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Fix many spelling errors

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This commit is contained in:
Landon Curt Noll
2021-02-12 22:09:47 -08:00
parent 486f4c5626
commit 507fe026e5
154 changed files with 482 additions and 476 deletions
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8
cal/Makefile
View File

@@ -181,14 +181,14 @@ FMT= fmt
# The calc files to install
#
# This list is prodiced by the detaillist rule when no WARNINGS are detected.
# This list is produced by the detaillist rule when no WARNINGS are detected.
#
# Please use:
#
# make calc_files_list
#
# to keep this list in nice sorted order and to check that these
# deailed help files are under RCS control.
# detailed help files are under RCS control.
#
CALC_FILES= README alg_config.cal beer.cal bernoulli.cal \
bernpoly.cal bigprime.cal bindings brentsolve.cal chi.cal chrem.cal \
@@ -236,7 +236,7 @@ all: ${CALC_FILES} ${MAKE_FILE} .all
# sub-directory called calc/cal.
#
# NOTE: Due to bogus shells found on one common system we must have
# an non-emoty else clause for every if condition. *sigh*
# an non-empty else clause for every if condition. *sigh*
#
##
@@ -391,7 +391,7 @@ uninstall:
if [ -f "${T}${CALC_SHAREDIR}/$$i" ]; then \
echo "cannot uninstall ${T}${CALC_SHAREDIR}/$$i"; \
else \
echo "uninstalled ${T}${CALC_SHAREDIR}/$$i"; \
echo "un-installed ${T}${CALC_SHAREDIR}/$$i"; \
fi; \
fi; \
done

34
cal/README
View File

@@ -213,12 +213,12 @@ brentsolve.cal
brentsolve(low, high,eps)
A root-finder implementwed with the Brent-Dekker trick.
A root-finder implemented 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
added to make it easier to hard-code the name of the helper function
different from the obligatory "f".
See:
@@ -392,7 +392,7 @@ factorial2.cal
bigcatalan(n)
Calculates the n-th Catalan number for n large. It is usefull
Calculates the n-th Catalan number for n large. It is useful
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:
@@ -433,9 +433,9 @@ factorial2.cal
k = 0
The other function stirling2caching(n,m) does it by way of the
reccurence relation and keeps all earlier results. This function
re-occurrence 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
is very useful if many Stirling numbers are needed, for example in
a series. See:
http://en.wikipedia.org/wiki/Stirling_numbers_of_the_second_kind
@@ -546,7 +546,7 @@ infinities.cal
pinf()
The symbolic handling of infinities. Needed for intnum.cal but might be
usefull elsewhere, too.
useful elsewhere, too.
intfile.cal
@@ -595,13 +595,13 @@ intnum.cal
This file offers some methods for numerical integration. Implemented are
the Gauss-Legendre and the tanh-sinh quadrature.
All functions are usefull to some extend but the main function for
All functions are useful to some extend but the main function for
quadrature is quad(), which is not much more than an abstraction layer.
The main workers are quadgl() for Gauss-legendre and quadts() for the
The main workers are quadgl() for Gauss-Legendre and quadts() for the
tanh-sinh quadrature. The limits of the integral can be anything in the
complex plane and the extended real line. The latter means that infinite
limits are supported by way of the smbolic infinities implemented in the
limits are supported by way of the symbolic infinities implemented in the
file infinities.cal (automatically linked in by intnum.cal).
Integration in parts and contour is supported by the "points" argument
@@ -661,7 +661,7 @@ intnum.cal
The quad*core functions do not offer anything fancy but the third parameter
controls the so called "order" which is just the number of nodes computed.
This can be quite usefull in some circumstances.
This can be quite useful in some circumstances.
; quadgldeletenodes()
; define f(x){ return exp(x);}
@@ -723,7 +723,7 @@ lambertw.cal
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
for values of z _very_ near the branch-point -exp(-1) only, and must
be given the branches explicitly. See the code in lambertw.cal
for further information.
@@ -746,7 +746,7 @@ lnseries.cal
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
logarithms of the rest of the sequence by adding the logarithms of
the primes in the factorization. This is faster for high precision
of the logarithms and/or long sequences.
@@ -806,7 +806,7 @@ mfactor.cal
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
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.
@@ -1317,7 +1317,7 @@ specialfunctions.cal
http://en.wikipedia.org/wiki/Polygamma
http://dlmf.nist.gov/5
for information on the n-th derivative ofthe Euler gamma function. This
for information on the n-th derivative of the Euler gamma function. This
function depends on the script zeta2.cal.
@@ -1334,7 +1334,7 @@ specialfunctions.cal
zeta(s)
Calculates the value of the Rieman Zeta function at s. See:
Calculates the value of the Riemann Zeta function at s. See:
http://en.wikipedia.org/wiki/Riemann_zeta_function
http://dlmf.nist.gov/25.2
@@ -1353,7 +1353,7 @@ statistics.cal
invbetainc(x,a,b)
Computes the inverse of the regularized beta function. Does so the
brute-force way wich makes it a bit slower.
brute-force way which makes it a bit slower.
betapdf(x,a,b)
betacdf(x,a,b)
@@ -1433,7 +1433,7 @@ sumtimes.cal
Give the user CPU time for various ways of evaluating sums, sums of
squares, etc, for large lists and matrices. N is the size of
the list or matrix to use. The doalltimes() function will run
all fo the sumtimes tests. For example:
all of the sumtimes tests. For example:
doalltimes(1e6);

