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Release calc version 2.11.0t10

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This commit is contained in:
Landon Curt Noll
1999-11-11 05:15:39 -08:00
parent 86c8e6dcf1
commit 96c34adee3
283 changed files with 2380 additions and 3032 deletions
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6
help/Makefile
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@@ -153,7 +153,7 @@ all: ${FULL_HELP_FILES} full ${DETAIL_HELP} ${DETAIL_CLONE} \
# used by the upper level Makefile to determine of we have done all
#
# 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-emoty else clause for every if condition. *sigh*
#
.all:
rm -f .all
@@ -341,7 +341,7 @@ ${SINGULAR_FILES}: ${PLURAL_FILES}
# Form the builtin file
#
# We ave a "chicken-and-egg" problem. We want the builtn help file to
# accurately reflect the function list. It would be nice if we could
# accurately reflect the function list. It would be nice if we could
# just execute calc show builtin, but calc may not have been built or
# buildable at this point. The hack-a-round used is to convert ../func.c
# into a standalone program that generates a suitable function list
@@ -379,7 +379,7 @@ builtin: builtin.top builtin.end ../func.c funclist.sed
##
#
# File list generation. You can ignore this section.
# File list generation. You can ignore this section.
#
#
# We will form the names of source files as if they were in a

2
help/acosh
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@@ -17,7 +17,7 @@ DESCRIPTION
acosh(x) is the nonnegative real number v for which cosh(v) = x.
It is given by
acosh(x) = ln(x + sqrt(x^2 - 1))
acosh(x) = ln(x + sqrt(x^2 - 1))
EXAMPLE
> print acosh(2, 1e-5), acosh(2, 1e-10), acosh(2, 1e-15), acosh(2, 1e-20)

2
help/acoth
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@@ -16,7 +16,7 @@ DESCRIPTION
acoth(x) is the real number v for which coth(v) = x.
It is given by
acoth(x) = ln((x + 1)/(x - 1))/2
acoth(x) = ln((x + 1)/(x - 1))/2
EXAMPLE
> print acoth(2, 1e-5), acoth(2, 1e-10), acoth(2, 1e-15), acoth(2, 1e-20)

2
help/acsch
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@@ -16,7 +16,7 @@ DESCRIPTION
acsch(x) is the real number v for which csch(v) = x. It is given by
acsch(x) = ln((1 + sqrt(1 + x^2))/x)
acsch(x) = ln((1 + sqrt(1 + x^2))/x)
EXAMPLE

6
help/address
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@@ -20,7 +20,7 @@ DESCRIPTION
otherwise accessing, such a vacated address may be catastrophic.
An octet is normally expressed by B[i] where B is a block and
0 <= i < sizeof(B). &B[i] then returns the address at which this
0 <= i < sizeof(B). &B[i] then returns the address at which this
octet is located until the block is freed or relocated. Freeing
of an unnamed block B occurs when a new value is assigned to B or
when B ceases to exist; a named block B is freed by blkfree(B().
@@ -96,7 +96,7 @@ DESCRIPTION
> define f(a) = 27 + a;
the three occurrences of 27 have the same address which may be displayed
by any of &27, &*x, &*y and &f(0). If x and y are assigned
by any of &27, &*x, &*y and &f(0). If x and y are assigned
other values and f is redefined or undefined and the 27 has not been
stored elsewhere (e.g. as the "old value" or in another function
definition or as an element in an association), the address assigned at
@@ -105,7 +105,7 @@ DESCRIPTION
When a function returns a number value, that number value is usually
placed at a newly allocated address, even if an equal number is stored
elsewhere. For example calls to f(a), as defined above, with the same
elsewhere. For example calls to f(a), as defined above, with the same
non-zero value for a will be assigned to different addresses as can be
seen from printing &*A, &*B, &*C after

2
help/appr
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@@ -84,7 +84,7 @@ DESCRIPTION
Complex x:
Returns appr(re(x), y, z) + appr(im(x), y, z) * 1i
Returns appr(re(x), y, z) + appr(im(x), y, z) * 1i
PROPERTIES
If appr(x,y,z) != x, then abs(x - appr(x,y,z)) < abs(y).

2
help/asech
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@@ -16,7 +16,7 @@ DESCRIPTION
asech(x) is the real number v for which sech(v) = x. It is given by
asech(x) = ln((1 + sqrt(1 - x^2))/x)
asech(x) = ln((1 + sqrt(1 - x^2))/x)
EXAMPLE
> print asech(.5,1e-5), asech(.5,1e-10), asech(.5,1e-15), asech(.5,1e-20)

2
help/asinh
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@@ -16,7 +16,7 @@ DESCRIPTION
asinh(x) is the real number v for which sinh(v) = x. It is given by
asinh(x) = ln(x + sqrt(1 + x^2))
asinh(x) = ln(x + sqrt(1 + x^2))
EXAMPLE
> print asinh(2, 1e-5), asinh(2, 1e-10), asinh(2, 1e-15), asinh(2, 1e-20)

4
help/assign
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@@ -44,7 +44,7 @@ DESCRIPTION
In simple assignments, = associates from right to left so that, for
example,
a = b = c
a = b = c
has the effect of a = (b = c) and results in assigning the value of c
to both a and b. The expression (a = b) = c is acceptable, but has the
@@ -66,7 +66,7 @@ DESCRIPTION
that of A[0] = A[1].
If, in execution of a = b, a is changed by the evaluation of b, the
value of b may be stored in an unintended or inaccessible location. For
value of b may be stored in an unintended or inaccessible location. For
example,
mat A[2]= {1,2};
A[0] = (A = 3);

4
help/assoc
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@@ -14,7 +14,7 @@ DESCRIPTION
assignments of the forms
A[a_1] = v_1
A[a_1, a_2] = v_2
A[a_1, a_2] = v_2
A[a_1, a_2, a_3] = v_3
A[a_1, a_2, a_3, a_4] = v_4
@@ -53,7 +53,7 @@ DESCRIPTION
a sequential scan through the elements difficult.
The search and rsearch functions can search for an element in an
association which has the specified value. They return the index
association which has the specified value. They return the index
of the found element, or a NULL value if the value was not found.
Associations can be copied by an assignment, and can be compared

4
help/base
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@@ -18,8 +18,8 @@ DESCRIPTION
The following convention is used to declare modes:
base config
value string
base config
value string
2 "binary" binary fractions
8 "octal" octal fractions

2
help/bit
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@@ -11,7 +11,7 @@ TYPES
return int
DESCRIPTION
Determine if the binary bit y is set in x. If:
Determine if the binary bit y is set in x. If:
x
int(---) mod 2 == 1

8
help/blk
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@@ -26,7 +26,7 @@ DESCRIPTION
... , B[len-1], these all initially having zero value.
The octets B[i] for i >= len always have zero value. If B[i] with
some i >= len is referenced, len is increased by 1. For example:
some i >= len is referenced, len is increased by 1. For example:
B[i] = x
@@ -70,7 +70,7 @@ DESCRIPTION
If a block value B created by B = blk(len, chunk) is assigned to
another variable by C = B, a new block of the same structure as B
is created to become the value of C, and the octets in B are copied
to this new block. A block with possibly different length or
to this new block. A block with possibly different length or
chunksize is created by C = blk(B, newlen, newchunk), only the first
min(len, newlen) octets being copied from B; later octets are
assigned zero value. If omitted, newlen and newchunk default to
@@ -120,14 +120,14 @@ DESCRIPTION
last two avoid printing of the new value for A.
Named blocks are assigned index numbers 0, 1, 2, ..., in the order
of their creation. The block with index id is returned by blocks(id).
of their creation. The block with index id is returned by blocks(id).
With no argument, blocks() returns the number of current unfreed
named blocks. A named block may be used
The memory allocated to a named block is freed by the blkfree()
function with argument the named block, its name, or its id number.
The block remains in existence but with a null data pointer,
its length and size being reduced to zero. A new block of memory
its length and size being reduced to zero. A new block of memory
may be allocated to it, with possibly new length and chunksize by:
blk(val [, len, chunk])

2
help/blkcpy
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@@ -90,7 +90,7 @@ DESCRIPTION
so that num can be at most size(B) - ssi.
For copying to a block B (named or unnamed), reallocation will be
required if dsi + num > sizeof(B). (This will not be permitted if
required if dsi + num > sizeof(B). (This will not be permitted if
protect(B) has bit 4 set.)
For copying from a file stream fs, num can be at most size(fs) - ssi.

