BC(1) | General Commands Manual | BC(1) |
bc
—
bc |
[-hilqsvw ] [long-options] [file
...] |
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.
-h
,
-
-help
-i
,
-
-interactive
-l
,
-
-mathlib
-q
,
-
-quiet
-s
,
-
-standard
bc
language.-v
,
-
-version
-w
,
-
-warn
bc
.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.
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.
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.
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
++
var
--
var
var
++
var
--
expr
+ expr
expr
- expr
expr
* expr
expr
/ expr
expr
% expr
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
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 )
var
= expr
var
<op>= expr
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
expr1
<= expr2
expr1
> expr2
expr1
>= expr2
expr1
== expr2
expr1
!= 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
expr
&& expr
expr
|| expr
The expression precedence is as follows: (lowest to highest)
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)read
()ibase
for the conversion base.scale
(expression)sqrt
(expression)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.)
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
.)print
listprint
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.if
(expression) statement1
[else
statement2]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) statementwhile
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]) statementfor
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
while
statement or for
statement.continue
continue
statement (an extension) causes the
most recent enclosing for
statement to start the
next iteration.halt
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
bc
to terminate because the halt is
not executed.return
return
(expression)limits
bc
This is an extension.quit
quit
statement is read, the
bc
processor is terminated, regardless of where
the quit statement is found. For example,
if (0 == 1) quit
bc
to terminate.warranty
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 }
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, "<---", "0; } define void px (x) { print "--->", x, "<---", "0; } py(1) --->1<--- 0 px(1) --->1<---
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.
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:
bc
:
POSIXLY_CORRECT
-s
option.BC_ENV_ARGS
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
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); }
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.
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
environmentLANG
environment variable and all environment
variables starting with LC_
.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.last
POSIX
bc
does not have a last
variable. Some implementations of bc
use the
period (.) in a similar way.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
clausebc
does not have an
else
clause.for
statementbc
requires all expressions to be present in
the for
statement.bc
does not have the logical operators.read
functionbc
does not have a
read
function.print
statementbc
does not have a
print
statement .continue
statementbc
does not have a
continue
statement.return
statementbc
requires parentheses around the return
expression.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.bc
requires the opening brace on the same
line as the define
key word and the
auto
statement on the next line.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.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
.a = 1 b = 2
{ a = 1 b = 2 }
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
.bc
processor. Some of them may have been changed by an
installation. Use the limits
statement to see the
actual values.
BC_BASE_MAX
BC_DIM_MAX
BC_SCALE_MAX
INT_MAX
digits. Also, the number of digits before
the decimal point is limited to INT_MAX
digits.BC_STRING_MAX
INT_MAX
characters.LONG_MAX
.bc
will report that the file is unavailable and terminate. Also, there are
compile and run time diagnostics that should be self-explanatory.
April 16, 2017 | NetBSD 9.4 |