52
cal/alg_config.cal
View File

@@ -33,7 +33,7 @@ static test_time; /* try for this many seconds in loop test */
* given:
* ratio the ratio of time between two algorithms
*
* retuns:
* returns:
* 1 When ratio is near 1.0
* 0 otherwise
*
@@ -354,7 +354,7 @@ define best_mul2()
local high; /* high loop value tested */
local mid; /* between low and high */
local best_val; /* value found with ratio closest to unity */
local best_ratio; /* cloest ratio found to unity */
local best_ratio; /* closest ratio found to unity */
local expand; /* how fast to expand the length */
/*
@@ -363,7 +363,7 @@ define best_mul2()
printf("WARNING: This tool may not be computing the correct best value\n");
test_time = 5.0;
printf("The best_mul2() function will take a LONG time to run!\n");
printf("It is important that best_mul2() run on an othwewise idle host!\n");
printf("It is important that best_mul2() run on an otherwise idle host!\n");
if (config("user_debug") <= 0) {
printf("To monitor progress, set user_debug to 2: "
"config(\"user_debug\", 2)\n");
@@ -392,7 +392,7 @@ define best_mul2()
*/
do {
/*
* determine the paramters of the next ratio test
* determine the parameters of the next ratio test
*
* We will multiplicatively expand our test level until
* the ratio drops below 1.0.
@@ -419,7 +419,7 @@ define best_mul2()
best_val = high;
best_ratio = ratio;
if (config("user_debug") > 1) {
printf(" len %d has a new cloest ratio to unity: %.6f\n",
printf(" len %d has a new closest ratio to unity: %.6f\n",
best_val, best_ratio);
}
}
@@ -442,7 +442,7 @@ define best_mul2()
high /= 2;
low = high / 2;
if (config("user_debug") > 0) {
printf("retesting multiply alg1/alg2 ratio for len = %d\n",
printf("re-testing multiply alg1/alg2 ratio for len = %d\n",
high);
}
ratio = mul_ratio(high);
@@ -450,7 +450,8 @@ define best_mul2()
best_val = high;
best_ratio = ratio;
if (config("user_debug") > 1) {
printf(" len %d has a new cloest ratio to unity: %.6f\n",
printf(" len %d has a new closest ratio "
"to unity: %.6f\n",
best_val, best_ratio);
}
}
@@ -483,7 +484,7 @@ define best_mul2()
best_val = mid;
best_ratio = ratio;
if (config("user_debug") > 1) {
printf(" len %d has a new cloest ratio to unity: %.6f\n",
printf(" len %d has a new closest ratio to unity: %.6f\n",
best_val, best_ratio);
}
}
@@ -535,7 +536,7 @@ define best_mul2()
printf("config(\"mul2\", %d),;\n", best_val);
printf("WARNING: It is believed that the output "
"of this resource file is bogus!\n");
printf("WARNING: You may NOT wish to follow the above suggeston.\n");
printf("WARNING: You may NOT wish to follow the above suggestion.\n");
}
return mid;
}
@@ -835,7 +836,7 @@ define best_sq2()
local high; /* high loop value tested */
local mid; /* between low and high */
local best_val; /* value found with ratio closest to unity */
local best_ratio; /* cloest ratio found to unity */
local best_ratio; /* closest ratio found to unity */
local expand; /* how fast to expand the length */
/*
@@ -844,7 +845,7 @@ define best_sq2()
printf("WARNING: This tool may not be computing the correct best value\n");
test_time = 5.0;
printf("The best_sq2() function will take a LONG time to run!\n");
printf("It is important that best_sq2() run on an othwewise idle host!\n");
printf("It is important that best_sq2() run on an otherwise idle host!\n");
if (config("user_debug") <= 0) {
printf("To monitor progress, set user_debug to 2: "
"config(\"user_debug\", 2)\n");
@@ -873,7 +874,7 @@ define best_sq2()
*/
do {
/*
* determine the paramters of the next ratio test
* determine the parameters of the next ratio test
*
* We will multiplicatively expand our test level until
* the ratio drops below 1.0.
@@ -900,7 +901,7 @@ define best_sq2()
best_val = high;
best_ratio = ratio;
if (config("user_debug") > 1) {
printf(" len %d has a new cloest ratio to unity: %.6f\n",
printf(" len %d has a new closest ratio to unity: %.6f\n",
best_val, best_ratio);
}
}
@@ -923,7 +924,7 @@ define best_sq2()
high /= 2;
low = high / 2;
if (config("user_debug") > 0) {
printf("retesting multiply alg1/alg2 ratio for len = %d\n",
printf("re-testing multiply alg1/alg2 ratio for len = %d\n",
high);
}
ratio = mul_ratio(high);
@@ -931,7 +932,8 @@ define best_sq2()
best_val = high;
best_ratio = ratio;
if (config("user_debug") > 1) {
printf(" len %d has a new cloest ratio to unity: %.6f\n",
printf(" len %d has a new closest ratio "
"to unity: %.6f\n",
best_val, best_ratio);
}
}
@@ -964,7 +966,7 @@ define best_sq2()
best_val = mid;
best_ratio = ratio;
if (config("user_debug") > 1) {
printf(" len %d has a new cloest ratio to unity: %.6f\n",
printf(" len %d has a new closest ratio to unity: %.6f\n",
best_val, best_ratio);
}
}
@@ -1017,7 +1019,7 @@ define best_sq2()
printf("config(\"sq2\", %d),;\n", best_val);
printf("WARNING: It is believed that the output "
"of this resource file is bogus!\n");
printf("WARNING: You may NOT wish to follow the above suggeston.\n");
printf("WARNING: You may NOT wish to follow the above suggestion.\n");
}
return mid;
}
@@ -1337,7 +1339,7 @@ define best_pow2()
local high; /* high loop value tested */
local mid; /* between low and high */
local best_val; /* value found with ratio closest to unity */
local best_ratio; /* cloest ratio found to unity */
local best_ratio; /* closest ratio found to unity */
local expand; /* how fast to expand the length */
local looped; /* 1 ==> we have expanded lengths before */
@@ -1347,7 +1349,7 @@ define best_pow2()
printf("WARNING: This tool may not be computing the correct best value\n");
test_time = 60.0;
printf("The best_pow2() function will take a LONG time to run!\n");
printf("It is important that best_pow2() run on an othwewise idle host!\n");
printf("It is important that best_pow2() run on an otherwise idle host!\n");
if (config("user_debug") <= 0) {
printf("To monitor progress, set user_debug to 2: "
"config(\"user_debug\", 2)\n");
@@ -1358,7 +1360,7 @@ define best_pow2()
* firewall - must have a >1.02 ratio for the initial length
*
* We select 1.02 because of the precision of the CPU timing. We
* want to firt move into an area where the 1st algoritm clearly
* want to first move into an area where the 1st algorithm clearly
* dominates.
*/
low = 4;
@@ -1375,7 +1377,7 @@ define best_pow2()
best_val = high;
best_ratio = ratio;
if (config("user_debug") > 1) {
printf(" len %d has a new cloest ratio to unity: %.6f\n",
printf(" len %d has a new closest ratio to unity: %.6f\n",
best_val, best_ratio);
}
}
@@ -1397,7 +1399,7 @@ define best_pow2()
looped = 0;
do {
/*
* determine the paramters of the next ratio test
* determine the parameters of the next ratio test
*
* We will multiplicatively expand our test level until
* the ratio drops below 1.0.
@@ -1435,7 +1437,7 @@ define best_pow2()
best_val = high;
best_ratio = ratio;
if (config("user_debug") > 1) {
printf(" len %d has a new cloest ratio to unity: %.6f\n",
printf(" len %d has a new closest ratio to unity: %.6f\n",
best_val, best_ratio);
}
}
@@ -1463,7 +1465,7 @@ define best_pow2()
best_val = mid;
best_ratio = ratio;
if (config("user_debug") > 1) {
printf(" len %d has a new cloest ratio to unity: %.6f\n",
printf(" len %d has a new closest ratio to unity: %.6f\n",
best_val, best_ratio);
}
}
@@ -1516,7 +1518,7 @@ define best_pow2()
printf("config(\"pow2\", %d),;\n", best_val);
printf("WARNING: It is believed that the output "
"of this resource file is bogus!\n");
printf("WARNING: You may NOT wish to follow the above suggeston.\n");
printf("WARNING: You may NOT wish to follow the above suggestion.\n");
}
return mid;
}

