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https://github.com/lcn2/calc.git
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Release calc version 2.10.2t30
This commit is contained in:
Landon Curt Noll
489
lib/README
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489
lib/README
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# Copyright (c) 1996 David I. Bell and Landon Curt Noll
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# Permission is granted to use, distribute, or modify this source,
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# provided that this copyright notice remains intact.
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The following calc library files are provided because they serve as
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examples of how use the calc language, and because the authors thought
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them to be useful!
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If you write something that you think is useful, please send it to:
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dbell@auug.org.au
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chongo@toad.com {uunet,pyramid,sun}!hoptoad!chongo
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By convention, a lib file only defines and/or initializes functions,
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objects and variables. (The regression test is an exception.) Also by
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convention, the a usage message regarding each important object and
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function is printed at the time of the read.
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If a lib file needs to load another lib file, it should use the -once
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version of read:
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/* pull in needed library files */
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read -once "surd"
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read -once "lucas"
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This will cause the needed library files to be read once. If these
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files have already been read, the read -once will act as a noop.
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By convention, the global variable lib_debug is used to control
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the verbosity of debug information printed by lib files. By default,
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the lib_debug has a value of 0. If lib_debug < 0, then no debug
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messages are printed. If lib_debug >= 0, then only usage message
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regarding each important object are printed at the time of the read.
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If lib_debug == 0, then only such usage messages are printed; no
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other debug information is printed.
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To conform to the above convention, your lib files should end with
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lines of the form:
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global lib_debug;
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if (lib_debug >= 0) {
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print "funcA(side_a, side_b, side_c) defined";
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print "funcB(size, mass) defined";
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}
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=-=
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bernoulli.cal
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B(n)
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Calculate the nth Bernoulli number.
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bigprime.cal
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bigprime(a, m, p)
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A prime test, base a, on p*2^x+1 for even x>m.
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chrem.cal
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chrem(r1,m1 [,r2,m2, ...])
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chrem(rlist, mlist)
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Chinese remainder theorem/problem solver.
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cryrand.cal
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obj cryobj
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cryrand(len)
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scryrand([seed, [len1, len2]])
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scryrand(seed, ip, iq, ir)
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random([a, [b]])
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srandom(seed)
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randstate([cryobj | 0])
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cryptographically strong pseudo-romandom number generator
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deg.cal
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dms(deg, min, sec)
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dms_add(a, b)
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dms_neg(a)
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dms_sub(a, b)
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dms_mul(a, b)
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dms_print(a)
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Calculate in degrees, minutes, and seconds.
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ellip.cal
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factor(iN, ia, B, force)
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Attempt to factor using the elliptic functions: y^2 = x^3 + a*x + b.
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lucas.cal
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lucas(h, n)
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Perform a primality test of h*2^n-1, with 1<=h<2*n.
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lucas_chk.cal
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lucas_chk(high_n)
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Test all primes of the form h*2^n-1, with 1<=h<200 and n <= high_n.
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Requires lucas.cal to be loaded. The highest useful high_n is 1000.
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Used by regress.cal during the 2100 test set.
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lucas_tbl.cal
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Lucasian criteria for primality tables.
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mersenne.cal
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mersenne(p)
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Perform a primality test of 2^p-1, for prime p>1.
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mfactor.cal
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mfactor(n [, start_k [, rept_loop])
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Return the lowest factor of 2^n-1, for n > 0. Starts looking for factors
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at 2*start_k*n+1. By default, start_k == 1.
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Be default, mfactor() does not report the search progress. When
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rept_loop > 0, then a report is given every 4*rept_loop loops.
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mod.cal
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mod(a)
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mod_print(a)
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mod_one()
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mod_cmp(a, b)
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mod_rel(a, b)
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mod_add(a, b)
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mod_sub(a, b)
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mod_neg(a)
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mod_mul(a, b)
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mod_square(a)
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mod_inc(a)
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mod_dec(a)
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mod_inv(a)
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mod_div(a, b)
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mod_pow(a, b)
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Routines to handle numbers modulo a specified number.
