Top ¶

1 Introduction ¶

• Description
• Command Line Options

2 Basic Elements ¶

• Numbers
• Variables
• Comments

3 Expressions ¶

• About Expressions and Special Variables
• Basic Expressions
• Relational Expressions
• Boolean Expressions
• Precedence
• Special Expressions

|| 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

a = 3 < 5

4 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 Environment Variables). 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 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 causes the side effect of assigning the printed value to 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. (Some installations may allow the use of a single period (.) which is not part of a number as a short hand notation for for 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 taken 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 to 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 (\e). The special characters recognized by bc are "a" (alert or bell), "b" (backspace), "f" (form feed), "n" (newline), "r" (carriage return), "q" (double quote), "t" (tab), and "\e" (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 [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.

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 Functions.)

return ( expression )

Return the value of the expression from a function. (See Functions.) As an extension, the parenthesis are not required.

• Pseudo Statements

5 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. 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.

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 because 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 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.

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 the define keyword and all other parts must be on following lines. This version of bc will allow any number 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 as void. A void funtion returns no value and thus may not be used in any place that needs a value. A void function does not produce any output when called by itself on an input line. The key word void is placed between the key word define and the function name. For example, consider the following session.

define py (y) { print "--->", y, "<---", "\n"; }
define void px (x) { print "--->", x, "<---", "\n"; }
py(1)
--->1<---
0
px(1)
--->1<---

Since py is not a void function, the call of py(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 statement is zero, the zero is printed. For px(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 variable array, the declaration of the array parameter in the function definition looks like "*name[]". The call to the function remains the same as call by value arrays.

• Math Library Functions

6 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) {
  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.\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);
}

7 Readline and Libedit Options ¶

GNU bc can be compiled (via a configure option) to use the GNU readline input editor library or the BSD libedit library. This allows the user to do more editing of lines before sending them to bc. It also allows for a history of previous lines typed. When this option is selected, bc has one more special variable. This special variable, history is the number of lines of history retained. A value of -1 means that an unlimited number of history lines are retained. This is the default value. Setting the value of history to a positive number restricts the number of history lines to the number given. The value of 0 disables the history feature. For more information, read the user manuals for the GNU readline, history and BSD libedit libraries. One can not enable both readline and libedit at the same time.

8 Comparison with Other Implementations ¶

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. 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 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 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 \fBlast 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.

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 (currently) support array parameters in full. The POSIX grammar allows for arrays in function definitions, but does not provide a method to specify an array as an actual parameter. (This is most likely an oversight in the grammar.) Traditional implementations of bc have only call by value array parameters.

function format

POSIX bc requires the opening brace on the same line as the define key word and the auto statement on the next line.

=+, =-, =*, =/, =%, =^

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

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.

9 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.

variable names

The current limit on the number of unique names is 32767 for each of simple variables, arrays and functions.

10 Environment Variables ¶

The following environment variables are processed by bc:

POSIXLY_CORRECT

This is the same as the -s option (see Command Line Options).

BC_ENV_ARGS

This is another mechanism to get arguments to bc. 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 command line argument files. This allows the user to set up "standard" options and files to be processed at every invocation of bc. The files in the environment variables would typically contain function definitions for functions the user wants defined every time bc is run.

BC_LINE_LENGTH

This should be an integer specifying the number of characters in an output line for numbers. This includes the backslash and newline characters for long numbers. As an extension, the value of zero disables the multi-line feature. Any other value of this variable that is less than 3 sets the line length to 70.