12
help/blkfree
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@@ -12,7 +12,7 @@ TYPES
DESCRIPTION
If val is a named block, or the name of a named block, or the
identifying index for a named block, blkfree(val) frees the
memory block allocated to this named block. The block remains
memory block allocated to this named block. The block remains
in existence with the same name, identifying index, and chunksize,
but its size and maxsize becomes zero and the pointer for the start
of its data block null.
@@ -26,16 +26,16 @@ EXAMPLE
> B1 = blk("foo")
> B2 = blk("Second block")
show blocks
id name
id name
---- -----
0 foo
1 Second block
0 foo
1 Second block
> blkfree(B1)
> show blocks
id name
id name
---- -----
1 Second block
1 Second block
> B1
block 0: foo

4
help/bround
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@@ -12,7 +12,7 @@ TYPES
Otherwise, if x is an object of type tt, or if x is not an object or
number but y is an object of type tt, and the function tt_bround has
to be defined; the types for x, plcs, rnd, and the returned value,
if any, are as required for specified in tt_bround. For the object
if any, are as required for specified in tt_bround. For the object
case, plcs and rnd default to the null value.
For other cases:
@@ -31,7 +31,7 @@ DESCRIPTION
If the number of binary places is n and eps = 10^-n, the
result is the same as for appr(x, eps, rnd). This will be
exactly x if x is a multiple of eps; otherwise rounding occurs
to one of the nearest multiples of eps on either side of x. Which
to one of the nearest multiples of eps on either side of x. Which
of these multiples is returned is determined by z = rnd & 31, i.e.
the five low order bits of rnd, as follows:

24
help/builtin.end
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@@ -4,25 +4,25 @@
to be set or read. If only one argument is given, then the current
value of the named parameter is returned. If two arguments are given,
then the named parameter is set to the value of the second argument,
and the old value of the parameter is returned. Therefore you can
and the old value of the parameter is returned. Therefore you can
change a parameter and restore its old value later. The possible
parameters are explained in the next section.
The scale function multiplies or divides a number by a power of 2.
This is used for fractional calculations, unlike the << and >>
operators, which are only defined for integers. For example,
operators, which are only defined for integers. For example,
scale(6, -3) is 3/4.
The quomod function is used to obtain both the quotient and remainder
of a division in one operation. The first two arguments a and b are
of a division in one operation. The first two arguments a and b are
the numbers to be divided. The last two arguments c and d are two
variables which will be assigned the quotient and remainder. For
nonnegative arguments, the results are equivalent to computing a//b
and a%b. If a is negative and the remainder is nonzero, then the
quotient will be one less than a//b. This makes the following three
properties always hold: The quotient c is always an integer. The
properties always hold: The quotient c is always an integer. The
remainder d is always 0 <= d < b. The equation a = b * c + d always
holds. This function returns 0 if there is no remainder, and 1 if
holds. This function returns 0 if there is no remainder, and 1 if
there is a remainder. For examples, quomod(10, 3, x, y) sets x to 3,
y to 1, and returns the value 1, and quomod(-4, 3.14159, x, y) sets x
to -2, y to 2.28318, and returns the value 1.
@@ -37,8 +37,8 @@
The digit and bit functions return individual digits of a number,
either in base 10 or in base 2, where the lowest digit of a number
is at digit position 0. For example, digit(5678, 3) is 5, and
bit(0b1000100, 2) is 1. Negative digit positions indicate places
is at digit position 0. For example, digit(5678, 3) is 5, and
bit(0b1000100, 2) is 1. Negative digit positions indicate places
to the right of the decimal or binary point, so that for example,
digit(3.456, -1) is 4.
@@ -139,11 +139,11 @@
The functions rcin, rcmul, rcout, rcpow, and rcsq are used to
perform modular arithmetic calculations for large odd numbers
faster than the usual methods. To do this, you first use the
faster than the usual methods. To do this, you first use the
rcin function to convert all input values into numbers which are
in a format called REDC format. Then you use rcmul, rcsq, and
in a format called REDC format. Then you use rcmul, rcsq, and
rcpow to multiply such numbers together to produce results also
in REDC format. Finally, you use rcout to convert a number in
in REDC format. Finally, you use rcout to convert a number in
REDC format back to a normal number. The addition, subtraction,
negation, and equality comparison between REDC numbers are done
using the normal modular methods. For example, to calculate the
@@ -185,8 +185,8 @@
The following convention is used to declare modes:
base config
value string
base config
value string
2 "binary" binary fractions
8 "octal" octal fractions

4
help/builtin.top
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@@ -1,8 +1,8 @@
Builtin functions
There is a large number of built-in functions. Many of the
There is a large number of built-in functions. Many of the
functions work on several types of arguments, whereas some only
work for the correct types (e.g., numbers or strings). In the
work for the correct types (e.g., numbers or strings). In the
following description, this is indicated by whether or not the
description refers to values or numbers. This display is generated
by the 'show builtin' command.

2
help/calclevel
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@@ -10,7 +10,7 @@ TYPES
DESCRIPTION
This function returns the calculation level at which it is called.
When a command is being read from a terminal or from a file,
calc is at calculation level zero. The level is increased
calc is at calculation level zero. The level is increased
by 1 each time calculation starts of a user-defined function
or of eval(S) for some expression S which evaluates to a string. It
decreases to zero if an error occurs or a quit or abort statement

4
help/cfappr
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@@ -6,7 +6,7 @@ SYNOPSIS
TYPES
x real
eps real with abs(eps) < 1, defaults to epsilon()
eps real with abs(eps) < 1, defaults to epsilon()
n real with n >= 1
rnd integer, defaults to config("cfappr")
@@ -21,7 +21,7 @@ DESCRIPTION
If n >= 1 and den(x) > n, cfappr(x, n) returns the nearest above,
nearest below, or nearest, approximation to x with denominator less
than or equal to n. If den(x) <= n, cfappr(x,n) returns x.
than or equal to n. If den(x) <= n, cfappr(x,n) returns x.
In either case when the result v is not x, how v relates to x is
determined by bits 0, 1, 2 and 4 of the argument rnd in the same way as

6
help/cfsim
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@@ -30,7 +30,7 @@ DESCRIPTION
This corresponds to the use of rnd for functions like round(x, n, rnd).
If bit 3 or 4 of rnd is set, the lower order bits are ignored; bit 3
is ignored if bit 4 is set. Thusi, for rnd > 3, it sufficient to
is ignored if bit 4 is set. Thusi, for rnd > 3, it sufficient to
consider the two cases rnd = 8 and rnd = 16.
If den(x) > 2, cfsim(x, 8) returns the value of the penultimate simple
@@ -55,7 +55,7 @@ DESCRIPTION
rnd integer x half-integer x den(x) > 2
8 0 x - sgn(x)/2 approximant
8 0 x - sgn(x)/2 approximant
16 x - sgn(x) x + sgn(x)/2 nearest
From either cfsim(x, 0) and cfsim(x, 1), the other is easily
@@ -72,7 +72,7 @@ DESCRIPTION
Iteration of cfsim(x,8) until an integer is obtained gives a sequence of
"good" approximations to x with decreasing denominators and
correspondingly decreasing accuracy; each denominator is less than half
the preceding denominator. (Unlike the "forward" sequence of
the preceding denominator. (Unlike the "forward" sequence of
continued-fraction approximants these are not necessarily alternately
greater than and less than x.)

4
help/cmp
View File

@@ -17,7 +17,7 @@ TYPES
return if x and y are both real: -1, 0, or 1
if x and y are both numbers but not both real:
-1, 0, 1, -1+1i, 1i, 1+1i, -1-1i, -1i, or 1-1i
-1, 0, 1, -1+1i, 1i, 1+1i, -1-1i, -1i, or 1-1i
if x and y are both strings: -1, 0, or 1
all other cases: the null value
@@ -47,7 +47,7 @@ DESCRIPTION
obj point {x,y};
if points with real components are to be partially ordered by their
euclidean distance from the origin, an appropriate point_rel
euclidean distance from the origin, an appropriate point_rel
function may be that given by
define point_rel(a,b) = sgn(a.x^2 + a.y^2 - b.x^2 - b.y^2);

14
help/command
View File

@@ -3,7 +3,7 @@ Command sequence
This is a sequence of any the following command formats, where
each command is terminated by a semicolon or newline. Long command
lines can be extended by using a back-slash followed by a newline
character. When this is done, the prompt shows a double angle
character. When this is done, the prompt shows a double angle
bracket to indicate that the line is still in progress. Certain
cases will automatically prompt for more input in a similar manner,
even without the back-slash. The most common case for this is when
@@ -25,7 +25,7 @@ Command sequence
The second form defines a simple function which calculates
the specified expression value from the specified parameters.
The expression cannot be a statement. However, the comma
and question mark operators can be useful. Examples of
and question mark operators can be useful. Examples of
simple functions are:
define sumcubes(a, b) = a^3 + b^3
@@ -45,7 +45,7 @@ Command sequence
read filename
read -once filename
This reads definitions from the specified filename.
The name can be quoted if desired. The calculator
The name can be quoted if desired. The calculator
uses the CALCPATH environment variable to search
through the specified directories for the filename,
similarly to the use of the PATH environment variable.
@@ -54,7 +54,7 @@ Command sequence
directory followed by a general calc library directory).
The ".cal" extension is defaulted for input files, so
that if "filename" is not found, then "filename.cal" is
then searched for. The contents of the filename are
then searched for. The contents of the filename are
command sequences which can consist of expressions to
evaluate or functions to define, just like at the top
level command level.
@@ -82,7 +82,7 @@ Command sequence
later read in order to recreate the variable values.
For speed reasons, values are written as hex fractions.
This command currently only saves simple types, so that
matrices, lists, and objects are not saved. Function
matrices, lists, and objects are not saved. Function
definitions are also not saved.
If the -m mode disallows opening of files for writing,
@@ -247,7 +247,7 @@ Command sequence
> <==== calc interactive prompt
because the '-i' calc causes ABORT to drop into an
interactive prompt. However typing a QUIT or ABORT
interactive prompt. However typing a QUIT or ABORT
at the interactive prompt level will always calc to exit,
even when calc is invoked with '-i'.
@@ -304,5 +304,5 @@ Command sequence
Also see the help topic:
statement flow control and declaration statements
statement flow control and declaration statements
usage how to invoke the calc command and calc -options

