Table of Contents
bc - An arbitrary precision calculator
language
bc [ -lwsqv ] [long-options] [ file ... ]
This
man page documents GNU bc version 1.04.
bc is a language that
supports arbitrary precision numbers with interactive execution of statements.
There are some similarities in the syntax to the C programming language.
A standard math library is available by command line option. If requested,
the math library is defined before processing any files. bc starts by
processing code from all the files listed on the command line in the order
listed. After all files have been processed, bc reads from the standard
input. All code is executed as it is read. (If a file contains a command
to halt the processor, bc will never read from the standard input.)
This
version of bc contains several extensions beyond traditional bc implementations
and the POSIX draft standard. Command line options can cause these extensions
to print a warning or to be rejected. This document describes the language
accepted by this processor. Extensions will be identified as such.
- -l
- Define the standard math library.
- -w
- Give warnings for extensions to POSIX
bc .
- -s
- Process exactly the POSIX bc language.
- -q
- Do not print the normal
GNU bc welcome.
- -v
- Print the version number and copyright and quit.
- --mathlib
- Define the standard math library.
- --warn
- Give warnings for extensions to
POSIX bc .
- --standard
- Process exactly the POSIX bc language.
- --quiet
- Do not
print the normal GNU bc welcome.
- --version
- Print the version number and copyright
and quit.
The most basic element in bc is the number. Numbers
are arbitrary precision numbers. This precision is both in the integer
part and the fractional part. All numbers are represented internally in
decimal and all computation is done in decimal. (This version truncates
results from divide and multiply operations.) There are two attributes
of numbers, the length and the scale. The length is the total number of
significant decimal digits in a number and the scale is the total number
of decimal digits after the decimal point. For example:
.000001 has a length of 6 and scale of 6.
1935.000 has a length of 7 and a scale of 3.
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 in bc start with the characters /*
and end with the characters */ . Comments may start anywhere and appear
as a single space in the input. (This causes comments to delimit other
input items. For example, a comment can not be found in the middle of
a variable name.) Comments include any newlines (end of line) between
the start and the end of the comment.
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 letters are variable names.) Single digit numbers always have
the value of the digit regardless of the value of ibase . (i.e. A = 10.)
For multi-digit numbers, bc changes all input digits greater or equal
to ibase to the value of ibase -1. This makes the number FFF always be
the largest 3 digit number of the input base.
Full expressions are similar
to many other high level languages. Since there is only one kind of number,
there are no rules for mixing types. Instead, there are rules on the scale
of expressions. Every expression has a scale. This is derived from the
scale of original numbers, the operation performed and in many cases,
the value of the variable scale . Legal values of the variable scale are
0 to the maximum number representable by a C integer.
In the following
descriptions of legal expressions, "expr" refers to a complete expression
and "var" refers to a simple or an array variable. A simple variable is
just a
name
and an array variable is specified as name [expr ]
Unless
specifically mentioned the scale of the result is the maximum scale of
the expressions involved.
- - expr
- The result is the negation of the expression.
- ++ var
- The variable is incremented by one and the new value is the result
of the expression.
- -- var
- The variable is decremented by one and the new
value is the result of the expression.
- var ++
- The result of the expression
is the value of the variable and then the variable is incremented by one.
- var --
- The result of the expression is the value of the variable and then
the variable is decremented by one.
- expr + expr
- The result of the expression
is the sum of the two expressions.
- expr - expr
- The result of the expression
is the difference of the two expressions.
- expr * expr
- The result of the
expression is the product of the two expressions.
- expr / expr
- The result
of the expression is the quotient of the two expressions. The scale of
the result is the value of the variable scale .
- expr % expr
- The result
of the expression is the "remainder" and it is computed in the following
way. To compute a%b, first a/b is computed to scale digits. That result
is used to compute a-(a/b)*b to the scale of the maximum of scale +scale(b)
and scale(a). If scale is set to zero and both expressions are integers
this expression is the integer remainder function.
- expr ^ expr
- The result
of the expression is the value of the first raised to the second. The second
expression must be an integer. (If the second expression is not an integer,
a warning is generated and the expression is truncated to get an integer
value.) The scale of the result is scale if the exponent is negative.
