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    Command:

    bc

    
    
    

    SYNTAX

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

    DESCRIPTION

           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.
    
       OPTIONS
           -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.
    
       NUMBERS
           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
           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.
    
       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.  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
                  name
           and an array variable is specified as
                  name[expr]
    
           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  expres-
                  sions.
    
           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
                  scale.
    
           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
                  difference if "var" is an array.
    
                  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
           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 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.
           They all appear as "name(parameters)".  See the  section  on  functions
           for user defined functions.  The standard functions are:
                  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-
                  ated.
    
       STATEMENTS
           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.)
    
           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  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
                  expression that printed the number.  Assigning to last is  legal
                  and  will  overwrite  the  last  printed value with the assigned
                  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:
                  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
    
       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.
    
           warranty
                  Print a longer warranty notice.  This is an extension.
    
       FUNCTIONS
           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
           function call.  Auto variables are  different  than  traditional  local
           variables because if function A calls function B, B may access function
           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; }
                  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
           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.
           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 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.
    
                  scale=2
                  print "\nCheck book program!\n"
                  print "  Remember, deposits are negative transactions.\n"
    
           The following is the definition of the recursive factorial function.
    
                  define f (x) {
                    if (x <= 1) return (1);
                    return (f(x-1) * x);
                  }
    
       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 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.
    
       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 "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
                  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 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.
    
           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
                  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" 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
                  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  parame-
                  ters  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.
    
           variable names
                  The  current  limit  on  the number of unique names is 32767 for
                  each of simple variables, arrays and functions.
    
    
    

    ENVIRONMENT VARIABLES

           The following environment variables are processed by bc:
    
           POSIXLY_CORRECT
                  This is the same as the -s option.
    
           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  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.
    
           Error recovery is not very good yet.
    
           Email  bug  reports  to  bug-bc@gnu.org.   Be  sure to include the word
           ''bc'' somewhere in the ''Subject:'' field.
    
    
    

    AUTHOR

           Philip A. Nelson
           philnelson@acm.org
    
    
    

    ACKNOWLEDGEMENTS

           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-
           ment.
    
    
    

    GNU Project 2006-06-11 bc(1)

    
    
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