add help in advance for new log2 and logn builtins

NOTE: The `log2(x [,eps])` and `logn(x, n [,eps])`
builtin functions are NOT yet implemented.

help/Makefile

@@ -217,15 +217,15 @@ DETAIL_HELP= abs access acos acosh acot acoth acsc acsch address agd \
 	islist islower ismat ismult isnull isnum isobj isobjtype isodd isprime \
 	isprint isptr ispunct isqrt isrand israndom isreal isrel issimple \
 	isspace issq isstr istype isupper isxdigit jacobi join lcm lcmfact \
-	lfactor ln log lowbit ltol makelist matdim matfill matmax matmin \
+	lfactor ln log log2 logn lowbit ltol makelist matdim matfill matmax \
-	matsum mattrace mattrans max memsize meq min minv mmin mne mod modify \
+	matmin matsum mattrace mattrans max memsize meq min minv mmin mne mod \
-	name near newerror nextcand nextprime norm null num oldvalue ord param \
+	modify name near newerror nextcand nextprime norm null num oldvalue \
-	perm pfact pi pix places pmod polar poly pop popcnt pound power \
+	ord param perm pfact pi pix places pmod polar poly pop popcnt pound \
-	prevcand prevprime printf prompt protect ptest push putenv quo quomod \
+	power prevcand prevprime printf prompt protect ptest push putenv quo \
-	r2d r2g rand randbit random randombit randperm rcin rcmul rcout rcpow \
+	quomod r2d r2g rand randbit random randombit randperm rcin rcmul rcout \
-	rcsq re remove reverse rewind rm root round rsearch runtime saveval \
+	rcpow rcsq re remove reverse rewind rm root round rsearch runtime \
-	scale scan scanf search sec sech seed segment select sgn sha1 sin sinh \
+	saveval scale scan scanf search sec sech seed segment select sgn sha1 \
-	size sizeof sleep sort sqrt srand srandom ssq stoponerror str \
+	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 \
@@ -234,7 +234,7 @@ DETAIL_HELP= abs access acos acosh acot acoth acsc acsch address agd \
 # This list is of files that are clones of DETAIL_HELP files.  They are
 # built from DETAIL_HELP files.
 #
-DETAIL_CLONE= copy
+DETAIL_CLONE= copy ilogn
 
 # Singular files
 #
@@ -501,6 +501,18 @@ releases: ../README.RELEASE
 	    ${TRUE}; \
 	fi
 
+ilogn: ilog
+	${RM} -f $@
+	${CP} ilog $@
+	${CHMOD} 0444 $@
+	-@if [ -z "${Q}" ]; then \
+	    echo ''; \
+	    echo '=-=-= skipping the ${CAT} of help/$@ =-=-='; \
+	    echo ''; \
+	else \
+	    ${TRUE}; \
+	fi
+
 full: ${FULL_HELP_FILES} ${MAKE_FILE}
 	${Q} echo "forming full"
 	${Q} ${RM} -f $@

help/ilog

@@ -1,8 +1,10 @@
 NAME
     ilog - floor of logarithm to specified integer base
+    ilogn - floor of logarithm to specified integer base
 
 SYNOPSIS
     ilog(x, b)
+    ilogn(x, b)
 
 TYPES
     x		nonzero real
@@ -13,10 +15,15 @@ TYPES
 DESCRIPTION
     Returns the greatest integer n for which b^n <= abs(x).
 
+    The ilogn function is an alias for ilog.
+
 EXAMPLE
     ; print ilog(2, 3), ilog(8, 3), ilog(8.9, 3), ilog(1/8, 3)
     0 1 1 -2
 
+    ; print ilogn(2, 3), ilogn(8, 3), ilogn(8.9, 3), ilogn(1/8, 3)
+    0 1 1 -2
+
 LIMITS
     x > 0
     b > 1
@@ -25,9 +32,9 @@ LINK LIBRARY
     long zlog(ZVALUE x, ZVALUE b)
 
 SEE ALSO
-    ilog2, ilog10
+    ilog10, ilog2, ln, log, log2, logn
 
-## Copyright (C) 1999  Landon Curt Noll
+## Copyright (C) 1999,2023  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/ilog10

@@ -23,9 +23,9 @@ LINK LIBRARY
     long qilog10(NUMBER *q)
 
 SEE ALSO
-    ilog2, ilog
+    ilog, ilogn, ilog2, ln, log, log2, logn
 
-## Copyright (C) 1999  Landon Curt Noll
+## Copyright (C) 1999,2023  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/ilog2

@@ -23,9 +23,9 @@ LINK LIBRARY
     long qilog2(NUMBER *q)
 
 SEE ALSO
-    ilog10, ilog
+    ilog, ilogn, ilog10, ln, log, log2, logn
 
-## Copyright (C) 1999  Landon Curt Noll
+## Copyright (C) 1999,2023  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/ln

