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calc/cal/README
2017-05-21 15:38:57 -07:00

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Calc standard resource files
----------------------------
To load a resource file, try:
read filename
You do not need to add the .cal extension to the filename. Calc
will search along the $CALCPATH (see ``help environment'').
Normally a resource file will simply define some functions. By default,
most resource files will print out a short message when they are read.
For example:
; read lucas
lucas(h,n) defined
gen_u0(h,n,v1) defined
gen_v1(h,n) defined
ldebug(funct,str) defined
will cause calc to load and execute the 'lucas.cal' resource file.
Executing the resource file will cause several functions to be defined.
Executing the lucas function:
; lucas(149,60)
1
; lucas(146,61)
0
shows that 149*2^60-1 is prime whereas 146*2^61-1 is not.
=-=
Calc resource file files are provided because they serve as examples of
how use the calc language, and/or because the authors thought them to
be useful!
If you write something that you think is useful, please send it to:
calc-contrib at asthe dot com
[[ NOTE: Replace 'at' with @, 'dot' is with . and remove the spaces ]]
[[ NOTE: The EMail address uses 'asthe' and the web site URL uses 'isthe' ]]
By convention, a resource file only defines and/or initializes functions,
objects and variables. (The regress.cal and testxxx.cal regression test
suite is an exception.) Also by convention, an additional usage message
regarding important object and functions is printed.
If a resource file needs to load another resource file, it should use
the -once version of read:
/* pull in needed resource files */
read -once "surd"
read -once "lucas"
This will cause the needed resource files to be read once. If these
files have already been read, the read -once will act as a noop.
The "resource_debug" parameter is intended for controlling the possible
display of special information relating to functions, objects, and
other structures created by instructions in calc resource files.
Zero value of config("resource_debug") means that no such information
is displayed. For other values, the non-zero bits which currently
have meanings are as follows:
n Meaning of bit n of config("resource_debug")
0 When a function is defined, redefined or undefined at
interactive level, a message saying what has been done
is displayed.
1 When a function is defined, redefined or undefined during
the reading of a file, a message saying what has been done
is displayed.
2 Show func will display more information about a functions
arguments as well as more argument summary information.
3 During execution, allow calc standard resource files
to output additional debugging information.
The value for config("resource_debug") in both oldstd and newstd is 3,
but if calc is invoked with the -d flag, its initial value is zero.
Thus, if calc is started without the -d flag, until config("resource_debug")
is changed, a message will be output when a function is defined
either interactively or during the reading of a file.
Sometimes the information printed is not enough. In addition to the
standard information, one might want to print:
* useful obj definitions
* functions with optional args
* functions with optional args where the param() interface is used
For these cases we suggest that you place at the bottom of your code
something that prints extra information if config("resource_debug") has
either of the bottom 2 bits set:
if (config("resource_debug") & 3) {
print "obj xyz defined";
print "funcA([val1 [, val2]]) defined";
print "funcB(size, mass, ...) defined";
}
If your the resource file needs to output special debugging information,
we recommend that you check for bit 3 of the config("resource_debug")
before printing the debug statement:
if (config("resource_debug") & 8) {
print "DEBUG: This a sample debug statement";
}
=-=
The following is a brief description of some of the calc resource files
that are shipped with calc. See above for example of how to read in
and execute these files.
alg_config.cal
global test_time
mul_loop(repeat,x) defined
mul_ratio(len) defined
best_mul2() defined
sq_loop(repeat,x) defined
sq_ratio(len) defined
best_sq2() defined
pow_loop(repeat,x,ex) defined
pow_ratio(len) defined
best_pow2() defined
These functions search for an optimal value of config("mul2"),
config("sq2"), and config("pow2"). The calc default values of these
configuration values were set by running this resource file on a
1.8GHz AMD 32-bit CPU of ~3406 BogoMIPS.
The best_mul2() function returns the optimal value of config("mul2").
The best_sq2() function returns the optimal value of config("sq2").
The best_pow2() function returns the optimal value of config("pow2").
The other functions are just support functions.
