usertime();
+   T1 = end-start;
+   start=usertime();B=comb(N,K);end=usertime();
+   T2 = end-start;
+   print "n=2^"limit,"k=2^"k,"	",T1,"	",T2,T1<T2?"-":"+","	"k/limit;
+   if(A!=B){
+     print "false";
+    break;
+   }
+  }
+}
+
+define __CZ__multiply_factored_factorial(matrix,stop){
+  local prime result shift prime_list k k1 k2 expo_list pix count start;
+  local hb flag;
+
+  result = 1;
+  shift  = 0;
+
+
+  if(!ismat(matrix))
+   return newerror("__CZ__multiply_factored_factorial(matrix): "
+   		   "argument matrix not a matrix ");
+  if(!matrix[0,0])
+    return
+      newerror("__CZ__multiply_factored_factorial(matrix): "
+      	       "matrix[0,0] is null/0");
+
+  if(!isnull(stop))
+    pix = stop;
+  else
+    pix   = size(matrix)/2-1;
+
+  if(matrix[0,0] == 2 && matrix[0,1] > 0){
+    shift = matrix[0,1];
+    if(pix-1 == 0)
+      return 2^matrix[0,1];
+  }
+
+  /*
+    This is a more general way to do the multiplication, so any optimization
+    must have been done by the caller.
+  */
+  k = 0;
+  /*
+     The size of the largest exponent in bits is calculated dynamically.
+     Can be done more elegantly and saves one run over the whole array if done
+     inside the main loop.
+   */
+  hb =0;
+  for(k=0;k<pix;k++){
+    k1=highbit(matrix[k,1]);
+    if(hb < k1)hb=k1;
+  }
+
+  k2 = pix;
+  start = 0;
+  if(shift) start++;
+
+  for(k1=hb;k1>=0;k1--){
+    /*
+       the cut-off for T-C-4 ist still too low, using T-C-3 here
+       TODO: check cutoffs
+     */
+    result = toomcook3square(result);
+
+    for(k=start; k<=k2; k++) {
+      if((matrix[k,1] & (1 << k1)) != 0) {
+        result *= matrix[k,0];
+      }
+    }
+  }
+
+  result <<= shift;
+  return result;
+}
+
+/*
+    Compute binomial coeficients n!/(k!(n-k)!)
+
+    One of the rare cases where a formula once meant to ease manual computation
+    is actually the (aymptotically) fastest way to do it (in July 2013) for
+    the extreme case binomial(2N,N) but for a high price, the memory
+    needed is pi(N)--theoretically.
+*/
+define binomial(n,k){
+  local ret factored_n factored_k factored_nk denom num quot K prime_list prime;
+  local pix diff;
+
+  if(!isint(n) || !isint(k))
+    return newerror("binomial(n,k): input is not integer");
+  if(n<0 || k<0)
+    return newerror("binomial(n,k): input is not >= 0"); ;
+  if(n<k )   return 0;
+  if(n==k)   return 1;
+  if(k==0)   return 1;
+  if(k==1)   return n;
+  if(n-k==1) return n;
+  /*
+      cut-off depends on real size of n,k and size of n/k
+      The current cut-off is to small for large n, e.g.:
+      for 2n=2^23, k=n-n/2 the quotient is q=2n/k=0.25. Empirical tests showed
+      that 2n=2^23 and k=2^16  with q=0.0078125 are still faster than the
+      builtin function.
+
+      The symmetry (n,k) = (n,n-k) is of not much advantage here. One way
+      might be to get closer to k=n/2 if k<n-k but only if the difference
+      is small and n very large.
+   */
+  if(n<2e4 && !isdefined("test8900"))  return comb(n,k);
+  if(n<2e4 && k< n-n/2 && !isdefined("test8900")) return comb(n,k);
+  /*
+    This should be done in parallel to save some memory, e.g. no temporary
+    arrays are needed, all can be done inline.
+    The theoretical memory needed is pi(k).
+    Which is still a lot.
+  */
+
+  prime = 2;
+  pix   = pix(n);
+  prime_list = mat[pix , 2];
+  K = 0;
+  do {
+    prime_list[K  ,0] = prime;
+    diff = __CZ__prime_divisors(n,prime)-
+	   ( __CZ__prime_divisors(n-k,prime)+__CZ__prime_divisors(k,prime));
+    if(diff != 0)
+      prime_list[K++,1] = diff;
+    prime          = nextprime(prime);
+  }while(prime <= k);
+
+  do {
+    prime_list[K  ,0] = prime;
+    diff = __CZ__prime_divisors(n,prime)-__CZ__prime_divisors(n-k,prime);
+    if(diff != 0)
+      prime_list[K++,1] = diff;
+    prime          = nextprime(prime);
+  }while(prime <= n-k);
+
+  do {
+    prime_list[K  ,0] = prime;
+    prime_list[K++,1] = __CZ__prime_divisors(n,prime);
+    prime          = nextprime(prime);
+  }while(prime <= n);
+  ##print K,pix(k),pix(n-k),pix(n);
+  ##factored_k  = __CZ__factor_factorial(k,1);
+  ##factored_nk = __CZ__factor_factorial(n-k,1);
+
+  ##denom = __CZ__add_factored_factorials(factored_k,factored_nk);
+    ##free(factored_k,factored_nk);
+  ##num  = __CZ__factor_factorial(n,1);
+  ##quot  = __CZ__subtract_factored_factorials( num , denom );
+    ##free(num,denom);
+
+  ret = __CZ__multiply_factored_factorial(`prime_list,K-1);
+
+  return ret;
+}
+
+/*
+    Compute large catalan numbers  C(n) = binomial(2n,n)/(n+1) with
+    cut-off: (n>5e4)
+    Needs a lot of memory.
+*/
+define bigcatalan(n){
+  if(!isint(n) )return newerror("bigcatalan(n): n is not integer");
+  if( n<0) return newerror("bigcatalan(n): n < 0");
+  if( n<5e4 && !isdefined("test8900") ) return catalan(n);
+  return binomial(2*n,n)/(n+1);
+}
+
+/*
+  df(-111) = -1/3472059605858239446587523014902616804783337112829102414124928
+  		7753332469144201839599609375
+
+ df(-3+1i) = 0.12532538977287649201-0.0502372106177184607i
+ df(2n + 1) = (2*n)!/(n!*2^n)
+*/
+define __CZ__double_factorial(n){
+  local n1 n2 diff prime pix K prime_list k;
+  prime = 3;
+  pix   = pix(2*n)+1;
+  prime_list = mat[pix , 2];
+  K = 0;
+  do {
+    prime_list[K  ,0] = prime;
+    diff = __CZ__prime_divisors(2*n,prime)-( __CZ__prime_divisors(n,prime));
+    if(diff != 0)
+      prime_list[K++,1] = diff;
+    prime          = nextprime(prime);
+  }while(prime <= n);
+  do {
+    prime_list[K  ,0] = prime;
+    prime_list[K++,1] = __CZ__prime_divisors(2*n,prime);
+    prime          = nextprime(prime);
+  }while(prime <= 2*n);
+  return __CZ__multiply_factored_factorial(prime_list,K);
+/*
+        n1=__CZ__factor_factorial(2*n,1);
+        n1[0,1] = n1[0,1]-n;
+        n2=__CZ__factor_factorial(n,1);
+        diff=__CZ__subtract_factored_factorials( n1 , n2 );
+        return __CZ__multiply_factored_factorial(diff);
+*/
+}
+
+##1, 1, 3, 15, 105, 945, 10395, 135135, 2027025, 34459425, 654729075,
+##13749310575, 316234143225, 7905853580625, 213458046676875,
+##6190283353629375, 191898783962510625, 6332659870762850625,
+##221643095476699771875, 8200794532637891559375
+
+## 1, 2, 8, 48, 384, 3840, 46080, 645120, 10321920, 185794560,
+##3715891200, 81749606400, 1961990553600, 51011754393600,
+##1428329123020800, 42849873690624000, 1371195958099968000,
+##46620662575398912000, 1678343852714360832000, 63777066403145711616000
+define doublefactorial(n){
+    local n1 n2 diff eps ret;
+    if(!isint(n) ){
+       /*
+           Probably one of the not-so-good ideas. See result of
+            http://www.wolframalpha.com/input/?i=doublefactorial%28a%2Bbi%29
+        */
+       eps=epsilon(epsilon()*1e-2);
+       ret =  2^(n/2-1/4 * cos(pi()* n)+1/4) * pi()^(1/4 *
+       	      cos(pi()* n)-1/4)* gamma(n/2+1);
+       epsilon(eps);
+       return ret;
+    }
+    if(n==2) return 2;
+    if(n==3) return 3;
+    switch(n){
+      case -1:
+      case 0 : return 1;break;
+      case 2 : return 2;break;
+      case 3 : return 3;break;
+      case 4 : return 8;break;
+      default: break;
+    }
+    if(isodd(n)){
+      /*
+        TODO: find reasonable cutoff
+        df(2n + 1) = (2*n)!/(n!*2^n)
+      */
+      if(n>0){
+         n = (n+1)//2;
+         return __CZ__double_factorial(n);
+      }
+      else{
+        if(n == -3 ) return -1;
+        n = ((-n)-1)/2;
+        return ((-1)^-n)/__CZ__double_factorial(n);
+       }
+    }
+    else{
+      /*
+         I'm undecided here. The formula for complex n is valid for the negative
+         integers, too.
+      */
+      n = n>>1;
+      if(n>0){
+        if(!isdefined("test8900"))
+          return factorial(n)<<n;
+        else
+          return n!<<n;
+      }
+      else
+        return newerror("doublefactorial(n): even(n) < 0");
+   }
+}
+
+/*
+    Algorithm 3.17,
+    Donald Kreher and Douglas Simpson,
+    Combinatorial Algorithms,
+    CRC Press, 1998, page 89.
+*/
+static __CZ__stirling1;
+static __CZ__stirling1_n = -1;
+static __CZ__stirling1_m = -1;
+
+define stirling1(n,m){
+  local i j k;
+  if(n<0)return newerror("stirling1(n,m): n <= 0");
+  if(m<0)return newerror("stirling1(n,m): m < 0");
+  if(n<m) return 0;
+  if(n==m) return 1;
+  if(m==0 || n==0) return 0;
+  /* We always use the list */
+  /*
+  if(m=1){
+    if(iseven(n)) return -factorial(n-1);
+    else return factorial(n-1);
+  }
+  if(m == n-1){
+    if(iseven(n)) return -binomial(n,2);
+    else return -binomial(n,2);
+  }
+  */
+  if(__CZ__stirling1_n >= n && __CZ__stirling1_m  >= m){
+    return __CZ__stirling1[n,m];
+  }
+  else{
+    __CZ__stirling1      = mat[n+1,m+1];
+    __CZ__stirling1[0,0] = 1;
+    for(i=1;i<=n;i++)
+      __CZ__stirling1[i,0] = 0;
+    for(i=1;i<=n;i++){
+      for(j=1;j<=m;j++){
+        if(j<=i){
+          __CZ__stirling1[i, j] =   __CZ__stirling1[i - 1, j - 1] - (i - 1)\
+                                  * __CZ__stirling1[i - 1, j];
+        }
+        else{
+         __CZ__stirling1[i, j] = 0;
+        }
+      }
+    }
+    __CZ__stirling1_n = n;
+    __CZ__stirling1_m = m;
+    return __CZ__stirling1[n,m];
+  }
+}
+
+define stirling2(n,m){
+  local k sum;
+  if(n<0)return newerror("stirling2(n,m): n < 0");
+  if(m<0)return newerror("stirling2(n,m): m < 0");
+  if(n<m) return 0;
+  if(n==0 && n!=m) return 0;
+  if(n==m) return 1;
+  if(m==0 )return 0;
+  if(m==1) return 1;
+  if(m==2) return 2^(n-1)-1;
+  /*
+    There are different methods to speed up alternating sums.
+    This one doesn't.
+   */
+  if(isdefined("test8900")){
+    for(k=0;k<=m;k++){
+      sum += (-1)^(m-k)*comb(m,k)*k^n;
+    }
+  return sum/(m!);
+  }
+  else{
+    for(k=0;k<=m;k++){
+      sum += (-1)^(m-k)*binomial(m,k)*k^n;
+    }
+  return sum/factorial(m);
+  }
+}
+
+static __CZ__stirling2;
+static __CZ__stirling2_n = -1;
+static __CZ__stirling2_m = -1;
+define stirling2caching(n,m){
+  local nm i j ;
+  if(n<0)return newerror("stirling2iter(n,m): n < 0");
+  if(m<0)return newerror("stirling2iter(n,m): m < 0");
+  /* no shortcuts here */
+
+  if(n<m) return 0;
+  if(n==0 && n!=m) return 0;
+  if(n==m) return 1;
+  if(m==0 )return 0;
+  if(m==1) return 1;
+  if(m==2) return 2^(n-1)-1;
+
+  nm = n-m;
+  if(__CZ__stirling2_n >= n && __CZ__stirling2_m >= m){
+    return __CZ__stirling2[n,m];
+  }
+  else{
+    __CZ__stirling2 = mat[n+1,m+1];
+    __CZ__stirling2[0,0] = 1;
+    for(i=1;i<=n;i++){
+      __CZ__stirling2[i,0] = 0;
+      for(j=1;j<=m;j++){
+        if(j<=i){
+          __CZ__stirling2[i, j] =   __CZ__stirling2[i -1, j -1] + (j )\
+                                  * __CZ__stirling2[i - 1, j];
+        }
+        else{
+         __CZ__stirling2[i, j] = 0;
+        }
+      }
+    }
+  }
+  __CZ__stirling2_n = (n);
+  __CZ__stirling2_m = (m);
+  return __CZ__stirling2[n,m];
+}
+
+define bell(n){
+  local sum s2list k A;
+
+  if(!isint(n)) return newerror("bell(n): n is not integer");
+  if(n < 0) return newerror("bell(n): n is not positive");
+  /* place some more shortcuts here?*/
+  if(n<=15){
+    mat A[16] = {
+                  1, 1, 2, 5, 15, 52, 203, 877, 4140, 21147, 115975, 678570,
+                  4213597, 27644437, 190899322, 1382958545
+                };
+    return A[n];
+  }
+  /* Start by generating the list of stirling numbers of the second kind */
+  s2list = stirling2caching(n,n//2);
+  if(iserror(s2list))
+    return newerror("bell(n): could not build stirling num. list");
+  sum = 0;
+  for(k=1;k<=n;k++){
+      sum += stirling2caching(n,k);
+  }
+  return sum;
+}
+
+define subfactorialrecursive(n){
+  if(n==0) return 1;
+  if(n==1) return 0;
+  if(n==2) return 1;
+  return n * subfactorialrecursive(n-1) + (-1)^n;
+}
+
+/* This is, quite amusingely, faster than the very same algorithm in
+   PARI/GP + GMP*/
+define subfactorialiterative(n){
+  local k temp1 temp2 ret;
+  if(n==0) return 1;
+  if(n==1) return 0;
+  if(n==2) return 1;
+  temp1 = 0;
+  ret   = 1;
+  for(k=3;k<=n;k++){
+    temp2 = temp1;
+    temp1 = ret;
+    ret =  (k-1) *(temp1 + temp2);
+  }
+  return ret;
+}
+
+define subfactorial(n){
+  local epsilon eps ret lnfact;
+  if(!isint(n))return  newerror("subfactorial(n): n is not integer.");
+  if(n < 0)return  newerror("subfactorial(n): n < 0");
+  return subfactorialiterative(n);
+}
+
+define risingfactorial(x,n){
+  local num denom quot ret;
+  if(n == 1) return x;
+  if(x==0) return newerror("risingfactorial(x,n): x == 0");
+  if(!isint(x) || !isint(n)){
+    return gamma(x+n)/gamma(x);
+  }
+  if(x<1)return newerror("risingfactorial(x,n): integer x and x < 1");
+  if(x+n < 1)return newerror("risingfactorial(x,n): integer x+n and x+n < 1");
+  if(x<9000&&n<9000){
+    return (x+n-1)!/(x-1)!;
+  }
+  else{
+    num   = __CZ__factor_factorial(x+n-1,1);
+    denom = __CZ__factor_factorial(x-1,1);
+    quot  = __CZ__subtract_factored_factorials( num , denom );
+      free(num,denom);
+    ret = __CZ__multiply_factored_factorial(quot);
+    return ret;
+  }
+}
+
+define fallingfactorial(x,n){
+  local num denom quot ret;
+  if(n == 0) return 1;
+
+  if(!isint(x) || !isint(n)){
+    if(x == n) return gamma(x+1);
+    return gamma(x+1)/gamma(x-n+1);
+  }
+  else{
+    if(x<0 || x-n < 0)
+     return newerror("fallingfactorial(x,n): integer x<0 or x-n < 0");
+    if(x == n) return factorial(x);
+    if(x<9000&&n<9000){
+      return (x)!/(x-n)!;
+    }
+    else{
+      num   = __CZ__factor_factorial(x,1);
+      denom = __CZ__factor_factorial(x-n,1);
+      quot  = __CZ__subtract_factored_factorials( num , denom );
+        free(num,denom);
+      ret = __CZ__multiply_factored_factorial(quot);
+      return ret;
+    }
+  }
+}
+
+
+/*
+ * restore internal function from resource debugging
+ * report important interface functions
+ */
+config("resource_debug", resource_debug_level),;
+if (config("resource_debug") & 3) {
+    print "binomial(n,k)";
+    print "bigcatalan(n)";
+    print "doublefactorial(n)";
+    print "subfactorial(n)";
+    print "stirling1(n,m)";
+    print "stirling2(n,m)";
+    print "stirling2caching(n,m)";
+    print "bell(n)";
+    print "subfactorial(n)";
+    print "risingfactorial(x,n)";
+    print "fallingfactorial(x,n)";
+}

