bc [ -hlwsqv ] [long-options] [  file ... ]


       bc  is a language that supports arbitrary precision numbers with inter-
       active 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 doc-
       ument describes the language accepted by  this  processor.   Extensions
       will be identified as such.

       -h, --help
              Print the usage and exit.

       -i, --interactive
              Force interactive mode.

       -l, --mathlib
              Define the standard math library.

       -w, --warn
              Give warnings for extensions to POSIX bc.

       -s, --standard
              Process exactly the POSIX bc language.

       -q, --quiet
              Do not print the normal GNU bc welcome.

       -v, --version
              Print the version number and copyright and quit.

       The most basic element in bc is the number.  Numbers are arbitrary pre-
       cision 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 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.

       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 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 exam-
       ple, 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 for bc, 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.

       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.  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  let-
       ters  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.
       Legal values of the variable scale are 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 a
       and an array variable is specified as

       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

       expr * expr
              The  result  of the expression is the product of the two expres-
              sions.  If a and b are the scales of the two  expressions,  then
              the scale of the result is: min(a+b,max(scale,a,b))

       expr / expr
              The  result of the expression is the quotient of the two expres-
              sions.  The scale of the result is the  value  of  the  variable

       expr % expr
              The  result  of the expression is the "remainder" and it is com-
              puted in the following way.  To compute a%b, first a/b  is  com-
              puted 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  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  expo-
              nent and the maximum of scale and the scale of the first expres-
              sion.   (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

       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.

       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

       !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 opera-
       tors  to  have  some unusual behavior when used with assignment expres-
       sions.  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.
              value of the read function is the number read from the  standard
              input using the current value of the variable ibase for the con-
              version 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 expres-
              sion.  If the expression is negative, a run time error is gener-

       Statements  (as  in most algebraic languages) provide the sequencing of
       expression evaluation.  In bc statements are executed "as soon as  pos-
       sible."   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 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 sepa-
       rated by semicolons and newlines.  The following is a list of bc state-
       ments and what they do: (Things enclosed in brackets ([]) are  optional
       parts of the statement.)

              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  out-
              put.   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  preci-
              sion, 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
              The  print  statement  (an extension) provides another method of
              output.  The "list" is a list of strings and  expressions  sepa-
              rated  by  commas.   Each string or expression is printed in the
              order of the list.  No terminating newline is printed.   Expres-
              sions  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 charac-
              ters start with the backslash character (\).  The special  char-
              acters   recognized   by   bc  are  "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 [else statement2]
              The  if  statement  evaluates the expression and executes state-
              ment1 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 expres-
              sion is non-zero.  It evaluates the expression before each  exe-
              cution  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 evalu-
              ated before each execution of the statement.  If it is non-zero,
              the  statement  is evaluated.  If it is zero, the loop is termi-
              nated.  After each execution of the  statement,  expression3  is
              evaluated  before  the  reevaluation of expression2.  If expres-
              sion1 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:
              while (expression2) {

       break  This statement causes a forced exit of the most recent enclosing
              while statement or for statement.

              section on functions.)  As an extension, the parenthesis are not

       These statements are not statements in the traditional sense.  They are
       not executed statements.  Their  function  is  performed  at  "compile"

       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.

              Print a longer warranty notice.  This is an extension.

       Functions provide a method of defining a computation that can  be  exe-
       cuted  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 defi-
       nition, zero or more parameters are defined by listing their names sep-
       arated 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 defin-
       ing array parameters.  The named array is passed by value to the  func-
       tion.   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  vari-
       able.   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
       out 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  func-
       tion name.  For example, consider the following session.
              define py (y) { print "--->", y, "<---", "0; }
              define void px (x) { print "--->", x, "<---", "0; }
       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.

       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, x is in radians.

       c (x)  The cosine of x, x is in radians.

       a (x)  The arctangent of x, arctangent returns radians.
       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 imple-
       ment 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.
              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()
                return (f(x-1) * x);

       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 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  num-
       ber  of  lines  of history retained.  For readline, a value of -1 means
       that an unlimited number of history lines are  retained.   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  fea-
       ture.   The  default  value is 100. 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.

       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 "undocu-
       mented" 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  pro-
              cessing  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-char-
              acter names that start with a letter and  may  contain  letters,
              numbers and the underscore character.

              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.

              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

       print statement
              POSIX bc does not have a print statement .

       continue statement
              POSIX bc does not have a continue statement.

       return statement
              POSIX bc requires parentheses around the return expression.

       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

       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" assign-
              ments.  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  exam-
              ple,  "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  interac-
              tive 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 execu-
              interactive session, the SIGINT signal will terminate the entire
              run of bc.

       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.

              The maximum output base is currently set at  999.   The  maximum
              input base is 16.

              This  is  currently  an arbitrary limit of 65535 as distributed.
              Your installation may be different.

              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.

              The limit on the number of characters in  a  string  is  INT_MAX

              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.


       The following environment variables are processed by bc:

              This is the same as the -s option.

              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 argu-
              ments 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  envi-
              ronment  variables  would typically contain function definitions
              for functions the user wants defined every time bc is run.

              This should be an integer specifying the number of characters in
              an output line for numbers. This includes the backslash and new-


       Philip A. Nelson


       The  author  would  like to thank Steve Sommars (Steve.Sommars@att.com)
       for his extensive help in testing the implementation.  Many great  sug-
       gestions were given.  This is a much better product due to his involve-

GNU Project 2006-06-11 bc(1)

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