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# Copyright (c) 1996 David I. Bell and Landon Curt Noll
# Permission is granted to use, distribute, or modify this source,
# provided that this copyright notice remains intact.
The following calc library files are provided because they serve as
examples of how use the calc language, and because the authors thought
them to be useful!
If you write something that you think is useful, please send it to:
dbell@auug.org.au
chongo@toad.com {uunet,pyramid,sun}!hoptoad!chongo
By convention, a lib file only defines and/or initializes functions,
objects and variables. (The regression test is an exception.) Also by
convention, the a usage message regarding each important object and
function is printed at the time of the read.
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.
By convention, the global variable lib_debug is used to control
the verbosity of debug information printed by lib files. By default,
the lib_debug has a value of 0. If lib_debug < 0, then no debug
messages are printed. If lib_debug >= 0, then only usage message
regarding each important object are printed at the time of the read.
If lib_debug == 0, then only such usage messages are printed; no
other debug information is printed.
To conform to the above convention, your lib files should end with
lines of the form:
global lib_debug;
if (lib_debug >= 0) {
print "funcA(side_a, side_b, side_c) defined";
print "funcB(size, mass) defined";
}
=-=
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.
cryrand.cal
obj cryobj
cryrand(len)
scryrand([seed, [len1, len2]])
scryrand(seed, ip, iq, ir)
random([a, [b]])
srandom(seed)
randstate([cryobj | 0])
cryptographically strong pseudo-romandom number generator
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
factor(iN, ia, B, force)
Attempt to factor using the elliptic functions: y^2 = x^3 + a*x + b.
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 [, rept_loop])
Return the lowest factor of 2^n-1, for n > 0. Starts looking for factors
at 2*start_k*n+1. By default, start_k == 1.
Be default, mfactor() does not report the search progress. When
rept_loop > 0, then a report is given every 4*rept_loop loops.
mod.cal
mod(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.
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.
pollard.cal
factor(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
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.
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.
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.
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.
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.
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.