Released calc 2.12.6.7 with help and input fixes

Fixed errors in various help files such as:

	mat randbit seed srandom types

    Removed the MAXSTRING symbol because it was no longer used by calc.

    Increased HIST_SIZE (depth of the history stack) from 10k to 32k.

    Increased TTYSIZE (reallocation size for terminal buffers) from 100 to 8191.

    Increased MAXDEPTH (maximum depth of input stack) from 10 to 255.

    Increased interactive input buffer size from 1024 to 256k.  This has the
    effect of increasing the maximum length of an input line from a tty.
    This helps with an interactive bug that was reported by Ruslan Kabatsayev
    (b7 dot 10110111 at gmail dot com).
k

CHANGES

@@ -1,4 +1,44 @@
-The following are the changes from calc version 2.12.6.1 to date:
+The following are the changes from calc version 2.12.6.6 to date:
+
+    For historical purposes, in lucas.cal, gen_v1(1, n) always returns 4.
+
+    Fixed some compiler warnings, thanks to a report by Mike
+    <michael dot d dot ince at gmail dot com>.
+
+    Added work around for a gcc warning bug, thanks to a report by Mike
+    <michael dot d dot ince at gmail dot com>.
+
+    Fixed errors in various help files such as:
+
+	mat randbit seed srandom types
+
+    Removed the MAXSTRING symbol because it was no longer used by calc.
+
+    Increased HIST_SIZE (depth of the history stack) from 10k to 32k.
+
+    Increased TTYSIZE (reallocation size for terminal buffers) from 100 to 8191.
+
+    Increased MAXDEPTH (maximum depth of input stack) from 10 to 255.
+
+    Increased interactive input buffer size from 1024 to 256k.  This has the
+    effect of increasing the maximum length of an input line from a tty.
+    This helps with an interactive bug that was reported by Ruslan Kabatsayev
+    (b7 dot 10110111 at gmail dot com).
+
+
+The following are the changes from calc version 2.12.6.4 to 2.12.6.5:
+
+    Fixed warning about undefined operations involving the qlink(q)
+    macro by replacing that macro with an inline-function.  Thanks goes
+    to David Haller <dnh at opensuse dot org> for this fix.
+
+    NOTE for Windows 10 users: Pavel Nemec <pane at seznam dot cz>
+    reported that calc version 2.12.6.4 has been successfully
+    compiled, installed and running on Windows 10.  See README.WINDOWS
+    for more details.
+
+
+The following are the changes from calc version 2.12.6.1 to 2.12.6.3:
 
     Improved gen_v1(h,n) in lucas.cal to use an even faster search method.
 
@@ -6,6 +46,22 @@ The following are the changes from calc version 2.12.6.1 to date:
     integers >= 1.  In the case of both rodseth_xhn(x, h, n) and gen_v1(h, n)
     h must be odd.
 
+    Fixed an C code indenting issue that was reported by Thomas Walter
+    <th dot walter42 at gmx dot de> in zfunc.c.
+
+    Fixed a man page warning about ./myfile where the leading dot
+    was mistook for an nroff macro.  Thanks goes to David Haller
+    <dnh at opensuse dot org> for providing the patch.
+
+    Improved gen_v1(h,n) in lucas.cal for cases where h is not a
+    multiple of 3. Optimized the search for v(1) when h is a
+    multiple of 3.
+
+    Fixed a Makefile problem, reported by Doug Hays <doughays6 at gmail
+    dot com>, where if a macOS user set BINDIR, LIBDIR, CALC_SHAREDIR
+    or INCDIR in the top section, their values will be overwritten by
+    the Darwin specific section.
+
 
 The following are the changes from calc version 2.12.6.0 to 2.12.6.0:
 

Makefile.ship

@@ -23,7 +23,7 @@
 #	 READLINE_LIB= -lreadline
 #	 READLINE_EXTRAS= -lhistory -lncurses
 #
-# Copyright (C) 1999-2017  Landon Curt Noll
+# Copyright (C) 1999-2018  Landon Curt Noll
 #
 # Calc is open software; you can redistribute it and/or modify it under
 # the terms of version 2.1 of the GNU Lesser General Public License
@@ -564,14 +564,30 @@ HAVE_UNUSED=
 #
 #	INCDIR= /dev/env/DJDIR/include
 #
-# If in doubt, set:
+# If in doubt, for non-macOS hosts set:
 #
 #	INCDIR= /usr/include
 #
+# However, if you are on macOS then set:
+#
+#	INCDIR= /usr/local/include
+#if 0	/* start of skip for non-Gnu makefiles */
+ifeq ($(target),Darwin)
 
+# default INCDIR for macOS
+INCDIR= /usr/local/include
+
+else
+#endif	/* end of skip for non-Gnu makefiles */
+
+# default INCDIR for non-macOS
+INCDIR= /usr/include
 #INCDIR= /usr/local/include
 #INCDIR= /dev/env/DJDIR/include
-INCDIR= /usr/include
+
+#if 0	/* start of skip for non-Gnu makefiles */
+endif
+#endif	/* end of skip for non-Gnu makefiles */
 
 # Where to install calc related things
 #
@@ -602,23 +618,71 @@ INCDIR= /usr/include
 #	LIBDIR= /dev/env/DJDIR/lib
 #	CALC_SHAREDIR= /dev/env/DJDIR/share/calc
 #
-# If in doubt, set:
+# If in doubt, for non-macOS hosts set:
 #
 #	BINDIR= /usr/bin
 #	LIBDIR= /usr/lib
 #	CALC_SHAREDIR= /usr/share/calc
 #
+# However, if you are on macOS then set:
+#
+#	BINDIR= /usr/local/bin
+#	LIBDIR= /usr/local/lib
+#	CALC_SHAREDIR= /usr/local/share/calc
+#
+# 	NOTE: Starting with macOS El Capitan OS X 10.11, root by default
+# 	      could not mkdir under system locations, so macOS must now
+# 	      use the /usr/local tree.
+
+#if 0	/* start of skip for non-Gnu makefiles */
+ifeq ($(target),Darwin)
+
+# default BINDIR for macOS
+BINDIR= /usr/local/bin
+
+else
+#endif	/* end of skip for non-Gnu makefiles */
+
+# default BINDIR for non-macOS
+BINDIR= /usr/bin
 #BINDIR= /usr/local/bin
 #BINDIR= /dev/env/DJDIR/bin
-BINDIR= /usr/bin
 