32
help/config
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@@ -1,10 +1,10 @@
Configuration parameters
Configuration parameters affect how the calculator performs certain
operations. Among features that are controlled by these parameters
operations. Among features that are controlled by these parameters
are the accuracy of some calculations, the displayed format of results,
the choice from possible alternative algorithms, and whether or not
debugging information is displayed. The parameters are
debugging information is displayed. The parameters are
read or set using the "config" built-in function; they remain in effect
until their values are changed by a config or equivalent instruction.
The following parameters can be specified:
@@ -65,7 +65,7 @@ Configuration parameters
It allows functions to control their configuration without impacting
the calling function.
There are two configuration state aliases that may be set. To
There are two configuration state aliases that may be set. To
set the backward compatible standard configuration:
config("all", "oldstd")
@@ -105,7 +105,7 @@ Configuration parameters
the decimal point to be printed in real or exponential mode in
normal unformatted printing (print, strprint, fprint) or in
formatted printing (printf, strprintf, fprintf) when precision is not
specified. The initial value for oldstd is 20, for newstd 10.
specified. The initial value for oldstd is 20, for newstd 10.
The parameter may be changed to the value d by either
config("display", d) or by display (d). This parameter does not change
the stored value of a number. Where rounding is necessary to
@@ -116,7 +116,7 @@ Configuration parameters
calculation of functions for which exact values are not possible or
not desired. For most functions, the
remainder = exact value - calculated value
remainder = exact value - calculated value
has absolute value less than epsilon, but, except when the sign of
the remainder is controlled by an appropriate parameter, the
@@ -133,7 +133,7 @@ Configuration parameters
The "mode" parameter is a string specifying the mode for printing of
numbers by the unformatted print functions, and the default
("%d" specifier) for formatted print functions. The initial mode
is "real". The available modes are:
is "real". The available modes are:
"frac" decimal fractions
"int" decimal integer
@@ -152,10 +152,10 @@ Configuration parameters
runs in a time of O(N^2). The second method is a recursive and
complicated method which runs in a time of O(N^1.585). The argument
for these parameters is the number of binary words at which the
second algorithm begins to be used. The minimum value is 2, and
second algorithm begins to be used. The minimum value is 2, and
the maximum value is very large. If 2 is used, then the recursive
algorithm is used all the way down to single digits, which becomes
slow since the recursion overhead is high. If a number such as
slow since the recursion overhead is high. If a number such as
1000000 is used, then the recursive algorithm is never used, causing
calculations for large numbers to slow down. For a typical example
on a 386, the two algorithms are about equal in speed for a value
@@ -174,9 +174,9 @@ Configuration parameters
Redc2 specifies the sizes of numbers at which calc switches from
its first to its second algorithm when using the REDC algorithm.
The first algorithm performs a multiply and a modular reduction
together in one loop which runs in O(N^2). The second algorithm
together in one loop which runs in O(N^2). The second algorithm
does the REDC calculation using three multiplies, and runs in
O(N^1.585). The argument for redc2 is the size of the modulus at
O(N^1.585). The argument for redc2 is the size of the modulus at
which the second algorithm begins to be used.
Config("tilde") controls whether or not a leading tilde ('~') is
@@ -185,7 +185,7 @@ Configuration parameters
specified maximum number. The initial "tilde" value is 1.
Config ("tab") controls the printing of a tab before results
automatically displayed when working interactively. It does not
automatically displayed when working interactively. It does not
affect the printing by the functions print, printf, etc. The initial
"tab" value is 1.
@@ -271,7 +271,7 @@ Configuration parameters
The default is to print only the first 256 octets.
The "blkverbose" determines if all lines, including duplicates
should be printed. If TRUE, then all lines are printed. If false,
should be printed. If TRUE, then all lines are printed. If false,
duplicate lines are skipped and only a "*" is printed in a style
similar to od. This config value has not meaning if "blkfmt" is "str".
@@ -319,7 +319,7 @@ Configuration parameters
The "calc_debug" is intended for controlling internal calc routines
that test its operation, or collect or display information that
might be useful for debug purposes. Much of the output from these
might be useful for debug purposes. Much of the output from these
will make sense only to calc wizards. Zero value (the default for
both oldstd and newstd) of config("lib_calc") corresponds to switching
off all these routines. For nonzero value, particular bits
@@ -401,16 +401,16 @@ Configuration parameters
The following are synonyms for true:
"on" "yes" "y" "true" "t" "1" any non-zero number
"on" "yes" "y" "true" "t" "1" any non-zero number
The following are synonyms for false:
"off" "no" "n" "false" "f" "0" the number zero (0)
"off" "no" "n" "false" "f" "0" the number zero (0)
Examples of setting some parameters are:
config("mode", "exp"); exponential output
config("display", 50); 50 digits of output
epsilon(epsilon() / 8); 3 bits more accuracy
config("tilde", 0) disable roundoff tilde printing
config("tilde", 0) disable roundoff tilde printing
config("tab", "off") disable leading tab printing

2
help/contrib
View File

@@ -40,7 +40,7 @@ You should send submissions to:
[[ Replace 'at' with @, 'dot' is with . and remove the spaces ]]
Thanks for considering submitting code to calc. Calc is a collective
Thanks for considering submitting code to calc. Calc is a collective
work by a number of people. It would not be what it is today without
your efforts and submissions!

2
help/credit
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@@ -15,7 +15,7 @@ Credits
hist.c which is used to do the command line editing.
Thanks to Ernest W. Bowen for supplying many improvements in
accuracy and generality for some numeric functions. Much of
accuracy and generality for some numeric functions. Much of
this was in terms of actual code which I gratefully accepted.
Ernest also supplied the original text for many of the help files.

4
help/custom
View File

@@ -28,7 +28,7 @@ DESCRIPTION
calc -C
In other words, explicit action must be taken in order to
enable the use of custom functions. By default (no -C arg)
enable the use of custom functions. By default (no -C arg)
custom functions are compiled in but disabled so that only
portable calc scripts may be used.
@@ -36,7 +36,7 @@ DESCRIPTION
multi-precision calculations in a C-like environment. You should
consider implementing algorithms in the calc language as a first
choice. Sometimes an algorithm requires use of special hardware, a
non-portable OS or pre-compiled C library. In these cases a custom
non-portable OS or pre-compiled C library. In these cases a custom
interface may be needed.
The custom function interface is intended to make is easy for

2
help/define
View File

@@ -9,7 +9,7 @@ Function definitions
by a return statement, and the function definition is ended with a
right brace.
There are some subtle differences, however. The types of parameters
There are some subtle differences, however. The types of parameters
and variables are not defined at compile time, and may vary during
execution and be different in different calls to the function. For
example, a two-argument function add may be defined by

2
help/den
View File

@@ -11,7 +11,7 @@ TYPES
DESCRIPTION
For real x, den(x) returns the denominator of x when x is expressed
in lowest terms with positive denominator. In calc,
in lowest terms with positive denominator. In calc,
real values are actually rational values. Each calc real
value can be uniquely expressed as:

2
help/environment
View File

@@ -14,7 +14,7 @@ Environment variables
/usr/local/lib/calc
This value is used by the READ command. It is an error
This value is used by the READ command. It is an error
if no such readable file is found.
The CALCBINDINGS file searches the CALCPATH as well.

2
help/errorcodes.sed
View File

@@ -1 +1 @@
/^#define E_[^_].*[ ][1-9][0-9]*[ ]\/\* .* \*\//s/#define E_.*[ ]\([1-9][0-9]*\)[ ]*\/\* \(.*\)[ ][ ]*\*\// \1 \2/p
/^#define E_[^_].*[ ][1-9][0-9]*[ ]\/\* .* \*\//s/#define E_.*[ ]\([1-9][0-9]*\)[ ]*\/\* \(.*\)[ ][ ]*\*\// \1 \2/p

2
help/eval
View File

@@ -11,7 +11,7 @@ TYPES
DESCRIPTION
For eval(str), the value of str is to be a string that could be the body
of the definition of a function f(). This string may declare local
of the definition of a function f(). This string may declare local
variables and include keywords (while, for, ...) other than the
reserved keywords (define, show, help, read, write, show, cd) intended
for interactive use or for reading from a file.

2
help/exp
View File

@@ -1,5 +1,5 @@
NAME
exp - exponential function
exp - exponential function
SYNOPSIS
exp(x [,eps])

2
help/factor
View File

@@ -14,7 +14,7 @@ TYPES
DESCRIPTION
If n >= 0 and n has a prime factor less than or equal to limit,
factor(n, limit) returns the smallest such factor. If n >= 0
factor(n, limit) returns the smallest such factor. If n >= 0
and the smallest prime factor of n exceeds limit, 1 is returned.
In particular, if n >= 0 and limit <= 1, factor(n, limit)
always returns 1; factor(n,2) returns 2 if and only if n is even.

4
help/fclose
View File

@@ -13,7 +13,7 @@ DESCRIPTION
This function closes the open file associated with the descriptor fd.
When this is done, the file value associated with the file remains
a file value, but appears 'closed', and cannot be used in further
file-related calls (except fclose) without causing errors. This same
file-related calls (except fclose) without causing errors. This same
action occurs to all copies of the file value. You do not need to
explicitly close all the copies of a file value.
@@ -26,7 +26,7 @@ DESCRIPTION
there had been an error using the file, or the null value if
there was no error.
Closing a closed file is permitted. Fclose returns null in
Closing a closed file is permitted. Fclose returns null in
this case.
EXAMPLE

8
help/feof
View File

@@ -14,7 +14,7 @@ DESCRIPTION
is set or clear.
The end-of-file flag for the stream fd is set if reading at the
end-of-file position is attempted. The flag is cleared by
end-of-file position is attempted. The flag is cleared by
positioning operations (fseek, rewind, fsetpos) and by freopen.
EXAMPLE
@@ -23,14 +23,14 @@ EXAMPLE
> fflush(fd1)
> fd2 = fopen("/tmp/newfile", "r")
> feof(fd2)
0
0
> fgetline(fd2)
"Chongo was here"
> feof(fd2)
0
0
> fgetline(fd2)
> feof(fd2)
1
1
LIMITS
none

2
help/ferror
View File

@@ -20,7 +20,7 @@ DESCRIPTION
EXAMPLE
> fd = fopen("/etc/motd", "r")
> ferror(fd)
0
0
LIMITS
fd must be associaed with an open file

2
help/fgetc
View File

@@ -14,7 +14,7 @@ DESCRIPTION
associated with fd.
If there is a next character, this function returns a 1
character string containing that character. In the case
character string containing that character. In the case
of EOF or error, nil is returned.
EXAMPLE

2
help/fgetfield
View File

@@ -16,7 +16,7 @@ DESCRIPTION
characters are skipped. If the reading reaches end-of-file, the
null value is returned. If non-whitespace is encountered, formation
of a string begins, continuing until whitespace of '\0' or end-of-file
is reached. The returned value is this string (terminated as usual
is reached. The returned value is this string (terminated as usual
by a null character). After the operation, the file position will
be immediately after the first whitespace character of '\0' or at
end-of-file.

