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Release calc version 2.12.4.9

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This commit is contained in:
Landon Curt Noll
2013-08-10 20:36:29 -07:00
parent 7cf611bca8
commit 7f125396c1
240 changed files with 2784 additions and 839 deletions
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cal/README
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@@ -173,7 +173,8 @@ alg_config.cal
beer.cal
Calc's contribution to the 99 Bottles of Beer web page:
This calc resource is calc's contribution to the 99 Bottles of Beer
web page:
http://www.ionet.net/~timtroyr/funhouse/beer.html#calc
@@ -191,6 +192,18 @@ bernoulli.cal
the builtin function.
bernpoly.cal
bernpoly(n,z)
Computes the nth Bernoulli polynomial at z for arbitrary n,z. See:
http://en.wikipedia.org/wiki/Bernoulli_polynomials
http://mathworld.wolfram.com/BernoulliPolynomial.html
for further information
bigprime.cal
bigprime(a, m, p)
@@ -198,6 +211,34 @@ bigprime.cal
A prime test, base a, on p*2^x+1 for even x>m.
brentsolve.cal
brentsolve(low, high,eps)
A root-finder implementwed with the Brent-Dekker trick.
brentsolve2(low, high,which,eps)
The second function, brentsolve2(low, high,which,eps) has some lines
added to make it easier to hardcode the name of the helper function
different from the obligatory "f".
See:
http://en.wikipedia.org/wiki/Brent%27s_method
http://mathworld.wolfram.com/BrentsMethod.html
to find out more about the Brent-Dekker method.
constants.cal
e()
G()
An implementation of different constants to arbitrary precision.
chi.cal
Z(x[, eps])
@@ -226,14 +267,37 @@ chrem.cal
deg.cal
deg(deg, min, sec)
deg_add(a, b)
deg_neg(a)
deg_sub(a, b)
deg_mul(a, b)
deg_print(a)
Calculate in degrees, minutes, and seconds. For a more functional
version see dms.cal.
dms.cal
dms(deg, min, sec)
dms_add(a, b)
dms_neg(a)
dms_sub(a, b)
dms_mul(a, b)
dms_print(a)
dms_abs(a)
dms_norm(a)
dms_test(a)
dms_int(a)
dms_frac(a)
dms_rel(a,b)
dms_cmp(a,b)
dms_inc(a)
dms_dec(a)
Calculate in degrees, minutes, and seconds.
Calculate in degrees, minutes, and seconds. Unlike deg.cal, increments
are on the arc second level. See also hms.cal.
dotest.cal
@@ -268,6 +332,166 @@ dotest.cal
dotest("set8700.line");
factorial.cal
factorial(n)
Calculates the product of the positive integers up to and including n.
See:
http://en.wikipedia.org/wiki/Factorial
for information on the factorial. This function depends on the script
toomcook.cal.
primorial(a,b)
Calculates the product of the primes between a and b. If a is not prime
the next higher prime is taken as the starting point. If b is not prime
the next lower prime is taking as the end point b. The end point b must
not exceed 4294967291. See:
http://en.wikipedia.org/wiki/Primorial
for information on the primorial.
factorial2.cal
This file contents a small variety of integer functions that can, with
more or less pressure, be related to the factorial.
doublefactorial(n)
Calculates the double factorial n!! with different algorithms for
- n odd
- n even and positive
- n (real|complex) sans the negative half integers
See:
http://en.wikipedia.org/wiki/Double_factorial
http://mathworld.wolfram.com/DoubleFactorial.html
for information on the double factorial. This function depends on
the script toomcook.cal, factorial.cal and specialfunctions.cal.
binomial(n,k)
Calculates the binomial coefficients for n large and k = k \pm
n/2. Defaults to the built-in function for smaller and/or different
values. Meant as a complete replacement for comb(n,k) with only a
very small overhead. See:
http://en.wikipedia.org/wiki/Binomial_coefficient
for information on the binomial. This function depends on the script
toomcook.cal factorial.cal and specialfunctions.cal.
