BC(1) NetBSD General Commands Manual BC(1)NAME

bc-- arbitrary precision calculator languageSYNOPSIS

bc[-hilqsvw] [long-options] [file ...]DESCRIPTION

bcis a language that supports arbitrary precision numbers with interac- tive execution of statements. There are some similarities in the syntax to the C programming language. A standard math library is available by command line option. If requested, the math library is defined before processing any files.bcstarts by processing code from all the files listed on the command line in the order listed. After all files have been processed,bcreads from the standard input. All code is executed as it is read. (If a file contains a command to halt the processor,bcwill never read from the standard input.) This version ofbccontains several extensions beyond traditionalbcimplementations and the POSIX draft standard. Command line options can cause these extensions to print a warning or to be rejected. This docu- ment describes the language accepted by this processor. Extensions will be identified as such.OPTIONS-h,--helpPrint the usage and exit.-i,--interactiveForce interactive mode.-l,--mathlibDefine the standard math library.-q,--quietQuiet mode.-s,--standardProcess exactly the POSIXbclanguage.-v,--versionPrint the version number and copyright and quit.-w,--warnGive warnings for extensions to POSIXbc.NUMBERSThe most basic element inbcis the number. Numbers are arbitrary preci- sion numbers. This precision is both in the integer part and the frac- tional part. All numbers are represented internally in decimal and all computation is done in decimal. (This version ofbctruncates results from divide and multiply operations.) There are two attributes of num- bers, the length and the scale. The length is the total number of sig- nificant decimal digits in a number and the scale is the total number of decimal digits after the decimal point. For example: .000001 has a length of 6 and scale of 6. 1935.000 has a length of 7 and a scale of 3.VARIABLESNumbers are stored in two types of variables, simple variables and arrays. Both simple variables and array variables are named. Names begin with a letter followed by any number of letters, digits and under- scores. All letters must be lower case. (Full alpha-numeric names are an extension. In POSIXbcall names are a single lower case letter.) The type of variable is clear by the context because all array variable names will be followed by brackets ([]). There are four special variables,scale,ibase,obase, andlast.scaledefines how some operations use digits after the decimal point. The default value ofscaleis 0.ibaseandobasedefine the conversion base for input and output numbers. The default for both input and output is base 10.last(an extension) is a variable that has the value of the last printed number. These will be discussed in further detail where appropriate. All of these variables may have values assigned to them as well as used in expressions.COMMENTSComments inbcstart with the characters ``/*'' and end with the charac- ters ``*/''. Comments may start anywhere and appear as a single space in the input. (This causes comments to delimit other input items. For example, a comment can not be found in the middle of a variable name.) Comments include any newlines (end of line) between the start and the end of the comment. To support the use of scripts forbc, a single line comment has been added as an extension. A single line comment starts at a ``#'' character and continues to the next end of the line. The end of line character is not part of the comment and is processed normally.EXPRESSIONSThe numbers are manipulated by expressions and statements. Since the language was designed to be interactive, statements and expressions are executed as soon as possible. There is no ``main'' program. Instead, code is executed as it is encountered. (Functions, discussed in detail later, are defined when encountered.) A simple expression is just a constant.bcconverts constants into internal decimal numbers using the current input base, specified by the variableibase. (There is an exception in functions.) The legal values ofibaseare 2 through 36. (Base values greater than 16 are an exten- sion.) Assigning a value outside this range toibasewill result in a value of 2 or 36. Input numbers may contain the characters 0-9 and A-Z. (Note: They must be capitals. Lower case letters are variable names.) Single digit numbers always have the value of the digit regardless of the value ofibase. (i.e. A = 10.) For multi-digit numbers,bcchanges all input digits greater or equal to ibase to the value ofibase - 1. This makes the number ``ZZZ'' always be the largest 3 digit number of the input base. Full expressions are similar to many other high level languages. Since there is only one kind of number, there are no rules for mixing types. Instead, there are rules on the scale of expressions. Every expression has a scale. This is derived from the scale of original numbers, the operation performed and in many cases, the value of the variablescale. Legal values of the variablescaleare 0 to the maximum number repre- sentable by a C integer. In the following descriptions of legal expressions, ``expr'' refers to a complete expression and ``var'' refers to a simple or an array variable. A simple variable is just anameand an array variable is specified asname[expr]. Unless specifically mentioned the scale of the result is the maximum scale of the expressions involved.