If the exponent is positive the scale of the result is the minimum of
the scale of the first expression times the value of the exponent and
the maximum of scale and the scale of the first expression. (e.g. scale(a^b)
= min(scale(a)*b, max( scale, scale(a))).) It should be noted that expr^0
will always return the value of 1.
- ( expr )
- This alters the standard precedence
to force the evaluation of the expression.
- var = expr
- The variable is assigned
the value of the expression.
- var <op>= expr
- This is equivalent to "var =
var <op> expr" with the exception that the "var" part is evaluated only
once. This can make a difference if "var" is an array.
Relational expressions
are a special kind of expression that always evaluate to 0 or 1, 0 if
the relation is false and 1 if the relation is true. These may appear
in any legal expression. (POSIX bc requires that relational expressions
are used only in if, while, and for statements and that only one relational
test may be done in them.) The relational operators are
- expr1 < expr2
- The
result is 1 if expr1 is strictly less than expr2.
- expr1 <= expr2
- The result
is 1 if expr1 is less than or equal to expr2.
- expr1 > expr2
- The result is
1 if expr1 is strictly greater than expr2.
- expr1 >= expr2
- The result is
1 if expr1 is greater than or equal to expr2.
- expr1 == expr2
- The result
is 1 if expr1 is equal to expr2.
- expr1 != expr2
- The result is 1 if expr1
is not equal to expr2.
Boolean operations are also legal. (POSIX bc does
NOT have boolean operations). The result of all boolean operations are
0 and 1 (for false and true) as in relational expressions. The boolean
operators are:
- !expr
- The result is 1 if expr is 0.
- expr && expr
- The result
is 1 if both expressions are non-zero.
- expr || expr
- The result is 1 if either
expression is non-zero.
The expression precedence is as follows: (lowest
to highest)
|| operator, left associative
&& operator, left associative
! operator, nonassociative
Relational operators, left associative
Assignment operator, right associative
+ and - operators, left associative
*, / and % operators, left associative
^ operator, right associative
unary - operator, nonassociative
++ and -- operators, nonassociative
This precedence was chosen so that POSIX compliant bc programs will
run correctly. This will cause the use of the relational and logical operators
to have some unusual behavior when used with assignment expressions. Consider
the expression:
a = 3 < 5
Most C programmers would assume this would
assign the result of "3 < 5" (the value 1) to the variable "a". What this
does in bc is assign the value 3 to the variable "a" and then compare
3 to 5. It is best to use parenthesis when using relational and logical
operators with the assignment operators.
There are a few more special expressions
that are provided in bc . These have to do with user defined functions
and standard functions. They all appear as "name(parameters)
". See the
section on functions for user defined functions. The standard functions
are:
- length ( expression )
- The value of the length function is the number
of significant digits in the expression.
- read ( )
- The read function (an
extension) will read a number from the standard input, regardless of where
the function occurs. Beware, this can cause problems with the mixing
of data and program in the standard input. The best use for this function
is in a previously written program that needs input from the user, but
never allows program code to be input from the user. The value of the
read function is the number read from the standard input using the current
value of the variable ibase for the conversion base.
- scale ( expression
)
- The value of the scale function is the number of digits after the decimal
point in the expression.
- sqrt ( expression )
- The value of the sqrt function
is the square root of the expression. If the expression is negative, a
run time error is generated.
Statements (as in most algebraic
languages) provide the sequencing of expression evaluation. In bc statements
are executed "as soon as possible." Execution happens when a newline in
encountered and there is one or more complete statements. Due to this
immediate execution, newlines are very important in bc . In fact, both
a semicolon and a newline are used as statement separators. An improperly
placed newline will cause a syntax error. Because newlines are statement
separators, it is possible to hide a newline by using the backslash character.
The sequence "\<nl>", where <nl> is the newline appears to bc as whitespace
instead of a newline. A statement list is a series of statements separated
by semicolons and newlines. The following is a list of bc statements
and what they do: (Things enclosed in brackets ([]) are optional parts
of the statement.)
- expression
- This statement does one of two things. If
the expression starts with "<variable> <assignment> ...", it is considered to
be an assignment statement. If the expression is not an assignment statement,
the expression is evaluated and printed to the output. After the number
is printed, a newline is printed. For example, "a=1" is an assignment
statement and "(a=1)" is an expression that has an embedded assignment.