bigcatalan(n)
Calculates the n-th Catalan number for n large. It is usefull
above n~50,000 but defaults to the builtin function for smaller
values.Meant as a complete replacement for catalan(n) with only a
very small overhead. See:
http://en.wikipedia.org/wiki/Catalan_number
http://mathworld.wolfram.com/CatalanNumber.html
for information on Catalan numbers. This function depends on the scripts
toomcook.cal, factorial.cal and specialfunctions.cal.
stirling1(n,m)
Calculates the Stirling number of the first kind. It does so with
building a list of all of the smaller results. It might be a good
idea, though, to run it once for the highest n,m first if many
Stirling numbers are needed at once, for example in a series. See:
http://en.wikipedia.org/wiki/Stirling_numbers_of_the_first_kind
http://mathworld.wolfram.com/StirlingNumberoftheFirstKind.html
Algorithm 3.17, Donald Kreher and Douglas Simpson, "Combinatorial
Algorithms", CRC Press, 1998, page 89.
for information on Stirling numbers of the first kind.
stirling2(n,m)
stirling2caching(n,m)
Calculate the Stirling number of the second kind.
The first function stirling2(n,m) does it with the sum
m
====
1 \ n m - k
-- > k (- 1) binomial(m, k)
m! /
====
k = 0
The other function stirling2caching(n,m) does it by way of the
reccurence relation and keeps all earlier results. This function
is much slower for computing a single value than stirling2(n,m) but
is very usefull if many Stirling numbers are needed, for example in
a series. See:
http://en.wikipedia.org/wiki/Stirling_numbers_of_the_second_kind
http://mathworld.wolfram.com/StirlingNumberoftheSecondKind.html
Algorithm 3.17, Donald Kreher and Douglas Simpson, "Combinatorial
Algorithms", CRC Press, 1998, page 89.
for information on Stirling numbers of the second kind.
bell(n)
Calculate the n-th Bell number. This may take some time for large n.
See:
http://oeis.org/A000110
http://en.wikipedia.org/wiki/Bell_number
http://mathworld.wolfram.com/BellNumber.html
for information on Bell numbers.
subfactorial(n)
Calculate the n-th subfactorial or derangement. This may take some
time for large n. See:
http://mathworld.wolfram.com/Derangement.html
http://en.wikipedia.org/wiki/Derangement
for information on subfactorials.
risingfactorial(x,n)
Calculates the rising factorial or Pochammer symbol of almost arbitrary
x,n. See:
http://en.wikipedia.org/wiki/Pochhammer_symbol
http://mathworld.wolfram.com/PochhammerSymbol.html
for information on rising factorials.
fallingfactorial(x,n)
Calculates the rising factorial of almost arbitrary x,n. See:
http://en.wikipedia.org/wiki/Pochhammer_symbol
http://mathworld.wolfram.com/PochhammerSymbol.html
for information on falling factorials.
ellip.cal
efactor(iN, ia, B, force)
@@ -275,6 +499,13 @@ ellip.cal
Attempt to factor using the elliptic functions: y^2 = x^3 + a*x + b.
gvec.cal
gvec(function, vector)
Vectorize any single-input function or trailing operator.
hello.cal
Calc's contribution to the Hello World! page:
@@ -285,6 +516,27 @@ hello.cal
NOTE: This resource produces a lot of output. :-)
hms.cal
hms(hour, min, sec)
hms_add(a, b)
hms_neg(a)
hms_sub(a, b)
hms_mul(a, b)
hms_print(a)
hms_abs(a)
hms_norm(a)
hms_test(a)
hms_int(a)
hms_frac(a)
hms_rel(a,b)
hms_cmp(a,b)
hms_inc(a)
hms_dec(a)
Calculate in hours, minutes, and seconds. See also dmscal.
intfile.cal
file2be(filename)
@@ -312,6 +564,37 @@ intfile.cal
of the integer become the last octets of the file.
lambertw.cal
lambertw(z,branch)
Computes Lambert's W-function at "z" at branch "branch". See
http://en.wikipedia.org/wiki/Lambert_W_function
http://mathworld.wolfram.com/LambertW-Function.html
https://cs.uwaterloo.ca/research/tr/1993/03/W.pdf
http://arxiv.org/abs/1003.1628
to get more information.