- exprThe result is the negation of the expression.++ varThe variable is incremented by one and the new value is the result of the expression.-- varThe variable is decremented by one and the new value is the result of the expression.var ++The result of the expression is the value of the vari- able and then the variable is incremented by one.var --The result of the expression is the value of the vari- able and then the variable is decremented by one.expr + exprThe result of the expression is the sum of the two expressions.expr - exprThe result of the expression is the difference of the two expressions.expr * exprThe result of the expression is the product of the two expressions.expr / exprThe result of the expression is the quotient of the two expressions. The scale of the result is the value of the variablescale.expr % exprThe result of the expression is the remainder and it is computed in the following way: To compute a%b, first a/b is computed toscaledigits. That result is used to compute a-(a/b)*b to the scale of the maximum ofscale +scale(b) and scale(a). Ifscaleis set to zero and both expressions are integers this expression is the integer remainder function.expr ^ exprThe result of the expression is the value of the first raised to the second. The second expression must be an integer. (If the second expression is not an integer, a warning is generated and the expression is truncated to get an integer value.) The scale of the result isscaleif the exponent is negative. If the exponent is posi- tive, the scale of the result is the minimum of the scale of the first expression times the value of the exponent and the maximum ofscaleand the scale of the first expression. (e.g. scale(a^b) = min(scale(a)*b, max(scale, scale(a))).) It should be noted that expr^0 will always return the value of 1.( expr )This alters the standard precedence to force the evalua- tion of the expression.var = exprThe variable is assigned the value of the expression.var <op>= exprThis is equivalent tovar = var <op> exprwith the exception that the ``var'' part is evaluated only once. This can make a difference if ``var'' is an array. Relational expressions are a special kind of expression that always eval- uate to 0 or 1, 0 if the relation is false and 1 if the relation is true. These may appear in any legal expression. (POSIXbcrequires that rela- tional expressions are used only inif,while, andforstatements and that only one relational test may be done in them.) The relational oper- ators are:expr1 < expr2The result is 1 if expr1 is strictly less than expr2.expr1 <= expr2The result is 1 if expr1 is less than or equal to expr2.expr1 > expr2The result is 1 if expr1 is strictly greater than expr2.expr1 >= expr2The result is 1 if expr1 is greater than or equal to expr2.expr1 == expr2The result is 1 if expr1 is equal to expr2.expr1 != expr2The result is 1 if expr1 is not equal to expr2. Boolean operations are also legal. (POSIXbcdoesNOThave boolean oper- ations.) The result of all boolean operations are 0 and 1 (for false and true) as in relational expressions. The boolean operators are:!exprThe result is 1 if expr is 0.expr && exprThe result is 1 if both expressions are non-zero.expr || exprThe result is 1 if either expression is non-zero. The expression precedence is as follows: (lowest to highest) 1. || operator, left associative 2. && operator, left associative 3. ! operator, nonassociative 4. Relational operators, left associative 5. Assignment operator, right associative 6. + and - operators, left associative 7. *, / and % operators, left associative 8. ^ operator, right associative 9. unary - operator, nonassociative 10. ++ and -- operators, nonassociative This precedence was chosen so that POSIX compliantbcprograms will run correctly. This will cause the use of the relational and logical opera- tors to have some unusual behavior when used with assignment expressions. Consider the expression:a = 3 < 5Most C programmers would assume this would assign the result of ``3 < 5'' (the value 1) to the variable ``a''. What this does inbcis assign the value 3 to the variable ``a'' and then compare 3 to 5. It is best to use parenthesis when using relational and logical operators with the assign- ment operators. There are a few more special expressions that are provided inbc. These have to do with user defined functions and standard functions. They all appear as ``name(parameters)''. See the section on functions for user defined functions. The standard functions are:length(expression) The value of the length function is the number of significant digits in the expression.read() The read function (an extension) will read a number from the standard input, regardless of where the function occurs. Beware, this can cause problems with the mixing of data and program in the standard input. The best use for this function is in a pre- viously