+#if 0	/* start of skip for non-Gnu makefiles */
+endif
+
+ifeq ($(target),Darwin)
+
+# default LIBDIR for macOS
+LIBDIR= /usr/local/lib
+
+else
+#endif	/* end of skip for non-Gnu makefiles */
+
+# default LIBDIR for non-macOS
+LIBDIR= /usr/lib
 #LIBDIR= /usr/local/lib
 #LIBDIR= /dev/env/DJDIR/lib
-LIBDIR= /usr/lib
 
+#if 0	/* start of skip for non-Gnu makefiles */
+endif
+
+ifeq ($(target),Darwin)
+
+# default CALC_SHAREDIR for macOS
+CALC_SHAREDIR= /usr/local/share/calc
+
+else
+#endif	/* end of skip for non-Gnu makefiles */
+
+# default CALC_SHAREDIR for non-macOS
+CALC_SHAREDIR= /usr/share/calc
 #CALC_SHAREDIR= /usr/local/lib/calc
 #CALC_SHAREDIR= /dev/env/DJDIR/share/calc
-CALC_SHAREDIR= /usr/share/calc
+
+#if 0	/* start of skip for non-Gnu makefiles */
+endif
+#endif	/* end of skip for non-Gnu makefiles */
 
 # NOTE: Do not set CALC_INCDIR to /usr/include or /usr/local/include!!!
 #	Always be sure that the CALC_INCDIR path ends in /calc to avoid
@@ -990,7 +1054,7 @@ EXT=
 
 # The default calc versions
 #
-VERSION= 2.12.6.1
+VERSION= 2.12.6.7
 
 # Names of shared libraries with versions
 #
@@ -1263,16 +1327,6 @@ LDCONFIG:=
 # DARWIN_ARCH= -arch ppc		# PPC binary
 # DARWIN_ARCH= -arch x86_64		# native 64-bit binary
 DARWIN_ARCH=				# native binary
-#
-# Starting with El Capitan OS X 10.11, root by default could not
-# mkdir under system locations, so we now use the /usr/local tree.
-#
-OPTDIR:= /usr/local
-BINDIR:= /${OPTDIR}/bin
-LIBDIR:= /${OPTDIR}/lib
-CALC_SHAREDIR:= /${OPTDIR}/share
-CALC_INCDIR:= /${OPTDIR}/include
-SCRIPTDIR:= ${BINDIR}/cscript
 endif
 
 ##################

README.WINDOWS

@@ -10,6 +10,21 @@ NOTE: The main developers do not have access to a Windoz based platform.
       Of course you are welcome to send us any patches that fix your
       Windoz build environment.
 
+
+=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
+=-= compiling with Windows Subsystem for Linux (WSL) =-Cygwin =-=
+=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
+
+It has been reported that calc version 2.12.6.4 has been successfully
+compiled, installed and running on Windows 10 on 2018 Jan 21.
+
+We were told:
+
+  "The Windows Subsystem for Linux (WSL) is a new Windows 10 feature that
+   enables you to run native Linux command-line tools directly on Windows"
+
+   https://docs.microsoft.com/cs-cz/windows/wsl/about
+
 =-=-=-=-=-=-=-=-=-=-=-=-=-=-=
 =-= compiling with Cygwin =-=
 =-=-=-=-=-=-=-=-=-=-=-=-=-=-=

cal/lucas.cal

@@ -1,7 +1,7 @@
 /*
  * lucas - perform a Lucas primality test on h*2^n-1
  *
- * Copyright (C) 1999,2017  Landon Curt Noll
+ * Copyright (C) 1999,2017,2018  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
@@ -28,6 +28,10 @@
  * For a general tutorial on how to find a new largest known prime, see:
  *
  *	http://www.isthe.com/chongo/tech/math/prime/prime-tutorial.pdf
+ *
+ * Also see the reference code, available both C and go:
+ *
+ *	https://github.com/arcetri/goprime
  */
 
 /*
@@ -154,6 +158,12 @@
  *
  * Finally, one should eliminate all values of 'h*2^n-1' where
  * 'h*2^n+1' is divisible by a small primes.
+ *
+ * NOTE: Today, for world record sized h*2^n-1 primes, one might
+ *	 search for factors < 2^46 or more.  By excluding h*2^n-1
+ *	 with prime factors < 2^46, where h*2^n-1 is a bit larger
+ *	 than the largest known prime, one may exclude about 96.5%
+ *	 of candidates that have "small" prime factors.
  */
 
 pprod256 = 0;	/* product of  "primes up to 256" / "primes up to 46" */
@@ -363,41 +373,53 @@ lucas(h, n)
 		return 1;		/* 239 is prime */
 	}
 