This file includes also an implementation for the series described in
Corless et al. (1996) eq. 4.22 (W-pdf) and Verebic (2010) (arxive link)
eqs.35-37.
The series has been implemented to get a different algorithm
for checking the results. This was necessary because the results
of the implementation in Maxima, the only program with a general
lambert-w implementation at hand at that time, differed slightly. The
Maxima versions tested were: Maxima 5.21.1 and 5.29.1. The current
version of this code concurs with the results of Mathematica`s(tm)
ProductLog[branch,z] with the tested values.
The series is only valid for the branches 0,-1, real z, converges
for values of z _very_ near the branchpoint -exp(-1) only, and must
be given the branches explicitly. See the code in lambertw.cal
for further information.
linear.cal
linear(x0, y0, x1, y1, x)
@@ -320,6 +603,24 @@ linear.cal
Requires x0 != y0.
lnseries.cal
lnseries(limit)
lnfromseries(n)
deletelnseries()
Calculates a series of n natural logarithms at 1,2,3,4...n. It
does so by computing the prime factorization of all of the number
sequence 1,2,3...n, calculates the natural logarithms of the primes
in 1,2,3...n and uses the above factorization to build the natural
logarithms of the rest of the sequence by sadding the logarithms of
the primes in the factorization. This is faster for high precision
of the logarithms and/or long sequences.
The sequence need to be initiated by running either lnseries(n) or
lnfromseries(n) once with n the upper limit of the sequence.
lucas.cal
lucas(h, n)
@@ -365,6 +666,7 @@ mfactor.cal
fastest even thought the initial startup overhead is larger than
for p_elim == 13.
mod.cal
lmod(a)
@@ -454,6 +756,7 @@ pi.cal
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)
@@ -536,10 +839,10 @@ 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.
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
@@ -591,8 +894,8 @@ repeat.cal
regress.cal
Test the correct execution of the calculator by reading this resource file.
Errors are reported with '****' messages, or worse. :-)
Test the correct execution of the calculator by reading this resource
file. Errors are reported with '****' messages, or worse. :-)
screen.cal
@@ -638,15 +941,17 @@ screen.cal
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.
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])
@@ -688,8 +993,247 @@ 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.
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.
specialfunctions.cal
beta(a,b)
Calculates the value of the beta function. See:
https://en.wikipedia.org/wiki/Beta_function
http://mathworld.wolfram.com/BetaFunction.html
http://dlmf.nist.gov/5.12
for information on the beta function.
betainc(a,b,z)
Calculates the value of the regularized incomplete beta function. See:
https://en.wikipedia.org/wiki/Beta_function
http://mathworld.wolfram.com/RegularizedBetaFunction.html
http://dlmf.nist.gov/8.17
for information on the regularized incomplete beta function.
expoint(z)
Calculates the value of the exponential integral Ei(z) function at z.
See:
http://en.wikipedia.org/wiki/Exponential_integral
http://www.cs.utah.edu/~vpegorar/research/2011_JGT/
for information on the exponential integral Ei(z) function.
erf(z)
Calculates the value of the error function at z. See:
http://en.wikipedia.org/wiki/Error_function
for information on the error function function.
erfc(z)
Calculates the value of the complementary error function at z. See:
http://en.wikipedia.org/wiki/Error_function
for information on the complementary error function function.
erfi(z)
Calculates the value of the imaginary error function at z. See:
http://en.wikipedia.org/wiki/Error_function
for information on the imaginary error function function.
erfinv(x)
Calculates the inverse of the error function at x. See:
http://en.wikipedia.org/wiki/Error_function
for information on the inverse of the error function function.
faddeeva(z)
Calculates the value of the complex error function at z. See:
http://en.wikipedia.org/wiki/Faddeeva_function
for information on the complex error function function.
gamma(z)
Calculates the value of the Euler gamma function at z. See:
http://en.wikipedia.org/wiki/Gamma_function
http://dlmf.nist.gov/5
for information on the Euler gamma function.
