Release calc version 2.12.4.14

BUGS

@@ -68,6 +68,9 @@ 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.
@@ -84,7 +87,7 @@ Problems that have known work-a-rounds:
 
 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 +132,7 @@ mis-features in calc:
 
       will not.
 
-## Copyright (C) 1999-2007  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
@@ -145,9 +148,9 @@ 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/cmd/calc/RCS/BUGS,v $
+## @(#) $Revision: 30.3 $
+## @(#) $Id: BUGS,v 30.3 2014/09/07 06:20:41 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

@@ -1,4 +1,250 @@
-The following are the changes from calc version 2.12.4.0 to date:
+The following are the changes from calc version 2.12.4.14 to date:
+
+    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 somtimes
+	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 improer
+	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 to calc.spec and rpm.mk file.
+    See calc.spec.in for details.  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 chmodded as 0644 to allow for building rpms
+    without root.
+
+    Silenced annoying warning about unused variable 'intp'
+    while compiline 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 implementwed with the Brent-Dekker trick
+    factorial.cal - product of the positive integers
+    factorial2.cal - variety of integer functions quasi-related to factoral
+    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 vareity of stastical 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
+    contans 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
+    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.
+
+    If is OK for the calc-symlink make rule to pre-remove a symlink.
+
+    Fixed bug was uncovered in calc that caused script failures when calc
+    is called within a while loop in BASH if the while loop is fed from
+    stdin due to calc's redirection/inheritance of stdin and no option
+    to change this behavior.  Thanks gores to David C. Rankin
+    <drankinatty at gmail dot com> for the bug fix and to David Haller
+    <dnh at opensuse dot org> for helping debug this problem.
+
+
+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.
 
@@ -58,6 +304,9 @@ The following are the changes from calc version 2.12.4.0 to date:
     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
+    and CALC_LITTLE_ENDIAN instead of BIG_ENDIAN and LITTLE_ENDIAN.
+
 
 The following are the changes from calc version 2.12.3.0 to 2.12.3.3:
 
@@ -1130,8 +1379,7 @@ 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
-    dot edu> for pointing this out.
+    Thanks goes to Michael Somos for pointing this out.
 
     Linux and gcc now compiled with -Wall -W -Wno-comment.
 
@@ -2086,7 +2334,7 @@ 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
@@ -2124,7 +2372,7 @@ 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
@@ -2318,7 +2566,7 @@ 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
@@ -4781,7 +5029,7 @@ 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
@@ -4879,7 +5127,7 @@ 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
@@ -5376,7 +5624,7 @@ 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.
 
@@ -5601,7 +5849,7 @@ 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.
 
@@ -6144,7 +6392,7 @@ 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:
 
@@ -6795,9 +7043,9 @@ 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: 30.20 $
-## @(#) $Id: CHANGES,v 30.20 2010/09/02 06:36:48 chongo Exp $
-## @(#) $Source: /usr/local/src/cmd/calc/RCS/CHANGES,v $
+## @(#) $Revision: 30.44 $
+## @(#) $Id: CHANGES,v 30.44 2014/09/22 03:40:07 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

@@ -12,11 +12,11 @@ This file is Copyrighted
 	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/cmd/calc/RCS/COPYING,v $
+    # @(#) $Revision: 30.4 $
+    # @(#) $Id: COPYING,v 30.4 2013/09/01 20:14:30 chongo Exp $
+    # @(#) $Source: /usr/local/src/bin/calc/RCS/COPYING,v $
 
-=-=
+-=-
 
 Calc is covered by the GNU Lesser General Public License
 --------------------------------------------------------
@@ -78,7 +78,7 @@ Calc is covered by the GNU Lesser General Public License
 
     Feel free to follow the name line with additional EMail text as desired.
 
-=-=
+-=-
 
     Calc bug reports and calc bug fixes should be sent to:
 
@@ -93,7 +93,7 @@ Calc is covered by the GNU Lesser General Public License
 
     You may have additional words in your subject line.
 
-=-=
+-=-
 
 Calc's relationship to the GNU Lesser General Public License
 ------------------------------------------------------------
@@ -149,7 +149,7 @@ 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 +165,7 @@ 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 +189,7 @@ 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 +203,7 @@ 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

@@ -1,8 +1,8 @@
-		  GNU LESSER GENERAL PUBLIC LICENSE
-		       Version 2.1, February 1999
+                  GNU LESSER GENERAL PUBLIC LICENSE
+                       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.
 
@@ -10,7 +10,7 @@
  as the successor of the GNU Library Public License, version 2, hence
  the version number 2.1.]
 
-			    Preamble
+                            Preamble
 
   The licenses for most software are designed to take away your
 freedom to share and change it.  By contrast, the GNU General Public
@@ -112,7 +112,7 @@ modification follow.  Pay close attention to the difference between a
 former contains code derived from the library, whereas the latter must
 be combined with the library in order to run.
 
-		  GNU LESSER GENERAL PUBLIC LICENSE
+                  GNU LESSER GENERAL PUBLIC LICENSE
    TERMS AND CONDITIONS FOR COPYING, DISTRIBUTION AND MODIFICATION
 
   0. This License Agreement applies to any software library or other
@@ -146,7 +146,7 @@ such a program is covered only if its contents constitute a work based
 on the Library (independent of the use of the Library in a tool for
 writing it).  Whether that is true depends on what the Library does
 and what the program that uses the Library does.
-  
+
   1. You may copy and distribute verbatim copies of the Library's
 complete source code as you receive it, in any medium, provided that
 you conspicuously and appropriately publish on each copy an
@@ -432,7 +432,7 @@ decision will be guided by the two goals of preserving the free status
 of all derivatives of our free software and of promoting the sharing
 and reuse of software generally.
 
-			    NO WARRANTY
+                            NO WARRANTY
 
   15. BECAUSE THE LIBRARY IS LICENSED FREE OF CHARGE, THERE IS NO
 WARRANTY FOR THE LIBRARY, TO THE EXTENT PERMITTED BY APPLICABLE LAW.
@@ -455,7 +455,7 @@ FAILURE OF THE LIBRARY TO OPERATE WITH ANY OTHER SOFTWARE), EVEN IF
 SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH
 DAMAGES.
 
-		     END OF TERMS AND CONDITIONS
+                     END OF TERMS AND CONDITIONS
 
            How to Apply These Terms to Your New Libraries
 
@@ -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

@@ -206,7 +206,7 @@ the calc help subsystem.  See the README file for details.
 ##
 ## @(#) $Revision: 30.6 $
 ## @(#) $Id: HOWTO.INSTALL,v 30.6 2007/10/16 12:22:22 chongo Exp $
-## @(#) $Source: /usr/local/src/cmd/calc/RCS/HOWTO.INSTALL,v $
+## @(#) $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

@@ -640,7 +640,7 @@ need call libcalc_call_me_last() only once.
 ##
 ## @(#) $Revision: 30.1 $
 ## @(#) $Id: LIBRARY,v 30.1 2007/03/16 11:09:46 chongo Exp $
-## @(#) $Source: /usr/local/src/cmd/calc/RCS/LIBRARY,v $
+## @(#) $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

@@ -136,7 +136,7 @@ The calc web site is located at:
 ##
 ## @(#) $Revision: 30.1 $
 ## @(#) $Id: README,v 30.1 2007/03/16 11:09:46 chongo Exp $
-## @(#) $Source: /usr/local/src/cmd/calc/RCS/README,v $
+## @(#) $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

@@ -144,7 +144,7 @@ the above Makefile list, follow the recommendation in the Makefile.
 ##
 ## @(#) $Revision: 30.2 $
 ## @(#) $Id: README.WINDOWS,v 30.2 2009/03/14 02:29:31 chongo Exp $
-## @(#) $Source: /usr/local/src/cmd/calc/RCS/README.WINDOWS,v $
+## @(#) $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

addop.c

@@ -21,7 +21,7 @@
  *
  * @(#) $Revision: 30.1 $
  * @(#) $Id: addop.c,v 30.1 2007/03/16 11:09:46 chongo Exp $
- * @(#) $Source: /usr/local/src/cmd/calc/RCS/addop.c,v $
+ * @(#) $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

@@ -19,7 +19,7 @@
  *
  * @(#) $Revision: 30.1 $
  * @(#) $Id: align32.c,v 30.1 2007/03/16 11:09:46 chongo Exp $
- * @(#) $Source: /usr/local/src/cmd/calc/RCS/align32.c,v $
+ * @(#) $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
@@ -17,9 +17,9 @@
  * 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/cmd/calc/RCS/alloc.h,v $
+ * @(#) $Revision: 30.5 $
+ * @(#) $Id: alloc.h,v 30.5 2014/08/24 21:56:51 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 +28,8 @@
  */
 
 
-#if !defined(__ALLOC_H__)
-#define __ALLOC_H__
+#if !defined(INCLUDE_ALLOC_H)
+#define INCLUDE_ALLOC_H
 
 
 #if defined(CALC_SRC)	/* if we are building from the calc source tree */
@@ -53,7 +53,8 @@
 # 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 +83,8 @@ 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 +92,4 @@ 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

@@ -17,9 +17,9 @@
  * 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/cmd/calc/RCS/assocfunc.c,v $
+ * @(#) $Revision: 30.2 $
+ * @(#) $Id: assocfunc.c,v 30.2 2013/08/11 08:41:38 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
@@ -332,7 +332,8 @@ 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 +341,8 @@ 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

@@ -19,9 +19,9 @@
  * 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/cmd/calc/RCS/blkcpy.c,v $
+ * @(#) $Revision: 30.2 $
+ * @(#) $Id: blkcpy.c,v 30.2 2013/08/11 08:41:38 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 +374,8 @@ 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 +721,8 @@ 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 +764,8 @@ 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 +985,8 @@ 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 +1037,8 @@ 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
  *
@@ -19,9 +19,9 @@
  * 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/cmd/calc/RCS/blkcpy.h,v $
+ * @(#) $Revision: 30.3 $
+ * @(#) $Id: blkcpy.h,v 30.3 2014/08/24 21:56:51 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 +30,8 @@
  */
 
 
-#if !defined(__BLKCPY_H__)
-#define __BLKCPY_H__
+#if !defined(INCLUDE_BLKCPY_H)
+#define INCLUDE_BLKCPY_H
 
 /*
  * the main copy gateway function
@@ -59,4 +59,4 @@ 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

@@ -21,7 +21,7 @@
  *
  * @(#) $Revision: 30.1 $
  * @(#) $Id: block.c,v 30.1 2007/03/16 11:09:46 chongo Exp $
- * @(#) $Source: /usr/local/src/cmd/calc/RCS/block.c,v $
+ * @(#) $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
  *
@@ -19,9 +19,9 @@
  * 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/cmd/calc/RCS/block.h,v $
+ * @(#) $Revision: 30.3 $
+ * @(#) $Id: block.h,v 30.3 2014/08/24 21:56:51 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 +31,8 @@
  */
 