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pell.cal
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pellx(D)
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pell(D)
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Solve Pell's equation; Returns the solution X to: X^2 - D * Y^2 = 1.
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Type the solution to pells equation for a particular D.
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pi.cal
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qpi(epsilon)
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Calculate pi within the specified epsilon using the quartic convergence
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iteration.
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pollard.cal
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factor(N, N, ai, af)
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Factor using Pollard's p-1 method.
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poly.cal
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Calculate with polynomials of one variable. There are many functions.
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Read the documentation in the library file.
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prompt.cal
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adder()
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showvalues(str)
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Demonstration of some uses of prompt() and eval().
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psqrt.cal
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psqrt(u, p)
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Calculate square roots modulo a prime
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quat.cal
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quat(a, b, c, d)
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quat_print(a)
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quat_norm(a)
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quat_abs(a, e)
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quat_conj(a)
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quat_add(a, b)
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quat_sub(a, b)
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quat_inc(a)
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quat_dec(a)
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quat_neg(a)
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quat_mul(a, b)
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quat_div(a, b)
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quat_inv(a)
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quat_scale(a, b)
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quat_shift(a, b)
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Calculate using quaternions of the form: a + bi + cj + dk. In these
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functions, quaternians are manipulated in the form: s + v, where
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s is a scalar and v is a vector of size 3.
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randbitrun.cal
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randbitrun([run_cnt])
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Using randbit(1) to generate a sequence of random bits, determine if
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the number and kength of identical bits runs match what is expected.
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By default, run_cnt is to test the next 65536 random values.
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randmprime.cal
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randmprime(bits, seed [,dbg])
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Find a prime of the form h*2^n-1 >= 2^bits for some given x. The initial
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search points for 'h' and 'n' are selected by a cryptographic pseudo-random
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number generator. The optional argument, dbg, if set to 1, 2 or 3
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turn on various debugging print statements.
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randrun.cal
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randrun([run_cnt])
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Perform the "G. Run test" (pp. 65-68) as found in Knuth's "Art of
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Computer Programming - 2nd edition", Volume 2, Section 3.3.2 on
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the builtin rand() function. This function will generate run_cnt
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64 bit values. By default, run_cnt is to test the next 65536
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random values.
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regress.cal
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Test the correct execution of the calculator by reading this library file.
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Errors are reported with '****' mssages, or worse. :-)
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seedrandom.cal
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seedrandom(seed1, seed2, bitsize [,trials])
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Given:
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seed1 - a large random value (at least 10^20 and perhaps < 10^93)
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seed2 - a large random value (at least 10^20 and perhaps < 10^93)
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size - min Blum modulus as a power of 2 (at least 100, perhaps > 1024)
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trials - number of ptest() trials (default 25) (optional arg)
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Returns:
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the previous random state
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Seed the cryptographically strong Blum generator. This functions allows
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one to use the raw srandom() without the burden of finding appropriate
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Blum primes for the modulus.
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solve.cal
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solve(low, high, epsilon)
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Solve the equation f(x) = 0 to within the desired error value for x.
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The function 'f' must be defined outside of this routine, and the low
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and high values are guesses which must produce values with opposite signs.
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sumsq.cal
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ss(p)
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Determine the unique two positive integers whose squares sum to the
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specified prime. This is always possible for all primes of the form
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4N+1, and always impossible for primes of the form 4N-1.
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surd.cal
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surd(a, b)
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surd_print(a)
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surd_conj(a)
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surd_norm(a)
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surd_value(a, xepsilon)
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surd_add(a, b)
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surd_sub(a, b)
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surd_inc(a)
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surd_dec(a)
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surd_neg(a)
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surd_mul(a, b)
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surd_square(a)
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surd_scale(a, b)
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surd_shift(a, b)
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surd_div(a, b)
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surd_inv(a)
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surd_sgn(a)
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surd_cmp(a, b)
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surd_rel(a, b)
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Calculate using quadratic surds of the form: a + b * sqrt(D).