gammainc(a,z)
Calculates the value of the lower incomplete gamma function for
arbitrary a, z. See:
http://en.wikipedia.org/wiki/Incomplete_gamma_function
for information on the lower incomplete gamma function.
gammap(a,z)
Calculates the value of the regularized lower incomplete gamma
function for a, z with a not in -N. See:
http://en.wikipedia.org/wiki/Incomplete_gamma_function
for information on the regularized lower incomplete gamma function.
gammaq(a,z)
Calculates the value of the regularized upper incomplete gamma
function for a, z with a not in -N. See:
http://en.wikipedia.org/wiki/Incomplete_gamma_function
for information on the regularized upper incomplete gamma function.
heavisidestep(x)
Computes the Heaviside stepp function (1+sign(x))/2
harmonic(limit)
Calculates partial values of the harmonic series up to limit. See:
http://en.wikipedia.org/wiki/Harmonic_series_(mathematics)
http://mathworld.wolfram.com/HarmonicSeries.html
for information on the harmonic series.
lnbeta(a,b)
Calculates the natural logarithm of the beta function. See:
https://en.wikipedia.org/wiki/Beta_function
http://mathworld.wolfram.com/BetaFunction.html
http://dlmf.nist.gov/5.12
for information on the beta function.
lngamma(z)
Calculates the value of the logarithm of the Euler gamma function
at z. See:
http://en.wikipedia.org/wiki/Gamma_function
http://dlmf.nist.gov/5.15
for information on the derivatives of the the Euler gamma function.
polygamma(m,z)
Calculates the value of the m-th derivative of the Euler gamma
function at z. See:
http://en.wikipedia.org/wiki/Polygamma
http://dlmf.nist.gov/5
for information on the n-th derivative ofthe Euler gamma function. This
function depends on the script zeta2.cal.
psi(z)
Calculates the value of the first derivative of the Euler gamma
function at z. See:
http://en.wikipedia.org/wiki/Digamma_function
http://dlmf.nist.gov/5
for information on the first derivative of the Euler gamma function.
zeta(s)
Calculates the value of the Rieman Zeta function at s. See:
http://en.wikipedia.org/wiki/Riemann_zeta_function
http://dlmf.nist.gov/25.2
for information on the Riemann zeta function. This function depends
on the script zeta2.cal.
statistics.cal
gammaincoctave(z,a)
Computes the regularized incomplete gamma function in a way to
correspond with the function in Octave.
invbetainc(x,a,b)
Computes the inverse of the regularized beta function. Does so the
brute-force way wich makes it a bit slower.
betapdf(x,a,b)
betacdf(x,a,b)
betacdfinv(x,a,b)
betamedian(a,b)
betamode(a,b)
betavariance(a,b)
betalnvariance(a,b)
betaskewness(a,b)
betakurtosis(a,b)
betaentropy(a,b)
normalpdf(x,mu,sigma)
normalcdf(x,mu,sigma)
probit(p)
normalcdfinv(p,mu,sigma)
normalmean(mu,sigma)
normalmedian(mu,sigma)
normalmode(mu,sigma)
normalvariance(mu,sigma)
normalskewness(mu,sigma)
normalkurtosis(mu,sigma)
normalentropy(mu,sigma)
normalmgf(mu,sigma,t)
normalcf(mu,sigma,t)
chisquaredpdf(x,k)
chisquaredpcdf(x,k)
chisquaredmean(x,k)
chisquaredmedian(x,k)
chisquaredmode(x,k)
chisquaredvariance(x,k)
chisquaredskewness(x,k)
chisquaredkurtosis(x,k)
chisquaredentropy(x,k)
chisquaredmfg(k,t)
chisquaredcf(k,t)
Calculates a bunch of (hopefully) aptly named statistical functions.
sumsq.cal
@@ -751,7 +1295,8 @@ test1700.cal
value
This resource files is used by regress.cal to test the read and use keywords.
This resource files is used by regress.cal to test the read and
use keywords.
test2600.cal
@@ -776,8 +1321,8 @@ test2600.cal
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.
