sum += entry 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 evaluate to 0 or 1 (0 false and 1 true).
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 :
| expr1 << expr2 | 1 if expr1 is strictly less than expr2.
| | expr1 <= expr2 | 1 if expr1 is less than or equal to expr2.
| | expr1 > expr2 | 1 if expr1 is strictly greater than expr2.
| | expr1 > expr2 | 1 if expr1 is greater than or equal to expr2.
| | expr1 == expr2 | 1 if expr1 is equal to expr2.
| | expr1 != expr2 | 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 i | is 1 if expr is 0.
| | expr && expr | 1 if both expressions are non-zero.
| | expr || expr | 1 if either expression is non-zero.
The expression precedence is: (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.
user defined functions and standard functions.
appear as "name(parameters)". See the section on functions
for user defined functions. The standard functions are:
length ( expression ) The value of the length function is the number of significant digits in the expression.
| read ( ) The read function (an extension) will read a number from the
standard input, regardless of where the function occurs.
Beware, this can cause problems with the mixing of data and pro gram in the standard input. The best use for this function is
in a previously written program that needs input from the user,
but never allows program code to be input from the user. The
value of the read function is the number read from the standard
input using the current value of the variable ibase for the conversion base.
| scale ( expression )
The value of the scale function is the number of digits after
the dot in the expression.
| sqrt ( expression )|
The value of the sqrt function is the square root of the expres sion. If the expression is negative, a run time error is generated.
| | | | |
STATEMENTS
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.
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 char acters recognized by bc are "a" (alert or bell), "b"
(backspace), "f" (form feed), "n" (newline), "r" (carriage
return), "q" (double quote), "t" (tab), and "\" (backslash).
Any other character following the backslash will be ignored.
| { statement_list }
| This is the compound statement. It allows multiple statements
to be grouped together for execution.
| if ( expression ) statement1 [else statement2]
|
The if statement evaluates the expression and executes 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
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) sine of x, x is in radians.
c (x) cosine of x, x is in radians.
a (x) arctangent of x, arctangent returns radians.
l (x) natural logarithm of x.
e (x) exponential function of raising e to the value x.
j (n,x) 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)
following definition of the exponential function used in the math library, 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 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"
is best kept in a file so that it can be used many times without having to retype it at every use.
scale=2
print "\nCheck book program!\n"
print " Remember, deposits are negative transactions.\n"
print " Exit by a 0 transaction.\n\n"
print "Initial balance? "; bal = read()
bal /= 1
print "\n"
while (1) {
"current balance = "; bal
"transaction? "; trans = read()
if (trans == 0) break;
bal -= trans
bal /= 1
}
quit
The following is the definition of the recursive factorial function.
define f (x) {
if (x <= 1) return (1);
return (f(x-1) * x);
}
READLINE OPTION
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.
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 pro cessing of the LANG environment variable and all environment
variables starting with LC_.
names Traditional and POSIX bc have single letter names for functions,
variables and arrays. They have been extended to be multi-char acter names that start with a letter and may contain letters,
numbers and the underscore character.
Strings
Strings are not allowed to contain NUL characters.
POSIX says all characters must be included in strings.
last POSIX bc does not have a last variable. Some implementations of
bc use the period (.) in a similar way.
comparisons
POSIX bc allows comparisons only in the if statement, the while
statement, and the second expression of the for statement.
Also, only one relational operation is allowed in each of those
statements.
if statement, else clause
POSIX bc does not have an else clause.
for statement
POSIX bc requires all expressions to be present in the for statement.
&&, ||, !
POSIX bc does not have
logical operators.
read function
print statement
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 parame ters are removed during the clean up process. During a non interactive session, the SIGINT signal will terminate the entire
run of bc.
LIMITS
limits statment:
BC_BASE_MAX = 2147483647
BC_DIM_MAX = 65535
BC_SCALE_MAX = 2147483647
BC_STRING_MAX = 2147483647
MAX Exponent = 9223372036854775807
Number of vars = 32767
BC_BASE_MAX| maximum output base is currently set at 999. The maximum input base is 16.
| BC_DIM_MAX arbitrary limit of 65535 as distributed.
| BC_SCALE_MAX number of digits after the dot is limited to INT_MAX digits.
The number of digits before the dot is limited to INT_MAX digits.
| BC_STRING_MAX| limit on the number of characters in a string is INT_MAX characters.
| exponent| value of the exponent in the raise operation (^) is limited to LONG_MAX.
| multiply| 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.
BC_MAX_SEGS can be changed to have more than 16 segments of 1024 bytes.
| variable names unique names for each of simple variables, arrays and functions.
| | | | | | | | |
ENVIRONMENT VARIABLES
POSIXLY_CORRECTsame as -s
| 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 environ ment 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 new line characters for long numbers.
| | |
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.
Email bug reports to bug-gnu-utils@prep.ai.mit.edu. Be sure to include
the word ``bc'' somewhere in the ``Subject:'' field.
VERSION This man page documents GNU bc version 1.04.
AUTHOR Philip A. Nelson phil@cs.wwu.edu
ACKNOWLEDGEMENTS 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.
|