 
-#if !defined(__BLOCK_H__)
-#define __BLOCK_H__
+#if !defined(INCLUDE_BLOCK_H)
+#define INCLUDE_BLOCK_H
 
 
 /*
@@ -222,4 +222,4 @@ E_FUNC int countnblocks(void);
 E_FUNC void shownblocks(void);
 
 
-#endif /* !__BLOCK_H__ */
+#endif /* !INCLUDE_BLOCK_H */

byteswap.c

@@ -17,9 +17,9 @@
  * 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/cmd/calc/RCS/byteswap.c,v $
+ * @(#) $Revision: 30.2 $
+ * @(#) $Id: byteswap.c,v 30.2 2013/08/11 08:41:38 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 +102,8 @@ 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
@@ -17,9 +17,9 @@
  * 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/cmd/calc/RCS/byteswap.h,v $
+ * @(#) $Revision: 30.3 $
+ * @(#) $Id: byteswap.h,v 30.3 2014/08/24 21:56:51 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 +29,8 @@
  */
 
 
-#if !defined(__BYTESWAP_H__)
-#define __BYTESWAP_H__
+#if !defined(INCLUDE_BYTESWAP_H)
+#define INCLUDE_BYTESWAP_H
 
 
 #if defined(CALC_SRC)	/* if we are building from the calc source tree */
@@ -178,4 +178,4 @@
 #endif /* LONG_BITS == 64 */
 
 
-#endif /* !__BYTESWAP_H__ */
+#endif /* !INCLUDE_BYTESWAP_H */

cal/Makefile

@@ -18,9 +18,9 @@
 # received a copy with calc; if not, write to Free Software Foundation, Inc.
 # 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 #
-# @(#) $Revision: 30.4 $
-# @(#) $Id: Makefile,v 30.4 2010/09/02 06:01:39 chongo Exp $
-# @(#) $Source: /usr/local/src/cmd/calc/cal/RCS/Makefile,v $
+# @(#) $Revision: 30.11 $
+# @(#) $Id: Makefile,v 30.11 2014/09/02 07:14:49 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 +179,37 @@ 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 \
-	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 \
-	sumsq.cal surd.cal unitfrac.cal varargs.cal chrem.cal mfactor.cal \
-	bindings randmprime.cal test1700.cal randrun.cal linear.cal \
-	randbitrun.cal bernoulli.cal test2300.cal test2600.cal \
-	test2700.cal test3100.cal test3300.cal test3400.cal prompt.cal \
-	test3500.cal seedrandom.cal test4000.cal test4100.cal test4600.cal \
-	beer.cal hello.cal test5100.cal test5200.cal randombitrun.cal \
-	randomrun.cal repeat.cal xx_print.cal natnumset.cal qtime.cal \
-	test8400.cal test8500.cal test8600.cal chi.cal intfile.cal screen.cal \
-	dotest.cal set8700.cal set8700.line alg_config.cal sumtimes.cal \
-	dms.cal hms.cal
+# This list is prodiced by the detaillist rule when no WARNINGS are detected.
+#
+# Please use:
+#
+#	make calc_files_list
+#
+# to keep this list in nice sorted order and to check that these
+# deailed help files are under RCS control.
+#
+CALC_FILES= README alg_config.cal beer.cal bernoulli.cal \
+	bernpoly.cal bigprime.cal bindings brentsolve.cal chi.cal chrem.cal \
+	constants.cal deg.cal dms.cal dotest.cal ellip.cal factorial.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 lucas_tbl.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 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
@@ -272,8 +308,8 @@ clobber: clean
 #
 install: all
 	-${Q} if [ ! -d ${T}${CALC_SHAREDIR} ]; then \
-	    echo ${MKDIR} ${T}${CALC_SHAREDIR}; \
-	    ${MKDIR} ${T}${CALC_SHAREDIR}; \
+	    echo ${MKDIR} -p ${T}${CALC_SHAREDIR}; \
+	    ${MKDIR} -p ${T}${CALC_SHAREDIR}; \
 	    if [ ! -d "${T}${CALC_SHAREDIR}" ]; then \
 		echo ${MKDIR} -p "${T}${CALC_SHAREDIR}"; \
 		${MKDIR} -p "${T}${CALC_SHAREDIR}"; \
@@ -293,7 +329,7 @@ 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

cal/README

@@ -173,7 +173,8 @@ alg_config.cal
 
 beer.cal
 
-    Calc's contribution to the 99 Bottles of Beer web page:
+    This calc resource is calc's contribution to the 99 Bottles of Beer
+    web page:
 
 	http://www.ionet.net/~timtroyr/funhouse/beer.html#calc
 
@@ -191,6 +192,18 @@ bernoulli.cal
 	  the builtin function.
 
 
+bernpoly.cal
+
+    bernpoly(n,z)
+
+    Computes the nth Bernoulli polynomial at z for arbitrary n,z.  See:
+
+        http://en.wikipedia.org/wiki/Bernoulli_polynomials
+        http://mathworld.wolfram.com/BernoulliPolynomial.html
+
+    for further information
+
+
 bigprime.cal
 
     bigprime(a, m, p)
@@ -198,6 +211,34 @@ bigprime.cal
     A prime test, base a, on p*2^x+1 for even x>m.
 
 
+brentsolve.cal
+
+    brentsolve(low, high,eps)
+
+    A root-finder implementwed with the Brent-Dekker trick.
+
+    brentsolve2(low, high,which,eps)
+
+    The second function, brentsolve2(low, high,which,eps) has some lines
+    added to make it easier to hardcode the name of the helper function
+    different from the obligatory "f".
+
+    See:
+
+        http://en.wikipedia.org/wiki/Brent%27s_method
+        http://mathworld.wolfram.com/BrentsMethod.html
+
+    to find out more about the Brent-Dekker method.
+
+
+constants.cal
+
+    e()
+    G()
+
+    An implementation of different constants to arbitrary precision.
+
+
 chi.cal
 
     Z(x[, eps])
@@ -291,6 +332,166 @@ dotest.cal
 	dotest("set8700.line");
 
 
+factorial.cal
+
+    factorial(n)
+
+    Calculates the product of the positive integers up to and including n.
+
+    See:
+
+	http://en.wikipedia.org/wiki/Factorial
+
+    for information on the factorial. This function depends on the script
+    toomcook.cal.
+
+
+    primorial(a,b)
+
+    Calculates the product of the primes between a and b. If a is not prime
+    the next higher prime is taken as the starting point. If b is not prime
+    the next lower prime is taking as the end point b. The end point b must
+    not exceed 4294967291.  See:
+
+	http://en.wikipedia.org/wiki/Primorial
+
+    for information on the primorial.
+
+
+factorial2.cal
+
+    This file contents a small variety of integer functions that can, with
+    more or less pressure, be related to the factorial.
+
+    doublefactorial(n)
+
+    Calculates the double factorial n!! with different algorithms for
+        - n odd
+        - n even and positive
+        - n (real|complex) sans the negative half integers
+
+    See:
+
+        http://en.wikipedia.org/wiki/Double_factorial
+        http://mathworld.wolfram.com/DoubleFactorial.html
+
+    for information on the double factorial. This function depends on
+    the script toomcook.cal, factorial.cal and specialfunctions.cal.
+
+
+    binomial(n,k)
+
+    Calculates the binomial coefficients for n large and k = k \pm
+    n/2. Defaults to the built-in function for smaller and/or different
+    values. Meant as a complete replacement for comb(n,k) with only a
+    very small overhead.  See:
+
+        http://en.wikipedia.org/wiki/Binomial_coefficient
+
+    for information on the binomial. This function depends on the script
+    toomcook.cal factorial.cal and specialfunctions.cal.
+
+
+    bigcatalan(n)
+
+    Calculates the n-th Catalan number for n large. It is usefull
+    above n~50,000 but defaults to the builtin function for smaller
+    values.Meant as a complete replacement for catalan(n) with only a
+    very small overhead.  See:
+
+        http://en.wikipedia.org/wiki/Catalan_number
+        http://mathworld.wolfram.com/CatalanNumber.html
+
+    for information on Catalan numbers. This function depends on the scripts
+    toomcook.cal, factorial.cal and specialfunctions.cal.
+
+
+    stirling1(n,m)
+
+    Calculates the Stirling number of the first kind. It does so with
+    building a list of all of the smaller results. It might be a good
+    idea, though, to run it once for the highest n,m first if many
+    Stirling  numbers are needed at once, for example in a series.  See:
+
+        http://en.wikipedia.org/wiki/Stirling_numbers_of_the_first_kind
+        http://mathworld.wolfram.com/StirlingNumberoftheFirstKind.html
+        Algorithm 3.17,  Donald Kreher and Douglas Simpson, "Combinatorial
+          Algorithms", CRC Press, 1998, page 89.
+
+    for information on Stirling numbers of the first kind.
+
+
+    stirling2(n,m)
+    stirling2caching(n,m)
+
+    Calculate the Stirling number of the second kind.
+    The first function stirling2(n,m) does it with the sum
+                       m
+                      ====
+                 1    \      n      m - k
+                 --    >    k  (- 1)      binomial(m, k)
+                 m!   /
+                      ====
+                      k = 0
+
+    The other function stirling2caching(n,m) does it by way of the
+    reccurence relation and keeps all earlier results. This function
+    is much slower for computing a single value than stirling2(n,m) but
+    is very usefull if many Stirling numbers are needed, for example in
+    a series.  See:
+
+        http://en.wikipedia.org/wiki/Stirling_numbers_of_the_second_kind
+        http://mathworld.wolfram.com/StirlingNumberoftheSecondKind.html
+
+        Algorithm 3.17,  Donald Kreher and Douglas Simpson, "Combinatorial
+          Algorithms", CRC Press, 1998, page 89.
+
+    for information on Stirling numbers of the second kind.
+
+
+    bell(n)
+
+    Calculate the n-th Bell number. This may take some time for large n.
+    See:
+
+        http://oeis.org/A000110
+        http://en.wikipedia.org/wiki/Bell_number
+        http://mathworld.wolfram.com/BellNumber.html
+
+    for information on Bell numbers.
+
+
+    subfactorial(n)
+
+    Calculate the n-th subfactorial or derangement. This may take some
+    time for large n.  See:
+
+        http://mathworld.wolfram.com/Derangement.html
+        http://en.wikipedia.org/wiki/Derangement
+
+    for information on subfactorials.
+
+
+    risingfactorial(x,n)
+
+    Calculates the rising factorial or Pochammer symbol of almost arbitrary
+    x,n.  See:
+
+        http://en.wikipedia.org/wiki/Pochhammer_symbol
+        http://mathworld.wolfram.com/PochhammerSymbol.html
+
+    for information on rising factorials.
+
+    fallingfactorial(x,n)
+
+    Calculates the rising factorial of almost arbitrary x,n.  See:
+
+        http://en.wikipedia.org/wiki/Pochhammer_symbol
+        http://mathworld.wolfram.com/PochhammerSymbol.html
+
+    for information on falling factorials.
+
+
 ellip.cal
 
     efactor(iN, ia, B, force)
@@ -298,6 +499,13 @@ ellip.cal
     Attempt to factor using the elliptic functions: y^2 = x^3 + a*x + b.
 