2
help/fgetline
View File

@@ -14,7 +14,7 @@ DESCRIPTION
the open file associated with fd. Unlike fgets, the trailing
newline is removed from the return string.
Empty lines return the null string. When the end of file is reached,
Empty lines return the null string. When the end of file is reached,
fgetline returns the null value. (Note the distinction between a null
string and a null value.)

18
help/file
View File

@@ -6,7 +6,7 @@ Using files
Some differences do occur, as will be explained here.
Names of files are subject to ~ expansion just like the C or
Korn shell. For example, the file name:
Korn shell. For example, the file name:
~/.rc.cal
@@ -19,8 +19,8 @@ Using files
A file can be opened for either reading, writing, or appending.
To do this, the 'fopen' function is used, which accepts a filename
and an open mode, both as strings. You use 'r' for reading, 'w'
for writing, and 'a' for appending. For example, to open the file
and an open mode, both as strings. You use 'r' for reading, 'w'
for writing, and 'a' for appending. For example, to open the file
'foo' for reading, the following could be used:
fd = fopen('foo', 'r');
@@ -53,7 +53,7 @@ Using files
The 'fclose' function is used to close a file which had been opened.
When this is done, the file value associated with the file remains
a file value, but appears 'closed', and cannot be used in further
file-related calls (except fclose) without causing errors. This same
file-related calls (except fclose) without causing errors. This same
action occurs to all copies of the file value. You do not need to
explicitly close all the copies of a file value. The 'fclose'
function returns the numeric value of errno if there had been an
@@ -67,7 +67,7 @@ Using files
print "error #" : badfile : ":", errno(badfile);
}
File values can be printed. When this is done, the filename of the
File values can be printed. When this is done, the filename of the
opened file is printed inside of quote marks. If the file value had
been closed, then the null string is printed. If a file value is the
result of a top-level expression, then in addition to the filename,
@@ -75,7 +75,7 @@ Using files
status is also displayed.
File values can be used inside of 'if' tests. When this is done,
an opened file is TRUE, and a closed file is FALSE. As an example
an opened file is TRUE, and a closed file is FALSE. As an example
of this, the following loop will print the names of all the currently
opened non-standard files with their indexes, and then close them:
@@ -89,9 +89,9 @@ Using files
The functions to read from files are 'fgetline' and 'fgetc'.
The 'fgetline' function accepts a file value, and returns the next
input line from a file. The line is returned as a string value, and
does not contain the end of line character. Empty lines return the
does not contain the end of line character. Empty lines return the
null string. When the end of file is reached, fgetline returns the
null value. (Note the distinction between a null string and a null
null value. (Note the distinction between a null string and a null
value.) If the line contained a numeric value, then the 'eval'
function can then be used to convert the string to a numeric value.
Care should be used when doing this, however, since eval will
@@ -103,7 +103,7 @@ Using files
The 'printf' and 'fprintf' functions are used to print results to a
file (which could be stdout or stderr). The 'fprintf' function
accepts a file variable, whereas the 'printf' function assumes the
use of 'files(1)' (stdout). They both require a format string, which
use of 'files(1)' (stdout). They both require a format string, which
is used in almost the same way as in normal C. The differences come
in the interpretation of values to be printed for various formats.
Unlike in C, where an unmatched format type and value will cause

2
help/files
View File

@@ -25,7 +25,7 @@ DESCRIPTION
files are already open by the calculator and cannot be closed.
When calc starts up, it scans for open file descriptors above
stderr (2) and below MAXFILES (20). Any open descriptor found
stderr (2) and below MAXFILES (20). Any open descriptor found
is assumed to be an open file opened in an unknown mode. Calc
will try to read and write to this file when directed.

2
help/fopen
View File

@@ -20,7 +20,7 @@ DESCRIPTION
"a" appending
Names of files are subject to ~ expansion just like the C or
Korn shell. For example, the file name:
Korn shell. For example, the file name:
~/lib/gleet

6
help/fputstr
View File

@@ -6,7 +6,7 @@ SYNOPSIS
TYPES
fs file stream open for writing
s_1, ... string
s_1, ... string
return null or error value
@@ -22,9 +22,9 @@ EXAMPLE
> fputstr(f, "Alpha", "Beta")
> freopen(f, "r")
> fgetstr(f)
"Alpha"
"Alpha"
> fgetstr(f)
"Beta"
"Beta"
> fgetstr(f)
>
> fputstr(f, "Gamma")

4
help/free
View File

@@ -5,14 +5,14 @@ SYNOPSIS
free(a, b, ...)
TYPES
a, b, ... any
a, b, ... any
return null value
DESCRIPTION
Those of the arguments a, b, ... that specify lvalues are assigned
the null value, effectively freeing whatever memory is used to
store their current values. Other arguments are ignored.
store their current values. Other arguments are ignored.
free(.) frees the current "old value".

16
help/freeglobals
View File

@@ -19,10 +19,10 @@ EXAMPLE
Name Level Type
---- ----- -----
a 1 real = 2
a 0 real = 1
b 0 list
c 0 matrix
a 1 real = 2
a 0 real = 1
b 0 list
c 0 matrix
Number: 4
> freeglobals()
@@ -30,10 +30,10 @@ EXAMPLE
Name Level Type
---- ----- -----
a 1 null
a 0 null
b 0 null
c 0 null
a 1 null
a 0 null
b 0 null
c 0 null
Number: 4

4
help/freeredc
View File

@@ -15,8 +15,8 @@ EXAMPLE
> a = rcin(10,27)
> b = rcin(10,15)
> show redc
0 1 27
1 2 15
0 1 27
1 2 15
> freeredc()
> show redc
>

2
help/freestatics
View File

@@ -26,7 +26,7 @@ EXAMPLE
Name Scopes Type
---- ------ -----
a 1 0 real = 6
a 1 0 real = 6
Number: 1
> freestatics()

2
help/frem
View File

@@ -14,7 +14,7 @@ DESCRIPTION
If x and y are not zero and n is the largest non-negative integer
for which y^n is a divisor of x, frem(x,y) returns abs(x/y^n).
In particular, abs(x) is returned if x is not divisible by
y or if abs(y) = 1. If abs(y) > 1, frem(x,y) is the greatest
y or if abs(y) = 1. If abs(y) > 1, frem(x,y) is the greatest
divisor of x not divisible by y.
For all x, frem(x,0) is defined to equal abs(x).

2
help/freopen
View File

@@ -18,7 +18,7 @@ DESCRIPTION
With three arguments, fs, if open, is closed, and an attempt is made to
open the file with the specified name and assign it to the stream
fs. A non-null value is returned only if the attempt fails.
fs. A non-null value is returned only if the attempt fails.
EXAMPLE

8
help/fscanf
View File

@@ -31,7 +31,7 @@ DESCRIPTION
'%'. A single '%' read from fmt is taken to indicate the beginning of
a conversion specification field consisting in succession of:
an optional '*',
an optional '*',
optional decimal digits,
one of 'c', 's', 'n', 'f', 'e', 'i' or a scanset specifier.
@@ -40,7 +40,7 @@ DESCRIPTION
other sequence of characters follows the '%', characters before the
first exceptional character (which could be the terminating null
character of the fmt string) are ignored, e.g. the sequence " %*3d " does
the same as " d ". If there is no '*' at the beginning of the specifier,
the same as " d ". If there is no '*' at the beginning of the specifier,
and the list x_1, x_2, ... has not been exhausted,
a value will be assigned to the next lvalue in the list; if no lvalue
remains, the reading of fs stops and the function returns the number
@@ -68,7 +68,7 @@ DESCRIPTION
The cases 'f', 'e', 'r', 'i' may be considered to indicate expectation of
floating-point, exponential, ratio, or integer representation of the
number to be read. For example, 'i'
number to be read. For example, 'i'
might be taken to suggest a number like +2345; 'r' might suggest
a representation like -27/49; 'e' might suggest a representation like
1.24e-7; 'f' might suggest a representation like 27.145. However, there
@@ -82,7 +82,7 @@ DESCRIPTION
2+3/4*7i+3.15e7
would be interpreted as for an ordinary evaluation. A decimal fraction
would be interpreted as for an ordinary evaluation. A decimal fraction
may have more than one dot: dots after the first, which is taken to be
the decimal point, are ignored. Thus "12.3..45e6.7" is interpreted
as if it were "12.345e67".

2
help/gcd
View File

@@ -5,7 +5,7 @@ SYNOPSIS
gcd(x1, x2, ...)
TYPES
x1, x2, ... rational number
x1, x2, ... rational number
return rational number

8
help/hash
View File

@@ -15,12 +15,12 @@ DESCRIPTION
The basis of this hash algorithm was taken from an idea sent
as reviewer comments to the IEEE POSIX P1003.2 committee by:
Phong Vo (http://www.research.att.com/info/kpv/)
Glenn Fowler (http://www.research.att.com/~gsf/)
Phong Vo (http://www.research.att.com/info/kpv/)
Glenn Fowler (http://www.research.att.com/~gsf/)
In a subsequent ballot round:
Landon Curt Noll (http://reality.sgi.com/chongo/)
Landon Curt Noll (http://reality.sgi.com/chongo/)
improved on their algorithm. Some people tried this hash
and found that it worked rather well. In an EMail message
@@ -30,7 +30,7 @@ DESCRIPTION
collision rate. The FNV speed allows one to quickly hash lots
of data while maintaining a reasonable collision rate. See:
http://reality.sgi.com/chongo/tech/comp/fnv/
http://reality.sgi.com/chongo/tech/comp/fnv/
for more details as well as other forms of the FNV hash.