written program that needs input from the user, but never allows program code to be input from the user. The value of the read function is the number read from the standard input using the current value of the variableibasefor the conver- sion base.scale(expression) The value of the scale function is the number of digits after the decimal point in the expression.sqrt(expression) The value of the sqrt function is the square root of the expression. If the expression is negative, a run time error is generated.STATEMENTSStatements (as in most algebraic languages) provide the sequencing of expression evaluation. Inbcstatements are executed ``as soon as possible''. Execution happens when a newline in encountered and there is one or more complete statements. Due to this immediate execution, new- lines are very important inbc. In fact, both a semicolon and a newline are used as statement separators. An improperly placed newline will cause a syntax error. Because newlines are statement separators, it is possible to hide a newline by using the backslash character. The sequence ``\<nl>'', where <nl> is the newline appears tobcas whitespace instead of a newline. A statement list is a series of statements sepa- rated by semicolons and newlines. The following is a list ofbcstate- ments and what they do: (Things enclosed in brackets ([]) are optional parts of the statement.)expressionThis statement does one of two things. If the expres- sion starts with <variable> <assignment> ..., it is con- sidered to be an assignment statement. If the expres- sion is not an assignment statement, the expression is evaluated and printed to the output. After the number is printed, a newline is printed. For example, ``a=1'' is an assignment statement and ``(a=1)'' is an expres- sion that has an embedded assignment. All numbers that are printed are printed in the base specified by the variableobase. The legal values forobaseare 2 through BC_BASE_MAX. (See the sectionLIMITS.) For bases 2 through 16, the usual method of writing numbers is used. For bases greater than 16,bcuses a multi- character digit method of printing the numbers where each higher base digit is printed as a base 10 number. The multi-character digits are separated by spaces. Each digit contains the number of characters required to represent the base ten value of ``obase-1''. Since num- bers are of arbitrary precision, some numbers may not be printable on a single output line. These long numbers will be split across lines using the ``\'' as the last character on a line. The maximum number of characters printed per line is 70. Due to the interactive nature ofbc, printing a number causes the side effect of assigning the printed value to the special variablelast. This allows the user to recover the last value printed without having to retype the expression that printed the number. Assigning tolastis legal and will overwrite the last printed value with the assigned value. The newly assigned value will remain until the next number is printed or another value is assigned tolast. (Some installations may allow the use of a single period (.) which is not part of a number as a short hand notation forlast.)stringThestringis printed to the output. Strings start with a double quote character and contain all characters until the next double quote character. All characters are take literally, including any newline. No newline character is printed after the string.listThelistis a list of strings and expressions separated by commas. Each string or expres- sion is printed in the order of the list. No terminat- ing newline is printed. Expressions are evaluated and their value is printed and assigned to the variablelast. Strings in thebcare `a' (alert or bell), `b' (backspace), `f' (form feed), `n' (newline), `r' (carriage return), `q' (double quote), `t' (tab), and `\' (backslash). Any other character following the backslash will be ignored. {statement_list }This is the compound statement. It allows multiple statements to be grouped together for execution.if(expression)statement1[elsestatement2] Theifstatement evaluates theexpressionand executesstatement1orstatement2depending on the value of theexpression. If theexpressionis non-zero,statement1is executed. Ifstatement2is present and the value of theexpressionis 0, thenstatement2is executed. (Theelseclause is an extension.)while(expression)statementThewhilestatement will execute thestatementwhile theexpressionis non-zero. It evaluates theexpressionbefore each execution of thestatement. Termination of the loop is caused by a zeroexpressionvalue or the execution of abreakstatement.for([expression1]; [expression2]; [expression3])statementTheforstatement controls repeated execution of thestatement.Expression1is evaluated before the loop.Expression2is evaluated before each execution of thestatement. If it is non-zero, thestatementis evalu- ated. If it is zero, the loop is terminated. After each execution of the statement,expression3is evalu- ated before the reevaluation ofexpression2. Ifexpression1orexpression3are missing, nothing is eval- uated at the point they would be evaluated. Ifexpression2is missing, it is the same as substituting