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=======================================================================
Fast Parser v1.2
Copyright (C) 1992, 1993 by Daniel Corbier
All rights reserved.
=======================================================================
Introduction
============
Fast Parser is a PowerBASIC library which allows math expressions to be
created and evaluated during runtime. It supports a number of built-in
functions, operators, numerical notations, and modes. Fast Parser is
especially designed to run fast inside loops. Expressions such as the
following can be evaluated:
5.19 + 2.3E+3 * x/(15.8792 + sin(pi)^2-length) + x mod 3
(16 xor 27) and 255
#h1fff + #haef and #b1010111
Table of Symbols
================
Symbol Equivalent Description Example
------ ---------- ----------- -------
( ) Prioritizes an expression 5*(1+1) = 10
^ ** Raised to the power of 4 ^ 5 = 1024
* Multiply by 3 * 6 = 18
/ Divide by 9 / 2 = 4.5
% MOD Modulo 7 % 4 = 3
+ Add 1 + 1 = 2
- Subtract 9 - 5 = 4
> Greater than 9 > 2 = 1
< Less than 7 < 4 = 0
= == Equal test 5 = 4 = 0
>= => Greater or equal 3 >= 3 = 1
<= =< Less or equal $3E <= 9 = 0
<> != Not Equal #b10101 <> 20 = 1
NOT Bitwise 'not' not(15) = -16
AND & Bitwise 'and' #b101 and #h1E = 4
OR | Bitwise 'or' 13 or 6 = 15
XOR Bitwise 'exclusive or' 9 xor 3 = 10
EQV Bitwise 'equivalence' 6 eqv 9 = -16
IMP Bitwise 'implication' 1 imp 5 = -1
SIN Sine sin(pi) = 0
COS Cosine cos(pi) = -1
TAN Tangent tan(pi) = 0
ASIN Arcsine asin(1) = 1.57079632
ACOS Arccosine acos(-1) = 3.14159265
ATAN ATN Arctangent atan(0) = 0
SINH Hyperbolic sine sinh(16) = 4443055.26
COSH Hyperbolic cosine cosh(11) = 29937.0708
TANH Hyperbolic tangent tanh(1) = 0.76159415
COTH Hyperbolic cotangent coth(1) = 1.31303528
SECH Hyperbolic secant sech(14) = 1.66305E-6
CSCH Hyperbolic cosecant csch(34) = 3.4278E-15
ASINH Hyperbolic arcsine asinh(2) = 1.44363547
ACOSH Hyperbolic arccosine acosh(9) = 2.88727095
ATANH Hyperbolic arctangent atanh(.5) = 1.09861228
ACOTH Hyperbolic arccotangent acoth(7) = 0.14384103
ASECH Hyperbolic arcsecant asech(.3) = 1.87382024
ACSCH Hyperbolic arccosecant acsch(2) = 0.48121182
ABS Absolute value abs(-8) = 8
EXP e to the power of exp(3) = 20.0855369
RND Random number rnd(1) = .968620060
INT Truncate to an integer int(6.8) = 6
EXP2 2 to the xth power exp2(17) = 131072
EXP10 10 to the xth power exp10(3) = 1000
FACT Factorial fact(11) = 39916800
LOG2 Log base 2 log2(19) = 4.24792751
LOG10 Log base 10 log10(7) = .845098040
LOG LN Natural log log(16) = 2.77258872
SGN SIGN Sign of expression sgn(-9) = -1
SQR SQRT Square root sqr(64) = 8
Order of Precedence
===================
Here is the precedence list from highest to lowest priority:
Anything inside parenthesis is performed first ( )
Exponentiation ^
Multiplication, division *, /
Modulo MOD
Addition, subtraction +, -
Relational operators <, >, >=, <=, =, <>
AND
OR, XOR (exclusive or)
EQV (equivalence)
IMP (implication)
Numerical Notations
===================
The default numerical type is DECIMAL. Binary, octal, and
hexadecimal number types are also supported. The latter types
must be preceded by the # (number sign) symbol, and one of
the letters "h", "b", or "o", for hexadecimal, binary, or octal
in that respective order. The $ sign for hexadecimal notation
can be used as a shortcut.