 
+gvec.cal
+
+    gvec(function, vector)
+
+    Vectorize any single-input function or trailing operator.
+
+
 hello.cal
 
     Calc's contribution to the Hello World! page:
@@ -329,6 +537,20 @@ hms.cal
     Calculate in hours, minutes, and seconds.  See also dmscal.
 
 
+infinities.cal
+
+    isinfinite(x)
+    iscinf(x)
+    ispinf(x)
+    isninf(x)
+    cinf()
+    ninf()
+    pinf()
+
+    The symbolic handling of infinities. Needed for intnum.cal but might be
+    usefull elsewhere, too.
+
+
 intfile.cal
 
     file2be(filename)
@@ -356,6 +578,158 @@ intfile.cal
 	of the integer become the last octets of the file.
 
 
+intnum.cal
+
+    quadtsdeletenodes()
+    quadtscomputenodes(order, expo, eps)
+    quadtscore(a, b, n)
+    quadts(a, b, points)
+    quadglcomputenodes(N)
+    quadgldeletenodes()
+    quadglcore(a, b, n)
+    quadgl(a, b, points)
+    quad(a, b, points = -1, method = "tanhsinh")
+    makerange(start, end, steps)
+    makecircle(radius, center, points)
+    makeellipse(angle, a, b, center, points)
+    makepoints()
+
+    This file offers some methods for numerical integration. Implemented are
+    the Gauss-Legendre and the tanh-sinh quadrature.
+
+    All functions are usefull to some extend but the main function for
+    quadrature is quad(), which is not much more than an abstraction layer.
+
+    The main workers are quadgl() for Gauss-legendre and quadts() for the
+    tanh-sinh quadrature. The limits of the integral can be anything in the
+    complex plane and the extended real line. The latter means that infinite
+    limits are supported by way of the smbolic infinities implemented in the
+    file infinities.cal (automatically linked in by intnum.cal).
+
+    Integration in parts and contour is supported by the "points" argument
+    which takes either a number or a list. the functions starting with "make"
+    allow for a less error prone use.
+
+    The function to evaluate must have the name "f".
+
+    Examples (shamelessly stolen from mpmath):
+
+        ; define f(x){return sin(x);}
+        f(x) defined
+        ; quadts(0,pi())  -  2
+	    0.00000000000000000000
+        ; quadgl(0,pi())  -  2
+	    0.00000000000000000000
+
+    Sometimes rounding errors accumulate, it might be a good idea to crank up
+    the working precision a notch or two.
+
+        ; define f(x){ return exp(-x^2);}
+        f(x) redefined
+        ; quadts(0,pinf())  - pi()
+	    0.00000000000000000000
+        ; quadgl(0,pinf())  - pi()
+	    0.00000000000000000001
+
+        ; define f(x){ return exp(-x^2);}
+        f(x) redefined
+        ; quadgl(ninf(),pinf()) - sqrt(pi())
+	    0.00000000000000000000
+        ; quadts(ninf(),pinf()) - sqrt(pi())
+	   -0.00000000000000000000
+
+    Using the "points" parameter is a bit tricky
+
+        ; define f(x){ return 1/x;  }
+        f(x) redefined
+        ; quadts(1,1,mat[3]={1i,-1,-1i})  -  2i*pi()
+	    0.00000000000000000001i
+        ; quadgl(1,1,mat[3]={1i,-1,-1i})  -  2i*pi()
+	    0.00000000000000000001i
+
+    The make* functions make it a bit simpler
+
+        ; quadts(1,1,makepoints(1i,-1,-1i))  -  2i*pi()
+	    0.00000000000000000001i
+        ; quadgl(1,1,makepoints(1i,-1,-1i))  -  2i*pi()
+	    0.00000000000000000001i
+
+        ; define f(x){ return abs(sin(x));}
+        f(x) redefined
+        ; quadts(0,2*pi(),makepoints(pi()))  - 4
+	    0.00000000000000000000
+        ; quadgl(0,2*pi(),makepoints(pi()))  - 4
+	    0.00000000000000000000
+
+    The quad*core functions do not offer anything fancy but the third parameter
+    controls the so called "order" which is just the number of nodes computed.
+    This can be quite usefull in some circumstances.
+
+        ; quadgldeletenodes()
+        ; define f(x){ return exp(x);}
+        f(x) redefined
+        ; s=usertime();quadglcore(-3,3)- (exp(3)-exp(-3));e=usertime();e-s
+	    0.00000000000000000001
+	    2.632164
+        ; s=usertime();quadglcore(-3,3)- (exp(3)-exp(-3));e=usertime();e-s
+	    0.00000000000000000001
+	    0.016001
+        ; quadgldeletenodes()
+        ; s=usertime();quadglcore(-3,3,14)- (exp(3)-exp(-3));e=usertime();e-s
+	   -0.00000000000000000000
+	    0.024001
+        ; s=usertime();quadglcore(-3,3,14)- (exp(3)-exp(-3));e=usertime();e-s
+	   -0.00000000000000000000
+	    0
+
+    It is not much but can sum up. The tanh-sinh algorithm is not optimizable
+    as much as the Gauss-Legendre algorithm but is per se much faster.
+
+        ; s=usertime();quadtscore(-3,3)- (exp(3)-exp(-3));e=usertime();e-s
+	    -0.00000000000000000001
+	     0.128008
+        ; s=usertime();quadtscore(-3,3)- (exp(3)-exp(-3));e=usertime();e-s
+	    -0.00000000000000000001
+	     0.036002
+        ; s=usertime();quadtscore(-3,3,49)- (exp(3)-exp(-3));e=usertime();e-s
+	    -0.00000000000000000000
+	     0.036002
+        ; s=usertime();quadtscore(-3,3,49)- (exp(3)-exp(-3));e=usertime();e-s
+	    -0.00000000000000000000
+	     0.01200
+
+
+lambertw.cal
+
+     lambertw(z,branch)
+
+     Computes Lambert's W-function at "z" at branch "branch". See
+
+         http://en.wikipedia.org/wiki/Lambert_W_function
+         http://mathworld.wolfram.com/LambertW-Function.html
+         https://cs.uwaterloo.ca/research/tr/1993/03/W.pdf
+         http://arxiv.org/abs/1003.1628
+
+     to get more information.
+
+     This file includes also an implementation for the series described in
+     Corless et al. (1996) eq. 4.22 (W-pdf) and Verebic (2010) (arxive link)
+     eqs.35-37.
+
+     The series has been implemented to get a different algorithm
+     for checking the results. This was necessary because the results
+     of the implementation in Maxima, the only program with a general
+     lambert-w implementation at hand at that time, differed slightly. The
+     Maxima versions tested were: Maxima 5.21.1 and 5.29.1. The current
+     version of this code concurs with the results of Mathematica`s(tm)
+     ProductLog[branch,z] with the tested values.
+
+     The series is only valid for the branches 0,-1, real z, converges
+     for values of z _very_ near the branchpoint -exp(-1) only, and must
+     be given the branches explicitly.  See the code in lambertw.cal
+     for further information.
+
+
 linear.cal
 
     linear(x0, y0, x1, y1, x)
@@ -364,6 +738,24 @@ linear.cal
     Requires x0 != y0.
 
 
+lnseries.cal
+
+    lnseries(limit)
+    lnfromseries(n)
+    deletelnseries()
+
+    Calculates a series of n natural logarithms at 1,2,3,4...n. It
+    does so by computing the prime factorization of all of the number
+    sequence 1,2,3...n, calculates the natural logarithms of the primes
+    in 1,2,3...n and uses the above factorization to build the natural
+    logarithms of the rest of the sequence by sadding the logarithms of
+    the primes in the factorization.  This is faster for high precision
+    of the logarithms and/or long sequences.
+
+    The sequence need to be initiated by running either lnseries(n) or
+    lnfromseries(n) once with n the upper limit of the sequence.
+
+
 lucas.cal
 
     lucas(h, n)
@@ -409,6 +801,7 @@ mfactor.cal
     fastest even thought the initial startup overhead is larger than
     for p_elim == 13.
 
+
 mod.cal
 
     lmod(a)
@@ -498,6 +891,7 @@ pi.cal
     Lambert Meertens.  See also the ABC Programmer's Handbook, by Geurts,
     Meertens & Pemberton, published by Prentice-Hall (UK) Ltd., 1990.
 
+
 pix.cal
 
     pi_of_x(x)
@@ -580,10 +974,10 @@ randmprime.cal
 
     randmprime(bits, seed [,dbg])
 
-    Find a prime of the form h*2^n-1 >= 2^bits for some given x.  The initial
-    search points for 'h' and 'n' are selected by a cryptographic pseudo-random
-    number generator.  The optional argument, dbg, if set to 1, 2 or 3
-    turn on various debugging print statements.
+    Find a prime of the form h*2^n-1 >= 2^bits for some given x.  The
+    initial search points for 'h' and 'n' are selected by a cryptographic
+    pseudo-random number generator.  The optional argument, dbg, if set
+    to 1, 2 or 3 turn on various debugging print statements.
 
 
 randombitrun.cal
@@ -635,8 +1029,8 @@ repeat.cal
 
 regress.cal
 
-    Test the correct execution of the calculator by reading this resource file.
-    Errors are reported with '****' messages, or worse. :-)
+    Test the correct execution of the calculator by reading this resource
+    file.  Errors are reported with '****' messages, or worse. :-)
 
 
 screen.cal
@@ -682,15 +1076,17 @@ screen.cal
     Cyan
     White
 
-    Define ANSI control sequences providing (i.e., cursor movement, changing
-    foreground or background color, etc.) for VT100 terminals and terminal
-    window emulators (i.e., xterm, Apple OS/X Terminal, etc.) that support them.
+    Define ANSI control sequences providing (i.e., cursor movement,
+    changing foreground or background color, etc.) for VT100 terminals
+    and terminal window emulators (i.e., xterm, Apple OS/X Terminal,
+    etc.) that support them.
 
     For example:
 
 	read screen
 	print green:"This is green. ":red:"This is red.":black
 
+
 seedrandom.cal
 
     seedrandom(seed1, seed2, bitsize [,trials])
@@ -727,13 +1123,276 @@ set8700.line
     The set8700.cal file (and dotest.cal) should be read first.
 
