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- bc(1) Minix Programmer's Manual bc(1)
- NAME
- bc - An arbitrary precision calculator language
- SYNTAX
- bc [ -lws ] [ file ... ]
- VERSION
- This man page documents GNU bc version 1.02.
- DESCRIPTION
- bc is a language that supports arbitrary precision numbers with
- interactive 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. bc starts by processing code from
- all the files listed on the command line in the order listed. After all
- files have been processed, bc reads from the standard input. All code is
- executed as it is read. (If a file contains a command to halt the
- processor, bc will never read from the standard input.)
- This version of bc contains several extensions beyond traditional bc
- implementations and the POSIX draft standard. Command line options can
- cause these extensions to print a warning or to be rejected. This
- document describes the language accepted by this processor. Extensions
- will be identified as such.
- OPTIONS
- -l Define the standard math library.
- -w Give warnings for extensions to POSIX bc.
- -s Process exactly the POSIX bc language.
- NUMBERS
- The most basic element in bc is the number. Numbers are arbitrary
- precision numbers. This precision is both in the integer part and the
- fractional part. All numbers are represented internally in decimal and
- all computation is done in decimal. (This version truncates results from
- divide and multiply operations.) There are two attributes of numbers,
- the length and the scale. The length is the total number of significant
- 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.
- . 1
- bc(1) Minix Programmer's Manual bc(1)
- VARIABLES
- Numbers 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
- underscores. All letters must be lower case. (Full alpha-numeric names
- are an extension. In POSIX bc all 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, and last. scale
- defines how some operations use digits after the decimal point. The
- default value of scale is 0. ibase and obase define 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.
- COMMENTS
- Comments in bc start with the characters /* and end with the characters
- */. 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.
- EXPRESSIONS
- The 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. bc converts constants into
- internal decimal numbers using the current input base, specified by the
- variable ibase. (There is an exception in functions.) The legal values
- of ibase are 2 through 16 (F). Assigning a value outside this range to
- ibase will result in a value of 2 or 16. Input numbers may contain the
- characters 0-9 and A-F. (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 of ibase. (i.e. A = 10.) For multi-
- digit numbers, bc changes all input digits greater or equal to ibase to
- the value of ibase-1. This makes the number FFF 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 variable scale.
- . 2
- bc(1) Minix Programmer's Manual bc(1)
- Legal values of the variable scale are 0 to the maximum number
- representable 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 a
- name
- and an array variable is specified as
- name[expr]
- Unless specifically mentioned the scale of the result is the maximum
- scale of the expressions involved.
- - expr
- The result is the negation of the expression.
- ++ var
- The variable is incremented by one and the new value is the result
- of the expression.
- -- var
- The 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 variable and then
- the variable is incremented by one.
- var --
- The result of the expression is the value of the variable and then
- the variable is decremented by one.
- expr + expr
- The result of the expression is the sum of the two expressions.
- expr - expr
- The result of the expression is the difference of the two
- expressions.
- expr * expr
- The result of the expression is the product of the two expressions.
- expr / expr
- The result of the expression is the quotient of the two expressions.
- The scale of the result is the value of the variable scale.
- expr % expr
- The result of the expression is the "remainder" and it is computed
- in the following way. To compute a%b, first a/b is computed to
- scale digits. That result is used to compute a-(a/b)*b to the scale
- of the maximum of scale+scale(b) and scale(a). If scale is set to
- . 3
- bc(1) Minix Programmer's Manual bc(1)
- zero and both expressions are integers this expression is the
- integer remainder function.
- expr ^ expr
- The 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 is scale if the exponent is negative. If the exponent is
- positive the scale of the result is the minimum of the scale of the
- first expression times the value of the exponent and the maximum of
- scale and 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 evaluation of the
- expression.
- var = expr
- The variable is assigned the value of the expression.
- var <op>= expr
- This is equivalent to "var = var <op> expr" with 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
- evaluate to 0 or 1, 0 if the relation is false and 1 if the relation is
- true. These may appear in any legal expression. (POSIX bc requires that
- relational expressions are used only in if, while, and for statements and
- that only one relational test may be done in them.) The relational
- operators are
- expr1 < expr2
- The result is 1 if expr1 is strictly less than expr2.
- expr1 <= expr2
- The result is 1 if expr1 is less than or equal to expr2.
- expr1 > expr2
- The result is 1 if expr1 is strictly greater than expr2.
- expr1 >= expr2
- The result is 1 if expr1 is greater than or equal to expr2.
- expr1 == expr2
- The result is 1 if expr1 is equal to expr2.
- . 4
- bc(1) Minix Programmer's Manual bc(1)
- expr1 != expr2
- The result is 1 if expr1 is not equal to expr2.
- Boolean operations are also legal. (POSIX bc does NOT have boolean
- operations). The result of all boolean operations are 0 and 1 (for false
- and true) as in relational expressions. The boolean operators are:
- !expr
- The result is 1 if expr is 0.
- expr && expr
- The result is 1 if both expressions are non-zero.
- expr || expr
- The result is 1 if either expression is non-zero.