All numbers that are printed are printed in the base specified by the
variable obase . The legal values for obase are 2 through BC_BASE_MAX.
(See the section LIMITS.) For bases 2 through 16, the usual method of
writing numbers is used. For bases greater than 16, bc uses a multi-character
digit method of printing the numbers where each higher base digit is printed
as a base 10 number. The multi-character digits are separated by spaces.
Each digit contains the number of characters required to represent the
base ten value of "obase-1". Since numbers are of arbitrary precision,
some numbers may not be printable on a single output line. These long numbers
will be split across lines using the "\" as the last character on a line.
The maximum number of characters printed per line is 70. Due to the interactive
nature of bc printing a number cause the side effect of assigning the
printed value the the special variable last . This allows the user to recover
the last value printed without having to retype the expression that printed
the number. Assigning to last is legal and will overwrite the last printed
value with the assigned value. The newly assigned value will remain until
the next number is printed or another value is assigned to last . (Some
installations may allow the use of a single period (.) which is not part
of a number as a short hand notation for for last .)
- string
- The string
is printed to the output. Strings start with a double quote character
and contain all characters until the next double quote character. All characters
are take literally, including any newline. No newline character is printed
after the string.
- print list
- The print statement (an extension) provides
another method of output. The "list" is a list of strings and expressions
separated by commas. Each string or expression is printed in the order
of the list. No terminating newline is printed. Expressions are evaluated
and their value is printed and assigned the the variable last . Strings
in the print statement are printed to the output and may contain special
characters. Special characters start with the backslash character (\).
The special characters recognized by bc are "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 statement1 or statement2 depending on the
value of the expression. If the expression is non-zero, statement1 is executed.
If statement2 is present and the value of the expression is 0, then statement2
is executed. (The else clause is an extension.)
- while ( expression ) statement
- The while statement will execute the statement while the expression is
non-zero. It evaluates the expression before each execution of the statement.
Termination of the loop is caused by a zero expression value or the
execution of a break statement.
- for ( [expression1] ; [expression2] ;
[expression3] ) statement
- The for statement controls repeated execution
of the statement. Expression1 is evaluated before the loop. Expression2
is evaluated before each execution of the statement. If it is non-zero,
the statement is evaluated. If it is zero, the loop is terminated. After
each execution of the statement, expression3 is evaluated before the reevaluation
of expression2. If expression1 or expression3 are missing, nothing is
evaluated at the point they would be evaluated. If expression2 is missing,
it is the same as substituting the value 1 for expression2. (The optional
expressions are an extension. POSIX bc requires all three expressions.)
The following is equivalent code for the for statement:
expression1;
while (expression2) {
statement;
expression3;
}
- break
- This statement causes a forced exit of the most recent enclosing
while statement or for statement.
- continue
- The continue statement (an
extension) causes the most recent enclosing for statement to start the
next iteration.
- halt
- The halt statement (an extension) is an executed
statement that causes the bc processor to quit only when it is executed.
For example, "if (0 == 1) halt" will not cause bc to terminate because
the halt is not executed.
- return
- Return the value 0 from a function. (See
the section on functions.)
- return ( expression )
- Return the value of the
expression from a function. (See the section on functions.)
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 provide a method
of defining a computation that can be executed later. Functions in bc
always compute a value and return it to the caller. Function definitions
are "dynamic" in the sense that a function is undefined until a definition
is encountered in the input. That definition is then used until another
definition function for the same name is encountered. The new definition
then replaces the older definition. A function is defined as follows:
define name ( parameters ) { newline
auto_list statement_list }
A function call is just an expression of the form "name(parameters)
".
Parameters are numbers or arrays (an extension). In the function definition,
zero or more parameters are defined by listing their names separated by
commas. Numbers are only call by value parameters. Arrays are only call
by variable. Arrays are specified in the parameter definition by the notation
"name[] ". In the function call, actual parameters are full expressions
for number parameters. The same notation is used for passing arrays as
for defining array parameters. The named array is passed by variable to
the function. Since function definitions are dynamic, parameter numbers
and types are checked when a function is called. Any mismatch in number
or types of parameters will cause a runtime error. A runtime error will
also occur for the call to an undefined function.
The auto_list is an
optional list of variables that are for "local" use. The syntax of the
auto list (if present) is "auto name , ... ;". (The semicolon is optional.)