+	/*
+	 * Verify that h*2^n-1 is not a multiple of 3
+	 *
+	 * The case for h*2^n-1 == 3 is handled above.
+	 */
+	if (((h % 3 == 1) && (n % 2 == 0)) || ((h % 3 == 2) && (n % 2 == 1))) {
+		/* no need to test h*2^n-1, it is a multiple of 3 */
+		ldebug("lucas","not-prime: != 3 and is a multiple of 3");
+		return 0;
+	}
+
 	/*
 	 * Avoid any numbers divisible by small primes
 	 */
 	/*
-	 * check for 3 <= prime factors < 29
-	 * pfact(28)/2 = 111546435
+	 * check for 5 <= prime factors < 31
+	 * pfact(30)/6 = 1078282205
 	 */
 	testval = h*2^n - 1;
-	if (gcd(testval, 111546435) > 1) {
-		/* a small 3 <= prime < 29 divides h*2^n-1 */
-		ldebug("lucas","not-prime: 3<=prime<29 divides h*2^n-1");
+	if (gcd(testval, 1078282205) > 1) {
+		/* a small 5 <= prime < 31 divides h*2^n-1 */
+		ldebug("lucas",\
+		    "not-prime: a small 5<=prime<31 divides h*2^n-1");
 		return 0;
 	}
 	/*
-	 * check for 29 <= prime factors < 47
-	 * pfact(46)/pfact(28) = 5864229
+	 * check for 31 <= prime factors < 53
+	 * pfact(52)/pfact(30) = 95041567
 	 */
-	if (gcd(testval, 58642669) > 1) {
-		/* a small 29 <= prime < 47 divides h*2^n-1 */
-		ldebug("lucas","not-prime: 29<=prime<47 divides h*2^n-1");
+	if (gcd(testval, 95041567) > 1) {
+		/* a small 31 <= prime < 53 divides h*2^n-1 */
+		ldebug("lucas","not-prime: 31<=prime<53 divides h*2^n-1");
 		return 0;
 	}
 	/*
-	 * check for prime 47 <= factors < 257, if h*2^n-1 is large
-	 * 2^282 > pfact(256)/pfact(46) > 2^281
+	 * check for prime 53 <= factors < 257, if h*2^n-1 is large
+	 * 2^276 > pfact(256)/pfact(52) > 2^275
 	 */
 	bits = highbit(testval);
-	if (bits >= 281) {
+	if (bits >= 275) {
 		if (pprod256 <= 0) {
-			pprod256 = pfact(256)/pfact(46);
+			pprod256 = pfact(256)/pfact(52);
 		}
 		if (gcd(testval, pprod256) > 1) {
-			/* a small 47 <= prime < 257 divides h*2^n-1 */
+			/* a small 53 <= prime < 257 divides h*2^n-1 */
 			ldebug("lucas",\
-			    "not-prime: 47<=prime<257 divides h*2^n-1");
+			    "not-prime: 53<=prime<257 divides h*2^n-1");
 			return 0;
 		}
 	}
@@ -413,7 +435,9 @@ lucas(h, n)
 	 * generate a test for h*2^n-1.	 The legacy function,
 	 * legacy_gen_v1() used by the Amdahl 6 could have returned
 	 * -1. The new gen_v1() based on the method outlined in Ref4
-	 * will never return -1.
+	 * will never return -1 if h*2^n-1 is not a multiple of 3.
+	 * Because the "multiple of 3" case is handled above, the
+	 * call below to gen_v1() will never return -1.
 	 */
 	v1 = gen_v1(h, n);
 	if (v1 < 0) {
@@ -739,7 +763,7 @@ rodseth_xhn(x, h, n)
  * We can show that X > 2.  See the comments in the rodseth_xhn(x,h,n) above.
  *
  * Some values of X satisfy more often than others. For example a large sample
- * of odd h, h odd multiple of 3 and large n (some around 1e4, some near 1e6,
+ * of h*2^n-1, h odd multiple of 3, and large n (some around 1e4, some near 1e6,
  * others near 3e7) where the sample size was 66 973 365, here is the count of
  * the smallest value of X that satisfies conditions in Ref4, condition 1:
  *
@@ -805,82 +829,155 @@ rodseth_xhn(x, h, n)
  *
  * The above distribution was found to hold fairly well over many values of
  * odd h that are also a multiple of 3 and for many values of n where h < 2^n.
- * For example for in a sample size of 835823 numbers of the form h*2^n-1
- * where odd h >= 12996351 is a multiple of 3, n >= 12996351, these are the
- * smallest v(1) values that were found:
  *
- *  smallest percentage
- *	v(1) used
- *  -------------------
- *	   3 40.000%
- *	   5 25.683%
- *	   9 11.693%
- *	  11 10.452%
- *	  15 4.806%
- *	  17 2.348%
- *	  21 1.656%
- *	  29 1.281%
- *	  27 0.6881%
- *	  35 0.4536%
- *	  39 0.3121%
- *	  41 0.1760%
- *	  31 0.1414%
- *	  45 0.1173%
- *	  51 0.05576%
- *	  55 0.03300%
- *	  49 0.03185%
- *	  59 0.02090%
- *	  69 0.00980%
- *	  65 0.009367%
- *	  71 0.007205%
- *	  57 0.006341%
- *	  85 0.004611%
- *	  81 0.004179%
- *	  95 0.002882%
- *	  99 0.001873%
- *	  77 0.001153%
- *	  53 0.0007205%
- *	  67 0.0005764%
- *	 125 0.0005764%
- *	 105 0.0005764%
- *	  87 0.0004323%
- *	 111 0.0004323%
- *	 101 0.0002882%
- *	  83 0.0001441%
- *	 127 0.0001196%
+ * For example for in a sample size of 1000000 numbers of the form h*2^n-1
+ * where h is an odd multiple of 3, 12996351 <= h <= 13002351,
+ * 4331116 <= n <= 4332116, these are the smallest v(1) values that were found:
  *
- * When h * 2^n-1 is prime and h is an odd multiple of 3, a smallest v(1) that
- * is even is extremely rate.  Of the list of 127287 known primes of the form
- * h*2^n-1 when h was a multiple of 3, none has an smallest v(1) that was even.
+ *  smallest  percentage
+ *	v(1)     used
+ *  --------  ---------
+ *	  3   40.0000 %
+ *	  5   25.6833 %
+ *	  9   11.6924 %
+ *	 11   10.4528 %
+ *	 15    4.8048 %
+ *	 17    2.3458 %
+ *	 21    1.3734 %
+ *	 29    1.0527 %
+ *	 20    0.8595 %
+ *	 27    0.5758 %
+ *	 35    0.4420 %
+ *	 36    0.2433 %
+ *	 39    0.1779 %
+ *	 41    0.0885 %
+ *	 45    0.0571 %
+ *	 32    0.0337 %
+ *	 51    0.0289 %
+ *	 44    0.0205 %
+ *	 49    0.0176 %
+ *	 56    0.0137 %
+ *	 59    0.0108 %
+ *	 57    0.0053 %
+ *	 65    0.0047 %
+ *	 55    0.0045 %
+ *	 69    0.0031 %
+ *	 71    0.0024 %
+ *	 66    0.0011 %
+ *	 95    0.0008 %
+ *	 81    0.0008 %
+ *	 77    0.0006 %
+ *	 72    0.0005 %
+ *	 99    0.0004 %
+ *	 80    0.0003 %
+ *	 74    0.0003 %
+ *	 84    0.0002 %
+ *	 67    0.0002 %
+ *	 87    0.0001 %
+ *	104    0.0001 %
+ *	129    0.0001 %
  *
- * About 1 out of 835000 cases when h is a multiple of 3 use v(1) > 127 as the
- * smallest value of v(1).
+ * However, a case can be made for considering only odd values for v(1)
+ * candidates.  When h * 2^n-1 is prime and h is an odd multiple of 3,
+ * a smallest v(1) that is even is extremely rate.  Of the list of 146553
+ * known primes of the form h*2^n-1 when h is an odd a multiple of 3,
+ * none has an smallest v(1) that was even.
+ *
+ * See:
+ *
+ *	https://github.com/arcetri/verified-prime
+ *
+ * for that list of 146553 known primes of the form h*2^n-1.
+ *
+ * That same example for in a sample size of 1000000 numbers of the
+ * form h*2^n-1 where h is an odd multiple of 3, 12996351 <= h <= 13002351,
+ * 4331116 <= n <= 4332116, these are the smallest odd v(1) values that were
+ * found:
+ *
+ *  smallest    percentage
+ *  odd v(1)       used
+ *  --------    ---------
+ *	  3	40.0000 %
+ *	  5	25.6833 %
+ *	  9	11.6924 %
+ *	 11	10.4528 %
+ *	 15	 4.8048 %
+ *	 17	 2.3458 %
+ *	 21	 1.6568 %
+ *	 29	 1.6174 %
+ *	 35	 0.4529 %
+ *	 27	 0.3546 %
+ *	 39	 0.3470 %
+ *	 41	 0.2159 %
+ *	 45	 0.1173 %
+ *	 31	 0.0661 %
+ *	 51	 0.0619 %
+ *	 55	 0.0419 %
+ *	 59	 0.0250 %
+ *	 49	 0.0170 %
+ *	 69	 0.0110 %
+ *	 65	 0.0098 %
+ *	 71	 0.0078 %
+ *	 85	 0.0048 %
+ *	 81	 0.0044 %
+ *	 95	 0.0038 %
+ *	 99	 0.0021 %
+ *	125	 0.0009 %
+ *	 57	 0.0007 %
+ *	111	 0.0005 %
+ *	 77	 0.0003 %
+ *	165	 0.0003 %
+ *	155	 0.0002 %
+ *	129	 0.0002 %
+ *	101	 0.0002 %
+ *	 53	 0.0001 %
+ *
+ * Moreover when evaluating odd candidates for v(1), one may cache Jacobi
+ * symbol evaluations to reduce the number of Jacobi symbol evaluations to
+ * a minimum. For example, if one tests 5 and finds that the 2nd case fails:
+ *
+ *	jacobi(5+2, h*2^n-1) != -1
+ *
+ * Then if one is later testing 9, the Jacobi symbol value for the first
+ * 1st case:
+ *
+ *	jacobi(7-2, h*2^n-1)
+ *
+ * is already known.
+ *
+ * Without Jacobi symbol value caching, it requires on average
+ * 4.851377 Jacobi symbol evaluations.  With Jacobi symbol value caching
+ * cacheing, an averare of 4.348820 Jacobi symbol evaluations is needed.
  *
  * Given this information, when odd h is a multiple of 3 we try, in order,
- * these sorted values of X:
+ * these odd values of X:
  *
- *      3, 5, 9, 11, 15, 17, 21, 27, 29, 31, 35, 39, 41, 45, 49, 51, 53, 55,
- *	57, 59, 65, 67, 69, 71, 77, 81, 83, 85, 87, 95, 99, 101, 105, 111, 125
+ *	3, 5, 9, 11, 15, 17, 21, 29, 27, 35, 39, 41, 31, 45, 51, 55, 49, 59,
+ *	69, 65, 71, 57, 85, 81, 95, 99, 77, 53, 67, 125, 111, 105, 87, 129,
+ *	101, 83, 165, 155, 149, 141, 121, 109
  *
  * And stop on the first value of X where:
  *
  *      jacobi(X-2, h*2^n-1) == 1
  *      jacobi(X+2, h*2^n-1) == -1
  *
- * If no value in that list works, we start simple search starting with X = 12/
+ * Less than 1 case out of 1000000 will not be satisifed by the above list.
+ * If no value in that list works, we start simple search starting with X = 167
  * and incrementing by 2 until a value of X is found.
  *
- * The x_tbl[] matrix contains those common values of X to try in order.
- * If all x_tbl_len fail to satisfy Ref4 condition 1, then we begin a
- * linear search at next_x until we find a proper X value.
+ * The x_tbl[] matrix contains those values of X to try in order.
+ * If all x_tbl_len fail to satisfy Ref4 condition 1 (this happens less than
+ * 1 in 1000000 cases), then we begin a linear search of odd values starting at
+ * next_x until we find a proper X value.
  */
-x_tbl_len = 35;
+x_tbl_len = 42;
 mat x_tbl[x_tbl_len];
 x_tbl = {
-    3, 5, 9, 11, 15, 17, 21, 27, 29, 31, 35, 39, 41, 45, 49, 51, 53, 55,
-    57, 59, 65, 67, 69, 71, 77, 81, 83, 85, 87, 95, 99, 101, 105, 111, 125
+    3, 5, 9, 11, 15, 17, 21, 29, 27, 35, 39, 41, 31, 45, 51, 55, 49, 59,
+    69, 65, 71, 57, 85, 81, 95, 99, 77, 53, 67, 125, 111, 105, 87, 129,
+    101, 83, 165, 155, 149, 141, 121, 109
 };
-next_x = 127;
+next_x = 167;	/* must be 2 more than the largest value in x_tbl[] */
 
