Release v2.14.0.6

The following are the changes in this release:

    Fixed typo in cal/statistics.cal thanks to a report by <GitHub user
    dennisaldea>.

    Fixed an old Windoz pun in README.WINDOWS as requested by <GitHub
    user marcodegio>.

    Fixed a really obscure bug in the internal initconstants()
    function of const.c that has been sitting for over 31 years!

	We are amazed that nobody has encountered this bug before
	now.  Nevertheless, our very extensive regression and
	multi-architecture testing found the bug.  Now, after all
	those years, it is fixed.

    Fixed issues identied by the default CodeUL GitHub security code scan:

	Wrong type of arguments to printf in have_fpos_pos.c
	Multiplication result converted to larger type in zfunc.c

.github/workflows/codeql-analysis.yml

@@ -0,0 +1,71 @@
+# For most projects, this workflow file will not need changing; you simply need
+# to commit it to your repository.
+#
+# You may wish to alter this file to override the set of languages analyzed,
+# or to provide custom queries or build logic.
+#
+# ******** NOTE ********
+# We have attempted to detect the languages in your repository. Please check
+# the `language` matrix defined below to confirm you have the correct set of
+# supported CodeQL languages.
+#
+name: "CodeQL"
+
+on:
+  push:
+    branches: [ master ]
+  pull_request:
+    # The branches below must be a subset of the branches above
+    branches: [ master ]
+  schedule:
+    - cron: '41 1 * * 6'
+
+jobs:
+  analyze:
+    name: Analyze
+    runs-on: ubuntu-latest
+    permissions:
+      actions: read
+      contents: read
+      security-events: write
+
+    strategy:
+      fail-fast: false
+      matrix:
+        language: [ 'cpp' ]
+        # CodeQL supports [ 'cpp', 'csharp', 'go', 'java', 'javascript', 'python' ]
+        # Learn more:
+        # https://docs.github.com/en/free-pro-team@latest/github/finding-security-vulnerabilities-and-errors-in-your-code/configuring-code-scanning#changing-the-languages-that-are-analyzed
+
+    steps:
+    - name: Checkout repository
+      uses: actions/checkout@v2
+
+    # Initializes the CodeQL tools for scanning.
+    - name: Initialize CodeQL
+      uses: github/codeql-action/init@v1
+      with:
+        languages: ${{ matrix.language }}
+        # If you wish to specify custom queries, you can do so here or in a config file.
+        # By default, queries listed here will override any specified in a config file.
+        # Prefix the list here with "+" to use these queries and those in the config file.
+        # queries: ./path/to/local/query, your-org/your-repo/queries@main
+
+    # Autobuild attempts to build any compiled languages  (C/C++, C#, or Java).
+    # If this step fails, then you should remove it and run the build manually (see below)
+    - name: Autobuild
+      uses: github/codeql-action/autobuild@v1
+
+    # ℹ️ Command-line programs to run using the OS shell.
+    # 📚 https://git.io/JvXDl
+
+    # ✏️ If the Autobuild fails above, remove it and uncomment the following three lines
+    #    and modify them (or add more) to build your code if your project
+    #    uses a compiled language
+
+    #- run: |
+    #   make bootstrap
+    #   make release
+
+    - name: Perform CodeQL Analysis
+      uses: github/codeql-action/analyze@v1

CHANGES

@@ -36,6 +36,180 @@ The following are the changes from calc version 2.14.0.0 to date:
     a call to base2(1000) would make calc unstable and likely to
     dump core.
 
+    Added builtin functions to convert between degrees, radians
+    and gradians:
+
+	d2r(deg)	- given degrees returns radians
+	g2r(grad)	- given gradians returns radians
+
+	r2d(rad)	- given radians returns degrees
+	g2d(grad)	- given gradians returns degrees
+
+	r2g(rad)	- given radians returns gradians
+	d2g(deg)	- given degrees returns gradians
+
+    Add 6 functions take a 2nd optional epsilon argument.
+    For d2r(deg, ep), r2d(rad, ep), the optional 2nd epsilon argument controls
+    the precision of the internal constant pi/180.
+    For g2r(grad, ep), r2g(rad, ep), the optional 2nd epsilon argument controls
+    the precision of the internal constant pi/200.
+    The optional 2nd argument is ignored by g2d(grad, ep) and d2g(deg, ep).
+
+    The clean and clobber makefile rules no longer list custom/Makefile
+    as a dependecy.
+
+    Unfortunately due to the complex dependency issues between
+    Makefile, Makefile.ship and custom/Makefile, parallel GNU make
+    is NOT recommended.  Sorry (tm Canada) :)
+
+    The clean and clobber makefile rules no longer list custom/Makefile
+    as a dependency.
+
+    Unfortunately due to the complex dependency issues between
+    Makefile, Makefile.ship and custom/Makefile, parallel GNU make
+    is NOT recommended.  Sorry (tm Canada) :)
+
+    Fixed a few typos in CHANGES.
+
+    As a side note: We stayed v2.13.x was kept for only a short time.
+    The move to 2.14.x was motivated by non-compatible changes due to
+    the default order of CALCRC, plus some new builtin functions.
+
+    More changes are likely, so we might see another v2.14.0.x release
+    before things are declared "recommended stable".
+
+    Not that we want to discourage people from trying v2.14.0, you should
+    try it.  We just want things to become stable and well field tested
+    before we reach the "recommended stable" release state.
+
+    Added builtin functions to convert between degrees and
+    degrees, minutes and seconds under the config("mod")
+    round rules:
+
+	d2dms(degs, d, m, s [,rnd]) - given degs, compute d, m, s
+	d2dm(degs, d, m [,rnd]) - given degs, compute d, m
+
+	See help/d2dms and help/d2dm.
+
+    Example:
+
+	; print d2dms(360.321,deg=,min=,sec=), deg, min, sec;
+	0.321 0 19 15.6
+
+	; print d2dm(360.321,deg=,min=), deg, min;
+	0.321 0 19.26
+
+    Added builtin functions to convert between gradians and
+    gradians, minutes and seconds under the config("mod")
+    round rules:
+
+	g2gms(grads, g, m, s [,rnd]) - given grads, compute g, m, s
+	g2gm(grads, g, m [,rnd]) - given grads, compute g, m
+
+	See help/g2gms and help/g2gm.
+
+    Example:
+
+	; print g2gms(400.321,grad=,min=,sec=), grad, min, sec;
+	0.321 0 19 15.6
+
+	; print g2gm(400.321,grad=,min=), grad, min;
+	0.321 0 19.26
+
+    Added builtin functions to convert between hours and
+    hours, minutes and seconds under the config("mod")
+    round rules:
+
+	h2hms(hours, h, m, s [,rnd]) - given hours, compute h, m, s
+	h2hm(hours, h, m [,rnd]) - given hours, compute h, m
+
+	See help/h2hms and help/h2hm.
+
+    Example:
+
+	; print h2hms(24.321,hour=,min=,sec=), hour, min, sec;
+	0.321 0 19 15.6
+
+	; print h2hm(24.321,hour=,min=), hour, min;
+	0.321 0 19.26
+
+    Renumbered regression tests 3408 thru 3437, to 9102 thru 9131.
+
+    Updated Added hms.cal resource file to use h2hms() builtin.
+    Updated Added dms.cal resource file to use d2dms() builtin.
+
+    Fix minor typo in help/mod SYNOPSIS.
+    Fix minor typo in help/quo SYNOPSIS.
+
+    Added a few more examples to help/strcmp.
+
+    Added builtin functions to convert between degrees, minutes and
+    seconds and degrees under the config("mod") round rules:
+
+	dms2d(d, m, s [,rnd]) - convert deg, min, and secs to deg
+	dm2d(d, m [,rnd]) - convert deg, min to deg
+
+	See help/dms2d and help/dm2d.
+
+    Example:
+
+	; print dms2d(12, 20, 44.16);
+	12.3456
+
+	; print dm2d(3601, -25.5594);
+	0.57401
+
+    Added builtin functions to convert between gradians, minutes and
+    seconds and gradians under the config("mod") round rules:
+
+	gms2g(g, m, s [,rnd]) - convert grad, min, and secs to grad
+	gm2g(g, m [,rnd]) - convert grad and min to grad
+
+	See help/g2gms and help/g2gm.
+
+    Example:
+
+	; print gms2g(12, 20, 44.16);
+	12.3456
+
+	; print gm2g(4001, -25.5594);
+	0.57401
+
+    Added builtin functions to convert between hours, minutes and
+    seconds and hours under the config("mod") round rules:
+
+	hms2h(h, m, s [,rnd]) - convert hours, min, and secs to hours
+	hm2h(h, m [,rnd]) - convert hours, min to hours
+
+	See help/hms2h and help/hm2h.
+
+    Example:
+
+	; print hms2h(12, 20, 44.16);
+	12.3456
+
+	; print hm2h(241, -25.5594);
+	0.57401
+
+    Fixed typo in cal/statistics.cal thanks to a report by <GitHub user
+    dennisaldea>.
+
+    Fixed an old Windoz pun in README.WINDOWS as requested by <GitHub
+    user marcodegio>.
+
+    Fixed a really obscure bug in the internal initconstants()
+    function of const.c that has been sitting for over 31 years!
+
+	We are amazed that nobody has encountered this bug before
+	now.  Nevertheless, our very extensive regression and
+	multi-architecture testing found the bug.  Now, after all
+	those years, it is fixed.
+
+    Fixed issues identied by the default CodeUL GitHub security code scan:
+
+	Wrong type of arguments to printf in have_fpos_pos.c
+	Multiplication result converted to larger type in zfunc.c
+
 
 The following are the changes from calc version 2.13.0.1 to 2.13.0.1:
 
@@ -74,7 +248,7 @@ The following are the changes from calc version 2.13.0.0 to 2.13.0.0:
 
     Fixed typo (missing quotes) in the env rule.
 
-    Fixed intendation problem in CHANGES.
+    Fixed indentation problem in CHANGES.
 
     Combined 2.12.9.1 changes into the 2.12.8.2 to 2.12.9.0
     range, and thus renamed the range to 2.12.8.2 to 2.12.9.1.
@@ -110,7 +284,7 @@ The following are the changes from calc version 2.13.0.0 to 2.13.0.0:
 	#!/usr/local/bin/calc -f
 	...
 
-    It is common that -q be usde with a calc script, so assuming the
+    It is common that -q be used with a calc script, so assuming the
     same /usr/local/bin/calc path:
 
 	#!/usr/local/bin/calc -q -f
@@ -1360,12 +1534,12 @@ The following are the changes from calc version 2.12.1.10 to 2.12.2:
     The custom/Makefile is now constructed from 3 parts: custom/Makefile.head,
     the host target section in Makefile, and the custom/Makefile.tail.
 
-    The top level Makefile and the custom/Makefile require a GNU Make
+    The top level Makefile and the custom/Makefile require a GNU make
     (such as gmake) or an equivalently advanced make.  On many targets,
     the default make is sufficient.  On FreeBSD for example, one must
     use gmake instead of make.
 
-    If your target system does not have GNU Make (or equivalent), then
+    If your target system does not have GNU make (or equivalent), then
     you should try using the Makefile.simple and custom/Makefile.simple
     files:
 

HOWTO.INSTALL

@@ -2,6 +2,14 @@
 IMPORTANT: Please see the section at the bottom of this file for
 	   some important information on Makefiles used in calc.
 
+###################################################################
+# IMPORTANT: DO NOT run GNU make in parallel mode!!!		  #
+###################################################################
+# Unfortunately due to the complex dependency issues between	  #
+# Makefile, Makefile.ship and custom/Makefile, parallel GNU make  #
+# is NOT recommended.  Sorry (tm Canada) :)			  #
+###################################################################
+
 Installing calc from the bzip2-ed tarball in 4 easy steps:
 
     (0)  If your platform supports i686 RPMs, you may want to go to:

Makefile

@@ -35,6 +35,12 @@
 # calculator by David I. Bell with help/mods from others
 # Makefile by Landon Curt Noll
 
+# Unfortunately due to the complex dependency issues between
+# Makefile, Makefile.ship and custom/Makefile, parallel GNU make
+# is NOT recommended.  Sorry.
+#
+.NOTPARALLEL:
+
 # Try uname -s if the target was not already set on the make command line
 #
 ifeq ($(target),)

Makefile.ship

@@ -59,6 +59,13 @@ SHELL= /bin/sh
 
 
 #if 0	/* start of skip for non-Gnu makefiles */
+
+# Unfortunately due to the complex dependency issues between
+# Makefile, Makefile.ship and custom/Makefile, parallel GNU make
+# is NOT recommended.  Sorry.
+#
+.NOTPARALLEL:
+
 ##############################################################################
 #-=-=-=-=-=-=-=-=- Identify the target machine, if possible -=-=-=-=-=-=-=-=-#
 ##############################################################################
@@ -1198,7 +1205,7 @@ EXT=
 
 # The default calc versions
 #
-VERSION= 2.14.0.0
+VERSION= 2.14.0.6
 
 # Names of shared libraries with versions
 #
@@ -4831,7 +4838,7 @@ tags: ${CALCSRC} ${LIBSRC} ${H_SRC} ${BUILD_H_SRC} ${MAKE_FILE}
 	-${CTAGS} ${CALCSRC} ${LIBSRC} ${H_SRC} ${BUILD_H_SRC} 2>&1 | \
 	    ${GREP} -v 'Duplicate entry|Second entry ignored'
 
-clean: custom/Makefile
+clean:
 	${V} echo '=-=-=-=-= ${MAKE_FILE} start of $@ rule =-=-=-=-='
 	${RM} -f ${LIBOBJS}
 	${RM} -f ${CALCOBJS}
@@ -4852,6 +4859,7 @@ clean: custom/Makefile
 	cd custom; ${MAKE} -f Makefile ${CUSTOM_PASSDOWN} clean
 	${V} echo '=-=-=-=-= Back to the main Makefile for $@ rule =-=-=-=-='
 	${V} echo '=-=-=-=-= Invoking $@ rule for cscript =-=-=-=-='
+	${MAKE} custom/Makefile
 	cd cscript; ${MAKE} -f Makefile ${CSCRIPT_PASSDOWN} clean
 	${V} echo '=-=-=-=-= Back to the main Makefile for $@ rule =-=-=-=-='
 	${Q} echo remove files that are obsolete
@@ -4861,7 +4869,7 @@ clean: custom/Makefile
 	${RM} -f win32dll.h have_malloc.h math_error.h string.h string.c
 	${V} echo '=-=-=-=-= ${MAKE_FILE} end of $@ rule =-=-=-=-='
 
-clobber: clean custom/Makefile
+clobber: clean
 	${V} echo '=-=-=-=-= ${MAKE_FILE} start of $@ rule =-=-=-=-='
 	${RM} -f ${SAMPLE_TARGETS}
 	${RM} -f ${SAMPLE_STATIC_TARGETS}
@@ -4898,6 +4906,7 @@ clobber: clean custom/Makefile
 	${V} echo '=-=-=-=-= Back to the main Makefile for $@ rule =-=-=-=-='
 	${V} echo '=-=-=-=-= Invoking $@ rule for custom =-=-=-=-='
 	-${RM} -f custom/all; \
+	    ${MAKE} custom/Makefile; \
 	    cd custom; ${MAKE} -f Makefile ${CUSTOM_PASSDOWN} $@
 	${V} echo '=-=-=-=-= Back to the main Makefile for $@ rule =-=-=-=-='
 	${V} echo '=-=-=-=-= Invoking $@ rule for cscript =-=-=-=-='

README.WINDOWS

@@ -1,4 +1,4 @@
-Dear calc user on a Windoz based system,
+Dear calc user on a Windows based system,
 
 See the HOWTO.INSTALL file for information on how to build and install calc.
 See also the README file.