Each name is the name of an auto variable. Arrays may be specified by
using the same notation as used in parameters. These variables have their
values pushed onto a stack at the start of the function. The variables
are then initialized to zero and used throughout the execution of the
function. At function exit, these variables are popped so that the original
value (at the time of the function call) of these variables are restored.
The parameters are really auto variables that are initialized to a value
provided in the function call. Auto variables are different than traditional
local variables in the fact that if function A calls function B, B may
access function A's auto variables by just using the same name, unless
function B has called them auto variables. Due to the fact that auto variables
and parameters are pushed onto a stack, bc supports recursive functions.
The function body is a list of bc statements. Again, statements are separated
by semicolons or newlines. Return statements cause the termination of
a function and the return of a value. There are two versions of the return
statement. The first form, "return ", returns the value 0 to the calling
expression. The second form, "return ( expression ) ", computes the value
of the expression and returns that value to the calling expression. There
is an implied "return (0) " at the end of every function. This allows
a function to terminate and return 0 without an explicit return statement.
Functions also change the usage of the variable ibase . All constants
in the function body will be converted using the value of ibase at the
time of the function call. Changes of ibase will be ignored during the
execution of the function except for the standard function read , which
will always use the current value of ibase for conversion of numbers.
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.
In /bin/sh, the following
will assign the value of "pi" to the shell variable pi . CW 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
.
CW
scale = 20
/* Uses the fact that e^x = (e^(x/2))^2
When x is small enough, we use the series:
e^x = 1 + x + x^2/2! + x^3/3! + ...
*/
define e(x) {
auto a, d, e, f, i, m, v, z
/* Check the sign of x. */
if (x<0) {
m = 1
x = -x
}
/* Precondition x. */
z = scale;
scale = 4 + z + .44*x;
while (x > 1) {
f += 1;
x /= 2;
}
/* Initialize the variables. */
v = 1+x
a = x
d = 1
for (i=2; 1; i++) {
e = (a *= x) / (d *= i)
if (e == 0) {
if (f>0) while (f--) v = v*v;
scale = z
if (m) return (1/v);
return (v/1);
}
v += e
}
}
The following is code that uses the extended features of bc to implement
a simple program for calculating checkbook balances. This program is best
kept in a file so that it can be used many times without having to retype
it at every use.
CW
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.
CW
define f (x) {
if (x <= 1) return (1);
return (f(x-1) * x);
}
GNU bc can be compiled (via a configure option) to
use the GNU readline input editor library. This allows the user to do
more editing of lines before sending them to bc . It also allows for a
history of previous lines typed. When this option is selected, bc has
one more special variable. This special variable, history is the number
of lines of history retained. A value of -1 means that an unlimited number
of history lines are retained. This is the default value. Setting the value
of history to a positive number restricts the number of history lines
to the number given. The value of 0 disables the history feature. For
more information, read the user manuals for the GNU readline and history
libraries.
This version of bc was implemented from the POSIX
P1003.2/D11 draft and contains several differences and extensions relative
to the draft and traditional implementations. It is not implemented in
the traditional way using dc(1)
. This version is a single process which
parses and runs a byte code translation of the program. There is an "undocumented"
option (-c) that causes the program to output the byte code to the standard
output instead of running it. It was mainly used for debugging the parser
and preparing the math library.
A major source of differences is extensions,
where a feature is extended to add more functionality and additions, where
new features are added. The following is the list of differences and extensions.
- LANG
- This version does not conform to the POSIX standard in the processing
of the LANG environment variable and all environment variables starting
with LC_.
- names
- Traditional and POSIX bc have single letter names for functions,
variables and arrays. They have been extended to be multi-character names
that start with a letter and may contain letters, numbers and the underscore
character.
- Strings
- Strings are not allowed to contain NUL characters. POSIX
says all characters must be included in strings.
- last
- POSIX bc does not
have a last variable. Some implementations of bc use the period (.) in
a similar way.
- comparisons
- POSIX bc allows comparisons only in the if
statement, the while statement, and the second expression of the for statement.
Also, only one relational operation is allowed in each of those statements.
- if statement, else clause
- POSIX bc does not have an else clause.
- for statement
- POSIX bc requires all expressions to be present in the for statement.
- &&, ||, !
- POSIX bc does not have the logical operators.
