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**PROGRAM:**

**NAME**

dc - an arbitrary precision calculator

**SYNOPSIS**

dc [-V] [--version] [-h] [--help]

[-e scriptexpression] [--expression=scriptexpression]

[-f scriptfile] [--file=scriptfile]

[file ...]

**DESCRIPTION**

__dc__is a reverse-polish desk calculator which supports unlimited precision arithmetic. 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

``_''. ``-'' cannot be used for this, as it is a binary operator for subtraction instead.

To enter two numbers in succession, separate them with spaces or newlines. These have no

meaning as commands.

**OPTIONS**

__dc__may be invoked with the following command-line options:

**-V**

**--version**

Print out the version of

__dc__that is being run 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

**-**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 it a string, it is simply 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~Ssd0<x]dsxxsx[q]Sq[Lsd0>qaPlxx]**

**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, rendering it empty.

**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.

**s**

__r__Pop the value off the top of the stack and store it into register

__r__.

**l**

__r__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. The current register value is the top of the

register's stack.

**S**

__r__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.

**L**

__r__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

**l**

__r__

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 simply 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.

**<**

__r__Similar but invokes the macro if the original top-of-stack is less.

**!<**

__r__Similar but invokes the macro if the original top-of-stack is not less than

(greater than or equal to) what was the second-to-top.

**=**

__r__Similar but invokes the macro if the two numbers popped are equal.

**!=**

__r__Similar but invokes the macro if the two numbers popped are not equal.

**?**Reads a line from the terminal and executes it. This command allows a macro to

request input from the user.

**q**exits from a macro and also from the macro which invoked it. If called from the

top level, or from a macro which was called directly from the top level, the

**q**

command will cause

__dc__to exit.

**Q**Pops a value off the stack and uses it as a count of levels of macro execution to

be exited. Thus,

**3Q**exits three levels. The

**Q**command will never cause

__dc__to

exit.

**Status** **Inquiry**

**Z**Pops a value off the stack, calculates the number of digits it has (or number of

characters, if it is a string) and pushes that number. The digit count for a

number does

__not__include any leading zeros, even if those appear to the right of the

radix point.

**X**Pops a value off the stack, calculates the number of fraction digits it has, and

pushes that number. For a string, the value pushed is 0.

**z**Pushes the current stack depth: the number of objects on the stack before the

execution of the

**z**command.

**Miscellaneous**

**!**Will run the rest of the line as a system command. Note that parsing of the !<,

!=, and !> 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.

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