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Release calc version 2.10.2t30

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This commit is contained in:
Landon Curt Noll
1996-07-06 04:17:00 -07:00
commit 4618313a82
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#
# help - makefile for calc help files
#
# Copyright (c) 1994 David I. Bell and Landon Curt Noll
# Permission is granted to use, distribute, or modify this source,
# provided that this copyright notice remains intact.
#
# Arbitrary precision calculator.
#
# calculator by David I. Bell
# makefile by Landon Curt Noll
# required vars
#
SHELL= /bin/sh
MAKE_FILE = Makefile
# Normally, the upper level makefile will set these values. We provide
# a default here just in case you want to build from this directory.
#
TOPDIR= /usr/local/lib
#TOPDIR= /usr/lib
#TOPDIR= /usr/libdata
LIBDIR= ${TOPDIR}/calc
HELPDIR= ${LIBDIR}/help
# Makefile debug
#
# Q=@ do not echo internal makefile actions (quiet mode)
# Q= echo internal makefile actions (debug / verbose mode)
#
#Q=
Q=@
# standard tools
#
NATIVE_CC= cc
NATIVE_CFLAGS=
SED= sed
SORT= sort
FMT= fmt
CMP= cmp
CAT= cat
# Standard help files
#
# The obj.file is special and is not listed here.
#
STD_HELP_FILES1= intro overview help command config \
define environment expression file history interrupt mat
STD_HELP_FILES2= operator statement types usage variable
STD_HELP_FILES3= todo credit
STD_HELP_FILES= ${STD_HELP_FILES1} ${STD_HELP_FILES2} ${STD_HELP_FILES3}
SYMBOL_HELP= assign
# These two lists are prodiced by the detaillist and missinglist rules
# when no WARNINGS are detected.
#
DETAIL_HELP= abs access acos acosh acot acoth acsc acsch append appr archive \
arg asec asech asin asinh assoc atan atan2 atanh avg base bround \
btrunc ceil cfappr cfsim char cmdbuf cmp comb conj cos cosh cot coth \
count cp csc csch ctime delete den det digit digits dp epsilon errno \
error eval exp fact factor fclose fcnt feof ferror fflush fgetc \
fgetfield fgetline fgets fgetstr fib files floor fopen forall fprintf \
fputc fputs fputstr frac frem freopen fscan fscanf fseek fsize ftell \
gcd gcdrem getenv hash head highbit hmean hypot ilog ilog10 ilog2 im \
insert int inverse iroot isassoc isatty isconfig iserror iseven \
isfile ishash isident isint islist ismat ismult isnull isnum isobj \
isodd isprime isqrt isrand israndom isreal isrel isset issimple issq \
isstr istype jacobi join lcm lcmfact lfactor list ln lowbit ltol \
makelist matdim matfill matmax matmin matsum mattrans max meq min \
minv mmin mne mod modify near newerror nextcand nextprime norm null \
num ord param perm pfact pi pix places pmod polar poly pop power \
prevcand prevprime printf prompt ptest push putenv quo quomod rand \
randbit randperm rcin rcmul rcout rcpow rcsq re rm remove reverse \
rewind root round rsearch runtime scale scan scanf search sec sech \
segment select sgn sin sinh size sizeof sort sqrt srand ssq str \
strcat strerror strlen strpos strprintf strscan strscanf substr swap \
system tail tan tanh time trunc xor
# Help files that are constructed from other sources
#
# The obj.file is special and is not listed here.
#
BUILT_HELP_FILES= bindings altbind changes libcalc stdlib bugs errorcodes
# Singular files
#
# These files are copies of their plural form.
#
PLURAL_FILES= bindings bugs changes errorcodes types
SINGULAR_FILES= binding bug change errorcode type
# These files are found (but not built) in the distribution
#
DISTLIST= ${STD_HELP_FILES} ${DETAIL_HELP} ${SYMBOL_HELP} ${MAKE_FILE} \
obj.file builtin.top builtin.end funclist.sed \
errorcodes.hdr errorcodes.sed
all: ${STD_HELP_FILES} obj.file ${BUILT_HELP_FILES} full \
${DETAIL_HELP} ${SINGULAR_FILES} builtin .all
# used by the upper level Makefile to determine of we have done all
#
# NOTE: Due to bogus shells found on one common system we must have
# an non-emoty else clause for every if condition. *sigh*
#
.all:
rm -f .all
touch .all
bindings: ../lib/bindings
rm -f bindings
cp ../lib/bindings bindings
chmod 0444 bindings
-@if [ -z "${Q}" ]; then \
echo ''; \
echo '=-=-= skipping the cat of help/$@ =-=-='; \
echo ''; \
else \
true; \
fi
altbind: ../lib/altbind
rm -f altbind
cp ../lib/altbind altbind
chmod 0444 altbind
-@if [ -z "${Q}" ]; then \
echo ''; \
echo '=-=-= skipping the cat of help/$@ =-=-='; \
echo ''; \
else \
true; \
fi
stdlib: ../lib/README
rm -f stdlib
cp ../lib/README stdlib
chmod 0444 stdlib
-@if [ -z "${Q}" ]; then \
echo ''; \
echo '=-=-= skipping the cat of help/$@ =-=-='; \
echo ''; \
else \
true; \
fi
changes: ../CHANGES
rm -f changes
cp ../CHANGES changes
chmod 0444 changes
-@if [ -z "${Q}" ]; then \
echo ''; \
echo '=-=-= skipping the cat of help/$@ =-=-='; \
echo ''; \
else \
true; \
fi
libcalc: ../LIBRARY
rm -f libcalc
${SED} -e 's:$${LIBDIR}:${LIBDIR}:g' < ../LIBRARY > libcalc
chmod 0444 libcalc
-@if [ -z "${Q}" ]; then \
echo ''; \
echo '=-=-= skipping the cat of help/$@ =-=-='; \
echo ''; \
else \
true; \
fi
bugs: ../BUGS
rm -f bugs
cp ../BUGS bugs
chmod 0444 bugs
-@if [ -z "${Q}" ]; then \
echo ''; \
echo '=-=-= skipping the cat of help/$@ =-=-='; \
echo ''; \
else \
true; \
fi
errorcodes: ../calcerr.h errorcodes.hdr errorcodes.sed
rm -f errorcodes
${CAT} errorcodes.hdr > errorcodes
${SED} -n -f errorcodes.sed < ../calcerr.h >> errorcodes
chmod 0444 errorcodes
-@if [ -z "${Q}" ]; then \
echo ''; \
echo '=-=-= skipping the cat of help/$@ =-=-='; \
echo ''; \
else \
true; \
fi
full: ${STD_HELP_FILES} ${BUILT_HELP_FILES} ${MAKE_FILE}
${Q}echo "forming full"
-${Q}rm -f full
-${Q}for i in ${STD_HELP_FILES1} obj.file ${STD_HELP_FILES2} \
${BUILT_HELP_FILES} ${STD_HELP_FILES3}; do \
if [ Xintro != X"$$i" ]; then \
echo " "; \
else \
true; \
fi; \
if [ Xobj.file = X"$$i" ]; then \
j=obj; \
else \
j=$$i; \
fi; \
echo "*************"; \
echo "* $$j"; \
echo "*************"; \
echo ""; \
cat $$i; \
done > full
${Q}echo "full formed"
-@if [ -z "${Q}" ]; then \
echo ''; \
echo '=-=-= skipping the cat of help/$@ =-=-='; \
echo ''; \
else \
true; \
fi
# Singular files are the same files as their plural form.
#
${SINGULAR_FILES}: ${PLURAL_FILES}
${Q}for i in ${SINGULAR_FILES}; do \
echo "rm -f $${i}"; \
rm -f $${i}; \
echo "cp $${i}s $${i}"; \
cp $${i}s $${i}; \
done
-@if [ -z "${Q}" ]; then \
echo ''; \
echo '=-=-= skipping the cat of help/SINGULAR_FILES =-=-='; \
echo ''; \
else \
true; \
fi
# Form the builtin file
#
# We ave a "chicken-and-egg" problem. We want the builtn help file to
# accurately reflect the function list. It would be nice if we could
# just execute calc show builtin, but calc may not have been built or
# buildable at this point. The hack-a-round used is to convert ../func.c
# into a standalone program that generates a suitable function list
# that is standwiched between the top and bottom builtin help text.
#
# We form funclist.c by sedding out unwanted stuff from builtins table,
# converting NUMBER* and VALUE into harmless types and converting
# the showbuiltins() function into main(). Combined with the -DFUNCLIST
# we will avoid all of the complex calc types, macros and defines and
# be left with just main() and a mininal builtins table.
#
# Building funclist.o a portable fashion is ugly because some systems
# do not treat -I.. correctly!
#
builtin: builtin.top builtin.end ../func.c funclist.sed
${Q}echo "forming builtin help file"
-${Q}rm -f builtin
${Q}cat builtin.top > builtin
-${Q}rm -f funclist.c
${Q}${SED} -n -f funclist.sed ../func.c > funclist.c
-${Q}rm -f ../funclist.c ../funclist.o ../funclist funclist
${Q}cp funclist.c ..
-${Q}(cd ..; \
${NATIVE_CC} ${NATIVE_CFLAGS} -DFUNCLIST funclist.c -o funclist; \
mv funclist help; \
rm -f funclist.c funclist.o funclist)
${Q}./funclist | \
${SED} -e 's/^/ /' -e 's/[ ][ ]*$$//' >> builtin
${Q}cat builtin.end >> builtin
${Q}echo "builtin help file formed"
-@if [ -z "${Q}" ]; then \
echo ''; \
echo '=-=-= skipping the cat of help/$@ =-=-='; \
echo ''; \
else \
true; \
fi
##
#
# File list generation. You can ignore this section.
#
#
# We will form the names of source files as if they were in a
# sub-directory called calc/help.
#
##
distlist: ${DISTLIST}
${Q}for i in ${DISTLIST}; do \
echo calc/help/$$i; \
done | ${SORT}
# The bsdi distribution has generated files as well as distributed files.
#
bsdilist: ${DISTLIST} ${BUILT_HELP_FILES}
${Q}for i in ${DISTLIST} ${BUILT_HELP_FILES}; do \
echo calc/help/$$i; \
done | ${SORT}
# The BSDI cdrom makefile expects all help files to be pre-built. This rule
# creats these fils so that the release can be shipped off to BSDI. You can
# ignore this rule.
#
bsdi: all
rm -f obj
cp obj.file obj
# These next rule help me form the ${DETAIL_HELP} makefile variables above.
#
detaillist:
${Q}-(echo "xxxxx"; \
for i in ${DETAIL_HELP}; do \
if [ ! -f SCCS/s.$$i ]; then \
echo "WARNING: $$i not under SCCS control" 1>&2; \
else \
echo $$i; \
fi; \
done | ${SORT}) | ${FMT} -70 | \
${SED} -e '1s/xxxxx/DETAIL_HELP=/' -e '2,$$s/^/ /' \
-e 's/$$/ \\/' -e '$$s/ \\$$//'
clean:
rm -f obj mkbuiltin funclist.c funclist.o funclist
clobber:
rm -f ${BUILT_HELP_FILES} full builtin .all
rm -f obj mkbuiltin funclist.c funclist.o funclist ${SINGULAR_FILES}
install: all
-${Q}if [ ! -d ${TOPDIR} ]; then \
echo mkdir ${TOPDIR}; \
mkdir ${TOPDIR}; \
else \
true; \
fi
-${Q}if [ ! -d ${LIBDIR} ]; then \
echo mkdir ${LIBDIR}; \
mkdir ${LIBDIR}; \
else \
true; \
fi
-${Q}if [ ! -d ${HELPDIR} ]; then \
echo mkdir ${HELPDIR}; \
mkdir ${HELPDIR}; \
else \
true; \
fi
${Q}for i in ${STD_HELP_FILES} ${BUILT_HELP_FILES} builtin \
full ${DETAIL_HELP} ${SINGULAR_FILES} ${SYMBOL_HELP}; do \
echo rm -f ${HELPDIR}/$$i; \
rm -f ${HELPDIR}/$$i; \
echo cp $$i ${HELPDIR}; \
cp $$i ${HELPDIR}; \
echo chmod 0444 ${HELPDIR}/$$i; \
chmod 0444 ${HELPDIR}/$$i; \
done
rm -f ${HELPDIR}/obj
cp obj.file ${HELPDIR}/obj
chmod 0444 ${HELPDIR}/obj

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NAME
abs - absolute value
SYNOPSIS
abs(x [,eps])
TYPES
If x is an object of type xx, the function xx_abs has to have
been defined; this will determine the types for x, eps and
the returned value.
For non-object x and eps:
x number (real or complex)
eps ignored if x is real, nonzero real for complex x,
defaults to epsilon().
return real
DESCRIPTION
If x is real, returns x if x is positive or zero, -x if x is negative.
For complex x, returns the multiple of eps nearest or next to nearest
to the absolute value of x. The result usually has error less in
absolute value than abs(eps), but should not exceed 0.75 * abs(eps).
EXAMPLE
> print abs(3.4), abs(-3.4)
3.4 3.4
> print abs(3+4i, 1e-5), abs(4+5i, 1e-5), abs(4+5i, 1e-10)
5 6.40312 6.4031242374
LIMITS
none
LIBRARY
none
SEE ALSO
cmp, epsilon, hypot, norm, near, obj

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NAME
access - determine existence or accessibility of named file
SYNOPSIS
access(name [, mode])
TYPES
name string
mode integer or string containing only 'r', 'w', 'x' characters
return null value or error
DESCRIPTION
access(name) or access(name, 0) or access(name, "") returns the null
value if a file with this name exists.
If non-null mode is specified, the null value is returned if there
is a file with the specified name and accessibility indicated by the
bits or characters of the mode argument: 'r' or bit 2 for reading,
'w' or bit 1 for writing, 'x' or bit 0 for execution.
EXAMPLE
> !rm -f junk
> access("junk")
Error 10002 XXX This number will probably be changed
> f = fopen("junk", "w")
> access("junk")
> fputs(f, "Now is the time");
> freopen(f, "r");
> !chmod u-w junk
> fgets(f)
"Now is the time"
> access("junk", "w")
Error 10013 XXX
> freopen(f, "w")
Error 10013 XXX
LIMITS
none - XXX - is this correct?
LIBRARY
none - XXX - is this correct?
SEE ALSO
errno, fclose, feof, ferror, fflush, fgetc, fgetline, fgets, files, fopen,
fprintf, fputc, fputs, fseek, fsize, ftell, isfile, printf, prompt

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NAME
acos - inverse trigonometric cosine
SYNOPSIS
acos(x [,eps])
TYPES
x real, -1 <= x <= 1
eps nonzero real, defaults to epsilon()
return real
DESCRIPTION
Returns the acos of x to a multiple of eps with error less in
absolute value than .75 * eps.
v = acos(x) is the number in [0, pi] for which cos(v) = x.
EXAMPLE
> print acos(.5, 1e-5), acos(.5, 1e-10), acos(.5, 1e-15), acos(.5, 1e-20)
1.0472 1.0471975512 1.047197551196598 1.04719755119659774615
LIMITS
unlike sin and cos, x must be real
abs(x) <= 1
eps > 0
LIBRARY
NUMBER *qacos(NUMBER *x, NUMBER *eps)
SEE ALSO
asin, atan, asec, acsc, acot, epsilon

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NAME
acosh - inverse hyperbolic cosine
SYNOPSIS
acosh(x [,eps])
TYPES
x real, x >= 1
eps nonzero real, defaults to epsilon()
return nonnegative real
DESCRIPTION
Returns the cosh of x to a multiple of eps with error less in
absolute value than .75 * eps.
acosh(x) = ln(x + sqrt(x^2 - 1)) is the nonnegative real number v
for which cosh(v) = x.
EXAMPLE
> print acosh(2, 1e-5), acosh(2, 1e-10), acosh(2, 1e-15), acosh(2, 1e-20)
1.31696 1.3169578969 1.316957896924817 1.31695789692481670862
LIMITS
unlike sin and cos, x must be real
eps > 0
LIBRARY
NUMBER *qacosh(NUMBER *x, NUMBER *eps)
SEE ALSO
asinh, atanh, asech, acsch, acoth, epsilon

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NAME
acot - inverse trigonometric cotangent
SYNOPSIS
acot(x [,eps])
TYPES
x real
eps nonzero real, defaults to epsilon()
return real
DESCRIPTION
Returns the acot of x to a multiple of eps with error less in
absolute value than .75 * eps.
v = acot(x) is the number in (0, pi) for which cot(v) = x.
EXAMPLE
> print acot(2, 1e-5), acot(2, 1e-10), acot(2, 1e-15), acot(2, 1e-20)
.46365 .463647609 .463647609000806 .46364760900080611621
LIMITS
unlike sin and cos, x must be real
eps > 0
LIBRARY
NUMBER *qacot(NUMBER *x, NUMBER *eps)
SEE ALSO
asin, acos, atan, asec, acsc, epsilon

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NAME
acoth - inverse hyperbolic cotangent
SYNOPSIS
acoth(x [,eps])
TYPES
x real, with abs(x) > 1
eps nonzero real, defaults to epsilon()
return real
DESCRIPTION
Returns the acoth of x to a multiple of eps with error less in
absolute value than .75 * eps.
acoth(x) = ln((x + 1)/(x - 1))/2 is the real number v for which
coth(v) = x.
EXAMPLE
> print acoth(2, 1e-5), acoth(2, 1e-10), acoth(2, 1e-15), acoth(2, 1e-20)
.54931 .5493061443 .549306144334055 .5493061443340548457
LIMITS
unlike sin and cos, x must be real
abs(x) > 1
eps > 0
LIBRARY
NUMBER *qacoth(NUMBER *x, NUMBER *eps)
SEE ALSO
asinh, acosh, atanh, asech, acsch, epsilon