cal/gvec.cal

@@ -8,10 +8,6 @@
  * operation "function" must be first; calc doesn't care how many more
  * arguments there actually are.
  *
- * @(#) $Revision: 30.3 $
- * @(#) $Id: gvec.cal,v 30.3 2011/05/23 23:00:55 chongo Exp $
- * @(#) $Source: /usr/local/src/bin/calc/cal/RCS/gvec.cal,v $
- *
  * Under source code control:   2011/03/31 17:54:55
  * File existed as early as:    2010
  *

cal/hello.cal

@@ -17,10 +17,6 @@
  * received a copy with calc; if not, write to Free Software Foundation, Inc.
  * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
  *
- * @(#) $Revision: 30.1 $
- * @(#) $Id: hello.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/bin/calc/cal/RCS/hello.cal,v $
- *
  * Under source code control:	1996/11/13 13:25:43
  * File existed as early as:	1996
  *

cal/hms.cal

@@ -17,10 +17,6 @@
  * received a copy with calc; if not, write to Free Software Foundation, Inc.
  * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
  *
- * @(#) $Revision: 30.2 $
- * @(#) $Id: hms.cal,v 30.2 2010/09/02 06:14:16 chongo Exp $
- * @(#) $Source: /usr/local/src/bin/calc/cal/RCS/hms.cal,v $
- *
  * Under source code control:	2010/09/01 17:14:55
  * File existed as early as:	2010
  *

cal/infinities.cal

@@ -0,0 +1,88 @@
+/*
+ * infinities - handle infinities symbolically, a little helper file
+ *
+ * Copyright (C) 2013 Christoph Zurnieden
+ *
+ * Calc is open software; you can redistribute it and/or modify it under
+ * the terms of the version 2.1 of the GNU Lesser General Public License
+ * as published by the Free Software Foundation.
+ *
+ * Calc is distributed in the hope that it will be useful, but WITHOUT
+ * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+ * or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
+ * Public License for more details.
+ *
+ * A copy of version 2.1 of the GNU Lesser General Public License is
+ * distributed with calc under the filename COPYING-LGPL.  You should have
+ * received a copy with calc; if not, write to Free Software Foundation, Inc.
+ * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
+ */
+
+
+static resource_debug_level;
+resource_debug_level = config("resource_debug", 0);
+
+
+define isinfinite(x)
+{
+    if (isstr(x)) {
+	if (strncmp(x, "cinf", 4) == 0
+	    || strncmp(x, "pinf", 4) == 0 || strncmp(x, "ninf", 4) == 0)
+	    return 1;
+    }
+    return 0;
+}
+
+define iscinf(x)
+{
+    if (isstr(x)) {
+	if (strncmp(x, "cinf", 4) == 0)
+	    return 1;
+    }
+    return 0;
+}
+
+define ispinf(x)
+{
+    if (isstr(x)) {
+	if (strncmp(x, "pinf", 4) == 0)
+	    return 1;
+    }
+    return 0;
+}
+
+define isninf(x)
+{
+    if (isstr(x)) {
+	if (strncmp(x, "ninf", 4) == 0)
+	    return 1;
+    }
+    return 0;
+}
+
+define cinf()
+{
+    return "cinf";
+}
+
+define ninf()
+{
+    return "ninf";
+}
+
+define pinf()
+{
+    return "pinf";
+}
+
+
+config("resource_debug", resource_debug_level),;
+if (config("resource_debug") & 3) {
+    print "isinfinite(x)";
+    print "iscinf(x)";
+    print "ispinf(x)";
+    print "isninf(x)";
+    print "cinf()";
+    print "ninf()";
+    print "pinf()";
+}

cal/intfile.cal

@@ -17,10 +17,6 @@
  * received a copy with calc; if not, write to Free Software Foundation, Inc.
  * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
  *
- * @(#) $Revision: 30.1 $
- * @(#) $Id: intfile.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/bin/calc/cal/RCS/intfile.cal,v $
- *
  * Under source code control:   2001/03/31 08:13:11
  * File existed as early as:    2001
  *