 /*
  * gen_v1 - compute the v(1) for a given h*2^n-1 if we can
@@ -938,12 +1035,22 @@ next_x = 127;
  *
  *	u(2) = v(h)				 (NOTE: some call this u(2))
  *
- * so we simply return
+ * so we can always return
  *
  *	v(1) = alpha^1 + alpha^(-1)
  *	     = (2+sqrt(3)) + (2-sqrt(3))
  *	     = 4
  *
+ * In 40% of the cases when h is not a multiple of 3, 3 is a valid value
+ * for v(1).  We can test if 3 is a valid value for v(1) in this case:
+ *
+ *	if jacobi(1, h*2^n-1) == 1 and jacobi(5, h*2^n-1) == -1, then
+ *	    v(1) = 3
+ *	else
+ *	    v(1) = 4
+ *
+ * HOTE: The above "if then else" works only of h is not a multiple of 3.
+ *
  ***
  *
  * Case 2:	(h mod 3 == 0)
@@ -1039,13 +1146,18 @@ next_x = 127;
  *	n	n as in h*2^n-1	(must be >= 1)
  *
  * output:
- *	returns v(1), or -1 is there is no quick way
+ *	returns v(1), or
+ *		-1 when h*2^n-1 is a multiple of 3
  */
 define
 gen_v1(h, n)
 {
 	local x;	/* potential v(1) to test */
 	local i;	/* x_tbl index */
+	local v1m2;	/* X-2 1st case */
+	local v1p2;	/* X+2 2nd case */
+	local testval;	/* h*2^n-1 - value we are testing if prime */
+	local mat cached_v1[next_x];	/* cached Jacobi symbol values or 0 */
 