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NAME
acsc - inverse trigonometric cosecant
SYNOPSIS
acsc(x [,eps])
TYPES
x real, with absolute value >= 1
eps nonzero real, defaults to epsilon()
return real
DESCRIPTION
Returns the acsc of x to a multiple of eps with error less in
absolute value than .75 * eps.
v = acsc(x) is the number in [-pi/2, pi/2] for which csc(v) = x.
EXAMPLE
> print acsc(2, 1e-5), acsc(2, 1e-10), acsc(2, 1e-15), acsc(2, 1e-20)
.5236 .5235987756 .523598775598299 .52359877559829887308
LIMITS
unlike sin and cos, x must be real
abs(x) >= 1
eps > 0
LIBRARY
NUMBER *qacsc(NUMBER *x, NUMBER *eps)
SEE ALSO
asin, acos, atan, asec, acot, epsilon

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NAME
acsch - inverse hyperbolic cosecant
SYNOPSIS
acsch(x [,eps])
TYPES
x nonzero real
eps nonzero real, defaults to epsilon()
return real
DESCRIPTION
Returns the acsch of x to a multiple of eps with error less in
absolute value than .75 * eps.
acsch(x) = ln((1 + sqrt(1 + x^2))/x) is the real number v for
which csch(v) = x.
EXAMPLE
> print acsch(2, 1e-5), acsch(2, 1e-10), acsch(2, 1e-15), acsch(2, 1e-20)
.48121 .4812118251 .481211825059603 .4812118250596034475
LIMITS
unlike sin and cos, x must be real
x != 0
eps > 0
LIBRARY
NUMBER *qacsch(NUMBER *x, NUMBER *eps)
SEE ALSO
asinh, acosh, atanh, asech, acoth, epsilon

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NAME
append - append one or more values to end of list
SYNOPSIS
append(x, y_0, y_1, ...)
TYPES
x lvalue whose value is a list
y_0, ... any
return null value
DESCRIPTION
If after evaluation of y_0, y_1, ..., x is a list with contents
(x_0, x_1, ...), then after append(x, y_0, y_1, ...), x has
contents (x_0, x_1, ..., y_0, y_1, ...).
If after evaluation of y_0, y_1, ..., x has size n,
append(x, y_0, y_1, ...) is equivalent to insert(x, n, y_0, y_1, ...).
EXAMPLE
> x = list(2,3,4)
> append(x, 5, 6)
> print x
list (5 elements, 5 nonzero):
[[0]] = 2
[[1]] = 3
[[2]] = 4
[[3]] = 5
[[4]] = 6
> append(x, pop(x), pop(x))
> print x
list (5 elements, 5 nonzero):
[[0]] = 4
[[1]] = 5
[[2]] = 6
[[3]] = 2
[[4]] = 3
> append(x, (remove(x), 7))
> print x
list (5 elements, 5 nonzero):
[[0]] = 4
[[1]] = 5
[[2]] = 6
[[3]] = 2
[[4]] = 7
LIMITS
append() can have at most 100 arguments
LIBRARY
none
SEE ALSO
delete, insert, islist, list, pop, push, remove, rsearch, search, size

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NAME
appr - approximate numbers by multiples of a specified number
SYNOPSIS
appr(x [,y [,z]])
TYPES
x real, complex, matrix, list
y real
z integer
return same type as x except that complex x may return a real number
DESCRIPTION
Return the approximate value of x as specified by a specific error
(epsilon) and config ("appr") value.
The default value for y is epsilon(). The default value for z is
the current value of the "appr" configuration parameter.
If y is zero or x is a multiple of y, appr(x,y,z) returns x. I.e.,
there is no "approximation" - the result represents x exactly.
In the following it is assumed y is nonzero and x is not a multiple of y.
For Real x:
appr(x,y,z) is either the nearest multiple of y greater
than x or the nearest multiple of y less than x. Thus, if
we write a = appr(x,y,z) and r = x - a, then a/y is an integer
and abs(r) < abs(y). If r > 0, we say x has been "rounded down"
to a; if r < 0, the rounding is "up". For particular x and y,
whether the rounding is down or up is determined by z.
Only the 5 lowest bits of z are used, so we may assume z has been
replaced by its value modulo 32. The type of rounding depends on
z as follows:
z = 0 round down or up according as y is positive or negative,
sgn(r) = sgn(y)
z = 1 round up or down according as y is positive or negative,
sgn(r) = -sgn(y)
z = 2 round towards zero, sgn(r) = sgn(x)
z = 3 round away from zero, sgn(r) = -sgn(x)
z = 4 round down
z = 5 round up
z = 6 round towards or from zero according as y is positive or
negative, sgn(r) = sgn(x/y)
z = 7 round from or towards zero according as y is positive or
negative, sgn(r) = -sgn(x/y)
z = 8 a/y is even
z = 9 a/y is odd
z = 10 a/y is even or odd according as x/y is positive or negative
z = 11 a/y is odd or even according as x/y is positive or negative
z = 12 a/y is even or odd according as y is positive or negative
z = 13 a/y is odd or even according as y is positive or negative
z = 14 a/y is even or odd according as x is positive or negative
z = 15 a/y is odd or even according as x is positive or negative
z = 16 to 31 abs(r) <= abs(y)/2; if there is a unique multiple
of y that is nearest x, appr(x,y,z) is that multiple of y
and then abs(r) < abs(y)/2. If x is midway between
successive multiples of y, then abs(r) = abs(y)/2 and
the value of a is as given by appr(x, y, z-16).
Matrix or List x:
appr(x,y,z) returns the matrix or list indexed in the same way as x,
in which each element t has been replaced by appr(t,y,z).
XXX - complex x needs to be documented
PROPERTIES
If appr(x,y,z) != x, then abs(x - appr(x,y,z)) < abs(y).
If appr(x,y,z) != x and 16 <= z <= 31, abs(x - appr(x,y,z)) <= abs(y)/2.
For z = 0, 1, 4, 5, 16, 17, 20 or 21, and any integer n,
appr(x + n*y, y, z) = appr(x, y, z) + n * y.
If y is nonzero, appr(x,y,8)/y = an odd integer n only if x = n * y.
EXAMPLES
> print appr(-5.44,0.1,0), appr(5.44,0.1,0), appr(5.7,1,0), appr(-5.7,1,0)
-5.5 5.4 5 -6
> print appr(-5.44,-.1,0), appr(5.44,-.1,0), appr(5.7,-1,0), appr(-5.7,-1,0)
-5.4 5.5 6 -5
> print appr(-5.44,0.1,3), appr(5.44,0.1,3), appr(5.7,1,3), appr(-5.7,1,3)
-5.5 5.5 6 -6
> print appr(-5.44,0.1,4), appr(5.44,0.1,4), appr(5.7,1,4), appr(-5.7,1,4)
-5.5 5.4 5 -6
> print appr(-5.44,0.1,6), appr(5.44,0.1,6), appr(5.7,1,6), appr(-5.7,1,6)
-5.4 5.4 6 -5
> print appr(-5.44,-.1,6), appr(5.44,-.1,6), appr(5.7,-1,6), appr(-5.7,-1,6)
-5.5 5.5 6 -6
> print appr(-5.44,0.1,9), appr(5.44,0.1,9), appr(5.7,1,9), appr(-5.7,1,9)
-5.5 5.5 5 -5
> print appr(-.44,0.1,11), appr(.44,0.1,11), appr(5.7,1,11), appr(-5.7,1,11)
-.4 .5 5 -6
> print appr(-.44,-.1,11),appr(.44,-.1,11),appr(5.7,-1,11),appr(-5.7,-1,11)
-.5 .4 6 -5
> print appr(-.44,0.1,12), appr(.44,0.1,12), appr(5.7,1,12), appr(-5.7,1,12)
-.4 .5 5 -6
> print appr(-.44,-.1,12),appr(.44,-.1,12),appr(5.7,-1,12),appr(-5.7,-1,12)
-.5 .4 6 -5
> print appr(-.44,0.1,15), appr(.44,0.1,15), appr(5.7,1,15), appr(-5.7,1,15)
-.4 .5 5 -6
> print appr(-.44,-.1,15),appr(.44,-.1,15),appr(5.7,-1,15),appr(-5.7,-1,15)
-.4 .5 5 -6
LIMITS
none
LIBRARY
NUMBER *qmappr(NUMBER *q, NUMBER *e, long R);
LIST *listappr(LIST *oldlp, VALUE *v2, VALUE *v3);
MATRIX *matappr(MATRIX *m, VALUE *v2, VALUE *v3);
SEE ALSO
round, bround, cfappr, cfsim

25
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Where to get the the latest versions of calc
Landon Noll maintains the official calc ftp archive at:
ftp://ftp.uu.net/pub/calc
Alpha test versions, complete with bugs, untested code and
experimental features may be fetched (if you are brave) under:
http://reality.sgi.com/chongo/calc/
One may join the calc testing group by sending a request to:
calc-tester-request@postofc.corp.sgi.com
Your message body (not the subject) should consist of:
subscribe calc-tester address
end
name your_full_name
where "address" is your EMail address and "your_full_name"
is your full name.
Landon Curt Noll <chongo@toad.com> /\oo/\

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NAME
arg - argument (the angle or phase) of a complex number
SYNOPSIS
arg(x [,eps])
TYPES
x number
eps nonzero real, defaults to epsilon()
return real
DESCRIPTION
Returns the argument of x to the nearest or next to nearest multiple of
eps; the error will be less in absolute value than 0.75 * abs(eps),
but usually less than 0.5 * abs(eps). By default, acc is epsilon().
EXAMPLE
> print arg(2), arg(2+3i, 1e-5), arg(2+3i, 1e-10), arg(2+3i, 1e-20)
0 .98279 .9827937232 .98279372324732906799
> pi = pi(1e-10); deg = pi/180; eps = deg/10000
> print arg(2+3i, eps)/deg, arg(-1 +1i, eps)/deg, arg(-1 - 1i,eps)/deg
56.3099 135 -135
LIMITS
none
LIBRARY
none
SEE ALSO
conj, im, polar, re

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NAME
asec - inverse trigonometric secant
SYNOPSIS
asec(x [,eps])
TYPES
x real, with absolute value >= 1
eps nonzero real, defaults to epsilon()
return real
DESCRIPTION
Returns the asec of x to a multiple of eps with error less in
absolute value than .75 * eps.
v = asec(x) is the number in [0, pi] for which sec(v) = x.
EXAMPLE
> print asec(2, 1e-5), asec(2, 1e-10), asec(2, 1e-15), asec(2, 1e-20)
1.0472 1.0471975512 1.047197551196598 1.04719755119659774615
LIMITS
unlike sin and cos, x must be real
abs(x) >= 1
eps > 0
LIBRARY
NUMBER *qasec(NUMBER *x, NUMBER *eps)
SEE ALSO
asin, acos, atan, acsc, acot, epsilon

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NAME
asech - inverse hyperbolic secant
SYNOPSIS
asech(x [,eps])
TYPES
x real, 0 < x <= 1
eps nonzero real, defaults to epsilon()
return real
DESCRIPTION
Returns the asech of x to a multiple of eps with error less in
absolute value than .75 * eps.
asech(x) = ln((1 + sqrt(1 - x^2))/x) is the real number v for which
sech(v) = x.
EXAMPLE
> print asech(.5,1e-5), asech(.5,1e-10), asech(.5,1e-15), asech(.5,1e-20)
1.31696 1.3169578969 1.316957896924817 1.31695789692481670862
LIMITS
unlike sin and cos, x must be real
0 < x <= 1
eps > 0
LIBRARY
NUMBER *qasech(NUMBER *x, NUMBER *eps)
SEE ALSO
asinh, acosh, atanh, acsch, acoth, epsilon

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NAME
asin - inverse trigonometric sine
SYNOPSIS
asin(x [,eps])
TYPES
x real, -1 <= x <= 1
eps nonzero real, defaults to epsilon()
return real
DESCRIPTION
Returns the asin of x to a multiple of eps with error less in
absolute value than .75 * eps.
v = asin(x) is the number in [-p1/2, pi/2] for which sin(v) = x.
EXAMPLE
> print asin(.5, 1e-5), asin(.5, 1e-10), asin(.5, 1e-15), asin(.5, 1e-20)
.5236 .5235987756 .523598775598299 .52359877559829887308
LIMITS
unlike sin and cos, x must be real
abs(x) <= 1
eps > 0
LIBRARY
NUMBER *qasin(NUMBER *q, NUMBER *epsilon)
SEE ALSO
acos, atan, asec, acsc, acot, epsilon

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NAME
asinh - inverse hyperbolic sine
SYNOPSIS
asinh(x [,eps])
TYPES
x real
eps nonzero real, defaults to epsilon()
return real
DESCRIPTION
Returns the asinh of x to a multiple of eps with error less in
absolute value than .75 * eps.
asinh(x) = ln(x + sqrt(1 + x^2)) is the real number v for which
sinh(v) = x.
EXAMPLE
> print asinh(2, 1e-5), asinh(2, 1e-10), asinh(2, 1e-15), asinh(2, 1e-20)
1.44363 1.4436354752 1.44363547517881 1.44363547517881034249
LIMITS
unlike sin and cos, x must be real
eps > 0
LIBRARY
NUMBER *qasinh(NUMBER *x, NUMBER *eps)
SEE ALSO
acosh, atanh, asech, acsch, acoth, epsilon

29
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NAME
=
SYNOPSIS
a = b
TYPES
a lvalue
b expression
return lvalue
DESCRIPTION
a = b evaluates b, assigns its value to a, and returns a.
EXAMPLE
> b = 3+1
> a = b
> print a, b
4 4
LIMITS
none
LIBRARY
none
SEE ALSO
XXX - fill in

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NAME
assoc - create a new association array
SYNOPSIS
assoc()
TYPES
return association
DESCRIPTION
This functions returns an empty association array.
Associations are special values that act like matrices, except
that they are more general (and slower) than normal matrices.
Unlike matrices, associations can be indexed by arbitrary values.
For example, if 'val' was an association, you could do the following:
val['hello'] = 11;
val[4.5] = val['hello'];
print val[9/2];
and 11 would be printed.
Associations are created by the 'assoc' function. It takes no
arguments, and simply returns an empty association. You can then
insert elements into the association by indexing the returned value
as shown above.
Associations are multi-dimensional. You can index them using one to
four dimensions as desired, and the elements with different numbers
of dimensions will remain separated. For example, 'val[3]' and
'val[3,0]' can both be used in the same association and will be
distinct elements.
When references are made to undefined elements of an association,
a null value is simply returned. Therefore no bounds errors can
occur when indexing an association. Assignments of a null value
to an element of an association does not delete the element, but
a later reference to that element will return the null value as if
the element was undefined. Elements with null values are implicitly
created on certain other operations which require an address to be
taken, such as the += operator and using & in a function call.
The elements of an association are stored in a hash table for
quick access. The index values are hashed to select the correct
hash chain for a small sequential search for the element. The hash
table will be resized as necessary as the number of entries in
the association becomes larger.
The size function returns the number of elements in an association.
This size will include elements with null values.
Double bracket indexing can be used for associations to walk through
the elements of the association. The order that the elements are
returned in as the index increases is essentially random. Any
change made to the association can reorder the elements, this making
a sequential scan through the elements difficult.
The search and rsearch functions can search for an element in an
association which has the specified value. They return the index
of the found element, or a NULL value if the value was not found.
Associations can be copied by an assignment, and can be compared
for equality. But no other operations on associations have meaning,
and are illegal.
EXAMPLE
> print assoc()
assoc (0 elements):
LIMITS
none
LIBRARY
none
SEE ALSO
isassoc, rsearch, search, size

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NAME
atan - inverse trigonometric tangent
SYNOPSIS
atan(x [,eps])
TYPES
x real
eps nonzero real, defaults to epsilon()
return real
DESCRIPTION
Returns the atan of x to a multiple of eps with error less in
absolute value than .75 * eps.
v = atan(x) is the number in (-p1/2, pi/2) for which tan(v) = x.
EXAMPLE
> print atan(2, 1e-5), atan(2, 1e-10), atan(2, 1e-15), atan(2, 1e-20)
1.10715 1.1071487178 1.107148717794091 1.10714871779409050302
LIMITS
unlike sin and cos, x must be real
eps > 0
LIBRARY
NUMBER *qatan(NUMBER *x, NUMBER *eps)
SEE ALSO
asin, acos, asec, acsc, acot, epsilon

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NAME
atan2 - angle to point
SYNOPSIS
atan2(y, x, [,acc])
TYPES
y real
x real
acc real
return real
DESCRIPTION
Return the angle which is determined by the point (x,y). This
function computes the arctangent of y/x in the range [-pi, pi].
The value acc specifies the accuracy of the result. By default, acc
is epsilon().
Note that by convention, y is the first argument.
To conform to the 4.3BSD ANSI/IEEE 754-1985 math lib, atan2(0,0) is
defined to return 0.
EXAMPLE
> print atan2(0,0), atan2(1,sqrt(3)), atan2(17,53,1e-100)
0 ~.52359877559829887307 ~.31038740713235146535
LIMITS
acc > 0
LIBRARY
NUMBER *qatan2(NUMBER *y, *x, *acc)
SEE ALSO
acos, asin, atan, cos, epsilon, sin, tan

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NAME
atanh - inverse hyperbolic tangent
SYNOPSIS
atanh(x [,eps])
TYPES
x real
eps nonzero real, defaults to epsilon()
return real
DESCRIPTION
Returns the atanh of x to a multiple of eps with error less in
absolute value than .75 * eps.
atanh(x) = ln((1 + x)/(1 - x))/2 is the real number v for whichi
tanh(v) = x.
EXAMPLE
> print atanh(.5,1e-5), atanh(.5,1e-10), atanh(.5,1e-15), atanh(.5,1e-20)
.54931 .5493061443 .549306144334055 .5493061443340548457
LIMITS
unlike sin and cos, x must be real
eps > 0
LIBRARY
NUMBER *qatanh(NUMBER *x, NUMBER *eps)
SEE ALSO
asinh, acosh, asech, acsch, acoth, epsilon