the value 1 forexpression2. (The optional expressions are an extension. POSIXbcrequires all three expres- sions.) The following is equivalent code for theforstatement: expression1; while (expression2) { statement; expression3; }breakThis statement causes a forced exit of the most recent enclosingwhilestatement orforstatement.continueThecontinuestatement (an extension) causes the most recent enclosingforstatement to start the next itera- tion.haltThehaltstatement (an extension) is an executed state- ment that causes thebcprocessor to quit only when it is executed. For example, if (0 == 1) halt will not causebcto terminate because the halt is not executed.returnReturn the value 0 from a function. (See the section on functions.)return(expression) Return the value of the expression from a function. (See the section on functions.) As an extension, the parenthesis are not required.PSEUDO STATEMENTSThese statements are not statements in the traditional sense. They are not executed statements. Their function is performed at "compile" time.limitsPrint the local limits enforced by the local version ofbcThis is an extension.quitWhen thequitstatement is read, thebcprocessor is terminated, regardless of where the quit statement is found. For example, if (0 == 1) quit will causebcto terminate.warrantyPrint a longer warranty notice. This is an extension.FUNCTIONSFunctions provide a method of defining a computation that can be executed later. Functions inbcalways compute a value and return it to the caller. Function definitions are "dynamic" in the sense that a function is undefined until a definition is encountered in the input. That defi- nition is then used until another definition function for the same name is encountered. The new definition then replaces the older definition. A function is defined as follows: define name ( parameters ) { newline auto_list statement_list } A function call is just an expression of the form ``name(parameters)''. Parameters are numbers or arrays (an extension). In the function defini- tion, zero or more parameters are defined by listing their names sepa- rated by commas. All parameters are call by value parameters. Arrays are specified in the parameter definition by the notation ``name[]''. In the function call, actual parameters are full expressions for number parameters. The same notation is used for passing arrays as for defining array parameters. The named array is passed by value to the function. Since function definitions are dynamic, parameter numbers and types are checked when a function is called. Any mismatch in number or types of parameters will cause a runtime error. A runtime error will also occur for the call to an undefined function. Theauto_listis an optional list of variables that are for "local" use. The syntax of the auto list (if present) is ``autoname,...;''. (The semicolon is optional.) Eachnameis the name of an auto variable. Arrays may be specified by using the same notation as used in parameters. These variables have their values pushed onto a stack at the start of the function. The variables are then initialized to zero and used throughout the execution of the function. At function exit, these variables are popped so that the original value (at the time of the function call) of these variables are restored. The parameters are really auto variables that are initialized to a value provided in the function call. Auto variables are different than traditional local variables because if func- tion A calls function B, B may access function A's auto variables by just using the same name, unless function B has called them auto variables. Due to the fact that auto variables and parameters are pushed onto a stack,bcsupports recursive functions. The function body is a list ofbcstatements. Again, statements are sep- arated by semicolons or newlines. Return statements cause the termina- tion of a function and the return of a value. There are two versions of the return statement. The first form, ``return'', returns the value 0 to the calling expression. The second form, ``return(expression)'', com- putes the value of the expression and returns that value to the calling expression. There is an implied ``return(0)'' at the end of every func- tion. This allows a function to terminate and return 0 without an explicit return statement. Functions also change the usage of the variableibase. All constants in the function body will be converted using the value ofibaseat the time of the function call. Changes ofibasewill be ignored during the execu- tion of the function except for the standard functionread, which will always use the current value ofibasefor conversion of numbers. Several extensions have been added to functions. First, the format of the definition has been slightly relaxed. The standard requires the opening brace be on the same line as thedefinekeyword and all other parts must be on following lines. This version ofbcwill allow any num- ber of newlines before and after the opening brace of the function. For example, the following definitions are legal. define d (n) { return (2*n); } define d (n) { return (2*n); } Functions may be defined asvoid. Avoidfuntion