SYNOPSIS
bc
[
DESCRIPTION
bc is a programming language which can perform arithmetic calculations to arbitrary precision. You can use it interactively by entering instructions from the terminal. It can also run programs taken from files.
If you specify file arguments on the command line, they should be text files containing bc instructions. bc performs the instructions from those files, in the order that they appear on the command line, and then performs instructions from the standard input. bc terminates when it receives a quit instruction or reaches the endoffile on standard input.
Options
i 
puts bc into interactive mode. In this mode, bc displays a prompt when waiting for input. In addition, it handles errors somewhat differently. Normally, when bc encounters an error while processing a file, the interpreter displays the error message and exits. In interactive mode, the interpreter displays the message and returns to the prompt mode to allow debugging.
l 
loads a library of standard mathematical functions before processing any other input. This library also sets the scale to 20. For a description of the functions in the
l library, see BuiltIn Functions.
The bc Language
bc is a simple but complete programming language with a syntax reminiscent of the C programming language. This version of bc is a superset of the standard language available on most systems. It has a number of additional features intended to make the language more flexible and useful. Features which are unique to this implementation are noted in the text.
Input consists of a series of instructions that assign values to variables or make calculations. It is also possible to define subprograms called functions which perform a sequence of instructions to calculate a single value. bc displays the result of any line that calculates a value, but does not assign it to a variable. For example, the instruction
2+2
displays
4
By default, bc displays the result of any evaluated instruction followed by a newline. bc also saves the last value displayed in a special variable . so that you can use it in subsequent calculations.
For example, continuing from the last example
.*10
displays
40
since the . variable has the value of 4 from the previous example.
Numbers
Numbers consist of an optional minus () sign followed by a sequence of zero or more digits, followed by an optional decimal point (.), followed by a sequence of zero or more digits. Valid digits are 0 through 9 and the hexadecimal digits A through F. The uppercase letters represent the values from 10 through 15. There must be at least one digit, either before or after the decimal point. If not, bc interprets the decimal point as the special variable . mentioned earlier.
A number can be arbitrarily long and may contain spaces. Here are some valid numbers with an input base of 10:
0 0. .0 3.14159 +09. 12 1 000 000
Here are some valid numbers with an input base of 16 (ibase=16):
0 FF FF.3 10.444 A1
See Bases for more information.
A final point is that you cannot break up numbers with commas; you can write 1000000 or 1 000 000, but 1,000,000 results in an error message.
Identifiers
Identifiers are used as names for variables, functions or arrays. Valid identifiers may include sequences containing any number of letters, digits or the underscore (_) character, but must start with a lowercase letter. Spaces are not allowed in identifiers. The ability to use identifiers more than one character in length is an extension not found in traditional implementations of bc.

A variable holds a single numeric value. You can declare variables as local to a function using the auto statement (see Functions). All other variables are global and can be used anywhere. You do not need to declare global variables. bc creates variables as it requires them, with an initial value of zero. (Remember that there is also the special variable . (dot) which contains the result of the last calculation.)

A function is a sequence of instructions that calculates a single value. A list of zero or more values enclosed in parentheses always follows a function name, as in my_func(3.14159). See Functions later in this reference page.