By design, best_mul2(), best_sq2(), and best_pow2() take a few
minutes to run. These functions increase the number of times a
given computational loop is executed until a minimum amount of CPU
time is consumed. To watch these functions progress, one can set
the config("user_debug") value.
Here is a suggested way to use this resource file:
; read alg_config
; config("user_debug",2),;
; best_mul2(); best_sq2(); best_pow2();
; best_mul2(); best_sq2(); best_pow2();
; best_mul2(); best_sq2(); best_pow2();
NOTE: It is perfectly normal for the optimal value returned to differ
slightly from run to run. Slight variations due to inaccuracy in
CPU timings will cause the best value returned to differ slightly
from run to run.
One can use a calc startup file to change the initial values of
config("mul2"), config("sq2"), and config("pow2"). For example one
can place into ~/.calcrc these lines:
config("mul2", 1780),;
config("sq2", 3388),;
config("pow2", 176),;
to automatically and silently change these config values.
See help/config and CALCRC in help/environment for more information.
beer.cal
Calc's contribution to the 99 Bottles of Beer web page:
http://www.ionet.net/~timtroyr/funhouse/beer.html#calc
NOTE: This resource produces a lot of output. :-)
bernoulli.cal
B(n)
Calculate the nth Bernoulli number.
NOTE: There is now a bernoulli() builtin function. This file is
left here for backward compatibility and now simply returns
the builtin function.
bigprime.cal
bigprime(a, m, p)
A prime test, base a, on p*2^x+1 for even x>m.
chi.cal
Z(x[, eps])
P(x[, eps])
chi_prob(chi_sq, v[, eps])
Computes the Probability, given the Null Hypothesis, that a given
Chi squared values >= chi_sq with v degrees of freedom.
The chi_prob() function does not work well with odd degrees of freedom.
It is reasonable with even degrees of freedom, although one must give
a sufficiently small error term as the degrees gets large (>100).
The Z(x) and P(x) are internal statistical functions.
eps is an optional epsilon() like error term.
chrem.cal
chrem(r1,m1 [,r2,m2, ...])
chrem(rlist, mlist)
Chinese remainder theorem/problem solver.
deg.cal
dms(deg, min, sec)
dms_add(a, b)
dms_neg(a)
dms_sub(a, b)
dms_mul(a, b)
dms_print(a)
Calculate in degrees, minutes, and seconds.
dotest.cal
dotest(dotest_file [,dotest_code [,dotest_maxcond]])
dotest_file
Search along CALCPATH for dotest_file, which contains lines that
should evaluate to 1. Comment lines and empty lines are ignored.
Comment lines should use ## instead of the multi like /* ... */
because lines are evaluated one line at a time.
dotest_code
Assign the code number that is to be printed at the start of
each non-error line and after **** in each error line.
The default code number is 999.
dotest_maxcond
The maximum number of error conditions that may be detected.
An error condition is not a sign of a problem, in some cases
a line deliberately forces an error condition. A value of -1,
the default, implies a maximum of 2147483647.
Global variables and functions must be declared ahead of time because
the dotest scope of evaluation is a line at a time. For example:
read dotest.cal
read set8700.cal
dotest("set8700.line");
ellip.cal
efactor(iN, ia, B, force)
Attempt to factor using the elliptic functions: y^2 = x^3 + a*x + b.
hello.cal
Calc's contribution to the Hello World! page:
http://www.latech.edu/~acm/HelloWorld.shtml
http://www.latech.edu/~acm/helloworld/calc.html
NOTE: This resource produces a lot of output. :-)
intfile.cal
file2be(filename)
Read filename and return an integer that is built from the
octets in that file in Big Endian order. The first octets
of the file become the most significant bits of the integer.
file2le(filename)
Read filename and return an integer that is built from the
octets in that file in Little Endian order. The first octets
of the file become the most significant bits of the integer.
be2file(v, filename)
Write the absolute value of v into filename in Big Endian order.
The v argument must be on integer. The most significant bits
of the integer become the first octets of the file.
le2file(v, filename)
Write the absolute value of v into filename in Little Endian order.