4
help/help
View File

@@ -60,7 +60,7 @@ For example:
help usage
will print the calc command usage information. One can obtain calc help
will print the calc command usage information. One can obtain calc help
without invoking any startup code by running calc as follows:
calc -q help topic
@@ -76,7 +76,7 @@ for details of the -m mode.
The help command is able to display installed help files for custom builtin
functions. However, if the custom name is the same as a standard help
file, the standard help file will be displayed instead. The custom help
file, the standard help file will be displayed instead. The custom help
builtin should be used to directly access the custom help file.
For example, the custom help builtin has the same name as the standard

2
help/highbit
View File

@@ -11,7 +11,7 @@ TYPES
DESCRIPTION
If x is a nonzero integer, highbit(x) returns the index of the
highest bit in the binary representation of abs(x). Equivalently,
highest bit in the binary representation of abs(x). Equivalently,
highbit(x) = n if 2^n <= abs(x) < 2^(n + 1); the binary
representation of x then has n + 1 digits.

8
help/history
View File

@@ -11,7 +11,7 @@ Command history
for future recall.
Before the return key is typed, the current line can be edited
using emacs-like editing commands. As examples, ^A moves to
using emacs-like editing commands. As examples, ^A moves to
the beginning of the line, ^F moves forwards through the line,
backspace removes characters from the line, and ^K kills the
rest of the line.
@@ -24,7 +24,7 @@ Command history
Typing <esc>h lists all of the commands in the command history
and numbers the lines. The most recently executed line is always
number 1, the next most recent number 2, and so on. The numbering
number 1, the next most recent number 2, and so on. The numbering
for a particular command therefore changes as lines are entered.
Typing a number at the beginning of a line followed by <esc>g
@@ -51,11 +51,11 @@ Command history
The actual keys used for editing are defined in a bindings file,
usually called /usr/local/lib/calc/bindings. Changing the entries
in this file will change the key bindings used for editing. If the
in this file will change the key bindings used for editing. If the
file is not readable, then a message will be output and command
line editing is disabled. In this case you can only edit each
line as provided by the terminal driver in the operating system.
A shell command can be executed by typing '!cmd', where cmd
is the command to execute. If cmd is not given, then a shell
is the command to execute. If cmd is not given, then a shell
command level is started.

4
help/inputlevel
View File

@@ -11,10 +11,10 @@ DESCRIPTION
This function returns the input level at which it is called.
When calc starts, it is at level zero. The level is increased
by 1 each time execution starts of a read file command or a call to
eval(S) for some expression S which evaluates to a string. It
eval(S) for some expression S which evaluates to a string. It
decreases by 1 when a file being read reaches EOF or a string
being eval-ed reaches '\0', or earlier if a quit statement is
encountered at top calculation-level in the flle or string. It
encountered at top calculation-level in the flle or string. It
decreases to zero if an abort statement is encountered at any
function-level in the file or string. If a quit or abort
statement is encountered at top calculation-level at top input-level,

6
help/interrupt
View File

@@ -9,13 +9,13 @@ Interrupts
You can generate the SIGINT signal multiple times if necessary,
and each time the calculator will abort the calculation at a more
risky place within the calculation. Each new interrupt prints a
risky place within the calculation. Each new interrupt prints a
message of the form:
[Abort level n]
where n ranges from 1 to 3. For n equal to 1, the calculator will
abort calculations at the next statement boundary. For n equal to 2,
where n ranges from 1 to 3. For n equal to 1, the calculator will
abort calculations at the next statement boundary. For n equal to 2,
the calculator will abort calculations at the next opcode boundary.
For n equal to 3, the calculator will abort calculations at the next
lowest level arithmetic operation boundary.

4
help/intro
View File

@@ -2,12 +2,12 @@ Quick introduction
This is an interactive calculator which provides for easy large
numeric calculations, but which also can be easily programmed
for difficult or long calculations. It can accept a command line
for difficult or long calculations. It can accept a command line
argument, in which case it executes that single command and exits.
Otherwise, it enters interactive mode. In this mode, it accepts
commands one at a time, processes them, and displays the answers.
In the simplest case, commands are simply expressions which are
evaluated. For example, the following line can be input:
evaluated. For example, the following line can be input:
3 * (4 + 1)

2
help/isblk
View File

@@ -14,7 +14,7 @@ DESCRIPTION
named block, 0 otherwise.
Note that a named block B retains its name after its data block is
freed by rmblk(B). That a named block B has null data block may be
freed by rmblk(B). That a named block B has null data block may be
tested using sizeof(B); this returns 0 if and only if the memory
has been freed.

2
help/iseven
View File

@@ -10,7 +10,7 @@ TYPES
return int
DESCRIPTION
Determine if x is an even integer. This function will return 1 if x is
Determine if x is an even integer. This function will return 1 if x is
even integer, 0 otherwise.
EXAMPLE

2
help/ismat
View File

@@ -10,7 +10,7 @@ TYPES
return int
DESCRIPTION
Determine if x is a matrix. This function will return 1 if x is
Determine if x is a matrix. This function will return 1 if x is
a matrix, 0 otherwise.
EXAMPLE

2
help/isnum
View File

@@ -10,7 +10,7 @@ TYPES
return int
DESCRIPTION
Determine if x is a numeric value. This function will return 1 if x
Determine if x is a numeric value. This function will return 1 if x
is a a numeric value, 0 otherwise.
EXAMPLE

4
help/isprime
View File

@@ -11,7 +11,7 @@ TYPES
return int
DESCRIPTION
Determine if x is is a small prime. This function will return
Determine if x is is a small prime. This function will return
1 if x is a small prime. If x is even, this function will
return 0. If x is negative or a small composite (non-prime),
0 will be returned.
@@ -39,7 +39,7 @@ EXAMPLE
-1 2 0
LIMITS
err not given and (y is even or y < 2^32)
err not given and (y is even or y < 2^32)
LIBRARY
FLAG zisprime(ZVALUE x) (return 1 if prime, 0 not prime, -1 if >= 2^32)

2
help/isrel
View File

@@ -11,7 +11,7 @@ TYPES
return int
DESCRIPTION
Determine if x and y are relatively prime. If gcd(x,y) == 1, then
Determine if x and y are relatively prime. If gcd(x,y) == 1, then
return 1, otherwise return 0.
EXAMPLE

2
help/issq
View File

@@ -10,7 +10,7 @@ TYPES
return int
DESCRIPTION
Determine if x is a square. If there exists integers a, b such that:
Determine if x is a square. If there exists integers a, b such that:
x == a^2 / b^2 (b != 0)

2
help/isstr
View File

@@ -10,7 +10,7 @@ TYPES
return int
DESCRIPTION
Determine if x is a string. This function will return 1 if x is
Determine if x is a string. This function will return 1 if x is
a string, 0 otherwise.
EXAMPLE

2
help/jacobi
View File

@@ -29,7 +29,7 @@ DESCRIPTION
where the p_i are primes, not necessarily distinct, the
jacobi symbol function is given by
jacobi(x,y) = (x/p_1) * (x/p_2) * ... * (x/p_k).
jacobi(x,y) = (x/p_1) * (x/p_2) * ... * (x/p_k).
where the functions on the right are Legendre symbol functions.

10
help/join
View File

@@ -23,11 +23,11 @@ EXAMPLE
> join(A, B)
list (5 elements, 5 nonzero):
[[0]] = 1
[[1]] = 2
[[2]] = 3
[[3]] = 4
[[4]] = 5
[[0]] = 1
[[1]] = 2
[[2]] = 3
[[3]] = 4
[[4]] = 5
LIMITS
none

2
help/lcm
View File

@@ -5,7 +5,7 @@ SYNOPSIS
lcm(x1, x2, ...)
TYPES
x1, x2, ... rational number
x1, x2, ... rational number
return rational number

8
help/list
View File

@@ -24,12 +24,12 @@ DESCRIPTION
4, 6, and 7.
The 'push' and 'pop' functions insert or remove an element from
the beginning of the list. The 'append' and 'remove' functions
the beginning of the list. The 'append' and 'remove' functions
insert or remove an element from the end of the list. The 'insert'
and 'delete' functions insert or delete an element from the middle
(or ends) of a list. The functions which insert elements return
the null value, but the functions which remove an element return
the element as their value. The 'size' function returns the number
the element as their value. The 'size' function returns the number
of elements in the list.
Note that these functions manipulate the actual list argument,
@@ -43,11 +43,11 @@ DESCRIPTION
An arbitrary element of a linked list can be accessed by using the
double-bracket operator. The beginning of the list has index 0.
Thus in the new list x above, the expression x[[0]] returns the
value of the first element of the list, which is 9. Note that this
value of the first element of the list, which is 9. Note that this
indexing does not remove elements from the list.
Since lists are doubly linked in memory, random access to arbitrary
elements can be slow if the list is large. However, for each list
elements can be slow if the list is large. However, for each list
a pointer is kept to the latest indexed element, thus relatively
sequential accesses to the elements in a list will not be slow.

2
help/lowbit
View File

@@ -11,7 +11,7 @@ TYPES
DESCRIPTION
If x is a nonzero integer, lowbit(x) returns the index of the
lowest nonzero bit in the binary representation of abs(x). Equivalently,
lowest nonzero bit in the binary representation of abs(x). Equivalently,
lowbit(x) is the greatest integer for which x/2^n is an integer;
the binary representation of x then ends with n zero bits.