cal/intnum.cal

@@ -0,0 +1,728 @@
+/*
+ * intnum - implementation of tanhsinh- and Gauss-Legendre quadrature
+ *
+ * Copyright (C) 2013 Christoph Zurnieden
+ *
+ * Calc is open software; you can redistribute it and/or modify it under
+ * the terms of the version 2.1 of the GNU Lesser General Public License
+ * as published by the Free Software Foundation.
+ *
+ * Calc is distributed in the hope that it will be useful, but WITHOUT
+ * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+ * or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
+ * Public License for more details.
+ *
+ * A copy of version 2.1 of the GNU Lesser General Public License is
+ * distributed with calc under the filename COPYING-LGPL.  You should have
+ * received a copy with calc; if not, write to Free Software Foundation, Inc.
+ * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
+ */
+
+
+static resource_debug_level;
+resource_debug_level = config("resource_debug", 0);
+
+
+read -once infinities;
+
+static __CZ__tanhsinh_x;
+static __CZ__tanhsinh_w;
+static __CZ__tanhsinh_order;
+static __CZ__tanhsinh_prec;
+
+define quadtsdeletenodes()
+{
+    free(__CZ__tanhsinh_x);
+    free(__CZ__tanhsinh_w);
+    free(__CZ__tanhsinh_order);
+    free(__CZ__tanhsinh_prec);
+}
+
+define quadtscomputenodes(order, expo, eps)
+{
+    local t cht sht chp sum k PI places;
+    local h t0 x w;
+    if (__CZ__tanhsinh_order == order && __CZ__tanhsinh_prec == eps)
+	return 1;
+    __CZ__tanhsinh_order = order;
+    __CZ__tanhsinh_prec = eps;
+    __CZ__tanhsinh_x = list();
+    __CZ__tanhsinh_w = list();
+    /* The tanhsinh algorithm needs a slightly higher precision than G-L */
+    eps = epsilon(eps * 1e-2);
+    places = highbit(1 + int (1 / epsilon())) +1;
+    PI = pi();
+    sum = 0;
+    t0 = 2 ^ (-expo);
+    h = 2 * t0;
+    /*
+     * The author wanted to use the mpmath trick here which was
+     * advertised---and reasonably so!---to be faster. Didn't work out
+     * so well with calc.
+     * PI4 = PI/4;
+     * expt0 = bround(exp(t0),places);
+     * a = bround( PI4 * expt0,places);
+     * b = bround(PI4 / expt0,places);
+     * udelta = bround(exp(h),places);
+     * urdelta = bround(1/udelta,places);
+     */
+    /* make use of x(-t) = -x(t), w(-t) = w(t)  */
+    for (k = 0; k < 20 * order + 1; k++) {
+	/*
+	 * x = tanh(pi/2 * sinh(t))
+	 * w = pi/2 * cosh(t) / cosh(pi/2 * sinh(t))^2
+	 */
+	t = bround(t0 + k * h, places);
+
+	cht = bround(cosh(t), places);
+	sht = bround(sinh(t), places);
+	chp = bround(cosh(0.5 * PI * sht), places);
+	x = bround(tanh(0.5 * PI * sht), places);
+	w = bround((PI * h * cht) / (2 * chp ^ 2), places);
+	/*
+	 * c = bround(exp(a-b),places);
+	 * d = bround(1/c,places);
+	 * co =bround( (c+d)/2,places);
+	 * si =bround( (c-d)/2,places);
+	 * x = bround(si / co,places);
+	 * w = bround((a+b) / co^2,places);
+	 */
+	if (abs(x - 1) <= eps)
+	    break;
+
+	append(__CZ__tanhsinh_x, x);
+	append(__CZ__tanhsinh_w, w);
+	/*
+	 * a *= udelta;
+	 * b *= urdelta;
+	 */
+    }
+
+    /* Normalize the weights to make them add up to 2 (two) */
+    /*
+     * for(k=0;k < size(__CZ__tanhsinh_w);k++)
+     * sum = bround(sum + __CZ__tanhsinh_w[k],places);
+     * sum *= 2;
+     * for(k=0;k < size(__CZ__tanhsinh_w);k++)
+     * __CZ__tanhsinh_w[k] = bround(2.0 * __CZ__tanhsinh_w[k] / sum,places);
+     */
+
+    epsilon(eps);
+    return 1;
+}
+
+define quadtscore(a, b, n)
+{
+    local k c d order eps places sum ret x x1 x2 xm w w1 w2 m sizel;
+
+    eps = epsilon(epsilon() * 1e-2);
+    places = highbit(1 + int (1 / epsilon())) +1;
+    m = int (4 + max(0, ln(places / 30.0) / ln(2))) + 2;
+    if (!isnull(n)) {
+	order = n;
+	m = ilog(order / 3, 2) + 1;
+    } else
+	order = 3 * 2 ^ (m - 1);
+
+    quadtscomputenodes(order, m, epsilon());
+    sizel = size(__CZ__tanhsinh_w);
+
+    if (isinfinite(a) || isinfinite(b)) {
+	/*
+	 *           x
+	 * t =  ------------
+	 *                2
+	 *      sqrt(1 - y )
+	 */
+	if (isninf(a) && ispinf(b)) {
+	    for (k = 0; k < sizel; k++) {
+		x1 = __CZ__tanhsinh_x[k];
+		x2 = -__CZ__tanhsinh_x[k];
+		w1 = __CZ__tanhsinh_w[k];
+
+		x = bround(x1 * (1 - x1 ^ 2) ^ (-1 / 2), places);
+		xm = bround(x2 * (1 - x2 ^ 2) ^ (-1 / 2), places);
+		w = bround(w1 * (((1 - x1 ^ 2) ^ (-1 / 2)) / (1 - x1 ^ 2)),
+			   places);
+		w2 = bround(w1 * (((1 - x2 ^ 2) ^ (-1 / 2)) / (1 - x2 ^ 2)),
+			    places);
+		sum += bround(w * f(x), places);
+		sum += bround(w2 * f(xm), places);
+	    }
+	}
+	/*
+	 *        1
+	 * t =  - - + b + 1
+	 *        x
+	 */
+	else if (isninf(a) && !iscinf(b)) {
+	    for (k = 0; k < sizel; k++) {
+		x1 = __CZ__tanhsinh_x[k];
+		x2 = -__CZ__tanhsinh_x[k];
+		w1 = __CZ__tanhsinh_w[k];
+
+		x = bround((b + 1) - (2 / (x1 + 1)), places);
+		xm = bround((b + 1) - (2 / (x2 + 1)), places);
+		w = bround(w1 * (1 / 2 * (2 / (x1 + 1)) ^ 2), places);
+		w2 = bround(w1 * (1 / 2 * (2 / (x2 + 1)) ^ 2), places);
+		sum += bround(w * f(x), places);
+		sum += bround(w2 * f(xm), places);
+	    }
+	}
+	/*
+	 *      1
+	 * t =  - + a - 1
+	 *      x
+	 */
+	else if (!iscinf(a) && ispinf(b)) {
+	    for (k = 0; k < sizel; k++) {
+		x1 = __CZ__tanhsinh_x[k];
+		x2 = -__CZ__tanhsinh_x[k];
+		w1 = __CZ__tanhsinh_w[k];
+		x = bround((a - 1) + (2 / (x1 + 1)), places);
+		xm = bround((a - 1) + (2 / (x2 + 1)), places);
+		w = bround(w1 * (((1 / 2) * (2 / (x1 + 1)) ^ 2)), places);
+		w2 = bround(w1 * (((1 / 2) * (2 / (x2 + 1)) ^ 2)), places);
+		sum += bround(w * f(x), places);
+		sum += bround(w2 * f(xm), places);
+	    }
+	} else if (isninf(a) || isninf(b)) {
+	    /*TODO: swap(a,b) and negate(w)? Lookup! */
+	    return newerror("quadtscore: reverse limits?");
+	} else {
+	    return
+		newerror("quadtscore: complex infinity not yet implemented");
+        }
+	ret = sum;
+    } else {
+	/* Avoid rounding errors */
+	if (a == -1 && b == 1) {
+	    c = 1;
+	    d = 0;
+	} else {
+	    c = (b - a) / 2;
+	    d = (b + a) / 2;
+	}
+	sum = 0;
+	for (k = 0; k < sizel; k++) {
+	    sum +=
+		bround(__CZ__tanhsinh_w[k] * f(c * __CZ__tanhsinh_x[k] + d),
+		       places);
+	    sum +=
+		bround(__CZ__tanhsinh_w[k] * f(c * -__CZ__tanhsinh_x[k] + d),
+		       places);
+	}
+	ret = c * sum;
+    }
+    epsilon(eps);
+    return ret;
+}
+
+static __CZ__quadts_error;
+
+define quadts(a, b, points)
+{
+    local k sp results epsbits nsect interval length segment slope C ;
+    local x1 x2 y1 y2  sum D1 D2 D3 D4;
+    if (param(0) < 2)
+	return newerror("quadts: not enough arguments");
+    epsbits = highbit(1 + int (1 / epsilon())) +1;
+    if (param(0) < 3 || isnull(points)) {
+	/* return as given */
+	return quadtscore(a, b);
+    } else {
+	if ((isinfinite(a) || isinfinite(b))
+	    && (!ismat(points) && !islist(points)))
+	    return
+		newerror(strcat
+			 ("quadts: segments of infinite length ",
+			  "are not yet supported"));
+	if (ismat(points) || islist(points)) {
+	    sp = size(points);
+	    if (sp == 0)
+		return
+		    newerror(strcat
+			     ("quadts: variable 'points` must be a list or ",
+			      "1d-matrix of a length > 0"));
+	    /* check if all points are numbers */
+	    for (k = 0; k < sp; k++) {
+		if (!isnum(points[k]))
+		    return
+			newerror(strcat
+				 ("quadts: elements of 'points` must be",
+				  " numbers only"));
+	    }
+	    /* We have n-1 intervals and a and b, hence n-1 + 2 results */
+	    results = mat[sp + 1];
+            if (a != points[0]) {
+	        results[0] = quadtscore(a, points[0]);
+            } else {
+                results[0] = 0;
+            }
+	    if (sp == 1) {
+                if (b != points[0]) {
+		    results[1] = quadtscore(points[0], b);
+                } else {
+                    results[1] = 0;
+                }
+	    } else {
+		for (k = 1; k < sp; k++) {
+		    results[k] = quadtscore(points[k - 1], points[k]);
+		}
+                if (b != points[k - 1]) {
+		    results[k] = quadtscore(points[k - 1], b);
+                } else {
+                    results[k] = 0;
+                }
+	    }
+	} else {
+	    if (!isint(points) || points <= 0)
+		return newerror(strcat("quadts: variable 'points` must be a ",
+				       "list or a positive integer"));
+	    /* Taking "points" as the number of equally spaced intervals */
+	    results = mat[points + 1];
+	    /* It is easy if a,b lie on the real line */
+	    if (isreal(a) && isreal(b)) {
+		length = abs(a - b);
+		segment = length / points;
+
+		for (k = 1; k <= points; k++) {
+		    results[k - 1] =
+			quadtscore(a + (k - 1) * segment, a + k * segment);
+		}
+	    } else {
+		/* We have at least one complex limit but treat "points" still
+                 * as the number of equally spaced intervals on a straight line
+                 * connecting a and b. Computing the segments here is a bit
+                 * more complicated but not much, it should have been taught in
+                 * highschool.
+		 * Other contours by way of a list of points */
+		slope = (im(b) - im(a)) / (re(b) - re(a));
+		C = (im(a) + slope) * re(a);
+		length = abs(re(a) - re(b));
+		segment = length / points;
+
+		/* y = mx+C where m is the slope, x is the real part and y the
+		 * imaginary part  */
+                if(re(a)>re(b))swap(a,b);
+		for (k = re(a); k <= (re(b)); k+=segment) {
+		    x1 = slope*(k) +  C;
+		    results[k] = quadtscore(k + x1 * 1i);
+		}
+	    }			/* else of isreal */
+	}			/* else of ismat|islist */
+    }				/* else of isnull(points) */
+    /* With a bit of undeserved luck we have a result by now. */
+    sp = size(results);
+    for (k = 0; k < sp; k++) {
+	sum += results[k];
+    }
+    return sum;
+}
+
+static __CZ__gl_x;
+static __CZ__gl_w;
+static __CZ__gl_order;
+static __CZ__gl_prec;
+
+define quadglcomputenodes(N)
+{
+    local places k l x w t1 t2 t3 t4 t5 r tmp;
+
+    if (__CZ__gl_order == N && __CZ__gl_prec == epsilon())
+	return;
+
+    __CZ__gl_x = mat[N];
+    __CZ__gl_w = mat[N];
+    __CZ__gl_order = N;
+    __CZ__gl_prec = epsilon();
+
+    places = highbit(1 + int (1 / epsilon())) +1;
+
+    /*
+     * Compute roots and weights (doing it inline seems to be fastest)
+     * Trick shamelessly stolen from D. Bailey et .al (program "arprec")
+     */
+    for (k = 1; k <= N//2; k++) {
+	r = bround(cos(pi() * (k - .25) / (N + .5)), places);
+	while (1) {
+	    t1 = 1, t2 = 0;
+	    for (l = 1; l <= N; l++) {
+		t3 = t2;
+		t2 = t1;
+		t1 = bround(((2 * l - 1) * r * t2 - (l - 1) * t3) / l, places);
+	    }
+	    t4 = bround(N * (r * t1 - t2) / ((r ^ 2) - 1), places);
+	    t5 = r;
+	    tmp = t1 / t4;
+	    r = r - tmp;
+	    if (abs(tmp) <= epsilon())
+		break;
+	}
+	x = r;
+	w = bround(2 / ((1 - r ^ 2) * t4 ^ 2), places);
+
+	__CZ__gl_x[k - 1] = x;
+	__CZ__gl_w[k - 1] = w;
+	__CZ__gl_x[N - k] = -__CZ__gl_x[k - 1];
+	__CZ__gl_w[N - k] = __CZ__gl_w[k - 1];
+    }
+    return;
+}
+
+define quadgldeletenodes()
+{
+    free(__CZ__gl_x);
+    free(__CZ__gl_w);
+    free(__CZ__gl_order);
+    free(__CZ__gl_prec);
+}
+
+define quadglcore(a, b, n)
+{
+    local k c d digs order eps places sum ret err x x1 w w1 m;
+    local phalf x2 px1 spx1 u b1 a1 half;
+
+    eps = epsilon(epsilon() * 1e-2);
+    places = highbit(1 + int (1 / epsilon())) +1;
+    if (!isnull(n))
+	order = n;
+    else {
+	m = int (4 + max(0, ln(places / 30.0) / ln(2))) + 2;
+	order = 3 * 2 ^ (m - 1);
+    }
+
+
+    quadglcomputenodes(order, 1);
+
+    if (isinfinite(a) || isinfinite(b)) {
+	if (isninf(a) && ispinf(b)) {
+	    for (k = 0; k < order; k++) {
+		x1 = __CZ__gl_x[k];
+		w1 = __CZ__gl_w[k];
+
+		x = bround(x1 * (1 - x1 ^ 2) ^ (-1 / 2), places);
+		w = bround(w1 * (((1 - x1 ^ 2) ^ (-1 / 2)) / (1 - x1 ^ 2)),
+			   places);
+		sum += bround(w * f(x), places);
+	    }
+	} else if (isninf(a) && !iscinf(b)) {
+	    for (k = 0; k < order; k++) {
+		x1 = __CZ__gl_x[k];
+		w1 = __CZ__gl_w[k];
+
+		x = bround((b + 1) - (2 / (x1 + 1)), places);
+		w = bround(w1 * (1 / 2 * (2 / (x1 + 1)) ^ 2), places);
+		sum += bround(w * f(x), places);
+	    }
+	} else if (!iscinf(a) && ispinf(b)) {
+	    for (k = 0; k < order; k++) {
+		x1 = __CZ__gl_x[k];
+		w1 = __CZ__gl_w[k];
+		x = bround((a - 1) + (2 / (x1 + 1)), places);
+		w = bround(w1 * (((1 / 2) * (2 / (x1 + 1)) ^ 2)), places);
+		sum += bround(w * f(x), places);
+	    }
+	} else if (isninf(a) || isninf(b)) {
+	    /*TODO: swap(a,b) and negate(w)? Lookup! */
+	    return newerror("quadglcore: reverse limits?");
+	} else
+	    return
+		newerror("quadglcore: complex infinity not yet implemented");
+	ret = sum;
+    } else {
+	/* Avoid rounding errors */
+	if (a == -1 && b == 1) {
+	    c = 1;
+	    d = 0;
+	} else {
+	    c = (b - a) / 2;
+	    d = (b + a) / 2;
+	}
+	sum = 0;
+	for (k = 0; k < order; k++) {
+	    sum += bround(__CZ__gl_w[k] * f(c * __CZ__gl_x[k] + d), places);
+	}
+	ret = c * sum;
+    }
+    epsilon(eps);
+    return ret;
+}
+
+define quadgl(a, b, points)
+{
+    local k sp results epsbits nsect interval length segment slope C x1 y1 x2
+	y2;
+    local sum D1 D2 D3 D4;
+    if (param(0) < 2)
+	return newerror("quadgl: not enough arguments");
+    epsbits = highbit(1 + int (1 / epsilon())) +1;
+    if (isnull(points)) {
+	/* return as given */
+	return quadglcore(a, b);
+    } else {
+	/* But if we could half the time needed to execute a single operation
+	 * we could do all of it in just twice that time. */
+	if (isinfinite(a) || isinfinite(b)
+	    && (!ismat(points) && !islist(points)))
+	    return
+		newerror(strcat
+			 ("quadgl: multiple segments of infinite length ",
+			  "are not yet supported"));
+	if (ismat(points) || islist(points)) {
+	    sp = size(points);
+	    if (sp == 0)
+		return
+		    newerror(strcat
+			     ("quadgl: variable 'points` must be a list or ",
+			      "1d-matrix of a length > 0"));
+	    /* check if all points are numbers */
+	    for (k = 0; k < sp; k++) {
+		if (!isnum(points[k]))
+		    return
+			newerror(strcat
+				 ("quadgl: elements of 'points` must be ",
+				  "numbers only"));
+	    }
+	    /* We have n-1 intervals and a and b, hence n-1 + 2 results */
+	    results = mat[sp + 1];
+            if (a != points[0]) {
+	        results[0] = quadglcore(a, points[0]);
+            } else {
+                results[0] = 0;
+            }
+	    if (sp == 1) {
+		if (b != points[0]) {
+		    results[1] = quadglcore(points[0], b);
+                } else {
+                    results[1] = 0;
+                }
+	    } else {
+		for (k = 1; k < sp; k++) {
+		    results[k] = quadglcore(points[k - 1], points[k]);
+		}
+                if (b != points[k - 1]) {
+		    results[k] = quadglcore(points[k - 1], b);
+                } else {
+                    results[k] = 0;
+                }
+	    }
+	} else {
+	    if (!isint(points) || points <= 0)
+		return newerror(strcat("quadgl: variable 'points` must be a ",
+				       "list or a positive integer"));
+	    /* Taking "points" as the number of equally spaced intervals */
+	    results = mat[points + 1];
+	    /* It is easy if a,b lie on the real line */
+	    if (isreal(a) && isreal(b)) {
+		length = abs(a - b);
+		segment = length / points;
+
+		for (k = 1; k <= points; k++) {
+		    results[k - 1] =
+			quadglcore(a + (k - 1) * segment, a + k * segment);
+		}
+	    } else {
+		/* Other contours by way of a list of points */
+		slope = (im(b) - im(a)) / (re(b) - re(a));
+		C = (im(a) + slope) * re(a);
+		length = abs(re(a) - re(b));
+		segment = length / points;
+
+		/* y = mx+C where m is the slope, x is the real part and y the
+		 * imaginary part  */
+                if(re(a)>re(b))swap(a,b);
+		for (k = re(a); k <= (re(b)); k+=segment) {
+		    x1 = slope*(k) +  C;
+		    results[k] = quadglcore(k + x1 * 1i);
+		}
+	    }			/* else of isreal */
+	}			/* else of ismat|islist */
+    }				/* else of isnull(points) */
+    /* With a bit of undeserved luck we have a result by now. */
+    sp = size(results);
+    for (k = 0; k < sp; k++) {
+	sum += results[k];
+    }
+    return sum;
+}
+
+define quad(a, b, points = -1, method = "tanhsinh")
+{
+    if (isnull(a) || isnull(b) || param(0) < 2)
+	return newerror("quad: both limits must be given");
+    if (isstr(a)) {
+	if (strncmp(a, "cinf", 1) == 0)
+	    return
+		newerror(strcat
+			 ("quad: complex infinity not yet supported, use",
+			  " 'pinf' or 'ninf' respectively"));
+    }
+    if (isstr(b)) {
+	if (strncmp(b, "cinf", 1) == 0)
+	    return
+		newerror(strcat
+			 ("quad: complex infinity not yet supported, use",
+			  " 'pinf' or 'ninf' respectively"));
+    }
+
+    if (param(0) == 3) {
+	if (isstr(points))
+	    method = points;
+    }
+
+    if (strncmp(method, "tanhsinh", 1) == 0) {
+	if (!isstr(points)) {
+	    if (points == -1) {
+		return quadts(a, b);
+	    } else {
+		return quadts(a, b, points);
+	    }
+	} else {
+	    return quadts(a, b);
+	}
+    }
+
+    if (strncmp(method, "gausslegendre", 1) == 0) {
+	if (!isstr(points)) {
+	    if (points == -1) {
+		return quadgl(a, b);
+	    } else {
+		return quadgl(a, b, points);
+	    }
+	} else {
+	    return quadgl(a, b);
+	}
+    }
+}
+
+define makerange(start, end, steps)
+{
+    local ret k l step C length slope x1 x2 y1 y2;
+    local segment;
+    steps = int (steps);
+    if (steps < 1) {
+	return newerror("makerange: number of steps must be > 0");
+    }
+    if (!isnum(start) || !isnum(end)) {
+	return newerror("makerange: only numbers are supported yet");
+    }
+    if (isreal(start) && isreal(end)) {
+	step = (end - start) / (steps);
+	print step;
+	ret = mat[steps + 1];
+	for (k = 0; k <= steps; k++) {
+	    ret[k] = k * step + start;
+	}
+    } else {
+	ret = mat[steps + 1];
+	if (re(start) > re(end)) {
+	    swap(start, end);
+	}
+
+	slope = (im(end) - im(start)) / (re(end) - re(start));
+	C = im(start) - slope * re(start);
+	length = abs(re(start) - re(end));
+	segment = length / (steps);
+
+	for (k = re(start), l = 0; k <= (re(end)); k += segment, l++) {
+	    x1 = slope * (k) + C;
+	    ret[l] = k + x1 * 1i;
+	}
+
+    }
+    return ret;
+}
+
+define makecircle(radius, center, points)
+{
+    local ret k a b twopi centerx centery;
+    if (!isint(points) || points < 2) {
+	return
+	    newerror("makecircle: number of points is not a positive integer");
+    }
+    if (!isnum(center)) {
+	return newerror("makecircle: center does not lie on the complex plane");
+    }
+    if (!isreal(radius) || radius <= 0) {
+	return newerror("makecircle: radius is not a real > 0");
+    }
+    ret = mat[points];
+    twopi = 2 * pi();
+    centerx = re(center);
+    centery = im(center);
+    for (k = 0; k < points; k++) {
+	a = centerx + radius * cos(twopi * k / points);
+	b = centery + radius * sin(twopi * k / points);
+	ret[k] = a + b * 1i;
+    }
+    return ret;
+}
+
+define makeellipse(angle, a, b, center, points)
+{
+    local ret k x y twopi centerx centery;
+    if (!isint(points) || points < 2) {
+	return
+	    newerror("makeellipse: number of points is not a positive integer");
+    }
+    if (!isnum(center)) {
+	return
+	    newerror("makeellipse: center does not lie on the complex plane");
+    }
+    if (!isreal(a) || a <= 0) {
+	return newerror("makecircle: a is not a real > 0");
+    }
+    if (!isreal(b) || b <= 0) {
+	return newerror("makecircle: b is not a real > 0");
+    }
+    if (!isreal(angle)) {
+	return newerror("makecircle: angle is not a real");
+    }
+    ret = mat[points];
+    twopi = 2 * pi();
+    centerx = re(center);
+    centery = im(center);
+    for (k = 0; k < points; k++) {
+	x = centerx + a * cos(twopi * k / points) * cos(angle)
+	    - b * sin(twopi * k / points) * sin(angle);
+	y = centerx + a * cos(twopi * k / points) * sin(angle)
+	    + b * sin(twopi * k / points) * cos(angle);
+	ret[k] = x + y * 1i;
+    }
+    return ret;
+}
+
+define makepoints()
+{
+    local ret k;
+    ret = mat[param(0)];
+    for (k = 0; k < param(0); k++) {
+	if (!isnum(param(k + 1))) {
+	    return
+		newerror(strcat
+			 ("makepoints: parameter number \"", str(k + 1),
+			  "\" is not a number"));
+	}
+	ret[k] = param(k + 1);
+    }
+    return ret;
+}
+
+
+config("resource_debug", resource_debug_level),;
+if (config("resource_debug") & 3) {
+    print "quadtsdeletenodes()";
+    print "quadtscomputenodes(order, expo, eps)";
+    print "quadtscore(a,b,n)";
+    print "quadts(a,b,points)";
+    print "quadglcomputenodes(N)";
+    print "quadgldeletenodes()";
+    print "quadglcore(a,b,n)";
+    print "quadgl(a,b,points)";
+    print "quad(a,b,points=-1,method=\"tanhsinh\")";
+    print "makerange(start, end, steps)";
+    print "makecircle(radius, center, points)";
+    print "makeellipse(angle, a, b, center, points)";
+    print "makepoints(a1,[...])";
+}