 	/*
 	 * check arg types
@@ -1066,18 +1178,56 @@ gen_v1(h, n)
 		quit "bad args: n must be an integer >= 1";
 	}
 
+	/*
+	 * pretest: Verify that h*2^n-1 is not a multiple of 3
+	 */
+	if (((h % 3 == 1) && (n % 2 == 0)) || ((h % 3 == 2) && (n % 2 == 1))) {
+		/* no need to test h*2^n-1, it is not prime */
+		return -1;
+	}
+
+	/*
+	 * Common Mersenne number case:
+	 *
+	 * For Mersenne numbers:
+	 *
+	 *	2^n-1
+	 *
+	 * we can use, 40% of the time, v(1) == 3.  However nearly all code that
+	 * implements the Lucas-Lehmer test uses v(1) == 4.  Whenever for
+	 * h != 0 mod 3, and particular the Mersenne number case of when h == 1:
+	 *
+	 *	1*2^n-1
+	 *
+	 * v(1) == 4 always works.  For this reason, we return 4 when h == 1.
+	 */
+	if (h == 1) {
+		/* v(1) == 4 always works for the Mersenne number case */
+		return 4;
+	}
+
 	/*
 	 * check for Case 1:      (h mod 3 != 0)
 	 */
 	if (h % 3 != 0) {
-		/* v(1) is easy to compute */
-		return 4;
+		if (rodseth_xhn(3, h, n) == 1) {
+			/* 40% of the time, 3 works when h mod 3 != 0 */
+			return 3;
+		} else {
+			/* otherwise 4 always works when h mod 3 != 0 */
+			return 4;
+		}
 	}
 
 	/*
 	 * What follow is Case 2:      (h mod 3 == 0)
 	 */
 
+	/*
+	 * clear cache
+	 */
+	matfill(cached_v1, 0);
+
 	/*
 	 * We will look for x that satisfies conditions in Ref4, condition 1:
 	 *
@@ -1089,26 +1239,51 @@ gen_v1(h, n)
 	 *	 to the next odd value, the now jacobi(X-2, h*2^n-1)
 	 *	 does not need to be re-evaluted.
 	 */
+	testval = h*2^n-1;
 	for (i=0; i < x_tbl_len; ++i) {
 
 		/*
-		 * test Ref4 condition 1:
+		 * obtain the next test candidate
 		 */
 		x = x_tbl[i];
-		if (rodseth_xhn(x, h, n) == 1) {
 
-			/*
-			 * found a x that satisfies Ref4 condition 1
-			 */
-			ldebug("gen_v1", "h= " + str(h) + " n= " + str(n) +
-				" v1= " + str(x) + " using tbl[ " +
-				str(i) + " ]");
-			return x;
+		/*
+		 * Check x for condition 1 part 1
+		 *
+		 *	jacobi(x-2, h*2^n-1) == 1
+		 */
+		v1m2 = x-2;
+		if (cached_v1[v1m2] == 0) {
+			cached_v1[v1m2] = jacobi(v1m2, testval);
 		}
+		if (cached_v1[v1m2] != 1) {
+			continue;
+		}
+
+		/*
+		 * Check x for condition 1 part 2
+		 *
+		 *	jacobi(x+2, h*2^n-1) == -1
+		 */
+		v1p2 = x+2;
+		if (cached_v1[v1p2] == 0) {
+			cached_v1[v1p2] = jacobi(v1p2, testval);
+		}
+		if (cached_v1[v1p2] != -1) {
+			continue;
+		}
+
+		/*
+		 * found a x that satisfies Ref4 condition 1
+		 */
+		ldebug("gen_v1", "h= " + str(h) + " n= " + str(n) +
+			" v1= " + str(x) + " using tbl[ " +
+			str(i) + " ]");
+		return x;
 	}
 
