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EVAL V1.06 Copyright (c) 1991-1992 Copy Con Incorporated Page 1 TO PRINT THIS FILE, TYPE "COPY EVAL.DOC PRN" AT THE DOS PROMPT. OVERVIEW -------- EVAL is a mathematical expression evaluator, capable of evaluating virtually any formula, including those with trigonometric functions, complex numbers, and user-defined variables. Formulas are typed in at the command line, and the formula and outcome (and optionally the variable values) are immediately displayed on your screen, or can be sent to any device or file via standard DOS redirection. DISCLAIMER ---------- EVAL is distributed on an "AS IS" basis without warranty, expressed or implied. Considerable testing effort has been expended, but the user is advised to check the program's suitability before relying on it. The user assumes full risk as to the results of using this program. Any liability of the author will be limited exclusively to product replacement. In no event shall the author be liable for any incidental or consequential damages arising from the use, or inability to use this program. REGISTRATION ------------ The unregistered version of EVAL is freely distributable and fully functional, and may be used for a 30-day trial period. If you plan to continue using EVAL after the trial period, you are obligated to pay the modest registration fee of $20. Registered users will receive the latest version of EVAL with the "nag" messages removed, along with a smaller, math-chip version of EVAL. Registration also entitles you to one free upgrade upon request, and half-priced subsequent upgrades. All registration information is contained in the REGISTER.TXT file. If that file is missing, register by sending a check or money order for $20 in U.S. dollars, drawn on a U.S. bank, to: Copy Con Incorporated P.O. Box 23255 Baltimore, MD 21203-5255 Please specify 3.5" or 5.25" diskette. MD residents add 5% sales tax. We thank you for your support. EVAL V1.06 Copyright (c) 1991-1992 Copy Con Incorporated Page 2 OPERATION --------- EVAL is activated from the command line, using the format EVAL [variable=expression;...] expression [options] Expressions are mathematical formulas built with the supported functions, operators, constants and variables. FUNCTIONS --------- Following are the functions that EVAL supports: Function Description -------- ----------- abs Absolute value acos Arc cosine arg Angle of input value in the complex plane asin Arc sine atan Arc tangent ceil Smallest integer not less than input value (rounds up) conj Complex conjugate of input value cos Cosine cosh Hyperbolic cosine csc Cosecant ctn Cotangent cub Cube root exp E to the power of input value flr Largest integer not more than input value (rounds down) frac Fractional part of input value imag Imaginary part of complex number int Integer part of input value ln Natural logarithm log Natural logarithm (same as LN) logt Base 10 logarithm norm Square of the absolute value rand Random integer between 1 and input value (max 32767) real Real part of complex number sec Secant sgn Sign of input value (positive=1, negative=-1, zero=0) sin Sine sinh Hyperbolic sine sqr Square (x^2) sqrt Square root tan Tangent tanh Hyperbolic tangent EVAL V1.06 Copyright (c) 1991-1992 Copy Con Incorporated Page 3 FUNCTIONS (continued) --------------------- Parentheses are optional when using functions; if they are not used, only the first value following the function will be considered the argument. For example: sin pi evaluates to sin(pi) sin pi/2 evaluates to sin(pi)/2 sin(pi/2) evaluates to sin(pi/2) Use of functions without parentheses is potentially dangerous, and it is generally preferable to use parens to indicate function arguments. OPERATORS --------- Each operator has a precedence, and operators with higher precedence are evaluated before operators with lower precedence. Operators with equal precedence are handled from left to right within a function. Precedence is indicated by order in the following table (the first line has the highest precedence): Operators Description --------- ----------- ( ) Left parenthesis,Right parenthesis ! Unary factorial + - Unary sign ^ Exponential * / % Multiplication,Division,Modulus + - Addition,Subtraction Where it is not ambiguous, multiplication can be indicated by adjacency: 8(6-4) = 8*(6-4) = 16. Implicit multiplication is potentially dangerous, and it is generally preferable to use * to indicate multiplication. CONSTANTS --------- EVAL supports numeric constants, and three alphabetic constants, PI, E, and I. Alphabetic constants cannot directly follow functions; use "cos pi" or "cos(pi)", not "cospi". Numeric constants need not be separated from functions; "sin3" is okay. Numerical constants are entered just as you would ordinarily write them. They can be preceeded with optional + or - signs. The following are all valid numerical entries: 6.78 0.678 .678 -678 Blanks are not permitted in numbers; the expression "7 8" would be evaluated as 7 times 8, not 78. EVAL V1.06 Copyright (c) 1991-1992 Copy Con Incorporated Page 4 CONSTANTS (continued) --------------------- Complex numbers can be used as easily as real numbers. Any of EVAL's functions which are mathematically defined for complex values (like SIN and EXP) will accept complex arguments. Complex numbers