@@ -32,9 +32,9 @@ LINK LIBRARY
     COMPLEX *c_ln(COMPLEX *x, NUMBER *eps)
 
 SEE ALSO
-    exp, acosh, asinh, atanh, log
+    acosh, asinh, atanh, exp, ilog, ilogn, ilog10, ilog2, log, log2, logn
 
-## Copyright (C) 1999,2021  Landon Curt Noll
+## Copyright (C) 1999,2021,2023  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/log

@@ -13,8 +13,9 @@ TYPES
 DESCRIPTION
     Approximate the base 10 logarithm function of x by a multiple of
     epsilon, the error having absolute value less than 0.75 * eps.
-    If n is a positive integer, log(x, 10^-n) will usually be correct
+
-    to the n-th decimal place.
+    If y is a positive integer, log(x, 10^-y) will usually be correct
+    to the y-th decimal place.
 
 EXAMPLE
     ; print log(10), log(100), log(1e10), log(1e500)
@@ -35,7 +36,7 @@ LINK LIBRARY
     COMPLEX *c_log(COMPLEX *x, NUMBER *eps)
 
 SEE ALSO
-    ln
+    ilog, ilogn, ilog10, ilog2, ln, log2, logn
 
 ## Copyright (C) 2006  Landon Curt Noll
 ##

help/log2

@@ -0,0 +1,64 @@
+NAME
+    log2 -  base 10 logarithm
+
+SYNOPSIS
+    log2(x [,eps])
+
+TYPES
+    x		nonzero real or complex
+    eps		nonzero real, defaults to epsilon()
+
+    return	real or complex
+
+DESCRIPTION
+    Approximate the base 2 logarithm function of x by a multiple of
+    epsilon, the error having absolute value less than 0.75 * eps.
+
+    If y is a positive integer, log(x, 2^-y) will usually be correct
+    to the y-th decimal place.
+
+    When x if a power of 2, log2(x) will return an integer regardless
+    of the value of eps or epsilon().
+
+EXAMPLE
+    ; print log2(2), log2(4), log2(1024), log2(2^500)
+    1 2 10 500
+
+    ; print log(127), log(23209), log(2^17-19)
+    ~ 6.98868468677216585326 ~ 14.50239674255407864468 ~ 16.99979085393743521984
+
+    ; print log(2+3i, 1e-5)
+    ~ 1.85020558320709803073 + ~ 1.41786049195700786266i
+
+LIMITS
+    x != 0
+    eps > 0
+
+LINK LIBRARY
+    NUMBER *qlog2(NUMBER *x, NUMBER *eps)
+    COMPLEX *c_log2(COMPLEX *x, NUMBER *eps)
+
+SEE ALSO
+    ilog, ilogn, ilog10, ilog2, ln, log, logn
+
+## Copyright (C) 2023  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:	2023/08/19 09:14:04
+## File existed as early as:	2023
+##
+## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
+## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/

help/logn

@@ -0,0 +1,68 @@
+NAME
+    logn -  base n logarithm
+
+SYNOPSIS
+    logn(x, n [,eps])
+
+TYPES
+    x		nonzero real or complex
+    n		nonzero real or complex
+    eps		nonzero real, defaults to epsilon()
+
+    return	real or complex
+
+DESCRIPTION
+    Approximate the base n logarithm function of x by a multiple of
+    epsilon, the error having absolute value less than 0.75 * eps.
+
+    The base, n, must not be 0 nor 1.
+
+    If y is a positive integer, log(x, n^-y) will usually be correct
+    to the y-th decimal place.
+
+EXAMPLE
+    ; print logn(15.625, 2.5), logn(15.625, 2.5, 1e-25)
+    ~ 3.00000000000000000001 3
+
+    ; print logn(127, 1/13), log(23209, sqrt(3)), logn(2^17-19, 17)
+    ~ -1.88860925162778125111 6 ~ 4.15900804831225415076
+
+    ; print logn(-1, 1i), logn(2+3i, 3i+2), logn(2+3i, 3i)
+    2 1 ~ 0.80360095345990217753 - ~ 0.25441159318835790311i
+
+    ; print logn(22+3i, 3i, 1e-50)
+    ~ 0.98489914201047045408 - ~ 1.28484657882287682702i
+
+LIMITS
+    x != 0
+    n != 0 && n != 1
+    eps > 0
+
+LINK LIBRARY
+    NUMBER *qlogn(NUMBER *x, NUMBER *n, NUMBER *eps)
+    COMPLEX *c_logn(COMPLEX *x, COMPLEX *n, NUMBER *eps)
+
+SEE ALSO
+    ilog, ilogn, ilog10, ilog2, ln, log, log2
+
+## Copyright (C) 2023  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:	2023/08/19 09:14:04
+## File existed as early as:	2023
+##
+## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
+## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/