returns no value and thus may not be used in any place that needs a value. Avoidfunction does not produce any output when called by itself on an input line. The key wordvoidis placed between the key worddefineand the function name. For example, consider the following session. define py (y) { print "--->", y, "<---", "0; } define void px (x) { print "--->", x, "<---", "0; } py(1) --->1<--- 0 px(1) --->1<--- Sincepyis not a void function, the call ofpy(1) prints the desired output and then prints a second line that is the value of the function. Since the value of a function that is not given an explicit return state- ment is zero, the zero is printed. Forpx(1), no zero is printed because the function is a void function. Also, call by variable for arrays was added. To declare a call by vari- able array, the declaration of the array parameter in the function defi- nition looks like ``name[]''. The call to the function remains the same as call by value arrays.MATH LIBRARYIfbcis invoked with the-loption, a math library is preloaded and the default scale is set to 20. The math functions will calculate their results to the scale set at the time of their call. The math library defines the following functions:s(x) The sine of x, x is in radians.c(x) The cosine of x, x is in radians.a(x) The arctangent of x, arctangent returns radians.l(x) The natural logarithm of x.e(x) The exponential function of raising e to the value x.j(n,x) The Bessel function of integer order n of x.ENVIRONMENT

The following environment variables are processed bybc: POSIXLY_CORRECT This is the same as the-soption. BC_ENV_ARGS This is another mechanism to get arguments tobc. The format is the same as the command line arguments. These arguments are processed first, so any files listed in the environment arguments are processed before any com- mand line argument files. This allows the user to set up "standard" options and files to be processed at every invocation ofbc. The files in the environment vari- ables would typically contain function definitions for functions the user wants defined every timebcis run. BC_LINE_LENGTH This should be an integer specifying the number of char- acters in an output line for numbers. This includes the backslash and newline characters for long numbers.EXAMPLES

In/bin/sh, the following will assign the value ofpito the shell vari- ablepi. pi=$(echo "scale=10; 4*a(1)" | bc -l) The following is the definition of the exponential function used in the math library. This function is written in POSIXbc. scale = 20 /* Uses the fact that e^x = (e^(x/2))^2 When x is small enough, we use the series: e^x = 1 + x + x^2/2! + x^3/3! + ... */ define e(x) { auto a, d, e, f, i, m, v, z /* Check the sign of x. */ if (x<0) { m = 1 x = -x } /* Precondition x. */ z = scale; scale = 4 + z + .44*x; while (x > 1) { f += 1; x /= 2; } /* Initialize the variables. */ v = 1+x a = x d = 1 for (i=2; 1; i++) { e = (a *= x) / (d *= i) if (e == 0) { if (f>0) while (f--) v = v*v; scale = z if (m) return (1/v); return (v/1); } v += e } } The following is code that uses the extended features ofbcto implement a simple program for calculating checkbook balances. This program is best kept in a file so that it can be used many times without having to retype it at every use. scale=2 print "\nCheck book program!\n" print " Remember, deposits are negative transactions.\n" print " Exit by a 0 transaction.\n\n" print "Initial balance? "; bal = read() bal /= 1 print "\n" while (1) { "current balance = "; bal "transaction? "; trans = read() if (trans == 0) break; bal -= trans bal /= 1 } quit The following is the definition of the recursive factorial function. define f (x) { if (x <= 1) return (1); return (f(x-1) * x); }EDITLINE OPTIONSbcis compiled using the editline(3) library. This allows the user to do editing of lines before sending them tobc. It also allows for a history of previous lines typed. This adds tobcone more special variable. This special variable,historyis the number of lines of history retained. The default value of -1 means that an unlimited number of his- tory lines are retained. Setting the value ofhistoryto a positive num- ber restricts the number of history lines to the number given. The value of 0 disables the history feature. For more information, read the user manual for the editline(3) library.DIFFERENCESThis version ofbcwas implemented from the POSIX P1003.2/D11 draft and contains several differences and extensions relative to the draft and traditional implementations. It is not implemented in the traditional way using dc(1). This version is a single process which parses and runs a byte code translation of the program. There is an "undocumented" option (-c) that causes the program to output the byte code to the stan- dard output instead of running it. It was mainly used for debugging the parser and preparing the math library. A major source of differences is extensions, where a feature is extended to add more functionality and additions, where new features are added. The following is the list of differences and extensions. LANG environment This version does not conform to the POSIX standard in the processing of the LANG