cal/lambertw.cal

@@ -0,0 +1,284 @@
+/*
+ * lambertw - Lambert's W-function
+ *
+ * Copyright (C) 2013 Christoph Zurnieden
+ *
+ * Calc is open software; you can redistribute it and/or modify it under
+ * the terms of the version 2.1 of the GNU Lesser General Public License
+ * as published by the Free Software Foundation.
+ *
+ * Calc is distributed in the hope that it will be useful, but WITHOUT
+ * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+ * or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
+ * Public License for more details.
+ *
+ * A copy of version 2.1 of the GNU Lesser General Public License is
+ * distributed with calc under the filename COPYING-LGPL.  You should have
+ * received a copy with calc; if not, write to Free Software Foundation, Inc.
+ * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
+ *
+ * Under source code control:	2013/08/11 01:31:28
+ * File existed as early as:	2013
+ */
+
+
+static resource_debug_level;
+resource_debug_level = config("resource_debug", 0);
+
+
+/*
+
+     R. M. Corless and G. H. Gonnet and D. E. G. Hare and D. J. Jeffrey and
+     D. E. Knuth, "On the Lambert W Function", Advances n Computational
+     Mathematics, 329--359, (1996)
+     http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.112.6117
+
+     D. J. Jeffrey, D. E. G. Hare, R. M. Corless, "Unwinding the branches of the
+     Lambert W function", The Mathematical Scientist, 21, pp 1-7, (1996)
+     http://www.apmaths.uwo.ca/~djeffrey/Offprints/wbranch.pdf
+
+     Darko Verebic, "Having Fun with Lambert W(x) Function"
+     arXiv:1003.1628v1, March 2010, http://arxiv.org/abs/1003.1628
+
+     Winitzki, S. "Uniform Approximations for Transcendental Functions",
+     In Part 1 of Computational Science and its Applications - ICCSA 2003,
+     Lecture Notes in Computer Science, Vol. 2667, Springer-Verlag,
+     Berlin, 2003, 780-789. DOI 10.1007/3-540-44839-X_82
+     A copy may be found by Google.
+
+
+*/
+static true = 1;
+static false = 0;
+
+/* Branch 0, Winitzki (2003) , the well known Taylor series*/
+define __CZ__lambertw_0(z,eps){
+  local a=2.344e0, b=0.8842e0, c=0.9294e0, d=0.5106e0, e=-1.213e0;
+  local y=sqrt(2*exp(1)*z+2);
+  return (2*ln(1+b*y)-ln(1+c*ln(1+d*y))+e)/(1+1/(2*ln(1+b*y)+2*a));
+}
+/* branch -1 */
+define __CZ__lambertw_m1(z,eps){
+  local wn k;
+  /* Cut-off found in Maxima */
+  if(z < 0.3) return __CZ__lambertw_app(z,eps);
+  wn = z;
+  /*  Verebic (2010) eqs. 16-18*/
+  for(k=0;k<10;k++){
+    wn = ln(-z)-ln(-wn);
+  }
+  return wn;
+}
+
+/*
+  generic approximation
+
+  series for 1+W((z-2)/(2 e))
+
+  Corless et al (1996) (4.22)
+  Verebic (2010) eqs. 35-37; more coefficients given at the end of sect. 3.1
+  or online
+     http://www.wolframalpha.com/input/?
+       i=taylor+%28+1%2Bproductlog%28+%28z-2%29%2F%282*e%29+%29+%29
+  or by using the function lambertw_series_print() after running
+  lambertw_series(z,eps,branch,terms) at least once with the wanted number of
+  terms and z = 1 (which might throw an error because the series will not
+  converge in anybodies lifetime for something that far from the branchpoint).
+
+
+*/
+define __CZ__lambertw_app(z,eps){
+  local  b0=-1, b1=1, b2=-1/3, b3=11/72;
+  local  y=sqrt(2*exp(1)*z+2);
+  return b0 + ( y * (b1 + (y * (b2 + (b3 * y)))));
+}
+
+static __CZ__Ws_a;
+static __CZ__Ws_c;
+static __CZ__Ws_len=0;
+
+define lambertw_series_print(){
+  local k;
+  for(k=0;k<__CZ__Ws_len;k++){
+    print num(__CZ__Ws_c[k]):"/":den(__CZ__Ws_c[k]):"*p^":k;
+  }
+}
+
+/*
+   The series is fast but only if _very_ close to the branchpoint
+   The exact branch must be given explicitly, e.g.:
+
+; lambertw(-exp(-1)+.001)-lambertw_series(-exp(-1)+.001,epsilon()*1e-10,0)
+	-0.14758879113205794065490184399030194122136720202792-
+                  0.00000000000000000000000000000000000000000000000000i
+; lambertw(-exp(-1)+.001)-lambertw_series(-exp(-1)+.001,epsilon()*1e-10,1)
+	0.00000000000000000000000000000000000000000000000000-
+                  0.00000000000000000000000000000000000000000000000000i
+ */
+define lambertw_series(z,eps,branch,terms){
+  local k l limit tmp sum A C P PP epslocal;
+  if(!isnull(terms))
+    limit = terms;
+  else
+    limit = 100;
+
+  if(isnull(eps))
+    eps = epsilon(epsilon()*1e-10);
+  epslocal = epsilon(eps);
+
+  P = sqrt(2*(exp(1)*z+1));
+  if(branch != 0) P = -P;
+  tmp=0;sum=0;PP=P;
+
+    __CZ__Ws_a   = mat[limit+1];
+    __CZ__Ws_c   = mat[limit+1];
+    __CZ__Ws_len = limit;
+   /*
+      c0 = -1; c1 = 1
+      a0 =  2; a1 =-1
+    */
+    __CZ__Ws_c[0] = -1; __CZ__Ws_c[1] =  1;
+    __CZ__Ws_a[0] =  2; __CZ__Ws_a[1] = -1;
+    sum += __CZ__Ws_c[0];
+    sum += __CZ__Ws_c[1] * P;
+    PP *= P;
+    for(k=2;k<limit;k++){
+      for(l=2;l<k;l++){
+         __CZ__Ws_a[k] += __CZ__Ws_c[l]*__CZ__Ws_c[k+1-l];
+      }
+
+      __CZ__Ws_c[k] = (k-1) * (  __CZ__Ws_c[k-2]/2
+                            +__CZ__Ws_a[k-2]/4)/
+                      (k+1)-__CZ__Ws_a[k]/2-__CZ__Ws_c[k-1]/(k+1);
+      tmp = __CZ__Ws_c[k] * PP;
+      sum += tmp;
+      if(abs(tmp) <= eps){
+        epsilon(epslocal);
+        return sum;
+      }
+      PP *= P;
+    }
+    epsilon(epslocal);
+    return
+      newerror(strcat("lambertw_series: does not converge in ",
+                        str(limit)," terms" ));
+}
+
+/* */
+define lambertw(z,branch){
+  local eps epslarge ret branchpoint bparea w we ew w1e wn k places m1e;
+  local closeness;
+
+  eps = epsilon();
+  if(branch == 0){
+    if(!im(z)){
+      if(abs(z) <= eps) return 0;
+      if(abs(z-exp(1)) <= eps) return 1;
+      if(abs(z - (-ln(2)/2)) <= eps ) return -ln(2);
+      if(abs(z - (-pi()/2)) <= eps ) return 1i*pi()/2;
+    }
+  }
+
+  branchpoint = -exp(-1);
+  bparea = .2;
+  if(branch == 0){
+    if(!im(z) && abs(z-branchpoint) == 0) return -1;
+    ret = __CZ__lambertw_0(z,eps);
+   /* Yeah, C&P, I know, sorry */
+   ##ret = ln(z) + 2*pi()*1i*branch - ln(ln(z)+2*pi()*1i*branch);
+  }
+  else if(branch == 1){
+    if(im(z)<0 && abs(z-branchpoint) <= bparea)
+      ret = __CZ__lambertw_app(z,eps);
+   /* Does calc have a goto? Oh, it does!  */
+    ret =ln(z) + 2*pi()*1i*branch - ln(ln(z)+2*pi()*1i*branch);
+  }
+  else if(branch == -1){##print "-1";
+    if(!im(z) && abs(z-branchpoint) == 0) return -1;
+    if(!im(z) && z>branchpoint && z < 0){##print "0";
+      ret = __CZ__lambertw_m1(z,eps);}
+    if(im(z)>=0 && abs(z-branchpoint) <= bparea){##print "1";
+      ret = __CZ__lambertw_app(z,eps);}
+    ret =ln(z) + 2*pi()*1i*branch - ln(ln(z)+2*pi()*1i*branch);
+  }
+  else
+    ret = ln(z) + 2*pi()*1i*branch - ln(ln(z)+2*pi()*1i*branch);
+
+  /*
+     Such a high precision is only needed _very_ close to the branchpoint
+     and might even be insufficient if z has not been computed with
+     sufficient precision itself (M below was calculated by Mathematica and also
+     with the series above with epsilon(1e-200)):
+    ; epsilon(1e-50)
+	0.00000000000000000001
+    ; display(50)
+	20
+    ; M=-0.9999999999999999999999997668356018402875796636464119050387
+    ; lambertw(-exp(-1)+1e-50,0)-M
+	-0.00000000000000000000000002678416515423276355643684
+    ; epsilon(1e-60)
+	0.0000000000000000000000000000000000000000000000000
+    ; A=-exp(-1)+1e-50
+    ; epsilon(1e-50)
+	0.00000000000000000000000000000000000000000000000000
+    ; lambertw(A,0)-M
+	-0.00000000000000000000000000000000000231185460220585
+    ; lambertw_series(A,epsilon(),0)-M
+	-0.00000000000000000000000000000000000132145133161626
+    ; epsilon(1e-100)
+	0.00000000000000000000000000000000000000000000000001
+    ; A=-exp(-1)+1e-50
+    ; epsilon(1e-65)
+	0.00000000000000000000000000000000000000000000000000
+    ; lambertw_series(A,epsilon(),0)-M
+	0.00000000000000000000000000000000000000000000000000
+    ; lambertw_series(-exp(-1)+1e-50,epsilon(),0)-M
+	-0.00000000000000000000000000000000000000002959444084
+    ; epsilon(1e-74)
+	0.00000000000000000000000000000000000000000000000000
+    ; lambertw_series(-exp(-1)+1e-50,epsilon(),0)-M
+	-0.00000000000000000000000000000000000000000000000006
+   */
+  closeness = abs(z-branchpoint);
+  if( closeness< 1){
+    if(closeness != 0)
+      eps = epsilon(epsilon()*( closeness));
+    else
+      eps = epsilon(epsilon()^2);
+  }
+  else
+    eps = epsilon(epsilon()*1e-2);
+
+
+  epslarge =epsilon();
+
+  places = highbit(1 + int(1/epslarge)) + 1;
+  w = ret;
+  for(k=0;k<100;k++){
+    ew = exp(w);
+    we = w*ew;
+    if(abs(we-z)<= 4*epslarge*abs(z))break;
+    w1e = (1+w)*ew;
+    wn = bround(w- ((we - z) / ( w1e - ( (w+2)*(we-z) )/(2*w+2)  ) ),places++) ;
+    if( abs(wn - w) <= epslarge*abs(wn)) break;
+    else  w = wn;
+  }
+
+  if(k==100){
+    epsilon(eps);
+    return newerror("lambertw: Halley iteration does not converge");
+  }
+  /* The Maxima coders added a check if the iteration converged to the correct
+     branch. This coder deems it superfluous. */
+
+  epsilon(eps);
+  return wn;
+}
+
+
+config("resource_debug", resource_debug_level),;
+if (config("resource_debug") & 3) {
+    print "lambertw(z,branch)";
+    print "lambertw_series(z,eps,branch,terms)";
+    print "lambertw_series_print()";
+}

cal/linear.cal

@@ -17,10 +17,6 @@
  * received a copy with calc; if not, write to Free Software Foundation, Inc.
  * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
  *
- * @(#) $Revision: 30.2 $
- * @(#) $Id: linear.cal,v 30.2 2007/03/17 05:57:42 chongo Exp $
- * @(#) $Source: /usr/local/src/bin/calc/cal/RCS/linear.cal,v $
- *
  * Under source code control:	2005/12/12 06:41:50
  * File existed as early as:	2005
  *

cal/lnseries.cal

@@ -0,0 +1,108 @@
+/*
+ * lnseries - special functions (e.g.: gamma, zeta, psi)
+ *
+ * Copyright (C) 2013 Christoph Zurnieden
+ *
+ * Calc is open software; you can redistribute it and/or modify it under
+ * the terms of the version 2.1 of the GNU Lesser General Public License
+ * as published by the Free Software Foundation.
+ *
+ * Calc is distributed in the hope that it will be useful, but WITHOUT
+ * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+ * or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
+ * Public License for more details.
+ *
+ * A copy of version 2.1 of the GNU Lesser General Public License is
+ * distributed with calc under the filename COPYING-LGPL.  You should have
+ * received a copy with calc; if not, write to Free Software Foundation, Inc.
+ * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
+ *
+ * Under source code control:	2013/08/11 01:31:28
+ * File existed as early as:	2013
+ */
+
+
+/*
+ * hide internal function from resource debugging
+ */
+static resource_debug_level;
+resource_debug_level = config("resource_debug", 0);
+
+
+static __CZ__int_logs;
+static __CZ__int_logs_limit;
+static __CZ__int_logs_prec;
+
+
+define deletelnseries(){
+  free(__CZ__int_logs,__CZ__int_logs_limit,__CZ__int_logs_prec);
+}
+
+define lnfromseries(n){
+  if(    isnull(__CZ__int_logs)
+      || __CZ__int_logs_limit < n
+      || __CZ__int_logs_prec < log(1/epsilon())){
+
+    lnseries(n+1);
+  }
+  return __CZ__int_logs[n,0];
+}
+
+define lnseries(limit){
+  local k j eps ;
+  if(    isnull(__CZ__int_logs)
+      || __CZ__int_logs_limit < limit
+      || __CZ__int_logs_prec < log(1/epsilon())){
+    __CZ__int_logs = mat[limit+1,2];
+    __CZ__int_logs_limit = limit;
+    __CZ__int_logs_prec = log(1/epsilon());
+
+    /* probably still too much */
+    eps = epsilon(epsilon()*10^(-(5+log(limit))));
+    k =2;
+    while(1){
+      /* the prime itself, compute logarithm */
+      __CZ__int_logs[k,0] = ln(k);
+      __CZ__int_logs[k,1] = k;
+
+      for(j = 2*k;j<=limit;j+=k){
+       /* multiples of prime k, add logarithm of k computed earlier */
+       __CZ__int_logs[j,0] += __CZ__int_logs[k,0];
+       /* First hit, set counter to number */
+       if(__CZ__int_logs[j,1] ==0)
+         __CZ__int_logs[j,1]=j;
+       /* reduce counter by prime added */
+       __CZ__int_logs[j,1] //= __CZ__int_logs[k,1];
+      }
+
+      k++;
+      if(k>=limit) break;
+      /* Erastothenes-sieve: look for next prime. */
+      while(__CZ__int_logs[k,0]!=0){
+        k++;
+        if(k>=limit) break;
+      }
+    }
+    /* Second run to include the last factor */
+    for(k=1;k<=limit;k++){
+      if(__CZ__int_logs[k,1] != k){
+        __CZ__int_logs[k,0] +=__CZ__int_logs[ __CZ__int_logs[k,1],0];
+        __CZ__int_logs[k,1] = 0;
+      }
+    }
+
+    epsilon(eps);
+  }
+  return 1;
+}
+
+
+/*
+ * restore internal function from resource debugging
+ */
+config("resource_debug", resource_debug_level),;
+if (config("resource_debug") & 3) {
+    print "lnseries(limit)";
+    print "lnfromseries(n)";
+    print "deletelnseries()";
+}

cal/lucas_chk.cal

@@ -17,10 +17,6 @@
  * received a copy with calc; if not, write to Free Software Foundation, Inc.
  * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
  *
- * @(#) $Revision: 30.1 $
- * @(#) $Id: lucas_chk.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/bin/calc/cal/RCS/lucas_chk.cal,v $
- *
  * Under source code control:	1991/01/11 05:41:43
  * File existed as early as:	1991
  *