The v argument must be on integer. The least significant bits
of the integer become the last octets of the file.
linear.cal
linear(x0, y0, x1, y1, x)
Returns the value y such that (x,y) in on the line (x0,y0), (x1,y1).
Requires x0 != y0.
lucas.cal
lucas(h, n)
Perform a primality test of h*2^n-1, with 1<=h<2*n.
lucas_chk.cal
lucas_chk(high_n)
Test all primes of the form h*2^n-1, with 1<=h<200 and n <= high_n.
Requires lucas.cal to be loaded. The highest useful high_n is 1000.
Used by regress.cal during the 2100 test set.
lucas_tbl.cal
Lucasian criteria for primality tables.
mersenne.cal
mersenne(p)
Perform a primality test of 2^p-1, for prime p>1.
mfactor.cal
mfactor(n [, start_k=1 [, rept_loop=10000 [, p_elim=17]]])
Return the lowest factor of 2^n-1, for n > 0. Starts looking for factors
at 2*start_k*n+1. Skips values that are multiples of primes <= p_elim.
By default, start_k == 1, rept_loop = 10000 and p_elim = 17.
The p_elim == 17 overhead takes ~3 minutes on an 200 Mhz r4k CPU and
requires about ~13 Megs of memory. The p_elim == 13 overhead
takes about 3 seconds and requires ~1.5 Megs of memory.
The value p_elim == 17 is best for long factorizations. It is the
fastest even thought the initial startup overhead is larger than
for p_elim == 13.
mod.cal
lmod(a)
mod_print(a)
mod_one()
mod_cmp(a, b)
mod_rel(a, b)
mod_add(a, b)
mod_sub(a, b)
mod_neg(a)
mod_mul(a, b)
mod_square(a)
mod_inc(a)
mod_dec(a)
mod_inv(a)
mod_div(a, b)
mod_pow(a, b)
Routines to handle numbers modulo a specified number.
natnumset.cal
isset(a)
setbound(n)
empty()
full()
isin(a, b)
addmember(a, n)
rmmember(a, n)
set()
mkset(s)
primes(a, b)
set_max(a)
set_min(a)
set_not(a)
set_cmp(a, b)
set_rel(a, b)
set_or(a, b)
set_and(a, b)
set_comp(a)
set_setminus(a, b)
set_diff(a,b)
set_content(a)
set_add(a, b)
set_sub(a, b)
set_mul(a, b)
set_square(a)
set_pow(a, n)
set_sum(a)
set_plus(a)
interval(a, b)
isinterval(a)
set_mod(a, b)
randset(n, a, b)
polyvals(L, A)
polyvals2(L, A, B)
set_print(a)
Demonstration of how the string operators and functions may be used
for defining and working with sets of natural numbers not exceeding a
user-specified bound.
pell.cal
pellx(D)
pell(D)
Solve Pell's equation; Returns the solution X to: X^2 - D * Y^2 = 1.
Type the solution to Pell's equation for a particular D.
pi.cal
qpi(epsilon)
piforever()
The qpi() calculate pi within the specified epsilon using the quartic
convergence iteration.
The piforever() prints digits of pi, nicely formatted, for as long
as your free memory space and system up time allows.
The piforever() function (written by Klaus Alexander Seistrup
<klaus@seistrup.dk>) was inspired by an algorithm conceived by
Lambert Meertens. See also the ABC Programmer's Handbook, by Geurts,
Meertens & Pemberton, published by Prentice-Hall (UK) Ltd., 1990.
pix.cal
pi_of_x(x)
Calculate the number of primes < x using A(n+1)=A(n-1)+A(n-2). This
is a SLOW painful method ... the builtin pix(x) is much faster.
Still, this method is interesting.
pollard.cal
pfactor(N, N, ai, af)
Factor using Pollard's p-1 method.
poly.cal
Calculate with polynomials of one variable. There are many functions.