SECURITY.md

@@ -0,0 +1,21 @@
+# Security Policy
+
+## Supported Versions
+
+Use this section to tell people about which versions of your project are
+currently being supported with security updates.
+
+| Version | Supported          |
+| ------- | ------------------ |
+| 5.1.x   | :white_check_mark: |
+| 5.0.x   | :x:                |
+| 4.0.x   | :white_check_mark: |
+| < 4.0   | :x:                |
+
+## Reporting a Vulnerability
+
+Use this section to tell people how to report a vulnerability.
+
+Tell them where to go, how often they can expect to get an update on a
+reported vulnerability, what to expect if the vulnerability is accepted or
+declined, etc.

cal/dms.cal

@@ -352,24 +352,8 @@ define fixdms(a)
 	quit "attempt to fix a non dms object";
     }
 
-    /* force minutes to be integral */
-    a.min += frac(a.deg) * 60;
-    a.deg = int(a.deg);
-
-    /* force degrees to be integral */
-    a.sec += frac(a.min) * 60;
-    a.min = int(a.min);
-
-    /* carry excess seconds into minutes */
-    a.min += a.sec // 60;
-    a.sec %= 60;
-
-    /* carry excess minutes into degrees */
-    a.deg += a.min // 60;
-    a.min %= 60;
-
-    /* round degrees :-) */
-    a.deg %= 360;
+    /* use builtin d2dms function */
+    d2dms(a.deg + a.min/60 + a.sec/3600, a.deg, a.min, a.sec),;
 
     /* return normalized result */
     return a;

cal/hms.cal

@@ -352,24 +352,8 @@ define fixhms(a)
 	quit "attempt to fix a non hms object";
     }
 
-    /* force minutes to be integral */
-    a.min += frac(a.hour) * 60;
-    a.hour = int(a.hour);
-
-    /* force hours to be integral */
-    a.sec += frac(a.min) * 60;
-    a.min = int(a.min);
-
-    /* carry excess seconds into minutes */
-    a.min += a.sec // 60;
-    a.sec %= 60;
-
-    /* carry excess minutes into hours */
-    a.hour += a.min // 60;
-    a.min %= 60;
-
-    /* round hours by day */
-    a.hour %= 24;
+    /* use builtin h2hms function */
+    h2hms(a.hour + a.min/60 + a.sec/3600, a.hour, a.min, a.sec),;
 
     /* return normalized result */
     return a;

cal/regress.cal

@@ -775,7 +775,9 @@ 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.
+ * See test_functions() (test 700 - 1238) for other built-in function tests.
+ * See test_functions2() (test 9000 - 9063) for other built-in function tests.
+ * See test_functions3() (test 9100 - 9214) for other built-in function tests.
  */
 define test_functions()
 {
@@ -3400,9 +3402,11 @@ define test_trig()
 
 	print '3400: Beginning test_trig';
 
+	/* test 3401-3407 */
 	tnum = test3400(1, 3401);
+	vrfy(tnum == 3407,	'3407: tnum == 3407');
 
-	print tnum: ': Ending test_trig';
+	print '3438: Ending test_trig';
 }
 print '051: parsed test_trig()';
 
@@ -8165,6 +8169,8 @@ ecnt = 211;
  * Test more of the built-in functions.
  *
  * See test_functions() (test 700 - 1238) for other built-in function tests.
+ * See test_functions2() (test 9000 - 9063) for other built-in function tests.
+ * See test_functions3() (test 9100 - 9214) for other built-in function tests.
  */
 define test_functions2()
 {
@@ -8278,6 +8284,401 @@ print;
 return test_functions2();
 