8
cal/bernoulli.cal
View File

@@ -1,5 +1,5 @@
/*
* bernoulli - clculate the Nth Bernoulli number B(n)
* bernoulli - calculate the Nth Bernoulli number B(n)
*
* Copyright (C) 2000 David I. Bell and Landon Curt Noll
*
@@ -26,9 +26,9 @@
/*
* Calculate the Nth Bernoulli number B(n).
*
* NOTE: This is now a bulitin function.
* NOTE: This is now a builtin function.
*
* The non-buildin code used the following symbolic formula to calculate B(n):
* The non-builtin code used the following symbolic formula to calculate B(n):
*
* (b+1)^(n+1) - b^(n+1) = 0
*
@@ -42,7 +42,7 @@
* B(3) = -(6*B(2) + 4*B(1) + 1) / 4
*
* The combinatorial factors in the expansion of the above formula are
* calculated interatively, and we use the fact that B(2i+1) = 0 if i > 0.
* calculated interactively, and we use the fact that B(2i+1) = 0 if i > 0.
* Since all previous B(n)'s are needed to calculate a particular B(n), all
* values obtained are saved in an array for ease in repeated calculations.
*/

2
cal/bernpoly.cal
View File

@@ -1,5 +1,5 @@
/*
* bernpoly - Bernoully polynomials B_n(z) for arbitrary n,z..
* bernpoly - Bernoulli polynomials B_n(z) for arbitrary n,z..
*
* Copyright (C) 2013 Christoph Zurnieden
*

2
cal/brentsolve.cal
View File

@@ -143,7 +143,7 @@ define brentsolve2(low, high,which,eps){
switch(param(0)){
case 0:
case 1: return newerror("brentsolve2: not enough argments");
case 1: return newerror("brentsolve2: not enough arguments");
case 2: eps = epsilon(epsilon()*1e-2);
which = 0;break;
case 3: eps = epsilon(epsilon()*1e-2);break;

8
cal/chi.cal
View File

@@ -51,7 +51,7 @@ define Z(x, eps_term)
/*
* P(x[, eps]) asymtotic P(x) expansion for x>0 to an given epsilon error term
* P(x[, eps]) asymptotic P(x) expansion for x>0 to an given epsilon error term
*
* NOTE: If eps is omitted, the stored epsilon value is used.
*
@@ -99,7 +99,7 @@ define P(x, eps_term)
}
/*
* aproximate sum(n=0; n < infinity){x^(2*n+1)/(1*3*5*...(2*n+1)}
* approximate sum(n=0; n < infinity){x^(2*n+1)/(1*3*5*...(2*n+1)}
*/
x2 = x*x;
x_term = x;
@@ -130,7 +130,7 @@ define P(x, eps_term)
*
* The chi_prob() function does not work well with odd degrees of freedom.
* It is reasonable with even degrees of freedom, although one must give
* a sifficently small error term as the degress gets large (>100).
* a sufficiently small error term as the degrees gets large (>100).
*
* NOTE: This function does not work well with odd degrees of freedom.
* Can somebody help / find a bug / provide a better method of
@@ -186,7 +186,7 @@ define chi_prob(chi_sq, v, eps_term)
local r; /* index in finite sum */
local r_lim; /* limit value for r */
local s; /* sum */
local d; /* demoninator (2*4*6*... or 1*3*5...) */
local d; /* denominator (2*4*6*... or 1*3*5...) */
local chi_term; /* chi_sq^r */
local ret; /* return value */