 
+smallfactors.cal
+
+    smallfactors(x0)
+    printsmallfactors(flist)
+
+    Lists the prime factors of numbers smaller than 2^32. Try for example:
+    printsmallfactors(smallfactors(10!)).
+
+
 solve.cal
 
     solve(low, high, epsilon)
 
     Solve the equation f(x) = 0 to within the desired error value for x.
-    The function 'f' must be defined outside of this routine, and the low
-    and high values are guesses which must produce values with opposite signs.
+    The function 'f' must be defined outside of this routine, and the
+    low and high values are guesses which must produce values with
+    opposite signs.
+
+
+specialfunctions.cal
+
+    beta(a,b)
+
+    Calculates the value of the beta function.  See:
+
+	https://en.wikipedia.org/wiki/Beta_function
+        http://mathworld.wolfram.com/BetaFunction.html
+        http://dlmf.nist.gov/5.12
+
+    for information on the beta function.
+
+
+    betainc(a,b,z)
+
+    Calculates the value of the regularized incomplete beta function.  See:
+
+	https://en.wikipedia.org/wiki/Beta_function
+        http://mathworld.wolfram.com/RegularizedBetaFunction.html
+        http://dlmf.nist.gov/8.17
+
+    for information on the regularized incomplete beta function.
+
+
+    expoint(z)
+
+    Calculates the value of the exponential integral Ei(z) function at z.
+    See:
+
+	http://en.wikipedia.org/wiki/Exponential_integral
+        http://www.cs.utah.edu/~vpegorar/research/2011_JGT/
+
+    for information on the exponential integral Ei(z) function.
+
+
+    erf(z)
+
+    Calculates the value of the error function at z.  See:
+
+	http://en.wikipedia.org/wiki/Error_function
+
+    for information on the error function function.
+
+
+    erfc(z)
+
+    Calculates the value of the complementary error function at z.  See:
+
+	http://en.wikipedia.org/wiki/Error_function
+
+    for information on the complementary error function function.
+
+
+    erfi(z)
+
+    Calculates the value of the imaginary error function at z.  See:
+
+	http://en.wikipedia.org/wiki/Error_function
+
+    for information on the imaginary error function function.
+
+
+    erfinv(x)
+
+    Calculates the inverse of the error function at x.  See:
+
+	http://en.wikipedia.org/wiki/Error_function
+
+    for information on the inverse of the error function function.
+
+
+    faddeeva(z)
+
+    Calculates the value of the complex error function at z.  See:
+
+	http://en.wikipedia.org/wiki/Faddeeva_function
+
+    for information on the complex error function function.
+
+
+    gamma(z)
+
+    Calculates the value of the Euler gamma function at z.  See:
+
+	http://en.wikipedia.org/wiki/Gamma_function
+        http://dlmf.nist.gov/5
+
+    for information on the Euler gamma function.
+
+
+    gammainc(a,z)
+
+    Calculates the value of the lower incomplete gamma function for
+    arbitrary a, z.  See:
+
+	http://en.wikipedia.org/wiki/Incomplete_gamma_function
+
+    for information on the lower incomplete gamma function.
+
+    gammap(a,z)
+
+    Calculates the value of the regularized lower incomplete gamma
+    function for a, z with a not in -N.  See:
+
+	http://en.wikipedia.org/wiki/Incomplete_gamma_function
+
+    for information on the regularized lower incomplete gamma function.
+
+    gammaq(a,z)
+
+    Calculates the value of the regularized upper incomplete gamma
+    function for a, z with a not in -N.  See:
+
+	http://en.wikipedia.org/wiki/Incomplete_gamma_function
+
+    for information on the regularized upper incomplete gamma function.
+
+
+    heavisidestep(x)
+
+    Computes the Heaviside stepp function (1+sign(x))/2
+
+
+    harmonic(limit)
+
+    Calculates partial values of the harmonic series up to limit.  See:
+
+	http://en.wikipedia.org/wiki/Harmonic_series_(mathematics)
+        http://mathworld.wolfram.com/HarmonicSeries.html
+
+    for information on the harmonic series.
+
+
+    lnbeta(a,b)
+
+    Calculates the natural logarithm of the beta function.  See:
+
+	https://en.wikipedia.org/wiki/Beta_function
+        http://mathworld.wolfram.com/BetaFunction.html
+        http://dlmf.nist.gov/5.12
+
+    for information on the beta function.
+
+    lngamma(z)
+
+    Calculates the value of the logarithm of the Euler gamma function
+    at z.  See:
+
+	http://en.wikipedia.org/wiki/Gamma_function
+        http://dlmf.nist.gov/5.15
+
+    for information on the derivatives of the the Euler gamma function.
+
+
+    polygamma(m,z)
+
+    Calculates the value of the m-th derivative of the Euler gamma
+    function at z.  See:
+
+	http://en.wikipedia.org/wiki/Polygamma
+        http://dlmf.nist.gov/5
+
+    for information on the n-th derivative ofthe Euler gamma function. This
+    function depends on the script zeta2.cal.
+
+
+    psi(z)
+
+    Calculates the value of the first derivative of the Euler gamma
+    function at z.  See:
+
+	http://en.wikipedia.org/wiki/Digamma_function
+        http://dlmf.nist.gov/5
+
+    for information on the first derivative of the Euler gamma function.
+
+
+    zeta(s)
+
+    Calculates the value of the Rieman Zeta function at s.  See:
+
+	http://en.wikipedia.org/wiki/Riemann_zeta_function
+        http://dlmf.nist.gov/25.2
+
+    for information on the Riemann zeta function. This function depends
+    on the script zeta2.cal.
+
+
+statistics.cal
+
+    gammaincoctave(z,a)
+
+    Computes the regularized incomplete gamma function in a way to
+    correspond with the function in Octave.
+
+    invbetainc(x,a,b)
+
+    Computes the inverse of the regularized beta function. Does so the
+    brute-force way wich makes it a bit slower.
+
+    betapdf(x,a,b)
+    betacdf(x,a,b)
+    betacdfinv(x,a,b)
+    betamedian(a,b)
+    betamode(a,b)
+    betavariance(a,b)
+    betalnvariance(a,b)
+    betaskewness(a,b)
+    betakurtosis(a,b)
+    betaentropy(a,b)
+    normalpdf(x,mu,sigma)
+    normalcdf(x,mu,sigma)
+    probit(p)
+    normalcdfinv(p,mu,sigma)
+    normalmean(mu,sigma)
+    normalmedian(mu,sigma)
+    normalmode(mu,sigma)
+    normalvariance(mu,sigma)
+    normalskewness(mu,sigma)
+    normalkurtosis(mu,sigma)
+    normalentropy(mu,sigma)
+    normalmgf(mu,sigma,t)
+    normalcf(mu,sigma,t)
+    chisquaredpdf(x,k)
+    chisquaredpcdf(x,k)
+    chisquaredmean(x,k)
+    chisquaredmedian(x,k)
+    chisquaredmode(x,k)
+    chisquaredvariance(x,k)
+    chisquaredskewness(x,k)
+    chisquaredkurtosis(x,k)
+    chisquaredentropy(x,k)
+    chisquaredmfg(k,t)
+    chisquaredcf(k,t)
+
+    Calculates a bunch of (hopefully) aptly named statistical functions.
+
+
+strings.cal
+
+    isascii(c)
+    isblank(c)
+
+    Implements some of the functions of libc's ctype.h and strings.h.
+
+    NOTE: A number of the ctype.h and strings.h functions are now builtin
+          functions in calc.
+
+   WARNING: If the remaining functions in this calc resource file become
+	    calc builtin functions, then strings.cal may be removed in
+	    a future release.
 
 
 sumsq.cal
@@ -795,7 +1454,8 @@ test1700.cal
 
     value
 
-    This resource files is used by regress.cal to test the read and use keywords.
+    This resource files is used by regress.cal to test the read and
+    use keywords.
 
 
 test2600.cal
@@ -820,8 +1480,8 @@ test2600.cal
     checkresult(x, y, z, a)
     test2600(verbose, tnum)
 
-    This resource files is used by regress.cal to test some of builtin functions
-    in terms of accuracy and roundoff.
+    This resource files is used by regress.cal to test some of builtin
+    functions in terms of accuracy and roundoff.
 
 
 test2700.cal
@@ -858,7 +1518,8 @@ test3100.cal
     res_inv(a)
     res(x)
 
-    This resource file is used by regress.cal to test determinants of a matrix
+    This resource file is used by regress.cal to test determinants of
+    a matrix.
 
 
 test3300.cal
@@ -869,8 +1530,9 @@ test3300.cal
     testr(str, n, N, verbose)
     test3300(verbose, tnum)
 
-    This resource file is used by regress.cal to provide for more determinant
-    tests.
+    This resource file is used by regress.cal to provide for more
+    determinant tests.
+
 
 test3400.cal
 
@@ -901,6 +1563,7 @@ test3500.cal
     This resource file is used by regress.cal to test the functions frem,
     fcnt, gcdrem.
 
+
 test4000.cal
 
     global defaultverbose
@@ -933,6 +1596,7 @@ test4000.cal
     This resource file is used by regress.cal to test ptest, nextcand and
     prevcand builtins.
 
+
 test4100.cal
 
     global defaultverbose
@@ -952,6 +1616,7 @@ test4100.cal
 
     This resource file is used by regress.cal to test REDC operations.
 
+
 test4600.cal
 
     stest(str [, verbose]) defined
@@ -963,6 +1628,7 @@ test4600.cal
 
     This resource file is used by regress.cal to test searching in files.
 
+
 test5100.cal
 
     global a5100
@@ -972,6 +1638,7 @@ test5100.cal
     This resource file is used by regress.cal to test the new code generator
     declaration scope and order.
 
+
 test5200.cal
 
     global a5200
@@ -983,6 +1650,7 @@ test5200.cal
     This resource file is used by regress.cal to test the fix of a
     global/static bug.
 
+
 test8400.cal
 
     test8400() defined
@@ -990,6 +1658,7 @@ test8400.cal
     This resource file is used by regress.cal to check for quit-based
     memory leaks.
 
+
 test8500.cal
 
     global err_8500
@@ -1002,6 +1671,7 @@ test8500.cal
 
     This resource file is used by regress.cal to the // and % operators.
 
+
 test8600.cal
 
     global min_8600
@@ -1012,6 +1682,25 @@ test8600.cal
     This resource file is used by regress.cal to test a change of
     allowing up to 1024 args to be passed to a builtin function.
 
+
+test8900.cal
+
+    This function tests a number of calc resource functions contributed
+    by Christoph Zurnieden.  These include:
+
+	bernpoly.cal
+	brentsolve.cal
+	constants.cal
+	factorial2.cal
+	factorial.cal
+	lambertw.cal
+	lnseries.cal
+	specialfunctions.cal
+	statistics.cal
+	toomcook.cal
+	zeta2.cal
+
+
 unitfrac.cal
 
     unitfrac(x)
@@ -1019,6 +1708,29 @@ unitfrac.cal
     Represent a fraction as sum of distinct unit fractions.
 