are entered using the form "x+yi" where "i" is equivalent to the square root of -1. The following are all valid complex number entries: 3+4i 5.2-3.45i -63i Alphabetic constants can also be used as easily as real numbers; just be careful not to string them together with functions, variables, and other alphabetic constants; instead of "lne+api", use "ln e + a pi", or "ln(e)+a*pi". "3pi/2" and "4i" are valid, as EVAL can tell where one constant ends and another begins. Following are the approximate values of the alphabetic constants: PI = 3.14159265 E = 2.71828183 I = sqrt(-1) VARIABLES --------- The letters A-Z (except for E and I) are set aside as user-definable variables. Variables have a default value of 0, and are assigned values using the equals sign. For example: EVAL a=pi;b=cub(8);b*cos(a) will assign a value of PI to A, a value of 2 to B, and will print out the value of B times the cosine of A. As with alphabetic constants, variables cannot directly follow functions; use a space delimiter, or parentheses as above. OPTIONS ------- Options must be in the form "OPTION:value", as in "a:g" or "d:5". Case is not important. Separate options with spaces. Option Description ------ ----------- A Angular unit - whether angles will be expressed as degrees, radians, or grads. Use the first letter of the unit, as in "a:d". By default, angular units are expressed as radians. D Significant Digits - the number of significant digits shown in the expression outcome. Range is 1 thru 18; the default is 10. V Show Variables - whether variables and their values will be displayed as they are assigned values. If this option is set to F, the formulas will also be shown. Default is Y. EVAL V1.06 Copyright (c) 1991-1992 Copy Con Incorporated Page 5 ERROR MESSAGES -------------- Following are error messages you may come across, along with their descriptions and corresponding DOS errorlevels: Level Message & Description ----- --------------------- 1 Invalid input - you have attempted to use an unsupported option, or you have exceeded an option's range. 2 Invalid function '(function)' - you have attempted to use an unsupported function. If it's a common function, let us know, and we will add it. 3 Abnormal program termination - either we erred in trapping a math function, or the program has been corrupted somehow. (Please drop us a line describing everything that led up to this error, if you happen to come across it.) 4 Expression too complex - your formula has 128 or more constants, or more than 255 combined constants, functions, and operators. 5 Invalid operator '(op)' - you have attempted to use an unsupported operator. If it's a common operator, let us know, and we will add it. 6 Mixmatched parentheses - there were an uneven amount of parentheses, or a right parenthesis was encountered before its matching left paren. 7 Invalid use of functions - functions cannot be directly followed by an operator (unless the operator is a "+" or "-" indicating the sign of the value that follows). 8 Invalid use of operators - operators cannot be directly followed by other operators (unless the second operator is a "+" or "-" indicating the sign of the value that follows). 9 Invalid variable '(variable)' - an attempt was made to assign a value to a constant or a non-variable. 10 Division by zero - a denominator in your formula has a value of zero, which is mathematically undefined. 11 Argument domain/range - a function in the formula cannot evaluate its input value, as the value is outside of the function's range. 12 Argument singularity - formula would result in a singularity. 13 Overflow - the formula evaluates to a result greater than the maximum allowed. EVAL V1.06 Copyright (c) 1991-1992 Copy Con Incorporated Page 6 ERROR MESSAGES (continued) -------------------------- Level Message & Description ----- --------------------- 14 Underflow - the formula evaluates to a result less than the minimum allowed. 15 Total significance loss - formula would produce a result with a total loss of significant digits. EXAMPLES -------- EVAL sqr3 d:4 displays the square root of 3, limited to 4 significant digits. ( sqr3 evaluates to sqr(3) ) EVAL a=pi ; b=cub 8 ; b*cos(a) assigns a value of PI to A, a value of 2 to B, and displays the value of B times the cosine of A. The values of A and B are also displayed. (The spaces around the semicolons are not required) EVAL x=1/10 ; asin(5x) a:d v:n assigns a value of .1 to X, and displays the arcsine of quantity 5 times X, expressed in degrees. The value of X is not displayed. ( 5x is equivalent to 5*x ) EVAL (2+4i)/(6-8i) displays the result of the first complex number divided by the second complex number. EVAL 3*4! displays the result of 4 factorial, times 3. Since factorials are higher in precedence than multiplication, use "EVAL (3*4)!" to show 3 times 4 quantity, factorial. CORRESPONDENCE -------------- If you have questions, comments, suggestions, bug reports, etc., feel free to contact us by one of the following methods: 1: By modem at The Programmer's Corner (301-596-1180 or 410-995-3744). Send a message to user number 3000, and check back in a couple of work days for a reply. 2: By U.S. Mail at the address given on the first page. If you would like a reply, please include a self-addressed, stamped envelope. We look forward to hearing from you.