An array is a list of values. Values in the list are called elements of the array. Each element in an array is numbered, beginning at zero. Such a number is known as a subscript or index of the array. Subscripts always appear in square brackets after the array. For example, a[0] refers to element zero in the array a. If a subscript value is a floating point number, the fractional part is discarded to make the subscript into an integer. For example, the following expressions all refer to the same element:
a[3] a[3.2] a[3.999]
The maximum number of elements in a bc array is given by the configuration variable {BC_DIM_MAX}. The valid array subscripts range from 0 to {BC_DIM_MAX}1 inclusive. Unlike many languages, you do not need to declare the size of an array. Elements are created dynamically as required, with an initial value of zero.
Since parentheses always follow function names and square brackets
always follow array names, bc can distinguish between the
three types of names.
Therefore, you can have variables, functions and arrays with the same name.
For example, foo may be a variable, while
BuiltIn Variables
bc has a number of builtin variables which are used to control various aspects of the interpreter. These are described in the following sections.
Scale
The scale value is the number of digits to be retained after the decimal point in arithmetic operations. For example, if the scale is three, each calculation retains at least three digits after the decimal point. This means that
5 / 3
has the value
1.666
If
The variable scale holds the current scale value. To change scales, assign a new value to scale, as in
scale = 5
Since scale is just a regular bc variable, it can be used in the full range of bc expressions.
The number of decimal places in the result of a calculation is affected not only by the scale, but also by the number of decimal places in the operands of the calculation. This is discussed in detail in the Arithmetic Operations section.
There is also a function
scale(1.1234)
returns the result four, which is the scale of the number 1.1234.
The result of the
The maximum value for scale is given by the configuration variable {BC_SCALE_MAX} and the minimum value is 0.
Bases
bc lets you specify numbers in different bases, for example, octal (base 8) or hexadecimal (base 16). You can input numbers in one base and output them in a different base, simplifying the job of converting from one base to another. bc does this using the builtin variables ibase and obase.
ibase is the base for input numbers. It has an initial value of 10 (normal decimal numbers). To use a different base for inputting numbers, assign an integer to ibase, as in
ibase = 8
This says that all future input numbers will be in base 8 (octal). The largest valid input base is 16 and the smallest valid input base is 2. Since there is no mechanism provided to represent digits larger than 15, bases larger than 16 are essentially useless. When the base is greater than 10, use the uppercase letters as digits. For example, base 16 uses the digits 0 through 9, and A through F. The digits are allowed in any number, regardless of the setting of ibase but are largely meaningless if the base is smaller than the digit. The one case where this is useful is in resetting the input base to 10. The constant A always has the value 10 no matter what ibase is set to, so to reset the input base to 10, type
ibase = A
obase is the base in which numbers are output. It has an initial value of 10 (normal decimal numbers). To change output bases, assign an appropriate integer to obase.
If the output base is 16 or less, bc displays numbers with normal digits and hexadecimal digits (if needed). The output base can also be greater than 16, in which case each digit is displayed as a decimal value and digits are separated by a single space. For example, if obase is 1000, the decimal number 123456789 is displayed as
123 456 789
Here, the digits are decimal values from 0 through 999. As a result, all output values are broken up into one or more chunks with three digits per chunk. Using output bases that are large powers of 10, you can columnate your output; for example, many users find that 100000 makes a good output base because numbers are grouped into chunks of five digits each.
Long numbers are output with a maximum of 70 characters per line. If a number is longer than this, bc puts a backslash (\) at the end of the line, indicating that the number is continued on the next line.
Internal calculations are performed in decimal, regardless of the input and output bases. Therefore, the number of places after the decimal point are dictated by the scale when numbers are expressed in decimal form.
The maximum value for obase is given by the configuration variable {BC_BASE_MAX}.
Arithmetic Operations
bc provides a large number of arithmetic operations. Following standard arithmetic conventions, some operations are calculated before others; for example, multiplication takes place before addition unless you use parentheses to group operations. Operations that take place first are said to have a higher precedence than operations which take place later.
Operations also have an associativity. The associativity dictates the order of evaluation when you have a sequence of operations with equal precedence. Some operations are evaluated left to right while others are evaluated right to left. The Operator Associativity table shows the operators of bc from highest precedence to lowest. Programmers familiar with C should note that bc's order of precedence is not the same as C's. In C, assignment operators have the lowest precedence. The precedence is shown in Table 1, bc Operators.
Operator  Associativity 


( )  left to right 
unary ++   not applicable 
unary  !  not applicable 
^  right to left 
* / %  left to right 
+   left to right 
= ^= *= /= %= +=  right to left 
== <= >= != < >  none 
&&  left to right 
  left to right 
Table 1: bc Operators
The following list describes each operator. In the descriptions, A and B can be numbers, variables, array elements, or other expressions. V must be either a variable or an array element.
 (A)