cal/lucas_tbl.cal

@@ -1,165 +0,0 @@
-/*
- * lucas_tbl - lucasian criteria for primality tables
- *
- * Copyright (C) 1999  Landon Curt Noll
- *
- * Calc is open software; you can redistribute it and/or modify it under
- * the terms of the version 2.1 of the GNU Lesser General Public License
- * as published by the Free Software Foundation.
- *
- * Calc is distributed in the hope that it will be useful, but WITHOUT
- * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
- * or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
- * Public License for more details.
- *
- * A copy of version 2.1 of the GNU Lesser General Public License is
- * distributed with calc under the filename COPYING-LGPL.  You should have
- * received a copy with calc; if not, write to Free Software Foundation, Inc.
- * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
- *
- * @(#) $Revision: 30.1 $
- * @(#) $Id: lucas_tbl.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/bin/calc/cal/RCS/lucas_tbl.cal,v $
- *
- * Under source code control:	1991/01/26 02:43:43
- * File existed as early as:	1991
- *
- * chongo <was here> /\oo/\	http://www.isthe.com/chongo/
- * Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
- */
-
-/*
- * Lucasian criteria for primality
- *
- * The following table is taken from:
- *
- *	"Lucasian Criteria for the Primality of N=h*2^n-1", by Hans Riesel,
- *	Mathematics of Computation, Vol 23 #108, p 872.
- *
- * The index of the *_val[] arrays correspond to the v(1) values found
- * in the table.  That is, for v(1) == x:
- *
- *	D == d_val[x]
- *	a == a_val[x]
- *	b == b_val[x]
- *	r == r_val[x]		(r == abs(a^2 - b^2*D))
- *
- *
- * Note that when *_val[i] is not a number, the related v(1) value
- * is not found in Table 1.
- */
-
-
-trymax = 100;
-mat d_val[trymax+1];
-mat a_val[trymax+1];
-mat b_val[trymax+1];
-mat r_val[trymax+1];
-/* v1= 0	    INVALID */
-/* v1= 1	    INVALID */
-/* v1= 2	    INVALID */
-d_val[ 3]=   5;	 a_val[ 3]= 1;	b_val[ 3]=1;  r_val[ 3]=4;
-d_val[ 4]=   3;	 a_val[ 4]= 1;	b_val[ 4]=1;  r_val[ 4]=2;
-d_val[ 5]=  21;	 a_val[ 5]= 3;	b_val[ 5]=1;  r_val[ 5]=12;
-d_val[ 6]=   2;	 a_val[ 6]= 1;	b_val[ 6]=1;  r_val[ 6]=1;
-/* v1= 7	    INVALID */
-d_val[ 8]=  15;	 a_val[ 8]= 3;	b_val[ 8]=1;  r_val[ 8]=6;
-d_val[ 9]=  77;	 a_val[ 9]= 7;	b_val[ 9]=1;  r_val[ 9]=28;
-d_val[10]=   6;	 a_val[10]= 2;	b_val[10]=1;  r_val[10]=2;
-d_val[11]=  13;	 a_val[11]= 3;	b_val[11]=1;  r_val[11]=4;
-d_val[12]=  35;	 a_val[12]= 5;	b_val[12]=1;  r_val[12]=10;
-d_val[13]= 165;	 a_val[13]=11;	b_val[13]=1;  r_val[13]=44;
-/* v1=14	    INVALID */
-d_val[15]= 221;	 a_val[15]=13;	b_val[15]=1;  r_val[15]=52;
-d_val[16]=   7;	 a_val[16]= 3;	b_val[16]=1;  r_val[16]=2;
-d_val[17]= 285;	 a_val[17]=15;	b_val[17]=1;  r_val[17]=60;
-/* v1=18	    INVALID */
-d_val[19]= 357;	 a_val[19]=17;	b_val[19]=1;  r_val[19]=68;
-d_val[20]=  11;	 a_val[20]= 3;	b_val[20]=1;  r_val[20]=2;
-d_val[21]= 437;	 a_val[21]=19;	b_val[21]=1;  r_val[21]=76;
-d_val[22]=  30;	 a_val[22]= 5;	b_val[22]=1;  r_val[22]=5;
-/* v1=23	    INVALID */
-d_val[24]= 143;	 a_val[24]=11;	b_val[24]=1;  r_val[24]=22;
-d_val[25]=  69;	 a_val[25]= 9;	b_val[25]=1;  r_val[25]=12;
-d_val[26]=  42;	 a_val[26]= 6;	b_val[26]=1;  r_val[26]=6;
-d_val[27]=  29;	 a_val[27]= 5;	b_val[27]=1;  r_val[27]=4;
-d_val[28]= 195;	 a_val[28]=13;	b_val[28]=1;  r_val[28]=26;
-d_val[29]=  93;	 a_val[29]= 9;	b_val[29]=1;  r_val[29]=12;
-d_val[30]=  14;	 a_val[30]= 4;	b_val[30]=1;  r_val[30]=2;
-d_val[31]= 957;	 a_val[31]=29;	b_val[31]=1;  r_val[31]=116;
-d_val[32]= 255;	 a_val[32]=15;	b_val[32]=1;  r_val[32]=30;
-d_val[33]=1085;	 a_val[33]=31;	b_val[33]=1;  r_val[33]=124;
-/* v1=34	    INVALID */
-d_val[35]=1221;	 a_val[35]=33;	b_val[35]=1;  r_val[35]=132;
-d_val[36]= 323;	 a_val[36]=17;	b_val[36]=1;  r_val[36]=34;
-d_val[37]=1365;	 a_val[37]=35;	b_val[37]=1;  r_val[37]=140;
-d_val[38]=  10;	 a_val[38]= 3;	b_val[38]=1;  r_val[38]=1;
-d_val[39]=1517;	 a_val[39]=37;	b_val[39]=1;  r_val[39]=148;
-d_val[40]= 399;	 a_val[40]=19;	b_val[40]=1;  r_val[40]=38;
-d_val[41]=1677;	 a_val[41]=39;	b_val[41]=1;  r_val[41]=156;
-d_val[42]= 110;	 a_val[42]=10;	b_val[42]=1;  r_val[42]=10;
-d_val[43]= 205;	 a_val[43]=15;	b_val[43]=1;  r_val[43]=20;
-d_val[44]= 483;	 a_val[44]=21;	b_val[44]=1;  r_val[44]=42;
-d_val[45]=2021;	 a_val[45]=43;	b_val[45]=1;  r_val[45]=172;
-d_val[46]=  33;	 a_val[46]= 6;	b_val[46]=1;  r_val[46]=3;
-/* v1=47	    INVALID */
-d_val[48]=  23;	 a_val[48]= 5;	b_val[48]=1;  r_val[48]=2;
-d_val[49]=2397;	 a_val[49]=47;	b_val[49]=1;  r_val[49]=188;
-d_val[50]=  39;	 a_val[50]= 6;	b_val[50]=1;  r_val[50]=3;
-d_val[51]=  53;	 a_val[51]= 7;	b_val[51]=1;  r_val[51]=4;
-/* v1=52	    INVALID */
-d_val[53]=2805;	 a_val[53]=51;	b_val[53]=1;  r_val[53]=204;
-d_val[54]= 182;	 a_val[54]=13;	b_val[54]=1;  r_val[54]=13;
-d_val[55]=3021;	 a_val[55]=53;	b_val[55]=1;  r_val[55]=212;
-d_val[56]=  87;	 a_val[56]= 9;	b_val[56]=1;  r_val[56]=6;
-d_val[57]=3245;	 a_val[57]=55;	b_val[57]=1;  r_val[57]=220;
-d_val[58]= 210;	 a_val[58]=14;	b_val[58]=1;  r_val[58]=14;
-d_val[59]=3477;	 a_val[59]=57;	b_val[59]=1;  r_val[59]=228;
-d_val[60]= 899;	 a_val[60]=29;	b_val[60]=1;  r_val[60]=58;
-d_val[61]= 413;	 a_val[61]=21;	b_val[61]=1;  r_val[61]=28;
-/* v1=62	    INVALID */
-d_val[63]=3965;	 a_val[63]=61;	b_val[63]=1;  r_val[63]=244;
-d_val[64]=1023;	 a_val[64]=31;	b_val[64]=1;  r_val[64]=62;
-d_val[65]= 469;	 a_val[65]=21;	b_val[65]=1;  r_val[65]=28;
-d_val[66]=  17;	 a_val[66]= 4;	b_val[66]=1;  r_val[66]=1;
-d_val[67]=4485;	 a_val[67]=65;	b_val[67]=1;  r_val[67]=260;
-d_val[68]=1155;	 a_val[68]=33;	b_val[68]=1;  r_val[68]=66;
-d_val[69]=4757;	 a_val[69]=67;	b_val[69]=1;  r_val[69]=268;
-d_val[70]=  34;	 a_val[70]= 6;	b_val[70]=1;  r_val[70]=2;
-d_val[71]=5037;	 a_val[71]=69;	b_val[71]=1;  r_val[71]=276;
-d_val[72]=1295;	 a_val[72]=35;	b_val[72]=1;  r_val[72]=70;
-d_val[73]= 213;	 a_val[73]=15;	b_val[73]=1;  r_val[73]=12;
-d_val[74]=  38;	 a_val[74]= 6;	b_val[74]=1;  r_val[74]=2;
-d_val[75]=5621;	 a_val[75]=73;	b_val[75]=1;  r_val[75]=292;
-d_val[76]=1443;	 a_val[76]=37;	b_val[76]=1;  r_val[76]=74;
-d_val[77]= 237;	 a_val[77]=15;	b_val[77]=1;  r_val[77]=12;
-d_val[78]=  95;	 a_val[78]=10;	b_val[78]=1;  r_val[78]=5;
-/* v1=79	    INVALID */
-d_val[80]=1599;	 a_val[80]=39;	b_val[80]=1;  r_val[80]=78;
-d_val[81]=6557;	 a_val[81]=79;	b_val[81]=1;  r_val[81]=316;
-d_val[82]= 105;	 a_val[82]=10;	b_val[82]=1;  r_val[82]=5;
-d_val[83]=  85;	 a_val[83]= 9;	b_val[83]=1;  r_val[83]=4;
-d_val[84]=1763;	 a_val[84]=41;	b_val[84]=1;  r_val[84]=82;
-d_val[85]=7221;	 a_val[85]=83;	b_val[85]=1;  r_val[85]=332;
-d_val[86]= 462;	 a_val[86]=21;	b_val[86]=1;  r_val[86]=21;
-d_val[87]=7565;	 a_val[87]=85;	b_val[87]=1;  r_val[87]=340;
-d_val[88]= 215;	 a_val[88]=15;	b_val[88]=1;  r_val[88]=10;
-d_val[89]=7917;	 a_val[89]=87;	b_val[89]=1;  r_val[89]=348;
-d_val[90]= 506;	 a_val[90]=22;	b_val[90]=1;  r_val[90]=22;
-d_val[91]=8277;	 a_val[91]=89;	b_val[91]=1;  r_val[91]=356;
-d_val[92]= 235;	 a_val[92]=15;	b_val[92]=1;  r_val[92]=10;
-d_val[93]=8645;	 a_val[93]=91;	b_val[93]=1;  r_val[93]=364;
-d_val[94]= 138;	 a_val[94]=12;	b_val[94]=1;  r_val[94]=6;
-d_val[95]=9021;	 a_val[95]=93;	b_val[95]=1;  r_val[95]=372;
-d_val[96]=  47;	 a_val[96]= 7;	b_val[96]=1;  r_val[96]=2;
-d_val[97]=1045;	 a_val[97]=33;	b_val[97]=1;  r_val[97]=44;
-/* v1=98	    INVALID */
-d_val[99]=9797;	 a_val[99]=97;	b_val[99]=1;  r_val[99]=388;
-d_val[100]=  51; a_val[100]= 7; b_val[100]=1; r_val[100]=2;
-
-if (config("resource_debug") & 3) {
-    print "d_val[100] defined";
-    print "a_val[100] defined";
-    print "b_val[100] defined";
-    print "r_val[100] defined";
-}

cal/mersenne.cal

@@ -19,10 +19,6 @@
  * received a copy with calc; if not, write to Free Software Foundation, Inc.
  * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
  *
- * @(#) $Revision: 30.1 $
- * @(#) $Id: mersenne.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/bin/calc/cal/RCS/mersenne.cal,v $
- *
  * Under source code control:	1991/05/22 21:56:36
  * File existed as early as:	1991
  *

cal/mfactor.cal

@@ -17,10 +17,6 @@
  * received a copy with calc; if not, write to Free Software Foundation, Inc.
  * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
  *
- * @(#) $Revision: 30.1 $
- * @(#) $Id: mfactor.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/bin/calc/cal/RCS/mfactor.cal,v $
- *
  * Under source code control:	1996/07/06 06:09:40
  * File existed as early as:	1996
  *

cal/mod.cal

@@ -17,10 +17,6 @@
  * received a copy with calc; if not, write to Free Software Foundation, Inc.
  * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
  *
- * @(#) $Revision: 30.1 $
- * @(#) $Id: mod.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/bin/calc/cal/RCS/mod.cal,v $
- *
  * Under source code control:	1990/02/15 01:50:34
  * File existed as early as:	before 1990
  *

cal/natnumset.cal

@@ -17,10 +17,6 @@
  * received a copy with calc; if not, write to Free Software Foundation, Inc.
  * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
  *
- * @(#) $Revision: 30.1 $
- * @(#) $Id: natnumset.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/bin/calc/cal/RCS/natnumset.cal,v $
- *
  * Under source code control:	1997/09/07 23:53:51
  * File existed as early as:	1997
  *

cal/pell.cal

@@ -17,10 +17,6 @@
  * received a copy with calc; if not, write to Free Software Foundation, Inc.
  * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
  *
- * @(#) $Revision: 30.1 $
- * @(#) $Id: pell.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/bin/calc/cal/RCS/pell.cal,v $
- *
  * Under source code control:	1990/02/15 01:50:34
  * File existed as early as:	before 1990
  *

cal/pi.cal

@@ -17,10 +17,6 @@
  * received a copy with calc; if not, write to Free Software Foundation, Inc.
  * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
  *
- * @(#) $Revision: 30.1 $
- * @(#) $Id: pi.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/bin/calc/cal/RCS/pi.cal,v $
- *
  * Under source code control:	1991/05/22 21:56:37
  * File existed as early as:	1991
  *

cal/pix.cal

@@ -17,10 +17,6 @@
  * received a copy with calc; if not, write to Free Software Foundation, Inc.
  * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
  *
- * @(#) $Revision: 30.1 $
- * @(#) $Id: pix.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/bin/calc/cal/RCS/pix.cal,v $
- *
  * Under source code control:	1996/07/09 03:14:14
  * File existed as early as:	1996
  *

cal/pollard.cal

@@ -17,10 +17,6 @@
  * received a copy with calc; if not, write to Free Software Foundation, Inc.
  * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
  *
- * @(#) $Revision: 30.1 $
- * @(#) $Id: pollard.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/bin/calc/cal/RCS/pollard.cal,v $
- *
  * Under source code control:	1991/05/22 21:56:37
  * File existed as early as:	1991
  *

cal/poly.cal

@@ -17,10 +17,6 @@
  * received a copy with calc; if not, write to Free Software Foundation, Inc.
  * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
  *
- * @(#) $Revision: 30.1 $
- * @(#) $Id: poly.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/bin/calc/cal/RCS/poly.cal,v $
- *
  * Under source code control:	1990/02/15 01:50:35
  * File existed as early as:	before 1990
  *

cal/prompt.cal

@@ -17,10 +17,6 @@
  * received a copy with calc; if not, write to Free Software Foundation, Inc.
  * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
  *
- * @(#) $Revision: 30.1 $
- * @(#) $Id: prompt.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/bin/calc/cal/RCS/prompt.cal,v $
- *
  * Under source code control:	1995/12/18 04:43:25
  * File existed as early as:	1995
  *

cal/psqrt.cal

@@ -17,10 +17,6 @@
  * received a copy with calc; if not, write to Free Software Foundation, Inc.
  * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
  *
- * @(#) $Revision: 30.1 $
- * @(#) $Id: psqrt.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/bin/calc/cal/RCS/psqrt.cal,v $
- *
  * Under source code control:	1990/02/15 01:50:35
  * File existed as early as:	before 1990
  *

cal/qtime.cal

@@ -20,10 +20,6 @@
  * received a copy with calc; if not, write to Free Software Foundation, Inc.
  * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
  *
- * @(#) $Revision: 30.1 $
- * @(#) $Id: qtime.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/bin/calc/cal/RCS/qtime.cal,v $
- *
  * Under source code control:	1999/10/13 04:10:33
  * File existed as early as:	1999
  *

cal/quat.cal

@@ -17,10 +17,6 @@
  * received a copy with calc; if not, write to Free Software Foundation, Inc.
  * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
  *
- * @(#) $Revision: 30.1 $
- * @(#) $Id: quat.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/bin/calc/cal/RCS/quat.cal,v $
- *
  * Under source code control:	1990/02/15 01:50:35
  * File existed as early as:	before 1990
  *
@@ -55,7 +51,8 @@ define quat(a,b,c,d)
 
 define quat_print(a)
 {
-	print "quat(" : a.s : ", " : a.v[0] : ", " : a.v[1] : ", " : a.v[2] : ")" :;
+	print "quat(" : a.s : ", " : a.v[0] : ", " :
+	      a.v[1] : ", " : a.v[2] : ")" :;
 }
 
