4.4BSD/usr/src/contrib/calc-1.26.4/lib/README

# Copyright (c) 1993 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:

    chongo@toad.com                 {uunet,pyramid,sun}!hoptoad!chongo
    (David I. Bell does not currently have an email address)

By convention, a lib file just defines functions, objects and variales.
(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.  This message printing may be disabled by assigning
the global value  lib_debug  to a numeric value > 0.


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

    shufrand()
    sshufrand(seed)
    rand([a, [b]])
    srand(seed)
    cryrand([a, [b]])
    scryrand([seed, [len1, len2]])
    random([a, [b]])
    srandom(seed)
    obj cryobj
    randstate([cryobj | 0])
    nxtprime(n, [val, modulus])

    Cryptographically strong pseudo-random number generator library.
    

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.


lucas_tbl.cal

    Lucasian criteria for primality tables.


mersenne.cal

    mersenne(p)

    Perform a primality test of 2^p-1, for prime p>1.


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.


nextprim.cal

    nextprime(n, tries)

    Function to find the next prime (probably).


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	

    pol()
    poly_print(a)
    poly_add(a, b)
    poly_neg(a)
    poly_sub(a, b)
    poly_mul(a, b)
    poly_div(a, b)
    ev(a, x)

    Calculate with polynomials of one variable


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.


regress.cal	

    Test the correct execution of the calculator by reading this library file.
    Errors are reported with '****' mssages, or worse.  :-)


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).


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.