dc

Desk calculator.

Syntax
      dc

Printing Commands

   p    Print the value on the top of the stack, without altering the
        stack. A newline is printed after the value.

   n    Print the value on the top of the stack, popping it off, and
        do not print a newline after.

   P    Pop off the value on top of the stack. If 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.

   f    Print 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.

dc works with postfix notation; rather like many HP Calculators. Basic arithmetic uses the standard + - / * symbols but entered after the digits

  so entering:
100
0.5
*
p will return 50

Arithmetic

   +    Pop two values off the stack, add them, and push the result.
        The precision of the result is determined only by the values of
        the arguments, and is enough to be exact.

   -    Pop two values, subtract the first one popped from the second
        one popped, and push the result.

   *    Pop two values,  multiply them, and push 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.

   /    Pop two values, divide the second one popped from the  first
        one popped, and push the result.  The number of fraction digits
        is specified by the precision value.

   %    Pop two values, compute the remainder of the division that the /
        command would do, and push that.  The value computed is the
        same as that computed by the sequence Sd dld/ Ld*- .

   ~    Pop two values, divide 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 differ-
        ent error checking.)

   ^    Pop two values and exponentiate, 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.

   |    Pop three values and compute 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-nega-
        tive number, and any fractional part of this  exponent  will  be
        ignored.  The third value popped is the base which gets exponen-
        tiated, which should be an integer.  For small integers this  is
        like  the sequence Sm^Lm%, but, unlike ^, this command will work
        with arbritrarily large exponents.

   v    Pop 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     Clear the stack, rendering it empty.

   d     Duplicate  the  value  on the top of the stack, pushing another
        copy of it.  Thus, `4d*p' computes 4 squared and prints it.

   r     Reverse the order of (swaps) the top two values on the stack.

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. The 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 can 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 original top-of-stack is less.

  !<r  Similar but invokes the macro if original top-of-stack is not less
       than (greater or equal to) what  was second-to-top.

   =r  Similar but invokes the macro if two numbers popped are equal.

   !=r Similar but invokes the macro if two numbers popped are not equal.

   ?   Reads a line from terminal and executes it.  this command
       allows to request input user.

   q   exit 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   Pop 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     Pop 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.

   X     Pop 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     Push 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    Pop 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.

“The best way to destroy the capitalist system is to debauch the currency” ~ John Keynes

Related:

dc man page - Apple.com
cal - Display a calendar
expr - Evaluate expressions
units - Convert units from one scale to another
wc - Print byte, word, and line counts


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