bc(1)
NAME
bc - An arbitrary precision calculator language
SYNTAX
bc [ -lws ] [ file ... ]
VERSION
This man page documents GNU bc version 1.02.
DESCRIPTION
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.
OPTIONS
-l Define the standard math library.
-w Give warnings for extensions to POSIX bc.
-s Process exactly the POSIX bc language.
NUMBERS
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.
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 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.
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 (F). 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
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.
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 "b" (bell), "f" (form feed), "n" (newline), "r" (carriage
return), "t" (tab), and "\" (backslash). Any other character
following the backslash will be ignored. This still does not allow
the double quote character to be part of any string.
{ statement_list }
This is the compound statement. It allows multiple statements to be
grouped together for execution.
if ( expression ) then 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.)
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 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.
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 in radians.
c (x)
The cosine of x in radians.
a (x)
The arctangent of x.
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 implement
a simple program for calculating checkbook balances. This program is
best kept in a file so that it can be used many times without having to
retype it at every use.
scale=2
print "\nCheck book program!\n"
print " Remember, deposits are negative transactions.\n"
print " Exit by a 0 transaction.\n\n"
print "Initial balance? "; bal = read()
bal /= 1
print "\n"
while (1) {
"current balance = "; bal
"transaction? "; trans = read()
if (trans == 0) break;
bal -= trans
bal /= 1
}
quit
The following is the definition of the recursive factorial function.
define f (x) {
if (x <= 1) return (1);
return (f(x-1) * x);
}
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 "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 have array parameters. Other
implementations of bc may have 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.
LIMITS
The following are the limits currently in place for this bc processor.
Some of them may have been changed by an installation. Use the limits
statement to see the actual values.
BC_BASE_MAX
The maximum output base is currently set at 999. The maximum
input base is 16.
BC_DIM_MAX This is currently an arbitrary limit of 65535 as distributed.
Your installation may be different.
BC_SCALE_MAX
The number of digits after the decimal point is limited to
INT_MAX digits. Also, the number of digits before the decimal
point is limited to INT_MAX digits.
BC_STRING_MAX
The limit on the number of characters in a string is INT_MAX
characters.
exponent The value of the exponent in the raise operation (^) is
limited to LONG_MAX.
multiply The multiply routine may yield incorrect results if a number
has more than LONG_MAX / 90 total digits. For 32 bit longs,
this number is 23,860,929 digits.
code size Each function and the "main" program are limited to 10240
bytes of compiled byte code each. This limit (BC_MAX_SEGS)
can be easily changed to have more than 10 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.
FILES
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.)
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.
AUTHOR
Philip A. Nelson
phil@cs.wwu.edu
ACKNOWLEDGEMENTS
The author would like to thank Steve Sommars (sesv@iwtsf.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.