a2p
accept
access
acct
addftinfo
addr2line
adjtime
afmtodit
after
aio_cancel
aio_error
aio_read
aio_return
aio_suspend
aio_waitcomplete
aio_write
alias
aliases
alloc
anvil
append
apply
apropos
ar
array
as
asa
asn1parse
at
atq
atrm
attemptckalloc
attemptckrealloc
authlib
authtest
autopoint
awk
b64decode
b64encode
basename
batch
bc
bdes
bell
bg
bgerror
biff
big5
binary
bind
bindkey
bindtags
bindtextdomain
bio
bitmap
blowfish
bn
bootparams
bootptab
bounce
brandelf
break
breaksw
brk
bsdiff
bsdtar
bsnmpd
bspatch
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buffer
builtin
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button
byacc
bzcat
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bzgrep
bzip2
c2ph
c89
c99
ca
cal
calendar
canvas
cap_mkdb
case
cat
catch
catman
cc
cd
cdcontrol
chdir
checkbutton
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chfn
chgrp
chio
chkey
chmod
chown
chpass
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ci
ciphers
ckalloc
ckdist
ckfree
ckrealloc
cksum
cleanup
clear
clipboard
clock
clock_getres
clock_gettime
clock_settime
close
cmp
co
col
colcrt
colldef
colors
colrm
column
comm
command
compile_et
complete
compress
concat
config
connect
console
continue
core
courierlogger
couriertcpd
cp
cpan
cpio
cpp
creat
crl
crontab
crunchgen
crunchide
crypt
crypto
csh
csplit
ctags
ctm
ctm_dequeue
ctm_rmail
ctm_smail
cu
cursor
cursors
cut
cvs
date
dbiprof
dbiproxy
dc
dcgettext
dcngettext
dd
dde
default
defer
deliverquota
des
destroy
devfs
df
dgettext
dgst
dh
dhparam
dialog
diff
diff3
dig
dir
dirent
dirname
dirs
discard
disktab
dngettext
do
domainname
done
dprofpp
dsa
dsaparam
dtmfdecode
du
dup
dup2
eaccess
ec
ecdsa
echo
echotc
ecparam
ed
edit
editrc
ee
egrep
elf
elfdump
elif
else
enc
enc2xs
encoding
end
endif
endsw
engine
enigma
entry
env
envsubst
eof
eqn
err
errno
error
errstr
esac
ethers
euc
eui64
eval
event
evp
ex
exec
execve
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expand
export
exports
expr
extattr
extattr_delete_fd
extattr_delete_file
extattr_get_fd
extattr_get_file
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extattr_set_file
f77
false
famm
famx
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fc
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fg
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fhstatfs
fi
file
file2c
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find2perl
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flock
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http
hup
i386_get_ioperm
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i386_vm86
iconv
id
ident
idprio
if
ifnames253
ifnames259
image
imapd
incr
indent
indxbib
info
infokey
inode
install
instmodsh
interp
intro
introduction
ioctl
ipcrm
ipcs
ipf
ipftest
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ippool
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label
labelframe
lam
lappend
last
lastcomm
lastlog
lchflags
lchmod
lchown
ld
ldap
ldapadd
ldapcompare
ldapdelete
ldapmodify
ldapmodrdn
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ldapsearch
ldapwhoami
ldd
leave
less
lesskey
lex
lgetfh
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libnetcfg
library
limit
limits
lindex
link
linprocfs
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lint
lio_listio
list
listbox
listen
lj4_font
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ln
load
loadfont
local
locale
locate
lock
lockf
log
logger
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lp
lpq
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lutimes
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magic
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nex
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nice
nl
nm
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notify
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nvi
nview
objcopy
objdump
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ocsp
od
onintr
open
openssl
opieaccess
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opiekey
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option
options
oqmgr
pack
package
packagens
pagesize
palette
pam_auth
panedwindow
parray
passwd
paste
patch
pathchk
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pawd
pax
pbm
pcre
pcreapi
pcrebuild
pcrecallout
pcrecompat
pcrecpp
pcregrep
pcrematching
pcrepartial
pcrepattern
pcreperform
pcreposix
pcreprecompile
pcresample
pcretest
perl
perl56delta
perl58delta
perl561delta
perl570delta
perl571delta
perl572delta
perl573delta
perl581delta
perl582delta
perl583delta
perl584delta
perl585delta
perl586delta
perl587delta
perl588delta
perl5004delta
perl5005delta
perlaix
perlamiga
perlapi
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perldebtut
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perldgux
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perldoc
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perlfaq1
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perlfaq3
perlfaq4
perlfaq5
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perlfaq8
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perlfilter
perlfork
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perlgpl
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perror
pfbtops
pftp
pgrep
phones
photo
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pid
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pkcs7
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pkg_add
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pkill
pl2pm
place
pod2html
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readv
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ree
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rev
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rlog
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rs
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sched_get_priority_max
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scrollbar
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sed
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semctl
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services
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set
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setitimer
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_exit
__syscall
 
FreeBSD/Linux/UNIX General Commands Manual
Hypertext Man Pages
bc
 
bc(1)									 bc(1)



NAME
       bc - An arbitrary precision calculator language

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

VERSION
       This man page documents GNU bc version 1.06.

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.
	       1935.000 has a length of 7 and a scale of 3.

   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 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]
       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  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 = expr
	      This  is	equivalent to "var = var  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	state-
       ments  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.

       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:

       length ( expression )
	      The  value  of  the length function is the number of significant
	      digits in the expression.

       read ( )
	      The read function (an extension) will read  a  number  from  the
	      standard	 input,  regardless  of  where	the  function  occurs.
	      Beware, this can cause problems with the mixing of data and pro-
	      gram  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 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-
	      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 "\", where  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 "  ...", 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
	      value.  The newly assigned value will remain until the next num-
	      ber  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 dou-
	      ble 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  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:
	      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  func-
	      tions.)

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

   PSEUDO 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.  Numbers are only call by value  parameters.	Arrays
       are only call by variable.  Arrays are specified in the parameter defi-
       nition by the notation "name[]".   In the function call, actual parame-
       ters  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 defini-
       tions are dynamic, parameter numbers and types are checked when a func-
       tion  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
       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  ter-
       mination  of  a function and the return of a value.  There are two ver-
       sions of the return statement.  The first form, "return",  returns  the
       value  0 to the calling expression.  The second form, "return ( expres-
       sion )", 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 with-
       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.

       As  an  extension,  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 defini-
       tions are legal.
	      define d (n) { return (2*n); }
	      define d (n)
		{ return (2*n); }

   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.

       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) {
		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"
	      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);
	      }

   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.

       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.

       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
       has two execution blocks and
	      { a = 1
		b = 2 }
       has one execution block.  Any runtime error will terminate  the	execu-
       tion of the current execution block.  A runtime warning will not termi-
       nate the current execution block.

       Interrupts
	      During an interactive session, the SIGINT signal (usually gener-
	      ated  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  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
       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.

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

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.

       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.



				       .				 bc(1)
=184427
+414
(65)