 
+toomcook.cal
+
+
+    toomcook3(a,b)
+    toomcook4(a,b)
+
+    Toom-Cook multiplication algorithm.  Multiply two integers a,b by
+    way of the Toom-Cook algorithm.  See:
+
+	http://en.wikipedia.org/wiki/Toom%E2%80%93Cook_multiplication
+
+    toomcook3square(a)
+    toomcook4square(a)
+
+    Square the integer a by way of the Toom-Cook algorithm.  See:
+
+	http://en.wikipedia.org/wiki/Toom%E2%80%93Cook_multiplication
+
+    The function toomCook4(a,b) calls the function toomCook3(a,b) which
+    calls built-in multiplication at a specific cut-off point. The
+    squaring functions act in the same way.
+
+
 varargs.cal
 
     sc(a, b, ...)
@@ -1026,6 +1738,7 @@ varargs.cal
     Example program to use 'varargs'.  Program to sum the cubes of all
     the specified numbers.
 
+
 xx_print.cal
 
     is_octet(a) defined
@@ -1040,6 +1753,19 @@ xx_print.cal
 
     Demo for the xx_print object routines.
 
+
+zeta2.cal
+
+    hurwitzzeta(s,a)
+
+    Calculate the value of the Hurwitz Zeta function.  See:
+
+	http://en.wikipedia.org/wiki/Hurwitz_zeta_function
+        http://dlmf.nist.gov/25.11
+
+    for information on this special zeta function.
+
+
 ## Copyright (C) 2000  David I. Bell and Landon Curt Noll
 ##
 ## Primary author: Landon Curt Noll
@@ -1058,9 +1784,9 @@ xx_print.cal
 ## 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,v 30.2 2010/09/02 06:01:39 chongo Exp $
-## @(#) $Source: /usr/local/src/cmd/calc/cal/RCS/README,v $
+## @(#) $Revision: 30.8 $
+## @(#) $Id: README,v 30.8 2013/09/02 01:46:05 chongo Exp $
+## @(#) $Source: /usr/local/src/bin/calc/cal/RCS/README,v $
 ##
 ## Under source code control:	1990/02/15 01:50:32
 ## File existed as early as:	before 1990

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
@@ -17,9 +17,9 @@
  * 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/cmd/calc/cal/RCS/alg_config.cal,v $
+ * @(#) $Revision: 30.11 $
+ * @(#) $Id: alg_config.cal,v 30.11 2014/09/07 06:13:04 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 +28,37 @@
  * 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 +109,8 @@ 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 +172,7 @@ 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 +195,7 @@ 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 +248,12 @@ 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",
-		ceil(test_time * (8 / loops)));
+	    printf("    we must expand alg1 loop test time to about %d secs\n",
+		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 +294,12 @@ 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",
-		ceil(test_time * (8 / loops)));
+	    printf("    we must expand alg2 loop test time to about %d secs\n",
+		ceil(test_time * (16 / loops)));
 	}
-	loops = 8;
+	loops = 16;
     }
     tlen = mul_loop(loops, &x);
     if (config("user_debug") > 3) {
@@ -297,7 +328,12 @@ 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 +355,39 @@ 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;
-    if (config("user_debug") > 0) {
-	printf("will start with loop test time of %d secs\n", test_time);
+    test_time = 30.0;
+    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;
+    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) {
-	quit "best_mul2: tests imply config(\"mul2\") should be < 4";
+    if (ratio < 1.0) {
+	quit "best_mul2: tests imply mul2 should be < 16, which seems bogus";
     }
 
     /*
@@ -355,7 +400,7 @@ 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 = ((ratio >= 10) ? 1024 : 2^round(ratio));
 	low = high;
 	high *= expand;
 	if (config("user_debug") > 1) {
@@ -367,19 +412,63 @@ 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 (config("user_debug") > 1) {
-	    printf("    multiply alg1/alg2 ratio = %.3f\n", ratio);
+	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);
+	    }
 	}
-    } 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("retesting 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("    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("alg1/alg2 ratio now < 1.0, starting binary search between %d and %d\n",
-	    low, high);
+	printf("Starting binary search between %d and %d\n", low, high);
     }
 
     /*
@@ -388,30 +477,54 @@ 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",
-	    	int((low+high)/2));
+	    printf("testing multiply alg1/alg2 ratio for len = %d\n", mid);
+	}
+	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("    len %d has a new cloest ratio to unity: %.6f\n",
+		       best_val, best_ratio);
+	    }
 	}
-	ratio = mul_ratio(int((low+high)/2));
 	if (config("user_debug") > 1) {
-	    printf("    multiply alg1/alg2 ratio = %.3f\n", ratio);
+	    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 +532,15 @@ define best_mul2()
      * return on the suggested config("mul2") value
      */
     if (config("user_debug") > 0) {
-	printf("best value of config(\"mul2\") is %d\n",
-	    (ratio >= 1.0) ? high : low);
+	printf("Best value for multiply is near %d\n", best_val);
+	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 +590,8 @@ 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 +678,7 @@ 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 +731,12 @@ 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",
-		ceil(test_time * (8 / loops)));
+	    printf("    we must expand alg1 loop test time to about %d secs\n",
+		ceil(test_time * (16 / loops)));
 	}
-	loops = 8;
+	loops = 16;
     }
     tlen = sq_loop(loops, &x);
     if (config("user_debug") > 3) {
@@ -654,12 +774,12 @@ 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",
-		ceil(test_time * (8 / loops)));
+	    printf("    we must expand alg2 loop test time to about %d secs\n",
+		ceil(test_time * (16 / loops)));
 	}
-	loops = 8;
+	loops = 16;
     }
     tlen = sq_loop(loops, &x);
     if (config("user_debug") > 3) {
@@ -688,7 +808,12 @@ 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 +835,39 @@ 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;
-    if (config("user_debug") > 0) {
-	printf("will start with loop test time of %d secs\n", test_time);
+    test_time = 30.0;
+    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;
+    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) {
-	quit "best_sq2: tests imply config(\"sq2\") should be < 4";
+    if (ratio < 1.0) {
+	quit "best_sq2: test implies sq2 < 16, which seems bogus";
     }
 
     /*
@@ -746,31 +880,75 @@ 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 = ((ratio >= 10) ? 1024 : 2^round(ratio));
 	low = high;
 	high *= expand;
 	if (config("user_debug") > 1) {
 	    printf("    expand the next test range by a factor of %d\n",
-	           expand);
+	    	   expand);
 	}
 
 	/*
 	 * 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("retesting 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("    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("alg1/alg2 ratio now < 1.0, starting binary search between %d and %d\n",
-	    low, high);
+	printf("Starting binary search between %d and %d\n", low, high);
     }
 
     /*
@@ -779,41 +957,71 @@ 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",
-	    	int((low+high)/2));
+	    printf("testing square alg1/alg2 ratio for len = %d\n", mid);
+	}
+	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("    len %d has a new cloest ratio to unity: %.6f\n",
+		       best_val, best_ratio);
+	    }
 	}
-	ratio = sq_ratio(int((low+high)/2));
 	if (config("user_debug") > 1) {
-	    printf("    square alg1/alg2 ratio = %.3f\n", ratio);
+	    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",
-	    (ratio >= 1.0) ? high : low);
+	printf("Best value for square is near %d\n", best_val);
+	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 +1074,8 @@ 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 +1172,7 @@ 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 +1195,7 @@ define pow_ratio(len)
     /*
      * setup
      */
-    ex = 5;
+    ex = 7;
 
     /*
      * initialize x, the values we will pmod
@@ -1021,12 +1231,12 @@ 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",
-		ceil(test_time * (8 / loops)));
+	    printf("    we must expand alg1 loop test time to about %d secs\n",
+		ceil(test_time * (16 / loops)));
 	}
-	loops = 8;
+	loops = 16;
     }
     tlen = pow_loop(loops, &x, ex);
     if (config("user_debug") > 3) {
@@ -1065,12 +1275,12 @@ 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",
-		ceil(test_time * (8 / loops)));
+	    printf("    we must expand alg2 loop test time to about %d secs\n",
+		ceil(test_time * (16 / loops)));
 	}
-	loops = 8;
+	loops = 16;
     }
     tlen = pow_loop(loops, &x, ex);
     if (config("user_debug") > 3) {
@@ -1099,7 +1309,12 @@ 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 +1336,24 @@ 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;
-    if (config("user_debug") > 0) {
-	printf("will start with loop test time of %d secs\n", test_time);
+    test_time = 60.0;
+    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 +1364,27 @@ 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 +1426,27 @@ 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("    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);
+	    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",
-	    low, high);
+	printf("Starting binary search between %d and %d\n", low, high);
     }
 
     /*
@@ -1215,39 +1455,69 @@ 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",
-	    	int((low+high)/2));
+	    printf("testing pow2 alg1/alg2 ratio for len = %d\n", mid);
+	}
+	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("    len %d has a new cloest ratio to unity: %.6f\n",
+		       best_val, best_ratio);
+	    }
 	}
-	ratio = pow_ratio(int((low+high)/2));
 	if (config("user_debug") > 1) {
-	    printf("    pmod alg1/alg2 ratio = %.3f\n", ratio);
+	    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",
-	    (ratio >= 1.0) ? high : low);
+	printf("Best value for pmod is near %d\n", best_val);
+	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

@@ -19,7 +19,7 @@
  *
  * @(#) $Revision: 30.1 $
  * @(#) $Id: beer.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/cmd/calc/cal/RCS/beer.cal,v $
+ * @(#) $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

@@ -19,7 +19,7 @@
  *
  * @(#) $Revision: 30.1 $
  * @(#) $Id: bernoulli.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/cmd/calc/cal/RCS/bernoulli.cal,v $
+ * @(#) $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 +1,59 @@
+/*
+ * 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.
+ *
+ * @(#) $Revision: 30.4 $
+ * @(#) $Id: bernpoly.cal,v 30.4 2013/08/18 20:01:53 chongo Exp $
+ * @(#) $Source: /usr/local/src/bin/calc/cal/RCS/bernpoly.cal,v $
+ *
+ * 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

@@ -19,7 +19,7 @@
  *
  * @(#) $Revision: 30.1 $
  * @(#) $Id: bigprime.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/cmd/calc/cal/RCS/bigprime.cal,v $
+ * @(#) $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

@@ -18,7 +18,7 @@
 #
 # @(#) $Revision: 30.1 $
 # @(#) $Id: bindings,v 30.1 2007/03/16 11:09:54 chongo Exp $
-# @(#) $Source: /usr/local/src/cmd/calc/cal/RCS/bindings,v $
+# @(#) $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 +1,258 @@
+/*
+ * 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.
+ *
+ * @(#) $Revision: 30.4 $
+ * @(#) $Id: brentsolve.cal,v 30.4 2013/08/18 20:01:53 chongo Exp $
+ * @(#) $Source: /usr/local/src/bin/calc/cal/RCS/brentsolve.cal,v $
+ *
+ * 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