Exponential notation is also supported. These are numbers followed
by the letter E, and an exponent number. For instance: 3.4E+5
translates to 3.4*10^5, and 3.4E-5 translates to 3.4*10^(-5).
Examples:
---------
#b110101110, #o656, #h1AE, $1AE, 430, 4.3E2
are all the same number.
#b10101^2 * 5/$1EF + sin(5.8+2)*cos(#o302)-7E6 is a valid expression.
Library Elements
================
Eval##( Expr$ ) Function
This evaluates an expression in one step. It may be preferable
to use Evaluate##() for speed when inside a time-critical loop
where a variable in the expression changes values. See the
Technical Notes for details on speed differences.
VarName$() Array
This array stores the names of variables you want Fast Parser to
recognize. The variable names should follow the PB convention for
naming variables (except they do not need to be followed by numeric
type identifiers). You may have up to 200 unique variable names
(subscripts 0 to 199). It is not case-sensitive. When assigning
variable names to the array VarName$(), make sure you start with
subscript 0, and add names consecutively.
VarValue##() Array
This array stores the values that correspond to the variable
names in VarName$(). VarValue##(0) matches VarName$(0),
VarValue##(1) matches VarName$(1), etc... These values can
be changed at any time.
EqParse%( Expr$ ) Function
This function parses the expression in Expr$, and returns a
pointer for that expression. The returned value is the parameter
you should pass to the Evaluate##() function. This method is more
efficient in time-critical loops where variables are being changed.
EqParse%() is usually outside the loop, and Evaluate##() inside the
loop. Ex: Ptr% = EqParse%( "3+x^2" )
Evaluate##( Ptr% ) Function
This returns the value for the parsed expression represented
by Ptr%. It is generally preceded by changing some values in
VarValue##(), while inside a loop. The difference between
Evaluate##() and Eval##() is mainly in speed. Eval##() normally
parses an expression every time it is invoked, whereas Evaluate##()
evaluates an expression which is already parsed, making it much
faster in a repetitious situation.
EqError% Variable
This variable stores one of the following error numbers each
time Eval##() or EqParse%() is invoked:
0 No error
1 Undefined function
2 Mismatched parenthesis
3 Undefined variable
4 Invalid binary number
5 Invalid octal number
6 Invalid hexadecimal number
7 Factorial overflow
8 (not available)
9 Invalid expression
10 Function definition space is full
TrigMode( mode ) Sub
This sub changes the angle mode for trigonometric operations.
1 Radian (default)
2 Degree
3 Gradient
UserFunction( Eq$ ) Sub
This let's you define functions during runtime. Only one
parameter is allowed, and that parameter must be "x". For
instance, if you enter the following lines, then the cot()
and the inv() functions will be recognized in subsequent
expressions just like any other built-in function:
Call UserFunction( "cot(x) = cos(x) / sin(x)" )
MyEquation$ = "inv(x) = 1/x"
Call UserFunction( MyEquation$ )
ReleaseLastEq() Sub
Each time EqParse%() or UserFunction() is invoked, it adds some
instructions to a list which may eventually get filled. Use this
function to remove the last user function or parsed expression
from memory.
ReleaseEq() Sub
When invoked, all functions defined with UserFunction() and
expressions parsed with EqParse%() are freed from memory.
This may be useful if EqError% returns 10.
Bin##(n$), Oct##(n$), Hex##(n$) Functions
These convert n$ from a binary, octal, or hexadecimal number into
a decimal number.
MatchParenth%( parenthesis, text$ ) Function
This finds a matching parenthesis. For instance, if
text$ = "3+(5/(4+8-(1+.5)*3+2.87)+7)-3"
^ ^
MatchParenth%(6,text$) returns 24
Technical Notes
===============
o The hex, binary, and octal notations are slightly different than in
PB. Instead of the "&" symbol, Fast Parser recognizes the "#" symbol.