 
+/*
+ * Test even more of the built-in functions.
+ *
+ * See test_functions() (test 700 - 1238) for other built-in function tests.
+ * See test_functions2() (test 9000 - 9063) for other built-in function tests.
+ * See test_functions3() (test 9100 - 9214) for other built-in function tests.
+ */
+define test_functions3()
+{
+	local d, m, s, g, h;
+
+	print '9101: Beginning test_functions3';
+
+	/* d2r & r2d */
+	vrfy(d2r(180) == pi(),
+		'9102: d2r(180) == pi()');
+	vrfy(d2r(180, 1e-100) == pi(1e-100),
+		'9103: d2r(180, 1e-100) == pi(1e-100)');
+	vrfy(r2d(pi()/2) == 90,
+		'9104: r2d(pi()/2) == 90');
+	vrfy(r2d(pi(1e-15)/2) == 14137166941154068500000/157079632679489661923,
+		'9105: r2d(pi(1e-15)/2) == ' +
+			'14137166941154068500000/157079632679489661923');
+	vrfy(r2d(d2r(40)) == 40,
+		'9106: r2d(d2r(40)) == 40');
+	vrfy(r2d(d2r(40,1e-90),1e-90) == 40,
+		'9107: r2d(d2r(40,1e-90),1e-90) == 40');
+	vrfy(d2r(180i) == 1i*pi(),
+		'9108: d2r(1808) == 1i*pi()');
+	vrfy(d2r(180i+90) == 1i*pi() + pi()/2,
+		'9109: d2r(180i+90) == 1i*pi() + pi()/2');
+	vrfy(r2d(d2r(40+40i)) == 40+40i,
+		'9110: r2d(d2r(40+40i)) == 40+40i');
+	vrfy(r2d(d2r(40+40i,1e-60),1e-60) == 40+40i,
+		'9111: r2d(d2r(40+40i,1e-60),1e-60) == 40+40i');
+
+	/* g2r & r2g */
+	vrfy(g2r(200) == pi(),
+		'9112: g2r(200) == pi()');
+	vrfy(g2r(200, 1e-100) == pi(1e-100),
+		'9113: g2r(180, 1e-100) == pi(1e-100)');
+	vrfy(r2g(pi()/2) == 100,
+		'9114: r2g(pi()/2) == 100');
+	vrfy(r2g(pi(1e-15)/2) == 15707963267948965000000/157079632679489661923,
+		'9115: r2g(pi(1e-15)/2) == ' +
+			'15707963267948965000000/157079632679489661923');
+	vrfy(r2g(g2r(40)) == 40,
+		'9116: r2g(g2r(40)) == 40');
+	vrfy(r2g(g2r(40,1e-90),1e-90) == 40,
+		'9117: r2g(g2r(40,1e-90),1e-90) == 40');
+	vrfy(g2r(200i) == 1i*pi(),
+		'9118: g2r(200i) == 1i*pi()');
+	vrfy(g2r(200i+150) == pi()*0.75 + 1i*pi(),
+		'9119: g2r(200i+150) == pi()*0.75 + 1i*pi()');
+	vrfy(r2g(g2r(40+40i)) == 40+40i,
+		'9120: r2g(g2r(40+40i)) == 40+40i');
+	vrfy(r2g(g2r(40+40i,1e-60),1e-60) == 40+40i,
+		'9121: r2g(g2r(40+40i,1e-60),1e-60) == 40+40i');
+
+	/* g2d & d2g */
+	vrfy(g2d(200) == 180,
+		'9122: g2d(200) == 180');
+	vrfy(g2d(200, 1e-100) == 180,
+		'9123: g2d(180, 1e-100) == 180');
+	vrfy(d2g(81) == 90,
+		'9124: d2g(81) == 90');
+	vrfy(d2g(pi(1e-15)/2) == 3141592653589793/1800000000000000,
+		'9125: d2g(pi(1e-15)/2) == 3141592653589793/1800000000000000');
+	vrfy(d2g(g2d(40)) == 40,
+		'9126: d2g(g2d(40)) == 40');
+	vrfy(d2g(g2d(40,1e-90),1e-90) == 40,
+		'9127: d2g(g2d(40,1e-90),1e-90) == 40');
+	vrfy(g2d(200i) == 180i,
+		'9128: g2d(200i) == 180i');
+	vrfy(g2d(200i+47) == 42.3 + 180i,
+		'9129: g2d(200i+47) == 42.3 + 180i');
+	vrfy(d2g(g2d(40+40i)) == 40+40i,
+		'9130: d2g(g2d(40+40i)) == 40+40i');
+	vrfy(d2g(g2d(40+40i,1e-90),1e-90) == 40+40i,
+		'9131: d2g(g2d(40+40i,1e-90),1e-90) == 40+40i');
+
+	/* d2dms */
+	vrfy(d2dms(12.3456,d,m,s) == 12.3456,
+		'9132: d2dms(12.3456,d,m,s) == 12.3456');
+	vrfy(d == 12,
+		'9133: d == 12');
+	vrfy(m == 20,
+		'9133: m == 20');
+	vrfy(s == 44.16,
+		'9134: s == 44.16');
+
+	vrfy(d2dms(1234.5678,d,m,s) == 154.5678,
+		'9135: d2dms(1234.5678,d,m,s) == 154.5678');
+	vrfy(d == 154,
+		'9136: d == 154');
+	vrfy(m == 34,
+		'9137: m == 34');
+	vrfy(s == 4.08,
+		'9138: s == 4.08');
+
+	vrfy(d2dms(-1234.5678,d,m,s) == 205.4322,
+		'9139: d2dms(-1234.5678,d,m,s) == 205.4322');
+	vrfy(d == 205,
+		'9140: d == 205');
+	vrfy(m == 25,
+		'9141: m == 25');
+	vrfy(s == 55.92,
+		'9142: s == 55.92');
+
+	vrfy(d2dms(360.321,d,m,s,1) == -359.679,
+		'9143: d2dms(360.321,d,m,s,1) == -359.679');
+	vrfy(d == -359,
+		'9144: d == -359');
+	vrfy(m == -40,
+		'9145: m == -40');
+	vrfy(s == -44.4,
+		'9146: s == -44.4');
+
+	/* d2dm */
+	vrfy(d2dm(12.3456,d,m) == 12.3456,
+		'9147: d2dm(12.3456,d,m) == 12.3456');
+	vrfy(d == 12,
+		'9148: d == 12');
+	vrfy(m == 20.736,
+		'9149: m == 20.736');
+
+	vrfy(d2dm(1234.5678,d,m) == 154.5678,
+		'9150: d2dm(1234.5678,d,m) == 154.5678');
+	vrfy(d == 154,
+		'9151: d == 154');
+	vrfy(m == 34.068,
+		'9152: m == 34.068');
+
+	vrfy(d2dm(-1234.5678,d,m) == 205.4322,
+		'9153: d2dm(-1234.5678,d,m) == 205.4322');
+	vrfy(d == 205,
+		'9154: d == 205');
+	vrfy(m == 25.932,
+		'9155: m == 25.932');
+
+	vrfy(d2dm(360.321,d,m,1) == -359.679,
+		'9156: d2dm(360.321,d,m,1) == -359.679');
+	vrfy(d == -359,
+		'9167: d == -359');
+	vrfy(m == -40.74,
+		'9158: m == -40.74');
+
+	/* g2gms */
+	vrfy(g2gms(12.3456,g,m,s) == 12.3456,
+		'9159: g2gms(12.3456,g,m,s) == 12.3456');
+	vrfy(g == 12,
+		'9133: g == 12');
+	vrfy(m == 20,
+		'9160: m == 20');
+	vrfy(s == 44.16,
+		'9161: s == 44.16');
+
+	vrfy(g2gms(1234.5678,g,m,s) == 34.5678,
+		'9162: g2gms(1234.5678,g,m,s) == 34.5678');
+	vrfy(g == 34,
+		'9163: g == 34');
+	vrfy(m == 34,
+		'9164: m == 34');
+	vrfy(s == 4.08,
+		'9165: s == 4.08');
+
+	vrfy(g2gms(-1234.5678,g,m,s) == 365.4322,
+		'9166: g2gms(-1234.5678,g,m,s) == 365.4322');
+	vrfy(g == 365,
+		'9167: g == 365');
+	vrfy(m == 25,
+		'9168: m == 25');
+	vrfy(s == 55.92,
+		'9169: s == 55.92');
+
+	vrfy(g2gms(400.321,g,m,s,1) == -399.679,
+		'9170: g2gms(400.321,g,m,s,1) == -399.679');
+	vrfy(g == -399,
+		'9171: g == -399');
+	vrfy(m == -40,
+		'9172: m == -40');
+	vrfy(s == -44.4,
+		'9173: s == -44.4');
+
+	/* g2gm */
+	vrfy(g2gm(12.3456,g,m) == 12.3456,
+		'9174: g2gm(12.3456,g,m) == 12.3456');
+	vrfy(g == 12,
+		'9175: g == 12');
+	vrfy(m == 20.736,
+		'9176: m == 20.736');
+
+	vrfy(g2gm(1234.5678,g,m) == 34.5678,
+		'9177: g2gm(1234.5678,g,m) == 34.5678');
+	vrfy(g == 34,
+		'9178: g == 34');
+	vrfy(m == 34.068,
+		'9179: m == 34.068');
+
+	vrfy(g2gm(-1234.5678,g,m) == 365.4322,
+		'9180: g2gm(-1234.5678,g,m) == 365.4322');
+	vrfy(g == 365,
+		'9181: g == 365');
+	vrfy(m == 25.932,
+		'9182: m == 25.932');
+
+	vrfy(g2gm(400.321,g,m,1) == -399.679,
+		'9183: g2gm(400.321,g,m,1) == -399.679');
+	vrfy(g == -399,
+		'9184: g == -399');
+	vrfy(m == -40.74,
+		'9185: m == -40.74');
+
+	/* h2hms */
+	vrfy(h2hms(12.3456,h,m,s) == 12.3456,
+		'9186: h2hms(12.3456,h,m,s) == 12.3456');
+	vrfy(h == 12,
+		'9187: h == 12');
+	vrfy(m == 20,
+		'9188: m == 20');
+	vrfy(s == 44.16,
+		'9189: s == 44.16');
+
+	vrfy(h2hms(1234.5678,h,m,s) == 10.5678,
+		'9190: h2hms(1234.5678,h,m,s) == 10.5678');
+	vrfy(h == 10,
+		'9191: h == 10');
+	vrfy(m == 34,
+		'9192: m == 34');
+	vrfy(s == 4.08,
+		'9193: s == 4.08');
+
+	vrfy(h2hms(-1234.5678,h,m,s) == 13.4322,
+		'9194: h2hms(-1234.5678,h,m,s) == 13.4322');
+	vrfy(h == 13,
+		'9195: h == 13');
+	vrfy(m == 25,
+		'9196: m == 25');
+	vrfy(s == 55.92,
+		'9197: s == 55.92');
+
+	vrfy(h2hms(24.321,h,m,s,1) == -23.679,
+		'9198: h2hms(24.321,h,m,s,1) == -23.679');
+	vrfy(h == -23,
+		'9199: h == -23');
+	vrfy(m == -40,
+		'9200: m == -40');
+	vrfy(s == -44.4,
+		'9201: s == -44.4');
+
+	/* h2hm */
+	vrfy(h2hm(12.3456,h,m) == 12.3456,
+		'9202: h2hm(12.3456,h,m) == 12.3456');
+	vrfy(h == 12,
+		'9203: h == 12');
+	vrfy(m == 20.736,
+		'9204: m == 20.736');
+
+	vrfy(h2hm(1234.5678,h,m) == 10.5678,
+		'9205: h2hm(1234.5678,h,m) == 10.5678');
+	vrfy(h == 10,
+		'9206: h == 10');
+	vrfy(m == 34.068,
+		'9207: m == 34.068');
+
+	vrfy(h2hm(-1234.5678,h,m) == 13.4322,
+		'9208: h2hm(-1234.5678,h,m) == 13.4322');
+	vrfy(h == 13,
+		'9209: h == 13');
+	vrfy(m == 25.932,
+		'9210: m == 25.932');
+
+	vrfy(h2hm(24.321,h,m,1) == -23.679,
+		'9211: h2hm(24.321,h,m,1) == -23.679');
+	vrfy(h == -23,
+		'9212: h == -23');
+	vrfy(m == -40.74,
+		'9213: m == -40.74');
+
+	/* dm2d */
+	vrfy(dm2d(203, 325.5594) == 208.42599,
+		'9214: dm2d(203, 325.5594) == 208.42599');
+	vrfy(dm2d(3601, -25.5594) == 0.57401,
+		'9215: dm2d(3601, -25.5594) == 0.57401');
+	vrfy(dm2d(-923, -25.5594) == 156.57401,
+		'9216: dm2d(-923, -25.5594) == 156.57401');
+	vrfy(dm2d(203, 325.5594, 1) == -151.57401,
+		'9217: dm2d(203, 325.5594, 1) == -151.57401');
+
+	vrfy(d2dm(dm2d(12, 20.16),d,m) == 12.336,
+		'9218: d2dm(dm2d(12, 20.16),d,m) == 12.336');
+	vrfy(d == 12,
+		'9219: d == 12');
+	vrfy(m == 20.16,
+		'9220: m == 20.16');
+
+	/* dms2d */
+	vrfy(dms2d(12, 20, 44.16) == 12.3456,
+		'9221: dms2d(12, 20, 44.16) == 12.3456');
+	vrfy(dms2d(123.456, -345.68, 4.08) == 117.6958,
+		'9222: dms2d(123.456, -345.68, 4.08) == 117.6958');
+	vrfy(dms2d(-65, -40, -44.4) == 294.321,
+		'9223: dms2d(-65, -40, -44.4) == 294.321');
+	vrfy(dms2d(12, 20, 44.16, 1) == -347.6544,
+		'9224: dms2d(12, 20, 44.16, 1) == -347.6544');
+
+	vrfy(d2dms(dms2d(13, 20, 44.16),d,m,s) == 13.3456,
+		'9225: d2dms(dms2d(13, 20, 44.16),d,m,s) == 13.3456');
+	vrfy(d == 13,
+		'9226: d == 13');
+	vrfy(m == 20,
+		'9227: m == 20');
+	vrfy(s == 44.16,
+		'9228: s == 44.16');
+
+	/* gm2g */
+	vrfy(gm2g(203, 325.5594) == 208.42599,
+		'9229: gm2g(203, 325.5594) == 208.42599');
+	vrfy(gm2g(3601, -25.5594) == 0.57401,
+		'9230: gm2g(3601, -25.5594) == 0.57401');
+	vrfy(gm2g(-923, -25.5594) == 276.57401,
+		'9231: gm2g(-923, -25.5594) == 276.57401');
+	vrfy(gm2g(203, 325.5594, 1) == -191.57401,
+		'9232: gm2g(203, 325.5594, 1) == -191.57401');
+
+	vrfy(g2gm(gm2g(12, 20.16),g,m) == 12.336,
+		'9233: g2gm(gm2g(12, 20.16),g,m) == 12.336');
+	vrfy(g == 12,
+		'9234: g == 12');
+	vrfy(m == 20.16,
+		'9235: m == 20.16');
+
+	/* gms2g */
+	vrfy(gms2g(12, 20, 44.16) == 12.3456,
+		'9236: gms2g(12, 20, 44.16) == 12.3456');
+	vrfy(gms2g(123.456, -345.68, 4.08) == 117.6958,
+		'9237: gms2g(123.456, -345.68, 4.08) == 117.6958');
+	vrfy(gms2g(-65, -40, -44.4) == 334.321,
+		'9238: gms2g(-65, -40, -44.4) == 334.321');
+	vrfy(gms2g(12, 20, 44.16, 1) == -387.6544,
+		'9239: gms2g(12, 20, 44.16, 1) == -387.6544');
+
+	vrfy(g2gms(gms2g(14, 20, 44.16),g,m,s) == 14.3456,
+		'9240: g2gms(gms2g(14, 20, 44.16),g,m,s) == 14.3456');
+	vrfy(g == 14,
+		'9241: g == 14');
+	vrfy(m == 20,
+		'9242: m == 20');
+	vrfy(s == 44.16,
+		'9243: s == 44.16');
+
+	/* hm2h */
+	vrfy(hm2h(203, 325.5594) == 16.42599,
+		'9244: hm2h(203, 325.5594) == 16.42599');
+	vrfy(hm2h(241, -25.5594) == 0.57401,
+		'9245: hm2h(241, -25.5594) == 0.57401');
+	vrfy(hm2h(-923, -25.5594) == 12.57401,
+		'9246: hm2h(-923, -25.5594) == 12.57401');
+	vrfy(hm2h(203, 325.5594, 1) == -7.57401,
+		'9247: hm2h(203, 325.5594, 1) == -7.57401');
+
+	vrfy(h2hm(hm2h(12, 20.16),h,m) == 12.336,
+		'9248: h2hm(hm2h(12, 20.16),h,m) == 12.336');
+	vrfy(h == 12,
+		'9249: h == 12');
+	vrfy(m == 20.16,
+		'9250: m == 20.16');
+
+	/* hms2h */
+	vrfy(hms2h(12, 20, 44.16) == 12.3456,
+		'9251: hms2h(12, 20, 44.16) == 12.3456');
+	vrfy(hms2h(123.456, -345.68, 4.08) == 21.6958,
+		'9252: hms2h(123.456, -345.68, 4.08) == 21.6958');
+	vrfy(hms2h(-65, -40, -44.4) == 6.321,
+		'9253: hms2h(-65, -40, -44.4) == 6.321');
+	vrfy(hms2h(12, 20, 44.16, 1) == -11.6544,
+		'9254: hms2h(12, 20, 44.16, 1) == -11.6544');
+
+	vrfy(h2hms(hms2h(15, 20, 44.16),h,m,s) == 15.3456,
+		'9255: h2hms(hms2h(15, 20, 44.16),h,m,s) == 15.3456');
+	vrfy(h == 15,
+		'9256: h == 15');
+	vrfy(m == 20,
+		'9257: m == 20');
+	vrfy(s == 44.16,
+		'9258: s == 44.16');
+
+	print '9259: Ending test_functions3';
+}
+print;
+print '9100: parsed test_functions3()';
+print;
+return test_functions3();
+
+
 /*
  * read various calc resource files
  *

cal/statistics.cal

@@ -371,7 +371,7 @@ define normalcdf(x,mu,sigma){
 
 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);
+  return sqrt(2)*erfinv(2*p-1);
 }
 
 define normalcdfinv(p,mu,sigma){

calcerr.tbl

@@ -1,7 +1,7 @@
 #
 # calcerr - error codes and messages
 #
-# Copyright (C) 1999-2006  Ernest Bowen
+# Copyright (C) 1999-2006,2021  Ernest Bowen
 #
 # 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
@@ -496,3 +496,49 @@ E_ATANH3	Invalid value for calculating atan
 E_ACOTH3	Invalid value for calculating acot
 E_ASECH3	Invalid value for calculating asec
 E_ACSCH3	Invalid value for calculating acsc
+E_D2R1		Bad epsilon for converting degrees to radians
+E_D2R2		Bad first argument converting degrees to radians
+E_R2D1		Bad epsilon for converting radians to degrees
+E_R2D2		Bad first argument converting radians to degrees
+E_G2R1		Bad epsilon for converting gradians to radians
+E_G2R2		Bad first argument converting gradians to radians
+E_R2G1		Bad epsilon for converting radians to gradians
+E_R2G2		Bad first argument converting radians to gradians
+E_D2G1		Bad first argument converting degrees to gradians
+E_G2D1		Bad first argument converting gradians to degrees
+E_D2DMS1	Non-lvalue arguments 2, 3 or 4 for d2dms
+E_D2DMS2	Non-real-number arg 1 for d2dms
+E_D2DMS3	No-assign-to argument 2, 3 or 4 for d2dms
+E_D2DMS4	Invalid rounding arg 5 for d2dms
+E_D2DM1		Non-lvalue arguments 2 or 3 for d2dm
+E_D2DM2		Non-real-number arg 1 for d2dm
+E_D2DM3		No-assign-to argument 2 or 3 for d2dm
+E_D2DM4		Invalid rounding arg 4 for d2dm
+E_G2GMS1	Non-lvalue arguments 2, 3 or 4 for g2gms
+E_G2GMS2	Non-real-number arg 1 for g2gms
+E_G2GMS3	No-assign-to argument 2 or 3 for g2gms
+E_G2GMS4	Invalid rounding arg 5 for g2gms
+E_G2GM1		Non-lvalue arguments 2 or 3 for g2gm
+E_G2GM2		Non-real-number arg 1 for g2gm
+E_G2GM3		No-assign-to argument 2, 3 or 4 for g2gm
+E_G2GM4		Invalid rounding arg 4 for g2gm
+E_H2HMS1	Non-lvalue arguments 2, 3 or 4 for h2hms
+E_H2HMS2	Non-real-number arg 1 for h2hms
+E_H2HMS3	No-assign-to argument 2, 3 or 4 for h2hms
+E_H2HMS4	Invalid rounding arg 5 for h2hms
+E_H2HM1		Non-lvalue arguments 2 or 3 for h2hm
+E_H2HM2		Non-real-number arg 1 for h2hm
+E_H2HM3		No-assign-to argument 2 or 3 for h2hm
+E_H2HM4		Invalid rounding arg 4 for h2hm
+E_DMS2D1	Non-real-number aarguments 1, 2 or 3 for dms2d
+E_DMS2D2	Invalid rounding arg 4 for dms2d
+E_DM2D1		Non-real-number aarguments 1 or 2 for dm2d
+E_DM2D2		Invalid rounding arg 4 for dm2d
+E_GMS2G1	Non-real-number aarguments 1, 2 or 3 for gms2g
+E_GMS2G2	Invalid rounding arg 4 for gms2g
+E_GM2G1		Non-real-number aarguments 1 or 2 for gm2g
+E_GM2G2		Invalid rounding arg 4 for gm2g
+E_HMS2H1	Non-real-number aarguments 1, 2 or 3 for hms2h
+E_HMS2H2	Invalid rounding arg 4 for hms2h
+E_HM2H1		Non-real-number aarguments 1 or 2 for hm2h
+E_HM2H2		Invalid rounding arg 4 for hm2h

const.c

@@ -44,16 +44,16 @@ initconstants(void)
 {
 	int i;
 