4
help/mat
View File

@@ -18,14 +18,14 @@ Using matrices
x = name[3,5];
The double-square bracket operator can be used on any matrix to
make references to the elements easy and efficient. This operator
make references to the elements easy and efficient. This operator
bypasses the normal indexing mechanism, and treats the array as if
it was one-dimensional and with a lower bound of zero. In this
indexing mode, elements correspond to the normal indexing mode where
the rightmost index increases most frequently. For example, when
using double-square bracket indexing on a two-dimensional matrix,
increasing indexes will reference the matrix elements left to right,
row by row. Thus in the following example, 'x' and 'y' are copied
row by row. Thus in the following example, 'x' and 'y' are copied
from the same matrix element:
mat m[1:2, 1:3];

4
help/max
View File

@@ -34,9 +34,9 @@ DESCRIPTION
and returns a real-number value for any comparison that has to be made,
max(x_1, x_2, ...) returns the value determined by max(x_1) = x_1,
and succesively for later arguments, by the use of the equivalent of
max(a,b) = (a < b) ? b : a. If the ordering determined by < is total,
max(a,b) = (a < b) ? b : a. If the ordering determined by < is total,
max(x_1, ...) will be the maximum value among the arguments. For a
preorder relation it may be one of several maximal values. For
preorder relation it may be one of several maximal values. For
other relations, it may be difficult to predict the result.
EXAMPLE

2
help/md5
View File

@@ -24,7 +24,7 @@ DESCRIPTION
The new arg1 HASH state is returned.
If arg1 is not a a HASH state, then the initial HASH is
used and modifed by arg1 and any val args supplied. The
used and modifed by arg1 and any val args supplied. The
return value is the new HASH state.
The following table gives a summary of actions and return values.

4
help/memsize
View File

@@ -10,7 +10,7 @@ TYPES
return integer
DESCRIPTION
This is analogous to the C operator sizeof. It attempts to assess
This is analogous to the C operator sizeof. It attempts to assess
the number of bytes in memory used to store a value and all its
components plus all of the related structue overhead. Unlike
sizeof(x), this builtin includes overhead.
@@ -19,7 +19,7 @@ DESCRIPTION
end of strings.
Unlike sizeof(x), this builtin includes the size demonitor for integers
and the imaginary part for complex values. Storage for holding
and the imaginary part for complex values. Storage for holding
0, 1 and -1 values are also included.
The number returned by memsize(x) may be less than the actual number

4
help/min
View File

@@ -34,9 +34,9 @@ DESCRIPTION
and returns a real-number value for any comparison that has to be made,
min(x_1, x_2, ...) returns the value determined by min(x_1) = x_1,
and succesively for later arguments, by the use of the equivalent of
min(a,b) = (a < b) ? a : b. If the ordering determined by < is total,
min(a,b) = (a < b) ? a : b. If the ordering determined by < is total,
min(x_1, ...) will be the minimum value among the arguments. For a
preorder relation it may be one of several minimal values. For other
preorder relation it may be one of several minimal values. For other
relations, it may be difficult to predict the result.
EXAMPLE

12
help/minv
View File

@@ -6,7 +6,7 @@ SYNOPSIS
TYPES
x integer
md integer
md integer
return integer
@@ -22,11 +22,11 @@ DESCRIPTION
0 0 < v < md md < v < 0
1 -md < v < 0 0 < v < -md
4 0 < v < md 0 < v < -md
5 -md < v < 0 md < v < 0
16 -md/2 < v <= md/2 md/2 <= v < -md/2
17 -md/2 <= v < md/2 md/2 < v <= -md/2
20 -md/2 < v <= md/2 md/2 < v <= -md/2
21 -md/2 <= v < md/2 md/2 <= v < -md/2
5 -md < v < 0 md < v < 0
16 -md/2 < v <= md/2 md/2 <= v < -md/2
17 -md/2 <= v < md/2 md/2 < v <= -md/2
20 -md/2 < v <= md/2 md/2 < v <= -md/2
21 -md/2 <= v < md/2 md/2 <= v < -md/2
EXAMPLE
> c = config("mod", 0)

2
help/mmin
View File

@@ -6,7 +6,7 @@ SYNOPSIS
TYPES
x number (real or complex), matrix, list, object
md real
md real
return real

6
help/mod
View File

@@ -44,10 +44,10 @@ DESCRIPTION
(Blank entries indicate that the description would be complicated
and probably not of much interest.)
rnd & 15 sign of r parity of q
rnd & 15 sign of r parity of q
0 sgn(y)
1 -sgn(y)
1 -sgn(y)
2 sgn(x)
3 -sgn(x)
4 +
@@ -55,7 +55,7 @@ DESCRIPTION
6 sgn(x/y)
7 -sgn(x/y)
8 even
9 odd
9 odd
10 even if x/y > 0, otherwise odd
11 odd if x/y > 0, otherwise even
12 even if y > 0, otherwise odd

2
help/nextcand
View File

@@ -43,7 +43,7 @@ DESCRIPTION
RUNTIME
The runtime for v = nextcand(n, ...) will depend strongly on the
number and nature of the integers between n and v. If this number
number and nature of the integers between n and v. If this number
is reasonably large the size of count is largely irrelevant as the
compositeness of the numbers between n and v will usually be
determined by the test for small prime factors or one pseudoprime

2
help/norm
View File

@@ -17,7 +17,7 @@ TYPES
DESCRIPTION
For real x, norm(x) returns:
x^2.
x^2.
For complex x, norm(x) returns:

2
help/null
View File

@@ -5,7 +5,7 @@ SYNOPSIS
null([v_1, v_2,...])
TYPES
v_1, v_2,... any
v_1, v_2,... any
return null
DESCRIPTION

76
help/obj.file
View File

@@ -15,7 +15,7 @@ Using objects
where D is a fixed integer, and 'a' and 'b' are arbitrary rational
numbers. Addition, subtraction, multiplication, and division can be
performed on such numbers, and the result can be put unambiguously
into the same form. (Complex numbers are an example of surds, where
into the same form. (Complex numbers are an example of surds, where
D is -1.)
The "obj" statement defines either an object type or an actual
@@ -53,8 +53,8 @@ Using objects
called.
The user function is called with the necessary arguments for that
operation. For example, for "surd_mul", there are two arguments,
which are the two numbers. The order of the arguments is always
operation. For example, for "surd_mul", there are two arguments,
which are the two numbers. The order of the arguments is always
the order of the binary operands. If only one of the operands to
a binary operator is an object, then the user function for that
object type is still called. If the two operands are of different
@@ -64,7 +64,7 @@ Using objects
The above rules mean that for full generality, user functions
should detect that one of their arguments is not of its own object
type by using the 'istype' function, and then handle these cases
specially. In this way, users can mix normal numbers with object
specially. In this way, users can mix normal numbers with object
types. (Functions which only have one operand don't have to worry
about this.) The following example of "surd_mul" demonstrates how
to handle regular numbers when used together with surds:
@@ -88,13 +88,13 @@ Using objects
x.b = a.a * b.b + a.b * b.a;
}
if (x.b == 0)
return x.a; /* normal number */
return x.a; /* normal number */
return x; /* return surd */
}
In order to print the value of an object nicely, a user defined
routine can be provided. For small amounts of output, the print
routine should not print a newline. Also, it is most convenient
routine should not print a newline. Also, it is most convenient
if the printed object looks like the call to the creation routine.
For output to be correctly collected within nested output calls,
output should only go to stdout. This means use the 'print'
@@ -121,50 +121,50 @@ Using objects
in order to make object calls quicker in general.
The double-bracket operator can be used to reference the elements
of any object in a generic manner. When this is done, index 0
of any object in a generic manner. When this is done, index 0
corresponds to the first element name, index 1 to the second name,
and so on. The 'size' function will return the number of elements
and so on. The 'size' function will return the number of elements
in an object.
The following is a list of the operations possible for objects.
The 'xx' in each function name is replaced with the actual object
type name. This table is displayed by the 'show objfuncs' command.
type name. This table is displayed by the 'show objfuncs' command.
Name Args Comments
xx_print 1 print value, default prints elements
xx_one 1 multiplicative identity, default is 1
xx_test 1 logical test (false,true => 0,1),
xx_print 1 print value, default prints elements
xx_one 1 multiplicative identity, default is 1
xx_test 1 logical test (false,true => 0,1),
default tests elements
xx_add 2
xx_sub 2 subtraction, default adds negative
xx_neg 1 negative
xx_mul 2
xx_div 2 non-integral division, default multiplies
xx_add 2
xx_sub 2 subtraction, default adds negative
xx_neg 1 negative
xx_mul 2
xx_div 2 non-integral division, default multiplies
by inverse
xx_inv 1 multiplicative inverse
xx_abs 2 absolute value within given error
xx_norm 1 square of absolute value
xx_conj 1 conjugate
xx_pow 2 integer power, default does multiply,
xx_inv 1 multiplicative inverse
xx_abs 2 absolute value within given error
xx_norm 1 square of absolute value
xx_conj 1 conjugate
xx_pow 2 integer power, default does multiply,
square, inverse
xx_sgn 1 sign of value (-1, 0, 1)
xx_cmp 2 equality (equal,non-equal => 0,1),
xx_sgn 1 sign of value (-1, 0, 1)
xx_cmp 2 equality (equal,non-equal => 0,1),
default tests elements
xx_rel 2 inequality (less,equal,greater => -1,0,1)
xx_quo 2 integer quotient
xx_mod 2 remainder of division
xx_int 1 integer part
xx_frac 1 fractional part
xx_inc 1 increment, default adds 1
xx_dec 1 decrement, default subtracts 1
xx_square 1 default multiplies by itself
xx_scale 2 multiply by power of 2
xx_shift 2 shift left by n bits (right if negative)
xx_round 2 round to given number of decimal places
xx_bround 2 round to given number of binary places
xx_root 3 root of value within given error
xx_sqrt 2 square root within given error
xx_rel 2 inequality (less,equal,greater => -1,0,1)
xx_quo 2 integer quotient
xx_mod 2 remainder of division
xx_int 1 integer part
xx_frac 1 fractional part
xx_inc 1 increment, default adds 1
xx_dec 1 decrement, default subtracts 1
xx_square 1 default multiplies by itself
xx_scale 2 multiply by power of 2
xx_shift 2 shift left by n bits (right if negative)
xx_round 2 round to given number of decimal places
xx_bround 2 round to given number of binary places
xx_root 3 root of value within given error
xx_sqrt 2 square root within given error
xx_or 2 boolean or
xx_and 2 boolean and
xx_not 1 boolean not

2
help/oldvalue
View File

@@ -12,7 +12,7 @@ DESCRIPTION
which at top level when directly from a file or keyboard
is automatically assigned the saved value for a line
of statements when evaluation of that line is completed and this saved
value is not null. A line of statements is normally completed by a
value is not null. A line of statements is normally completed by a
'\n' not within a block bounded by braces or an expression bounded by
parentheses.