- The expression precedence is as follows: (lowest to highest)
- || operator, left associative
- && operator, left associative
- ! operator, nonassociative
- Relational operators, left associative
- Assignment operator, right associative
- + and - operators, left associative
- *, / and % operators, left associative
- ^ operator, right associative
- unary - operator, nonassociative
- ++ and -- operators, nonassociative
- This precedence was chosen so that POSIX compliant bc programs will run
- correctly. This will cause the use of the relational and logical
- operators to have some unusual behavior when used with assignment
- expressions. Consider the expression:
- a = 3 < 5
- Most C programmers would assume this would assign the result of "3 < 5"
- (the value 1) to the variable "a". What this does in bc is 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
- assignment operators.
- There are a few more special expressions that are provided in bc. 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.
- . 5
- bc(1) Minix Programmer's Manual bc(1)
- 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 previously
- 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 variable ibase for the conversion 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.
- STATEMENTS
- Statements (as in most algebraic languages) provide the sequencing of
- expression evaluation. In bc statements 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,
- newlines are very important in bc. 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 to bc as whitespace
- instead of a newline. A statement list is a series of statements
- separated by semicolons and newlines. The following is a list of bc
- statements and what they do: (Things enclosed in brackets ([]) are
- optional parts of the statement.)
- expression
- This statement does one of two things. If the expression starts
- with "<variable> <assignment> ...", it is considered to be an
- assignment statement. If the expression 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 expression that
- has an embedded assignment. All numbers that are printed are
- printed in the base specified by the variable obase. The legal
- values for obase are 2 through BC_BASE_MAX. (See the section
- LIMITS.) For bases 2 through 16, the usual method of writing
- numbers is used. For bases greater than 16, bc uses 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 numbers are of arbitrary precision, some numbers may not be
- . 6
- bc(1) Minix Programmer's Manual bc(1)
- 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 of bc printing a number cause the side effect of
- assigning the printed value the the special variable last. This
- allows the user to recover the last value printed without having to
- retype the expression that printed the number. Assigning to last is
- 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 to last.
- string
- The string is 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.
- print list
- The print statement (an extension) provides another method of
- output. The "list" is a list of strings and expressions separated
- by commas. Each string or expression is printed in the order of the
- list. No terminating newline is printed. Expressions are evaluated
- and their value is printed and assigned the the variable last.
- Strings in the print statement are printed to the output and may
- contain special characters. Special characters start with the
- backslash character (). The special characters recognized by bc
- are "b" (bell), "f" (form feed), "n" (newline), "r" (carriage
- return), "t" (tab), and "" (backslash). Any other character
- following the backslash will be ignored. This still does not allow
- the double quote character to be part of any string.
- { statement_list }
- This is the compound statement. It allows multiple statements to be
- grouped together for execution.
- if ( expression ) then statement1 [else statement2]
- The if statement evaluates the expression and executes statement1 or
- statement2 depending on the value of the expression. If the
- expression is non-zero, statement1 is executed. If statement2 is
- present and the value of the expression is 0, then statement2 is
- executed. (The else clause is an extension.)
- while ( expression ) statement
- The while statement will execute the statement while the expression
- is non-zero. It evaluates the expression before each execution of
- the statement. Termination of the loop is caused by a zero
- expression value or the execution of a break statement.
- . 7
- bc(1) Minix Programmer's Manual bc(1)
- for ( [expression1] ; [expression2] ; [expression3] ) statement
- The for statement controls repeated execution of the statement.
- Expression1 is evaluated before the loop. Expression2 is evaluated
- before each execution of the statement. If it is non-zero, the
- statement is evaluated. If it is zero, the loop is terminated.
- After each execution of the statement, expression3 is evaluated
- before the reevaluation of expression2. If expression1 or
- expression3 are missing, nothing is evaluated at the point they
- would be evaluated. If expression2 is missing, it is the same as
- substituting the value 1 for expression2. (The optional expressions
- are an extension. POSIX bc requires all three expressions.) The
- following is equivalent code for the for statement:
- expression1;
- while (expression2) {
- statement;
- expression3;
- }
- break
- This statement causes a forced exit of the most recent enclosing
- while statement or for statement.
- continue
- The continue statement (an extension) causes the most recent
- enclosing for statement to start the next iteration.
- halt The halt statement (an extension) is an executed statement that
- causes the bc processor to quit only when it is executed. For
- example, "if (0 == 1) halt" will not cause bc to terminate because
- the halt is not executed.
- return
- Return 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.)
- PSEUDO STATEMENTS
- These statements are not statements in the traditional sense. They are
- not executed statements. Their function is performed at "compile" time.
- limits
- Print the local limits enforced by the local version of bc. This is
- an extension.
- quit When the quit statement is read, the bc processor is terminated,
- regardless of where the quit statement is found. For example, "if
- (0 == 1) quit" will cause bc to terminate.
- . 8
- bc(1) Minix Programmer's Manual bc(1)
- warranty
- Print a longer warranty notice. This is an extension.
