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calc/lib/README
Landon Curt Noll 9b6c308b42 Release calc version 2.11.0t8.9
2017-05-21 15:38:31 -07:00

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To load a library, try:
read filename
You to not need to add the .cal extension to the filename. Calc
will search along the $CALCPATH (see ``help environment'').
Normally a library will simply define some functions. By default,
most libraries will print out a short message when thei 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' library.
Executing the library 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 library 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-tester@postofc.corp.sgi.com
By convention, a lib 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 lib file needs to load another lib file, it should use the -once
version of read:
/* pull in needed library files */
read -once "surd"
read -once "lucas"
This will cause the needed library files to be read once. If these
files have already been read, the read -once will act as a noop.
The "lib_debug" parameter is intended for controlling the possible
display of special information relating to functions, objects, and
other structures created by instructions in calc scripts.
Zero value of config("lib_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("lib_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.
The value for config("lib_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("lib_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("lib_debug") has
either of the bottom 2 bits set:
if (config("lib_debug") & 3) {
print "obj xyz defined";
print "funcA([val1 [, val2]]) defined";
print "funcB(size, mass, ...) defined";
}
=-=
The following is a brief description of some of the calc library files
that are shipped with calc. See above for example of how to read in
and execute these files.
beer.cal
Calc's contribution to the 99 Bottles of Beer web page:
http://www.ionet.net/~timtroyr/funhouse/beer.html#calc
bernoulli.cal
B(n)
Calculate the nth Bernoulli number.
bigprime.cal
bigprime(a, m, p)
A prime test, base a, on p*2^x+1 for even x>m.
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.
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
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 pells equation for a particular D.
pi.cal
qpi(epsilon)
Calculate pi within the specified epsilon using the quartic convergence
iteration.
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 library 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, quaternians 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 kength 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 kength 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.
regress.cal
Test the correct execution of the calculator by reading this library file.
Errors are reported with '****' mssages, or worse. :-)
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.
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.
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 script 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 script 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 script 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 script 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 script 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 script 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 script 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 script is used by regress.cal to test ptest, nextcand and
prevcand buildins.
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 script 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 script is used by regress.cal to test searching in files.
test5100.cal
global a5100
global b5100
test5100(x) defined
This script 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 script is used by regress.cal to test the fix of a global/static bug.
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) 1999 David I. Bell and Landon Curt Noll
# Permission is granted to use, distribute, or modify this source,
# provided that this copyright notice remains intact.
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