An expression in parentheses is evaluated before any other operations are performed on it.
 A

is the negation of the expression.
 !A

is the logical complement of the expression. If A evaluates to zero, !A evaluates to one. If A is not zero, !A evaluates to zero. This operator is unique to this version of bc.
 ++V

adds 1 to the value of V. The result of the expression is the new value of V.
 V

subtracts 1 from the value of V. The result of the expression is the new value of V.
 V++

adds 1 to the value of V, but the result of the expression is the old value of V.
 V

subtracts 1 from the value of V, but the result of the expression is the old value of V.
 A ^ B

calculates A to the power B. B must be an integer. The scale of the result of A^B is
min(scale(A) * abs(B), max(scale, scale(A)))
where
min() calculates the minimum of a set of numbers andmax() calculates the maximum.  A * B

calculates A multiplied by B. The scale of the result is
min(scale(A) + scale(B), max(scale, scale(A), scale(B)))
 A / B

calculates A divided by B. The scale of the result is the value of scale.
 A % B

calculates the remainder from the division of A by B. This is calculated in two steps. First, bc calculates A/B to the current scale. It then obtains the remainder through the formula
A  (A / B) * B
calculated to the scale
max(scale + scale(B), scale(A))
 A + B

adds A plus B. The scale of the result is the maximum of the two scales of the operands.
 A  B

calculates A minus B. The scale of the result is the maximum of the two scales of the operands.
The next group of operators are all assignment operators. They assign values to objects. An assignment operation has a value: the value that is being assigned. Therefore you can write operations like a=1+(b=2). In this operation, the value of the assignment in parentheses is 2 because that is the value assigned to b. Therefore, the value 3 is assigned to a. The possible assignment operators are:
 V = B

assigns the value of B to V.
 V ^= B

is equivalent to V=V^B.
 V *= B

is equivalent to V=V*B.
 V /= B

is equivalent to V=V/B.
 V %= B

is equivalent to V=V%B.
 V += B

is equivalent to V=V+B.
 V = B

is equivalent to V=VB.
The following expressions are called relations and their values can be either true (one) or false (zero). This version of bc lets you use the relational operators in any expression, not just in the conditional parts of if, while, or for statements. These operators work in exactly the same way as their equivalents in the C language. The result of a relation is zero if the relation is false and one if the relation is true.
 A == B

is true if and only if A equals B.
 A <= B

is true if and only if A is less than or equal to B.
 A >= B

is true if and only if A is greater than or equal to B.
 A != B

is true if and only if A is not equal to B.
 A < B

is true if and only if A is less than B.
 A > B

is true if and only if A is greater than B.
 A && B

is true if and only if A is true (nonzero) and B is true. If A is not true, the expression B is never evaluated.
 A  B

is true if A is true or B is true. If A is true, the expression B is never evaluated.
Comments and White Space
A comment has the form
/* Any string */
Comments can extend over more than one line of text. When bc sees /* at the start of a comment, it discards everything up to the next */. The only effect a comment has is to indicate the end of a token.
As an extension, this version of bc also provides an additional comment convention using the # character. All text from the # to the end of the current line is treated as a single blank, as in
2+2 # this is a comment
bc is free format. You may freely insert blanks or horizontal tab characters to improve the readability of the code. Instructions are assumed to end at the end of the line. If you have an instruction that is so long you need to continue it onto a new line, put a backslash (\) as the last character of the first line and continue the instruction on the next line. For example,
a = 2\ + 3
is equivalent to
a = 2 + 3
Instructions
A bc instruction may be an expression that performs a calculation, an assignment, a function definition or a statement. If an instruction is not an assignment, bc displays the result of the instruction when it has completed the calculation. For example, if you enter
3.14 * 23
bc displays the result of the calculation. However, with
a = 3.14 * 23
bc does not display anything because the expression is an assignment. If you do want to display the value of an assignment expression, place the expression in parentheses.
The following list shows the instruction formats recognized by bc.
 expression

calculates the value of the expression.
 \(dqstring\(dq

is a string constant. When bc sees a statement with this format, it displays the contents of the string. For example,
"Hello world!"
tells bc to display Hello world! A newline character is not output after the string. This makes it possible to do things like
foo = 15 "The value of foo is "; foo
With these instructions, bc displays
The value of foo is 15
The maximum length of a string in bc is given by the configuration variable {BC_STRING_MAX}.
 statement ; statement ...