-	consttable = (NUMBER **) malloc(sizeof(NUMBER *) * CONSTALLOCSIZE);
+	consttable = (NUMBER **) calloc(sizeof(NUMBER *), CONSTALLOCSIZE);
 	if (consttable == NULL) {
 		math_error("Unable to allocate constant table");
 		/*NOTREACHED*/
 	}
-	for (i = 0; i < INITCONSTCOUNT; i++)
+	for (i = 0; initnumbs[i] != NULL; i++) {
 		consttable[i] = initnumbs[i];
-	consttable[INITCONSTCOUNT] = NULL;	/* firewall */
-	constcount = INITCONSTCOUNT;
-	constavail = CONSTALLOCSIZE - INITCONSTCOUNT;
+	}
+	constcount = i-1;
+	constavail = CONSTALLOCSIZE - constcount;
 }
 
 
@@ -123,6 +123,9 @@ addqconstant(NUMBER *q)
 	tp = consttable;
 	for (index = 0; index < constcount; index++, tp++) {
 		t = *tp;
+		if (t == NULL) {	/* paranoia */
+			break;
+		}
 		if (t->links == 0) {
 			if (!havefirst) {
 				havefirst = TRUE;

custom/Makefile

@@ -145,6 +145,13 @@ CCBAN= -UUNBAN
 
 
 #if 0	/* start of skip for non-Gnu makefiles */
+
+# Unfortunately due to the complex dependency issues between
+# Makefile, Makefile.ship and custom/Makefile, parallel GNU make
+# is NOT recommended.  Sorry.
+#
+.NOTPARALLEL:
+
 ##############################################################################
 #-=-=-=-=-=-=-=-=- Identify the target machine, if possible -=-=-=-=-=-=-=-=-#
 ##############################################################################
@@ -489,7 +496,7 @@ EXT=
 
 # The default calc versions
 #
-VERSION= 2.14.0.0
+VERSION= 2.14.0.6
 
 # Names of shared libraries with versions
 #

custom/Makefile.head

@@ -145,6 +145,13 @@ CCBAN= -UUNBAN
 
 
 #if 0	/* start of skip for non-Gnu makefiles */
+
+# Unfortunately due to the complex dependency issues between
+# Makefile, Makefile.ship and custom/Makefile, parallel GNU make
+# is NOT recommended.  Sorry.
+#
+.NOTPARALLEL:
+
 ##############################################################################
 #-=-=-=-=-=-=-=-=- Identify the target machine, if possible -=-=-=-=-=-=-=-=-#
 ##############################################################################
@@ -489,7 +496,7 @@ EXT=
 
 # The default calc versions
 #
-VERSION= 2.14.0.0
+VERSION= 2.14.0.6
 
 # Names of shared libraries with versions
 #

have_fpos_pos.c

@@ -56,8 +56,8 @@ main(void)
 	printf("#define FPOS_POS_BITS %d\n", FPOS_POS_BITS);
 	printf("#define FPOS_POS_LEN %d\n", int(FPOS_POS_BITS/8));
 # else
-	printf("#define FPOS_POS_BITS %d\n", sizeof(pos.__pos)*8);
-	printf("#define FPOS_POS_LEN %d\n", sizeof(pos.__pos));
+	printf("#define FPOS_POS_BITS %lu\n", sizeof(pos.__pos)*8);
+	printf("#define FPOS_POS_LEN %lu\n", sizeof(pos.__pos));
 # endif
 
 #else

help.c

@@ -83,6 +83,9 @@ STATIC struct help_alias {
 	{"show", "command"},
 	{"stdlib", "resource"},
 	{"question", "questions"},
+	{"dm2d", "dms2d"},
+	{"gm2g", "gms2g"},
+	{"hm2d", "hms2d"},
 	{NULL, NULL}
 };
 

help/Makefile

@@ -356,7 +356,7 @@ BLT_HELP_FILES= ${BLT_HELP_FILES_3} ${BLT_HELP_FILES_5} \
 #
 # Please use:
 #
-#	make detail_help_list
+#	make clobber >/dev/null && make detail_help_list
 #
 # to keep this list in nice sorted order.
 #
@@ -364,14 +364,15 @@ DETAIL_HELP= abs access acos acosh acot acoth acsc acsch address agd \
 	append appr arg argv arrow asec asech asin asinh assign atan atan2 \
 	atanh avg base base2 bernoulli bit blk blkcpy blkfree blocks bround \
 	btrunc calc_tty calclevel calcpath catalan ceil cfappr cfsim char \
-	cmdbuf cmp comb conj cos cosh cot coth count cp csc csch ctime delete \
-	den dereference det digit digits display dp epsilon errcount errmax \
-	errno error estr euler eval exp fact factor fclose fcnt feof ferror \
-	fflush fgetc fgetfield fgetfile fgetline fgets fgetstr fib files floor \
-	fopen forall fpathopen fprintf fputc fputs fputstr frac free \
-	freebernoulli freeeuler freeglobals freeredc freestatics frem freopen \
-	fscan fscanf fseek fsize ftell gcd gcdrem gd getenv hash head highbit \
-	hmean hnrmod hypot ilog ilog10 ilog2 im indices inputlevel insert int \
+	cmdbuf cmp comb conj cos cosh cot coth count cp csc csch ctime d2dm \
+	d2dms d2g d2r delete den dereference det digit digits display dms2d dp \
+	epsilon errcount errmax errno error estr euler eval exp fact factor \
+	fclose fcnt feof ferror fflush fgetc fgetfield fgetfile fgetline fgets \
+	fgetstr fib files floor fopen forall fpathopen fprintf fputc fputs \
+	fputstr frac free freebernoulli freeeuler freeglobals freeredc \
+	freestatics frem freopen fscan fscanf fseek fsize ftell g2d g2gm g2gms \
+	g2r gcd gcdrem gd getenv gms2g h2hm h2hms hash head highbit hmean \
+	hms2h hnrmod hypot ilog ilog10 ilog2 im indices inputlevel insert int \
 	inverse iroot isalnum isalpha isassoc isatty isblk iscntrl isconfig \
 	isdefined isdigit iserror iseven isfile isgraph ishash isident isint \
 	islist islower ismat ismult isnull isnum isobj isobjtype isodd isprime \
@@ -381,11 +382,11 @@ DETAIL_HELP= abs access acos acosh acot acoth acsc acsch address agd \
 	matsum mattrace mattrans max memsize meq min minv mmin mne mod modify \
 	name near newerror nextcand nextprime norm null num oldvalue ord param \
 	perm pfact pi pix places pmod polar poly pop popcnt pound power \
-	prevcand prevprime printf prompt protect ptest push putenv questions \
-	quo quomod rand randbit random randombit randperm rcin rcmul rcout \
-	rcpow rcsq re remove reverse rewind rm root round rsearch runtime \
-	saveval scale scan scanf search sec sech seed segment select sgn sha1 \
-	sin sinh size sizeof sleep sort sqrt srand srandom ssq stoponerror str \
+	prevcand prevprime printf prompt protect ptest push putenv quo quomod \
+	r2d r2g rand randbit random randombit randperm rcin rcmul rcout rcpow \
+	rcsq re remove reverse rewind rm root round rsearch runtime saveval \
+	scale scan scanf search sec sech seed segment select sgn sha1 sin sinh \
+	size sizeof sleep sort sqrt srand srandom ssq stoponerror str \
 	strcasecmp strcat strcmp strcpy strerror strlen strncasecmp strncmp \
 	strncpy strpos strprintf strscan strscanf strtolower strtoupper substr \
 	sum swap system systime tail tan tanh test time trunc usertime version \
@@ -730,7 +731,7 @@ distlist: ${DISTLIST}
 	    if [ X"$$i" != X"/dev/null" ]; then \
 		echo help/$$i; \
 	    fi; \
-	done | LANG=C ${SORT}
+	done | fgrep -v '.bak' | LANG=C ${SORT}
 
 distdir:
 	${Q} echo help

help/d2dm

@@ -0,0 +1,117 @@
+NAME
+    d2dm - convert degrees into degrees, and minutes
+
+SYNOPSIS
+    d2dm(degs, d, m [,rnd])
+
+TYPES
+    degs	real
+    d		null-or-real-valued lvalue with assign-to permission
+    m		null-or-real-valued lvalue with assign-to permission
+    rnd		nonnegative integer, defaults to config("mod")
+
+    return	mod(degs, 360, rnd)
+
+DESCRIPTION
+    Convert degs degrees into d degrees, and m minutes.
+
+    The return value is a normalized number of degrees, and is equivalent
+    to the following:
+
+	return_value = mod(degs, 360, rnd);
+
+    The argument rnd, if not given, defaults to config("mod").
+    For more information on the effects of rnd, see "help mod".
+
+    Depending on the rounding mode, the return could be a real value
+    in the interval [0, 360) or a real value in the interval (-360, 0].
+    For the default round mode, the return value is in the interval [0, 360).
+
+    The d argument will be an integer number of degrees.
+
+    The value d will be set as if the following were used:
+
+    	d = int(return_value);
+
+    For some rounding modes, d will be an integer in the interval [0, 360).
+    For other rounding modes, d will be an integer in the interval (-360, 0].
+    For the default round mode, d is in the interval [0, 360).
+
+    The m argument will be a real number of minutes.
+
+    The value m will be set as if the following were used:
+
+	tmp = return_value - d;
+	m = tmp * 60;
+	free(tmp);
+
+    For some rounding modes, m will be a real value in the interval [0, 60).
+    For other rounding modes, m will be a real value in the interval (-60, 0].
+    For the default round mode, m will be in the interval [0, 60).
+
+    The following shows relationship between the return value and the resulting
+    d, and m values:
+
+    	return_value == d + m/60;
+
+
+EXAMPLE
+    /* if args are undefined, pre-declare them or assign them as args */
+
+    ; global d, m;
+
+    ; print d2dm(12.3456,d,m), d, m;
+    12.3456 12 20.736
+    ; print d2dm(1234.5678,d,m), d, m;
+    154.5678 154 34.068
+    ; print d2dm(-1234.5678,d,m), d, m;
+    205.4322 205 25.932
+
+    ; print d2dm(654.321,deg=,min=), deg, min;
+    294.321 294 19.26
+    ; print d2dm(-654.321,deg=,min=), deg, min;
+    65.679 65 40.74
+    ; print d2dm(360.321,deg=,min=), deg, min;
+    0.321 0 19.26
+
+    /* certain non-default rounding modes can return negative values */
+
+    ; print d2dm(654.321,deg=,min=,1), deg, min;
+    -65.679 -65 -40.74
+    ; print d2dm(-654.321,deg=,min=,1), deg, min;
+    -294.321 -294 -19.26
+    ; print d2dm(360.321,deg=,min=,1), deg, min;
+    -359.679 -359 -40.74
+
+
+LIMITS
+    none
+
+LINK LIBRARY
+    none
+
+SEE ALSO
+    config, d2dms, dm2d, dms2d, g2gm, g2gms, gm2g, gms2g,
+    h2hm, h2hms, hm2d, hms2d, mod
+
+## Copyright (C) 2021  Landon Curt Noll
+##
+## Calc is open software; you can redistribute it and/or modify it under
+## the terms of the version 2.1 of the GNU Lesser General Public License
+## as published by the Free Software Foundation.
+##
+## Calc is distributed in the hope that it will be useful, but WITHOUT
+## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## Public License for more details.
+##
+## A copy of version 2.1 of the GNU Lesser General Public License is
+## distributed with calc under the filename COPYING-LGPL.  You should have
+## received a copy with calc; if not, write to Free Software Foundation, Inc.
+## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
+##
+## Under source code control:	2021/09/25 17:24:51
+## File existed as early as:	2021
+##
+## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
+## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/