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NAME
avg - average (arithmetic) mean of values
SYNOPSIS
avg(x_1, x_2, ...)
TYPES
x_1, ... arithmetic or list
return as determined by types of items averaged
DESCRIPTION
If there are n non-list arguments x_1, x_2, ..., x_n,
for which the required additions and division by n are defined,
avg(x_1, x_2, ..., x_n) returns the value of:
(x_1 + x_2 + ... + x_n)/n.
If the x_i are real, the result will be a real number; if the
x_i are real or complex numbers, the result will be a real or complex
number. If the x_i are summable matrices the result will be a matrix
of the same size (e.g. if the x_i are all 3 x 4 matrices with real
entries, the result will be a 3 x 4 matrix with real entries).
If an argument x_i is list-valued, e.g. list(y_1, y_2, ...), this
is treated as contributing y_1, y_2, ... to the list of items to
be averaged.
EXAMPLE
> print avg(1,2,3,4,5), avg(list(1,2,3,4,5)), avg(1,2,list(3,4,5))
3 3 3
> mat x[2,2] = {1,2,3,4}
> mat y[2,2] = {1,2,4,8}
> avg(x,y)
mat [2,2] (4 elements, 4 nonzero):
[0,0] = 1
[0,1] = 2
[1,0] = 3.5
[1,1] = 6
LIMITS
The number of arguments is not to exceed 100.
LIBRARY
none
SEE ALSO
hmean

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NAME
base - set default output base
SYNOPSIS
base([mode])
TYPES
mode real
return real
DESCRIPTION
The base function allows one to specify how numbers should be
printer. The base function provides a numeric shorthand to the
config("mode") interface. With no args, base() will return the
current mode. With 1 arg, base(val) will set the mode according to
the arg and return the previous mode.
The following convention is used to declare modes:
base config
value string
2 "binary" binary fractions
8 "octal" octal fractions
10 "real" decimal floating point
16 "hex" hexadecimal fractions
-10 "int" decimal integer
1/3 "frac" decimal fractions
1e20 "exp" decimal exponential
For convenience, any non-integer value is assumed to mean "frac",
and any integer >= 2^64 is assumed to mean "exp".
EXAMPLE
> base()
10
> base(8)
012
> print 10
012
LIMITS
none
LIBRARY
int math_setmode(int newmode)
NOTE: newmode must be one of MODE_DEFAULT, MODE_FRAC, MODE_INT,
MODE_REAL, MODE_EXP, MODE_HEX, MODE_OCTAL, MODE_BINARY
SEE ALSO
config

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NAME
bround - round numbers to a specified number of binary digits
SYNOPSIS
bround(x [,plcs [, rnd]])
TYPES
If x is a matrix or a list, bround(x[[i]], ...) is to return
a value for each element x[[i]] of x; the value returned will be
a matrix or list with the same structure as x.
Otherwise, if x is an object of type tt, or if x is not an object or
number but y is an object of type tt, and the function tt_bround has
to be defined; the types for x, plcs, rnd, and the returned value,
if any, are as required for specified in tt_bround. For the object
case, plcs and rnd default to the null value.
For other cases:
x number (real or complex)
plcs integer, defaults to zero
rnd integer, defaults to config("round")
return number
DESCRIPTION
For real x, bround(x, plcs, rnd) returns x rounded to either
plcs significant binary digits (if rnd & 32 is nonzero) or to plcs
binary places (if rnd & 32 is zero). In the significant-figure
case the rounding is to plcs - ilog10(x) - 1 binary places.
If the number of binary places is n and eps = 10^-n, the
result is the same as for appr(x, eps, rnd). This will be
exactly x if x is a multiple of eps; otherwise rounding occurs
to one of the nearest multiples of eps on either side of x. Which
of these multiples is returned is determined by z = rnd & 31, i.e.
the five low order bits of rnd, as follows:
z = 0 or 4: round down, i.e. towards minus infinity
z = 1 or 5: round up, i.e. towards plus infinity
z = 2 or 6: round towards zero
z = 3 or 7: round away from zero
z = 8 or 12: round to the nearest even multiple of eps
z = 9 or 13: round to the nearest odd multiple of eps
z = 10 or 14: round to nearest even or odd multiple of eps
according as x > or < 0
z = 11 or 15: round to nearest odd or even multiple of eps
according as x > or < 0
z = 16 to 31: round to the nearest multiple of eps when
this is uniquely determined. Otherwise
rounding is as if z is replaced by z - 16
For complex x:
The real and imaginary parts are rounded as for real x; if the
imaginary part rounds to zero, the result is real.
For matrix or list x:
The returned values has element bround(x[[i]], plcs, rnd) in
the same position as x[[i]] in x.
For object x or plcs:
When bround(x, plcs, rnd) is called, x is passed by address so may be
changed by assignments; plcs and rnd are copied to temporary
variables, so their values are not changed by the call.
EXAMPLES
> a = 7/32, b = -7/32
> print a, b
.21875 -.21875
> print round(a,3,0), round(a,3,1), round(a,3,2), print round(a,3,3)
.218, .219, .218, .219
> print round(b,3,0), round(b,3,1), round(b,3,2), print round(b,3,3)
-.219, -.218, -.218, -.219
> print round(a,3,16), round(a,3,17), round(a,3,18), print round(a,3,19)
.2188 .2188 .2188 .2188
> print round(a,4,16), round(a,4,17), round(a,4,18), print round(a,4,19)
.2187 .2188 .2187 .2188
> print round(a,2,8), round(a,3,8), round(a,4,8), round(a,5,8)
.22 .218 .2188 .21875
> print round(a,2,24), round(a,3,24), round(a,4,24), round(a,5,24)
.22 .219 .2188 .21875
> c = 21875
> print round(c,-2,0), round(c,-2,1), round(c,-3,0), round(c,-3,16)
21800 21900 21000 22000
> print round(c,2,32), round(c,2,33), round(c,2,56), round(c,4,56)
21000 22000 22000 21880
> A = list(1/8, 2/8, 3/8, 4/8, 5/8, 6/8, 7/8)
> print round(A,2,24)
list(7 elements, 7 nonzero):
[[0]] = .12
[[1]] = .25
[[3]] = .38
[[4]] = .5
[[5]] = .62
[[6]] = .75
[[7]] = .88
LIMITS
For non-object case:
0 <= abs(plcs) < 2^31
0 <= abs(rnd) < 2^31
LIBRARY
void broundvalue(VALUE *x, VALUE *plcs, VALUE *rnd, VALUE *result)
MATRIX *matbround(MATRIX *m, VALUE *plcs, VALUE *rnd);
LIST *listbround(LIST *m, VALUE *plcs, VALUE *rnd);
NUMBER *qbround(NUMBER *m, long plcs, long rnd);
SEE ALSO
round, trunc, btrunc, int, appr

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NAME
btrunc - truncate a value to a number of binary places
SYNOPSIS
btrunc(x [,j])
TYPES
x real
j int
return real
DESCRIPTION
Truncate x to j binary places. If j is omitted, 0 places is assumed.
Specifying zero places makes the result identical to int().
Truncation of a non-integer prodcues values nearer to zero.
EXAMPLE
> print btrunc(pi()), btrunc(pi(), 10)
3 3.140625
> print btrunc(3.3), btrunc(3.7), btrunc(3.3, 2), btrunc(3.7, 2)
3 3 3.25 3.5
> print btrunc(-3.3), btrunc(-3.7), btrunc(-3.3, 2), btrunc(-3.7, 2)
-3 -3 -3.25 -3.5
LIMITS
0 <= j < 2^31
LIBRARY
NUMBER *qbtrunc(NUMBER *x, *j)
SEE ALSO
bround, int, round, trunc

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The config function sets or reads the value of a configuration
parameter. The first argument is a string which names the parameter
to be set or read. If only one argument is given, then the current
value of the named parameter is returned. If two arguments are given,
then the named parameter is set to the value of the second argument,
and the old value of the parameter is returned. Therefore you can
change a parameter and restore its old value later. The possible
parameters are explained in the next section.
The scale function multiplies or divides a number by a power of 2.
This is used for fractional calculations, unlike the << and >>
operators, which are only defined for integers. For example,
scale(6, -3) is 3/4.
The quomod function is used to obtain both the quotient and remainder
of a division in one operation. The first two arguments a and b are
the numbers to be divided. The last two arguments c and d are two
variables which will be assigned the quotient and remainder. For
nonnegative arguments, the results are equivalent to computing a//b
and a%b. If a is negative and the remainder is nonzero, then the
quotient will be one less than a//b. This makes the following three
properties always hold: The quotient c is always an integer. The
remainder d is always 0 <= d < b. The equation a = b * c + d always
holds. This function returns 0 if there is no remainder, and 1 if
there is a remainder. For examples, quomod(10, 3, x, y) sets x to 3,
y to 1, and returns the value 1, and quomod(-4, 3.14159, x, y) sets x
to -2, y to 2.28318, and returns the value 1.
The eval function accepts a string argument and evaluates the
expression represented by the string and returns its value.
The expression can include function calls and variable references.
For example, eval("fact(3) + 7") returns 13. When combined with
the prompt function, this allows the calculator to read values from
the user. For example, x=eval(prompt("Number: ")) sets x to the
value input by the user.
The digit and isset functions return individual digits of a number,
either in base 10 or in base 2, where the lowest digit of a number
is at digit position 0. For example, digit(5678, 3) is 5, and
isset(0b1000100, 2) is 1. Negative digit positions indicate places
to the right of the decimal or binary point, so that for example,
digit(3.456, -1) is 4.
The ptest builtin is a primality testing function. The
1st argument is the suspected prime to be tested. The
absolute value of the 2nd argument is an iteration count.
If ptest is called with only 2 args, the 3rd argument is
assumed to be 0. If ptest is called with only 1 arg, the
2nd argument is assumed to be 1. Thus, the following
calls are equivalent:
ptest(a)
ptest(a,1)
ptest(a,1,0)
Normally ptest performs a some checks to determine if the
value is divisable by some trivial prime. If the 2nd
argument is < 0, then the trivial check is omitted.
For example, ptest(a,10) performs the same work as:
ptest(a,-3) (7 tests without trivial check)
ptest(a,-7,3) (3 more tests without the trivial check)
The ptest function returns 0 if the number is definitely not
prime, and 1 is the number is probably prime. The chance
of a number which is probably prime being actually composite
is less than 1/4 raised to the power of the iteration count.
For example, for a random number p, ptest(p, 10) incorrectly
returns 1 less than once in every million numbers, and you
will probably never find a number where ptest(p, 20) gives
the wrong answer.
The first 3 args of nextcand and prevcand functions are the same
arguments as ptest. But unlike ptest, nextcand and prevcand return
the next and previous values for which ptest is true.
For example, nextcand(2^1000) returns 2^1000+297 because
2^1000+297 is the smallest value x > 2^1000 for which
ptest(x,1) is true. And for example, prevcand(2^31-1,10,5)
returns 2147483629 (2^31-19) because 2^31-19 is the largest
value y < 2^31-1 for which ptest(y,10,5) is true.
The nextcand and prevcand functions also have a 5 argument form:
nextcand(num, count, skip, modval, modulus)
prevcand(num, count, skip, modval, modulus)
return the smallest (or largest) value ans > num (or < num) that
is also == modval % modulus for which ptest(ans,count,skip) is true.
The builtins nextprime(x) and prevprime(x) return the
next and previous primes with respect to x respectively.
As of this release, x must be < 2^32. With one argument, they
will return an error if x is out of range. With two arguments,
they will not generate an error but instead will return y.
The builtin function pix(x) returns the number of primes <= x.
As of this release, x must be < 2^32. With one argument, pix(x)
will return an error if x is out of range. With two arguments,
pix(x,y) will not generate an error but instead will return y.
The builtin function factor may be used to search for the
smallest factor of a given number. The call factor(x,y)
will attempt to find the smallest factor of x < min(x,y).
As of this release, y must be < 2^32. If y is omitted, y
is assumed to be 2^32-1.
If x < 0, factor(x,y) will return -1. If no factor <
min(x,y) is found, factor(x,y) will return 1. In all other
cases, factor(x,y) will return the smallest prime factor
of x. Note except for the case when abs(x) == 1, factor(x,y)
will not return x.
If factor is called with y that is too large, or if x or y
is not an integer, calc will report an error. If a 3rd argument
is given, factor will return that value instead. For example,
factor(1/2,b,c) will return c instead of issuing an error.
The builtin lfactor(x,y) searches a number of primes instead
of below a limit. As of this release, y must be <= 203280221
(y <= pix(2^32-1)). In all other cases, lfactor is operates
in the same way as factor.
If lfactor is called with y that is too large, or if x or y
is not an integer, calc will report an error. If a 3rd argument
is given, lfactor will return that value instead. For example,
lfactor(1/2,b,c) will return c instead of issuing an error.
The lfactor function is slower than factor. If possible factor
should be used instead of lfactor.
The builtin isprime(x) will attempt to determine if x is prime.
As of this release, x must be < 2^32. With one argument, isprime(x)
will return an error if x is out of range. With two arguments,
isprime(x,y) will not generate an error but instead will return y.
The functions rcin, rcmul, rcout, rcpow, and rcsq are used to
perform modular arithmetic calculations for large odd numbers
faster than the usual methods. To do this, you first use the
rcin function to convert all input values into numbers which are
in a format called REDC format. Then you use rcmul, rcsq, and
rcpow to multiply such numbers together to produce results also
in REDC format. Finally, you use rcout to convert a number in
REDC format back to a normal number. The addition, subtraction,
negation, and equality comparison between REDC numbers are done
using the normal modular methods. For example, to calculate the
value 13 * 17 + 1 (mod 11), you could use:
p = 11;
t1 = rcin(13, p);
t2 = rcin(17, p);
t3 = rcin(1, p);
t4 = rcmul(t1, t2, p);
t5 = (t4 + t3) % p;
answer = rcout(t5, p);
The swap function exchanges the values of two variables without
performing copies. For example, after:
x = 17;
y = 19;
swap(x, y);
then x is 19 and y is 17. This function should not be used to
swap a value which is contained within another one. If this is
done, then some memory will be lost. For example, the following
should not be done:
mat x[5];
swap(x, x[0]);
The hash function returns a relatively small non-negative integer
for one or more input values. The hash values should not be used
across runs of the calculator, since the algorithms used to generate
the hash value may change with different versions of the calculator.
The base function allows one to specify how numbers should be
printer. The base function provides a numeric shorthand to the
config("mode") interface. With no args, base() will return the
current mode. With 1 arg, base(val) will set the mode according to
the arg and return the previous mode.
The following convention is used to declare modes:
base config
value string
2 "binary" binary fractions
8 "octal" octal fractions
10 "real" decimal floating point
16 "hex" hexadecimal fractions
-10 "int" decimal integer
1/3 "frac" decimal fractions
1e20 "exp" decimal exponential
For convenience, any non-integer value is assumed to mean "frac",
and any integer >= 2^64 is assumed to mean "exp".

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Builtin functions
There is a large number of built-in functions. Many of the
functions work on several types of arguments, whereas some only
work for the correct types (e.g., numbers or strings). In the
following description, this is indicated by whether or not the
description refers to values or numbers. This display is generated
by the 'show builtin' command.