6
cal/chrem.cal
View File

@@ -1,5 +1,5 @@
/*
* chrem - chinese remainder theorem/problem solver
* chrem - Chinese remainder theorem/problem solver
*
* Copyright (C) 1999 Ernest Bowen and Landon Curt Noll
*
@@ -26,7 +26,7 @@
*/
/*
* When possible, chrem finds solutions for x of a set of congruences
* When possible, chrem finds solutions for x of a set of congruence
* of the form:
*
* x = r1 (mod m1)
@@ -35,7 +35,7 @@
*
* where the residues r1, r2, ... and the moduli m1, m2, ... are
* given integers. The Chinese remainder theorem states that if
* m1, m2, ... are relatively prime in pairs, the above congruences
* m1, m2, ... are relatively prime in pairs, the above congruence
* have a unique solution modulo m1 * m2 * ... If m1, m2, ...
* are not relatively prime in pairs, it is possible that no solution
* exists. If solutions exist, the general solution is expressible as:

8
cal/dms.cal
View File

@@ -53,7 +53,7 @@ define dms_add(a, b)
{
local obj dms ans; /* return value */
/* initalize value to 1st arg */
/* initialize value to 1st arg */
if (istype(a, ans)) {
/* 1st arg is dms object, load it */
ans.deg = a.deg;
@@ -110,7 +110,7 @@ define dms_sub(a, b)
{
local obj dms ans; /* return value */
/* initalize value to 1st arg */
/* initialize value to 1st arg */
if (istype(a, ans)) {
/* 1st arg is dms object, load it */
ans.deg = a.deg;
@@ -352,11 +352,11 @@ define fixdms(a)
quit "attempt to fix a non dms object";
}
/* force minutes to be intergral */
/* force minutes to be integral */
a.min += frac(a.deg) * 60;
a.deg = int(a.deg);
/* force degrees to be intergral */
/* force degrees to be integral */
a.sec += frac(a.min) * 60;
a.min = int(a.min);

6
cal/dotest.cal
View File

@@ -8,8 +8,8 @@
* copyright this dotest_code.
*
* ERNEST BOWEN AND LANDON CURT NOLL DISCLAIMS ALL WARRANTIES WITH REGARD TO
* THIS SOFTWARE, INCLUDING ALL IMPLIED WARRANTIES OF MER-
* CHANTABILITY AND FITNESS. IN NO EVENT SHALL LANDON CURT
* THIS SOFTWARE, INCLUDING ALL IMPLIED WARRANTIES OF MER-
* CHANTABILITY AND FITNESS. IN NO EVENT SHALL LANDON CURT
* NOLL BE LIABLE FOR ANY SPECIAL, INDIRECT OR CONSEQUENTIAL
* DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF
* USE, DATA OR PROFITS, WHETHER IN AN ACTION OF CONTRACT,
@@ -173,7 +173,7 @@ define dotest(dotest_file, dotest_code = 0, dotest_maxcond = -1)
}
/*
* preppare to return to the caller environment
* prepare to return to the caller environment
*
* We increase the caller's error count by the number
* of line tests that failed, not the number of internal

6
cal/factorial2.cal
View File

@@ -281,10 +281,10 @@ define __CZ__multiply_factored_factorial(matrix,stop){
}
/*
Compute binomial coeficients n!/(k!(n-k)!)
Compute binomial coefficients n!/(k!(n-k)!)
One of the rare cases where a formula once meant to ease manual computation
is actually the (aymptotically) fastest way to do it (in July 2013) for
is actually the (asymptotically) fastest way to do it (in July 2013) for
the extreme case binomial(2N,N) but for a high price, the memory
needed is pi(N)--theoretically.
*/
@@ -626,7 +626,7 @@ define subfactorialrecursive(n){
return n * subfactorialrecursive(n-1) + (-1)^n;
}
/* This is, quite amusingely, faster than the very same algorithm in
/* This is, quite amusingly, faster than the very same algorithm in
PARI/GP + GMP*/
define subfactorialiterative(n){
local k temp1 temp2 ret;

8
cal/hms.cal
View File

@@ -53,7 +53,7 @@ define hms_add(a, b)
{
local obj hms ans; /* return value */
/* initalize value to 1st arg */
/* initialize value to 1st arg */
if (istype(a, ans)) {
/* 1st arg is hms object, load it */
ans.hour = a.hour;
@@ -110,7 +110,7 @@ define hms_sub(a, b)
{
local obj hms ans; /* return value */
/* initalize value to 1st arg */
/* initialize value to 1st arg */
if (istype(a, ans)) {
/* 1st arg is hms object, load it */
ans.hour = a.hour;
@@ -352,11 +352,11 @@ define fixhms(a)
quit "attempt to fix a non hms object";
}
/* force minutes to be intergral */
/* force minutes to be integral */
a.min += frac(a.hour) * 60;
a.hour = int(a.hour);
/* force hours to be intergral */
/* force hours to be integral */
a.sec += frac(a.min) * 60;
a.min = int(a.min);