- read function
- POSIX
bc does not have a read function.
- print statement
- POSIX bc does not have
a print statement .
- continue statement
- POSIX bc does not have a continue
statement.
- array parameters
- POSIX bc does not (currently) support array
parameters in full. The POSIX grammar allows for arrays in function definitions,
but does not provide a method to specify an array as an actual parameter.
(This is most likely an oversight in the grammar.) Traditional implementations
of bc have only call by value array parameters.
- =+, =-, =*, =/, =%, =^
- POSIX
bc does not require these "old style" assignment operators to be defined.
This version may allow these "old style" assignments. Use the limits
statement to see if the installed version supports them. If it does support
the "old style" assignment operators, the statement "a =- 1" will decrement
a by 1 instead of setting a to the value -1.
- spaces in numbers
- Other implementations
of bc allow spaces in numbers. For example, "x=1 3" would assign the
value 13 to the variable x. The same statement would cause a syntax error
in this version of bc .
- errors and execution
- This implementation varies
from other implementations in terms of what code will be executed when
syntax and other errors are found in the program. If a syntax error is
found in a function definition, error recovery tries to find the beginning
of a statement and continue to parse the function. Once a syntax error
is found in the function, the function will not be callable and becomes
undefined. Syntax errors in the interactive execution code will invalidate
the current execution block. The execution block is terminated by an end
of line that appears after a complete sequence of statements. For example,
a = 1
b = 2
has two execution blocks and
{ a = 1
b = 2 }
has one execution block. Any runtime error will terminate the execution
of the current execution block. A runtime warning will not terminate the
current execution block.
- Interrupts
- During an interactive session, the
SIGINT signal (usually generated by the control-C character from the terminal)
will cause execution of the current execution block to be interrupted.
It will display a "runtime" error indicating which function was interrupted.
After all runtime structures have been cleaned up, a message will be
printed to notify the user that bc is ready for more input. All previously
defined functions remain defined and the value of all non-auto variables
are the value at the point of interruption. All auto variables and function
parameters are removed during the clean up process. During a non-interactive
session, the SIGINT signal will terminate the entire run of bc .
The following are the limits currently in place for this bc processor.
Some of them may have been changed by an installation. Use the limits
statement to see the actual values.
- BC_BASE_MAX
- The maximum output base
is currently set at 999. The maximum input base is 16.
- BC_DIM_MAX
- This
is currently an arbitrary limit of 65535 as distributed. Your installation
may be different.
- BC_SCALE_MAX
- The number of digits after the decimal point
is limited to INT_MAX digits. Also, the number of digits before the decimal
point is limited to INT_MAX digits.
- BC_STRING_MAX
- The limit on the number
of characters in a string is INT_MAX characters.
- exponent
- The value of
the exponent in the raise operation (^) is limited to LONG_MAX.
- multiply
- The multiply routine may yield incorrect results if a number has more
than LONG_MAX / 90 total digits. For 32 bit longs, this number is 23,860,929
digits.
- code size
- Each function and the "main" program are limited to 16384
bytes of compiled byte code each. This limit (BC_MAX_SEGS) can be easily
changed to have more than 16 segments of 1024 bytes.
- variable names
- The
current limit on the number of unique names is 32767 for each of simple
variables, arrays and functions.
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 environent arguments are
processed before any command line argument files. This allows the user
to set up "standard" options and files to be processed at every invocation
of bc . The files in the environment variables would typically contain
function definitions for functions the user wants defined every time bc
is run.
- BC_LINE_LENGTH
- This should be an integer specifing the number
of characters in an output line for numbers. This includes the backslash
and newline characters for long numbers.
In most installations,
bc is completely self-contained. Where executable size is of importance
or the C compiler does not deal with very long strings, bc will read
the standard math library from the file /usr/local/lib/libmath.b. (The actual
location may vary. It may be /lib/libmath.b.)
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.
Error recovery is not very good yet.
Email bug
reports to bug-gnu-utils@prep.ai.mit.edu. Be sure to include the word ``bc'' somewhere
in the ``Subject:'' field.
Philip A. Nelson
phil@cs.wwu.edu
The author would like to thank Steve Sommars (Steve.Sommars@att.com)
for his extensive help in testing the implementation. Many great suggestions
were given. This is a much better product due to his involvement.
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