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NAME
ceil - ceiling
SYNOPSIS
ceil(x)
TYPES
x real, complex, list, matrix
return real or complex, list, matrix
DESCRIPTION
For real x, ceil(x) is the least integer not less than x.
For complex, ceil(x) returns the real or complex number v for
which re(v) = ceil(re(x)), im(v) = ceil(im(x)).
For list or matrix x, ceil(x) returns the list or matrix of the
same structure as x for which each element t of x has been replaced
by ceil(t).
EXAMPLE
> print ceil(27), ceil(1.23), ceil(-4.56), ceil(7.8 - 9.1i)
27 2 -4 8-9i
LIMITS
none
LIBRARY
none
SEE ALSO
floor, int

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NAME
cfappr - approximate a real number using continued fractions
SYNOPSIS
cfappr(x [,eps [,rnd]]) or cfappr(x, n [,rnd])
TYPES
x real
eps real with abs(eps) < 1, defaults to epsilon()
n real with n >= 1
rnd integer, defaults to config("cfappr")
return real
DESCRIPTION
If x is an integer or eps is zero, either form returns x.
If abs(eps) < 1, cfappr(x, eps) returns the smallest-denominator
number in one of the three intervals, [x, x + abs(eps)],
[x - abs(eps], x], [x - abs(eps)/2, x + abs(eps)/2].
If n >= 1 and den(x) > n, cfappr(x, n) returns the nearest above,
nearest below, or nearest, approximation to x with denominator less
than or equal to n. If den(x) <= n, cfappr(x,n) returns x.
In either case when the result v is not x, how v relates to x is
determined by bits 0, 1, 2 and 4 of the argument rnd in the same way as
these bits are used in the functions round() and appr(). In the
following y is either eps or n.
rnd sign of remainder x - v
0 sgn(y)
1 -sgn(y
2 sgn(x), "rounding to zero"
3 -sgn(x), "rounding from zero"
4 +, "rounding down"
5 -, "rounding up"
6 sgn(x/y)
7 -sgn(x/y)
If bit 4 of rnd is set, the other bits are irrelevant for the eps case;
thus for 16 <= rnd < 24, cfappr(x, eps, rnd) is the smallest-denominator
number differing from x by at most abs(eps)/2.
If bit 4 of rnd is set and den(x) > 2, the other bits are irrelevant for
the bounded denominator case; in the case of two equally near nearest
approximations with denominator less than n, cfappr(x, n, rnd)
returns the number with smaller denominator. If den(x) = 2, bits
0, 1 and 2 of rnd are used as described above.
If -1 < eps < 1, cfappr(x, eps, 0) may be described as the smallest
denominator number in the closed interval with end-points x and x - eps.
It follows that if abs(a - b) < 1, cfappr(a, a - b, 0) gives the smallest
denominator number in the interval with end-points a and b; the same
result is returned by cfappr(b, b - a, 0) or cfappr(a, b - a, 1).
If abs(eps) < 1 and v = cfappr(x, eps, rnd), then
cfappr(x, sgn(eps) * den(v), rnd) = v.
If 1 <= n < den(x), u = cfappr(x, n, 0) and v = cfappr(x, n, 1), then
u < x < v, den(u) <= n, den(v) <= n, den(u) + den(v) > n, and
v - u = 1/(den(u) * den(v)).
If x is not zero, the nearest approximation with numerator not
exceeding n is 1/cfappr(1/x, n, 16).
EXAMPLE
> c = config("mode", "frac")
> x = 43/30; u = cfappr(x, 10, 0); v = cfappr(x, 10, 1);
> print u, v, x - u, v - x, v - u, cfappr(x, 10, 16)
10/7 13/9 1/210 1/90 1/63 10/7
> pi = pi(1e-10)
> print cfappr(pi, 100, 16), cfappr(pi, .01, 16), cfappr(pi, 1e-6, 16)
311/99 22/7 355/113
> x = 17/12; u = cfappr(x,4,0); v = cfappr(x,4,1);
> print u, v, x - u, v - x, cfappr(x,4,16)
4/3 3/2 1/12 1/12 3/2
LIMITS
none
LIBRARY
NUMBER *qcfappr(NUMBER *q, NUMBER *epsilon, long R)
SEE ALSO
appr, cfsim

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NAME
cfsim - simplify a value using continued fractions
SYNOPSIS
cfsim(x [,rnd])
TYPES
x real
rnd integer, defaults to config("cfsim")
return real
DESCRIPTION
If x is not an integer, cfsim(x, rnd) returns either the nearest
above x, or the nearest below x, number with denominator less than
den(x). If x is an integer, cfsim(x, rnd) returns x + 1, x - 1, or 0.
Which of the possible results is returned is controlled
by bits 0, 1, 3 and 4 of the parameter rnd.
For 0 <= rnd < 4, the sign of the remainder x - cfsim(x, rnd) is
as follows:
rnd sign of x - cfsim(x, rnd)
0 +, as if rounding down
1 -. as if rounding up
2 sgn(x), as if rounding to zero
3 -sgn(x), as if rounding from zero
This corresponds to the use of rnd for functions like round(x, n, rnd).
If bit 3 or 4 of rnd is set, the lower order bits are ignored; bit 3
is ignored if bit 4 is set. Thusi, for rnd > 3, it sufficient to
consider the two cases rnd = 8 and rnd = 16.
If den(x) > 2, cfsim(x, 8) returns the value of the penultimate simple
continued-fraction approximant to x, i.e. if:
x = a_0 + 1/(a_1 + 1/(a_2 + ... + 1/a_n) ...)),
where a_0 is an integer, a_1, ..., a_n are positive integers,
and a_n >= 2, the value returned is that of the continued fraction
obtained by dropping the last quotient 1/a_n.
If den(x) > 2, cfsim(x, 16) returns the nearest number to x with
denominator less than den(x). In the continued-fraction representation
of x described above, this is given by replacing a_n by a_n - 1.
If den(x) = 2, the definition adopted is to round towards zero for the
approximant case (rnd = 8) and from zero for the "nearest" case (rnd = 16).
For integral x, cfsim(x, 8) returns zero, cfsim(x,16) returns x - sgn(x).
In summary, for cfsim(x, rnd) when rnd = 8 or 16, the results are:
rnd integer x half-integer x den(x) > 2
8 0 x - sgn(x)/2 approximant
16 x - sgn(x) x + sgn(x)/2 nearest
From either cfsim(x, 0) and cfsim(x, 1), the other is easily
determined: if one of them has value w, the other has value
(num(x) - num(w))/(den(x) - den(w)). From x and w one may find
other optimal rational numbers near x; for example, the smallest-
denominator number between x and w is (num(x) + num(w))/(den(x) + den(w)).
If x = n/d and cfsim(x, 8) = u/v, then for k * v < d, the k-th member of
the sequence of nearest approximations to x with decreasing denominators
on the other side of x is (n - k * u)/(d - k * v). This is nearer
to or further from x than u/v according as 2 * k * v < or > d.
Iteration of cfsim(x,8) until an integer is obtained gives a sequence of
"good" approximations to x with decreasing denominators and
correspondingly decreasing accuracy; each denominator is less than half
the preceding denominator. (Unlike the "forward" sequence of
continued-fraction approximants these are not necessarily alternately
greater than and less than x.)
Some other properties:
For rnd = 0 or 1 and any x, or rnd = 8 or 16 and x with den(x) > 2:
cfsim(n + x, rnd) = n + cfsim(x, rnd).
This equation also holds for the other values of rnd if n + x and x
have the same sign.
For rnd = 2, 3, 8 or 16, and any x:
cfsim(-x, rnd) = -cfsim(x, rnd).
If rnd = 8 or 16, except for integer x or 1/x for rnd = 8, and
zero x for rnd = 16:
cfsim(1/x, rnd) = 1/cfsim(x, rnd).
EXAMPLE
> c = config("mode", "frac");
> print cfsim(43/30, 0), cfsim(43/30, 1), cfsim(43/30, 8), cfsim(43/30,16)
10/7 33/23 10/7 33/23
> x = pi(1e-20); c = config("mode", "frac");
> while (!isint(x)) {x = cfsim(x,8); if (den(x) < 1e6) print x,:;}
1146408/364913 312689/99532 104348/33215 355/113 22/7 3
LIMITS
none
LIBRARY
NUMBER *qcfsim(NUMBER *x, long rnd)
SEE ALSO
cfappr

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NAME
char - character corresponding to a value
SYNOPSIS
char(j)
TYPES
j integer, 0 <= j < 256
return string
DESCRIPTION
For j > 0, returns a string of length 1 with a character that has
the same value as j. For j = 0, returns the null string "".
EXAMPLE
> print char(0102), char(0x6f), char(119), char(0145), char(0x6e)
B o w e n
LIMITS
none
LIBRARY
none
SEE ALSO
ord

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NAME
cmdbuf - print the command buffer
SYNOPSIS
cmdbuf()
TYPES
return str
DESCRIPTION
This function returns the command string that was formed by calc based
on its command line arguments. If calc was invoked without arguments,
this function will return an empty string.
EXAMPLE
> cmdbuf("")
""
LIMITS
none
LIBRARY
none
SEE ALSO
XXX - fill in

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NAME
cmp - compare two values
SYNOPSIS
cmp(x, y)
TYPES
If x is an object of type xx or x is not an object and y is an object
of type xx, the funcion xx_cmp has to have been defined; any
further conditions on x and y, and the type of the returned
value depends on the definition of xx_cmp.
For non-object x and y:
x number or string
y same as x
return -1, 0, 1 (real & string)
-1, 0, 1, -1+1i, 1i, 1+1i, -1-1i, -1i or 1-1i (complex)
DESCRIPTION
Compare two values and return a value based on their relationship.
Comparison by type is indicated below. Where more than one test is
indicated, tests are performed in the order listed. If the test is
inconclusive, the next test is performed. If all tests are
inconclusive, the values are considered equivalent.
real (returns -1, 0, or 1)
the greater number is greater
complex (returns -1, 0, 1, -1+1i, 1i, 1+1i, -1-1i, -1i or 1-1i)
sgn(re(x) - re(y)) + sgn(im(x) - im(y)) * 1i
string (returns -1, 0, or 1)
the string with the greater first different character is greater
the longer string is greater
object (depends on xx_cmp)
the greater object as defined by xx_cmp is greater
String comparison is performed via the strcmp() libc function.
Note that this function is not a substitution for equality. The ==
operator always takes epsilon() into account when comparing numeric
values. For example:
> cmp(1, 1+epsilon()/2)
-1
> 1 == 1+epsilon()/2
0
It should be noted epsilon() is used when comparing complex values.
Properties of cmp(a,b) for real or complex a and b are:
cmp(a + c, b + c) = cmp(a,b)
cmp(a, b) == 0 if and only if a == b
cmp(b, a) = -cmp(a,b)
if c is real or pure imaginary, cmp(c * a, c * b) = c * cmp(a,b)
cmp(a,b) == cmp(b,c) if and only if b is "between" a and c
The numbers between 2 + 3i and 4 + 5i are those with real part between
2 and 4, imaginary part between 3 and 5; the numbers between 2 + 3i
and 4 + 3i are those with real part between 2 and 4, imaginary part = 3.
EXAMPLE
> print cmp(3,4), cmp(4,3), cmp(4,4), cmp("a","b"), cmp("abcd","abc")
-1 1 0 -1 1
> print cmp(3,4i), cmp(4,4i), cmp(5,4i), cmp(-5,4i), cmp(-4i,5), cmp(-4i,-5)
1-1i 1-1i 1-1i -1-1i -1-1i 1-1i
> print cmp(3i,4i), cmp(4i,4i), cmp(5i,4i), cmp(3+4i,5), cmp(3+4i,-5)
-1i 0 1i -1+1i 1+1i
> print cmp(3+4i,3+4i), cmp(3+4i,3-4i), cmp(3+4i,2+3i), cmp(3+4i,-4-5i)
0 1i 1+1i 1+1i
LIMITS
none
LIBRARY
none
SEE ALSO
abs, epsilon, sgn

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NAME
comb - combinatorial number
SYNOPSIS
comb(x, y)
TYPES
x int
y int
return int
DESCRIPTION
Return the combinatorial number C(x,y) which is defined as:
x!
---------
y!*(x-y)!
This function computes the number of combinations in which y things
may be chosen from x items ignoring the order in which they are chosen.
EXAMPLE
> print comb(7,3), comb(7,4), comb(7,5), comb(3,0), comb(0,0)
35 35 21 1 1
> print comb(2^31+1,2^31-1)
2305843010287435776
LIMITS
x >= y >= 0
y < 2^24
x-y < 2^24
LIBRARY
void zcomb(NUMBER x, y, *ret)
SEE ALSO
fact, perm

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Command sequence
This is a sequence of any the following command formats, where
each command is terminated by a semicolon or newline. Long command
lines can be extended by using a back-slash followed by a newline
character. When this is done, the prompt shows a double angle
bracket to indicate that the line is still in progress. Certain
cases will automatically prompt for more input in a similar manner,
even without the back-slash. The most common case for this is when
a function is being defined, but is not yet completed.
Each command sequence terminates only on an end of file. In
addition, commands can consist of expression sequences, which are
described in the next section.
NOTE: Calc commands are in lower case. UPPER case is used below
for emphasis only, and should be considered in lower case.
DEFINE function(params) { body }
DEFINE function(params) = expression
This first form defines a full function which can consist
of declarations followed by many statements which implement
the function.
The second form defines a simple function which calculates
the specified expression value from the specified parameters.
The expression cannot be a statement. However, the comma
and question mark operators can be useful. Examples of
simple functions are:
define sumcubes(a, b) = a^3 + b^3;
define pimod(a) = a % pi();
HELP
This displays a general help message.
READ filename
This reads definitions from the specified filename.
The name can be quoted if desired. The calculator
uses the CALCPATH environment variable to search
through the specified directories for the filename,
similarly to the use of the PATH environment variable.
If CALCPATH is not defined, then a default path which is
usually ":/usr/local/lib/calc" is used (that is, the current
directory followed by a general calc library directory).
The ".cal" extension is defaulted for input files, so
that if "filename" is not found, then "filename.cal" is
then searched for. The contents of the filename are
command sequences which can consist of expressions to
evaluate or functions to define, just like at the top
level command level.
If the -m mode disallows opening of files for reading,
this command will be disabled.
READ -once filename
This command acts like the regular READ expect that it
will ignore filename if is has been previously read.
This command is particularly useful in a library that
needs to read a 2nd library. By using the READ -once
command, one will not reread that 2nd library, nor will
once risk entering into a infinite READ loop (where
that 2nd library directly or indirectly does a READ of
the first library).
If the -m mode disallows opening of files for reading,
this command will be disabled.
WRITE filename
This writes the values of all global variables to the
specified filename, in such a way that the file can be
later read in order to recreate the variable values.
For speed reasons, values are written as hex fractions.
This command currently only saves simple types, so that
matrices, lists, and objects are not saved. Function
definitions are also not saved.
If the -m mode disallows opening of files for writing,
this command will be disabled.
QUIT
This leaves the calculator, when given as a top-level
command.
CD
Change the current directory to the home directory, if $HOME
is set in the environment.
CD dir
Change the current directory to dir.
Also see the help topic:
statement flow control and declaration statements
usage for -m modes

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Configuration parameters
Configuration parameters affect how the calculator performs certain
operations. Among features that are controlled by these parameters
are the accuracy of some calculations, the displayed format of results,
the choice from possible alternative algorithms, and whether or not
debugging information is displayed. The parameters are
read or set using the "config" built-in function; they remain in effect
until their values are changed by a config or equivalent instruction.
The following parameters can be specified:
"all" all configuration values listed below
"trace" turns tracing features on or off
"display" sets number of digits in prints.
"epsilon" sets error value for transcendentals.
"maxprint" sets maximum number of elements printed.
"mode" sets printout mode.
"mul2" sets size for alternative multiply.
"sq2" sets size for alternative squaring.
"pow2" sets size for alternate powering.
"redc2" sets size for alternate REDC.
"tilde" enable/disable printing of the roundoff '~'
"tab" enable/disable printing of leading tabs
"quomod" sets rounding mode for quomod
"quo" sets rounding mode for //, default for quo
"mod" sets "rounding" mode for %, default for mod
"sqrt" sets rounding mode for sqrt
"appr" sets rounding mode for appr
"cfappr" sets rounding mode for cfappr
"cfsim" sets rounding mode for cfsim
"round" sets rounding mode for round and bround
"outround" sets rounding mode for printing of numbers
"leadzero" enables/disables printing of 0 as in 0.5
"fullzero" enables/disables padding zeros as in .5000
"maxerr" maximum number of scan errors before abort
"prompt" default interactive prompt
"more" default interactive multi-line input prompt
The "all" config value allows one to save/restore the configuration
set of values. The return of:
config("all")
is a CONFIG type which may be used as the 2rd arg in a later call.
One may save, modify and restore the configuration state as follows:
oldstate = config("all")
...
config("tab", 0)
config("mod", 10)
...
config("all", oldstate)
This save/restore method is useful within functions.
It allows functions to control their configuration without impacting
the calling function.
There are two configuration state aliases that may be set. To
set the backward compatible standard configuration:
config("all", "oldstd")
The "oldstd" will restore the configuration to the default at startup.
A new configuration that some people prefer may be set by:
config("all", "newstd")
The "newstd" is not backward compatible with the historic
configuration. Even so, some people prefer this configuration
and place the config("all", "newstd") command in their CALCRC
startup files.
When nonzero, the "trace" parameter activates one or more features
that may be useful for debugging. These features correspond to
powers of 2 which contribute additively to config("trace"):
1: opcodes are displayed as functions are evaluated
2: disables the inclusion of debug lines in opcodes for functions
whose definitions are introduced with a left-brace.
4: the number of links for real and complex numbers are displayed
when the numbers are printed; for real numbers "#" or for
complex numbers "##", followed by the number of links, are
printed immediately after the number.
8: the opcodes for a new functions are displayed when the function
is successfully defined.
The "display" parameter specifies the maximum number of digits after
the decimal point to be printed in real or exponential mode in
normal unformatted printing (print, strprint, fprint) or in
formatted printing (printf, strprintf, fprintf) when precision is not
specified. The initial value is 20. This parameter does not change
the stored value of a number. Where rounding is necessary, the type
of rounding to be used is controlled by "outround".
The "epsilon" parameter specifies the default accuracy for the
calculation of functions for which exact values are not possible or
not desired. For most functions, the
remainder = exact value - calculated value
has absolute value less than epsilon, but, except when the sign of
the remainder is controlled by an appropriate parameter, the
absolute value of the remainder usually does not exceed epsilon/2.
Functions which require an epsilon value accept an
optional argument which overrides this default epsilon value for
that single call. (The value v can be assigned to the "epsilon"
parameter by epsilon(v) as well as by config("epsilon", v), and the
current value obtained by epsilon() as well as by config("epsilon").)
For the transcendental functions and the functions sqrt() and
appr(), the calculated value is always a multiple of epsilon.
The "mode" parameter is a string specifying the mode for printing of
numbers by the unformatted print functions, and the default
("%d" specifier) for formatted print functions. The initial mode
is "real". The available modes are:
"frac" decimal fractions
"int" decimal integer
"real" decimal floating point
"exp" decimal exponential
"hex" hex fractions
"oct" octal fractions
"bin" binary fractions
The "maxprint" parameter specifies the maximum number of elements to
be displayed when a matrix or list is printed. The initial value is 16.
Mul2 and sq2 specify the sizes of numbers at which calc switches
from its first to its second algorithm for multiplying and squaring.
The first algorithm is the usual method of cross multiplying, which
runs in a time of O(N^2). The second method is a recursive and
complicated method which runs in a time of O(N^1.585). The argument
for these parameters is the number of binary words at which the
second algorithm begins to be used. The minimum value is 2, and
the maximum value is very large. If 2 is used, then the recursive
algorithm is used all the way down to single digits, which becomes
slow since the recursion overhead is high. If a number such as
1000000 is used, then the recursive algorithm is never used, causing
calculations for large numbers to slow down. For a typical example
on a 386, the two algorithms are about equal in speed for a value
of 20, which is about 100 decimal digits. A value of zero resets
the parameter back to its default value. Usually there is no need
to change these parameters.
Pow2 specifies the sizes of numbers at which calc switches from
its first to its second algorithm for calculating powers modulo
another number. The first algorithm for calculating modular powers
is by repeated squaring and multiplying and dividing by the modulus.
The second method uses the REDC algorithm given by Peter Montgomery
which avoids divisions. The argument for pow2 is the size of the
modulus at which the second algorithm begins to be used.
Redc2 specifies the sizes of numbers at which calc switches from
its first to its second algorithm when using the REDC algorithm.
The first algorithm performs a multiply and a modular reduction
together in one loop which runs in O(N^2). The second algorithm
does the REDC calculation using three multiplies, and runs in
O(N^1.585). The argument for redc2 is the size of the modulus at
which the second algorithm begins to be used.
Config("tilde") controls whether or not a leading tilde ('~') is
printed to indicate that a number has not been printed exactly
because the number of decimal digits required would exceed the
specified maximum number. The initial "tilde" value is 1.
Config ("tab") controls the printing of a tab before results
automatically displayed when working interactively. It does not
affect the printing by the functions print, printf, etc. The inital
"tab" value is 1.
The "quomod", "quo", "mod", "sqrt", "appr", "cfappr", "cfsim", and
"round" control the way in which any necessary rounding occurs.
Rounding occurs when for some reason, a calculated or displayed
value (the "approximation") has to differ from the "true value",
e.g. for quomod and quo, the quotient is to be an integer, for sqrt
and appr, the approximation is to be a multiple of an explicit or
implicit "epsilon", for round and bround (both controlled by
config("round")) the number of decimal places or fractional bits
in the approximation is limited. Zero value for any of these
parameters indicates that the true value is greater than the approximation,
i.e. the rounding is "down", or in the case of mod, that the
residue has the same sign as the divisor. If bit 4 of the
parameter is set, the rounding of to the nearest acceptable candidate
when this is uniquely determined; in the remaining ambiguous cases,
the type of rounding is determined by the lower bits of the parameter
value. If bit 3 is set, the rounding for quo, appr and sqrt,
is to the nearest even integer or the nearest even multiple of epsilon,
and for round to the nearest even "last decimal place". The effects
of the 3 lowest bits of the parameter value are as follows:
Bit 0: Unconditional reversal (down to up, even to odd, etc.)
Bit 1: Reversal if the exact value is negative
Bit 2: Reversal if the divisor or epsilon is negative
(Bit 2 is irrelevant for the functions round and bround since the
equivalent epsilon (a power of 1/10 or 1/2) is always positive.)
For quomod, the quotient is rounded to an integer value as if
evaluating quo with config("quo") == config("quomod"). Similarly,
quomod and mod give the same residues if config("mod") == config("quomod").
For the sqrt function, if bit 5 of config("sqrt") is set, the exact
square-root is returned when this is possible; otherwise the
result is rounded to a multiple of epsilon as determined by the
five lower order bits. Bit 6 of config("sqrt") controls whether the
principal or non-principal square-root is returned.
For the functions cfappr and cfsim, whether the "rounding" is down
or up, etc. is controlled by the appropriate bits of config("cfappr")
and config("cfsim") as for quomod, quo, etc.
The "outround" parameter determines the type of rounding to be used
by the various kinds of printing to the output: bits 0, 1, 3 and 4
are used in the same way as for the functions round and bround.
The "leadzero" parameter controls whether or not a 0 is printed
before the decimal point in non-zero fractions with absolute value
less than 1, e.g. whether 1/2 is printed as 0.5 or .5. The
initial value is 0, corresponding to the printing .5.
The "fullzero" parameter controls whether or not in decimal floating-
point printing, the digits are padded with zeros to reach the
number of digits specified by config("display") or by a precision
specification in formatted printing. The initial value for this
parameter is 0, so that, for example, if config("display") >= 2,
5/4 will print in "real" mode as 1.25.
The maxerr value controls how many scan errors are allowed
before the compiling phase of a computation is aborted. The initial
value of "maxerr" is 20. Setting maxerr to 0 disables this feature.
The default prompt when in teractive mode is "> ". One may change
this prompt to a more cut-and-paste friendly prompt by:
config("prompt", "; ")
On windowing systems that support cut/paste of a line, one may
cut/copy an input line and paste it directly into input. The
leading ';' will be ignored.
When inside multi-line input, the more prompt is used. One may
change it by:
config("more", ";; ")
The following are synonyms for true:
"on" "yes" "y" "true" "t" "1" any non-zero number
The following are synonyms for false:
"off" "no" "n" "false" "f" "0" the number zero (0)
Examples of setting some parameters are:
config("mode", "exp"); exponential output
config("display", 50); 50 digits of output
epsilon(epsilon() / 8); 3 bits more accuracy
config("tilde", 0) disable roundoff tilde printing
config("tab", "off") disable leading tab printing