help/d2dms

@@ -0,0 +1,132 @@
+NAME
+    d2dms - convert degrees into degrees, minutes, and seconds
+
+SYNOPSIS
+    d2dms(degs, d, m, s [,rnd])
+
+TYPES
+    degs	real
+    d		null-or-real-valued lvalue with assign-to permission
+    m		null-or-real-valued lvalue with assign-to permission
+    s		null-or-real-valued lvalue with assign-to permission
+    rnd		nonnegative integer, defaults to config("mod")
+
+    return	mod(degs, 360, rnd)
+
+DESCRIPTION
+    Convert degs degrees into d degrees, m minutes, and s seconds.
+
+    The return value is a normalized number of degrees, and is equivalent
+    to the following:
+
+	return_value = mod(degs, 360, rnd);
+
+    The argument rnd, if not given, defaults to config("mod").
+    For more information on the effects of rnd, see "help mod".
+
+    Depending on the rounding mode, the return could be a real value
+    in the interval [0, 360) or a real value in the interval (-360, 0].
+    For the default round mode, the return value is in the interval [0, 360).
+
+    The d argument will be an integer number of degrees.
+
+    The value d will be set as if the following were used:
+
+    	d = int(return_value);
+
+    For some rounding modes, d will be an integer in the interval [0, 360).
+    For other rounding modes, d will be an integer in the interval (-360, 0].
+    For the default round mode, d is in the interval [0, 360).
+
+    The m argument will be an integer number of minutes.
+
+    The value m will be set as if the following were used:
+
+	tmp = return_value - d;
+	tmp_m = tmp * 60;
+	free(tmp);
+	m = int(tmp_m);
+
+    For some rounding modes, m will be an integer in the interval [0, 60).
+    For other rounding modes, m will be an integer in the interval (-60, 0].
+    For the default round mode, m will be in the interval [0, 60).
+
+    The s argument will be a real number of seconds.
+
+    The value s will be set as if the following were used:
+
+	tmp = tmp_m - m;
+	free(tmp_m);
+	s = tmp * 60;
+	free(tmp);
+
+    For some rounding modes, s will be a real value in the interval [0, 60).
+    For other rounding modes, s will be a real value in the interval (-60, 0].
+    For the default round mode, s will be in the interval [0, 60).
+
+    The following shows relationship between the return value and the resulting
+    d, m, and s values:
+
+    	return_value == d + m/60 + s/3600;
+
+
+EXAMPLE
+    /* if args are undefined, pre-declare them or assign them as args */
+
+    ; global d, m, s;
+
+    ; print d2dms(12.3456,d,m,s), d, m, s;
+    12.3456 12 20 44.16
+    ; print d2dms(1234.5678,d,m,s), d, m, s;
+    154.5678 154 34 4.08
+    ; print d2dms(-1234.5678,d,m,s), d, m, s;
+    205.4322 205 25 55.92
+
+    ; print d2dms(654.321,deg=,min=,sec=), deg, min, sec;
+    294.321, 294, 19, 15.6
+    ; print d2dms(-654.321,deg=,min=,sec=), deg, min, sec;
+    65.679 65 40 44.4
+    ; print d2dms(360.321,deg=,min=,sec=), deg, min, sec;
+    0.321 0 19 15.6
+
+    /* certain non-default rounding modes can return negative values */
+
+    ; print d2dms(654.321,deg=,min=,sec=,1), deg, min, sec;
+    -65.679 -65 -40 -44.4
+    ; print d2dms(-654.321,deg=,min=,sec=,1), deg, min, sec;
+    -294.321 -294 -19 -15.6
+    ; print d2dms(360.321,deg=,min=,sec=,1), deg, min, sec;
+    -359.679 -359 -40 -44.4
+
+
+LIMITS
+    none
+
+LINK LIBRARY
+    none
+
+SEE ALSO
+    config, d2dm, dm2d, dms2d, g2gm, g2gms, gm2g, gms2g,
+    h2hm, h2hms, hm2d, hms2d, mod
+
+## Copyright (C) 2021  Landon Curt Noll
+##
+## Calc is open software; you can redistribute it and/or modify it under
+## the terms of the version 2.1 of the GNU Lesser General Public License
+## as published by the Free Software Foundation.
+##
+## Calc is distributed in the hope that it will be useful, but WITHOUT
+## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## Public License for more details.
+##
+## A copy of version 2.1 of the GNU Lesser General Public License is
+## distributed with calc under the filename COPYING-LGPL.  You should have
+## received a copy with calc; if not, write to Free Software Foundation, Inc.
+## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
+##
+## Under source code control:	2021/09/25 17:24:51
+## File existed as early as:	2021
+##
+## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
+## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/

help/d2g

@@ -0,0 +1,55 @@
+NAME
+    d2g - convert degrees to gradians
+
+SYNOPSIS
+    d2g(x [,eps])
+
+TYPES
+    x		number (real or complex)
+    eps		nonzero real, defaults to epsilon()
+
+    return	number
+
+DESCRIPTION
+    Given x degrees, return the equivalent number of gradians.
+
+    The eps argument is ignored.
+
+EXAMPLE
+    ; print d2g(45), d2g(180), d2g(30)
+    50 200 ~33.33333333333333333333
+
+    ; print d2g(3i+2)
+    ~2.22222222222222222222+~3.33333333333333333333i
+
+LIMITS
+    none
+
+LINK LIBRARY
+    none
+
+SEE ALSO
+    d2r, r2d, g2r, r2g, g2d,
+    sin, cos, tan, sec, csc, cot, epsilon
+
+## Copyright (C) 2021  Landon Curt Noll
+##
+## Calc is open software; you can redistribute it and/or modify it under
+## the terms of the version 2.1 of the GNU Lesser General Public License
+## as published by the Free Software Foundation.
+##
+## Calc is distributed in the hope that it will be useful, but WITHOUT
+## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## Public License for more details.
+##
+## A copy of version 2.1 of the GNU Lesser General Public License is
+## distributed with calc under the filename COPYING-LGPL.  You should have
+## received a copy with calc; if not, write to Free Software Foundation, Inc.
+## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
+##
+## Under source code control:	2021/09/07 12:04:28
+## File existed as early as:	2021
+##
+## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
+## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/

help/d2r

@@ -0,0 +1,59 @@
+NAME
+    d2r - convert degrees to radians
+
+SYNOPSIS
+    d2r(x [,eps])
+
+TYPES
+    x		number (real or complex)
+    eps		nonzero real, defaults to epsilon()
+
+    return	number
+
+DESCRIPTION
+    Given x degrees, return the equivalent number of radians.
+
+    The eps controls the precision of the calculated internal
+    constant pi / 180.
+
+EXAMPLE
+    ; print d2r(45), d2r(180), d2r(30)
+    ~0.78539816339744830962 3.14159265358979323846 ~0.52359877559829887308
+
+    ; print d2r(3i+2)
+    ~0.03490658503988659154+~0.05235987755982988731i
+
+    ; print sin(d2r(30)), cos(d2r(60)), tan(d2r(45))
+    0.5 0.5 1
+
+LIMITS
+    eps > 0
+
+LINK LIBRARY
+    NUMBER *qpidiv180(NUMBER *eps)
+
+SEE ALSO
+    r2d, g2r, r2g, d2g, g2d,
+    sin, cos, tan, sec, csc, cot, epsilon
+
+## Copyright (C) 2021  Landon Curt Noll
+##
+## Calc is open software; you can redistribute it and/or modify it under
+## the terms of the version 2.1 of the GNU Lesser General Public License
+## as published by the Free Software Foundation.
+##
+## Calc is distributed in the hope that it will be useful, but WITHOUT
+## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## Public License for more details.
+##
+## A copy of version 2.1 of the GNU Lesser General Public License is
+## distributed with calc under the filename COPYING-LGPL.  You should have
+## received a copy with calc; if not, write to Free Software Foundation, Inc.
+## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
+##
+## Under source code control:	2021/09/07 12:04:28
+## File existed as early as:	2021
+##
+## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
+## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/

help/dms2d

@@ -0,0 +1,84 @@
+NAME
+    dm2d, dms2d - convert degrees, minutes, and seconds to degrees
+
+SYNOPSIS
+    dm2d(d, m [,rnd])
+    dms2d(d, m, s [,rnd])
+
+TYPES
+    d		real
+    m		real
+    s		real (defauls to 0)
+    rnd		nonnegative integer, defaults to config("mod")
+
+    return	degrees
+
+DESCRIPTION
+    Convert degrees, m minutes, and s seconds returning degrees.
+
+    The return value in degrees, is quivalent to the following:
+
+	mod(d + m/60 + s/3600, 360, rnd);
+
+    Depending on the rounding mode, the return could be a real value
+    in the interval [0, 360) or a real value in the interval (-360, 0].
+    For the default round mode, the return value is in the interval [0, 360).
+
+    A missing rnd defaults to config("mod").
+    For more information on the effects of rnd, see "help mod".
+
+    The dm2d(d, m, rnd) builtin is an alias for dms2d(d, m, 0, rnd).
+
+
+EXAMPLE
+    ; print dm2d(203, 325.5594);
+    208.42599
+    ; print dm2d(3601, -25.5594);
+    0.57401
+    ; print dm2d(-923, -25.5594);
+    156.57401
+
+    ; print dms2d(12, 20, 44.16);
+    12.3456
+    ; print dms2d(123.456, -345.68, 4.08);
+    117.6958
+    ; print dms2d(-65, -40, -44.4);
+    294.321
+
+    ; print dm2d(203, 325.5594, 1);
+    -151.57401
+    ; print dms2d(12, 20, 44.16, 1);
+    -347.6544
+
+
+LIMITS
+    none
+
+LINK LIBRARY
+    none
+
+SEE ALSO
+    config, d2dm, d2dms, dm2d, dms2d, g2gm, g2gms, gm2g, gms2g,
+    h2hm, h2hms, hm2d, hms2d, mod
+
+## Copyright (C) 2021  Landon Curt Noll
+##
+## Calc is open software; you can redistribute it and/or modify it under
+## the terms of the version 2.1 of the GNU Lesser General Public License
+## as published by the Free Software Foundation.
+##
+## Calc is distributed in the hope that it will be useful, but WITHOUT
+## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## Public License for more details.
+##
+## A copy of version 2.1 of the GNU Lesser General Public License is
+## distributed with calc under the filename COPYING-LGPL.  You should have
+## received a copy with calc; if not, write to Free Software Foundation, Inc.
+## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
+##
+## Under source code control:	2021/09/25 17:24:51
+## File existed as early as:	2021
+##
+## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
+## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/

help/g2d

@@ -0,0 +1,55 @@
+NAME
+    g2d - convert gradians to degrees
+
+SYNOPSIS
+    g2d(x [,eps])
+
+TYPES
+    x		number (real or complex)
+    eps		nonzero real, defaults to epsilon()
+
+    return	number
+
+DESCRIPTION
+    Given x gradians, return the equivalent number of degrees.
+
+    The eps argument is ignored.
+
+EXAMPLE
+    ; print g2d(50), g2d(200), g2d(30)
+    45 180 27
+
+    ; print g2d(3i+2)
+    1.8+2.7i
+
+LIMITS
+    none
+
+LINK LIBRARY
+    none
+
+SEE ALSO
+    d2r, r2d, g2r, r2g, d2g,
+    sin, cos, tan, sec, csc, cot, epsilon
+
+## Copyright (C) 2021  Landon Curt Noll
+##
+## Calc is open software; you can redistribute it and/or modify it under
+## the terms of the version 2.1 of the GNU Lesser General Public License
+## as published by the Free Software Foundation.
+##
+## Calc is distributed in the hope that it will be useful, but WITHOUT
+## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## Public License for more details.
+##
+## A copy of version 2.1 of the GNU Lesser General Public License is
+## distributed with calc under the filename COPYING-LGPL.  You should have
+## received a copy with calc; if not, write to Free Software Foundation, Inc.
+## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
+##
+## Under source code control:	2021/09/07 12:04:28
+## File existed as early as:	2021
+##
+## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
+## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/

help/g2gm

@@ -0,0 +1,117 @@
+NAME
+    g2gm - convert gradians into gradians, and minutes
+
+SYNOPSIS
+    g2gm(grads, g, m [,rnd])
+
+TYPES
+    grads	real
+    g		null-or-real-valued lvalue with assign-to permission
+    m		null-or-real-valued lvalue with assign-to permission
+    rnd		nonnegative integer, defaults to config("mod")
+
+    return	mod(grads, 400, rnd)
+
+DESCRIPTION
+    Convert grads gradians into g gradians, and m minutes.
+
+    The return value is a normalized number of gradians, and is equivalent
+    to the following:
+
+	return_value = mod(grads, 400, rnd);
+
+    The argument rnd, if not given, defaults to config("mod").
+    For more information on the effects of rnd, see "help mod".
+
+    Depending on the rounding mode, the return could be a real value
+    in the interval [0, 400) or a real value in the interval (-400, 0].
+    For the default round mode, the return value is in the interval [0, 400).
+
+    The g argument will be an integer number of gradians.
+
+    The value g will be set as if the following were used:
+
+    	g = int(return_value);
+
+    For some rounding modes, g will be an integer in the interval [0, 400).
+    For other rounding modes, g will be an integer in the interval (-400, 0].
+    For the default round mode, g is in the interval [0, 400).
+
+    The m argument will be a real number of minutes.
+
+    The value m will be set as if the following were used:
+
+	tmp = return_value - g;
+	m = tmp * 60;
+	free(tmp);
+
+    For some rounding modes, m will be a real value in the interval [0, 60).
+    For other rounding modes, m will be a real value in the interval (-60, 0].
+    For the default round mode, m will be in the interval [0, 60).
+
+    The following shows relationship between the return value and the resulting
+    g, and m values:
+
+    	return_value == g + m/60;
+
+
+EXAMPLE
+    /* if args are undefined, pre-declare them or assign them as args */
+
+    ; global g, m;
+
+    ; print g2gm(12.3456,g,m), g, m;
+    12.3456 12 20.736
+    ; print g2gm(1234.5678,g,m), g, m;
+    34.5678 34 34.068
+    ; print g2gm(-1234.5678,g,m), g, m;
+    365.4322 365 25.932
+
+    ; print g2gm(654.321,grad=,min=), grad, min;
+    254.321 254 19.26
+    ; print g2gm(-654.321,grad=,min=), grad, min;
+    145.679 145 40.74
+    ; print g2gm(400.321,grad=,min=), grad, min;
+    0.321 0 19.26
+
+    /* certain non-default rounding modes can return negative values */
+
+    ; print g2gm(654.321,grad=,min=,1), grad, min;
+    -145.679 -145 -40.74
+    ; print g2gm(-654.321,grad=,min=,1), grad, min;
+    -254.321 -254 -19.26
+    ; print g2gm(400.321,grad=,min=,1), grad, min;
+    -399.679 -399 -40.74
+
+
+LIMITS
+    none
+
+LINK LIBRARY
+    none
+
+SEE ALSO
+    config, d2dm, d2dms, dm2d, dms2d, g2gms, gm2g, gms2g,
+    h2hm, h2hms, hm2d, hms2d, mod
+
+## Copyright (C) 2021  Landon Curt Noll
+##
+## Calc is open software; you can redistribute it and/or modify it under
+## the terms of the version 2.1 of the GNU Lesser General Public License
+## as published by the Free Software Foundation.
+##
+## Calc is distributed in the hope that it will be useful, but WITHOUT
+## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## Public License for more details.
+##
+## A copy of version 2.1 of the GNU Lesser General Public License is
+## distributed with calc under the filename COPYING-LGPL.  You should have
+## received a copy with calc; if not, write to Free Software Foundation, Inc.
+## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
+##
+## Under source code control:	2021/09/25 17:24:51
+## File existed as early as:	2021
+##
+## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
+## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/