This resource files is used by regress.cal to test some of builtin
functions in terms of accuracy and roundoff.
test2700.cal
@@ -814,7 +1359,8 @@ test3100.cal
res_inv(a)
res(x)
This resource file is used by regress.cal to test determinants of a matrix
This resource file is used by regress.cal to test determinants of
a matrix.
test3300.cal
@@ -825,8 +1371,9 @@ test3300.cal
testr(str, n, N, verbose)
test3300(verbose, tnum)
This resource file is used by regress.cal to provide for more determinant
tests.
This resource file is used by regress.cal to provide for more
determinant tests.
test3400.cal
@@ -857,6 +1404,7 @@ test3500.cal
This resource file is used by regress.cal to test the functions frem,
fcnt, gcdrem.
test4000.cal
global defaultverbose
@@ -889,6 +1437,7 @@ test4000.cal
This resource file is used by regress.cal to test ptest, nextcand and
prevcand builtins.
test4100.cal
global defaultverbose
@@ -908,6 +1457,7 @@ test4100.cal
This resource file is used by regress.cal to test REDC operations.
test4600.cal
stest(str [, verbose]) defined
@@ -919,6 +1469,7 @@ test4600.cal
This resource file is used by regress.cal to test searching in files.
test5100.cal
global a5100
@@ -928,6 +1479,7 @@ test5100.cal
This resource file is used by regress.cal to test the new code generator
declaration scope and order.
test5200.cal
global a5200
@@ -939,6 +1491,7 @@ test5200.cal
This resource file is used by regress.cal to test the fix of a
global/static bug.
test8400.cal
test8400() defined
@@ -946,6 +1499,7 @@ test8400.cal
This resource file is used by regress.cal to check for quit-based
memory leaks.
test8500.cal
global err_8500
@@ -958,6 +1512,7 @@ test8500.cal
This resource file is used by regress.cal to the // and % operators.
test8600.cal
global min_8600
@@ -968,6 +1523,25 @@ test8600.cal
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.
test8900.cal
This function tests a number of calc resource functions contributed
by Christoph Zurnieden. These include:
bernpoly.cal
brentsolve.cal
constants.cal
factorial2.cal
factorial.cal
lambertw.cal
lnseries.cal
specialfunctions.cal
statistics.cal
toomcook.cal
zeta2.cal
unitfrac.cal
unitfrac(x)
@@ -975,6 +1549,29 @@ unitfrac.cal
Represent a fraction as sum of distinct unit fractions.
toomcook.cal
toomcook3(a,b)
toomcook4(a,b)
Toom-Cook multiplication algorithm. Multiply two integers a,b by
way of the Toom-Cook algorithm. See:
http://en.wikipedia.org/wiki/Toom%E2%80%93Cook_multiplication
toomcook3square(a)
toomcook4square(a)
Square the integer a by way of the Toom-Cook algorithm. See:
http://en.wikipedia.org/wiki/Toom%E2%80%93Cook_multiplication
The function toomCook4(a,b) calls the function toomCook3(a,b) which
calls built-in multiplication at a specific cut-off point. The
squaring functions act in the same way.
varargs.cal
sc(a, b, ...)
@@ -982,6 +1579,7 @@ varargs.cal
Example program to use 'varargs'. Program to sum the cubes of all
the specified numbers.
xx_print.cal
is_octet(a) defined
@@ -996,6 +1594,19 @@ xx_print.cal
Demo for the xx_print object routines.
zeta2.cal
hurwitzzeta(s,a)
Calculate the value of the Hurwitz Zeta function. See:
http://en.wikipedia.org/wiki/Hurwitz_zeta_function
http://dlmf.nist.gov/25.11
for information on this special zeta function.
## Copyright (C) 2000 David I. Bell and Landon Curt Noll
##
## Primary author: Landon Curt Noll
@@ -1014,8 +1625,8 @@ xx_print.cal
## 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 $
## @(#) $Revision: 30.5 $
## @(#) $Id: README,v 30.5 2013/08/11 03:26:46 chongo Exp $
## @(#) $Source: /usr/local/src/cmd/calc/cal/RCS/README,v $
##
## Under source code control: 1990/02/15 01:50:32