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NAME
conj - complex conjugate
SYNOPSIS
conj(x)
TYPES
If x is an object of type xx, conj(x) calls xx_conj(x).
For non-object x:
x real, complex, or matrix
return real, complex, or matrix
DESCRIPTION
For real x, conj(x) returns x.
For complex x, conj(x) returns re(x) - im(x) * 1i.
For matrix x, conj(x) returns a matrix of the same structure as x
in which each element t of x has been replaced by conj(t).
EXAMPLE
> print conj(3), conj(3 + 4i)
3 3-4i
LIMITS
none
LIBRARY
void conjvalue(VALUE *x, *res)
SEE ALSO
norm, abs, arg

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NAME
cos - cosine
SYNOPSIS
cos(x [,eps])
TYPES
x number (real or complex)
eps nonzero real, defaults to epsilon()
return number
DESCRIPTION
Calculate the cosine of x to a multiple of eps with error less in
absolute value than .75 * eps.
EXAMPLE
> print cos(1, 1e-5), cos(1, 1e-10), cos(1, 1e-15), cos(1, 1e-20)
.5403 .5403023059 .54030230586814 .5403023058681397174
> print cos(2 +3i, 1e-5), cos(2 + 3i, 1e-10)
-4.18963-9.10923i -4.189625691-9.1092278938i
> pi = pi(1e-20)
> print cos(pi/3, 1e-10), cos(pi/2, 1e-10), cos(pi, 1e-10)
.5 0 -1
LIMITS
eps > 0
LIBRARY
NUMBER *qcos(NUMBER *x, NUMBER *eps)
COMPLEX *ccos(COMPLEX *x, NUMBER *eps)
SEE ALSO
sin, tan, sec, csc, cot, epsilon

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NAME
cosh - hyperbolic cosine
SYNOPSIS
cosh(x [,eps])
TYPES
x real
eps nonzero real, defaults to epsilon()
return real
DESCRIPTION
Calculate the cosh of x to the nearest or next to nearest multiple of
epsilon, with absolute error less than .75 * abs(eps).
cosh(x) = (exp(x) + exp(-x))/2
EXAMPLE
> print cosh(1, 1e-5), cosh(1, 1e-10), cosh(1, 1e-15), cosh(1, 1e-20)
1.54308 1.5430806348 1.543080634815244 1.54308063481524377848
LIMITS
unlike sin and cos, x must be real
eps > 0
LIBRARY
NUMBER *qcosh(NUMBER *x, NUMBER *eps)
SEE ALSO
sinh, tanh, sech, csch, coth, epsilon

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NAME
cot - trigonometric cotangent
SYNOPSIS
cot(x [,eps])
TYPES
x nonzero real
acc nonzero real, defaults to epsilon()
return real
DESCRIPTION
Calculate the cotangent of x to a multiple of eps, with error less
in absolute value than .75 * eps.
EXAMPLE
> print cot(1, 1e-5), cot(1, 1e-10), cot(1, 1e-15), cot(1, 1e-20)
.64209 .6420926159 .642092615934331 .64209261593433070301
LIMITS
unlike sin and cos, x must be real
x != 0
eps > 0
LIBRARY
NUMBER *qcot(NUMBER *x, *eps)
SEE ALSO
sin, cos, tan, sec, csc, epsilon

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NAME
coth - hyperbolic cotangent
SYNOPSIS
coth(x [,eps])
TYPES
x nonzero real
eps nonzero real, defaults to epsilon()
return real
DESCRIPTION
Calculate the coth of x to a multiple of eps with error less in
absolute value than .75 * eps.
coth(x) = (exp(2*x) + 1)/(exp(2*x) - 1)
EXAMPLE
> print coth(1, 1e-5), coth(1, 1e-10), coth(1, 1e-15), coth(1, 1e-20)
1.31304 1.3130352855 1.313035285499331 1.31303528549933130364
LIMITS
unlike sin and cos, x must be real
x != 0
eps > 0
LIBRARY
NUMBER *qcoth(NUMBER *x, NUMBER *eps)
SEE ALSO
sinh, cosh, tanh, sech, csch, epsilon

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NAME
count - count elements of list or matrix satisfying a stated condition
SYNOPSIS
count(x, y)
TYPES
x list or matrix
y string
return int
DESCRIPTION
For count(x, y), y is to be the name of a user-defined function;
count(x,y) then returns the number of elements of x for which y
tests as "true".
EXAMPLE
> define f(a) = (a < 5)
> A = list(1,2,7,6,4,8)
> count(A, "f")
3
LIMITS
none
LIBRARY
none
SEE ALSO
XXX - fill in

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NAME
cp - cross product of two 3 element vectors
SYNOPSIS
cp(x, y)
TYPES
x, y 1-dimensional matrices with 3 elements
return 1-dimensional matrix with 3 elements
DESCRIPTION
Calculate the product of two 3 1-dimensional matrices.
If x has elements (x0, x1, x2), and y has elements (y0, y1, y2),
cp(x,y) returns the matrix of type [0:2] with elements:
{x1 * y2 - x2 * y1, x3 * y1 - x1 * y3, x1 * y2 - x2 * y1}
EXAMPLE
> mat x[3] = {2,3,4}
> mat y[3] = {3,4,5}
> print cp(x,y)
mat [3] (3 elements, 3 nonzero):
[0] = -1
[1] = 2
[2] = -1
LIMITS
x 1-dimensional matrix with 3 elements
y 1-dimensional matrix with 3 elements
LIBRARY
MATRIX *matcross(MATRIX *x, MATRIX *y)
SEE ALSO
dp

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Credits
The majority of calc was written by David I. Bell.
Calc archives and calc-tester mailing list maintained by Landon Curt Noll.
Thanks for suggestions and encouragement from Peter Miller,
Neil Justusson, and Landon Noll.
Thanks to Stephen Rothwell for writing the original version of
hist.c which is used to do the command line editing.
Thanks to Ernest W. Bowen for supplying many improvements in
accuracy and generality for some numeric functions. Much of
this was in terms of actual code which I gratefully accepted.
Ernest also supplied the original text for many of the help files.
Portions of this program are derived from an earlier set of
public domain arbitrarily precision routines which was posted
to the net around 1984. By now, there is almost no recognizable
code left from that original source.
Most of this source and binary has one of the following copyrights:
Copyright (c) 19xx David I. Bell
Copyright (c) 19xx David I. Bell and Landon Curt Noll
Copyright (c) 19xx Landon Curt Noll
Copyright (c) 19xx Ernest Bowen and Landon Curt Noll
Permission is granted to use, distribute, or modify this source,
provided that this copyright notice remains intact.
Send calc comments, suggestions, bug fixes, enhancements and
interesting calc scripts that you would like you see included in
future distributions to:
dbell@auug.org.au
chongo@toad.com
Landon Noll maintains the official calc ftp archive at:
ftp://ftp.uu.net/pub/calc
Alpha test versions, complete with bugs, untested code and
experimental features may be fetched (if you are brave) under:
http://reality.sgi.com/chongo/calc/
One may join the calc testing group by sending a request to:
calc-tester-request@postofc.corp.sgi.com
Your message body (not the subject) should consist of:
subscribe calc-tester address
end
name your_full_name
where "address" is your EMail address and "your_full_name"
is your full name.
Enjoy!

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NAME
csc - trigonometric cosecant function
SYNOPSIS
csc(x [,eps])
TYPES
x real
eps nonzero real, defaults to epsilon()
return real
DESCRIPTION
Calculate the cosecant of x to a multiple of eps, with error less
in absolute value than .75 * eps.
EXAMPLE
> print csc(1, 1e-5), csc(1, 1e-10), csc(1, 1e-15), csc(1, 1e-20)
1.1884 1.1883951058 1.188395105778121 1.18839510577812121626
LIMITS
unlike sin and cos, x must be real
eps > 0
LIBRARY
NUMBER *qcsc(NUMBER *x, NUMBER *eps)
SEE ALSO
sin, cos, tan, sec, cot, epsilon

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NAME
csch - hyperbolic cosecant
SYNOPSIS
csch(x [,eps])
TYPES
x nonzero real
eps nonzero real, defaults to epsilon()
return real
DESCRIPTION
Calculate the csch of x to a multiple of epsilon, with error less in
absolute value than .75 * eps.
csch(x) = 2/(exp(x) - exp(-x))
EXAMPLE
> print csch(1, 1e-5), csch(1, 1e-10), csch(1, 1e-15), csch(1, 1e-20)
.85092 .8509181282 .850918128239322 .85091812823932154513
LIMITS
unlike sin and cos, x must be real
x != 0
eps > 0
LIBRARY
NUMBER *qcsch(NUMBER *x, NUMBER *eps)
SEE ALSO
sinh, cosh, tanh, sech, coth, epsilon

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NAME
ctime - current local time
SYNOPSIS
ctime()
TYPES
return string
DESCRIPTION
The ctime() builtin returns the string formed by the first 24
characters returned by the C library function, ctime():
"Mon Oct 28 00:47:00 1996"
The 25th ctime() character, '\n' is removed.
EXAMPLE
> printf("The time is now %s.\n", time())
The time is now Mon Apr 15 12:41:44 1996.
LIMITS
none
LIBRARY
none
SEE ALSO
runtime, time

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Function definitions
Function definitions are introduced by the 'define' keyword.
Other than this, the basic structure of a function is like in C.
That is, parameters are specified for the function within parenthesis,
the function body is introduced by a left brace, variables are
declared for the function, statements implementing the function
follow, and the function is ended with a right brace.
There are some subtle differences, however. The types of parameters
and variables are not defined at compile time, but instead are typed
at runtime. Thus there is no definitions needed to distinguish
between integers, fractions, complex numbers, matrices, and so on.
Thus when declaring parameters for a function, only the name of
the parameter is needed. Thus there are never any declarations
between the function parameter list and the body of the function.
For example, the following function computes a factorial:
define factorial(n)
{
local ans;
ans = 1;
while (n > 1)
ans *= n--;
return ans;
}
If a function is very simple and just returns a value, then the
function can be defined in shortened manner by using an equals sign
in place of the left brace. In this case, the function declaration
is terminated by a newline character, and its value is the specified
expression. Statements such as 'if' are not allowed. An optional
semicolon ending the expression is allowed. As an example, the
average of two numbers could be defined as:
define average(a, b) = (a + b) / 2;
Functions can be defined which can be very complex. These can be
defined on the command line if desired, but editing of partial
functions is not possible past a single line. If an error is made
on a previous line, then the function must be finished (with probable
errors) and reentered from the beginning. Thus for complicated
functions, it is best to use an editor to create the function in a
file, and then enter the calculator and read in the file containing
the definition.
The parameters of a function can be referenced by name, as in
normal C usage, or by using the 'param' function. This function
returns the specified parameter of the function it is in, where
the parameters are numbered starting from 1. The total number
of parameters to the function is returned by using 'param(0)'.
Using this function allows you to implement varargs-like routines
which can handle any number of calling parameters. For example:
define sc()
{
local s, i;
s = 0;
for (i = 1; i <= param(0); i++)
s += param(i)^3;
return s;
}
defines a function which returns the sum of the cubes of all it's
parameters.