is a sequence of statements on the same line. In bc, a semicolon (;) is equivalent to a newline. They both indicate the end of a statement. bc performs these statements from left to right.
 {statement}

is a bracebracketed statement. Brace brackets are used to group sequences of statements together, as in
{ statement statement ... }
Brace brackets can group a series of statements which are split over several lines. They are usually used with control statements like if and while.
 break

can only be used inside a while or for loop. break terminates the loop.
 for (initexp ; relation ; endexp statement

is equivalent to
initexp while (relation) { statement endexp }
where initexp and endexp are expressions and relation is a relation. For example,
a = 0 for (i = 1; i <= 10; ++i) a += i
is equivalent to the while example given earlier. C programmers should note that all three items inside the parentheses must be specified; unlike C, bc does not let you omit any of these expressions.
 if (relation statement

tests whether the given relation is true. If it is, bc performs the statement; otherwise, bc skips over statement and goes to the next instruction. For example,
if ((a%2) == 0) "a is even"
displays a is even if a has an even value.
 if (relation statement1 else statement2

is similar to the simple if statement. If relation is true, it performs statement1; otherwise, it performs statement2. It may be used as follows:
if ((a%2) == 0) "a is even" else "a is odd"
There is no statement separator between "a is even" and the else keyword. This differs from the C language.
Here is another example:
if (a<10) { "a " "is "; "less than 10 " a } else { "a is" " greater than 10 " a }
The braces must be on the same line as the if and the else keywords. This is because a newline or a semicolon right after (relation indicates that the body of the statement is null. One common source of errors in bc programs is typing the statement portion of an if statement on a separate line. If
i is used, the interpreter displays a warning when if statements with null bodies are encountered.  while (relation statement

repeatedly performs the given statement while relation is true. For example,
i = 1 a = 0 while (i <= 10) { a += i ++i }
adds the integers from 1 through 10 and stores the result in a.
If the relation is not true when bc encounters the while loop, bc does not perform statement.
 print expression , expression ...

displays the results of the expressions. Normally bc displays the value of each expression or string it encounters. This makes it difficult to format your output in programs. For this reason, the PTC MKS Toolkit version of bc has a print statement to give you more control over how things are displayed. print lets you display several numbers on the same line with strings. This statement displays all of its arguments on a single line. A single space is displayed between adjacent numbers (but not between numbers and strings). A print statement with no arguments displays a newline. If the last argument is null, subsequent output continues on the same line. Here are some examples of how to use print:
/* basic print statement */ print "The square of ", 2, "is ", 2*2 The square of 2 is 4 /* inserts a space between adjacent numbers */ print 1,2,3 1 2 3 /* note  no spaces */ print 1,"",2,"",3 123 /* just print a blank line */ print /* two statements with output on same line */ print 1,2,3, ; print 4, 5, 6 1 2 3 4 5 6
 quit

terminates bc.
 sh ...

lets you send a line to the system command interpreter for execution, as in
sh more <foo
This command passes everything from the first nonblank character until the end of the line to the command interpreter for execution.
 void expression