16
cal/intfile.cal
View File

@@ -27,20 +27,20 @@
/*
* NOTE: Because leading HALF values are trimmed from integer, a file
* that begins with lots of 0 bits (in the case of big endian)
* or that ends with lots of 0 bits (in the case of little endian)
* that begins with lots of 0 bits (in the case of big Endian)
* or that ends with lots of 0 bits (in the case of little Endian)
* will be changed when the subsequent integer is written back.
*/
/*
* file2be - convert a file into an big endian integer
* file2be - convert a file into an big Endian integer
*
* given:
* filename filename to read
*
* returns:
* integer read from its contents on big endian order
* integer read from its contents on big Endian order
*/
define file2be(filename)
{
@@ -75,13 +75,13 @@ define file2be(filename)
/*
* file2le - convert a file into an little endian integer
* file2le - convert a file into an little Endian integer
*
* given:
* filename filename to read
*
* returns:
* integer read from its contents on little endian order
* integer read from its contents on little Endian order
*/
define file2le(filename)
{
@@ -118,7 +118,7 @@ define file2le(filename)
/*
* be2file - convert a big endian integer into a file
* be2file - convert a big Endian integer into a file
*
* given:
* v integer to write to the file
@@ -168,7 +168,7 @@ define be2file(v, filename)
/*
* le2file - convert a little endian integer into a file
* le2file - convert a little Endian integer into a file
*
* given:
* v integer to write to the file

2
cal/intnum.cal
View File

@@ -295,7 +295,7 @@ define quadts(a, b, points)
* as the number of equally spaced intervals on a straight line
* connecting a and b. Computing the segments here is a bit
* more complicated but not much, it should have been taught in
* highschool.
* high school.
* Other contours by way of a list of points */
slope = (im(b) - im(a)) / (re(b) - re(a));
C = (im(a) + slope) * re(a);

4
cal/lambertw.cal
View File

@@ -83,7 +83,7 @@ define __CZ__lambertw_m1(z,eps){
or by using the function lambertw_series_print() after running
lambertw_series(z,eps,branch,terms) at least once with the wanted number of
terms and z = 1 (which might throw an error because the series will not
converge in anybodies lifetime for something that far from the branchpoint).
converge in anybodies lifetime for something that far from the branch point).
*/
@@ -105,7 +105,7 @@ define lambertw_series_print(){
}
/*
The series is fast but only if _very_ close to the branchpoint
The series is fast but only if _very_ close to the branch point
The exact branch must be given explicitly, e.g.:
; lambertw(-exp(-1)+.001)-lambertw_series(-exp(-1)+.001,epsilon()*1e-10,0)

2
cal/linear.cal
View File

@@ -29,7 +29,7 @@
*
* given:
* x0, y0 first known point on the line
* x1, y1 second knonw point on the line
* x1, y1 second known point on the line
* x a given point to interpolate on
*
* returns:

12
cal/lucas.cal
View File

@@ -947,7 +947,7 @@ rodseth_xhn(x, h, n)
*
* Without Jacobi symbol value caching, it requires on average
* 4.851377 Jacobi symbol evaluations. With Jacobi symbol value caching
* cacheing, an averare of 4.348820 Jacobi symbol evaluations is needed.
* cacheing, an average of 4.348820 Jacobi symbol evaluations is needed.
*
* Given this information, when odd h is a multiple of 3 we try, in order,
* these odd values of X:
@@ -961,7 +961,7 @@ rodseth_xhn(x, h, n)
* jacobi(X-2, h*2^n-1) == 1
* jacobi(X+2, h*2^n-1) == -1
*
* Less than 1 case out of 1000000 will not be satisifed by the above list.
* Less than 1 case out of 1000000 will not be satisfied by the above list.
* If no value in that list works, we start simple search starting with X = 167
* and incrementing by 2 until a value of X is found.
*
@@ -1049,7 +1049,7 @@ next_x = 167; /* must be 2 more than the largest value in x_tbl[] */
* else
* v(1) = 4
*
* HOTE: The above "if then else" works only of h is not a multiple of 3.
* NOTE: The above "if then else" works only of h is not a multiple of 3.
*
***
*
@@ -1234,10 +1234,10 @@ gen_v1(h, n)
* jacobi(X-2, h*2^n-1) == 1 part 1
* jacobi(X+2, h*2^n-1) == -1 part 2
*
* NOTE: If we wanted to be super optimial, we would cache
* NOTE: If we wanted to be super optimal, we would cache
* jacobi(X+2, h*2^n-1) that that when we increment X
* to the next odd value, the now jacobi(X-2, h*2^n-1)
* does not need to be re-evaluted.
* does not need to be re-evaluated.
*/
testval = h*2^n-1;
for (i=0; i < x_tbl_len; ++i) {
@@ -1285,7 +1285,7 @@ gen_v1(h, n)
/*
* We are in that rare case (less than 1 in 1 000 000) where none of the
* common X values satisfy Ref4 condition 1. We start a linear search
* of odd vules at next_x from here on.
* of odd values at next_x from here on.
*/
x = next_x;
while (rodseth_xhn(x, h, n) != 1) {

2
cal/lucas_chk.cal
View File

@@ -303,7 +303,7 @@ read -once "lucas.cal";
* [quiet] if given and != 0, then do not print individual test results
*
* returns:
* 1 all is ok
* 1 all is OK
* 0 something went wrong
*/
define

