About dc
Short for "desk calculator", dc is an arbitrary-precision arithmetic package.
Description
dc is a desk calculator which supports arbitrary, unlimited-precision arithmetic and reverse-polish (postfix) notation. It also allows you to define and call macros. Normally dc reads from the standard input; if any command arguments are given to it, they are filenames, and dc reads and executes the contents of the files before reading from standard input. All normal output is to standard output; all error output is to standard error.
A reverse-polish calculator stores numbers on a stack. Entering a number pushes it on the stack. Arithmetic operations pop arguments off the stack and push the results.
To enter a number in dc, type the digits (using upper case letters A through F as "digits" when working with input bases greater than ten), with an optional decimal point. Exponential notation is not supported. To enter a negative number, begin the number with "_" (an underscore). "-" (dash or hyphen) cannot be used for this, as it is a binaryoperator for subtraction instead. To enter two numbers in succession, separate them with spaces or newlines. These have no meaning as commands.
dc syntax
dc [-V] [--version] [-h] [--help] [-e scriptexpression]
[--expression=scriptexpression] [-f scriptfile] [--file=scriptfile]
[file ...]
Options
-V, --version Print out the version information of dc and a Copyright notice, then exit.
-h, --help Print a usage message briefly summarizing these command-line options and the bug-reporting address, then exit.
-e script, --expression=script Add the commands in script to the set of commands to be run while processing the input.
-f script-file, --file=script-file Add the commands contained in the file script-file to the set of commands to be run while processing the input.
If any command-line parameters remain after processing the above, these parameters are interpreted as the names of input files to be processed. A file name of "-" (dash or hyphen) refers to the standard input stream. The standard input will processed if no script files or expressions are specified.
Printing Commands
p Prints the value on the top of the stack, without altering the stack. A newline is printed after the value.
n Prints the value on the top of the stack, popping it off, and does not print a newline after.
P Pops off the value on top of the stack. If it is a string, it is printed without a trailing newline. Otherwise, it is a number, and the integer portion of its absolute value is printed out as a "base (UCHAR_MAX+1)" byte stream. Assuming that (UCHAR_MAX+1) is 256 (as it is on most machines with 8-bit bytes), the sequence KSK0k1/_1Ss [ls*]Sxd0>x [256~Ssd0qaPlxx] dsxxsx0sqLqsxLxLK+k could also accomplish this function. (Much of the complexity of the above native-dc code is due to the ~ computing the characters backwards, and the desire to ensure that all registers wind up back in their original states.)
f Prints the entire contents of the stack without altering anything. This is a good command to use if you are lost or want to figure out what the effect of some command has been.
Arithmetic
+ Pops two values off the stack, adds them, and pushes the result. The precision of the result is determined only by the values of the arguments, and is enough to be exact.
- Pops two values, subtracts the first one popped from the second one popped, and pushes the result.
* Pops two values, multiplies them, and pushes the result. The number of fraction digits in the result depends on the current precision value and the number of fraction digits in the two arguments.
/ Pops two values, divides the second one popped from the first one popped, and pushes the result. The number of fraction digits is specified by the precision value.
% Pops two values, computes the remainder of the division that the / command would do, and pushes that. The value computed is the same as that computed by the sequence Sd dld/ Ld*- .
~ Pops two values, divides the second one popped from the first one popped. The quotient is pushed first, and the remainder is pushed next. The number of fraction digits used in the division is specified by the precision value. (The sequence SdSn lnld/ LnLd% could also accomplish this function, with slightly different error checking.)
^ Pops two values and exponentiates, using the first value popped as the exponent and the second popped as the base. The fraction part of the exponent is ignored. The precision value specifies the number of fraction digits in the result.
| Pops three values and computes a modular exponentiation. The first value popped is used as the reduction modulus; this value must be a non-zero number, and should be an integer. The second popped is used as the exponent; this value must be a non-negative number, and any fractional part of this exponent will be ignored. The third value popped is the base which gets exponentiated, which should be an integer. For small integers this is like the sequence Sm^Lm%, but, unlike ^, this command will work with arbitrarily large exponents.
v Pops one value, computes its square root, and pushes that. The precision value specifies the number of fraction digits in the result.
Most arithmetic operations are affected by the "precision value", which you can set with the k command. The default precision value is zero, which means that all arithmetic except for addition and subtraction produces integer results.
Stack Control
c Clears the stack, emptying it.
d Duplicates the value on the top of the stack, pushing another copy of it. Thus, "4d*p" computes 4 squared and prints it.
r Reverses the order of (swaps) the top two values on the stack. (This can also be accomplished with the sequence SaSbLaLb.)
Registers
dc provides at least 256 memory registers, each named by a single character. You can store a number or a string in a register and retrieve it later.
sr Pop the value off the top of the stack and store it into register r.
lr Copy the value in register r and push it onto the stack. This does not alter the contents of r.
Each register also contains its own stack. He current register value is the top of the register's stack.
Sr Pop the value off the top of the (main) stack and push it onto the stack of register r. The previous value of the register becomes inaccessible.
Lr Pop the value off the top of register r's stack and push it onto the main stack. The previous value in register r's stack, if any, is now accessible via the lr command.
Parameters
dc has three parameters that control its operation: the precision, the input radix, and the output radix. The precision specifies the number of fraction digits to keep in the result of most arithmetic operations. The input radix controls the interpretation of numbers typed in; all numbers typed in use this radix. The output radix is used for printing numbers.