environment variable and all environment variables starting with LC_. names Traditional and POSIXbchave single letter names for functions, variables and arrays. They have been extended to be multi-character names that start with a letter and may contain letters, numbers and the under- score character. strings Strings are not allowed to contain NUL characters. POSIX says all characters must be included in strings.lastPOSIXbcdoes not have alastvariable. Some implementations ofbcuse the period (.) in a similar way. comparisons POSIXbcallows comparisons only in theifstatement, thewhilestatement, and the second expression of theforstatement. Also, only one relational operation is allowed in each of those statements.ifstatement,elseclause POSIXbcdoes not have anelseclause.forstatement POSIXbcrequires all expressions to be present in theforstatement. &&, ||, ! POSIXbcdoes not have the logical operators.readfunction POSIXbcdoes not have areadfunction.bcdoes not have acontinuestatement POSIXbcdoes not have acontinuestatement.returnstatement POSIXbcrequires parentheses around the return expres- sion. array parameters POSIXbcdoes not (currently) support array parameters in full. The POSIX grammar allows for arrays in func- tion definitions, but does not provide a method to spec- ify an array as an actual parameter. (This is most likely an oversight in the grammar.) Traditional imple- mentations ofbchave only call-by-value array parame- ters. function format POSIXbcrequires the opening brace on the same line as thedefinekey word and theautostatement on the next line. =+, =-, =*, =/, =%, =^ POSIXbcdoes not require these "old style" assignment operators to be defined. This version may allow these "old style" assignments. Use thelimitsstatement to see if the installed version supports them. If it does support the "old style" assignment operators, the state- ment ``a =- 1'' will decrementaby 1 instead of settingato the value -1. spaces in numbers Other implementations ofbcallow spaces in numbers. For example, ``x=1 3'' would assign the value 13 to the variablex. The same statement would cause a syntax error in this version ofbc. errors and execution This implementation varies from other implementations in terms of what code will be executed when syntax and other errors are found in the program. If a syntax error is found in a function definition, error recovery tries to find the beginning of a statement and continue to parse the function. Once a syntax error is found in the function, the function will not be callable and becomes undefined. Syntax errors in the interactive execution code will invalidate the current execution block. The execution block is terminated by an end of line that appears after a complete sequence of state- ments. For example, a = 1 b = 2 has two execution blocks and { a = 1 b = 2 } has one execution block. Any runtime error will termi- nate the execution of the current execution block. A runtime warning will not terminate the current execution block. interrupts During an interactive session, the SIGINT signal (usu- ally generated by the control-C character from the ter- minal) will cause execution of the current execution block to be interrupted. It will display a "runtime" error indicating which function was interrupted. After all runtime structures have been cleaned up, a message will be printed to notify the user thatbcis ready for more input. All previously defined functions remain defined and the value of all non-auto variables are the value at the point of interruption. All auto variables and function parameters are removed during the clean up process. During a non-interactive session, the SIGINT signal will terminate the entire run ofbc.LIMITSThe following are the limits currently in place for thisbcprocessor. Some of them may have been changed by an installation. Use thelimitsstatement to see the actual values. BC_BASE_MAX The maximum output base is currently set at 999. The maximum input base is 16. BC_DIM_MAX This is currently an arbitrary limit of 65535 as dis- tributed. Your installation may be different. BC_SCALE_MAX The number of digits after the decimal point is limited to INT_MAX digits. Also, the number of digits before the decimal point is limited to INT_MAX digits. BC_STRING_MAX The limit on the number of characters in a string is INT_MAX characters. exponent The value of the exponent in the raise operation (^) is limited to LONG_MAX. variable names The current limit on the number of unique names is 32767 for each of simple variables, arrays and functions.DIAGNOSTICS

If any file on the command line can not be opened,bcwill report that the file is unavailable and terminate. Also, there are compile and run time diagnostics that should be self-explanatory.HISTORY

This man page documents bc version nb1.0.AUTHORS

Philip A. Nelson <phil@NetBSD.org>ACKNOWLEDGEMENTSThe author would like to thank Steve Sommars for his extensive help in testing the implementation. Many great suggestions were given. This is a much better product due to his involvement.BUGS

Error recovery is not very good yet. NetBSD 9.0 April 16, 2017 NetBSD 9.0

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