Read the documentation in the resource file.
prompt.cal
adder()
showvalues(str)
Demonstration of some uses of prompt() and eval().
psqrt.cal
psqrt(u, p)
Calculate square roots modulo a prime
qtime.cal
qtime(utc_hr_offset)
Print the time as English sentence given the hours offset from UTC.
quat.cal
quat(a, b, c, d)
quat_print(a)
quat_norm(a)
quat_abs(a, e)
quat_conj(a)
quat_add(a, b)
quat_sub(a, b)
quat_inc(a)
quat_dec(a)
quat_neg(a)
quat_mul(a, b)
quat_div(a, b)
quat_inv(a)
quat_scale(a, b)
quat_shift(a, b)
Calculate using quaternions of the form: a + bi + cj + dk. In these
functions, quaternions are manipulated in the form: s + v, where
s is a scalar and v is a vector of size 3.
randbitrun.cal
randbitrun([run_cnt])
Using randbit(1) to generate a sequence of random bits, determine if
the number and length of identical bits runs match what is expected.
By default, run_cnt is to test the next 65536 random values.
This tests the a55 generator.
randmprime.cal
randmprime(bits, seed [,dbg])
Find a prime of the form h*2^n-1 >= 2^bits for some given x. The initial
search points for 'h' and 'n' are selected by a cryptographic pseudo-random
number generator. The optional argument, dbg, if set to 1, 2 or 3
turn on various debugging print statements.
randombitrun.cal
randombitrun([run_cnt])
Using randombit(1) to generate a sequence of random bits, determine if
the number and length of identical bits runs match what is expected.
By default, run_cnt is to test the next 65536 random values.
This tests the Blum-Blum-Shub generator.
randomrun.cal
randomrun([run_cnt])
Perform the "G. Run test" (pp. 65-68) as found in Knuth's "Art of
Computer Programming - 2nd edition", Volume 2, Section 3.3.2 on
the builtin rand() function. This function will generate run_cnt
64 bit values. By default, run_cnt is to test the next 65536
random values.
This tests the Blum-Blum-Shub generator.
randrun.cal
randrun([run_cnt])
Perform the "G. Run test" (pp. 65-68) as found in Knuth's "Art of
Computer Programming - 2nd edition", Volume 2, Section 3.3.2 on
the builtin rand() function. This function will generate run_cnt
64 bit values. By default, run_cnt is to test the next 65536
random values.
This tests the a55 generator.
repeat.cal
repeat(digit_set, repeat_count)
Return the value of the digit_set repeated repeat_count times.
Both digit_set and repeat_count must be integers > 0.
For example repeat(423,5) returns the value 423423423423423,
which is the digit_set 423 repeated 5 times.
regress.cal
Test the correct execution of the calculator by reading this resource file.
Errors are reported with '****' messages, or worse. :-)
screen.cal
up
CUU /* same as up */
down = CUD
CUD /* same as down */
forward
CUF /* same as forward */
back = CUB
CUB /* same as back */
save
SCP /* same as save */
restore
RCP /* same as restore */
cls
home
eraseline
off
bold
faint
italic
blink
rapidblink
reverse
concealed
/* Lowercase indicates foreground, uppercase background */
black
red
green
yellow
blue
magenta
cyan
white
Black
Red
Green
Yellow
Blue
Magenta
Cyan
White
Define ANSI control sequences providing (i.e., cursor movement, changing
foreground or background color, etc.) for VT100 terminals and terminal
window emulators (i.e., xterm, Apple OS/X Terminal, etc.) that support them.
For example:
read screen
print green:"This is green. ":red:"This is red.":black
seedrandom.cal
seedrandom(seed1, seed2, bitsize [,trials])
Given:
seed1 - a large random value (at least 10^20 and perhaps < 10^93)
seed2 - a large random value (at least 10^20 and perhaps < 10^93)
size - min Blum modulus as a power of 2 (at least 100, perhaps > 1024)
trials - number of ptest() trials (default 25) (optional arg)
Returns:
the previous random state
Seed the cryptographically strong Blum generator. This functions allows
one to use the raw srandom() without the burden of finding appropriate
Blum primes for the modulus.
set8700.cal
set8700_getA1() defined
set8700_getA2() defined
set8700_getvar() defined
set8700_f(set8700_x) defined
set8700_g(set8700_x) defined
Declare globals and define functions needed by dotest() (see
dotest.cal) to evaluate set8700.line a line at a time.
set8700.line
A line-by-line evaluation file for dotest() (see dotest.cal).
