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Release calc version 2.10.2t30

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Landon Curt Noll
1996-07-06 04:17:00 -07:00
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Configuration parameters
Configuration parameters affect how the calculator performs certain
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
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:
"all" all configuration values listed below
"trace" turns tracing features on or off
"display" sets number of digits in prints.
"epsilon" sets error value for transcendentals.
"maxprint" sets maximum number of elements printed.
"mode" sets printout mode.
"mul2" sets size for alternative multiply.
"sq2" sets size for alternative squaring.
"pow2" sets size for alternate powering.
"redc2" sets size for alternate REDC.
"tilde" enable/disable printing of the roundoff '~'
"tab" enable/disable printing of leading tabs
"quomod" sets rounding mode for quomod
"quo" sets rounding mode for //, default for quo
"mod" sets "rounding" mode for %, default for mod
"sqrt" sets rounding mode for sqrt
"appr" sets rounding mode for appr
"cfappr" sets rounding mode for cfappr
"cfsim" sets rounding mode for cfsim
"round" sets rounding mode for round and bround
"outround" sets rounding mode for printing of numbers
"leadzero" enables/disables printing of 0 as in 0.5
"fullzero" enables/disables padding zeros as in .5000
"maxerr" maximum number of scan errors before abort
"prompt" default interactive prompt
"more" default interactive multi-line input prompt
The "all" config value allows one to save/restore the configuration
set of values. The return of:
config("all")
is a CONFIG type which may be used as the 2rd arg in a later call.
One may save, modify and restore the configuration state as follows:
oldstate = config("all")
...
config("tab", 0)
config("mod", 10)
...
config("all", oldstate)
This save/restore method is useful within functions.
It allows functions to control their configuration without impacting
the calling function.
There are two configuration state aliases that may be set. To
set the backward compatible standard configuration:
config("all", "oldstd")
The "oldstd" will restore the configuration to the default at startup.
A new configuration that some people prefer may be set by:
config("all", "newstd")
The "newstd" is not backward compatible with the historic
configuration. Even so, some people prefer this configuration
and place the config("all", "newstd") command in their CALCRC
startup files.
When nonzero, the "trace" parameter activates one or more features
that may be useful for debugging. These features correspond to
powers of 2 which contribute additively to config("trace"):
1: opcodes are displayed as functions are evaluated
2: disables the inclusion of debug lines in opcodes for functions
whose definitions are introduced with a left-brace.
4: the number of links for real and complex numbers are displayed
when the numbers are printed; for real numbers "#" or for
complex numbers "##", followed by the number of links, are
printed immediately after the number.
8: the opcodes for a new functions are displayed when the function
is successfully defined.
The "display" parameter specifies the maximum number of digits after
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 is 20. This parameter does not change
the stored value of a number. Where rounding is necessary, the type
of rounding to be used is controlled by "outround".
The "epsilon" parameter specifies the default accuracy for the
calculation of functions for which exact values are not possible or
not desired. For most functions, the
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
absolute value of the remainder usually does not exceed epsilon/2.
Functions which require an epsilon value accept an
optional argument which overrides this default epsilon value for
that single call. (The value v can be assigned to the "epsilon"
parameter by epsilon(v) as well as by config("epsilon", v), and the
current value obtained by epsilon() as well as by config("epsilon").)
For the transcendental functions and the functions sqrt() and
appr(), the calculated value is always a multiple of epsilon.
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:
"frac" decimal fractions
"int" decimal integer
"real" decimal floating point
"exp" decimal exponential
"hex" hex fractions
"oct" octal fractions
"bin" binary fractions
The "maxprint" parameter specifies the maximum number of elements to
be displayed when a matrix or list is printed. The initial value is 16.
Mul2 and sq2 specify the sizes of numbers at which calc switches
from its first to its second algorithm for multiplying and squaring.
The first algorithm is the usual method of cross multiplying, which
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
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
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
of 20, which is about 100 decimal digits. A value of zero resets
the parameter back to its default value. Usually there is no need
to change these parameters.