 	/*
-	 * We are in that rare case (about 1 in 835 000) where none of the
+	 * We are in that rare case (less than 1 in 1 000 000) where none of the
 	 * common X values satisfy Ref4 condition 1.  We start a linear search
 	 * of odd vules at next_x from here on.
 	 */

calc.c

@@ -104,6 +104,8 @@ main(int argc, char **argv)
 	int c;			/* option */
 	int index;
 	int maxindex;
+	/* fix gcc warning bug */
+	int unusedint = 0;
 	char *cp;
 	char *endcp;
 	char *bp;
@@ -278,7 +280,9 @@ main(int argc, char **argv)
 						    exit(6);
 						}
 						calc_debug = cp;
-						(void) strtol(cp, &endcp, 10);
+						/* fix gcc warning bug */
+						unusedint =
+						    strtol(cp, &endcp, 10);
 						cp = endcp;
 						if (*cp != '\0' &&
 						    *cp != ' ' && *cp != ':') {
@@ -310,7 +314,9 @@ main(int argc, char **argv)
 						    exit(9);
 						}
 						resource_debug = cp;
-						(void) strtol(cp, &endcp, 10);
+						/* fix gcc warning bug */
+						unusedint =
+						    strtol(cp, &endcp, 10);
 						cp = endcp;
 						if (*cp != '\0' &&
 						    *cp != ' ' && *cp != ':') {
@@ -340,7 +346,8 @@ main(int argc, char **argv)
 					    exit(12);
 					}
 					user_debug = cp;
-					(void) strtol(cp, &endcp, 10);
+					/* unusedint avoids gcc warning bug */
+					unusedint = strtol(cp, &endcp, 10);
 					cp = endcp;
 					if (*cp != '\0' && *cp != ' ') {
 						fprintf(stderr, "Bad syntax in"
@@ -721,8 +728,10 @@ main(int argc, char **argv)
 		printf("main: run_state = %s\n", run_state_name(run_state));
 
 	/*
-	 * all done
+	 * All done! - Jessica Noll, Age 2
 	 */
+	/* fix gcc warning bug */
+	unusedint++;
 	libcalc_call_me_last();
 	return (run_state == RUN_EXIT_WITH_ERROR ||
 		run_state == RUN_ZERO) ? 1 : 0;

calc.h

@@ -65,7 +65,6 @@
 
 #define SYMBOLSIZE	256	/* maximum symbol name size */
 #define MAXLABELS	100	/* maximum number of user labels in function */
-#define MAXSTRING	1024	/* maximum size of string constant */
 #define MAXSTACK	2048	/* maximum depth of evaluation stack */
 #define MAXFILES	20	/* maximum number of opened files */
 #define PROMPT1		"> "	/* default normal prompt*/

calc.man

@@ -657,8 +657,8 @@ searches in succession:
 .sp 1
 .in +5n
 .nf
-./myfile
-./myfile.cal
+\a./myfile
+\a./myfile.cal
 ${LIBDIR}/myfile
 ${LIBDIR}/myfile.cal
 ${CUSTOMCALDIR}/myfile

custom/Makefile

@@ -348,7 +348,7 @@ EXT=
 
 # The default calc versions
 #
-VERSION= 2.12.6.1
+VERSION= 2.12.6.7
 
 # Names of shared libraries with versions
 #
@@ -628,16 +628,6 @@ LDCONFIG:=
 # DARWIN_ARCH= -arch ppc		# PPC binary
 # DARWIN_ARCH= -arch x86_64		# native 64-bit binary
 DARWIN_ARCH=				# native binary
-#
-# Starting with El Capitan OS X 10.11, root by default could not
-# mkdir under system locations, so we now use the /usr/local tree.
-#
-OPTDIR:= /usr/local
-BINDIR:= /${OPTDIR}/bin
-LIBDIR:= /${OPTDIR}/lib
-CALC_SHAREDIR:= /${OPTDIR}/share
-CALC_INCDIR:= /${OPTDIR}/include
-SCRIPTDIR:= ${BINDIR}/cscript
 endif
 
 ##################

custom/Makefile.head

@@ -348,7 +348,7 @@ EXT=
 
 # The default calc versions
 #
-VERSION= 2.12.6.1
+VERSION= 2.12.6.7
 
 # Names of shared libraries with versions
 #

custom/c_sysinfo.c

@@ -173,8 +173,6 @@ STATIC struct infoname sys_info[] = {
      (FULL)MAXSCANCOUNT},
     {"MAXSTACK", "max depth of evaluation stack", NULL,
      (FULL)MAXSTACK},
-    {"MAXSTRING", "max size of string constant", NULL,
-     (FULL)MAXSTRING},
     {"MAXUFULL", "largest FULL value", NULL,
      (FULL)MAXUFULL},
     {"MAXULONG", "largest unsigned long val", NULL,

help/mat

@@ -54,13 +54,13 @@ DESCRIPTION
     The elements of the matrix are stored internally as a linear array
     in which locations are arranged in order of increasing indices.
     For example, in order of location, the six element of A = mat [2,3]
-    are
+    are:
 
-	A[0,0], A[0,1], A[0,2], A[1,0], A[1,,1], A[1,2].
+	A[0,0], A[0,1], A[0,2], A[1,0], A[1,1], and A[1,2].
 