22
help/operator
View File

@@ -1,7 +1,7 @@
operators
The operators are similar to C, but there are some differences in
the associativity and precedence rules for some operators. In
the associativity and precedence rules for some operators. In
addition, there are several operators not in C, and some C
operators are missing. A more detailed discussion of situations
that may be unexpected for the C programmer may be found in
@@ -64,7 +64,7 @@ operators
E.g., if A is a matrix, A[(a, b), c] evaluates a, b, and c, and
returns the value of A[b, c].
+= -= *= /= %= //= &= |= <<= >>= ^= **=
+= -= *= /= %= //= &= |= <<= >>= ^= **=
Operator-with-assignments.
These associate from left to right, e.g. a += b *= c has the
effect of a = (a + b) * c, where only a is required to be an
@@ -76,7 +76,7 @@ operators
e.g. a = b = c has the effect of a = (b = c). Here both a and b
are to be lvalues.
? : Conditional value.
? : Conditional value.
a ? b : c returns b if a tests as true (i.e. nonzero if
a is a number), c otherwise. Thus it is equivalent to:
if (a) return b; else return c;.
@@ -99,7 +99,7 @@ operators
true, b is returned, otherwise a. The effect in a
test like "if (a && b) ... " is the same as in C.
== != <= >= < >
== != <= >= < >
Relations.
+ -
@@ -134,7 +134,7 @@ operators
For the shift operators both arguments are to be
integers, or if the first is complex, it is to have
integral real and imaginary parts. Changing the
integral real and imaginary parts. Changing the
sign of the second argument reverses the shift, e.g.
a >> -b = a << b. The result has the same sign as
the first argument except that a nonzero value is
@@ -143,8 +143,8 @@ operators
e.g. a << b ^ c = a << (b ^ c).
+ - !
Plus (+) and minus (-) have their usual meanings as unary
prefix operators at this level of precedence when applied to
Plus (+) and minus (-) have their usual meanings as unary
prefix operators at this level of precedence when applied to
other than a first or only term.
As a prefix operator, '!' is the logical NOT: !a returns 0 if
@@ -156,13 +156,13 @@ operators
As a postfix operator ! gives the factorial function, i.e.
a! = fact(a).
++ --
++ --
Pre or post incrementing or decrementing.
These are applicable only to variables.
[ ] [[ ]] . ( )
[ ] [[ ]] . ( )
Indexing, double-bracket indexing, element references,
and function calls. Indexing can only be applied to matrices,
and function calls. Indexing can only be applied to matrices,
element references can only be applied to objects, but
double-bracket indexing can be applied to matrices, objects,
or lists.
@@ -199,7 +199,7 @@ operators
| &
Both both arguments must be integers.
<< >>
<< >>
The shift amount must be an integer. The value being
shifted must be an integer or a complex number with
integral real and imaginary parts.

20
help/overview
View File

@@ -6,13 +6,13 @@
All numbers are represented as fractions with arbitrarily large
numerators and denominators which are always reduced to lowest terms.
Real or exponential format numbers can be input and are converted
to the equivalent fraction. Hex, binary, or octal numbers can be
to the equivalent fraction. Hex, binary, or octal numbers can be
input by using numbers with leading '0x', '0b' or '0' characters.
Complex numbers can be input using a trailing 'i', as in '2+3i'.
Strings and characters are input by using single or double quotes.
Commands are statements in a C-like language, where each input
line is treated as the body of a procedure. Thus the command
line is treated as the body of a procedure. Thus the command
line can contain variable declarations, expressions, labels,
conditional tests, and loops. Assignments to any variable name
will automatically define that name as a global variable. The
@@ -20,7 +20,7 @@
which are evaluated are automatically printed. Thus, you can evaluate
an expression's value by simply typing it in.
Many useful built-in mathematical functions are available. Use
Many useful built-in mathematical functions are available. Use
the 'show builtins' command to list them. You can also define
your own functions by using the 'define' keyword, followed by a
function declaration very similar to C. Functions which only
@@ -29,7 +29,7 @@
Variables in functions can be defined as either 'global', 'local',
or 'static'. Global variables are common to all functions and the
command line, whereas local variables are unique to each function
level, and are destroyed when the function returns. Static variables
level, and are destroyed when the function returns. Static variables
are scoped within single input files, or within functions, and are
never destroyed. Variables are not typed at definition time, but
dynamically change as they are used. So you must supply the correct
@@ -80,7 +80,7 @@
help full
By default, arguments to functions are passed by value (even
matrices). For speed, you can put an ampersand before any
matrices). For speed, you can put an ampersand before any
variable argument in a function call, and that variable will be
passed by reference instead. However, if the function changes
its argument, the variable will change. Arguments to built-in
@@ -117,17 +117,17 @@
example 'x.real'. All user-defined routines have names composed
of the object type and the action to perform separated by an
underscore, as in the example 'complex_add'. The command 'show
objfuncs' lists all the definable routines. Object routines
objfuncs' lists all the definable routines. Object routines
which accept two arguments should be prepared to handle cases
in which either one of the arguments is not of the expected
object type.
These are the differences between the normal C operators and
the ones defined by the calculator. The '/' operator divides
the ones defined by the calculator. The '/' operator divides
fractions, so that '7 / 2' evaluates to 7/2. The '//' operator
is an integer divide, so that '7 // 2' evaluates to 3. The '^'
operator is a integral power function, so that 3^4 evaluates to
81. Matrices of any dimension can be treated as a zero based
81. Matrices of any dimension can be treated as a zero based
linear array using double square brackets, as in 'foo[[3]]'.
Matrices can be indexed by using commas between the indices, as
in foo[3,4]. Object and list elements can be referenced by
@@ -144,10 +144,10 @@
affect calculations or the display of values. For example, the
output display mode can be set using 'config(\"mode\", type)',
where 'type' is one of 'frac', 'int', 'real', 'exp', 'hex',
'oct', or 'bin'. The default output mode is real. For the
'oct', or 'bin'. The default output mode is real. For the
integer, real, or exponential formats, a leading '~' indicates
that the number was truncated to the number of decimal places
specified by the default precision. If the '~' does not
specified by the default precision. If the '~' does not
appear, then the displayed number is the exact value.
The number of decimal places printed is set by using

10
help/pmod
View File

@@ -25,11 +25,11 @@ DESCRIPTION
0 0 < v < md md < v < 0
1 -md < v < 0 0 < v < -md
4 0 < v < md 0 < v < -md
5 -md < v < 0 md < v < 0
16 -md/2 < v <= md/2 md/2 <= v < -md/2
17 -md/2 <= v < md/2 md/2 < v <= -md/2
20 -md/2 < v <= md/2 md/2 < v <= -md/2
21 -md/2 <= v < md/2 md/2 <= v < -md/2
5 -md < v < 0 md < v < 0
16 -md/2 < v <= md/2 md/2 <= v < -md/2
17 -md/2 <= v < md/2 md/2 < v <= -md/2
20 -md/2 < v <= md/2 md/2 < v <= -md/2
21 -md/2 <= v < md/2 md/2 <= v < -md/2
EXAMPLE
> c = config("mod",0)

2
help/polar
View File

@@ -6,7 +6,7 @@ SYNOPSIS
TYPES
r real
t real
t real
eps nonzero real, defaults to epsilon()
return number (real or complex)

10
help/poly
View File

@@ -24,7 +24,7 @@ TYPES
Here an arithmetic type is one for which the required + and *
operations are defined, e.g. real or complex numbers or square
matrices of the same size. A coefficient is either of arithmetic
matrices of the same size. A coefficient is either of arithmetic
type or a list of coefficients.
DESCRIPTION
@@ -48,11 +48,11 @@ DESCRIPTION
In particular:
poly(a, x) returns the value of a.
poly(a, x) returns the value of a.
poly(a, b, x) returns the value of b + a * x
poly(a, b, x) returns the value of b + a * x
poly(a, b, c, x) returns the value of c + (b + a * x) * x
poly(a, b, c, x) returns the value of c + (b + a * x) * x
If the first argument is a list as if defined by:
@@ -90,7 +90,7 @@ DESCRIPTION
returns the same as poly(list(1,2,3), x). If the number of
arguments is less than greatest depth of lists in clist, the
"missing" arguments are deemed to be zero. E.g.:
"missing" arguments are deemed to be zero. E.g.:
poly(list(list(1,2), list(3,4), 5), x)

2
help/prevcand
View File

@@ -45,7 +45,7 @@ DESCRIPTION
RUNTIME
The runtime for v = prevcand(n, ...) will depend strongly on the
number and nature of the integers between n and v. If this number
number and nature of the integers between n and v. If this number
is reasonably large the size of count is largely irrelevant as the
compositeness of the numbers between n and v will usually be
determined by the test for small prime factors or one pseudoprime