@@ -19,7 +19,7 @@
  *
  * @(#) $Revision: 30.1 $
  * @(#) $Id: chi.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/cmd/calc/cal/RCS/chi.cal,v $
+ * @(#) $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

@@ -21,7 +21,7 @@
  *
  * @(#) $Revision: 30.1 $
  * @(#) $Id: chrem.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/cmd/calc/cal/RCS/chrem.cal,v $
+ * @(#) $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 +1,104 @@
+/*
+ * 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.
+ *
+ * @(#) $Revision: 30.4 $
+ * @(#) $Id: constants.cal,v 30.4 2013/08/18 20:01:53 chongo Exp $
+ * @(#) $Source: /usr/local/src/bin/calc/cal/RCS/constants.cal,v $
+ *
+ * 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

@@ -19,7 +19,7 @@
  *
  * @(#) $Revision: 30.2 $
  * @(#) $Id: deg.cal,v 30.2 2010/09/02 06:01:14 chongo Exp $
- * @(#) $Source: /usr/local/src/cmd/calc/cal/RCS/deg.cal,v $
+ * @(#) $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

@@ -19,7 +19,7 @@
  *
  * @(#) $Revision: 30.2 $
  * @(#) $Id: dms.cal,v 30.2 2010/09/02 06:14:16 chongo Exp $
- * @(#) $Source: /usr/local/src/cmd/calc/cal/RCS/dms.cal,v $
+ * @(#) $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

@@ -18,7 +18,7 @@
  *
  * @(#) $Revision: 30.2 $
  * @(#) $Id: dotest.cal,v 30.2 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/cmd/calc/cal/RCS/dotest.cal,v $
+ * @(#) $Source: /usr/local/src/bin/calc/cal/RCS/dotest.cal,v $
  *
  * This file is not covered under version 2.1 of the GNU LGPL.
  *

cal/ellip.cal

@@ -19,7 +19,7 @@
  *
  * @(#) $Revision: 30.1 $
  * @(#) $Id: ellip.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/cmd/calc/cal/RCS/ellip.cal,v $
+ * @(#) $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 +1,204 @@
+/*
+ * 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.
+ *
+ * @(#) $Revision: 30.4 $
+ * @(#) $Id: factorial.cal,v 30.4 2013/08/18 20:01:53 chongo Exp $
+ * @(#) $Source: /usr/local/src/bin/calc/cal/RCS/factorial.cal,v $
+ *
+ * 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 +1,723 @@
+/*
+ * 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.
+ *
+ * @(#) $Revision: 30.4 $
+ * @(#) $Id: factorial2.cal,v 30.4 2013/08/18 20:01:53 chongo Exp $
+ * @(#) $Source: /usr/local/src/bin/calc/cal/RCS/factorial2.cal,v $
+ *
+ * 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

@@ -0,0 +1,107 @@
+/*
+ * gvec - vectorize any single-input function or trailing operator
+ *
+ * This version accepts arbitrary number of arguments, but of course
+ * they must all be same length vectors.
+ *
+ * The gvec function is for use in either a two-arg function or a two-arg
+ * 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
+ *
+ * By Carl Witthoft carl at witthoft dot com
+ */
+
+define gvec(function, vector)
+{
+    local xlen,y,foo;
+    local precx = 1e-50;	/* default for now */
+    local argc = param(0)-1;
+    local old_tilde;		/* previous config("tilde") */
+
+    /*
+     * parse args
+     */
+    local plist = mat[argc];
+    if (config("resource_debug") & 8) {
+	print "plist=", plist;
+	print "argc=", argc;
+    }
+    for(local i = 0; i< argc; i++) {
+	local ii = i + 2;
+	if (config("resource_debug") & 8) {
+	    print "ii=", ii;
+	    print "param(" : ii : "}=", param(ii);
+	    print "size(param(" : ii : ")=", size(param(ii));
+	}
+	plist[i] = size(param(ii));
+    }
+    local slist=sort(plist);
+    if (config("resource_debug") & 8) {
+	print "plist=", plist;
+    }
+    local argm = argc-1;
+    if (config("resource_debug") & 8) {
+	print "argm=", argm;
+    }
+    if (slist[0] != slist[argm]) {
+	quit "lengths don't match";
+    }
+    xlen = size(vector);
+    y = mat[xlen];
+
+    /*
+     * We can't do str(vector[j]) outside loop, eval() petulantly refuses to
+     * look at local variables.
+     *
+     * Also we need to config("tilde",0) to turn off lead tilde
+     * (so str(vector[j]) looks like a number.
+     */
+    old_tilde = config("tilde",0);
+
+    /*
+     * Ok, now check to see if "function" is a function.  If not, it's an
+     * operation and it's up to user to make it valid
+     */
+    if (isdefined(function)) {
+
+	/* yep, it's a function, either builtin or user-defined */
+	for (local j=0; j<xlen; j++) {
+
+	    /* build the function call */
+	    foo = strcat(function, "(");
+	    for (local jj = 0; jj<argc; jj++) {
+		foo = strcat(foo , str(param(jj+2)[j]), ",");
+	    }
+	    foo = strcat(foo, str(precx), ")");
+	    if (config("resource_debug") & 8) {
+		print "foo=", foo;
+	    }
+	    y[j] = eval(foo);
+	}
+
+    /*
+     * it is an operator --  multi-argument operator makes no sense
+     */
+    } else {
+	if (argc > 1) {
+	    quit "Error: operator can accept only one argument";
+	}
+	for (j=0; j<xlen; j++) {
+	    foo = strcat(str(vector[j]), function);
+	    y[j] = eval(foo);
+	}
+    }
+
+    /* restore tilde mode if needed */
+    config("tilde", old_tilde);
+
+    /* return result */
+    return y;
+}

cal/hello.cal

@@ -19,7 +19,7 @@
  *
  * @(#) $Revision: 30.1 $
  * @(#) $Id: hello.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/cmd/calc/cal/RCS/hello.cal,v $
+ * @(#) $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

@@ -19,7 +19,7 @@
  *
  * @(#) $Revision: 30.2 $
  * @(#) $Id: hms.cal,v 30.2 2010/09/02 06:14:16 chongo Exp $
- * @(#) $Source: /usr/local/src/cmd/calc/cal/RCS/hms.cal,v $
+ * @(#) $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

@@ -19,7 +19,7 @@
  *
  * @(#) $Revision: 30.1 $
  * @(#) $Id: intfile.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/cmd/calc/cal/RCS/intfile.cal,v $
+ * @(#) $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 +1,288 @@
+/*
+ * 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.
+ *
+ * @(#) $Revision: 30.4 $
+ * @(#) $Id: lambertw.cal,v 30.4 2013/08/18 20:01:53 chongo Exp $
+ * @(#) $Source: /usr/local/src/bin/calc/cal/RCS/lambertw.cal,v $
+ *
+ * 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

@@ -19,7 +19,7 @@
  *
  * @(#) $Revision: 30.2 $
  * @(#) $Id: linear.cal,v 30.2 2007/03/17 05:57:42 chongo Exp $
- * @(#) $Source: /usr/local/src/cmd/calc/cal/RCS/linear.cal,v $
+ * @(#) $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 +1,112 @@
+/*
+ * 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.
+ *
+ * @(#) $Revision: 30.4 $
+ * @(#) $Id: lnseries.cal,v 30.4 2013/08/18 20:01:53 chongo Exp $
+ * @(#) $Source: /usr/local/src/bin/calc/cal/RCS/lnseries.cal,v $
+ *
+ * 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.cal

@@ -17,9 +17,9 @@
  * 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.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/cmd/calc/cal/RCS/lucas.cal,v $
+ * @(#) $Revision: 30.2 $
+ * @(#) $Id: lucas.cal,v 30.2 2013/09/27 08:58:46 chongo Exp $
+ * @(#) $Source: /usr/local/src/bin/calc/cal/RCS/lucas.cal,v $
  *
  * Under source code control:	1990/05/03 16:49:51
  * File existed as early as:	1990
@@ -442,7 +442,7 @@ lucas(h, n)
  * See the function gen_v1() for details on the value of v(1).
  *
  * input:
- *	h	- h as in h*2^n-1	(h mod 2 != 0)
+ *	h	- h as in h*2^n-1
  *	n	- n as in h*2^n-1
  *	v1	- gen_v1(h,n)		(see function below)
  *
@@ -475,13 +475,6 @@ gen_u0(h, n, v1)
 		quit "bogus arg: v1 is <= 0";
 	}
 
-	/*
-	 * enforce the h mod rules
-	 */
-	if (h%2 == 0) {
-		quit "h must not be even";
-	}
-
 	/*
 	 * enforce the h > 0 and n >= 2 rules
 	 */

cal/lucas_chk.cal

@@ -19,7 +19,7 @@
  *
  * @(#) $Revision: 30.1 $
  * @(#) $Id: lucas_chk.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/cmd/calc/cal/RCS/lucas_chk.cal,v $
+ * @(#) $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

@@ -19,7 +19,7 @@
  *
  * @(#) $Revision: 30.1 $
  * @(#) $Id: lucas_tbl.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/cmd/calc/cal/RCS/lucas_tbl.cal,v $
+ * @(#) $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

cal/mersenne.cal

@@ -21,7 +21,7 @@
  *
  * @(#) $Revision: 30.1 $
  * @(#) $Id: mersenne.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/cmd/calc/cal/RCS/mersenne.cal,v $
+ * @(#) $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

@@ -19,7 +19,7 @@
  *
  * @(#) $Revision: 30.1 $
  * @(#) $Id: mfactor.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/cmd/calc/cal/RCS/mfactor.cal,v $
+ * @(#) $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

@@ -19,7 +19,7 @@
  *
  * @(#) $Revision: 30.1 $
  * @(#) $Id: mod.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/cmd/calc/cal/RCS/mod.cal,v $
+ * @(#) $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

@@ -19,7 +19,7 @@
  *
  * @(#) $Revision: 30.1 $
  * @(#) $Id: natnumset.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/cmd/calc/cal/RCS/natnumset.cal,v $
+ * @(#) $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

@@ -19,7 +19,7 @@
  *
  * @(#) $Revision: 30.1 $
  * @(#) $Id: pell.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/cmd/calc/cal/RCS/pell.cal,v $
+ * @(#) $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

@@ -19,7 +19,7 @@
  *
  * @(#) $Revision: 30.1 $
  * @(#) $Id: pi.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/cmd/calc/cal/RCS/pi.cal,v $
+ * @(#) $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

@@ -19,7 +19,7 @@
  *
  * @(#) $Revision: 30.1 $
  * @(#) $Id: pix.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/cmd/calc/cal/RCS/pix.cal,v $
+ * @(#) $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