The set8700.cal file (and dotest.cal) should be read first.
solve.cal
solve(low, high, epsilon)
Solve the equation f(x) = 0 to within the desired error value for x.
The function 'f' must be defined outside of this routine, and the low
and high values are guesses which must produce values with opposite signs.
sumsq.cal
ss(p)
Determine the unique two positive integers whose squares sum to the
specified prime. This is always possible for all primes of the form
4N+1, and always impossible for primes of the form 4N-1.
sumtimes.cal
timematsum(N)
timelistsum(N)
timematsort(N)
timelistsort(N)
timematreverse(N)
timelistreverse(N)
timematssq(N)
timelistssq(N)
timehmean(N,M)
doalltimes(N)
Give the user CPU time for various ways of evaluating sums, sums of
squares, etc, for large lists and matrices. N is the size of
the list or matrix to use. The doalltimes() function will run
all fo the sumtimes tests. For example:
doalltimes(1e6);
surd.cal
surd(a, b)
surd_print(a)
surd_conj(a)
surd_norm(a)
surd_value(a, xepsilon)
surd_add(a, b)
surd_sub(a, b)
surd_inc(a)
surd_dec(a)
surd_neg(a)
surd_mul(a, b)
surd_square(a)
surd_scale(a, b)
surd_shift(a, b)
surd_div(a, b)
surd_inv(a)
surd_sgn(a)
surd_cmp(a, b)
surd_rel(a, b)
Calculate using quadratic surds of the form: a + b * sqrt(D).
test1700.cal
value
This resource files is used by regress.cal to test the read and use keywords.
test2600.cal
global defaultverbose
global err
testismult(str, n, verbose)
testsqrt(str, n, eps, verbose)
testexp(str, n, eps, verbose)
testln(str, n, eps, verbose)
testpower(str, n, b, eps, verbose)
testgcd(str, n, verbose)
cpow(x, n, eps)
cexp(x, eps)
cln(x, eps)
mkreal()
mkcomplex()
mkbigreal()
mksmallreal()
testappr(str, n, verbose)
checkappr(x, y, z, verbose)
checkresult(x, y, z, a)
test2600(verbose, tnum)
This resource files is used by regress.cal to test some of builtin functions
in terms of accuracy and roundoff.
test2700.cal
global defaultverbose
mknonnegreal()
mkposreal()
mkreal_2700()
mknonzeroreal()
mkposfrac()
mkfrac()
mksquarereal()
mknonsquarereal()
mkcomplex_2700()
testcsqrt(str, n, verbose)
checksqrt(x, y, z, v)
checkavrem(A, B, X, eps)
checkrounding(s, n, t, u, z)
iscomsq(x)
test2700(verbose, tnum)
This resource files is used by regress.cal to test sqrt() for real and
complex values.
test3100.cal
obj res
global md
res_test(a)
res_sub(a, b)
res_mul(a, b)
res_neg(a)
res_inv(a)
res(x)
This resource file is used by regress.cal to test determinants of a matrix
test3300.cal
global defaultverbose
global err
testi(str, n, N, verbose)
testr(str, n, N, verbose)
test3300(verbose, tnum)
This resource file is used by regress.cal to provide for more determinant
tests.
test3400.cal
global defaultverbose
global err
test1(str, n, eps, verbose)
test2(str, n, eps, verbose)
test3(str, n, eps, verbose)
test4(str, n, eps, verbose)
test5(str, n, eps, verbose)
test6(str, n, eps, verbose)
test3400(verbose, tnum)
This resource file is used by regress.cal to test trig functions.
containing objects.
test3500.cal
global defaultverbose
global err
testfrem(x, y, verbose)
testgcdrem(x, y, verbose)
testf(str, n, verbose)
testg(str, n, verbose)
testh(str, n, N, verbose)
test3500(verbose, n, N)
This resource file is used by regress.cal to test the functions frem,
fcnt, gcdrem.