 

cal/randbitrun.cal

@@ -17,10 +17,6 @@
  * received a copy with calc; if not, write to Free Software Foundation, Inc.
  * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
  *
- * @(#) $Revision: 30.1 $
- * @(#) $Id: randbitrun.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/bin/calc/cal/RCS/randbitrun.cal,v $
- *
  * Under source code control:	1995/02/13 03:43:11
  * File existed as early as:	1995
  *

cal/randmprime.cal

@@ -17,10 +17,6 @@
  * received a copy with calc; if not, write to Free Software Foundation, Inc.
  * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
  *
- * @(#) $Revision: 30.1 $
- * @(#) $Id: randmprime.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/bin/calc/cal/RCS/randmprime.cal,v $
- *
  * Under source code control:	1994/03/14 23:11:21
  * File existed as early as:	1994
  *

cal/randombitrun.cal

@@ -17,10 +17,6 @@
  * received a copy with calc; if not, write to Free Software Foundation, Inc.
  * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
  *
- * @(#) $Revision: 30.1 $
- * @(#) $Id: randombitrun.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/bin/calc/cal/RCS/randombitrun.cal,v $
- *
  * Under source code control:	1995/02/13 03:43:11
  * File existed as early as:	1995
  *

cal/randomrun.cal

@@ -17,10 +17,6 @@
  * received a copy with calc; if not, write to Free Software Foundation, Inc.
  * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
  *
- * @(#) $Revision: 30.1 $
- * @(#) $Id: randomrun.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/bin/calc/cal/RCS/randomrun.cal,v $
- *
  * Under source code control:	1997/02/19 03:35:59
  * File existed as early as:	1997
  *

cal/randrun.cal

@@ -17,10 +17,6 @@
  * received a copy with calc; if not, write to Free Software Foundation, Inc.
  * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
  *
- * @(#) $Revision: 30.1 $
- * @(#) $Id: randrun.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/bin/calc/cal/RCS/randrun.cal,v $
- *
  * Under source code control:	1995/02/12 20:00:06
  * File existed as early as:	1995
  *

cal/regress.cal

@@ -1,7 +1,7 @@
 /*
  * regress - calc regression and correctness test suite
  *
- * Copyright (C) 1999-2006  David I. Bell and Landon Curt Noll
+ * Copyright (C) 1999-2017  David I. Bell and Landon Curt Noll
  *
  * Calc is open software; you can redistribute it and/or modify it under
  * the terms of the version 2.1 of the GNU Lesser General Public License
@@ -17,10 +17,6 @@
  * received a copy with calc; if not, write to Free Software Foundation, Inc.
  * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
  *
- * @(#) $Revision: 30.6 $
- * @(#) $Id: regress.cal,v 30.6 2010/09/02 06:09:06 chongo Exp $
- * @(#) $Source: /usr/local/src/bin/calc/cal/RCS/regress.cal,v $
- *
  * Under source code control:	1990/02/15 01:50:36
  * File existed as early as:	before 1990
  *
@@ -403,14 +399,14 @@ define test_config()
 					'512: config("trace") == 0');
 	vrfy(config("maxprint") == 16,
 					'513: config("maxprint") == 16');
-	vrfy(config("mul2") == 1780,
+	vrfy(config("mul2") == 28,
-					'514: config("mul2") == 1780');
+					'514: config("mul2") == 28');
-	vrfy(config("sq2") == 3388,
+	vrfy(config("sq2") == 28,
-					'515: config("sq2") == 3388');
+					'515: config("sq2") == 28');
-	vrfy(config("pow2") == 176,
+	vrfy(config("pow2") == 20,
-					'516: config("pow2") == 176');
+					'516: config("pow2") == 20');
-	vrfy(config("redc2") == 220,
+	vrfy(config("redc2") == 25,
-					'517: config("redc2") == 220');
+					'517: config("redc2") == 25');
 	vrfy(config("tilde"),
 					'518: config("tilde")');
 	vrfy(config("tab"),
@@ -768,6 +764,8 @@ print '016: parsed test_bignums()';
 
 /*
  * Test many of the built-in functions.
+ *
+ * See test_functionss() starting at test 9000 for more built-in function tests.
  */
 define test_functions()
 {
@@ -1397,7 +1395,8 @@ define test_functions()
 	vrfy(quomod(10,-3,a,b,12) == 1, '1193: vrfy(quomod(10,-3,a,b,12) == 1');
 	vrfy(a == -3,			'1194: a == -3');
 	vrfy(b == 1,			'1195: b == 1');
-	vrfy(quomod(-10,-3,a,b,13) == 1,'1196: vrfy(quomod(-10,-3,a,b,13) == 1');
+	vrfy(quomod(-10,-3,a,b,13) == 1,
+	    '1196: vrfy(quomod(-10,-3,a,b,13) == 1');
 	vrfy(a == 4,			'1197: a == 4');
 	vrfy(b == 2,			'1198: b == 2');
 	vrfy(quomod(10,3,a,b,14) == 1,	'1199: vrfy(quomod(10,3,a,b,14) == 1');
@@ -1444,7 +1443,12 @@ define test_functions()
 	vrfy(jacobi(-1,-1) == 0,	'1236: jacobi(-1,-1) == 0');
 	vrfy(jacobi(0,-1) == 0,		'1237: jacobi(0,-1) == 0');
 
-	print '1238: Ending test_functions';
+	/*
+	 * NOTE: Function tests are continued in test_functionss()
+	 *	 starting at test 9000.
+	 */
+
+	print '1293: Ending test_functions';
 }
 print '017: parsed test_functions()';
 
@@ -1461,14 +1465,14 @@ define _test_underscore()
 	local _a = 27;
 	local __a = 23209;
 
-	print "1290: Beginning _test_underscore";
+	print "1294: Beginning _test_underscore";
 
-	vrfy(_a == 27,			    '1291: _a == 27');
+	vrfy(_a == 27,			    '1295: _a == 27');
-	vrfy(_ == 49,			    '1292: _ == 49');
+	vrfy(_ == 49,			    '1296: _ == 49');
-	vrfy(__ == 63,			    '1293: __ == 63');
+	vrfy(__ == 63,			    '1297: __ == 63');
-	vrfy(__a == 23209,		    '1294: __a == 23209');
+	vrfy(__a == 23209,		    '1298: __a == 23209');
 
-	print "1295: Ending _test_underscore";
+	print "1299: Ending _test_underscore";
 }
 print '020: parsed _test_underscore';
 
@@ -1509,8 +1513,10 @@ define test_assoc()
 	vrfy(isnull(search(a,16)),	'1312: isnull(search(a,16))');
 	a["curds","whey"] = "spider";
 	print				'1313: a["curds","whey"] = "spider"';
-	vrfy(a["curds","whey"] == "spider", '1314: a["curds","whey"] == "spider"');
+	vrfy(a["curds","whey"] == "spider",
-	vrfy(a[[rsearch(a,"spider")]] == "spider", '1315: a[[rsearch(a,"spider")]] == "spider"');
+		'1314: a["curds","whey"] == "spider"');
+	vrfy(a[[rsearch(a,"spider")]] == "spider",
+		'1315: a[[rsearch(a,"spider")]] == "spider"');
 	b = a;
 	print				'1316: b = a';
 	vrfy(b[17] == 19,		'1317: b[17] == 19');
@@ -4892,7 +4898,8 @@ define test_newsyn()
 		vrfy(s5500 == 55,		  '5510: s5500 == 45');
 		vrfy(i == 11,		  '5511: i == 11');
 	}
-	print "5512: { local i; for (s5500 = 0, i = 0; i < 10; i++) s5500 += i; ... }";
+	print "5512: { local i; for (s5500 = 0, i = 0; i < 10; i++) ":
+	      "s5500 += i; ... }";
 	vrfy(s5500 == 55,			  '5513: s5500 == 55');
 	vrfy(i == 11,			  '5514: i == 11');
 
@@ -5027,7 +5034,7 @@ vrfy(i == 9,		'151: i == 9');
 
 
 /*
- * test_commaeq - test changes to , and =
+ * test_commaeq - test changes to = and ,
  */
 obj xx5600 {} xx5600;
 print '152: obj xx5600 {} xx5600';
@@ -6506,7 +6513,8 @@ define test_blk()
 	/* A second named block */
 
 	B1 = blk("+++6700", 15, 10) = {1,2,3,4,5};
-	print				  '6746: B1 = blk("+++6700", 15 , 10) = {1,2,3,4,5};';
+	print
+	    '6746: B1 = blk("+++6700", 15 , 10) = {1,2,3,4,5};';
 	vrfy(size(B1) == 15,		  '6747: size(B1) == 15');
 	vrfy(sizeof(B1) == 20,		  '6748: sizeof(B1) == 20');
 	vrfy(test(B1) == 1,		  '6749: test(B1) == 1');
@@ -6871,7 +6879,8 @@ define test_sha1()
 
 
 	z = sha1(list(1,2,3), "curds and whey", 2^21701-1, pi(1e-100));
-	print '7210: z = sha1(list(1,2,3), "curds and whey", 2^21701-1, pi(1e-100));';
+	print '7210: z = sha1(list(1,2,3), "curds and whey",',
+	      '2^21701-1, pi(1e-100));';
 	vrfy(sha1(z) == 0x158cc87deeb9dd478ca14e3ab359205b0fb15b83,
 		'7211: sha1(z) == 0x158cc87deeb9dd478ca14e3ab359205b0fb15b83');
 
@@ -7914,6 +7923,137 @@ return test_exponentiation();
 /* 88xx: test exponentiation */
 
 
+/*
+ * calc resource functions by Christoph Zurnieden
+ */
+print;
+print '8900: Starting test of calc resource functions by Christoph Zurnieden';
+print '8901: read -once "test8900"';
+read -once "test8900";
+print '8902: about to run test8900(1,,8903)';
+testnum = test8900(1,,8903);
+print '8999: ecnt = 203;'
+ecnt = 203;
+/* 89xx: test calc resource functions by Christoph Zurnieden */
+
+
+/*
+ * Test more of the built-in functions.
+ *
+ * See test_functions() (test 700 - 1238) for other built-in function tests.
+ */
+define test_functions2()
+{
+	print '9001: Beginning test_functions2';
+
+	/* ctype function tests */
+	vrfy(isalnum("A") == 1,		'9002: isalnum("A") == 1');
+	vrfy(isalnum("a") == 1,		'9003: isalnum("a") == 1');
+	vrfy(isalnum("2") == 1,		'9004: isalnum("2") == 1');
+	vrfy(isalnum("\t") == 0,	'9005: isalnum("\\t") == 0');
+
+	vrfy(isalpha("A") == 1,		'9006: isalpha("A") == 1');
+	vrfy(isalpha("a") == 1,		'9007: isalpha("a") == 1');
+	vrfy(isalpha("2") == 0,		'9008: isalpha("2") == 0');
+	vrfy(isalpha("\t") == 0,	'9009: isalpha("\\t") == 0');
+
+	vrfy(iscntrl("A") == 0,		'9010: iscntrl("A") == 0');
+	vrfy(iscntrl("a") == 0,		'9011: iscntrl("a") == 0');
+	vrfy(iscntrl("2") == 0,		'9012: iscntrl("2") == 0');
+	vrfy(iscntrl("\t") == 1,	'9013: iscntrl("\\t") == 1');
+
+	vrfy(isdigit("A") == 0,		'9014: isdigit("A") == 0');
+	vrfy(isdigit("a") == 0,		'9015: isdigit("a") == 0');
+	vrfy(isdigit("2") == 1,		'9016: isdigit("2") == 1');
+	vrfy(isdigit("\t") == 0,	'9017: isdigit("\\t") == 0');
+
+	vrfy(isgraph("A") == 1,		'9018: isgraph("A") == 1');
+	vrfy(isgraph("a") == 1,		'9019: isgraph("a") == 1');
+	vrfy(isgraph("2") == 1,		'9020: isgraph("2") == 1');
+	vrfy(isgraph("\t") == 0,	'9021: isgraph("\\t") == 0');
+
+	vrfy(islower("A") == 0,		'9022: islower("A") == 0');
+	vrfy(islower("a") == 1,		'9023: islower("a") == 1');
+	vrfy(islower("1") == 0,		'9024: islower("1") == 0');
+
+	vrfy(isprint("A") == 1,		'9025: isprint("A") == 1');
+	vrfy(isprint("a") == 1,		'9026: isprint("a") == 1');
+	vrfy(isprint(" ") == 1,		'9027: isprint(" ") == 1');
+	vrfy(isprint("\t") == 0,	'9028: isprint("\\t") == 0');
+
+	vrfy(ispunct("A") == 0,		'9029: ispunct("A") == 0');
+	vrfy(ispunct("a") == 0,		'9030: ispunct("a") == 0');
+	vrfy(ispunct(" ") == 0,		'9031: ispunct(" ") == 0');
+	vrfy(ispunct("?") == 1,		'9032: ispunct("?") == 1');
+
+	vrfy(isspace("A") == 0,		'9033: isspace("A") == 0');
+	vrfy(isspace("Krik") == 0,	'9034: isspace("Krik") == 0');
+	vrfy(isspace(" ") == 1,		'9035: isspace(" ") == 1');
+	vrfy(isspace("?") == 0,		'9036: isspace("?") == 0');
+
+	vrfy(isupper("A") == 1,		'9037: isupper("A") == 1');
+	vrfy(isupper("a") == 0,		'9038: isupper("a") == 0');
+	vrfy(isupper("1") == 0,		'9039: isupper("1") == 0');
+
+	vrfy(isxdigit("A") == 1,	'9040: isxdigit("A") == 1');
+	vrfy(isxdigit("f") == 1,	'9041: isxdigit("f") == 1');
+	vrfy(isxdigit("2") == 1,	'9042: isxdigit("2") == 1');
+	vrfy(isxdigit("x") == 0,	'9043: isxdigit("x") == 0');
+
+	vrfy(strcasecmp("ab", "aBc") == -1,
+			     '9044: strcasecmp("ab", "aBc") == -1');
+	vrfy(strcasecmp("abc", "aBb") == 1,
+			     '9045: strcasecmp("abc", "aBb") == 1');
+	vrfy(strcasecmp("abc", "abc") == 0,
+			     '9046: strcasecmp("abc", "abc") == 0');
+	vrfy(strcasecmp("abc", "aBc") == 0,
+			     '9047: strcasecmp("abc", "aBc") == 0');
+	vrfy(strcasecmp("abc", "aBd") == -1,
+			     '9048: strcasecmp("abc", "aBd") == -1');
+	vrfy(strcasecmp("abc\0", "aBc") == 1,
+			     '9049: strcasecmp("a8c\\0", "aBc") == 1');
+	vrfy(strcasecmp("a\0b", "A\0c") == -1,
+			     '9050: strcasecmp("a\\0b", "A\\0c") == -1');
+
+	vrfy(strncasecmp("abc", "xyz", 0) == 0,
+			     '9051: strncasecmp("abc", "xyz", 0) == 0');
+	vrfy(strncasecmp("abc", "xyz", 1) == -1,
+			     '9052: strncasecmp("abc", "xyz", 1) == -1');
+	vrfy(strncasecmp("abc", "", 1) == 1,
+			     '9053: strncasecmp("abc", "", 1) == 1');
+	vrfy(strncasecmp("a", "b", 2) == -1,
+			     '9054: strncasecmp("a", "b", 2) == -1');
+	vrfy(strncasecmp("ab", "Ac", 2) == -1,
+			     '9055: strncasecmp("ab", "Ac", 2) == -1');
+	vrfy(strncasecmp("\0ac", "\0b", 2) == -1,
+			     '9056: strncasecmp("\\0ac", "\\0b", 2) == -1');
+	vrfy(strncasecmp("ab", "aBc", 2) == 0,
+			     '9057: strncasecmp("ab", "aBc", 2) == 0');
+	vrfy(strncasecmp("abc", "abd", 2) == 0,
+			     '9058: strncasecmp("abc", "abd", 2) == 0');
+
+	local s1 = " gnu lesser general public license";
+	print '9059: local s1 = " gnu lesser general public license";';
+
+	vrfy(strcmp(strtolower(" GNU Lesser General Public License"), s1) == 0,
+	    '9060: strcmp(strtolower(" GNU Lesser General Public License"),' +
+	    ' s1) == 0');
+
+	local s2 = " GNU LESSER GENERAL PUBLIC LICENSE";
+	print '9061: local s2 = " GNU LESSER GENERAL PUBLIC LICENSE";';
+
+	vrfy(strcmp(strtoupper(" GNU Lesser General Public License"), s2) == 0,
+	    '9062: strcmp(strtoupper(" GNU Lesser General Public License"),' +
+	    ' s2) == 0');
+
+	print '9063: Ending test_functions2';
+}
+print;
+print '9000: parsed test_functions2()';
+print;
+return test_functions2();
+
+
 /*
  * read various calc resource files
  *
@@ -7924,7 +8064,6 @@ return test_exponentiation();
  *	hello.cal	- designed to go into an infinite loop
  *	lucal.cal	- already read by this file
  *	lucas_chk.cal	- already read by this file
- *	lucas_tbl.cal	- duplicatres code already read by another file
  *	regress.cal	- this file
  *	surd.cal	- already read by this file
  *	test9999.cal	- files of this form are already read by this file
@@ -7997,8 +8136,6 @@ read -once intfile;
 print	'9830: read -once intfile';
 read -once lucas;
 print	'9831: read -once lucas';
-read -once lucas_tbl;
-print	'9832: read -once lucas_tbl';
 read -once natnumset;
 print	'9833: read -once natnumset';
 read -once repeat;

cal/repeat.cal

@@ -17,10 +17,6 @@
  * received a copy with calc; if not, write to Free Software Foundation, Inc.
  * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
  *
- * @(#) $Revision: 30.1 $
- * @(#) $Id: repeat.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/bin/calc/cal/RCS/repeat.cal,v $
- *
  * Under source code control:	2003/01/05 00:00:01
  * File existed as early as:	2003
  *