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NAME
delete - delete an element from a list at a given position
SYNOPSIS
delete(lst, idx)
TYPES
lst list, &list
idx int, &int
return any
DESCRIPTION
Delete element at index idx from list lst.
The index must refer to an element in the list. That is, idx must
be in the range [0, size(lst)-1].
EXAMPLE
> lst = list(2,3,4,5)
list (4 elements, 4 nonzero):
[[0]] = 2
[[1]] = 3
[[2]] = 4
[[3]] = 5
> delete(lst, 2)
4
> print lst
list (3 elements, 3 nonzero):
[[0]] = 2
[[1]] = 3
[[2]] = 5
LIMITS
none
LIBRARY
none
SEE ALSO
append, insert, islist, list, pop, push, remove, rsearch, search, size

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NAME
den - denominator of a real number
SYNOPSIS
den(x)
TYPES
x real
return integer
DESCRIPTION
For real x, den(x) returns the denominator of x. In calc,
real values are actually rational values. Each calc real
value can be uniquely expressed as:
n / d
where:
n and d are integers
gcd(n,d) == 1
d > 0
If x = n/x, then den(x) == d.
EXAMPLE
> print den(7), den(-1.25), den(121/33)
1 4 3
LIMITS
none
LIBRARY
NUMBER *qden(NUMBER *x)
SEE ALSO
num

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NAME
det - determinant
SYNOPSIS
det(m)
TYPES
m square matrix with elements of suitable type
return zero or value of type determined by types of elements
DESCRIPTION
The matrix m has to be square, i.e. of dimension 2 with:
matmax(m,1) - matmin(m,1) == matmax(m,2) - matmin(m,2).
If the elements of m are numbers (real or complex), det(m)
returns the value of the determinant of m.
If some or all of the elements of m are not numbers, the algorithm
used to evaluate det(m) assumes the definitions of *, unary -, binary -,
being zero or nonzero, are consistent with commutative ring structure,
and if the m is larger than 2 x 2, division by nonzero elements is
consistent with integral-domain structure.
If m is a 2 x 2 matrix with elements a, b, c, d, where a tests as
nonzero, det(m) is evaluated by
det(m) = (a * d) - (c * b).
If a tests as zero, det(m) = - ((c * b) - (a * d)) is used.
If m is 3 * 3 with elements a, b, c, d, e, f, g, h, i, where a and
a * e - d * b test as nonzero, det(m) is evaluated by
det(m) = ((a * e - d * b) * (a * i - g * c)
- (a * h - g * b) * (a * f - d * c))/a.
EXAMPLE
> mat A[3,3] = {2, 3, 5, 7, 11, 13, 17, 19, 23}
> c = config("mode", "frac")
> print det(A), det(A^2), det(A^3), det(A^-1)
-78 6084 -474552 -1/78
> obj res {r}
> global md
> define res_test(a) = !ismult(a.r, md)
> define res_sub(a,b) {local obj res v = {(a.r - b.r) % md}; return v;}
> define res_mul(a,b) {local obj res v = {(a.r * b.r) % md}; return v;}
> define res_neg(a) {local obj res v = {(-a.r) % md}; return v;}
> define res(x) {local obj res v = {x % md}; return v;}
> md = 0
> mat A[2,2] = {res(2), res(3), res(5), res(7)}
> md = 5
> print det(A)
obj res {4}
> md = 6
> print det(A)
obj res {5}
Note that if A had been a 3 x 3 or larger matrix, res_div(a,b) for
non-zero b would have had to be defined (assuming at least one
division is necessary); for consistent results when md is composite,
res_div(a,b) should be defined only when b and md are relatively
prime; there is no problem when md is prime.
LIMITS
none
LIBRARY
VALUE matdet(MATRIX *m)
SEE ALSO
matdim, matmax, matmin, inverse

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NAME
digit - digit at specified position in a decimal representation
SYNOPSIS
digit(x, y)
TYPES
x real
y integer
return integer
DESCRIPTION
By extending the digits on the left, and if necessary, the digits
on the right, by infinite strings of zeros, abs(x) may be considered
to have the decimal representation:
... d_2 d_1 d_0.d_-1 d_-2 ...
digit(x,y) then returns the digit d_y.
EXAMPLE
> x = 12.34
> print digit(x,2), digit(x,1), digit(x,0), digit(x,-1), digit(x,-2)
0 1 2 3 4
> x = 10/7
> print digit(x,1), digit(x,0), digit(x,-1), digit(x,-2), digit(x,-3)
0 1 4 2 8
LIMITS
none
LIBRARY
long qdigit(NUMBER *x, long y)
SEE ALSO
bit

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NAME
digits - return number of digits in an integer or integer part
SYNOPSIS
digits(x)
TYPES
x real
return integer
DESCRIPTION
For real x, digits(x) returns the number of digits in the decimal
representation of int(abs(x)).
EXAMPLE
> print digits(0), digits(0.0123), digits(3.7), digits(-27), digits(-99.7)
1 1 1 2 2
LIMITS
none
LIBRARY
long qdigits(NUMBER *x)
SEE ALSO
places

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NAME
dp - dot product of two vectors
SYNOPSIS
dp(x, y)
TYPES
x, y 1-dimensional matrices with the same number of elements
return depends on the nature of the elements of x and y
DESCRIPTION
Compute the dot product of two 1-dimensional matrices.
Let:
x = {x0, x1, ... xn}
y = {y0, y1, ... yn}
Then dp(x,y) returns the result of the calculation:
x0*y0 + x1*y1 + ... + xn*yn
EXAMPLE
> mat x[3] = {2,3,4}
> mat y[3] = {3,4,5}
> print dp(x,y)
38
LIMITS
x and y are 1-dimensional matrices
x and y have the same number of elements
LIBRARY
VALUE matdot(MATRIX *x, MATRIX *y)
SEE ALSO
cp

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Environment variables
CALCPATH
A :-separated list of directories used to search for
scripts filenames that do not begin with /, ./ or ~.
If this variable does not exist, a compiled value
is used. Typically compiled in value is:
.:./lib:~/lib:${LIBDIR}/calc
where ${LIBDIR} is usually:
/usr/local/lib/calc
This value is used by the READ command. It is an error
if no such readable file is found.
The CALCBINDINGS file searches the CALCPATH as well.
CALCRC
On startup (unless -h or -q was given on the command
line), calc searches for files along the :-separated
$CALCRC environment variable.
If this variable does not exist, a compiled value
is used. Typically compiled in value is:
${LIBDIR}/startup:~/.calcrc
where ${LIBDIR} is usually:
/usr/local/lib/calc
Missing files along the $CALCRC path are silently ignored.
CALCBINDINGS
On startup (unless -h or -q was given on the command
line), calc reads key bindings from the filename specified
in the $CALCRC environment variable. These key bindings
are used for command line editing and the command history.
If this variable does not exist, a compiled value is used.
Typically compiled in value is:
bindings
or:
altbind (bindings where ^D means exit)
The bindings file is searched along the CALCPATH. Unlike
the READ command, a .cal extension is not added.
If the file could not be opened, or if standard input is not
a terminal, then calc will still run, but fancy command line
editing is disabled.
HOME
This value is taken to be the home directory of the
current user. It is used when files begin with '~/'.
If this variable does not exist, the home directory password
entry of the current user is used. If that information
is not available, '.' is used.
PAGER
When invoking help, this environment variable is used
to display a help file.
If this variable does not exist, a compiled value
is used. Typically compiled in value is something
such as 'more', 'less', 'pg' or 'cat'.
SHELL
When a !-command is used, the program indicated by
this environment variable is used.
If this variable does not exist, a compiled value
is used. Typically compiled in value is something
such as 'sh' is used.

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NAME
epsilon - set or read the stored epsilon value
SYNOPSIS
epsilon([eps])
TYPES
eps real number greater than 0 and less than 1
return real number greater than 0 and less than 1
DESCRIPTION
Without args, epsilon() returns the current epsilon value.
With one arg, epsilon(eps) returns the current epsilon value
and sets the stored epsilon value to eps.
The stored epsilon value is used as default value for eps in
the functions appr(x, eps, rnd), sqrt(x, eps, rnd), etc.
EXAMPLE
> oldeps = epsilon(1e-6)
> print epsilon(), sqrt(2), epsilon(1e-4), sqrt(2), epsilon(oldeps)
> .000001 1.414214 .000001 1.4142 .0001
LIMITS
0 < eps < 1
LIBRARY
void setepsilon(NUMBER *eps)
NUMBER *_epsilon_
SEE ALSO
XXX - fill in

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NAME
errno - return a system error message
SYNOPSIS
errno(errnum)
TYPES
errnum int
return string
DESCRIPTION
If a file builtin function such as fopen() encounters an error,
it will return an errno number. This function will convert this
number into a somewhat more meaningful string.
Note that errno() may return different strings on different systems.
EXAMPLE
> badfile = fopen("not_a_file", "r")
> if (!isfile(badfile)) print "error #" : badfile : ":", errno(badfile);
error #2: No such file or directory
> print errno(13)
Permission denied
> errno(31)
"Too many links"
LIMITS
none
LIBRARY
none
SEE ALSO
errno, fclose, feof, ferror, fflush, fgetc, fgetline, files, fopen,
fprintf, isfile, printf, prompt

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NAME
error - generate a value of an error type
SYNOPSIS
error(n)
TYPES
n integer less than 32768
return null value or error value
DESCRIPTION
If n is zero or negative, error(n) returns the null value.
For positive n, error(n) returns a value of error type n.
EXAMPLE
> a = error(10009)
a
Error 10009
LIMITS
0 <= n < 32768
LIBRARY
none
SEE ALSO
errorcodes, iserror

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Calc generated error codes (see the error help file):

1
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/^#define E_[^_].*[ ][1-9][0-9]*[ ]\/\* .* \*\//s/#define E_.*[ ]\([1-9][0-9]*\)[ ]*\/\* \(.*\)[ ][ ]*\*\// \1 \2/p

61
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NAME
eval - evaluate a string
SYNOPSIS
eval(str)
TYPES
str string
return any
DESCRIPTION
For eval(str), the value of str is to be a string that could be the body
of the definition of a function f(). This string may declare local
variables and include keywords (while, for, ...) other than the
reserved keywords (define, show, help, read, write, show, cd) intended
for interactive use or for reading from a file.
If str is the empty string "", eval(str) returns the null value.
The call to eval(str) may return a value by explicit use of a return
statement: "return;" returns the null value, "return expr;" returns the
value of expr. If execution reaches the end of str and the
value on the execution stack is not null, eval(str) returns that value;
otherwise eval(str) returns the most recently saved value.
Each time eval(str) is called, a temporary function is compiled from
the commands in str, and if there are no syntax errors, this function
is then evaluated. If str contains syntax errors, eval(str) displays
the scanerror messages and returns the value error(49).
EXAMPLE
> str1 = "2 + 3"; print eval(str1);
5
> i = 10; str2 = "local i = 0; 7; while (i++ < 5) print i^2,:;"
> print i, eval(str2), i
10 1 4 9 16 25 7 10
(The print statements in str2 return the null value, so execution of
eval(str2) ends by returning the saved value 7. The global variable
i is unchanged.)
> eval("2 + ");
Missing expression
49
LIMITS
The string str in eval(str) should not include a call to itself as in
str = "2 + eval(str)"
For this str, eval(str) causes an "Evaluation stack depth exceeded" error.
Similarly, if str1 = "2 + eval(str2)", str2 should not include a call
to eval(str1), etc.
LIBRARY
none
SEE ALSO
XXX = fill in

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NAME
exp - exponential function
SYNOPSIS
exp(x [,eps])
TYPES
x real or complex
eps nonzero real, defaults to epsilon()
return real or complex
DESCRIPTION
Approximate the exponential function of x by a multiple of epsilon,
the error having absolute value less than 0.75 * eps.
If n is a positive integer, exp(x, 10^-n) will usually be
correct to the n-th decimal place, which, for large positive x
will give many significant figures.
EXAMPLE
> print exp(2, 1e-5), exp(2,1e-10), exp(2, 1e-15), exp(2, 1e-20)
7.38906 7.3890560989 7.38905609893065 7.38905609893065022723
> print exp(30, 1e5), exp(30, 1), exp(30, 1e-10)
10686474600000 10686474581524 10686474581524.4621469905
> print exp(-20, 1e-5), exp(-20, 1e-10), exp(-20, 1e-15), exp(-20, 1e-20)
0 .0000000021 .000000002061154 .00000000206115362244
> print exp(1+2i, 1e-5), exp(1+2i, 1e-10)
-1.1312+2.47173i -1.1312043838+2.471726672i
LIMITS
x < 100000
LIBRARY
NUMBER *qexp(NUMBER *x, NUMBER *eps)
COMPLEX *cexp(COMPLEX *x, NUMBER *eps)
SEE ALSO
ln, cosh, sinh, tanh

35
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Expression sequences
This is a sequence of statements, of which expression statements
are the commonest case. Statements are separated with semicolons,
and the newline character generally ends the sequence. If any
statement is an expression by itself, or is associated with an
'if' statement which is true, then two special things can happen.
If the sequence is executed at the top level of the calculator,
then the value of '.' is set to the value of the last expression.
Also, if an expression is a non-assignment, then the value of the
expression is automatically printed if its value is not NULL.
Some operations such as pre-increment and plus-equals are also
treated as assignments.
Examples of this are the following:
expression sets '.' to prints
---------- ----------- ------
3+4 7 7
2*4; 8+1; fact(3) 6 8, 9, and 6
x=3^2 9 -
if (3 < 2) 5; else 6 6 6
x++ old x -
print fact(4) - 24
null() null() -
Variables can be defined at the beginning of an expression sequence.
This is most useful for local variables, as in the following example,
which sums the square roots of the first few numbers:
local s, i; s = 0; for (i = 0; i < 10; i++) s += sqrt(i); s
If a return statement is executed in an expression sequence, then
the result of the expression sequence is the returned value. In
this case, '.' is set to the value, but nothing is printed.

33
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NAME
fact - factorial
SYNOPSIS
fact(x)
TYPES
x int
return int
DESCRIPTION
Return the factorial of a number. Factorial is defined as:
x! = 1 * 2 * 3 * ... * x-1 * x
0! = 1
EXAMPLE
> print fact(10), fact(5), fact(2), fact(1), fact(0)
3628800 120 2 1 1
> print fact(40)
815915283247897734345611269596115894272000000000
LIMITS
2^24 > x >= 0
y < 2^24
LIBRARY
void zfact(NUMBER x, *ret)
SEE ALSO
comb, perm

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NAME
factor - smallest prime factor not exceeding specified limit
SYNOPSIS
factor(n [, limit [, err]])
TYPES
n integer
limit integer with abs(limit) < 2^32, defaults to 2^32 - 1
err integer
return positive integer, -1 or err
DESCRIPTION
If n >= 0 and n has a prime factor less than or equal to limit,
factor(n, limit) returns the smallest such factor. If n >= 0
and the smallest prime factor of n exceeds limit, 1 is returned.
In particular, if n >= 0 and limit <= 1, factor(n, limit)
always returns 1; factor(n,2) returns 2 if and only if n is even.
If n < 0, -1 is returned.
If abs(limit) >= 2^32, factor(n, limit) causes an error,
factor(n, limit, err) returns the value of err.
EXAMPLE
> print factor(35,4), factor(35,5), factor(35), factor(-35)
1 5 5 -1
> print factor(2^32 + 1), factor(2^47 - 1), factor(2^59 - 1)
641 2351 179951
LIMITS
none
LIBRARY
FLAG zfactor(ZVALUE n, ZVALUE limit, ZVALUE *res)
SEE ALSO
lfactor

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NAME
fclose - close a file
SYNOPSIS
fclose(fd)
TYPES
fd file
return nul or int
DESCRIPTION
This function closes the open file associated with the descriptor fd.
When this is done, the file value associated with the file remains
a file value, but appears 'closed', and cannot be used in further
file-related calls (except fclose) without causing errors. This same
action occurs to all copies of the file value. You do not need to
explicitly close all the copies of a file value.
Standard input, standard output and standard error are always opened
and cannot be closed.
The truth value of an closed file is FALSE.
The fclose function returns the numeric value of errno if
there had been an error using the file, or the null value if
there was no error.
Closing a closed file is permitted. Fclose returns null in
this case.
EXAMPLE
> fd = fopen("/etc/motd", "r")
> if (fd) print "file is open";
file is open
> err = fclose(fd);
> if (isnull(err)) print "close successful"; else errno(err);
close successful
> if (!fd) print "file is closed";
file is closed
LIMITS
fd != files(0) && fd != files(1) && fd != files(2)
LIBRARY
none
SEE ALSO
errno, fclose, feof, ferror, fflush, fgetc, fgetline, fgets, files, fopen,
fprintf, fputc, fputs, fseek, fsize, ftell, isfile, printf, prompt

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NAME
fcnt - count of number of times a specified integer divides an integer
SYNOPSIS
fcnt(x,y)
TYPES
x integer
y integer
return non-negative integer
DESCRIPTION
If x is nonzero and abs(y) > 1, fcnt(x,y) returns the greatest
non-negative n for which y^n is a divisor of x. In particular,
zero is returned if x is not divisible by y.
If x is zero or if y = -1, 0 or 1, fcnt(x,y) is defined to be zero.
EXAMPLE
> print fcnt(7,4), fcnt(24,4), fcnt(48,4)
0 1 2
LIMITS
none
LIBRARY
long zfacrem(ZVALUE x, ZVALUE y, ZVALUE *rem)
SEE ALSO
frem, gcdrem

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NAME
feof - determine if end-of-file flag is set
SYNOPSIS
feof(fd)
TYPES
fd file stream open for reading
return 0 or 1
DESCRIPTION
The function feof(fd) returns 1 or 0 according as the end-of-file flag
is set or clear.
The end-of-file flag for the stream fd is set if reading at the
end-of-file position is attempted. The flag is cleared by
positioning operations (fseek, rewind, fsetpos) and by freopen.
EXAMPLE
> fd1 = fopen("/tmp/newfile", "w")
> fputs(fd1, "Chongo was here\n")
> fflush(fd1)
> fd2 = fopen("/tmp/newfile", "r")
> feof(fd2)
0
> fgetline(fd2)
"Chongo was here"
> feof(fd2)
0
> fgetline(fd2)
> feof(fd2)
1
LIMITS
none
LIBRARY
none
SEE ALSO
errno, fclose, feof, ferror, fflush, fgetc, fgetline, fgets, files, fopen,
fprintf, fputc, fputs, fseek, fsize, ftell, isfile, printf, prompt

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NAME
ferror - determine if an error has occurred for file
SYNOPSIS
ferror(fd)
TYPES
fd file
return int
DESCRIPTION
This function determines whether the error condition was detected
while performing some operation on the file associated with fd.
The error need not have been the previous file operation.
If an error was previously reported 1 will be returned, otherwise
0 is returned.
EXAMPLE
> fd = fopen("/etc/motd", "r")
> ferror(fd)
0
LIMITS
fd must be associaed with an open file
LIBRARY
none
SEE ALSO
errno, fclose, feof, ferror, fflush, fgetc, fgetline, fgets, files, fopen,
fprintf, fputc, fputs, fseek, fsize, ftell, isfile, printf, prompt

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NAME
fflush - flush output to file
SYNOPSIS
fflush(fd)
TYPES
fd file
return nil
DESCRIPTION
This function forces and buffered output to the file associated with fd.
EXAMPLE
> fd = fopen("/tmp/file", "w")
> fputc(fd, "@");
> fflush(fd)
LIMITS
fd must be associaed with an open file
LIBRARY
none
SEE ALSO
errno, fclose, feof, ferror, fflush, fgetc, fgetline, fgets, files, fopen,
fprintf, fputc, fputs, fseek, fsize, ftell, isfile, printf, prompt

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NAME
fgetc - read the next char from a file
SYNOPSIS
fgetc(fd)
TYPES
fd file
return str or nil
DESCRIPTION
This function reads the next character from the open file
associated with fd.
If there is a next character, this function returns a 1
character string containing that character. In the case
of EOF or error, nil is returned.
EXAMPLE
> fd = fopen("/tmp/newfile", "w")
> fputs(fd, "chongo was here\n")
> fd2 = fopen("/tmp/newfile", "r")
> fgetc(fd2)
"c"
LIMITS
fd must be associaed with an open file
LIBRARY
none
SEE ALSO
errno, fclose, feof, ferror, fflush, fgetc, fgetline, fgets, files, fopen,
fprintf, fputc, fputs, fseek, fsize, ftell, isfile, printf, prompt