@@ -19,7 +19,7 @@
  *
  * @(#) $Revision: 30.1 $
  * @(#) $Id: pollard.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/cmd/calc/cal/RCS/pollard.cal,v $
+ * @(#) $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

@@ -19,7 +19,7 @@
  *
  * @(#) $Revision: 30.1 $
  * @(#) $Id: poly.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/cmd/calc/cal/RCS/poly.cal,v $
+ * @(#) $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

@@ -19,7 +19,7 @@
  *
  * @(#) $Revision: 30.1 $
  * @(#) $Id: prompt.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/cmd/calc/cal/RCS/prompt.cal,v $
+ * @(#) $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

@@ -19,7 +19,7 @@
  *
  * @(#) $Revision: 30.1 $
  * @(#) $Id: psqrt.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/cmd/calc/cal/RCS/psqrt.cal,v $
+ * @(#) $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

@@ -22,7 +22,7 @@
  *
  * @(#) $Revision: 30.1 $
  * @(#) $Id: qtime.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/cmd/calc/cal/RCS/qtime.cal,v $
+ * @(#) $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

@@ -17,9 +17,9 @@
  * 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/cmd/calc/cal/RCS/quat.cal,v $
+ * @(#) $Revision: 30.2 $
+ * @(#) $Id: quat.cal,v 30.2 2013/08/11 08:41:38 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 +55,8 @@ 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

@@ -19,7 +19,7 @@
  *
  * @(#) $Revision: 30.1 $
  * @(#) $Id: randbitrun.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/cmd/calc/cal/RCS/randbitrun.cal,v $
+ * @(#) $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

@@ -19,7 +19,7 @@
  *
  * @(#) $Revision: 30.1 $
  * @(#) $Id: randmprime.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/cmd/calc/cal/RCS/randmprime.cal,v $
+ * @(#) $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

@@ -19,7 +19,7 @@
  *
  * @(#) $Revision: 30.1 $
  * @(#) $Id: randombitrun.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/cmd/calc/cal/RCS/randombitrun.cal,v $
+ * @(#) $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

@@ -19,7 +19,7 @@
  *
  * @(#) $Revision: 30.1 $
  * @(#) $Id: randomrun.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/cmd/calc/cal/RCS/randomrun.cal,v $
+ * @(#) $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

@@ -19,7 +19,7 @@
  *
  * @(#) $Revision: 30.1 $
  * @(#) $Id: randrun.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/cmd/calc/cal/RCS/randrun.cal,v $
+ * @(#) $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

@@ -17,9 +17,9 @@
  * 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/cmd/calc/cal/RCS/regress.cal,v $
+ * @(#) $Revision: 30.12 $
+ * @(#) $Id: regress.cal,v 30.12 2013/09/02 02:32:55 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
@@ -768,6 +768,8 @@ 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 +1399,8 @@ 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 +1447,12 @@ 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 +1469,14 @@ 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(_ == 49,			    '1292: _ == 49');
-	vrfy(__ == 63,			    '1293: __ == 63');
-	vrfy(__a == 23209,		    '1294: __a == 23209');
+	vrfy(_a == 27,			    '1295: _a == 27');
+	vrfy(_ == 49,			    '1296: _ == 49');
+	vrfy(__ == 63,			    '1297: __ == 63');
+	vrfy(__a == 23209,		    '1298: __a == 23209');
 
-	print "1295: Ending _test_underscore";
+	print "1299: Ending _test_underscore";
 }
 print '020: parsed _test_underscore';
 
@@ -1509,8 +1517,10 @@ 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[[rsearch(a,"spider")]] == "spider", '1315: a[[rsearch(a,"spider")]] == "spider"');
+	vrfy(a["curds","whey"] == "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 +4902,8 @@ 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 +5038,7 @@ 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 +6517,8 @@ 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 +6883,8 @@ 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 +7927,137 @@ 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
  *

cal/repeat.cal

@@ -19,7 +19,7 @@
  *
  * @(#) $Revision: 30.1 $
  * @(#) $Id: repeat.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/cmd/calc/cal/RCS/repeat.cal,v $
+ * @(#) $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

@@ -17,7 +17,7 @@
  *
  * @(#) $Revision: 30.2 $
  * @(#) $Id: screen.cal,v 30.2 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/cmd/calc/cal/RCS/screen.cal,v $
+ * @(#) $Source: /usr/local/src/bin/calc/cal/RCS/screen.cal,v $
  *
  * This file is not covered under version 2.1 of the GNU LGPL.
  *

cal/seedrandom.cal

@@ -19,7 +19,7 @@
  *
  * @(#) $Revision: 30.1 $
  * @(#) $Id: seedrandom.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/cmd/calc/cal/RCS/seedrandom.cal,v $
+ * @(#) $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

@@ -19,7 +19,7 @@
  *
  * @(#) $Revision: 30.1 $
  * @(#) $Id: set8700.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/cmd/calc/cal/RCS/set8700.cal,v $
+ * @(#) $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

@@ -19,7 +19,7 @@
 ##
 ## @(#) $Revision: 30.1 $
 ## @(#) $Id: set8700.line,v 30.1 2007/03/16 11:09:54 chongo Exp $
-## @(#) $Source: /usr/local/src/cmd/calc/cal/RCS/set8700.line,v $
+## @(#) $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

@@ -17,9 +17,9 @@
  * 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/cmd/calc/cal/RCS/solve.cal,v $
+ * @(#) $Revision: 30.3 $
+ * @(#) $Id: solve.cal,v 30.3 2013/08/11 08:41:38 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 +52,8 @@ 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 +1,502 @@
+/*
+ * 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.
+ *
+ * @(#) $Revision: 30.4 $
+ * @(#) $Id: statistics.cal,v 30.4 2013/08/18 20:01:53 chongo Exp $
+ * @(#) $Source: /usr/local/src/bin/calc/cal/RCS/statistics.cal,v $
+ *
+ * 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

@@ -19,7 +19,7 @@
  *
  * @(#) $Revision: 30.1 $
  * @(#) $Id: sumsq.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/cmd/calc/cal/RCS/sumsq.cal,v $
+ * @(#) $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

@@ -19,7 +19,7 @@
  *
  * @(#) $Revision: 30.1 $
  * @(#) $Id: sumtimes.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/cmd/calc/cal/RCS/sumtimes.cal,v $
+ * @(#) $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

@@ -19,7 +19,7 @@
  *
  * @(#) $Revision: 30.1 $
  * @(#) $Id: surd.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/cmd/calc/cal/RCS/surd.cal,v $
+ * @(#) $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

@@ -19,7 +19,7 @@
  *
  * @(#) $Revision: 30.1 $
  * @(#) $Id: test1700.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/cmd/calc/cal/RCS/test1700.cal,v $
+ * @(#) $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

@@ -19,7 +19,7 @@
  *
  * @(#) $Revision: 30.1 $
  * @(#) $Id: test2300.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/cmd/calc/cal/RCS/test2300.cal,v $
+ * @(#) $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

@@ -19,9 +19,9 @@
  * 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/cmd/calc/cal/RCS/test2600.cal,v $
+ * @(#) $Revision: 30.3 $
+ * @(#) $Id: test2600.cal,v 30.3 2013/08/11 08:41:38 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 +91,8 @@ 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 +134,8 @@ 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 +180,8 @@ 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 +238,8 @@ 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

@@ -19,9 +19,9 @@
  * 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/cmd/calc/cal/RCS/test2700.cal,v $
+ * @(#) $Revision: 30.2 $
+ * @(#) $Id: test2700.cal,v 30.2 2013/08/11 08:41:38 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 +127,8 @@ 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

@@ -21,7 +21,7 @@
  *
  * @(#) $Revision: 30.1 $
  * @(#) $Id: test3100.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/cmd/calc/cal/RCS/test3100.cal,v $
+ * @(#) $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

@@ -21,7 +21,7 @@
  *
  * @(#) $Revision: 30.1 $
  * @(#) $Id: test3300.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/cmd/calc/cal/RCS/test3300.cal,v $
+ * @(#) $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

@@ -21,7 +21,7 @@
  *
  * @(#) $Revision: 30.1 $
  * @(#) $Id: test3400.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/cmd/calc/cal/RCS/test3400.cal,v $
+ * @(#) $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

@@ -21,7 +21,7 @@
  *
  * @(#) $Revision: 30.1 $
  * @(#) $Id: test3500.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/cmd/calc/cal/RCS/test3500.cal,v $
+ * @(#) $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

@@ -19,9 +19,9 @@
  * 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/cmd/calc/cal/RCS/test4000.cal,v $
+ * @(#) $Revision: 30.2 $
+ * @(#) $Id: test4000.cal,v 30.2 2013/08/11 08:41:38 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 +199,8 @@ 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 +307,8 @@ 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

@@ -21,7 +21,7 @@
  *
  * @(#) $Revision: 30.1 $
  * @(#) $Id: test4100.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/cmd/calc/cal/RCS/test4100.cal,v $
+ * @(#) $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

@@ -21,7 +21,7 @@
  *
  * @(#) $Revision: 30.1 $
  * @(#) $Id: test4600.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/cmd/calc/cal/RCS/test4600.cal,v $
+ * @(#) $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

@@ -21,7 +21,7 @@
  *
  * @(#) $Revision: 30.1 $
  * @(#) $Id: test5100.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/cmd/calc/cal/RCS/test5100.cal,v $
+ * @(#) $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

@@ -21,7 +21,7 @@
  *
  * @(#) $Revision: 30.1 $
  * @(#) $Id: test5200.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/cmd/calc/cal/RCS/test5200.cal,v $
+ * @(#) $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

@@ -19,7 +19,7 @@
  *
  * @(#) $Revision: 30.1 $
  * @(#) $Id: test8400.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/cmd/calc/cal/RCS/test8400.cal,v $
+ * @(#) $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