cal/screen.cal

@@ -15,10 +15,6 @@
  * NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR  IN
  * CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
  *
- * @(#) $Revision: 30.2 $
- * @(#) $Id: screen.cal,v 30.2 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/bin/calc/cal/RCS/screen.cal,v $
- *
  * This file is not covered under version 2.1 of the GNU LGPL.
  *
  * Under source code control:	2006/03/08 05:54:09

cal/seedrandom.cal

@@ -17,10 +17,6 @@
  * received a copy with calc; if not, write to Free Software Foundation, Inc.
  * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
  *
- * @(#) $Revision: 30.1 $
- * @(#) $Id: seedrandom.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/bin/calc/cal/RCS/seedrandom.cal,v $
- *
  * Under source code control:	1996/01/01 08:21:00
  * File existed as early as:	1996
  *

cal/set8700.cal

@@ -17,10 +17,6 @@
  * received a copy with calc; if not, write to Free Software Foundation, Inc.
  * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
  *
- * @(#) $Revision: 30.1 $
- * @(#) $Id: set8700.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/bin/calc/cal/RCS/set8700.cal,v $
- *
  * Under source code control:	2006/05/20 14:10:11
  * File existed as early as:	2006
  *

cal/set8700.line

@@ -17,10 +17,6 @@
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## @(#) $Revision: 30.1 $
-## @(#) $Id: set8700.line,v 30.1 2007/03/16 11:09:54 chongo Exp $
-## @(#) $Source: /usr/local/src/bin/calc/cal/RCS/set8700.line,v $
-##
 ## Under source code control:	2006/05/20 14:10:11
 ## File existed as early as:	2006
 ##

cal/smallfactors.cal

@@ -0,0 +1,71 @@
+/*
+ * smallfactors - find the factors of a number < 2^32
+ *
+ * Copyright (C) 2013 Christoph Zurnieden
+ *
+ * Calc is open software; you can redistribute it and/or modify it under
+ * the terms of the version 2.1 of the GNU Lesser General Public License
+ * as published by the Free Software Foundation.
+ *
+ * Calc is distributed in the hope that it will be useful, but WITHOUT
+ * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+ * or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
+ * Public License for more details.
+ *
+ * A copy of version 2.1 of the GNU Lesser General Public License is
+ * distributed with calc under the filename COPYING-LGPL.  You should have
+ * received a copy with calc; if not, write to Free Software Foundation, Inc.
+ * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
+ */
+
+
+static resource_debug_level;
+resource_debug_level = config("resource_debug", 0);
+
+
+define smallfactors(x0)
+{
+    local d q x flist tuple w;
+
+    if (x >= (2 ^ 32) - 1)
+	return newerror("smallfactors: number must be < 2^32 -1");
+
+    tuple = mat[2];
+    flist = list();
+    x = x0;
+    d = 2;
+    q = 0;
+    tuple[0] = d;
+    if (x < 2)
+	return 0;
+    do {
+	q = x // d;
+	    while (x == (q * d)) {
+	    tuple[0] = d;
+	    tuple[1]++;
+	    x = floor(q);
+	    q = x // d;
+	}
+	d = nextprime(d);
+	if (tuple[1] > 0)
+	    append(flist, tuple);
+	tuple = mat[2];
+    } while (d <= x);
+    return flist;
+}
+
+define printsmallfactors(flist)
+{
+    local k;
+    for (k = 0; k < size(flist); k++) {
+	print flist[k][0]:"^":flist[k][1];
+    }
+}
+
+
+config("resource_debug", resource_debug_level),;
+if (config("resource_debug") & 3) {
+    print "smallfactors(x0)";
+    print "printsmallfactors(flist)";
+
+}

cal/solve.cal

@@ -17,10 +17,6 @@
  * received a copy with calc; if not, write to Free Software Foundation, Inc.
  * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
  *
- * @(#) $Revision: 30.2 $
- * @(#) $Id: solve.cal,v 30.2 2008/05/10 13:30:00 chongo Exp $
- * @(#) $Source: /usr/local/src/bin/calc/cal/RCS/solve.cal,v $
- *
  * Under source code control:	1990/02/15 01:50:37
  * File existed as early as:	before 1990
  *
@@ -52,7 +48,8 @@ define solve(low, high, epsilon)
 	if (sgn(flow) == sgn(fhigh))
 		quit "Non-opposite signs";
 	while (1) {
-		mid = bround(high - fhigh * (high - low) / (fhigh - flow), places);
+		mid = bround(high - fhigh * (high - low) / (fhigh - flow),
+			     places);
 		if ((mid == low) || (mid == high))
 			places++;
 		fmid = f(mid);

cal/statistics.cal

@@ -0,0 +1,498 @@
+/*
+ * statistics - Some assorted statistics functions.
+ *
+ * Copyright (C) 2013 Christoph Zurnieden
+ *
+ * Calc is open software; you can redistribute it and/or modify it under
+ * the terms of the version 2.1 of the GNU Lesser General Public License
+ * as published by the Free Software Foundation.
+ *
+ * Calc is distributed in the hope that it will be useful, but WITHOUT
+ * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+ * or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
+ * Public License for more details.
+ *
+ * A copy of version 2.1 of the GNU Lesser General Public License is
+ * distributed with calc under the filename COPYING-LGPL.  You should have
+ * received a copy with calc; if not, write to Free Software Foundation, Inc.
+ * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
+ *
+ * Under source code control:	2013/08/11 01:31:28
+ * File existed as early as:	2013
+ */
+
+
+static resource_debug_level;
+resource_debug_level = config("resource_debug", 0);
+
+
+/*
+ *  get dependencies
+ */
+read -once factorial2 brentsolve
+
+
+/*******************************************************************************
+ *
+ *
+ *                Continuous distributions
+ *
+ *
+ ******************************************************************************/
+
+/* regularized incomplete gamma function like in Octave, hence the name */
+define gammaincoctave(z,a){
+  local tmp;
+  tmp = gamma(z);
+  return (tmp-gammainc(a,z))/tmp;
+}
+
+/* Inverse incomplete beta function. Old and slow. */
+static __CZ__invbeta_a;
+static __CZ__invbeta_b;
+static __CZ__invbeta_x;
+define __CZ__invbeta(x){
+   return __CZ__invbeta_x-__CZ__ibetaas63(x,__CZ__invbeta_a,__CZ__invbeta_b);
+}
+
+define invbetainc_slow(x,a,b){
+  local flag ret eps;
+  /* place checks and balances here */
+  eps = epsilon();
+  if(.5 < x){
+    __CZ__invbeta_x = 1 - x;
+    __CZ__invbeta_a = b;
+    __CZ__invbeta_b = a;
+    flag = 1;
+  }
+  else{
+    __CZ__invbeta_x = x;
+    __CZ__invbeta_a = a;
+    __CZ__invbeta_b = b;
+    flag = 0;
+  }
+
+  ret =  brentsolve2(0,1,1);
+
+  if(flag == 1)
+    ret = 1-ret;
+  epsilon(eps);
+  return ret;
+}
+
+/* Inverse incomplete beta function. Still old but not as slow as the function
+   above. */
+/*
+  Purpose:
+
+    invbetainc computes inverse of the incomplete Beta function.
+
+  Licensing:
+
+    This code is distributed under the GNU LGPL license.
+
+  Modified:
+
+    10 August 2013
+
+  Author:
+
+    Original FORTRAN77 version by GW Cran, KJ Martin, GE Thomas.
+    C version by John Burkardt.
+    Calc version by Christoph Zurnieden
+
+  Reference:
+
+    GW Cran, KJ Martin, GE Thomas,
+    Remark AS R19 and Algorithm AS 109:
+    A Remark on Algorithms AS 63: The Incomplete Beta Integral
+    and AS 64: Inverse of the Incomplete Beta Integeral,
+    Applied Statistics,
+    Volume 26, Number 1, 1977, pages 111-114.
+
+  Parameters:
+
+    Input,  P, Q, the parameters of the incomplete
+    Beta function.
+
+    Input,  BETA, the logarithm of the value of
+    the complete Beta function.
+
+    Input,  ALPHA, the value of the incomplete Beta
+    function.  0 <= ALPHA <= 1.
+
+    Output,  the argument of the incomplete
+    Beta function which produces the value ALPHA.
+
+  Local Parameters:
+
+    Local, SAE, the most negative decimal exponent
+    which does not cause an underflow.
+*/
+define invbetainc(x,a,b){
+  return __CZ__invbetainc(a,b,lnbeta(a,b),x);
+}
+
+define __CZ__invbetainc(p,q,beta,alpha){
+  local a acu adj fpu g h iex indx pp prev qq r s sae sq t tx value;
+  local w xin y yprev places eps;
+
+  /* Dirty trick, don't try at home */
+  eps= epsilon(epsilon()^2);
+  sae = -((log(1/epsilon())/log(2))//2);
+  fpu = 10.0^sae;
+
+  places = highbit(1 + int(1/epsilon())) + 1;
+  value = alpha;
+  if( p <= 0.0 ){
+    epsilon(eps);
+    return newerror("invbeta: argument p <= 0");
+  }
+  if( q <= 0.0 ){
+    epsilon(eps);
+    return newerror("invbeta: argument q <= 0");
+  }
+
+  if( alpha < 0.0 || 1.0 < alpha ){
+    epsilon(eps);
+    return newerror("invbeta: argument alpha out of domain");
+  }
+  if( alpha == 0.0 ){
+    epsilon(eps);
+    return 0;
+  }
+  if( alpha == 1.0 ){
+    epsilon(eps);
+    return 1;
+  }
+  if ( 0.5 < alpha ){
+    a = 1.0 - alpha;
+    pp = q;
+    qq = p;
+    indx = 1;
+  }
+  else{
+    a = alpha;
+    pp = p;
+    qq = q;
+    indx = 0;
+  }
+  r = sqrt ( - ln ( a * a ) );
+
+  y = r-(2.30753+0.27061*r)/(1.0+(0.99229+0.04481*r)*r);
+
+  if ( 1.0 < pp && 1.0 < qq ){
+    r = ( y * y - 3.0 ) / 6.0;
+    s = 1.0 / ( pp + pp - 1.0 );
+    t = 1.0 / ( qq + qq - 1.0 );
+    h = 2.0 / ( s + t );
+    w = y*sqrt(h+r)/h-(t-s)*(r+5.0/6.0-2.0/(3.0*h));
+    value = pp / ( pp + qq * exp ( w + w ) );
+  }
+  else{
+    r = qq + qq;
+    t = 1.0 / ( 9.0 * qq );
+    t = r *  ( 1.0 - t + y * sqrt ( t )^ 3 );
+
+    if ( t <= 0.0 ){
+      value = 1.0 - exp ( ( ln ( ( 1.0 - a ) * qq ) + beta ) / qq );
+    }
+    else{
+      t = ( 4.0 * pp + r - 2.0 ) / t;
+
+      if ( t <= 1.0 ) {
+        value = exp ( ( ln ( a * pp ) + beta ) / pp );
+      }
+      else{
+        value = 1.0 - 2.0 / ( t + 1.0 );
+      }
+    }
+  }
+  r = 1.0 - pp;
+  t = 1.0 - qq;
+  yprev = 0.0;
+  sq = 1.0;
+  prev = 1.0;
+
+  if ( value < 0.0001 )
+    value = 0.0001;
+
+  if ( 0.9999 < value )
+    value = 0.9999;
+
+  acu = 10^sae;
+
+  for ( ; ; ){
+    y = bround(__CZ__ibetaas63( value, pp, qq, beta),places);
+    xin = value;
+    y = bround(exp(ln(y-a)+(beta+r*ln(xin)+t*ln(1.0- xin ) )),places);
+
+    if ( y * yprev <= 0.0 ) {
+      prev = max ( sq, fpu );
+    }
+
+    g = 1.0;
+
+    for ( ; ; ){
+      for ( ; ; ){
+        adj = g * y;
+        sq = adj * adj;
+        if ( sq < prev ){
+          tx = value - adj;
+          if ( 0.0 <= tx && tx <= 1.0 )  break;
+        }
+        g = g / 3.0;
+      }
+      if ( prev <= acu ){
+        if ( indx )
+          value = 1.0 - value;
+        epsilon(eps);
+        return value;
+      }
+      if ( y * y <= acu ){
+        if ( indx )
+          value = 1.0 - value;
+        epsilon(eps);
+        return value;
+      }
+      if ( tx != 0.0 && tx != 1.0 )
+        break;
+      g = g / 3.0;
+    }
+    if ( tx == value )  break;
+    value = tx;
+    yprev = y;
+  }
+  if ( indx )
+    value = 1.0 - value;
+
+  epsilon(eps);
+  return value;
+}
+
+/*******************************************************************************
+ *
+ *
+ *                Beta distribution
+ *
+ *
+ ******************************************************************************/
+
+define betapdf(x,a,b){
+  if(x<0 || x>1) return newerror("betapdf: parameter x out of domain");
+  if(a<=0) return newerror("betapdf: parameter a out of domain");
+  if(b<=0) return newerror("betapdf: parameter b out of domain");
+
+  return 1/beta(a,b) *x^(a-1)*(1-x)^(b-1);
+}
+
+define betacdf(x,a,b){
+  if(x<0 || x>1) return newerror("betacdf: parameter x out of domain");
+  if(a<=0) return newerror("betacdf: parameter a out of domain");
+  if(b<=0) return newerror("betacdf: parameter b out of domain");
+
+  return betainc(x,a,b);
+}
+
+define betacdfinv(x,a,b){
+  return invbetainc(x,a,b);
+}
+
+define betamedian(a,b){
+  local t106 t104 t103 t105 approx ret;
+  if(a == b) return 1/2;
+  if(a == 1 && b > 0) return 1-(1/2)^(1/b);
+  if(a > 0 && b == 1) return   (1/2)^(1/a);
+  if(a == 3 && b == 2){
+    /* Yes, the author is not ashamed to ask Maxima for the exact solution
+       of a quartic equation. */
+    t103 = ( (2^(3/2))/27 +4/27  )^(1/3);
+    t104 = sqrt( ( 9*t103^2 + 4*t103 + 2  )/(t103)  )/3;
+    t105 = -t103-2/(9*t103) +8/9;
+    t106 = sqrt( (27*t104*t105+16)/(t104)  )/(2*3^(3/2));
+    return -t106+t104/2+1/3;
+  }
+  if(a == 2 && b == 3){
+    t103 = ( (2^(3/2))/27 +4/27  )^(1/3);
+    t104 = sqrt( ( 9*t103^2 + 4*t103 + 2  )/(t103)  )/3;
+    t105 = -t103-2/(9*t103) +8/9;
+    t106 = sqrt( (27*t104*t105+16)/(t104)  )/(2*3^(3/2));
+    return 1-(-t106+t104/2+1/3);
+  }
+  return invbetainc(1/2,a,b);
+}
+
+define betamode(a,b){
+  if(a + b == 2) return newerror("betamod: a + b = 2 = division by zero");
+  return (a-1)/(a+b-2);
+}
+
+define betavariance(a,b){
+  return (a*b)/( (a+b)^2*(a+b+1) );
+}
+
+define betalnvariance(a,b){
+  return polygamma(1,a)-polygamma(a+b);
+}
+
+define betaskewness(a,b){
+  return (2*(b-a)*sqrt(a+b+1))/( (a+b+1)*sqrt(a*b) );
+}
+
+define betakurtosis(a,b){
+  local num denom;
+
+  num = 6*( (a-b)^2*(a+b+1)-a*b*(a+b+2));
+  denom = a*b*(a+b+2)*(a+b+3);
+  return num/denom;
+}
+
+define betaentropy(a,b){
+  return lnbeta(a,b)-(a-1)*psi(a)-(b-1)*psi(b)+(a+b+1)*psi(a+b);
+
+}
+
+/*******************************************************************************
+ *
+ *
+ *                Normal (Gaussian) distribution
+ *
+ *
+ ******************************************************************************/
+
+
+define normalpdf(x,mu,sigma){
+  return 1/(sqrt(2*pi()*sigma^2))*exp( ( (x-mu)^2 )/( 2*sigma^2 ) );
+}
+
+define normalcdf(x,mu,sigma){
+  return 1/2*(1+erf( ( x-mu )/( sqrt(2*sigma^2) )  )  );
+}
+
+define probit(p){
+  if(p<0 || p > 1) return newerror("probit: p out of domain 0<=p<=1");
+  return sqrt(2)*ervinv(2*p-1);
+}
+
+define normalcdfinv(p,mu,sigma){
+  if(p<0 || p > 1) return newerror("normalcdfinv: p out of domain 0<=p<=1");
+  return mu+ sigma*probit(p);
+}
+
+define normalmean(mu,sigma){return mu;}
+
+define normalmedian(mu,sigma){return mu;}
+
+define normalmode(mu,sigma){return mu;}
+
+define normalvariance(mu,sigma){return sigma^2;}
+
+define normalskewness(mu,sigma){return 0;}
+
+define normalkurtosis(mu,sigma){return 0;}
+
+define normalentropy(mu,sigma){
+  return 1/3*ln( 2*pi()*exp(1)*sigma^2 );
+}
+
+/* moment generating f. */
+define normalmgf(mu,sigma,t){
+  return exp(mu*t+1/2*sigma^2*t^2);
+}
+
+/* characteristic f. */
+define normalcf(mu,sigma,t){
+  return exp(mu*t-1/2*sigma^2*t^2);
+}
+
+
+/*******************************************************************************
+ *
+ *
+ *                Chi-squared distribution
+ *
+ *
+ ******************************************************************************/
+
+define chisquaredpdf(x,k){
+  if(!isint(k) || k<0) return newerror("chisquaredpdf: k not in N");
+  if(im(x) || x<0) return newerror("chisquaredpdf: x not in +R");
+  /* The gamma function does not check for half integers, do it here? */
+  return 1/(2^(k/2)*gamma(k/2))*x^((k/2)-1)*exp(-x/2);
+}
+
+define chisquaredpcdf(x,k){
+  if(!isint(k) || k<0) return newerror("chisquaredcdf: k not in N");
+  if(im(x) || x<0) return newerror("chisquaredcdf: x not in +R");
+
+  return 1/(gamma(k/2))*gammainc(k/2,x/2);
+}
+
+define chisquaredmean(x,k){return k;}
+
+define chisquaredmedian(x,k){
+  /* TODO: implement a FAST inverse incomplete gamma-{q,p} function */
+  return k*(1-2/(9*k))^3;
+}
+
+define chisquaredmode(x,k){return max(k-2,0);}
+define chisquaredvariance(x,k){return 2*k;}
+define chisquaredskewness(x,k){return sqrt(8/k);}
+define chisquaredkurtosis(x,k){return 12/k;}
+define chisquaredentropy(x,k){
+  return k/2+ln(2*gamma(k/2)) + (1-k/2)*psi(k/2);
+}
+
+define chisquaredmfg(k,t){
+  if(t>=1/2)return newerror("chisquaredmfg: t >= 1/2");
+  return (1-2*t)^(k/2);
+}
+
+define chisquaredcf(k,t){
+  return (1-2*1i*t)^(k/2);
+}
+
+
+/*
+ * restore internal function from resource debugging
+ */
+config("resource_debug", resource_debug_level),;
+if (config("resource_debug") & 3) {
+    print "gammaincoctave(z,a)";
+    print "invbetainc(x,a,b)";
+    print "betapdf(x,a,b)";
+    print "betacdf(x,a,b)";
+    print "betacdfinv(x,a,b)";
+    print "betamedian(a,b)";
+    print "betamode(a,b)";
+    print "betavariance(a,b)";
+    print "betalnvariance(a,b)";
+    print "betaskewness(a,b)";
+    print "betakurtosis(a,b)";
+    print "betaentropy(a,b)";
+    print "normalpdf(x,mu,sigma)";
+    print "normalcdf(x,mu,sigma)";
+    print "probit(p)";
+    print "normalcdfinv(p,mu,sigma)";
+    print "normalmean(mu,sigma)";
+    print "normalmedian(mu,sigma)";
+    print "normalmode(mu,sigma)";
+    print "normalvariance(mu,sigma)";
+    print "normalskewness(mu,sigma)";
+    print "normalkurtosis(mu,sigma)";
+    print "normalentropy(mu,sigma)";
+    print "normalmgf(mu,sigma,t)";
+    print "normalcf(mu,sigma,t)";
+    print "chisquaredpdf(x,k)";
+    print "chisquaredpcdf(x,k)";
+    print "chisquaredmean(x,k)";
+    print "chisquaredmedian(x,k)";
+    print "chisquaredmode(x,k)";
+    print "chisquaredvariance(x,k)";
+    print "chisquaredskewness(x,k)";
+    print "chisquaredkurtosis(x,k)";
+    print "chisquaredentropy(x,k)";
+    print "chisquaredmfg(k,t)";
+    print "chisquaredcf(k,t)";
+}
+