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NAME
fgetfield - read the next word from a file
SYNOPSIS
fgetfield(fs)
TYPES
fs file stream open for reading
return string, null or error value
DESCRIPTION
If characters cannot be read from the file, an error value is returned.
Otherwise starting at the current file position, any whitespace
characters are skipped. If the reading reaches end-of-file, the
null value is returned. If non-whitespace is encountered, formation
of a string begins, continuing until whitespace of '\0' or end-of-file
is reached. The returned value is this string (terminated as usual
by a null character). After the operation, the file position will
be immediately after the first whitespace character of '\0' or at
end-of-file.
EXAMPLE
> f = fopen("/tmp/junk", "w")
> fputs(f, " Alpha Beta \n")
> freopen(f, "r")
> fgetfield(f)
"Alpha"
> fgetfield(f)
"Beta"
> fgetfield(f)
>
> freopen(f, "w")
> fputstr(f, " Alpha ", "Beta")
> freopen(f, "r")
> fgetfield(f)
"Alpha"
> fgetfield(f)
""
> fgetfield(f)
"Beta"
LIMITS
none - XXX - is this correct?
LIBRARY
none - XXX - is this correct?
SEE ALSO
fgetstr, fputstr, fgets, fputs, fopen, files, fprintf

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NAME
fgetline - read the next line from a file, newline is tossed
SYNOPSIS
fgetline(fd)
TYPES
fd file
return str or nil
DESCRIPTION
This function reads the next line, including any trailing newline from
the open file associated with fd. Unlike fgets, the trailing
newline is removed from the return string.
Empty lines return the null string. When the end of file is reached,
fgetline returns the null value. (Note the distinction between a null
string and a null value.)
If the line contained a numeric value, then the 'eval' function can
then be used to convert the string to a numeric value.
If a line is read, is returned minus the trailing newline, otherwise
(EOF or ERROR) nil is returned.
EXAMPLE
> fd = fopen("/tmp/newfile", "w")
> fputs(fd, "chongo was here\n")
> fputs(fd, "123\n")
> fd2 = fopen("/tmp/newfile", "r")
> fgets(fd2)
"chongo was here
"
> fclose(fd2)
> fd2 = fopen("/tmp/newfile", "r")
> fgetline(fd2)
"chongo was here"
> eval(fgetline(fd2))
123
LIMITS
fd must be associaed with an open file
LIBRARY
none
SEE ALSO
errno, fclose, feof, ferror, fflush, fgetc, fgetline, fgets, files, fopen,
fprintf, fputc, fputs, fseek, fsize, ftell, isfile, printf, prompt

40
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NAME
fgets - read the next line from a file, newline is kept
SYNOPSIS
fgets(fd)
TYPES
fd file
return str or nil
DESCRIPTION
This function reads the next line, including any trailing newline from
the open file associated with fd. Unlike fgetline, the trailing
newline is included in the return string.
If a line is read, is returned, otherwise (EOF or ERROR) nil is returned.
EXAMPLE
> fd = fopen("/tmp/newfile", "w")
> fputs(fd, "chongo was here\n")
> fd2 = fopen("/tmp/newfile", "r")
> fgets(fd2)
"chongo was here
"
> fclose(fd2)
> fd2 = fopen("/tmp/newfile", "r")
> fgetline(fd2)
"chongo was here"
LIMITS
fd must be associaed with an open file
LIBRARY
none
SEE ALSO
errno, fclose, feof, ferror, fflush, fgetc, fgetline, fgets, files, fopen,
fprintf, fputc, fputs, fseek, fsize, ftell, isfile, printf, prompt

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NAME
fgetstr - read the next null-terminated string from a file
SYNOPSIS
fgetstr(fs)
TYPES
fs file stream open for reading
return string, null or error value
DESCRIPTION
If the stream is at end of file, the null value is returned.
If the stream cannot be read, an error value is returned.
Otherwise the function retrurns the string of characters from the
current file position to the first null character ('\0') (the file
position for further reading then being immediately after the '\0'),
or if no null character is encountered, the string of characters to
the end of file (the string as usual being terminated by '\0').
If the stream being read is from stdin (i.e. files(0)), the
characters entered are not displayed and reading ends when a '\0' is
entered (on many terminals this is by ctrl-@).
EXAMPLE
> f = fopen("/tmp/junk", "w")
> fputstr(f, " Alpha Beta ", "", "Gamma\n\tDelta")
> freopen(f, "r")
> fgetstr(f)
" Alpha Beta "
> fgetstr(f)
""
> fgetstr(f)
"Gamma
Delta"
> fgetstr(f)
>
LIMITS
none - XXX - is this correct?
LIBRARY
none - XXX - is this correct?
SEE ALSO
fputstr, fgetword, fgets, fputs, fopen, files, fprintf

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NAME
fib - Fibonacci number
SYNOPSIS
fib(n)
TYPES
n integer
return integer
DESCRIPTION
For any integer n, fib(n) returns the Fibonacci number with index n.
This may be defined by fib(0) = 0, fib(1) = 1 and for any n (positive
or negative) fib(n) = fib(n-1) + fib(n-2).
EXAMPLE
> print fib(-2), fib(-1), fib(0), fib(1), fib(2), fib(3), fib(4), fib(5)
-1 1 0 1 1 2 3 5 -8
LIMITS
none
LIBRARY
NUMBER *qfib(NUMBER *n)
SEE ALSO
XXX - fill in

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Using files
The calculator provides some functions which allow the program to
read or write text files. These functions use stdio internally,
and the functions appear similar to some of the stdio functions.
Some differences do occur, as will be explained here.
Names of files are subject to ~ expansion just like the C or
Korn shell. For example, the file name:
~/.rc.cal
refers to the file '.rc.cal' under your home directory. The
file name:
~chongo/.rc.cal
refers to the a file 'rc.cal' under the home directory of 'chongo'.
A file can be opened for either reading, writing, or appending.
To do this, the 'fopen' function is used, which accepts a filename
and an open mode, both as strings. You use 'r' for reading, 'w'
for writing, and 'a' for appending. For example, to open the file
'foo' for reading, the following could be used:
fd = fopen('foo', 'r');
If the open is unsuccessful, the numeric value of errno is returned.
If the open is successful, a value of type 'file' will be returned.
You can use the 'isfile' function to test the return value to see
if the open succeeded. You should assign the return value of fopen
to a variable for later use. File values can be copied to more than
one variable, and using any of the variables with the same file value
will produce the same results.
If you overwrite a variable containing a file value or don't save the
result of an 'fopen', the opened file still remains open. Such 'lost'
files can be recovered by using the 'files' function. This function
either takes no arguments or else takes one integer argument. If no
arguments are given, then 'files' returns the maximum number of opened
files. If an argument is given, then the 'files' function uses it as
an index into an internal table of open files, and returns a value
referring to one the open files. If that entry in the table is not
in use, then the null value is returned instead. Index 0 always
refers to standard input, index 1 always refers to standard output,
and index 2 always refers to standard error. These three files are
already open by the calculator and cannot be closed. As an example
of using 'files', if you wanted to assign a file value which is
equivalent to stdout, you could use:
stdout = files(1);
The 'fclose' function is used to close a file which had been opened.
When this is done, the file value associated with the file remains
a file value, but appears 'closed', and cannot be used in further
file-related calls (except fclose) without causing errors. This same
action occurs to all copies of the file value. You do not need to
explicitly close all the copies of a file value. The 'fclose'
function returns the numeric value of errno if there had been an
error using the file, or the null value if there was no error.
The builtin 'errno' can be use to convert an errno number into
a slightly more meaningful error message:
badfile = fopen("not_a_file", "r");
if (!isfile(badfile)) {
print "error #" : badfile : ":", errno(badfile);
}
File values can be printed. When this is done, the filename of the
opened file is printed inside of quote marks. If the file value had
been closed, then the null string is printed. If a file value is the
result of a top-level expression, then in addition to the filename,
the open mode, file position, and possible EOF, error, and closed
status is also displayed.
File values can be used inside of 'if' tests. When this is done,
an opened file is TRUE, and a closed file is FALSE. As an example
of this, the following loop will print the names of all the currently
opened non-standard files with their indexes, and then close them:
for (i = 3; i < files(); i++) {
if (files(i)) {
print i, files(i);
fclose(files(i));
}
}
The functions to read from files are 'fgetline' and 'fgetc'.
The 'fgetline' function accepts a file value, and returns the next
input line from a file. The line is returned as a string value, and
does not contain the end of line character. Empty lines return the
null string. When the end of file is reached, fgetline returns the
null value. (Note the distinction between a null string and a null
value.) If the line contained a numeric value, then the 'eval'
function can then be used to convert the string to a numeric value.
Care should be used when doing this, however, since eval will
generate an error if the string doesn't represent a valid expression.
The 'fgetc' function returns the next character from a file as a
single character string. It returns the null value when end of file
is reached.
The 'printf' and 'fprintf' functions are used to print results to a
file (which could be stdout or stderr). The 'fprintf' function
accepts a file variable, whereas the 'printf' function assumes the
use of 'files(1)' (stdout). They both require a format string, which
is used in almost the same way as in normal C. The differences come
in the interpretation of values to be printed for various formats.
Unlike in C, where an unmatched format type and value will cause
problems, in the calculator nothing bad will happen. This is because
the calculator knows the types of all values, and will handle them
all reasonably. What this means is that you can (for example), always
use %s or %d in your format strings, even if you are printing a non-
string or non-numeric value. For example, the following is valid:
printf("Two values are %d and %s\n", "fred", 4567);
and will print "Two values are fred and 4567".
Using particular format characters, however, is still useful if
you wish to use width or precision arguments in the format, or if
you wish to print numbers in a particular format. The following
is a list of the possible numeric formats:
%d print in currently defined numeric format
%f print as floating point
%e print as exponential
%r print as decimal fractions
%x print as hex fractions
%o print as octal fractions
%b print as binary fractions
Note then, that using %d in the format makes the output configurable
by using the 'config' function to change the output mode, whereas
the other formats override the mode and force the output to be in
the specified format.
Using the precision argument will override the 'config' function
to set the number of decimal places printed. For example:
printf("The number is %.100f\n", 1/3);
will print 100 decimal places no matter what the display configuration
value is set to.
The %s and %c formats are identical, and will print out the string
representation of the value. In these cases, the precision argument
will truncate the output the same way as in standard C.
If a matrix or list is printed, then the output mode and precision
affects the printing of each individual element. However, field
widths are ignored since these values print using multiple lines.
Field widths are also ignored if an object value prints on multiple
lines.
The functions 'fputc' and 'fputs' write a character and string to
a file respectively.
The final file-related functions are 'fflush', 'ferror', and 'feof'.
The 'fflush' function forces buffered output to a file. The 'ferror'
function returns nonzero if an error had occurred to a file. The
'feof' function returns nonzero if end of file has been reached
while reading a file.
The 'strprintf' function formats output similarly to 'printf',
but the output is returned as a string value instead of being
printed.

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NAME
files - return a file or the maximum number of open files
SYNOPSIS
files([fnum])
TYPES
fnum int
return files, int or null
DESCRIPTION
This function, then given the argument fnum, will use it as an
index into an internal table of open file and return a file value.
If that entry in the table is not in use, then the null value is
returned instead. When no args are given, the maximum number of
open files is returned.
If you overwrite a variable containing a file value or don't save the
result of an 'fopen', the opened file still remains open. Such 'lost'
files can be recovered by using the 'files' function.
The first 3 file entries always refer to standard input, output
and error respectively. (see the example below) These three
files are already open by the calculator and cannot be closed.
When calc starts up, it scans for open file descriptors above
stderr (2) and below MAXFILES (20). Any open descriptor found
is assumed to be an open file opened in an unknown mode. Calc
will try to read and write to this file when directed.
Consider the following commands:
$ echo "A line of text in the file on descriptor 5" > datafile
$ calc 5<datafile
then one could do the following:
> files(5)
FILE 5 "descriptor[5]" (unknown_mode, pos 0)
> fgetline(files(5))
"A line of text in the file on descriptor 5"
EXAMPLE
> fd = fopen("/etc/motd", "r")
> fd
FILE 3 "/etc/motd" (reading, pos 0)
> files(3)
FILE 3 "/etc/motd" (reading, pos 0)
> if (isnull(files(4))) print "not open"
not open
> stdin = files(0)
> stdout = files(1)
> stderr = files(2)
> print files()
20
LIMITS
none
LIBRARY
none
SEE ALSO
errno, fclose, feof, ferror, fflush, fgetc, fgetline, fgets, files, fopen,
fprintf, fputc, fputs, fseek, fsize, ftell, isfile, printf, prompt

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NAME
floor - floor
SYNOPSIS
floor(x)
TYPES
x real, complex, list, matrix
return real or complex, list, matrix
DESCRIPTION
For real x, floor(x) is the greatest integer not greater than x.
For complex, floor(x) returns the real or complex number v for
which re(v) = floor(re(x)), im(v) = floor(im(x)).
For list or matrix x, floor(x) returns the list or matrix of the
same structure as x for which each element t of x has been replaced
by floor(t).
EXAMPLE
> print floor(27), floor(1.23), floor(-4.56), floor(7.8 - 9.1i)
27 1 -5 7-10i
LIMITS
none
LIBRARY
none
SEE ALSO
ceil, int

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NAME
fopen - open a file
SYNOPSIS
fopen(filename, mode)
TYPES
filename string
mode string
return file
DESCRIPTION
This function opens the file named filename. A file can be
opened for either reading, writing, or appending. The mode
is controlled by the mode flag as folllows:
"r" reading
"w" writing
"a" appending
Names of files are subject to ~ expansion just like the C or
Korn shell. For example, the file name:
~/lib/gleet
refers to the file 'gleet' under the directory lib located
in your home directory. The file name:
~chongo/was_here
refers to the a file 'was_here' under the home directory of
the user 'chongo'.
If the open is successful, a value of type 'file' will be returned.
You can use the 'isfile' function to test the return value to see
if the open succeeded. You should assign the return value of fopen
to a variable for later use. File values can be copied to more than
one variable, and using any of the variables with the same file value
will produce the same results.
Standard input, standard output and standard error are always opened
and cannot be closed.
The truth value of an opened file is TRUE.
If the open is unsuccessful, the numeric value of errno is returned.
You can the errno() builtin to determine what the errno number means.
EXAMPLE
> fd = fopen("/etc/motd", "r")
> print fd
"/etc/motd"
> fd
FILE 3 "/etc/motd" (reading, pos 0)
> outfile = fopen("~/tmp/output", "w")
> print outfile
"~/tmp/output"
> outfile
FILE 4 "~/tmp/output" (writing, pos 0)
> badfile = fopen("not_a_file", "r")
> if (!isfile(badfile)) print "error #" : badfile : ":", errno(badfile);
error #2: No such file or directory
LIMITS
none
LIBRARY
none
SEE ALSO
errno, fclose, feof, ferror, fflush, fgetc, fgetline, fgets, files, fopen,
fprintf, fputc, fputs, fseek, fsize, ftell, isfile, printf, prompt

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NAME
forall - to evaluate a function for all values of a list or matrix
SYNOPSIS
forall(x, y)
TYPES
x list or matrix
y string
return null value
DESCRIPTION
In forall(x,y), y is to the the name of a function; that function
is performed in succession for all elements of x. This is similar
to modify(x, y) but x is not changed.
EXAMPLE
> global n = 0
> define s(a) {n += a;}
> A = list(1,2,3,4)
> forall(A, "s")
> n
10
> define e(a) {if (iseven(a)) print a;}
> forall(A, "e")
2
4
LIMITS
none
LIBRARY
none
SEE ALSO
modify

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NAME
fprintf - formatted print to a file
SYNOPSIS
fprintf(fd, fmt, x_1, x_2, ...)
TYPES
fd file
fmt string
x_1, x_2, ... any
return null
DESCRIPTION
This prints to the file fd exactly what would be printed to
the standard output by printf(fmt, x_1, x_2, ...).
EXAMPLE
> fprintf(files(1), "h=%d, i=%d\n", 2, 3);
h=2, i=3
> c = config("epsilon", 1e-6); c = config("display", 6);
> c = config("tilde", 1); c = config("outround", 0);
> c = config("fullzero", 0);
> fmt = "%f,%10f,%-10f,%10.4f,%.4f,%.f.\n";
> a = sqrt(3);
> fprintf(files(2), fmt,a,a,a,a,a,a);
1.732051, 1.732051,1.732051 , ~1.7320,~1.7320,~1.
> file = fopen("/tmp/foo", "w");
> mat A[4] = {sqrt(2), 3/7, "undefined", null()};
> fprintf(file, "%f%r",A,A);
> fclose(file);
> !cat /tmp/foo
mat [4] (4 elements, 4 nonzero):
[0] = 1.4142135623730950488
[1] = ~.42857142857142857142
[2] = "undefined"
[3] = NULL
mat [4] (4 elements, 4 nonzero):
[0] = 1767766952966368811/1250000000000000000
[1] = 3/7
[2] = "undefined"
[3] = NULL
LIMITS
The number of arguments of fprintf() is not to exceed 100.
LIBRARY
none
SEE ALSO
printf, strprintf, print

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NAME
fputc - write a character to a file
SYNOPSIS
fputc(fd, data)
TYPES
fd file
data str
return nil
DESCRIPTION
This function writes the first character in data to the file
associated with fd.
EXAMPLE
> fd = fopen("/tmp/newfile", "w")
> fputc(fd, "c")
> fd2 = fopen("/tmp/newfile", "r")
> fgetc(fd2)
"c"
LIMITS
fd must be associaed with an open file
LIBRARY
none
SEE ALSO
errno, fclose, feof, ferror, fflush, fgetc, fgetline, fgets, files, fopen,
fprintf, fputc, fputs, fseek, fsize, ftell, isfile, printf, prompt