- FUNCTIONS
- Functions provide a method of defining a computation that can be executed
- later. Functions in bc always 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
- definition 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
- definition, zero or more parameters are defined by listing their names
- separated by commas. Numbers are only call by value parameters. Arrays
- are only call by variable. 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 variable 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.
- The auto_list is an optional list of variables that are for "local" use.
- The syntax of the auto list (if present) is "auto name, ... ;". (The
- semicolon is optional.) Each name is 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 in the fact that
- if function 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, bc supports recursive functions.
- The function body is a list of bc statements. Again, statements are
- separated by semicolons or newlines. Return statements cause the
- termination 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
- )", computes the value of the expression and returns that value to the
- . 9
- bc(1) Minix Programmer's Manual bc(1)
- calling expression. There is an implied "return (0)" at the end of every
- function. This allows a function to terminate and return 0 without an
- explicit return statement.
- Functions also change the usage of the variable ibase. All constants in
- the function body will be converted using the value of ibase at the time
- of the function call. Changes of ibase will be ignored during the
- execution of the function except for the standard function read, which
- will always use the current value of ibase for conversion of numbers.
- MATH LIBRARY
- If bc is invoked with the -l option, 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 in radians.
- c (x)
- The cosine of x in radians.
- a (x)
- The arctangent of x.
- 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.
- EXAMPLES
- In /bin/sh, the following will assign the value of "pi" to the shell
- variable pi.
- 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 POSIX bc.
- 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) {
- . 10
- bc(1) Minix Programmer's Manual bc(1)
- 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 of bc to 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.nn"
- print "Initial balance? "; bal = read()
- bal /= 1
- print "n"
- while (1) {
- "current balance = "; bal
- "transaction? "; trans = read()
- . 11
- bc(1) Minix Programmer's Manual bc(1)
- 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);
- }
- DIFFERENCES
- This version of bc was 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 standard
- 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 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 POSIX bc have 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 underscore character.
- Strings Strings are not allowed to contain NUL characters. POSIX says
- all characters must be included in strings.
- last POSIX bc does not have a last variable. Some implementations
- of bc use the period (.) in a similar way.
- comparisons
- POSIX bc allows comparisons only in the if statement, the
- while statement, and the second expression of the for
- statement. Also, only one relational operation is allowed in
- each of those statements.
- . 12
- bc(1) Minix Programmer's Manual bc(1)
- if statement, else clause
- POSIX bc does not have an else clause.
- for statement
- POSIX bc requires all expressions to be present in the for
- statement.
- &&, ||, ! POSIX bc does not have the logical operators.
- read function
- POSIX bc does not have a read function.
- print statement
- POSIX bc does not have a print statement .
- continue statement
- POSIX bc does not have a continue statement.
- array parameters
- POSIX bc does not have array parameters. Other
- implementations of bc may have call by value array parameters.
- =+, =-, =*, =/, =%, =^
- POSIX bc does not require these "old style" assignment
- operators to be defined. This version may allow these "old
- style" assignments. Use the limits statement to see if the
- installed version supports them. If it does support the "old
- style" assignment operators, the statement "a =- 1" will
- decrement a by 1 instead of setting a to the value -1.
- spaces in numbers
- Other implementations of bc allow spaces in numbers. For
- example, "x=1 3" would assign the value 13 to the variable x.
- The same statement would cause a syntax error in this version
- of bc.
- 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 statements.
- For example,
- a = 1
- b = 2
- . 13
- bc(1) Minix Programmer's Manual bc(1)
- has two execution blocks and
- { a = 1
- b = 2 }
- has one execution block. Any runtime error will terminate 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 (usually
- generated by the control-C character from the terminal) 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 that bc is 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 of bc.
- LIMITS
- The following are the limits currently in place for this bc processor.
- Some of them may have been changed by an installation. Use the limits
- statement 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 distributed.
- 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.
- multiply The multiply routine may yield incorrect results if a number
- has more than LONG_MAX / 90 total digits. For 32 bit longs,
- this number is 23,860,929 digits.
- . 14
- bc(1) Minix Programmer's Manual bc(1)
- code size Each function and the "main" program are limited to 10240
- bytes of compiled byte code each. This limit (BC_MAX_SEGS)
- can be easily changed to have more than 10 segments of 1024
- bytes.
- variable names
- The current limit on the number of unique names is 32767 for
- each of simple variables, arrays and functions.
- FILES
- In most installations, bc is completely self-contained. Where executable
- size is of importance or the C compiler does not deal with very long
- strings, bc will read the standard math library from the file
- /usr/local/lib/libmath.b. (The actual location may vary. It may be
- /lib/libmath.b.)
- DIAGNOSTICS
- If any file on the command line can not be opened, bc will report that
- the file is unavailable and terminate. Also, there are compile and run
- time diagnostics that should be self-explanatory.
- BUGS
- Error recovery is not very good yet.
- AUTHOR
- Philip A. Nelson
- phil@cs.wwu.edu
- ACKNOWLEDGEMENTS
- The author would like to thank Steve Sommars (sesv@iwtsf.att.com) for his
- extensive help in testing the implementation. Many great suggestions
- were given. This is a much better product due to his involvement.
- . 15