12
cal/mfactor.cal
View File

@@ -79,7 +79,7 @@
* hindx = 0;
* } while (test_factor < some_limit);
*
* The test, mfactor(67, 1, 10000) took on an 200 Mhz r4k (user CPU seconds):
* The test, mfactor(67, 1, 10000) took on an 200 MHz r4k (user CPU seconds):
*
* 210.83 (prior to use of hset[])
* 78.35 (hset[] for p_elim = 7)
@@ -99,7 +99,7 @@
* 57.78 (hset[] for p_elim = 17)
* p_elim == 19 rejected because of memory size
*
* The p_elim == 17 overhead takes ~3 minutes on an 200 Mhz r4k CPU and
* 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.
*
@@ -256,7 +256,7 @@ define mfactor(n, start_k, rept_loop, p_elim)
return q;
} else {
/* report this loop */
printf("at 2*%d*%d+1, cpu: %f\n",
printf("at 2*%d*%d+1, CPU: %f\n",
(q-1)/(2*n), n, usertime());
fflush(files(1));
loop = 0;
@@ -269,14 +269,14 @@ define mfactor(n, start_k, rept_loop, p_elim)
*/
if (rept_loop <= ++loop) {
/* report this loop */
printf("at 2*%d*%d+1, cpu: %f\n",
printf("at 2*%d*%d+1, CPU: %f\n",
(q-1)/(2*n), n, usertime());
fflush(files(1));
loop = 0;
}
/*
* skip if divisable by a prime <= 449
* skip if divisible by a prime <= 449
*
* The value 281 was determined by timing loops
* which found that 281 was at or near the
@@ -285,7 +285,7 @@ define mfactor(n, start_k, rept_loop, p_elim)
* The addition of the do { ... } while (factor(q, 449)>1);
* loop reduced the factoring loop time (36504 k values with
* the hset[] initialization time removed) from 25.69 sec to
* 15.62 sec of CPU time on a 200Mhz r4k.
* 15.62 sec of CPU time on a 200MHz r4k.
*/
do {
/*

4
cal/natnumset.cal
View File

@@ -76,7 +76,7 @@
* A \ B = set difference, integers in A but not in B
*
* ~A = complement of A, integers not in A
* #A = number ofintegers in A
* #A = number of integers in A
* !A = 1 or 0 according as A is empty or not empty
* +A = sum of the members of A
*
@@ -100,7 +100,7 @@
* A >= B = (B <= A)
* A > B = (B < A)
*
* Expresssions may be formed from the above "arithmetic" operations in
* Expressions may be formed from the above "arithmetic" operations in
* the usual way, with parentheses for variations from the usual precedence
* rules. For example
*

2
cal/pell.cal
View File

@@ -25,7 +25,7 @@
/*
* 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.
* Type the solution to Pell's equation for a particular D.
*/

4
cal/poly.cal
View File

@@ -35,7 +35,7 @@
* variable has only one name. For some purposes, a name like
* "sin(t)" or "(a + b)" or "\lambda" might be useful;
* names like "*" or "-27" are legal but might give expressions
* that are difficult to intepret.
* that are difficult to interpret.
*
* Polynomial expressions may be constructed from numbers and the
* independent variable and other polynomials by the algebraic
@@ -43,7 +43,7 @@
* The operations // and % are defined to have the quotient and
* remainder meanings as usually defined for polynomials.
*
* When polynomials are assigned to idenfifiers, it is convenient to
* When polynomials are assigned to identifiers, it is convenient to
* think of the polynomials as values. For example, p = (x - 1)^2
* assigns to p a polynomial value in the same way as q = (7 - 1)^2
* would assign to q a number value. As with number expressions

8
cal/prompt.cal
View File

@@ -1,5 +1,5 @@
/*
* prompt - eemonstration of some uses of prompt() and eval()
* prompt - demonstration of some uses of prompt() and eval()
*
* Copyright (C) 1999 Ernest Bowen
*
@@ -61,9 +61,9 @@
* nothing to sum. The last line returns the value 3, i.e. the last
* non-null value found for the expressions separated by semicolons,
* so sum will be increased by 3 after the "print sum^2;" command
* is executed. xxx The terminating semicolon is essential in the
* is executed. XXX The terminating semicolon is essential in the
* last two lines. A command like eval("print 7;") is acceptable to
* calc but eval("print 7") causes an exit from calc. xxx)
* calc but eval("print 7") causes an exit from calc. XXX)
*
* If the value returned is not a number (e.g. the name of a list or matrix,
* or if the string has syntax errors as in "2 + ", in which case the
@@ -75,7 +75,7 @@
* "sin(x)", "x^2 + 3*x", "exp(x, 1e-5)".
*
* Values of the function so defined are returned for values of x
* entered in reponse to the ? prompt. Operation is terminated by
* entered in response to the ? prompt. Operation is terminated by
* entering "end", "exit" or "quit".
*/

2
cal/quat.cal
View File

@@ -1,5 +1,5 @@
/*
* quat - alculate using quaternions of the form: a + bi + cj + dk
* quat - calculate using quaternions of the form: a + bi + cj + dk
*
* Copyright (C) 1999 David I. Bell
*

6
cal/randmprime.cal
View File

@@ -45,9 +45,9 @@ randmprime(bits, seed, dbg)
local n; /* n as in h*2^n-1 */
local h; /* h as in h*2^n-1 */
local plush; /* value added to h since the beginning */
local init; /* initial cpu time */
local start; /* cpu time before last test */
local stop; /* cpu time afte last test */
local init; /* initial CPU time */
local start; /* CPU time before last test */
local stop; /* CPU time after last test */
local tmp; /* just a tmp place holder value */
local ret; /* h*2^n-1 that is prime */