cal/strings.cal

@@ -0,0 +1,41 @@
+/*
+ * strings - implementation of some of the macros in ctype.h
+ *
+ * Copyright (C) 2013 Christoph Zurnieden
+ *
+ * Calc is open software; you can redistribute it and/or modify it under
+ * the terms of the version 2.1 of the GNU Lesser General Public License
+ * as published by the Free Software Foundation.
+ *
+ * Calc is distributed in the hope that it will be useful, but WITHOUT
+ * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+ * or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
+ * Public License for more details.
+ *
+ * A copy of version 2.1 of the GNU Lesser General Public License is
+ * distributed with calc under the filename COPYING-LGPL.  You should have
+ * received a copy with calc; if not, write to Free Software Foundation, Inc.
+ * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
+ */
+
+
+static resource_debug_level;
+resource_debug_level = config("resource_debug", 0);
+
+define isascii(c){
+  c = ord(c);
+  return (c >= 0 && c< 128);
+}
+
+define isblank(c){
+  c = ord(c);
+  return ( c == 32 || c == 9 );
+}
+
+
+config("resource_debug", resource_debug_level),;
+if (config("resource_debug") & 3) {
+    print "isascii(c)";
+    print "isblank(c)";
+}
+

cal/sumsq.cal

@@ -17,10 +17,6 @@
  * received a copy with calc; if not, write to Free Software Foundation, Inc.
  * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
  *
- * @(#) $Revision: 30.1 $
- * @(#) $Id: sumsq.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/bin/calc/cal/RCS/sumsq.cal,v $
- *
  * Under source code control:	1990/02/15 01:50:37
  * File existed as early as:	before 1990
  *

cal/sumtimes.cal

@@ -17,10 +17,6 @@
  * received a copy with calc; if not, write to Free Software Foundation, Inc.
  * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
  *
- * @(#) $Revision: 30.1 $
- * @(#) $Id: sumtimes.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/bin/calc/cal/RCS/sumtimes.cal,v $
- *
  * Under source code control:	2006/06/22 17:29
  * File existed as early as:	2006
  *

cal/surd.cal

@@ -17,10 +17,6 @@
  * received a copy with calc; if not, write to Free Software Foundation, Inc.
  * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
  *
- * @(#) $Revision: 30.1 $
- * @(#) $Id: surd.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/bin/calc/cal/RCS/surd.cal,v $
- *
  * Under source code control:	1990/02/15 01:50:38
  * File existed as early as:	before 1990
  *

cal/test1700.cal

@@ -17,10 +17,6 @@
  * received a copy with calc; if not, write to Free Software Foundation, Inc.
  * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
  *
- * @(#) $Revision: 30.1 $
- * @(#) $Id: test1700.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/bin/calc/cal/RCS/test1700.cal,v $
- *
  * Under source code control:	1994/03/14 23:12:51
  * File existed as early as:	1994
  *

cal/test2300.cal

@@ -17,10 +17,6 @@
  * received a copy with calc; if not, write to Free Software Foundation, Inc.
  * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
  *
- * @(#) $Revision: 30.1 $
- * @(#) $Id: test2300.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/bin/calc/cal/RCS/test2300.cal,v $
- *
  * Under source code control:	1995/07/09 06:12:13
  * File existed as early as:	1995
  *

cal/test2600.cal

@@ -19,10 +19,6 @@
  * received a copy with calc; if not, write to Free Software Foundation, Inc.
  * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
  *
- * @(#) $Revision: 30.2 $
- * @(#) $Id: test2600.cal,v 30.2 2007/07/11 22:57:23 chongo Exp $
- * @(#) $Source: /usr/local/src/bin/calc/cal/RCS/test2600.cal,v $
- *
  * Under source code control:	1995/10/13 00:13:14
  * File existed as early as:	1995
  *
@@ -91,7 +87,8 @@ define testismult(str, n, verbose)
 		if (!ismult(c,a)) {
 			m++;
 			if (verbose > 1) {
-				printf("*** Failure with:\na = %d\nb = %d\n", a,b);
+				printf("*** Failure with:\na = %d\nb = %d\n",
+				       a,b);
 			}
 		}
 	}
@@ -133,7 +130,8 @@ define testsqrt(str, n, eps, verbose)
 		if (abs(c) > 1) {
 			m++;
 			if (verbose > 1) {
-				printf("*** Failure with:\na = %d\neps = %d\n", a,eps);
+				printf("*** Failure with:\na = %d\neps = %d\n",
+				       a,eps);
 			}
 		}
 	}
@@ -178,7 +176,8 @@ define testexp(str, n, eps, verbose)
 		if (abs(c) > 0.02) {
 			m++;
 			if (verbose > 1) {
-				printf("*** Failure with:\na = %d\neps = %d\n", a,eps);
+				printf("*** Failure with:\na = %d\neps = %d\n",
+				       a,eps);
 			}
 		}
 	}
@@ -235,7 +234,8 @@ define testln(str, n, eps, verbose)
 		if (abs(c) > 0.5) {
 			m++;
 			if (verbose > 1) {
-				printf("*** Failure with:\na = %d\neps = %d\n", a,eps);
+				printf("*** Failure with:\na = %d\neps = %d\n",
+				       a,eps);
 			}
 		}
 	}

cal/test2700.cal

@@ -19,10 +19,6 @@
  * received a copy with calc; if not, write to Free Software Foundation, Inc.
  * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
  *
- * @(#) $Revision: 30.1 $
- * @(#) $Id: test2700.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/bin/calc/cal/RCS/test2700.cal,v $
- *
  * Under source code control:	1995/11/01 22:52:25
  * File existed as early as:	1995
  *
@@ -127,7 +123,8 @@ define testcsqrt(str, n, verbose)
 			if (p) {
 			if (verbose > 0)
 				printf(
-				 "*** Type %d failure for x = %r, y = %r, z = %d\n",
+				 "*** Type %d failure for x = %r, "
+				 "y = %r, z = %d\n",
 				    p, x, y, z);
 				m++;
 			}

cal/test3100.cal

@@ -19,10 +19,6 @@
  * received a copy with calc; if not, write to Free Software Foundation, Inc.
  * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
  *
- * @(#) $Revision: 30.1 $
- * @(#) $Id: test3100.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/bin/calc/cal/RCS/test3100.cal,v $
- *
  * Under source code control:	1995/11/28 11:56:57
  * File existed as early as:	1995
  *

cal/test3300.cal

@@ -19,10 +19,6 @@
  * received a copy with calc; if not, write to Free Software Foundation, Inc.
  * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
  *
- * @(#) $Revision: 30.1 $
- * @(#) $Id: test3300.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/bin/calc/cal/RCS/test3300.cal,v $
- *
  * Under source code control:	1995/12/02 04:27:41
  * File existed as early as:	1995
  *

cal/test3400.cal

@@ -19,10 +19,6 @@
  * received a copy with calc; if not, write to Free Software Foundation, Inc.
  * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
  *
- * @(#) $Revision: 30.1 $
- * @(#) $Id: test3400.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/bin/calc/cal/RCS/test3400.cal,v $
- *
  * Under source code control:	1995/12/02 05:20:11
  * File existed as early as:	1995
  *

cal/test3500.cal

@@ -19,10 +19,6 @@
  * received a copy with calc; if not, write to Free Software Foundation, Inc.
  * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
  *
- * @(#) $Revision: 30.1 $
- * @(#) $Id: test3500.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/bin/calc/cal/RCS/test3500.cal,v $
- *
  * Under source code control:	1995/12/18 22:50:46
  * File existed as early as:	1995
  *

cal/test4000.cal

@@ -19,10 +19,6 @@
  * received a copy with calc; if not, write to Free Software Foundation, Inc.
  * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
  *
- * @(#) $Revision: 30.1 $
- * @(#) $Id: test4000.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/bin/calc/cal/RCS/test4000.cal,v $
- *
  * Under source code control:	1996/03/13 02:38:45
  * File existed as early as:	1996
  *
@@ -199,7 +195,8 @@ define ctimes(str, N, n, count, skip, verbose)
 		p = ptest(A[i], count, skip);
 		if (p) {
 			if (verbose > 0) {
-				printf("*** Error, what should be rare has occurred for x = %d \n", A[i]);
+				printf("*** Error, what should be rare "
+				       "has occurred for x = %d \n", A[i]);
 				m++;
 			}
 		}
@@ -306,7 +303,8 @@ define ntimes(str, N, n, count, skip, residue, modulus, verbose)
 	}
 	tprev = round(usertime() - t, 4);
 	if (verbose > 0) {
-		printf("%d evaluations, nextcand: %d, prevcand: %d\n", n, tnext, tprev);
+		printf("%d evaluations, nextcand: %d, "
+		       "prevcand: %d\n", n, tnext, tprev);
 	}
 }
 

cal/test4100.cal

@@ -19,10 +19,6 @@
  * received a copy with calc; if not, write to Free Software Foundation, Inc.
  * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
  *
- * @(#) $Revision: 30.1 $
- * @(#) $Id: test4100.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/bin/calc/cal/RCS/test4100.cal,v $
- *
  * Under source code control:	1996/03/13 03:53:22
  * File existed as early as:	1996
  *

cal/test4600.cal

@@ -19,10 +19,6 @@
  * received a copy with calc; if not, write to Free Software Foundation, Inc.
  * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
  *
- * @(#) $Revision: 30.1 $
- * @(#) $Id: test4600.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/bin/calc/cal/RCS/test4600.cal,v $
- *
  * Under source code control:	1996/07/02 20:04:40
  * File existed as early as:	1996
  *

cal/test5100.cal

@@ -19,10 +19,6 @@
  * received a copy with calc; if not, write to Free Software Foundation, Inc.
  * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
  *
- * @(#) $Revision: 30.1 $
- * @(#) $Id: test5100.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/bin/calc/cal/RCS/test5100.cal,v $
- *
  * Under source code control:	1996/12/02 23:57:10
  * File existed as early as:	1996
  *

cal/test5200.cal

@@ -19,10 +19,6 @@
  * received a copy with calc; if not, write to Free Software Foundation, Inc.
  * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
  *
- * @(#) $Revision: 30.1 $
- * @(#) $Id: test5200.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/bin/calc/cal/RCS/test5200.cal,v $
- *
  * Under source code control:	1997/02/07 02:48:10
  * File existed as early as:	1997
  *

cal/test8400.cal

@@ -17,10 +17,6 @@
  * received a copy with calc; if not, write to Free Software Foundation, Inc.
  * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
  *
- * @(#) $Revision: 30.1 $
- * @(#) $Id: test8400.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/bin/calc/cal/RCS/test8400.cal,v $
- *
  * Under source code control:	1999/10/31 01:00:03
  * File existed as early as:	1999
  *

cal/test8500.cal

@@ -19,10 +19,6 @@
  * received a copy with calc; if not, write to Free Software Foundation, Inc.
  * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
  *
- * @(#) $Revision: 30.1 $
- * @(#) $Id: test8500.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/bin/calc/cal/RCS/test8500.cal,v $
- *
  * Under source code control:	1999/11/12 20:59:59
  * File existed as early as:	1999
  *
@@ -134,8 +130,8 @@ define onetest_8500(a,b,rnd) {
  * The rounding parameter is randomly chosen.
  *
  * After a run of divmod_8500 the a, b, rnd values which gave failure are
- * stored in the list L_8500.  L_8500[0], L_8500[1], L_8500[2] are a, b, rnd for the first
+ * stored in the list L_8500.  L_8500[0], L_8500[1], L_8500[2] are a, b,
- * test, etc.
+ * rnd for the first* test, etc.
  */
 define divmod_8500(N = 10, M1 = 2^128, M2 = 2^64, testnum = 0)
 {

cal/test8600.cal

@@ -19,10 +19,6 @@
  * received a copy with calc; if not, write to Free Software Foundation, Inc.
  * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
  *
- * @(#) $Revision: 30.1 $
- * @(#) $Id: test8600.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/bin/calc/cal/RCS/test8600.cal,v $
- *
  * Under source code control:	2000/12/04 19:57:02
  * File existed as early as:	2000
  *