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NAME
fputs - write a string to a file
SYNOPSIS
fputs(fd, data)
TYPES
fd file
data str
return nil
DESCRIPTION
This function writes the string found in data to the file
associated with fd.
EXAMPLE
> fd = fopen("/tmp/newfile", "w")
> fputs(fd, "chongo was here\n")
> fd2 = fopen("/tmp/newfile", "r")
> fgetline(fd2)
"chongo was here"
LIMITS
fd must be associaed with an open file
LIBRARY
none
SEE ALSO
errno, fclose, feof, ferror, fflush, fgetc, fgetline, fgets, files, fopen,
fprintf, fputc, fputs, fseek, fsize, ftell, isfile, printf, prompt

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NAME
fputstr - send one or more null-terminated strings to a file
SYNOPSIS
fputstr(fs, s_1, s_2, ...)
TYPES
fs file stream open for writing
s_1, ... string
return null or error value
DESCRIPTION
If the stream cannot be written to or an argument is of the wrong
type, an error value is returned.
Otherwise the strings s_1, s_2, ..., including the terminating
null characters ('\0') are written to the file stream fs.
EXAMPLE
> f = fopen("/tmp/junk", "w")
> fputstr(f, "Alpha", "Beta")
> freopen(f, "r")
> fgetstr(f)
"Alpha"
> fgetstr(f)
"Beta"
> fgetstr(f)
>
> fputstr(f, "Gamma")
Error 72
LIMITS
none - XXX - is this correct?
LIBRARY
none - XXX - is this correct?
SEE ALSO
fgetstr, fgetfield, fgets, fputs, fopen, files, fprintf

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NAME
frac - return the fractional part of a number or of numbers in a value
SYNOPSIS
frac(x)
TYPES
If x is an object of type xx, frac(x) requires xx_frac to have been
defined; other conditions on x and the value returned depend on
the definition of xx_frac.
For other x:
x number (real or complex), matrix
return number or matrix
DESCRIPTION
If x is an integer, frac(x) returns zero. For other real values of x,
frac(x) returns the real number f for which x = i + f, where i is an
integer, sgn(f) = sgn(x), and abs(f) < 1.
If x is complex, frac(x) returns frac(re(x)) + frac(im(x))*1i.
If x is a matrix, frac(x) returns the matrix m with the same structure
as x in which m[[i]] = frac(x[[i]]).
EXAMPLE
> c = config("mode", "frac")
> print frac(3), frac(22/7), frac(27/7), frac(-3.125), frac(2.15 - 3.25i)
0 1/7 6/7 -1/8 3/20-1i/4
LIMITS
none
LIBRARY
NUMBER *qfrac(NUMBER *x)
COMPLEX *cfrac(COMPLEX *x)
MATRIX *matfrac(MATRIX *x)
SEE ALSO
int, ceil, floor

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NAME
frem - remove specified integer factors from specified integer
SYNOPSIS
frem(x,y)
TYPES
x integer
y integer
return non-negative integer
DESCRIPTION
If x and y are not zero and n is the largest non-negative integer
for which y^n is a divisor of x, frem(x,y) returns abs(x/y^n).
In particular, abs(x) is returned if x is not divisible by
y or if abs(y) = 1. If abs(y) > 1, frem(x,y) is the greatest
divisor of x not divisible by y.
For all x, frem(x,0) is defined to equal abs(x).
For all y, frem(0,y) is defined to be zero.
For all x and y, abs(x) = frem(x,y) * abs(y) ^ fcnt(x,y).
EXAMPLE
> print frem(7,4), frem(24,4), frem(48,4), frem(-48,4)
7 6 3 3
LIMITS
none
LIBRARY
NUMBER *qfacrem(NUMBER *x, NUMBER *y);
SEE ALSO
fcnt, gcdrem

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NAME
freopen - close (if necessary) and reopen a filestream
SYNOPSIS
freopen(fs, mode) or freopen(fs, mode, filename)
TYPES
fs open or closed file stream
mode one of the strings "r", "w", "a", "r+", "w+, "a+"
filename string
return null or error value
DESCRIPTION
With two arguments, this function closes the file stream fs and
attempts to reopen it with the specified mode. A non-null value
is returned only if the attempt fails.
With three arguments, fs, if open, is closed, and an attempt is made to
open the file with the specified name and assign it to the stream
fs. A non-null value is returned only if the attempt fails.
EXAMPLE
> f = fopen("/tmp/junk", "w")
> fputs(f, "Leonard Euler")
> freopen(f, "r")
> fgets(f)
"Leonard Euler"
> !chmod u-w /tmp/junk
> freopen(f, "w")
Error 10013
LIMITS
none - XXX - is this correct?
LIBRARY
none - XXX - is this correct?
SEE ALSO
errno, fclose, feof, ferror, fflush, fgetc, fgetline, fgets, files, fopen,
fprintf, fputc, fputs, fseek, fsize, ftell, isfile, printf, prompt

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NAME
fscan - scan a file for possible assignment to variables
SYNOPSIS
fscan(fs, x_1, x_2, ..., x_n)
TYPES
fs file stream open for reading
x_1, x_2, ... any
return integer
DESCRIPTION
Starting at the current position on fs and while values remain in the
x_i arguments, fields of non-whitespace characters are read and evaluated
in succession and if the corresponding x_i is an lvalue, the value of
the field is assigned to x_i. Scanning ceases when no x_i remain or
when the stream reaches end-of-file.
The function returns the number of fields evaluated.
EXAMPLE
> global a, b, c, d;
> f = fopen("/tmp/junk", "w+");
> fputs(f, "\t3+4\t\ta-2i d=a^2 'word'")
> rewind(f)
> fscan(f, a, b, , c)
4
> print a, b, c, d
7 a-2i word 49
LIMITS
none - XXX - is this correct?
LIBRARY
none - XXX - is this correct?
SEE ALSO
scan, strscan, fscanf, scanf, strscanf, printf, fprintf, strprintf

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NAME
fscanf - formatted scan of a file stream
SYNOPSIS
fscanf(fs, fmt, x_1, x_2, ...)
TYPES
fs file stream open for reading
fmt string
x_1, x_2, ... lvalues
return null, nonnegative integer, or error value
DESCRIPTION
If the current position for fs is EOF, the null value is returned.
Otherwise, until the terminating null character of fmt is encountered
or end-of-file for fs is reached, characters other than '%' and white
space are read from fmt and compared with the corresponding chracters
read from fs. If the characters match, the reading continues. If they
do not match, an integer value is returned and the file position for
fs is the position of the non-matching character. If white space
is encountered in fmt, any white space characters read from
fs are skipped until either end-of-file is reached or a non-white-space
character is read and comparisons continue under the control of the
next non-white character and following characters in fmt.
When a '%' is encountered in fmt, if this is immediately followed by
another '%', the pair is considered as if just one '%' were read and
if reading from fmt and fs continues if and only if fs has a matching
'%'. A single '%' read from fmt is taken to indicate the beginning of
a conversion specification field consisting in succession of:
an optional '*',
optional decimal digits,
one of 'c', 's', 'n', 'f', 'e', 'i' or a scanset specifier.
A scanset specifier starts with '[' and an optional '^', then an optional
']', then optional other characters, and ends with ']'. If any
other sequence of characters follows the '%', characters before the
first exceptional character (which could be the terminating null
character of the fmt string) are ignored, e.g. the sequence " %*3d " does
the same as " d ". If there is no '*' at the beginning of the specifier,
and the list x_1, x_2, ... has not been exhausted,
a value will be assigned to the next lvalue in the list; if no lvalue
remains, the reading of fs stops and the function returns the number
of assignments that have been made.
Occurrence of '*' indicates that characters as specified are to be read
but no assignment will be made.
The digits, if any, read at this stage in the specifier are taken to
be decimal digits of an integer which becomes the maximum "width"
(i.e. for string-type values, the number of characters to be read from
fs); absence of digits or all zero digits in the 'c'
case are taken to mean width = 1. Zero width for the other cases are
treated as if infinite. Fewer characters than the specifier width
may be read if end-of-file is reached or in the case of scanset
specification, an exceptional character is encountered.
If the ending character is 'c', characters are read from fs to
form a string, which will be ignored or in the non-'*' case, assigned
to the next lvalue.
In the 's' case, reading to form the string starts at the first non-white
character (if any) and ceases when end-of-file or further white space
is encountered or the specified width has been attained.
The cases 'f', 'e', 'r', 'i' may be considered to indicate expectation of
floating-point, exponential, ratio, or integer representation of the
number to be read. For example, 'i'
might be taken to suggest a number like +2345; 'r' might suggest
a representation like -27/49; 'e' might suggest a representation like
1.24e-7; 'f' might suggest a representation like 27.145. However, there
is no test that the the result conforms to the specifier. Whatever
the specifier in these cases, the result depends on the characters read
until a space or other exceptional character is read. The
characters read may include one or more occurrences of +, -, * as
well as /, interpreted in the usual way, with left-to-right associativity
for + and -, and for * and /. Also acceptable is a trailing i to
indicate an imaginary number. For example the expression
2+3/4*7i+3.15e7
would be interpreted as for an ordinary evaluation. A decimal fraction
may have more than one dot: dots after the first, which is taken to be
the decimal point, are ignored. Thus "12.3..45e6.7" is interpreted
as if it were "12.345e67".
For the number specifiers 'f', 'e', 'r', 'i', any specified width is
ignored.
For the specifier 'n', the current value of the file-position indicator
is assigned to the corresponding lvalue. (Any width or skip specification
is ignored.)
EXAMPLE
> global a, b, c
> f = fopen("/tmp/junk", "w+")
> fputs(f, "Alpha Beta Gamma")
> rewind(f)
> fscanf(f, "Alpha Gamma")
> fgets(f)
"Beta Gamma"
> rewind(f)
> fscanf(f, "%5c", a)
1
> a
"Alpha"
> fgets(f)
" Beta Gamma"
> rewind(f)
> fscanf(f, "%3c%s%[^m]", a, b, c)
3
> print a, b
Alp ha
> print c
Beta Ga
> fgets(f)
"mma"
LIMITS
none - XXX - is this correct?
LIBRARY
none - XXX - is this correct?
SEE ALSO
scanf, strscanf, printf, fprintf, strprintf, fscan, scan, strscan

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NAME
fseek - set a file position
SYNOPSIS
fseek(fd, offset [, whence])
TYPES
fd open file stream
pos integer
whence 0, 1 or 2, defaulting to 0
return null or error value
DESCRIPTION
This function sets the file position indicator for the stream by
adding offset to zero, the current value, or the size of the
file, according as whence is 0, 1 or 2. The effect is equivalent to
moving the signed distance offset from the beginning, the current
position, or the end of the file.
The function also clears the end-of-file flag and flushes any
buffered data waiting to be output to the stream.
An implementation-defined error occurs if the effect would be to
give a negative value to the position indicator; on some systems, the
file position will be set to end-of-file.
The file position indicator may have a value greater than the file
size. If characters are then written to the file, the gap is
filled by null ('\0') characters.
EXAMPLE
> fd = fopen("/tmp/curds", "w")
> fputs(fd, "0123456789abcdef")
> freopen(fd, "r")
> fsize(fd)
16
> fseek(fd, 5)
> fgets(fd)
"56789abcdef"
> fseek(fd, 0)
> fscanf(fd, "%*5c")
0
> fseek(fd, 5, 1)
> fgets(fd)
"abcdef"
> ftell(fd)
16
> fseek(fd, -5, 2)
> fgets(fd)
"bcdef"
> fseek(fd, -2)
System error 22
> ftell(fd)
16
The results for the last four lines may be different for different systems.
LIMITS
Some details of the operation of this function may be implementation-
dependent, particularly for older systems.
LIBRARY
none
SEE ALSO
ftell, fgetpos, fsetpos, rewind, strerror

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NAME
fsize - return the file size
SYNOPSIS
fsize(fd)
TYPES
fd file
return int
DESCRIPTION
This function returns the number of bytes in a file. When at
the end of file, ftell returns a value which is 1 greater than
the file size as reported by fsize.
EXAMPLE
> fd = fopen("/etc/motd", "r")
> fsize(fd)
784
LIMITS
fd must be associaed with an open file
LIBRARY
none
SEE ALSO
errno, fclose, feof, ferror, fflush, fgetc, fgetline, fgets, files, fopen,
fprintf, fputc, fputs, fseek, fsize, ftell, isfile, printf, prompt

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NAME
ftell - return a file position
SYNOPSIS
ftell(fd)
TYPES
fd open file stream
return non-negative integer or error value
DESCRIPTION
This function attempts to return the current value of the file position
indicator for the stream. This is the number of characters (bytes)
between the beginning of the file and the position of the
next character for output in "w" or "w+" mode or for input.
On failure, this returns an error value.
EXAMPLE
> fd = fopen("/tmp/curds", "w")
> fputs(fd, "0123456789")
> ftell(fd)
10
> fputs(fd, "abcdef")
> ftell(fd)
16
> fseek(fd, 20, 0)
> ftell(fd)
20
> fputs(fd, "01234")
> ftell(fd)
25
> freopen(fd, "r")
> fscanf(fd, "%*5c")
0
> ftell(fd)
5
LIMITS
none
LIBRARY
none
SEE ALSO
fseek, fgetpos, fsetpos, rewind, strerror

9
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s/VALUE/int/
s/NUMBER[ ]*\*/int /
s/NUMBER/int/
s/STRINGHEAD/int/
s/\(".*",.*,.*\),.*,.*,.*,.*,/\1, 0, 0, 0, 0,/
/sed me out/d
s/showbuiltins/main/
s/[ ][ ]*$//
p

28
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NAME
gcd - greatest common divisor of a set of rational numbers
SYNOPSIS
gcd(x1, x2, ...)
TYPES
x1, x2, ... rational number
return rational number
DESCRIPTION
If at least one xi is nonzero, gcd(x1, x2, ...) is the
greatest positive number g for which each xi is a multiple of g.
If all xi are zero, the gcd is zero.
EXAMPLE
> print gcd(12, -24, 30), gcd(9/10, 11/5, 4/25), gcd(0,0,0,0,0)
6 .02 0
LIMITS
The number of arguments may not to exceed 100.
LIBRARY
NUMBER *qgcd(NUMBER *x1, NUMBER *x2)
SEE ALSO
lcm

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NAME
gcdrem - result of removing factors of integer common to a specified integer
SYNOPSIS
gcdrem(x, y)
TYPES
x integer
y integer
return non-negative integer
DESCRIPTION
If x and y are not zero, gcdrem(x, y) returns the greatest integer
divisor d of x relatively prime to y, i.e. for which gcd(d,y) = 1.
In particular, gcdrem(x,y) = abs(x) if x and y are relatively
prime.
For all x, gcdrem(x, 0) = 1.
For all nonzero y, gcdrem(0, y) = 0.
PROPERTIES
gcdrem(x,y) = gcd(abs(x), abs(y)).
If x is not zero, gcdrem(x,y) = gcdrem(x, gcd(x,y)) = gcdrem(x, y % x).
For fixed nonzero x, gcdrem(x,y) is periodic with period abs(x).
gcdrem(x,y) = 1 if and only if every prime divisor of x
is a divisor of y.
If x is not zero, gcdrem(x,y) == abs(x) if and only if gcd(x,y) = 1.
If y is not zero and p_1, p_2, ..., p_k are the prime divisors of y,
gcdrem(x,y) = frem(...(frem(frem(x,p_1),p_2)...,p_k)
EXAMPLE
> print gcdrem(6,15), gcdrem(15,6), gcdrem(72,6), gcdrem(6,72)
2 5 1 1
> print gcdrem(630,6), gcdrem(6,630)
35 1
LIMITS
none
LIBRARY
NUMBER *qgcdrem(NUMBER *x, NUMBER *y)
SEE ALSO
gcd, frem, isrel

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help/getenv Normal file
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NAME
getenv - get an environment variable
SYNOPSIS
getenv(env)
TYPES
env str
return str or nil
DESCRIPTION
This function returns the value of the environment variable named by
the string env. If no such environment variable exists, nil is returned.
EXAMPLE
> putenv("name", "value")
0
> getenv("name")
"value"
> putenv("name=val2")
0
> getenv("name")
"val2"
> isnull(getenv("unknown"))
1
LIMITS
none
LIBRARY
none
SEE ALSO
putenv

26
help/hash Normal file
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NAME
hash - hash value
SYNOPSIS
hash(x_1 [, x_2, x_3, ...])
TYPES
x_1, x_1, ... any
return integer v, 0 <= v < 2^32
DESCRIPTION
Returns a hash value for one or more values of arbitrary types.
EXAMPLE
> a = isqrt(2e1000); s = "xyz";
> hash(a,s)
870000771
LIMITS
The number of arguments is not to exceed 100.
LIBRARY
none
SEE ALSO

49
help/head Normal file
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NAME
head - create a list of specified size from the head of a list
SYNOPSIS
head(x, y)
TYPES
x list
y int
return list
DESCRIPTION
If 0 <= y <= size(x), head(x,y) returns a list of size y whose
elements in succession have values x[[0]]. x[[1]], ..., x[[y - 1]].
If y > size(x), head(x,y) is a copy of x.
If -size(x) < y < 0, head(x,y) returns a list of size (size(x) + y)
whose elements in succession have values x[[0]]. x[[1]], ...,
i.e. a copy of x from which the last -y members have been deleted.
If y <= -size(x), head(x,y) returns a list with no members.
For any integer y, x == join(head(x,y), tail(x,-y)).
EXAMPLE
> A = list(2, 3, 5, 7, 11)
> head(A, 2)
list (2 members, 2 nonzero):
[[0]] = 2
[[1]] = 3
> head(A, -2)
list (3 members, 3 nonzero):
[[0]] = 2
[[1]] = 3
[[2]] = 5
LIMITS
none
LIBRARY
none
SEE ALSO
tail, segment

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