help/g2gms

@@ -0,0 +1,132 @@
+NAME
+    g2gms - convert gradians into gradians, minutes, and seconds
+
+SYNOPSIS
+    g2gms(grads, g, m, s [,rnd])
+
+TYPES
+    grads	real
+    g		null-or-real-valued lvalue with assign-to permission
+    m		null-or-real-valued lvalue with assign-to permission
+    s		null-or-real-valued lvalue with assign-to permission
+    rnd		nonnegative integer, defaults to config("mod")
+
+    return	mod(grads, 400, rnd)
+
+DESCRIPTION
+    Convert grads gradians into g gradians, m minutes, and s seconds.
+
+    The return value is a normalized number of gradians, and is equivalent
+    to the following:
+
+	return_value = mod(grads, 400, rnd);
+
+    The argument rnd, if not given, defaults to config("mod").
+    For more information on the effects of rnd, see "help mod".
+
+    Depending on the rounding mode, the return could be a real value
+    in the interval [0, 400) or a real value in the interval (-400, 0].
+    For the default round mode, the return value is in the interval [0, 400).
+
+    The g argument will be an integer number of gradians.
+
+    The value g will be set as if the following were used:
+
+    	g = int(return_value);
+
+    For some rounding modes, g will be an integer in the interval [0, 400).
+    For other rounding modes, g will be an integer in the interval (-400, 0].
+    For the default round mode, g is in the interval [0, 400).
+
+    The m argument will be an integer number of minutes.
+
+    The value m will be set as if the following were used:
+
+	tmp = return_value - g;
+	tmp_m = tmp * 60;
+	free(tmp);
+	m = int(tmp_m);
+
+    For some rounding modes, m will be an integer in the interval [0, 60).
+    For other rounding modes, m will be an integer in the interval (-60, 0].
+    For the default round mode, m will be in the interval [0, 60).
+
+    The s argument will be a real number of seconds.
+
+    The value s will be set as if the following were used:
+
+	tmp = tmp_m - m;
+	free(tmp_m);
+	s = tmp * 60;
+	free(tmp);
+
+    For some rounding modes, s will be a real value in the interval [0, 60).
+    For other rounding modes, s will be a real value in the interval (-60, 0].
+    For the default round mode, s will be in the interval [0, 60).
+
+    The following shows relationship between the return value and the resulting
+    g, m, and s values:
+
+    	return_value == g + m/60 + s/3600;
+
+
+EXAMPLE
+    /* if args are undefined, pre-declare them or assign them as args */
+
+    ; global g, m, s;
+
+    ; print g2gms(12.3456,g,m,s), g, m, s;
+    12.3456 12 20 44.16
+    ; print g2gms(1234.5678,g,m,s), g, m, s;
+    34.5678 34 34 4.08
+    ; print g2gms(-1234.5678,g,m,s), g, m, s;
+    365.4322 365 25 55.92
+
+    ; print g2gms(654.321,grad=,min=,sec=), grad, min, sec;
+    254.321 254 19 15.6
+    ; print g2gms(-654.321,grad=,min=,sec=), grad, min, sec;
+    145.679 145 40 44.4
+    ; print g2gms(400.321,grad=,min=,sec=), grad, min, sec;
+    0.321 0 19 15.6
+
+    /* certain non-default rounding modes can return negative values */
+
+    ; print g2gms(654.321,grad=,min=,sec=,1), grad, min, sec;
+    -145.679 -145 -40 -44.4
+    ; print g2gms(-654.321,grad=,min=,sec=,1), grad, min, sec;
+    -254.321 -254 -19 -15.6
+    ; print g2gms(400.321,grad=,min=,sec=,1), grad, min, sec;
+    -399.679 -399 -40 -44.4
+
+
+LIMITS
+    none
+
+LINK LIBRARY
+    none
+
+SEE ALSO
+    config, d2dm, d2dms, dm2d, dms2d, g2gm, gm2g, gms2g,
+    h2hm, h2hms, hm2d, hms2d, mod
+
+## Copyright (C) 2021  Landon Curt Noll
+##
+## Calc is open software; you can redistribute it and/or modify it under
+## the terms of the version 2.1 of the GNU Lesser General Public License
+## as published by the Free Software Foundation.
+##
+## Calc is distributed in the hope that it will be useful, but WITHOUT
+## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## Public License for more details.
+##
+## A copy of version 2.1 of the GNU Lesser General Public License is
+## distributed with calc under the filename COPYING-LGPL.  You should have
+## received a copy with calc; if not, write to Free Software Foundation, Inc.
+## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
+##
+## Under source code control:	2021/09/25 17:24:51
+## File existed as early as:	2021
+##
+## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
+## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/

help/g2r

@@ -0,0 +1,59 @@
+NAME
+    g2r - convert gradians to radians
+
+SYNOPSIS
+    g2r(x [,eps])
+
+TYPES
+    x		number (real or complex)
+    eps		nonzero real, defaults to epsilon()
+
+    return	number
+
+DESCRIPTION
+    Given x gradians, return the equivalent number of radians.
+
+    The eps controls the precision of the calculated internal
+    constant pi / 200.
+
+EXAMPLE
+    ; print g2r(50), g2r(200), g2r(50)
+    ~0.78539816339744830962 3.14159265358979323846 ~0.78539816339744830962
+
+    ; print g2r(3i+2)
+    ~0.03141592653589793238+~0.04712388980384689858i
+
+    ; print sin(g2r(100/3)), cos(g2r(200/3)), tan(g2r(50))
+    0.5 0.5 1
+
+LIMITS
+    eps > 0
+
+LINK LIBRARY
+    NUMBER *qpidiv200(NUMBER *eps)
+
+SEE ALSO
+    d2r, r2d, r2g, d2g, g2d,
+    sin, cos, tan, sec, csc, cot, epsilon
+
+## Copyright (C) 2021  Landon Curt Noll
+##
+## Calc is open software; you can redistribute it and/or modify it under
+## the terms of the version 2.1 of the GNU Lesser General Public License
+## as published by the Free Software Foundation.
+##
+## Calc is distributed in the hope that it will be useful, but WITHOUT
+## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## Public License for more details.
+##
+## A copy of version 2.1 of the GNU Lesser General Public License is
+## distributed with calc under the filename COPYING-LGPL.  You should have
+## received a copy with calc; if not, write to Free Software Foundation, Inc.
+## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
+##
+## Under source code control:	2021/09/07 12:04:28
+## File existed as early as:	2021
+##
+## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
+## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/

help/gms2g

@@ -0,0 +1,84 @@
+NAME
+    gm2g, gms2g - convert gradians, minutes, and seconds to gradians
+
+SYNOPSIS
+    gm2g(d, m [,rnd])
+    gms2g(d, m, s [,rnd])
+
+TYPES
+    d		real
+    m		real
+    s		real (defauls to 0)
+    rnd		nonnegative integer, defaults to config("mod")
+
+    return	gradians
+
+DESCRIPTION
+    Convert gradians, m minutes, and s seconds returning gradians.
+
+    The return value in gradians, is quivalent to the following:
+
+	mod(d + m/60 + s/4000, 400, rnd);
+
+    Depending on the rounding mode, the return could be a real value
+    in the interval [0, 400) or a real value in the interval (-400, 0].
+    For the default round mode, the return value is in the interval [0, 400).
+
+    A missing rnd defaults to config("mod").
+    For more information on the effects of rnd, see "help mod".
+
+    The gm2g(d, m, rnd) builtin is an alias for gms2g(d, m, 0, rnd).
+
+
+EXAMPLE
+    ; print gm2g(203, 325.5594);
+    208.42599
+    ; print gm2g(4001, -25.5594);
+    0.57401
+    ; print gm2g(-923, -25.5594);
+    276.57401
+
+    ; print gms2g(12, 20, 44.16);
+    12.3456
+    ; print gms2g(123.456, -345.68, 4.08);
+    117.6958
+    ; print gms2g(-65, -40, -44.4);
+    334.321
+
+    ; print gm2g(203, 325.5594, 1);
+    -191.57401
+    ; print gms2g(12, 20, 44.16, 1);
+    -387.6544
+
+
+LIMITS
+    none
+
+LINK LIBRARY
+    none
+
+SEE ALSO
+    config, d2dm, d2dms, dm2d, dms2d, g2gm, g2gms, gm2g, gms2g,
+    h2hm, h2hms, hm2d, hms2d, mod
+
+## Copyright (C) 2021  Landon Curt Noll
+##
+## Calc is open software; you can redistribute it and/or modify it under
+## the terms of the version 2.1 of the GNU Lesser General Public License
+## as published by the Free Software Foundation.
+##
+## Calc is distributed in the hope that it will be useful, but WITHOUT
+## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## Public License for more details.
+##
+## A copy of version 2.1 of the GNU Lesser General Public License is
+## distributed with calc under the filename COPYING-LGPL.  You should have
+## received a copy with calc; if not, write to Free Software Foundation, Inc.
+## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
+##
+## Under source code control:	2021/09/25 17:24:51
+## File existed as early as:	2021
+##
+## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
+## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/

help/h2hm

@@ -0,0 +1,117 @@
+NAME
+    h2hm - convert hours into hours, and minutes
+
+SYNOPSIS
+    h2hm(hours, h, m [,rnd])
+
+TYPES
+    hours	real
+    h		null-or-real-valued lvalue with assign-to permission
+    m		null-or-real-valued lvalue with assign-to permission
+    rnd		nonnegative integer, defaults to config("mod")
+
+    return	mod(hours, 24, rnd)
+
+DESCRIPTION
+    Convert hours hours into h hours, and m minutes.
+
+    The return value is a normalized number of hours, and is equivalent
+    to the following:
+
+	return_value = mod(hours, 24, rnd);
+
+    The argument rnd, if not given, defaults to config("mod").
+    For more information on the effects of rnd, see "help mod".
+
+    Depending on the rounding mode, the return could be a real value
+    in the interval [0, 24) or a real value in the interval (-24, 0].
+    For the default round mode, the return value is in the interval [0, 24).
+
+    The h argument will be an integer number of hours.
+
+    The value h will be set as if the following were used:
+
+    	h = int(return_value);
+
+    For some rounding modes, h will be an integer in the interval [0, 24).
+    For other rounding modes, h will be an integer in the interval (-24, 0].
+    For the default round mode, h is in the interval [0, 24).
+
+    The m argument will be a real number of minutes.
+
+    The value m will be set as if the following were used:
+
+	tmp = return_value - h;
+	m = tmp * 60;
+	free(tmp);
+
+    For some rounding modes, m will be a real value in the interval [0, 60).
+    For other rounding modes, m will be a real value in the interval (-60, 0].
+    For the default round mode, m will be in the interval [0, 60).
+
+    The following shows relationship between the return value and the resulting
+    h, and m values:
+
+    	return_value == h + m/60;
+
+
+EXAMPLE
+    /* if args are undefined, pre-declare them or assign them as args */
+
+    ; global h, m;
+
+    ; print h2hm(12.3456,h,m), h, m;
+    12.3456 12 20.736
+    ; print h2hm(1234.5678,h,m), h, m;
+    10.5678 10 34.068
+    ; print h2hm(-1234.5678,h,m), h, m;
+    13.4322 13 25.932
+
+    ; print h2hm(654.321,hour=,min=), hour, min;
+    6.321 6 19.26
+    ; print h2hm(-654.321,hour=,min=), hour, min;
+    17.679 17 40.74
+    ; print h2hm(24.321,hour=,min=), hour, min;
+    0.321 0 19.26
+
+    /* certain non-default rounding modes can return negative values */
+
+    ; print h2hm(654.321,hour=,min=,1), hour, min;
+    -17.679 -17 -40.74
+    ; print h2hm(-654.321,hour=,min=,1), hour, min;
+    -6.321 -6 -19.26
+    ; print h2hm(24.321,hour=,min=,1), hour, min;
+    -23.679 -23 -40.7
+
+
+LIMITS
+    none
+
+LINK LIBRARY
+    none
+
+SEE ALSO
+    config, d2dm, d2dms, dm2d, dms2d, g2gm, g2gms, gm2g, gms2g,
+    h2hms, hm2d, hms2d, mod
+
+## Copyright (C) 2021  Landon Curt Noll
+##
+## Calc is open software; you can redistribute it and/or modify it under
+## the terms of the version 2.1 of the GNU Lesser General Public License
+## as published by the Free Software Foundation.
+##
+## Calc is distributed in the hope that it will be useful, but WITHOUT
+## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## Public License for more details.
+##
+## A copy of version 2.1 of the GNU Lesser General Public License is
+## distributed with calc under the filename COPYING-LGPL.  You should have
+## received a copy with calc; if not, write to Free Software Foundation, Inc.
+## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
+##
+## Under source code control:	2021/09/25 17:24:51
+## File existed as early as:	2021
+##
+## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
+## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/