test4000.cal
global defaultverbose
global err
global BASEB
global BASE
global COUNT
global SKIP
global RESIDUE
global MODULUS
global K1
global H1
global K2
global H2
global K3
global H3
plen(N) defined
rlen(N) defined
clen(N) defined
ptimes(str, N, n, count, skip, verbose) defined
ctimes(str, N, n, count, skip, verbose) defined
crtimes(str, a, b, n, count, skip, verbose) defined
ntimes(str, N, n, count, skip, residue, mod, verbose) defined
testnextcand(str, N, n, cnt, skip, res, mod, verbose) defined
testnext1(x, y, count, skip, residue, modulus) defined
testprevcand(str, N, n, cnt, skip, res, mod, verbose) defined
testprev1(x, y, count, skip, residue, modulus) defined
test4000(verbose, tnum) defined
This resource file is used by regress.cal to test ptest, nextcand and
prevcand builtins.
test4100.cal
global defaultverbose
global err
global K1
global K2
global BASEB
global BASE
rlen_4100(N) defined
olen(N) defined
test1(x, y, m, k, z1, z2) defined
testall(str, n, N, M, verbose) defined
times(str, N, n, verbose) defined
powtimes(str, N1, N2, n, verbose) defined
inittimes(str, N, n, verbose) defined
test4100(verbose, tnum) defined
This resource file is used by regress.cal to test REDC operations.
test4600.cal
stest(str [, verbose]) defined
ttest([m, [n [,verbose]]]) defined
sprint(x) defined
findline(f,s) defined
findlineold(f,s) defined
test4600(verbose, tnum) defined
This resource file is used by regress.cal to test searching in files.
test5100.cal
global a5100
global b5100
test5100(x) defined
This resource file is used by regress.cal to test the new code generator
declaration scope and order.
test5200.cal
global a5200
static a5200
f5200(x) defined
g5200(x) defined
h5200(x) defined
This resource file is used by regress.cal to test the fix of a
global/static bug.
test8400.cal
test8400() defined
This resource file is used by regress.cal to check for quit-based
memory leaks.
test8500.cal
global err_8500
global L_8500
global ver_8500
global old_seed_8500
global cfg_8500
onetest_8500(a,b,rnd) defined
divmod_8500(N, M1, M2, testnum) defined
This resource file is used by regress.cal to the // and % operators.
test8600.cal
global min_8600
global max_8600
global hash_8600
global hmean_8600
This resource file is used by regress.cal to test a change of
allowing up to 1024 args to be passed to a builtin function.
unitfrac.cal
unitfrac(x)
Represent a fraction as sum of distinct unit fractions.
varargs.cal
sc(a, b, ...)
Example program to use 'varargs'. Program to sum the cubes of all
the specified numbers.
xx_print.cal
is_octet(a) defined
list_print(a) defined
mat_print (a) defined
octet_print(a) defined
blk_print(a) defined
nblk_print (a) defined
strchar(a) defined
file_print(a) defined
error_print(a) defined
Demo for the xx_print object routines.
## Copyright (C) 2000 David I. Bell and Landon Curt Noll
##
## Primary author: Landon Curt Noll
##
## Calc is open software; you can redistribute it and/or modify it under
## the terms of the version 2.1 of the GNU Lesser General Public License
## as published by the Free Software Foundation.
##
## Calc is distributed in the hope that it will be useful, but WITHOUT
## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
## or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General
## Public License for more details.
##
## A copy of version 2.1 of the GNU Lesser General Public License is
## distributed with calc under the filename COPYING-LGPL. You should have
## received a copy with calc; if not, write to Free Software Foundation, Inc.
## 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
##
## @(#) $Revision: 30.1 $
## @(#) $Id: README,v 30.1 2007/03/16 11:09:54 chongo Exp $
## @(#) $Source: /usr/local/src/cmd/calc/cal/RCS/README,v $
##
## Under source code control: 1990/02/15 01:50:32
## File existed as early as: before 1990
##
## chongo <was here> /\oo/\ http://www.isthe.com/chongo/
## Share and enjoy! :-) http://www.isthe.com/chongo/tech/comp/calc/