BC(1) FreeBSD General Commands Manual BC(1)
NAME
bc - arbitrary precision calculator language
SYNOPSIS
bc [-hilqsvw] [long-options] [file ...]
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
-h, --help Print the usage and exit.
-i, --interactive Force interactive mode.
-l, --mathlib Define the standard math library.
-q, --quiet Quiet mode.
-s, --standard Process exactly the POSIX bc language.
-v, --version Print the version number and copyright and quit.
-w, --warn Give warnings for extensions to POSIX bc.
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 of bc 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.
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 36. (Base values greater than 16 are an
extension.) Assigning a value outside this range to ibase will result in
a value of 2 or 36. Input numbers may contain the characters 0-9 and A-
Z. (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 `ZZZ' 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)
1. `||' operator, left associative
2. `&&' operator, left associative
3. `!' operator, nonassociative
4. Relational operators, left associative
5. Assignment operator, right associative
6. `+' and `-' operators, left associative
7. `*', `/' and `%' operators, left associative
8. `^' operator, right associative
9. unary `-' operator, nonassociative
10. `++' 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
parentheses 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
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 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 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 to 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
executed. 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.) As an extension, the
parentheses 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 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. All parameters are call by value parameters.
Arrays are specified in the parameter definition by the notation
"name[]". In the function call, actual parameters are full expressions
for number parameters. The same notation is used for passing arrays as
for defining array parameters. The named array is passed by value 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 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
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.
Several extensions have been added to functions. First, the format of
the definition has been slightly relaxed. The standard requires the
opening brace be on the same line as the define keyword and all other
parts must be on following lines. This version of bc will allow any
number of newlines before and after the opening brace of the function.
For example, the following definitions are legal.
define d (n) { return (2*n); }
define d (n)
{ return (2*n); }
Functions may be defined as void. A void funtion returns no value and
thus may not be used in any place that needs a value. A void function
does not produce any output when called by itself on an input line. The
key word void is placed between the key word define and the function
name. For example, consider the following session.
define py (y) { print "--->", y, "<---", "\n"; }
define void px (x) { print "--->", x, "<---", "\n"; }
py(1)
--->1<---
0
px(1)
--->1<---
Since py() is not a void function, the call of `py(1)' prints the desired
output and then prints a second line that is the value of the function.
Since the value of a function that is not given an explicit return
statement is zero, the zero is printed. For `px(1)', no zero is printed
because the function is a void function.
Also, call by variable for arrays was added. To declare a call by
variable array, the declaration of the array parameter in the function
definition looks like "name[]". The call to the function remains the
same as call by value arrays.
MATH LIBRARY
If bc is invoked with the -l option, a math library is preloaded and the
default scale is set to 20. The math functions will calculate their
results to the scale set at the time of their call. The math library
defines the following functions:
s(x) The sine of x, x is in radians.
c(x) The cosine of x, x is in radians.
a(x) The arctangent of x, arctangent returns radians.
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.
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 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 specifying the number of
characters in an output line for numbers. This includes
the backslash and newline characters for long numbers.
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);
}
EDITLINE OPTIONS
bc is compiled using the editline(3) 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. This adds to bc one more special variable.
This special variable, history is the number of lines of history
retained. The default 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 feature. For more information, read the
user manual for the editline(3) library.
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 environment
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.
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" 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.
variable names The current limit on the number of unique names is 32767
for each of simple variables, arrays and functions.
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.
HISTORY
This man page documents bc version nb1.0.
AUTHORS
Philip A. Nelson <
[email protected]>
ACKNOWLEDGEMENTS
The author would like to thank Steve Sommars for his extensive help in
testing the implementation. Many great suggestions were given. This is
a much better product due to his involvement.
BUGS
Error recovery is not very good yet.
FreeBSD 14.1-RELEASE-p8 April 16, 2017 FreeBSD 14.1-RELEASE-p8