The input and output radices are separate parameters; you can make them unequal, which can be useful or confusing. The input radix must be between 2 and 16 inclusive. The output radix must be at least 2. The precision must be zero or greater. The precision is always measured in decimal digits, regardless of the current input or output radix.
i Pops the value off the top of the stack and uses it to set the input radix.
o Pops the value off the top of the stack and uses it to set the output radix.
k Pops the value off the top of the stack and uses it to set the precision.
I Pushes the current input radix on the stack.
O Pushes the current output radix on the stack.
K Pushes the current precision on the stack.
Strings
dc has a limited ability to operate on strings as well as on numbers; the only things you can do with strings are print them and execute them as macros (which means that the contents of the string are processed as dc commands). All registers and the stack can hold strings, and dc always knows whether any given object is a string or a number. Some commands such as arithmetic operations demand numbers as arguments and print errors if given strings. Other commands can accept either a number or a string; for example, the p command can accept either and prints the object according to its type.
[characters] Makes a string containing characters (contained between balanced [ and ]characters), and pushes it on the stack. For example, [foo]P prints the characters foo with no newline.
a The top-of-stack is popped. If it was a number, then the low-order byte of this number is converted into a string and pushed onto the stack. Otherwise, the top-of-stack was a string, and the first character of that string is pushed back.
x Pops a value off the stack and executes it as a macro. Normally it should be a string; if it is a number, it is pushed back onto the stack. For example, [1p]x executes the macro 1p which pushes 1 on the stack and prints 1 on a separate line.
Macros are most often stored in registers; [1p]sa stores a macro to print 1 into register a, and lax invokes this macro.
>r Pops two values off the stack and compares them assuming they are numbers, executing the contents of register r as a macro if the original top-of-stack is greater. Thus, 1 2>a will invoke register a's contents and 2 1>a will not.
!>r Similar but invokes the macro if the original top-of-stack is not greater than (less than or equal to) what was the second-to-top.
commands take precedence, so if you want to run a command starting with <, =, or > you will need to add a space after the !.
# Will interpret the rest of the line as a comment.
:r Will pop the top two values off of the stack. The old second-to-top value will be stored in the array r, indexed by the old top-of-stack value.
;r Pops the top-of-stack and uses it as an index into the array r. The selected value is then pushed onto the stack.
Note that each stacked instance of a register has its own array associated with it. Thus 1 0:a 0Sa 2 0:a La 0;ap will print 1, because the 2 was stored in an instance of 0:a that was later popped.
dc examples
First, at the command line, let's enter the desktop calculator.
dc
Nothing appears to have happened. dc's prompt is just a blank line, and it's ready to take our commands. First, let's push a number onto the stack. How about 1234:
1234
Again, nothing seems to have happened. Let's use f to look at the entire contents of the stack:
f
This prints the following:
1234
So 1234 is on the stack, and ready to be operated on. Here we're going to multiply it by 2, and print the result. dc uses reverse-polish (postfix) notation, which places the operands first and the operators second. The below command in English says, "Take the top item on the stack, operate on it with the number two, using the operation multiplication, and print the result." The command is:
2 * p
This takes our top stack item 1234, multiplies it by 2, and prints the resulting value:
2468
Great. Now let's subtract 468 and print the result:
468 - p
2000
Keep in mind that if we weren't putting p at the end of the command, the same thing would be happening, but without any output. Okay, now let's divide ("/") our result 2000 by 2, and print the result:
2 / p
1000
And now let's take the square root:
v p
31
Because the default precision is 0 (calculate zero places after the decimal point), and we haven't changed it, the result has been rounded down to the nearest integer. The answer is actually closer to 31.62. To get a more precise answer, we have to tell dc to use greater precision. Let's tell it to calculate to ten places using the k command:
10 k 1000 v p
31.6227766016
Here, we combined several operations into one command. The command did the following, in the following order:
pushed 10 onto the stack,
told k to pop that number from the stack and set the precision to that many decimal places,
pushed 1000 onto the stack,
told v to pop 1000 off the stack, calculate the square root, and push the result onto the stack, and
printed the result with p.
If we wanted to, we could set the precision to something ridiculous like 100000000, but that might take hours to compute, and we have better things to do.
Let's look at the stack a bit closer. Remember, the stack is like a pile of items. If you push an item onto the stack, it's on top. If you pop an item off of the stack, you take the top (most recently pushed) item off the stack.
First, let's clear the stack:
c
To make sure it has been cleared, let's print the top item on the stack with the pcommand:
p
dc: stack empty
Now, let's push two items onto the stack. Let's say 1 and 2.
1
2
If we use the p command, it will show the item on the top of the stack. Here, that will be the most recently-pushed item, 2:
p
2
Or, we can use the f command to display the entire contents of the stack. This will show the items top-to-bottom, in other words most-recently-pushed-first:
f
2
1
Now let's operate on the stack. Let's add the top two items and print the result:
+ p
3
Now let's look at the full contents of the stack using f:
f
3
The numbers 1 and 2 are gone. They were both popped off the stack by the addition operation, which added them together and then pushed the result, 3, onto the stack.
When adding numbers together, as we just did, the order of the operands doesn't matter (1 + 2 is the same as 2 + 1). Let's use division now, to illustrate the order in which the items on the stack are used. First, let's set the precision to two decimal points:
2 k
Now let's clear the stack, and then push 1 and then 2 onto the stack:
c 1 2
Let's check the stack real quick:
f
2
1
Now let's divide, and print the result:
/ p
.50
As you can see, this is the result of 1 divided by 2, not the other way around.
We're done for now, so let's quit dc:
q
Which returns us to the shell's command prompt.