@@ -19,9 +19,9 @@
  * 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/cmd/calc/cal/RCS/test8500.cal,v $
+ * @(#) $Revision: 30.2 $
+ * @(#) $Id: test8500.cal,v 30.2 2013/08/11 08:41:38 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 +134,8 @@ 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
- * test, etc.
+ * stored in the list L_8500.  L_8500[0], L_8500[1], L_8500[2] are a, b,
+ * rnd for the first* test, etc.
  */
 define divmod_8500(N = 10, M1 = 2^128, M2 = 2^64, testnum = 0)
 {

cal/test8600.cal

@@ -21,7 +21,7 @@
  *
  * @(#) $Revision: 30.1 $
  * @(#) $Id: test8600.cal,v 30.1 2007/03/16 11:09:54 chongo Exp $
- * @(#) $Source: /usr/local/src/cmd/calc/cal/RCS/test8600.cal,v $
+ * @(#) $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

cal/toomcook.cal

@@ -0,0 +1,362 @@
+/*
+ * toomcook - implementation of Toom-Cook(3,4) multiplication algorithm
+ *
+ * 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.
+ *
+ * @(#) $Revision: 30.4 $
+ * @(#) $Id: toomcook.cal,v 30.4 2013/08/18 20:01:53 chongo Exp $
+ * @(#) $Source: /usr/local/src/bin/calc/cal/RCS/toomcook.cal,v $
+ *
+ * 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);
+
+
+/* */
+define toomcook3(a,b){
+  local alen blen  a0 a1 a2  b0 b1 b2 m ret sign mask;
+  local S0 S1 S2 S3 S4 T1 T2;
+
+  if(!isint(a) || !isint(b))
+      return newerror("toomcook3(a,b): a and/or b is not an integer");
+
+  alen = digits(a,2);
+  blen = digits(b,2);
+
+  sign = sgn(a) * sgn(b);
+  /* sgn(x) returns 0 if x = 0 */
+  if(sign == 0) return 0;
+
+  m = min(alen,blen)//3;
+  mask = ~-(1<<m);
+
+  /*
+    Cut-off at about 4,000 dec. digits
+    TODO: check
+  */
+  if(isdefined("test8900")){
+    if(m < 20) return a*b;
+  }
+  else{
+    if(m < 4096 ) return a*b;
+  }
+  a = abs(a);
+  b = abs(b);
+
+  a0 = a & mask;
+  a1 = (a>>m) & mask;
+  a2 = (a>>(2*m));
+
+  b0 =  b         & mask;
+  b1 = (b>>m)     & mask;
+  b2 = (b>>(2*m));
+
+  /*
+    Zimmermann
+  */
+
+  S0 = toomcook3(a0 , b0);
+  S1 = toomcook3((a2+a1+a0) , (b2+b1+b0));
+  S2 = toomcook3(((a2<<2)+(a1<<1)+a0) , ((b2<<2)+(b1<<1)+b0));
+  S3 = toomcook3((a2-a1+a0) , (b2-b1+b0));
+  S4 = toomcook3(a2,b2);
+  T1 = (S3<<1) + S2;
+  T1 /= 3;
+  T1 += S0;
+  T1 >>= 1;
+  T1 -= S4<<1;
+  T2 = (S1 + S3)>>1;
+  S1 -= T1;
+  S2 = T2 - S0 - S4;
+  S3 = T1 - T2;
+
+  ret =  (S4<<(4*m)) + (S3<<(3*m)) + (S2<<(2*m)) + (S1<<(1*m)) + S0;
+
+
+  ret = sign *ret;
+
+  return ret;
+}
+
+define toomcook3square(a){
+  local alen  a0 a1 a2  m tmp tmp2 ret sign S0 S1 S2 S3 S4 T1 mask;
+
+  if(!isint(a))return newerror("toomcook3square(a): a is not integer");
+
+  alen = digits(a,2);
+
+  sign = sgn(a) * sgn(a);
+  if(sign == 0) return 0;
+
+  m = alen//3;
+  mask = ~-(1<<m);
+  /*
+    Cut-off at about 5,000 dec. digits
+    TODO: check
+  */
+
+  if(isdefined("test8900")){
+    if(m < 20) return a^2;
+  }
+  else{
+    if(m < 5000 ) return a^2;
+  }
+
+  a = abs(a);
+
+  a0 = a & mask;
+  a1 = (a>>m) & mask;
+  a2 = (a>>(2*m));
+
+  /*
+   Bodrato/Zanoni
+   */
+  S0 = toomcook3square(a0);
+  S1 = toomcook3square(a2+a1+a0);
+  S2 = toomcook3square(a2-a1+a0);
+  S3 = toomcook3(a1<<1,a2);
+  S4 = toomcook3square(a2);
+
+  T1 = (S1 + S2)>>1;
+  S1 = S1 - T1 - S3;
+  S2 = T1 - S4 -S0;
+
+
+  S1 = S1<<(1*m);
+  S2 = S2<<(2*m);
+  S3 = S3<<(3*m);
+  S4 = S4<<(4*m);
+
+  ret = S0 + S1 + S2 + S3 + S4;
+  ret = sign *ret;
+
+  return ret;
+}
+
+define toomcook4(a,b)
+{
+
+  local  a0 a1 a2 a3 b0 b1 b2 b3 b4 ret tmp tmp2 tmp3 sign;
+  local  m alen blen mask;
+  local w1, w2, w3, w4, w5, w6, w7;
+
+  if(!isint(a) || !isint(b))
+    return newerror("toomcook4(a,b): a and/or b is not integer");
+
+  alen = digits(a,2);
+  blen = digits(b,2);
+
+  sign = sgn(a) * sgn(b);
+
+  if(sign == 0) return 0;
+
+  m = min(alen//4,blen//4);
+  mask = ~-(1<<m);
+
+  if(isdefined("test8900")){
+    if(m < 100) return toomcook3(a,b);
+  }
+  else{
+    if(m < 256*3072) return toomcook3(a,b);
+  }
+
+  a = abs(a);
+  b = abs(b);
+
+
+  a0 = a & mask;
+  a1 = (a>>m) & mask;
+  a2 = (a>>(2*m)) & mask;
+  a3 = (a>>(3*m));
+
+  b0 =  b         & mask;
+  b1 = (b>>m)     & mask;
+  b2 = (b>>(2*m)) & mask;
+  b3 = (b>>(3*m));
+
+  /*
+    Bodrato / Zanoni
+  */
+
+  w3 = a3 + (a1 + (a2 + a0));
+  w7 = b3 + (b1 + (b2 + b0));
+
+  w4 = -a3 + (-a1 + (a2 + a0));
+  w5 = -b3 + (-b1 + (b2 + b0));
+
+  w3 = toomcook4(w3, w7);
+  w4 = toomcook4(w4, w5);
+
+  w5 = a3 + ((a1<<2) + ((a2<<1) + (a0<<3)));
+  w2 = b3 + ((b1<<2) + ((b2<<1) + (b0<<3)));
+
+  w6 = -a3 + (-(a1<<2) + ((a2<<1) + (a0<<3)));
+  w7 = -b3 + (-(b1<<2) + ((b2<<1) + (b0<<3)));
+
+  w5 = toomcook4(w5, w2);
+  w6 = toomcook4(w6, w7);
+
+
+  w2 = (a3<<3) + ((a1<<1) + ((a2<<2) + a0));
+  w7 = (b3<<3) + ((b1<<1) + ((b2<<2) + b0));
+
+
+  w2 = toomcook4(w2, w7);
+
+  w1 = toomcook4(a3, b3);
+  w7 = toomcook4(a0, b0);
+
+  w2 = w2 + w5;
+  w6 = w5 - w6;
+  w4 = w3 - w4;
+  w5 = w5 - w1;
+  w5 -= w7 << 6;
+  w4 = w4>>1;
+  w3 = w3 - w4;
+  w5 = w5<<1;
+  w5 = w5 - w6;
+  w2 -= w3 * 65;
+  w3 = w3 - w7;
+  w3 = w3 - w1;
+  w2 += w3 * 45;
+  w5 -= w3<<3;
+  w5 = w5//24;
+  w6 =  w6 - w2;
+  w2 -= w4<<4;
+  w2 = w2//18;
+  w3 = w3 - w5;
+  w4 = w4 - w2;
+  w6 += w2 * 30;
+  w6 = w6//60;
+  w2 = w2 - w6;
+
+
+  ret = w7 + (w6<<m) + (w5<<(2*m)) + (w4<<(3*m))+ (w3<<(4*m))+
+        (w2<<(5*m))+ (w1<<(6*m));
+
+  ret = sign *ret;
+
+  return ret;
+}
+
+define toomcook4square(a){
+  local  a0 a1 a2 a3 ret S0 S1 S2 S3 S4 S5 S6 S7 tmp tmp2 tmp3;
+  local  sign m alen mask;
+  local T0 T1 T2 T3 T4 T5 T6 T7 T8;
+
+  if(!isint(a) )return newerror("toomcook3square(a): a is not integer");
+
+  alen = digits(a,2);
+
+  sign = sgn(a) * sgn(a);
+  /* sgn(x) returns 0 if x = 0 */
+  if(sign == 0) return 0;
+
+  m = (alen)//4;
+  mask = ~-( 1 << m );
+
+  /*
+    cut-off at about 2 mio. dec. digits
+    TODO: check!
+  */
+
+  if(isdefined("test8900")){
+    if(m < 100) return toomcook3square(a);
+  }
+  else{
+    if(m < 512*3072) return toomcook3square(a);
+  }
+
+  a = abs(a);
+
+  a0 = a          & mask;
+  a1 = (a>>m)     & mask;
+  a2 = (a>>(2*m)) & mask;
+  a3 = (a>>(3*m)) ;
+
+  /*
+    Bodrato / Zanoni
+  */
+
+  S1 = toomcook4square(a0);
+  S2 = toomcook4(a0<<1,a1);
+  S3 = toomcook4((a0 + a1 - a2 - a3 ) , (a0 - a1 - a2 + a3 ));
+  S4 = toomcook4square(a0 + a1 + a2 + a3 );
+  S5 = toomcook4( (a0 - a2 )<<1 , (a1 - a3 ));
+  S6 = toomcook4(a3<<1 , a2);
+  S7 = toomcook4square(a3);
+
+  T1 = S3 + S4;
+  T2 = (T1 + S5 )>>1;
+  T3 = S2 + S6;
+  T4 = T2 - T3;
+  T5 = T3 - S5;
+  T6 = T4 - S3;
+  T7 = T4 - S1;
+  T8 = T6 - S7;
+
+  ret =   (S7<<(6*m)) + (S6<<(5*m)) + (T7<<(4*m))
+        + (T5<<(3*m)) + (T8<<(2*m)) + (S2<<(1*m))  + S1;
+
+  ret = sign *ret;
+
+  return ret;
+}
+
+/*
+  TODO: Implement the asymmetric variations
+*/
+
+/*
+  produce_long_random_number(n) returns large pseudorandom numbers. Really large
+  numbers, e.g.:
+      produce_long_random_number(16)
+  is ca 4,128,561 bits (ca 1,242,821 dec. digits) large. Exact length is not
+  predeterminable because of the chaotic output of the function random().
+*/
+define __CZ__produce_long_random_number(n)
+{
+  local ret k;
+  ret = 1;
+  if(!isint(n) || n<1)
+    return newerror("__CZ__produce_long_random_number(n): "
+    		    "n is not an integer >=1");
+  for(k=0;k<n;k++){
+    ret += random();
+    ret  = toomcook4square(ret);
+  }
+  return ret;
+}
+
+
+/*
+ * restore internal function from resource debugging
+ * report important interface functions
+ */
+config("resource_debug", resource_debug_level),;
+if (config("resource_debug") & 3) {
+    print "toomcook3(a,b)";
+    print "toomcook3square(a)";
+    print "toomcook4(a,b)";
+    print "toomcook4square(a)";
+}