Pow2 specifies the sizes of numbers at which calc switches from
its first to its second algorithm for calculating powers modulo
another number. The first algorithm for calculating modular powers
is by repeated squaring and multiplying and dividing by the modulus.
The second method uses the REDC algorithm given by Peter Montgomery
which avoids divisions. The argument for pow2 is the size of the
modulus at which the second algorithm begins to be used.
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
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
which the second algorithm begins to be used.
Config("tilde") controls whether or not a leading tilde ('~') is
printed to indicate that a number has not been printed exactly
because the number of decimal digits required would exceed the
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
affect the printing by the functions print, printf, etc. The inital
"tab" value is 1.
The "quomod", "quo", "mod", "sqrt", "appr", "cfappr", "cfsim", and
"round" control the way in which any necessary rounding occurs.
Rounding occurs when for some reason, a calculated or displayed
value (the "approximation") has to differ from the "true value",
e.g. for quomod and quo, the quotient is to be an integer, for sqrt
and appr, the approximation is to be a multiple of an explicit or
implicit "epsilon", for round and bround (both controlled by
config("round")) the number of decimal places or fractional bits
in the approximation is limited. Zero value for any of these
parameters indicates that the true value is greater than the approximation,
i.e. the rounding is "down", or in the case of mod, that the
residue has the same sign as the divisor. If bit 4 of the
parameter is set, the rounding of to the nearest acceptable candidate
when this is uniquely determined; in the remaining ambiguous cases,
the type of rounding is determined by the lower bits of the parameter
value. If bit 3 is set, the rounding for quo, appr and sqrt,
is to the nearest even integer or the nearest even multiple of epsilon,
and for round to the nearest even "last decimal place". The effects
of the 3 lowest bits of the parameter value are as follows:
Bit 0: Unconditional reversal (down to up, even to odd, etc.)
Bit 1: Reversal if the exact value is negative
Bit 2: Reversal if the divisor or epsilon is negative
(Bit 2 is irrelevant for the functions round and bround since the
equivalent epsilon (a power of 1/10 or 1/2) is always positive.)
For quomod, the quotient is rounded to an integer value as if
evaluating quo with config("quo") == config("quomod"). Similarly,
quomod and mod give the same residues if config("mod") == config("quomod").
For the sqrt function, if bit 5 of config("sqrt") is set, the exact
square-root is returned when this is possible; otherwise the
result is rounded to a multiple of epsilon as determined by the
five lower order bits. Bit 6 of config("sqrt") controls whether the
principal or non-principal square-root is returned.
For the functions cfappr and cfsim, whether the "rounding" is down
or up, etc. is controlled by the appropriate bits of config("cfappr")
and config("cfsim") as for quomod, quo, etc.
The "outround" parameter determines the type of rounding to be used
by the various kinds of printing to the output: bits 0, 1, 3 and 4
are used in the same way as for the functions round and bround.
The "leadzero" parameter controls whether or not a 0 is printed
before the decimal point in non-zero fractions with absolute value
less than 1, e.g. whether 1/2 is printed as 0.5 or .5. The
initial value is 0, corresponding to the printing .5.
The "fullzero" parameter controls whether or not in decimal floating-
point printing, the digits are padded with zeros to reach the
number of digits specified by config("display") or by a precision
specification in formatted printing. The initial value for this
parameter is 0, so that, for example, if config("display") >= 2,
5/4 will print in "real" mode as 1.25.
The maxerr value controls how many scan errors are allowed
before the compiling phase of a computation is aborted. The initial
value of "maxerr" is 20. Setting maxerr to 0 disables this feature.
The default prompt when in teractive mode is "> ". One may change
this prompt to a more cut-and-paste friendly prompt by:
config("prompt", "; ")
On windowing systems that support cut/paste of a line, one may
cut/copy an input line and paste it directly into input. The
leading ';' will be ignored.
When inside multi-line input, the more prompt is used. One may
change it by:
config("more", ";; ")
The following are synonyms for true:
"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)
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("tab", "off") disable leading tab printing