     These elements may also be specified using the double-bracket operator
     with a single integer index as in A[[0]], A[[1]], ..., A[[5]].
-    If p is assigned the value &A[0.0], the address of A[[i]] for 0 <= i < 6
+    If p is assigned the value &A[0,0], the address of A[[i]] for 0 <= i < 6
     is p + i as long as A exists and a new value is not assigned to A.
 
     When a matrix is created, each element is initially assigned the
@@ -414,7 +414,7 @@ SEE ALSO
     det, inverse, isident, test, config, search, rsearch, reverse, copy,
     blkcpy, dp, cp, randperm, sort
 
-## Copyright (C) 1999-2006  Landon Curt Noll
+## Copyright (C) 1999-2006,2018  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

help/randbit

@@ -1,5 +1,5 @@
 NAME
-    randbit - additive 55 shuffle pseudo-random number generator
+    randbit - subtractive 100 shuffle pseudo-random number generator
 
 SYNOPSIS
     randbit([x])
@@ -42,7 +42,7 @@ LINK LIBRARY
 SEE ALSO
     seed, srand, randbit, isrand, random, srandom, israndom
 
-## Copyright (C) 1999  Landon Curt Noll
+## Copyright (C) 1999,2018  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

help/seed

@@ -18,14 +18,7 @@ DESCRIPTION
 	It should be pointed out that the information collected by seed
 	is almost certainly non-chaotic.  This function is likely not
 	suitable for applications (such as cryptographic applications)
-	where the unpredictability of seeds is critical.  For such critical
-	applications, LavaRnd should be used.	See the URL:
-
-		http://www.LavaRnd.org/
-
-	for information about seeding a pseudo-random number generator
-	(such as rand() or random()) with the cryptographic hash of the
-	digitization of chaotic system.
+	where the unpredictability of seeds is critical.
 
     Given the above warning, this builtin function produces a seed that is
     suitable for most applications that desire a different pseudo-random
@@ -51,7 +44,7 @@ LINK LIBRARY
 SEE ALSO
     seed, srand, randbit, isrand, rand, random, srandom, israndom
 
-## Copyright (C) 1999  Landon Curt Noll
+## Copyright (C) 1999,2018  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

help/srandom

@@ -332,13 +332,13 @@ LIMITS
     iq >= 2^16
 
 LINK LIBRARY
-    RAND *zsrandom(ZVALUE *pseed, MATRIX *pmat55)
-    RAND *zsetrandom(RAND *state)
+    RANDOM *zsrandom(ZVALUE *pseed, MATRIX *pmat55)
+    RANDOM *zsetrandom(RAND *state)
 
 SEE ALSO
     seed, srand, randbit, isrand, random, srandom, israndom
 
-## Copyright (C) 1999  Landon Curt Noll
+## Copyright (C) 1999,2018  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

help/types

@@ -1,6 +1,6 @@
 Builtin types
 
-    The calculator has the following built-in types.
+    The calculator has the following built-in types:
 
     null value
 	    This is the undefined value type.  The function 'null'
@@ -101,7 +101,20 @@ Builtin types
 	    using the result of the 'files' function.  Such copies are
 	    indistinguishable from each other.
 
-## Copyright (C) 1999  Landon Curt Noll
+    The calculator also has a number of special types that as used
+    by some special builtin functions:
+
+    rand
+	    A subtractive 100 shuffle pseudo-random number generator
+	    state.  This state is used by functions such as isrand()
+	    and srand().
+
+    random
+	    A Blum-Blum-Shub pseudo-random number generator state.
+	    This state is used by functions such as israndom() and
+	    srandom().
+
+## Copyright (C) 1999,2018  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

hist.h

@@ -36,7 +36,7 @@
 #endif
 
 #ifndef HIST_SIZE
-#define HIST_SIZE		(1024*10)
+#define HIST_SIZE		(1024*32)
 #endif
 
 

input.c

@@ -59,8 +59,8 @@ E_FUNC FILE *f_open(char *name, char *mode);
 E_FUNC FILE *curstream(void);
 
 
-#define TTYSIZE		100	/* reallocation size for terminal buffers */
-#define MAXDEPTH		10	/* maximum depth of input */
+#define TTYSIZE		8191	/* reallocation size for terminal buffers */
+#define MAXDEPTH	255	/* maximum depth of input */
 #define IS_READ		1	/* reading normally */
 #define IS_REREAD	2	/* reread current character */
 #define chartoint(ch)	((ch) & 0xff)	/* make sure char is not negative */
@@ -789,7 +789,7 @@ ttychar(void)
 {
 	int ch;			/* current char */
 	int len;		/* length of current command */
-	STATIC char charbuf[1024];
+	STATIC char charbuf[256*1024];
 
 	/*
 	 * If we have more to read from the saved command line, then do that.

qmath.h

@@ -254,7 +254,9 @@ E_FUNC NUMBER *swap_HALF_in_NUMBER(NUMBER *dest, NUMBER *src, BOOL all);
 #define qhighbit(q)	(zhighbit((q)->num))
 #define qlowbit(q)	(zlowbit((q)->num))
 #define qdivcount(q1, q2)	(zdivcount((q1)->num, (q2)->num))
-#define qlink(q)	((q)->links++, (q))
+/* operation on #q may be undefined, so replace with an inline-function */
+/* was: #define qlink(q)	((q)->links++, (q)) */
+static inline NUMBER* qlink(NUMBER* q) { if(q) { (q)->links++; } return q; }
 
 #define qfree(q)	{if (--((q)->links) <= 0) qfreenum(q);}
 

value.c

@@ -2944,7 +2944,7 @@ printestr(VALUE *vp)
 				bp = vp->v_nblock->blk;
 			}
 			i = bp->datalen;
-			math_fmt("%ld,%d)", i, bp->blkchunk);
+			math_fmt("%ld,%d)", i, (int) bp->blkchunk);
 			cp = bp->data;
 			if (i > 0) {
 				math_str("={");

version.c

@@ -45,7 +45,7 @@ static char *program;
 #define MAJOR_VER	2	/* major library version */
 #define MINOR_VER	12	/* minor library version */
 #define MAJOR_PATCH	6	/* major software level under library version */
-#define MINOR_PATCH	1	/* minor software level or 0 if not patched */
+#define MINOR_PATCH	7	/* minor software level or 0 if not patched */
 