For instance, #b1011 is recognized instead of &b1011.
o Relational operators return a 1 (instead of -1) for true expressions,
and 0 for false ones. For instance, 5 > 3 = 1, and 5 < 3 = 0.
o There are two .PBU files. CALC21.PBU will work with PowerBASIC 2.1,
and CALC30.PBU will work with PB 3.0. Change the $LINK statement in
CALC.INC to set the appropriate .PBU file.
o In order for it to run faster, compile your program with either
the floating point Procedure option, or NPX option, instead of
the Emulate option.
o When inside a loop, where a variable in your expression is changing
values, the program will run faster if you Use EqParse%() along with
Evaluate##(), instead of Eval##(). However, if you are only dealing
with one expression inside the loop, the Eval##() function will run
almost as fast, because the parsed expression is still in memory.
o There is a limit of 128 instructions (like +, -, *, etc...) which can
be used for defining functions & parsing expressions. Every time
UserFunction() or EqParse%() is called, part of the instruction list
is filled. If this happens, you can use ReleaseEq to release all
parsed expressions and user functions from memory.
Distribution
============
Fast Parser can be freely distributed through BBSs, online services
and other shareware collections. No charge can be made for Fast Parser.
However, you can charge a modest fee for the media it is stored in and
shipment, as long as it is made clear that the user is not buying Fast
Parser by paying this fee, and it is not placed in a public domain
category. The following files must all be present and unmodified
when distributed:
FASTPARS DOC Documentation for Fast Parser
CALC INC $INCLUDE file for Fast Parser.
CALC21 PBU Unit file compatible with PowerBASIC 2.1
CALC30 PBU Unit file compatible with PB 3.0
EVAL BAS A sample expression evaluator using Eval##()
XYPLOT BAS Plots the 2-D graph of equations given at runtime
3DPLOT BAS Plots 3-D surfaces of equations given at runtime
Registration
============
Fast Parser v1.2 is free for non-commercial personal use, and for
writing shareware and freeware (excluding public domain) programs,
as long as due credit is given (citing the use of Fast Parser by
Daniel Corbier). If you want to encourage me to continue writing
shareware & freeware programs, a gift of $10 or any amount would
be greatly appreciated. It should be a check or money order in US
funds (since it might cost more than $10 to change foreign currency).
You may also mail cash in US dollars.
IMPORTANT!!
-----------
Please be advised that the registration options from the previous
version of Fast Parser are no longer supported, and the source code
can no longer be purchased. Also, please keep in mind that although
Fast Parser v1.2 can be used free of charge, it is NOT public domain.
Disclaimer
==========
The Fast Parser library is provided on an "as is" basis without warranty
of any kind, expressed or implied. The person using it bears all risk
as to the quality and performance of the library. The author will not
be held liable for any special, incidental, consequential, direct or
indirect damages due to any problem caused by this software.
My Address
==========
Since Fast Parser can be used free of charge, I do NOT plan on
supporting it in any special way. This simply means that I'm not
obliged to assist anyone in the use of Fast Parser. However, I would
like to hear suggestions, and know what kind of programs it is used
in. I can be reached at either of the following addresses:
US Mail: (note that this address is different from last year)
Daniel Corbier
571 NE 110th Terrace
Miami, FL 33161
Internet:
corbier@andrews.edu
Fidonet:
Daniel Corbier at 1:135/110 or 1:135/23
Compuserve:
INTERNET: corbier@andrews.edu
I frequent the following BBSs quite often:
Telcom Central 305-828-7909
MACC 305-596-1854
SOX 305-821-3317
I occasionally frequent the PowerBASIC BBS.
I read the following conferences regularly:
Fido: Shareware, ECPROG, Q-BASIC and more
Internet: alt.lang.basic, and various msdos & pc newsgroups
New features in this version include:
=====================================
- Functions can be defined at runtime
- Unary + and - are now supported
- More trig functions
- Hyperbolic functions
- Relational & bitwise operators
- Up to 200 variables can be defined
- Exponential notation is accepted (like 5.3E+25)
- Hex, binary, and octal notations
- Support for PB 3.0
- Extended precision
Ultimate Calculator
===================
If you are interested in seeing a program which uses the Fast Parser
library, please get a copy of Ucalc (Ultimate Calculator) from a BBS
near you. It has more examples, and will give you a better idea of
how Fast Parser can be used. The file name is UCALCxx.??? (where
xx is the version, and ??? is ZIP, ARJ, SDN or another extention).
In addition to the features in this library, Ucalc can also solve
equations, and do numerical integrations & summations.