8
help/printf
View File

@@ -60,14 +60,14 @@ DESCRIPTION
number of format specifiers in fmt, the "missing" arguments
may be taken to be null values - these contribute nothing to the
output; if a positive width w has been specified, the effect is
to produce w spaces, e.g. printf("abc%6dxyz") prints "abc xyz".
to produce w spaces, e.g. printf("abc%6dxyz") prints "abc xyz".
If i <= the number of specifiers in fmt, the value of argument x_i
is printed in the format specified by the i-th specifier.
If a positive width w has been specified and normal printing of x_i
does not include a '\n' character, what is printed will if necessary
be padded with spaces so that the length of the printed output
is at least the w. Note that control
is at least the w. Note that control
characters like '\t', '\b' each count as one character. If
the 'right-pad' flag has been set, the padding is on the right;
otherwise it is on the left.
@@ -79,13 +79,13 @@ DESCRIPTION
If the i-th specifier is of numerical type, any numbers in the
printing of x_i will be printed in the specified format, unless
this is modified by the printing procedure for x_i's type. Any
this is modified by the printing procedure for x_i's type. Any
specified precision will be ignored except for floating-point
mode.
In the case of floating-point (f) format the precision determines
the maximum number of decimal places to be
displayed. Other aspects of this printing may be affected by the
displayed. Other aspects of this printing may be affected by the
configuration parameters "outround", "tilde", "fullzero", "leadzero".
EXAMPLE

6
help/prompt
View File

@@ -19,13 +19,13 @@ EXAMPLE
> x = prompt("? ");
? 273
> x
"273"
"273"
> for (;;) {s = prompt("? "); if (s=="end") break; print "\t":eval(s)^2;}
? 3
9
9
? 2 + 3
25
25
? end
>

6
help/protect
View File

@@ -17,7 +17,7 @@ DESCRIPTION
protection status for var or nblk.
With two arguments, protect(var, sts) or protect(nblk, sts) sets the
protection status for var or nblk to the value sts. Each nonzero bit
protection status for var or nblk to the value sts. Each nonzero bit
of sts corresponds to one kind of protection as follows:
sts protection
@@ -42,7 +42,7 @@ DESCRIPTION
protect(A, 1);
an error state is established if A = expr is attempted. It does
an error state is established if A = expr is attempted. It does
not imply constancy if, for example, the current value of A is a list
or matrix; such a value may be changed by assignments to the elements
of A, or by push or copy commands.
@@ -169,7 +169,7 @@ EXAMPLE
mat [2] (2 elements, 1 nonzero):
[0] = 0
[1] = 4
[1] = 4
> A = blk("alpha") = {1,2,3,4}
> protect(A, 0)

6
help/ptest
View File

@@ -55,7 +55,7 @@ DESCRIPTION
For the random case (skip = 0), the probability that any one test
with random base b will return 1 if n is composite is always
less than 1/4, so with count = k, the probability is less
than 1/4^k. For most values of n the probability is much
than 1/4^k. For most values of n the probability is much
smaller, possible zero.
RUNTIME
@@ -77,7 +77,7 @@ RUNTIME
If the word-count for n is less than conf("redc2"), REDC algorithms
are used in evaluating ptest(n, count, skip) when small-factor
cases have been eliminated. For small word-counts (say < 10)
cases have been eliminated. For small word-counts (say < 10)
this may more than double the speed of evaluation compared with
the standard algorithms.
@@ -114,7 +114,7 @@ EXAMPLE
These results show that a is a strong pseudoprime for all 11 prime
bases less than or equal to 31, and for all positive integer bases
less than or equal to 21, but not for the bases 37 and 22. The
less than or equal to 21, but not for the bases 37 and 22. The
probability that ptest(a,-1,0) (or ptest(a,1,0)) will return 1 is
about 0.19.

6
help/quo
View File

@@ -35,10 +35,10 @@ DESCRIPTION
one of the two integers v for which abs(x/y - v) < 1. Which
integer is returned is controlled by rnd as follows:
rnd sign of x/y - v Description of rounding
rnd sign of x/y - v Description of rounding
0 + down, towards minus infinity
1 - up, towards infinity
0 + down, towards minus infinity
1 - up, towards infinity
2 sgn(x/y) towards zero
3 -sgn(x/y) from zero
4 sgn(y)

4
help/quomod
View File

@@ -14,7 +14,7 @@ TYPES
DESCRIPTION
Returns 0 or 1 according as x is or is not a multiple of y.
Let x = q * y + r where q is an integer and 0 <= r < y
Let x = q * y + r where q is an integer and 0 <= r < y
This function assigns the values q and r to the variables
Q and R. If x >= 0, the results for Q and R are the same as
those given by Q = x // y, R = x % y.
@@ -39,4 +39,4 @@ LIBRARY
BOOL qquomod(NUMBER *q1, NUMBER *q2, NUMBER **retqdiv, NUMBER **retqmod)
SEE ALSO
//, %
//, %

20
help/rand
View File

@@ -19,7 +19,7 @@ DESCRIPTION
pseudo-random generator. If you need a fast generator and do not
need a cryptographically strong one, this generator is likely to do
the job. Casual direct use of the shuffle generator may be
acceptable. For a much higher quality cryptographically strong
acceptable. For a much higher quality cryptographically strong
(but slower) generator use the Blum-Blum-Shub generator (see the
random help page).
@@ -55,9 +55,9 @@ DESCRIPTION
by Knuth, Vol 2, 2nd edition (1981), Section 3.2.2, page 32,
Algorithm B.
The rand generator has a good period, and is fast. It is reasonable as
The rand generator has a good period, and is fast. It is reasonable as
generators go, though there are better ones available. The shuffle
method has a very good period, and is fast. It is fairly good as
method has a very good period, and is fast. It is fairly good as
generators go, particularly when it is feed reasonably random
numbers. Because of this, we use feed values from the additive 55
method into the shuffle method.
@@ -120,7 +120,7 @@ DESCRIPTION
perceptions that are noted above.
It should be noted that the purpose of randreseed64 is to scramble a
seed ONLY. We do not care if these generators produce good random
seed ONLY. We do not care if these generators produce good random
numbers. We only want to help eliminate the human factors & perceptions
noted above.
@@ -144,8 +144,8 @@ DESCRIPTION
We will select the randreseed64 multiplier 'a' such that:
a mod 8 == 5 (based on note iii)
0.01*m < a < 0.99*m (based on note iv)
a mod 8 == 5 (based on note iii)
0.01*m < a < 0.99*m (based on note iv)
0.01*2^64 < a < 0.99*2^64
a is prime (help keep the generators independent)
@@ -159,10 +159,10 @@ DESCRIPTION
gcd(a, c) == 1 (adders & multipliers will be more independent)
The values 'a' and 'c for randreseed64 are taken from the Rand book
of numbers. Because m=2^64 is 20 decimal digits long, we will
of numbers. Because m=2^64 is 20 decimal digits long, we will
search the Rand book of numbers 20 at a time. We will skip any of
the 55 values that were used to initialize the additive 55
generators. The values obtained from the Rand book are:
generators. The values obtained from the Rand book are:
a = 6316878969928993981
c = 1363042948800878693
@@ -180,12 +180,12 @@ DESCRIPTION
One might object to the complexity of the seed scramble/mapping via
the randreseed64 process. But Calling srand(0) with the randreseed64
process would be the same as calling srand(10239951819489363767)
without it. No extra security is gained or reduced by using the
without it. No extra security is gained or reduced by using the
randreseed64 process. The meaning of seeds are exchanged, but not
lost or favored (used by more than one input seed).
The randreseed64 process does not reduce the security of the rand
generator. Every seed is converted into a different unique seed.
generator. Every seed is converted into a different unique seed.
No seed is ignored or favored.
The truly paranoid might suggest that my claims in the MAGIC NUMBERS

2
help/randbit
View File

@@ -11,7 +11,7 @@ TYPES
DESCRIPTION
If x > 0, randbit(x) returns a pseudo-random integer in [0, 2^x),
i.e. the same as rand(2^x). If the integer returned is
i.e. the same as rand(2^x). If the integer returned is
b_1 * 2^(x-1) + b_2 * 2^(x-2) + ... + b_n,

12
help/random
View File

@@ -25,7 +25,7 @@ DESCRIPTION
random() Same as rand(0, 2^64)
random(max) Same as rand(0, max)
The random generator generates the highest order bit first. Thus:
The random generator generates the highest order bit first. Thus:
random(256)
@@ -37,7 +37,7 @@ DESCRIPTION
The basic idea behind the Blum-Blum-Shub generator is to use
the low bit bits of quadratic residues modulo a product of
two 3 mod 4 primes. The lowest int(log2(log2(p*q))) bits are used
two 3 mod 4 primes. The lowest int(log2(log2(p*q))) bits are used
where log2() is log base 2 and p,q are two primes 3 mod 4.
The Blum-Blum-Shub generator is described in the papers:
@@ -52,7 +52,7 @@ DESCRIPTION
U. V. Vazirani and V. V. Vazirani, "Trapdoor Pseudo-Random
Number Generators with Applications to Protocol Design",
Proceedings of the 24th IEEE Symposium on the Foundations
Proceedings of the 24th IEEE Symposium on the Foundations
of Computer Science, 1983, pp. 23-30.
U. V. Vazirani and V. V. Vazirani, "Efficient and Secure
@@ -71,7 +71,7 @@ DESCRIPTION
1st edition (1994), pp 365-366.
This generator is considered 'strong' in that it passes all
polynomial-time statistical tests. The sequences produced are
polynomial-time statistical tests. The sequences produced are
random in an absolutely precise way. There is absolutely no better
way to predict the sequence than by tossing a coin (as with TRULY
random numbers) EVEN IF YOU KNOW THE MODULUS! Furthermore, having
@@ -86,7 +86,7 @@ DESCRIPTION
To compromise the generator, an adversary must either factor the
modulus or perform an exhaustive search just to determine the next
(or previous) bit. If we make the modulus hard to factor (such as
(or previous) bit. If we make the modulus hard to factor (such as
the product of two large well chosen primes) breaking the sequence
could be intractable for todays computers and methods.
@@ -130,7 +130,7 @@ DESCRIPTION
is given in the source. While this does not reduce the quality
of the generator, knowing the factors of the Blum modulus would
help someone determine the next or previous bit when they did
not know the seed. If this bothers you, feel free to use one
not know the seed. If this bothers you, feel free to use one
of the other compiled in Blum moduli or provide your own. See
the srandom help page for details.

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