 
 /*

zfunc.c

@@ -1029,93 +1029,98 @@ zgcd(ZVALUE z1, ZVALUE z2, ZVALUE *res)
 				needw = FALSE;
 			}
 			g = *a0 * w;
-			if (h < BASEB) g &= (1 << h) - 1;
-			else g &= BASE1;
+			if (h < BASEB) {
+			    g &= (1 << h) - 1;
+			} else {
+			    g &= BASE1;
+			}
+		} else {
+			g = 1;
 		}
-		else g = 1;
-	   } else
+	    } else {
 		g = (HALF) *a0 * w;
-		a = a0;
-		b = b0;
-		i = n;
-		if (g > 1) {			/* a - g * b case */
-			f = 0;
-			while (i--) {
-				f = (FULL) *a - g * *b++ - f;
-				*a++ = (HALF) f;
-				f >>= BASEB;
-				f = -f & BASE1;
-			}
-			if (f) {
-				i = m - n;
-				while (i-- && f) {
-					f = *a - f;
-					*a++ = (HALF) f;
-					f >>= BASEB;
-					f = -f & BASE1;
-				}
-			}
-			while (m && !*a0) { /* Removing trailing zeros */
-				m--;
-				a0++;
-			}
-			if (f) {		/* a - g * b < 0 */
-				while (m > 1 && a0[m-1] == BASE1) m--;
-				*a0 = - *a0;
-				a = a0;
-				i = m;
-				while (--i) {
-					a++;
-					*a = ~*a;
-				}
-			}
-		} else {				/* abs(a - b) case */
-			while (i && *a++ == *b++) i--;
-			q = n - i;
-			if (m == n) {		/* a and b same length */
-				if (i) {	 /* a not equal to b */
-					while (m && a0[m-1] == b0[m-1]) m--;
-					if (a0[m-1] < b0[m-1]) {
-						/* Swapping since a < b */
-						a = a0;
-						a0 = b0;
-						b0 = a;
-						k = j;
-					}
-					a = a0 + q;
-					b = b0 + q;
-					i = m - q;
-					f = 0;
-					while (i--) {
-						f = (FULL) *a - *b++ - f;
-						*a++ = (HALF) f;
-						f >>= BASEB;
-						f = -f & BASE1;
-					}
-				}
-			} else {		/* a has more digits than b */
-				a = a0 + q;
-				b = b0 + q;
-				i = n - q;
-				f = 0;
-				while (i--) {
-					f = (FULL) *a - *b++ - f;
-					*a++ = (HALF) f;
-					f >>= BASEB;
-					f = -f & BASE1;
-				}
-				if (f) { while (!*a) *a++ = BASE1;
-					(*a)--;
-				}
-			}
-			a0 += q;
-			m -= q;
-			while (m && !*a0) { /* Removing trailing zeros */
-				m--;
-				a0++;
-			}
-		}
-		while (m && !a0[m-1]) m--;	/* Removing leading zeros */
+	    }
+	    a = a0;
+	    b = b0;
+	    i = n;
+	    if (g > 1) {			/* a - g * b case */
+		    f = 0;
+		    while (i--) {
+			    f = (FULL) *a - g * *b++ - f;
+			    *a++ = (HALF) f;
+			    f >>= BASEB;
+			    f = -f & BASE1;
+		    }
+		    if (f) {
+			    i = m - n;
+			    while (i-- && f) {
+				    f = *a - f;
+				    *a++ = (HALF) f;
+				    f >>= BASEB;
+				    f = -f & BASE1;
+			    }
+		    }
+		    while (m && !*a0) { /* Removing trailing zeros */
+			    m--;
+			    a0++;
+		    }
+		    if (f) {		/* a - g * b < 0 */
+			    while (m > 1 && a0[m-1] == BASE1) m--;
+			    *a0 = - *a0;
+			    a = a0;
+			    i = m;
+			    while (--i) {
+				    a++;
+				    *a = ~*a;
+			    }
+		    }
+	    } else {				/* abs(a - b) case */
+		    while (i && *a++ == *b++) i--;
+		    q = n - i;
+		    if (m == n) {		/* a and b same length */
+			    if (i) {	 /* a not equal to b */
+				    while (m && a0[m-1] == b0[m-1]) m--;
+				    if (a0[m-1] < b0[m-1]) {
+					    /* Swapping since a < b */
+					    a = a0;
+					    a0 = b0;
+					    b0 = a;
+					    k = j;
+				    }
+				    a = a0 + q;
+				    b = b0 + q;
+				    i = m - q;
+				    f = 0;
+				    while (i--) {
+					    f = (FULL) *a - *b++ - f;
+					    *a++ = (HALF) f;
+					    f >>= BASEB;
+					    f = -f & BASE1;
+				    }
+			    }
+		    } else {		/* a has more digits than b */
+			    a = a0 + q;
+			    b = b0 + q;
+			    i = n - q;
+			    f = 0;
+			    while (i--) {
+				    f = (FULL) *a - *b++ - f;
+				    *a++ = (HALF) f;
+				    f >>= BASEB;
+				    f = -f & BASE1;
+			    }
+			    if (f) { while (!*a) *a++ = BASE1;
+				    (*a)--;
+			    }
+		    }
+		    a0 += q;
+		    m -= q;
+		    while (m && !*a0) { /* Removing trailing zeros */
+			    m--;
+			    a0++;
+		    }
+	    }
+	    while (m && !a0[m-1]) m--;	/* Removing leading zeros */
 	}
 	if (m == 1) {				/* a has one digit */
 		v = *a0;