help/h2hms

@@ -0,0 +1,132 @@
+NAME
+    h2hms - convert hours into hours, minutes, and seconds
+
+SYNOPSIS
+    h2hms(hours, h, m, s [,rnd])
+
+TYPES
+    hours	real
+    h		null-or-real-valued lvalue with assign-to permission
+    m		null-or-real-valued lvalue with assign-to permission
+    s		null-or-real-valued lvalue with assign-to permission
+    rnd		nonnegative integer, defaults to config("mod")
+
+    return	mod(hours, 24, rnd)
+
+DESCRIPTION
+    Convert hours hours into h hours, m minutes, and s seconds.
+
+    The return value is a normalized number of hours, and is equivalent
+    to the following:
+
+	return_value = mod(hours, 24, rnd);
+
+    The argument rnd, if not given, defaults to config("mod").
+    For more information on the effects of rnd, see "help mod".
+
+    Depending on the rounding mode, the return could be a real value
+    in the interval [0, 24) or a real value in the interval (-24, 0].
+    For the default round mode, the return value is in the interval [0, 24).
+
+    The h argument will be an integer number of hours.
+
+    The value h will be set as if the following were used:
+
+    	h = int(return_value);
+
+    For some rounding modes, h will be an integer in the interval [0, 24).
+    For other rounding modes, h will be an integer in the interval (-24, 0].
+    For the default round mode, h is in the interval [0, 24).
+
+    The m argument will be an integer number of minutes.
+
+    The value m will be set as if the following were used:
+
+	tmp = return_value - h;
+	tmp_m = tmp * 60;
+	free(tmp);
+	m = int(tmp_m);
+
+    For some rounding modes, m will be an integer in the interval [0, 60).
+    For other rounding modes, m will be an integer in the interval (-60, 0].
+    For the default round mode, m will be in the interval [0, 60).
+
+    The s argument will be a real number of seconds.
+
+    The value s will be set as if the following were used:
+
+	tmp = tmp_m - m;
+	free(tmp_m);
+	s = tmp * 60;
+	free(tmp);
+
+    For some rounding modes, s will be a real value in the interval [0, 60).
+    For other rounding modes, s will be a real value in the interval (-60, 0].
+    For the default round mode, s will be in the interval [0, 60).
+
+    The following shows relationship between the return value and the resulting
+    h, m, and s values:
+
+    	return_value == h + m/60 + s/3600;
+
+
+EXAMPLE
+    /* if args are undefined, pre-declare them or assign them as args */
+
+    ; global h, m, s;
+
+    ; print h2hms(12.3456,h,m,s), h, m, s;
+    12.3456 12 20 44.16
+    ; print h2hms(1234.5678,h,m,s), h, m, s;
+    10.5678 10 34 4.08
+    ; print h2hms(-1234.5678,h,m,s), h, m, s;
+    13.4322 13 25 55.92
+
+    ; print h2hms(654.321,hour=,min=,sec=), hour, min, sec;
+    6.321 6 19 15.6
+    ; print h2hms(-654.321,hour=,min=,sec=), hour, min, sec;
+    17.679 17 40 44.4
+    ; print h2hms(24.321,hour=,min=,sec=), hour, min, sec;
+    0.321 0 19 15.6
+
+    /* certain non-default rounding modes can return negative values */
+
+    ; print h2hms(654.321,hour=,min=,sec=,1), hour, min, sec;
+    -17.679 -17 -40 -44.4
+    ; print h2hms(-654.321,hour=,min=,sec=,1), hour, min, sec;
+    -6.321 -6 -19 -15.6
+    ; print h2hms(24.321,hour=,min=,sec=,1), hour, min, sec;
+    -23.679 -23 -40 -44.4
+
+
+LIMITS
+    none
+
+LINK LIBRARY
+    none
+
+SEE ALSO
+    config, d2dm, d2dms, dm2d, dms2d, g2gm, g2gms, gm2g, gms2g,
+    h2hm, hm2d, hms2d, mod
+
+## Copyright (C) 2021  Landon Curt Noll
+##
+## Calc is open software; you can redistribute it and/or modify it under
+## the terms of the version 2.1 of the GNU Lesser General Public License
+## as published by the Free Software Foundation.
+##
+## Calc is distributed in the hope that it will be useful, but WITHOUT
+## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## Public License for more details.
+##
+## A copy of version 2.1 of the GNU Lesser General Public License is
+## distributed with calc under the filename COPYING-LGPL.  You should have
+## received a copy with calc; if not, write to Free Software Foundation, Inc.
+## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
+##
+## Under source code control:	2021/09/25 17:24:51
+## File existed as early as:	2021
+##
+## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
+## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/

help/hms2h

@@ -0,0 +1,84 @@
+NAME
+    hm2h, hms2h - convert hours, minutes, and seconds to hours
+
+SYNOPSIS
+    hm2h(h, m [,rnd])
+    hms2h(h, m, s [,rnd])
+
+TYPES
+    h		real
+    m		real
+    s		real (defauls to 0)
+    rnd		nonnegative integer, defaults to config("mod")
+
+    return	hours
+
+DESCRIPTION
+    Convert hours, m minutes, and s seconds returning hours.
+
+    The return value in hours, is quivalent to the following:
+
+	mod(h + m/60 + s/3600, 24, rnd);
+
+    Depending on the rounding mode, the return could be a real value
+    in the interval [0, 24) or a real value in the interval (-24, 0].
+    For the default round mode, the return value is in the interval [0, 24).
+
+    A missing rnd defaults to config("mod").
+    For more information on the effects of rnd, see "help mod".
+
+    The hm2h(h, m, rnd) builtin is an alias for hms2h(h, m, 0, rnd).
+
+
+EXAMPLE
+    ; print hm2h(203, 325.5594);
+    16.42599
+    ; print hm2h(241, -25.5594);
+    0.57401
+    ; print hm2h(-923, -25.5594);
+    12.57401
+
+    ; print hms2h(12, 20, 44.16);
+    12.3456
+    ; print hms2h(123.456, -345.68, 4.08);
+    21.6958
+    ; print hms2h(-65, -40, -44.4);
+    6.321
+
+    ; print hm2h(203, 325.5594, 1);
+    -7.57401
+    ; print hms2h(12, 20, 44.16, 1);
+    -11.6544
+
+
+LIMITS
+    none
+
+LINK LIBRARY
+    none
+
+SEE ALSO
+    config, d2dm, d2dms, dm2d, dms2d, g2gm, g2gms, gm2g, gms2g,
+    h2hm, h2hms, hm2d, hms2d, mod
+
+## Copyright (C) 2021  Landon Curt Noll
+##
+## Calc is open software; you can redistribute it and/or modify it under
+## the terms of the version 2.1 of the GNU Lesser General Public License
+## as published by the Free Software Foundation.
+##
+## Calc is distributed in the hope that it will be useful, but WITHOUT
+## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## Public License for more details.
+##
+## A copy of version 2.1 of the GNU Lesser General Public License is
+## distributed with calc under the filename COPYING-LGPL.  You should have
+## received a copy with calc; if not, write to Free Software Foundation, Inc.
+## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
+##
+## Under source code control:	2021/09/25 17:24:51
+## File existed as early as:	2021
+##
+## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
+## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/

help/mod

@@ -2,7 +2,7 @@ NAME
     mod - compute the remainder for an integer quotient
 
 SYNOPSIS
-    mod(x, y, rnd)
+    mod(x, y [,rnd])
     x % y
 
 TYPES

help/quo

@@ -2,7 +2,7 @@ NAME
     quo - compute integer quotient of a value by a real number
 
 SYNOPSIS
-    quo(x, y, rnd) or x // y
+    quo(x, y [,rnd]) or x // y
 
 TYPES
     If x is a matrix or list, the returned value is a matrix or list v of

help/r2d

@@ -0,0 +1,57 @@
+NAME
+    r2d - convert radians to degrees
+
+SYNOPSIS
+    r2d(x [,eps])
+
+TYPES
+    x		number (real or complex)
+    eps		nonzero real, defaults to epsilon()
+
+    return	number
+
+DESCRIPTION
+    Given x radians, return the equivalent number of degrees.
+
+    The eps controls the precision of the calculated internal
+    constant pi / 180.
+
+EXAMPLE
+    ; pi = pi(1e-20)
+    ; print r2d(pi), r2d(pi/3), r2d(2*pi)
+    180 60 360
+
+    ; print r2d(pi+4i), r2d(pi/3 + 1i*pi), r2d(pi/5 + 5i*pi)
+    180+~229.18311805232928350739i 60+180, 36+900i
+
+LIMITS
+    eps > 0
+
+LINK LIBRARY
+    NUMBER *qpidiv180(NUMBER *eps)
+
+SEE ALSO
+    d2r, g2r, r2g, d2g, g2d,
+    sin, cos, tan, sec, csc, cot, epsilon
+
+## Copyright (C) 2021  Landon Curt Noll
+##
+## Calc is open software; you can redistribute it and/or modify it under
+## the terms of the version 2.1 of the GNU Lesser General Public License
+## as published by the Free Software Foundation.
+##
+## Calc is distributed in the hope that it will be useful, but WITHOUT
+## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## Public License for more details.
+##
+## A copy of version 2.1 of the GNU Lesser General Public License is
+## distributed with calc under the filename COPYING-LGPL.  You should have
+## received a copy with calc; if not, write to Free Software Foundation, Inc.
+## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
+##
+## Under source code control:	2021/09/07 12:04:28
+## File existed as early as:	2021
+##
+## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
+## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/

help/r2g

@@ -0,0 +1,57 @@
+NAME
+    r2g - convert radians to gradians
+
+SYNOPSIS
+    r2g(x [,eps])
+
+TYPES
+    x		number (real or complex)
+    eps		nonzero real, defaults to epsilon()
+
+    return	number
+
+DESCRIPTION
+    Given x radians, return the equivalent number of gradians.
+
+    The eps controls the precision of the calculated internal
+    constant pi / 200.
+
+EXAMPLE
+    ; pi = pi()
+    ; print r2g(pi), r2g(pi/3), r2g(2*pi)
+    200 ~66.66666666666666666667 400
+
+    ; print r2g(pi+4i), r2g(pi/4 + 1i*pi), r2g(pi/5 + 5i*pi)
+    200+~254.64790894703253723043i 50+200i 40+1000i
+
+LIMITS
+    eps > 0
+
+LINK LIBRARY
+    NUMBER *qpidiv200(NUMBER *eps)
+
+SEE ALSO
+    d2r, r2d, g2r, d2g, g2d,
+    sin, cos, tan, sec, csc, cot, epsilon
+
+## Copyright (C) 2021  Landon Curt Noll
+##
+## Calc is open software; you can redistribute it and/or modify it under
+## the terms of the version 2.1 of the GNU Lesser General Public License
+## as published by the Free Software Foundation.
+##
+## Calc is distributed in the hope that it will be useful, but WITHOUT
+## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## Public License for more details.
+##
+## A copy of version 2.1 of the GNU Lesser General Public License is
+## distributed with calc under the filename COPYING-LGPL.  You should have
+## received a copy with calc; if not, write to Free Software Foundation, Inc.
+## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
+##
+## Under source code control:	2021/09/07 12:04:28
+## File existed as early as:	2021
+##
+## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
+## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/

help/strcmp

@@ -26,6 +26,8 @@ EXAMPLE
     strcmp("abc", "abb") == 1
     strcmp("abc", "abc") == 0
     strcmp("abc", "abd") == -1
+    strcmp("desk", "Shabisky") == 1
+    strcmp("Shabisky", "desk") == -1
     strcmp("abc\0", "abc") == 1
     strcmp("a\0b", "a\0c") == -1
 
@@ -39,7 +41,7 @@ SEE ALSO
     strcat, strcpy, strerror, strlen, strncmp, strncpy, strpos,
     strprintf, strscan, strscanf, substr
 
-## Copyright (C) 2006  Ernest Bowen
+## Copyright (C) 2006,2021  Ernest Bowen
 ##
 ## 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

help/unexpected

@@ -228,7 +228,7 @@ Unexpected
 
 	1<<8/2
 
-    evalues to 128, not 16, because <<8 is performed before the /2.
+    evaluates to 128, not 16, because <<8 is performed before the /2.
 