throws away or voids the result of the evaluation of expression instead of displaying it. This is useful when using ++ and  operators, or when you want to use a function but do not want to use the return value for anything. For example,
void foo++
increments foo but does not display the result. The void statement is unique to this version of bc.
Several other types of statements are only relevant in function definitions. These are described in the next section.
Functions
A function is a subprogram to calculate a result based on argument values. For example, the following function converts a temperature given in Fahrenheit into the equivalent temperature in Celsius.
define f_to_c(f) { return ((f32) * 5 / 9) }
This defines a function named
return (expression)
returns the value of expression as the result of the function. The parentheses around the expression are optional.
To activate the subprogram you use a function call. This has the form
name(expression[,expression] ...)
where name is the name of the function and the
expressions are argument values for the function.
A function call can be used anywhere you might use any other expression.
The value of the function call is the value that the function returns.
For example, with the function
The general form of a function definition is
define name([parameter][,parameter]...) { auto local, local, ... statement statement ... }
The parameters on the first line may be variable names
or array names.
Array names are indicated by putting square brackets after them.
For example, if
define cmpvec(a[],b[]) {
Parameters do not conflict with arrays or variables of the same name. For example, you may have a parameter named a inside a function, and a variable named a outside, and the two are considered entirely separate entities. Assigning a value to the variable does not change the parameter and vice versa. All parameters are passed by value. This means that a copy is made of the argument value and is assigned to the formal parameter. This also applies to arrays. If you pass an array to a function, a copy is made of the whole array, so any changes made to the array parameter do not affect the original array.
A function may not need any arguments. In this case, the define line does not have any parameters inside the parentheses, as in
define f() {
The auto statement declares a sequence of local variables. When a variable or array name appears in an auto statement, the current values of those items are saved and the items are initialized to zero. For the duration of the function, the items have their new values. When the function terminates, the old values of the items are restored. Note, however, that bc uses dynamic scoping rules, unlike C which uses lexical scoping rules (see the NOTES section for more details). For example,
define addarr(a[],l) { auto i, s for (i=0; i < l; ++i) s += a[i] return (s) }
is a function that adds the elements in an array.
The argument l stands for the number of elements in the array.
The function uses two local names: a variable named i
and a variable named s.
These variables are local to the function
define func_with_local_array() { auto local_array[]; for(i=0; i<100; i++) local_array[i] = i*2 }
This example defines a local array called local_array. Local arrays start out with no elements in them.
If a function refers to an object that is not a parameter and not declared auto, the object is assumed to be external. External objects may be referred to by other functions or by statements which are outside of functions. For example,
define sum_c(a[],b[],l) { auto i for (i=0; i < l; ++i) c[i] = a[i] + b[i] }
references an external array named c which is the
elementbyelement sum of two other arrays.
If c does not exist prior to calling
Functions usually require a return statement. This has the form
return (expression)
The expression is evaluated and used as the result of the function. The expression must have a single numeric value; it cannot be an array.
A return statement terminates a function, even if there are more statements left in the function. For example,
define abs(i) { if (i < 0) return (i) return (i) }
is a function that returns the absolute value of its argument. If i is less than zero, the function takes the first return; otherwise, it takes the second.
A function can also terminate by performing the last statement in the function.
If so, the result of the function is zero.
The function
return ()
or simply
return
If there are no parameters to the return statement, a default value of zero is returned.
BuiltIn Functions
bc has a number of builtin functions that perform various operations. These functions are similar to userdefined functions with the exception that you do not have to define them yourself  they are already set up for you. These functions are:
 length(expression)

calculates the total number of decimal digits in expression. This includes digits both before and after the decimal point. The result of
length() is an integer. For example, length(123.456) returns 6.  scale(expression)

returns the scale of expression. For example, scale(123.456) returns 3. The result of
scale() is always an integer. Subtracting the scale of a number from the length of a number lets you determine the number of digits before the decimal point.  sqrt(expression)

calculates the square root of the value of expression. The result is truncated in the least significant decimal place (not rounded). The scale of the result is the scale of expression, or the value of scale, whichever is larger.
You can use the following functions if
 arctan(expression) or a(expression)

calculates the arctangent of expression, returning an angle in radians. This function can also be called as atan(expression).
 cos(expression) or c(expression)

calculates the cosine of expression, where expression is an angle in radians.
 exp(expression) or e(expression)

calculates the exponential of expression (that is, the value e to the power of expression).
 bessel(integer,expression) or j(integer,expression)

calculates the Bessel function of expression with order integer. This function can also be called as jn(integer,expression).
 ln(expression) or l(expression)

calculates the natural logarithm of expression. This function can also be called as log(expression).
 sin(expression) or s(expression)