28
cal/regress.cal
View File

@@ -43,7 +43,7 @@ global prob; /* libregress.cal problem counter */
prob = 0; /* clear problem counter */
errcount(0),; /* clear error count */
errmax(-1),; /* prevent errcount from abouting */
errmax(-1),; /* prevent errcount from aborting */
global ecnt; /* expected value of errcount() */
ecnt = 0; /* clear expected errcount() value */
@@ -453,7 +453,7 @@ define test_config()
'539: config("more", ">> ") == ";; "');
vrfy(config("all") == oldcfg, '540: config("all") == oldcfg');
/* restore the configation at the start of this function */
/* restore the configuration at the start of this function */
vrfy(config("all",callcfg) == oldcfg,
'541: config("all",callcfg) == oldcfg');
@@ -3156,7 +3156,7 @@ print '047: parsed test_poly()';
/*
* test_det - more determinent testing
* test_det - more determinant testing
*/
read -once "test3300";
print '048: read -once test3300';
@@ -3473,7 +3473,7 @@ print '065: parsed test_param()';
/*
* test_noarg - test missing argment functionality
* test_noarg - test missing argument functionality
*/
define test_noarg()
{
@@ -5183,7 +5183,7 @@ define test_size()
'5715: sizeof(17^139 + 674)*2 == sizeof(q)');
/*
* recipricals are the same size of their integer inverses
* reciprocals are the same size of their integer inverses
*/
q = 1/13;
print '5716: q = 1/13';
@@ -5261,7 +5261,7 @@ define test_size()
/*
* size of a matrix is the sum of the sizes of the elements
* sizeof of a matrix is the sum of the sizeofs of the elements
* sizeof of a matrix is the sum of the sizeof's of the elements
*/
mat m[] = {z,q,c};
print '5752: mat m[] = {z,q,c}';
@@ -5381,7 +5381,7 @@ define test_is()
{
local loc; /* unassigned local variable */
local a; /* assoc */
local ofd; /* open file desriptor */
local ofd; /* open file descriptor */
local cfd; /* closed file descriptor */
local blk; /* unnamed block */
local nblk; /* named block */
@@ -5398,7 +5398,7 @@ define test_is()
local object; /* object */
local rand; /* rand seed */
local random; /* random seed */
local real; /* real non-intger value */
local real; /* real non-integer value */
local prime; /* odd prime */
local square; /* square of an odd prime */
local string; /* string */
@@ -7482,7 +7482,7 @@ print '190: parsed test_somenew()';
/*
* test_exponentiation - test new exponentiation functionaltiy
* test_exponentiation - test new exponentiation functionality
*/
define test_exponentiation()
{
@@ -7573,7 +7573,7 @@ define test_quit()
quit;
prob('quit did not end the test_quit() function');
/* 8400 serise continued after return, do not print end here */
/* 8400 series continued after return, do not print end here */
}
print '191: parsed test_quit()';
@@ -7874,7 +7874,7 @@ print '8406: Ending test_quit';
/*
* test_divmod - psuedo-random tests on the // and % with various rounding modes
* test_divmod - pseudo-random tests on the // and % with various rounding modes
*/
print;
print '8500: Starting test of divmod'
@@ -7900,7 +7900,7 @@ vrfy(config("redecl_warn",0), '8651: config("redecl_warn",0)');
vrfy(config("dupvar_warn",0), '8652: config("dupvar_warn",0)');
vrfy(u_glob == 6, '8653: u_glob == 6');
global u_glob = 555;
print '8654: reclare u_glob';
print '8654: declare u_glob';
vrfy(u_glob == 555, '8655: u_glob == 555');
define func_8650(u_glob) { local u_glob; return u_glob; }
print '8656: u_glob as both local and parameter';
@@ -7928,7 +7928,7 @@ vrfy(dotest("set8700.line", 8703) == 0,
/*
* new exponentiation functionaltiy
* new exponentiation functionality
*/
print;
return test_exponentiation();
@@ -8074,7 +8074,7 @@ return test_functions2();
*
* beer.cal - prints a bunch of things when loaded
* hello.cal - designed to go into an infinite loop
* lucal.cal - already read by this file
* lucas.cal - already read by this file
* lucas_chk.cal - already read by this file
* regress.cal - this file
* surd.cal - already read by this file

20
cal/specialfunctions.cal
View File

@@ -442,8 +442,8 @@ define lngamma(z)
if (tmp2 < tmp) {
return
newerror(strcat
("lngamma(1): something happend that ",
"should not have happend"));
("lngamma(1): something happened ",
"that shouldn't have happened"));
}
}
}
@@ -519,8 +519,8 @@ define lngamma(z)
if (tmp2 < tmp) {
return
newerror(strcat
("lngamma(1): something happend ",
"that should not have happend"));
("lngamma(1): something happened ",
"that should not have happened"));
}
}
}
@@ -576,8 +576,8 @@ define lngamma(z)
if (tmp2 < tmp) {
return
newerror(strcat
("lngamma(1): something happend ",
"that should not have happend"));
("lngamma(1): something happened ",
"that should not have happened"));
}
}
}
@@ -1047,7 +1047,7 @@ define __CZ__ibeta_cf_var_dm(a, b, z, max)
}
}
if (m > max) {
return newerror("ibeta: continous fraction does not converge");
return newerror("ibeta: continuous fraction does not converge");
}
return f;
}
@@ -1290,7 +1290,7 @@ define __CZ__erfinvapprox(x)
- (2 / (pi() * a) + (ln(1 - x ^ 2)) / 2));
}
/* complementary inverse errror function, faster at about x < 1-.91
/* complementary inverse error function, faster at about x < 1-.91
Henry E. Fettis. "A stable algorithm for computing the inverse error function
in the 'tail-end' region" Math. Comp., 28:585-587, 1974.
*/
@@ -1324,7 +1324,7 @@ define __CZ__fettiscf(y, n)
return t / (1 + r);
}
/* inverse errror function, faster at about x<=.91*/
/* inverse error function, faster at about x<=.91*/
define __CZ__inverfbin(x)
{
local places approx flow fhigh eps high low mid fmid epsilon;
@@ -1370,7 +1370,7 @@ define erfinv(x)
x = -x;
flag = 1;
}
/* No need for full pecision */
/* No need for full precision */
eps = epsilon(1e-20);
if (eps >= 1e-40) {
/* Winitzki, Sergei (6 February 2008). "A handy approximation for the