 
     &A[0] and A are different things in calc
@@ -529,6 +529,34 @@ Unexpected
 	; help fclose
 
 
+    trig functions use only radians
+    ===============================
+
+    Some might be surprised to discover that all of the trigonometric in calc:
+
+	sin, cos, tan, sec, csc, cot
+	asin, acos, atan, asec, acsc, acot
+
+    work in only radians.
+
+    Calc as builtin functions to convert between degrees, radians and gradians:
+
+	d2r(deg)	- given degrees returns radians
+	g2r(grad)	- given gradians returns radians
+
+	r2d(rad)	- given radians returns degrees
+	g2d(grad)	- given gradians returns degrees
+
+	r2g(rad)	- given radians returns gradians
+	d2g(deg)	- given degrees returns gradians
+
+    For example, if you want to take the sin of 30 degrees, convert
+    the 30 degrees into radians and pass the result to sin():
+
+	; print sin(d2r(30))
+	0.5
+
+
 ## Copyright (C) 1999-2007,2014,2017,2021  Landon Curt Noll
 ##
 ## Calc is open software; you can redistribute it and/or modify it under

qmath.c

@@ -44,9 +44,21 @@ NUMBER _qnegone_ =	{ { _oneval_, 1, 1 }, { _oneval_, 1, 0 }, 1, NULL };
 NUMBER _qonehalf_ =	{ { _oneval_, 1, 0 }, { _twoval_, 1, 0 }, 1, NULL };
 NUMBER _qneghalf_ = 	{ { _oneval_, 1, 1 }, { _twoval_, 1, 0 }, 1, NULL };
 NUMBER _qonesqbase_ =	{ { _oneval_, 1, 0 }, { _sqbaseval_, 2, 0 }, 1, NULL };
+NUMBER _qtendivnine_ =	{ { _tenval_, 1, 0 }, { _nineval_, 1, 0 }, 1, NULL };
+NUMBER _qninedivten_ =	{ { _nineval_, 1, 0 }, { _tenval_, 1, 0 }, 1, NULL };
+NUMBER _qthreesixty =	{ { _threesixtyval_, 1, 0 },
+			  { _oneval_, 1, 0 }, 1, NULL };
+NUMBER _qfourhundred =	{ { _fourhundredval_, 1, 0 },
+			  { _oneval_, 1, 0 }, 1, NULL };
+NUMBER _qtwentyfour =	{ { _twentyfourval_, 1, 0 },
+			  { _oneval_, 1, 0 }, 1, NULL };
 
-NUMBER * initnumbs[INITCONSTCOUNT] = {&_qzero_, &_qone_, &_qtwo_, &_qthree_,
-	&_qfour_, &_qten_, &_qnegone_, &_qonehalf_, &_qneghalf_};
+NUMBER * initnumbs[] = {&_qzero_, &_qone_, &_qtwo_, &_qthree_,
+	&_qfour_, &_qten_, &_qnegone_, &_qonehalf_, &_qneghalf_,
+	&_qonesqbase_, &_qtendivnine_, &_qninedivten_,
+	&_qthreesixty, &_qfourhundred, &_qtwentyfour,
+	NULL	/* must be last */
+};
 
 
 /*
@@ -1478,7 +1490,7 @@ shownumbers(void)
 	printf("Index  Links  Digits	       Value\n");
 	printf("-----  -----  ------	       -----\n");
 
-	for (i = 0, k = 0; i < INITCONSTCOUNT; i++) {
+	for (i = 0, k = 0; initnumbs[i] != NULL; i++) {
 		count++;
 		vp = initnumbs[i];
 		printf("%6ld  %4ld  ", k++, vp->links);

qmath.h

@@ -1,7 +1,7 @@
 /*
  * qmath - declarations for extended precision rational arithmetic
  *
- * Copyright (C) 1999-2007,2014  David I. Bell
+ * Copyright (C) 1999-2007,2014,2021  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
@@ -35,8 +35,6 @@
 #endif
 
 
-#define INITCONSTCOUNT 9    /* number of initnumbs[] pre-defined constants */
-
 /*
  * Rational arithmetic definitions.
  */
@@ -213,6 +211,8 @@ E_FUNC NUMBER *qacsch(NUMBER *q, NUMBER *epsilon);
 E_FUNC NUMBER *qacoth(NUMBER *q, NUMBER *epsilon);
 E_FUNC NUMBER *qlegtoleg(NUMBER *q, NUMBER *epsilon, BOOL wantneg);
 E_FUNC NUMBER *qpi(NUMBER *epsilon);
+E_FUNC NUMBER *qpidiv180(NUMBER *epsilon);
+E_FUNC NUMBER *qpidiv200(NUMBER *epsilon);
 E_FUNC NUMBER *qcatalan(NUMBER *);
 E_FUNC NUMBER *qbern(ZVALUE z);
 E_FUNC void qfreebern(void);
@@ -273,6 +273,8 @@ static inline NUMBER* qlink(NUMBER* q) { if(q) { (q)->links++; } return q; }
  */
 EXTERN NUMBER _qzero_, _qone_, _qnegone_, _qonehalf_, _qneghalf_, _qonesqbase_;
 EXTERN NUMBER _qtwo_, _qthree_, _qfour_, _qten_;
+EXTERN NUMBER _qtendivnine_, _qninedivten_;
+EXTERN NUMBER _qthreesixty, _qfourhundred, _qtwentyfour;
 EXTERN NUMBER * initnumbs[];
 
 

qtrans.c

@@ -47,7 +47,40 @@ NUMBER _qlge_ = { { _qlgenum_, 1, 0 }, { _qlgeden_, 1, 0 }, 1, NULL };
 STATIC NUMBER *ln_10 = NULL;
 STATIC NUMBER *ln_10_epsilon = NULL;
 
-STATIC NUMBER *pivalue[2];
+/*
+ * cache pi
+ *
+ * pivalue[LAST_PI_EPSILON] - last epsilon used to calculate pi
+ * pivalue[LAST_PI_VALUE] - last calculated pi
+ *			      given pivalue[LAST_PI_EPSILON] epsilon
+ * pivalue[LAST_PI_DIV_180_EPSILON] - last epsilon used to calculate pi/180
+ * pivalue[LAST_PI_DIV_180_VALUE] - last calculated pi/180 given
+ *				      pivalue[LAST_PI_DIV_180_EPSILON] epsilon
+ * pivalue[LAST_PI_DIV_200_EPSILON] - last epsilon used to calculate pi/200
+ * pivalue[LAST_PI_DIV_200_VALUE] - last calculated pi/200 given
+ *				      pivalue[LAST_PI_DIV_200_EPSILON] epsilon
+ */
+enum pi_cache {
+	LAST_PI_EPSILON = 0,
+	LAST_PI_VALUE,
+	LAST_PI_DIV_180_EPSILON,
+	LAST_PI_DIV_180_VALUE,
+	LAST_PI_DIV_200_EPSILON,
+	LAST_PI_DIV_200_VALUE,
+	PI_CACHE_LEN	/* must be last */
+};
+STATIC NUMBER *pivalue[PI_CACHE_LEN] = {
+	NULL,	/* LAST_PI_EPSILON */
+	NULL,	/* LAST_PI_VALUE */
+	NULL,	/* LAST_PI_DIV_180_EPSILON */
+	NULL,	/* LAST_PI_DIV_180_VALUE */
+	NULL,	/* LAST_PI_DIV_200_EPSILON */
+	NULL,	/* LAST_PI_DIV_200_VALUE */
+};
+
+/*
+ * other static function decls
+ */
 STATIC NUMBER *qexprel(NUMBER *q, long bitnum);
 
 /*
@@ -725,16 +758,25 @@ qpi(NUMBER *epsilon)
 	long bits;			/* needed number of bits of precision */
 	long t;
 
+	/* firewall */
 	if (qiszero(epsilon)) {
 		math_error("zero epsilon value for pi");
 		/*NOTREACHED*/
 	}
-	if (epsilon == pivalue[0])
-		return qlink(pivalue[1]);
-	if (pivalue[0]) {
-		qfree(pivalue[0]);
-		qfree(pivalue[1]);
+
+	/* use pi cache if epsilon marches, else flush if needed */
+	if (pivalue[LAST_PI_EPSILON] != NULL &&
+	    pivalue[LAST_PI_VALUE] != NULL &&
+	    epsilon == pivalue[LAST_PI_EPSILON]) {
+		return qlink(pivalue[LAST_PI_VALUE]);
 	}
+	if (pivalue[LAST_PI_EPSILON] != NULL) {
+		qfree(pivalue[LAST_PI_EPSILON]);
+	}
+	if (pivalue[LAST_PI_VALUE] != NULL) {
+		qfree(pivalue[LAST_PI_VALUE]);
+	}
+
 	bits = -qilog2(epsilon) + 4;
 	if (bits < 4)
 		bits = 4;
@@ -768,11 +810,100 @@ qpi(NUMBER *epsilon)
 	zfree(sum);
 	r = qmappr(t1, epsilon, 24L);
 	qfree(t1);
-	pivalue[0] = qlink(epsilon);
-	pivalue[1] = qlink(r);
+	pivalue[LAST_PI_EPSILON] = qlink(epsilon);
+	pivalue[LAST_PI_VALUE] = qlink(r);
 	return r;
 }
 
+
+/*
+ * qpidiv180 - calcucalte pi / 180
+ *
+ * This function returns pi/180 as used to covert between radians and degrees.
+ */
+NUMBER *
+qpidiv180(NUMBER *epsilon)
+{
+	NUMBER *pi, *pidiv180;
+
+	/* firewall */
+	if (qiszero(epsilon)) {
+		math_error("zero epsilon value for qpidiv180");
+		/*NOTREACHED*/
+	}
+
+	/* use pi/180 cache if epsilon marches, else flush if needed */
+	if (pivalue[LAST_PI_DIV_180_EPSILON] != NULL &&
+	    pivalue[LAST_PI_DIV_180_VALUE] != NULL &&
+	    epsilon == pivalue[LAST_PI_DIV_180_EPSILON]) {
+		return qlink(pivalue[LAST_PI_DIV_180_VALUE]);
+	}
+	if (pivalue[LAST_PI_DIV_180_EPSILON] != NULL) {
+		qfree(pivalue[LAST_PI_DIV_180_EPSILON]);
+	}
+	if (pivalue[LAST_PI_DIV_180_VALUE] != NULL) {
+		qfree(pivalue[LAST_PI_DIV_180_VALUE]);
+	}
+
+	/* let qpi() returned cached pi or calculate new as needed */
+	pi = qpi(epsilon);
+
+	/* calculate pi/180 */
+	pidiv180 = qdivi(pi, 180);
+
+	/* cache epsilon and pi/180 */
+	pivalue[LAST_PI_DIV_180_EPSILON] = qlink(epsilon);
+	pivalue[LAST_PI_DIV_180_VALUE] = qlink(pidiv180);
+
+	/* return pi/180 */
+	return pidiv180;
+}
+
+
+/*
+ * qpidiv200 - calcucalte pi / 200
+ *
+ * This function returns pi/200 as used to covert between radians and gradians.
+ */
+NUMBER *
+qpidiv200(NUMBER *epsilon)
+{
+	NUMBER *pi, *pidiv200;
+
+	/* firewall */
+	if (qiszero(epsilon)) {
+		math_error("zero epsilon value for qpidiv200");
+		/*NOTREACHED*/
+	}
+
+	/* use pi/200 cache if epsilon marches, else flush if needed */
+	if (pivalue[LAST_PI_DIV_200_EPSILON] != NULL &&
+	    pivalue[LAST_PI_DIV_200_VALUE] != NULL &&
+	    epsilon == pivalue[LAST_PI_DIV_200_EPSILON]) {
+		return qlink(pivalue[LAST_PI_DIV_200_VALUE]);
+	}
+	if (pivalue[LAST_PI_DIV_200_EPSILON] != NULL) {
+		qfree(pivalue[LAST_PI_DIV_200_EPSILON]);
+	}
+	if (pivalue[LAST_PI_DIV_200_VALUE] != NULL) {
+		qfree(pivalue[LAST_PI_DIV_200_VALUE]);
+	}
+
+	/* let qpi() returned cached pi or calculate new as needed */
+	pi = qpi(epsilon);
+
+	/* calculate pi/200 */
+	pidiv200 = qdivi(pi, 200);
+
+	/* cache epsilon and pi/200 */
+	pivalue[LAST_PI_DIV_200_EPSILON] = qlink(epsilon);
+	pivalue[LAST_PI_DIV_200_VALUE] = qlink(pidiv200);
+
+	/* return pi/200 */
+	return pidiv200;
+}
+
+
 /*
  * Calculate the exponential function to the nearest or next to nearest
  * multiple of the positive number epsilon.

version.c

@@ -54,7 +54,7 @@ static char *program;
 #define MAJOR_VER	2	/* major library version */
 #define MINOR_VER	14	/* minor library version */
 #define MAJOR_PATCH	0	/* major software version level */
-#define MINOR_PATCH	0	/* minor software version level */
+#define MINOR_PATCH	6	/* minor software version level */
 
 
 /*

zfunc.c

@@ -1034,7 +1034,7 @@ zgcd(ZVALUE z1, ZVALUE z2, ZVALUE *res)
 				}
 				needw = FALSE;
 			}
-			g = *a0 * w;
+			g = (FULL) (*a0 * w);
 			if (h < BASEB) {
 			    g &= (1 << h) - 1;
 			} else {
@@ -1044,7 +1044,7 @@ zgcd(ZVALUE z1, ZVALUE z2, ZVALUE *res)
 			g = 1;
 		}
 	    } else {
-		g = (HALF) *a0 * w;
+		g = (FULL) (*a0 * w);
 	    }
 	    a = a0;
 	    b = b0;

zmath.c

@@ -58,6 +58,9 @@ HALF _twentyval_[] = { 20 };
 HALF _sqbaseval_[] = { 0, 1 };
 HALF _pow4baseval_[] = { 0, 0, 1 };
 HALF _pow8baseval_[] = { 0, 0, 0, 0, 1 };
+HALF _threesixtyval_[] = { 360 };
+HALF _fourhundredval_[] = { 400 };
+HALF _twentyfourval_[] = { 24 };
 
 ZVALUE zconst[] = {
     { _zeroval_, 1, 0}, { _oneval_, 1, 0}, { _twoval_, 1, 0},
@@ -66,7 +69,9 @@ ZVALUE zconst[] = {
     { _nineval_, 1, 0}, { _tenval_, 1, 0}, { _elevenval_, 1, 0},
     { _twelveval_, 1, 0}, { _thirteenval_, 1, 0}, { _fourteenval_, 1, 0},
     { _fifteenval_, 1, 0}, { _sixteenval_, 1, 0}, { _seventeenval_, 1, 0},
-    { _eightteenval_, 1, 0}, { _nineteenval_, 1, 0}, { _twentyval_, 1, 0}
+    { _eightteenval_, 1, 0}, { _nineteenval_, 1, 0}, { _twentyval_, 1, 0},
+    { _threesixtyval_, 1, 0}, { _fourhundredval_, 1, 0},
+    { _twentyfourval_, 1, 0}
 };
 
 ZVALUE _zero_ = { _zeroval_, 1, 0};

zmath.h

@@ -648,6 +648,7 @@ EXTERN HALF _tenval_[], _elevenval_[], _twelveval_[], _thirteenval_[];
 EXTERN HALF _fourteenval_[], _fifteenval_[];
 EXTERN HALF _sqbaseval_[];
 EXTERN HALF _fourthbaseval_[];
+EXTERN HALF _threesixtyval_[], _fourhundredval_[], _twentyfourval_[];
 
 EXTERN ZVALUE zconst[];		/* ZVALUE integers from 0 thru 15 */