calculates the sine of expression, where expression is an angle in radians.
EXAMPLES
This section provides some examples of how to use the bc language to accomplish various things.
Here is a simple function to calculate the sales tax on a purchase. The amount of the purchase is given by purchase, and the amount of the sales tax (in per cent) is given by tax.
define sales_tax(purchase,tax) { auto old_scale old_scale = scale; scale = 2 tax = purchase*(tax/100) scale = old_scale return (tax) }
For example,
sales_tax(23.99,6)
calculates 6% tax on a purchase of $23.99.
The function temporarily sets the scale value to 2 so that the monetary
figures have two figures after the decimal point.
Remember that bc truncates calculations instead of rounding,
so some accuracy may be lost.
It is better to use one more digit than needed
and perform the rounding at the end.
The
Division resets the scale of a number to the value of scale. This can be used as follows to extract the integer portion of a number.
define integer_part(x) { # a local to save the value of scale auto old_scale # save the old scale, and set scale to 0 old_scale = scale; scale = 0 # divide by 1 to truncate the number x /= 1 # restore the old scale scale = old_scale return (x) }
With this function defined, you can now define one to return the fractional part of a number.
define fractional_part(x) { return (x  integer_part(x)) }
The following function lets you set the scale of a number to a given number of decimal places.
define set_scale(x, s) { auto os os = scale scale = s x /= 1 scale = os return (x) }
define round2(num) { auto temp; if(scale(num) < 2) return (set_scale(num, 2)) temp = (num  set_scale(num, 2)) * 1000 if(temp > 5) num += 0.01 return (set_scale(num,2)) }
This is a very useful function if you want to work with monetary values.
For example, you can now rewrite
define sales_tax(purchase,tax) { auto old_scale old_scale = scale scale = 2 tax = round2(purchase*(tax/100)) scale = old_scale return (tax) }
Here is a function which recursively calculates the factorial of its argument.
define fact (x) { if(x < 1) return 1 return (x*fact(x1)) }
The factorial function can also be written iteratively as:
define fact (x) { auto result result = 1 while(x>1) result *= x return (result) }
With either version, fact(6) returns 720.
Here is another recursive function. This one calculates the nth element of the Fibonacci sequence.
define fib(n) { if(n < 3) { return (1) } else { return (fib(n1)+fib(n2)) } }
FILES
DIAGNOSTICS
Possible exit status values are:
 0

Successful completion.
 1

Failure due to any of the following errors:
 — break statement found outside of loop
 — parser stack overflow
 — syntax error
 — end of file in comment
 — end of file in string
 — numerical constant is too long
 — string is too long
 — empty evaluation stack
 — cannot pass scalar to array
 — cannot pass array to scalar
 — invalid array index
 — builtin variable cannot be used as a parameter or auto variable
 — name is not a function
 — invalid value for builtin variable
 — shell command failed to execute
 — division by 0
 — invalid value for exponentiation operator
 — attempt to take square root of negative number
 — out of memory
 2

Unknown command line option.
PORTABILITY
POSIX.2. x/OPEN Portability Guide 4.0. All UNIX systems. Windows 7. Windows Server 2008 R2. Windows 8. Windows Server 2012. Windows 10. Windows Server 2016.
The
LIMITS
The parser stack depth is limited to 150 levels. Attempting to process extremely complicated programs may result in an overflow of this stack, causing an error.
NOTES
This section describes some additional details about bc that may be useful to know.
Unlike the C language which uses lexical scoping rules, bc uses dynamic scoping. This is most easily explained with an example:
a=10 define f1() { auto a; a = 13; return (f2()) } define f2() { return (a) } f1() 13 f2() 10
If
Numbers are stored as strings in the program and converted into numbers each time they are used. This is important because the value of a constant number may change depending on the setting of the ibase variable. For example, suppose the following instructions are given to bc:
define ten() { return (10) } ten() 10 ibase=16 ten() 16
In this example, when the base is set to 10,
Finally, the library of functions loaded using the
ROOTDIR/etc/lib.b
under your root directory. This is a simple text file which you can examine and change to add new functions as desired.
AVAILABILITY
PTC MKS Toolkit for Power Users
PTC MKS Toolkit for System Administrators
PTC MKS Toolkit for Developers
PTC MKS Toolkit for Interoperability
PTC MKS Toolkit for Professional Developers
PTC MKS Toolkit for Professional Developers 64Bit Edition
PTC MKS Toolkit for Enterprise Developers
PTC MKS Toolkit for Enterprise Developers 64Bit Edition
SEE ALSO
PTC MKS Toolkit 10.1 patch 1 Documentation Build 2.