2
cal/statistics.cal
View File

@@ -106,7 +106,7 @@ define invbetainc_slow(x,a,b){
GW Cran, KJ Martin, GE Thomas,
Remark AS R19 and Algorithm AS 109:
A Remark on Algorithms AS 63: The Incomplete Beta Integral
and AS 64: Inverse of the Incomplete Beta Integeral,
and AS 64: Inverse of the Incomplete Beta integral,
Applied Statistics,
Volume 26, Number 1, 1977, pages 111-114.

2
cal/test2600.cal
View File

@@ -50,7 +50,7 @@
* of b in power(a, b, eps) is large, the computation required for
* a test may be very heavy.
*
* Test funcations are called as:
* Test functions are called as:
*
* testabc(str, ..., verbose)
*

2
cal/test2700.cal
View File

@@ -84,7 +84,7 @@ define mkfrac() = rand(2) ? mkposfrac() : -mkposfrac();
define mksquarereal() = mknonnegreal()^2;
/*
* We might be able to do better than the following. For nonsquare
* We might be able to do better than the following. For non-square
* positive integer less than 1e6, could use:
* x = rand(1, 1000);
* return rand(x^2 + 1, (x + 1)^2);

2
cal/test5100.cal
View File

@@ -35,7 +35,7 @@ defaultverbose = 1; /* default verbose value */
* with zero value, when the definition is read.
*
* The variable a5100 is initialized with the value x if and when this
* function is first called with a positive even x. The varable b5100
* function is first called with a positive even x. The variable b5100
* is similarly initialized if and when this function is first called positive
* odd x.
*

2
cal/test8500.cal
View File

@@ -169,7 +169,7 @@ define divmod_8500(N = 10, M1 = 2^128, M2 = 2^64, testnum = 0)
}
/*
* seelect one of the 32 rounding modes at random
* select one of the 32 rounding modes at random
*/
rnd = rand(32);

6
cal/test8900.cal
View File

@@ -26,7 +26,7 @@ static __CZ__eps = 1e-20;
/*
* load once, the calc resource functions contribued by Christoph Zurnieden
* load once, the calc resource functions contributed by Christoph Zurnieden
*/
read -once bernpoly.cal;
read -once brentsolve.cal;
@@ -45,7 +45,7 @@ read -once intnum.cal;
/*
* tests of correctness of the functions implemented by the above listed
* author. All values tested against have been computed with at least two
* independant algorithms where possible (indicated if not).
* independent algorithms where possible (indicated if not).
*/
define t01()
{
@@ -1649,7 +1649,7 @@ define t03()
/* test 04 tests polygamma(m,z) for the following values (m==0 gets computed
* by psi()).
* Values tested against were computed with Mathematica(TM) only
* (z in the left complex halfplane does not get computed yet)
* (z in the left complex half plane does not get computed yet)
*/
define t04()
{

16
cal/toomcook.cal
View File

@@ -320,16 +320,16 @@ define toomcook4square(a){
}
/*
TODO: Implement the asymmetric variations
*/
* TODO: Implement the asymmetric variations
*/
/*
produce_long_random_number(n) returns large pseudorandom numbers. Really large
numbers, e.g.:
produce_long_random_number(16)
is ca 4,128,561 bits (ca 1,242,821 dec. digits) large. Exact length is not
predeterminable because of the chaotic output of the function random().
*/
* produce_long_random_number(n) returns large pseudo-random numbers.
* Really large numbers, e.g.:
* produce_long_random_number(16)
* is ca 4,128,561 bits (ca 1,242,821 dec. digits) large. Exact length is not
* pre-determinable because of the chaotic output of the function random().
*/
define __CZ__produce_long_random_number(n)
{
local ret k;

2
cal/unitfrac.cal
View File

@@ -1,5 +1,5 @@
/*
* unixfrac - represent a fraction as a sum of distince unit fractions
* unixfrac - represent a fraction as a sum of distance unit fractions
*
* Copyright (C) 1999 David I. Bell
*

4
cal/zeta2.cal
View File

@@ -34,7 +34,7 @@ define hurwitzzeta(s,a){
/*
According to Linas Vepstas' "An efficient algorithm for accelerating
the convergence of oscillatory series, useful for computing the
polylogarithm and Hurwitz zeta functions" the Euler-Maclaurin series
poly-logarithm and Hurwitz zeta functions" the Euler-Maclaurin series
is the fastest in most cases.
With a lot of help of the PARI/GP implementation by Prof. Henri Cohen,
@@ -78,7 +78,7 @@ define hurwitzzeta(s,a){
print "limit = " limit;
print "prec = " precision;
}
/* Full precison plus 5 digits angstzuschlag*/
/* Full precision plus 5 digits angstzuschlag*/
epsilon( (10^(-precision)) * 1e-5);
tmp3=(a+limit_function+0.)^(-s);
sum3 = tmp3/2;