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test1700.cal
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value
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This script is used by regress.cal to test the read and use keywords.
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test2600.cal
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global defaultverbose
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global err
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testismult(str, n, verbose)
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testsqrt(str, n, eps, verbose)
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testexp(str, n, eps, verbose)
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testln(str, n, eps, verbose)
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testpower(str, n, b, eps, verbose)
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testgcd(str, n, verbose)
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cpow(x, n, eps)
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cexp(x, eps)
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cln(x, eps)
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mkreal()
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mkcomplex()
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mkbigreal()
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mksmallreal()
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testappr(str, n, verbose)
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checkappr(x, y, z, verbose)
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checkresult(x, y, z, a)
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test2600(verbose, tnum)
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This script is used by regress.cal to test some of builtin functions
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in terms of accuracy and roundoff.
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test2700.cal
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global defaultverbose
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mknonnegreal()
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mkposreal()
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mkreal_2700()
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mknonzeroreal()
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mkposfrac()
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mkfrac()
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mksquarereal()
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mknonsquarereal()
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mkcomplex_2700()
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testcsqrt(str, n, verbose)
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checksqrt(x, y, z, v)
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checkavrem(A, B, X, eps)
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checkrounding(s, n, t, u, z)
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iscomsq(x)
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test2700(verbose, tnum)
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This script is used by regress.cal to test sqrt() for real and complex
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values.
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test3100.cal
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obj res
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global md
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res_test(a)
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res_sub(a, b)
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res_mul(a, b)
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res_neg(a)
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res_inv(a)
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res(x)
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This script is used by regress.cal to test determinants of a matrix
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test3300.cal
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global defaultverbose
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global err
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testi(str, n, N, verbose)
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testr(str, n, N, verbose)
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test3300(verbose, tnum)
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This script is used by regress.cal to provide for more determinant tests.
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test3400.cal
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global defaultverbose
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global err
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test1(str, n, eps, verbose)
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test2(str, n, eps, verbose)
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test3(str, n, eps, verbose)
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test4(str, n, eps, verbose)
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test5(str, n, eps, verbose)
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test6(str, n, eps, verbose)
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test3400(verbose, tnum)
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This script is used by regress.cal to test trig functions.
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containing objects.
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test4000.cal
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global defaultverbose
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global err
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global BASEB
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global BASE
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global COUNT
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global SKIP
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global RESIDUE
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global MODULUS
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global K1
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global H1
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global K2
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global H2
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global K3
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global H3
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plen(N) defined
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rlen(N) defined
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clen(N) defined
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ptimes(str, N, n, count, skip, verbose) defined
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ctimes(str, N, n, count, skip, verbose) defined
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crtimes(str, a, b, n, count, skip, verbose) defined
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ntimes(str, N, n, count, skip, residue, mod, verbose) defined
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testnextcand(str, N, n, cnt, skip, res, mod, verbose) defined
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testnext1(x, y, count, skip, residue, modulus) defined
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testprevcand(str, N, n, cnt, skip, res, mod, verbose) defined
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testprev1(x, y, count, skip, residue, modulus) defined
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test4000(verbose, tnum) defined
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This script is used by regress.cal to test ptest, nextcand and
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prevcand buildins.
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test4100.cal
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global defaultverbose
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global err
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global K1
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global K2
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global BASEB
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global BASE
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rlen_4100(N) defined
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olen(N) defined
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test1(x, y, m, k, z1, z2) defined
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testall(str, n, N, M, verbose) defined
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times(str, N, n, verbose) defined
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powtimes(str, N1, N2, n, verbose) defined
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inittimes(str, N, n, verbose) defined
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test4100(verbose, tnum) defined
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This script is used by regress.cal to test REDC operations.
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unitfrac.cal
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unitfrac(x)
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Represent a fraction as sum of distinct unit fractions.
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varargs.cal
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sc(a, b, ...)
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Example program to use 'varargs'. Program to sum the cubes of all
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the specified numbers.
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Reference in New Issue
Block a user