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GNU dc
******

This manual documents version 1.4.1 of GNU 'dc', an arbitrary precision
calculator.

   Copyright (C) 1984, 1994, 1997, 1998, 2000, 2005, 2006, 2008, 2013,
2016 Free Software Foundation, Inc.

     Permission is granted to copy, distribute and/or modify this
     document under the terms of the GNU Free Documentation License,
     Version 1.2 or any later version published by the Free Software
     Foundation; with no Invariant Sections, with no Front-Cover Texts,
     and with no Back-Cover Texts.  A copy of the license can be found
     at <http://www.gnu.org/licenses/fdl.html> .

* Menu:

* Introduction::                Introduction
* Invocation::                  Invocation
* Printing Commands::           Printing Commands
* Arithmetic::                  Arithmetic
* Stack Control::               Stack Control
* Registers::                   Registers
* Parameters::                  Parameters
* Strings::                     Strings
* Status Inquiry::              Status Inquiry
* Miscellaneous::               Other commands
* Reporting bugs::              Reporting bugs

File: dc.info,  Node: Introduction,  Next: Invocation,  Prev: Top,  Up: Top

1 Introduction
**************

'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 instead of reading from standard input.  All
normal output is to standard output; all error messages are written to
standard error.

   To exit, use 'q'.  'C-c' (or whatever other keystroke your system
uses to generate a 'SIGINT') does not exit; it is used to abort macros
that are looping, etc.

   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.

File: dc.info,  Node: Invocation,  Next: Printing Commands,  Prev: Introduction,  Up: Top

2 Invocation
************

'dc' may be invoked with the following command-line options:

'-e EXPR'
'--expression=EXPR'
     Evaluate EXPR as 'dc' commands.

'-f FILE'
'--file=FILE'
     Read and evaluate 'dc' commands from FILE.

'-h'
'--help'
     Print a usage message summarizing the command-line options, then
     exit.

'-V'
'--version'
     Print the version information for this program, then exit.

   If any command-line parameters remain after processing the options,
these parameters are interpreted as additional FILEs whose contents are
read and evaluated.  A file name of '-' refers to the standard input
stream.  If no '-e' option was specified, and no files were specified,
then the standard input will be read for commands to evaluate.

File: dc.info,  Node: Printing Commands,  Next: Arithmetic,  Prev: Invocation,  Up: Top

3 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.  (This command is a GNU extension.)

'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]dsxx
     sx[q]Sq[Lsd0>qaPlxx]dsxx sx0sqLqsxLxLK+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.)  (Details of the behavior with a number are a GNU
     extension.  Traditional 'dc' happened to "support" similar
     functionality for a limited range of inputs as an accidental
     side-effect of its internal representation of numbers.)

'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.

   All numeric output is split to fit within 70 columns, by default.
When a number is broken up in this way, the split is indicated by a "\"
at the end of the to-be-continued output lines.  The column width at
which output is split can be overridden by setting the DC_LINE_LENGTH
environment variable to the desired width.  A DC_LINE_LENGTH of 0 (zero)
disables the line-split feature altogether.  Invalid values of
DC_LINE_LENGTH are silently ignored.  (The DC_LINE_LENGTH variable is a
GNU extension.)

File: dc.info,  Node: Arithmetic,  Next: Stack Control,  Prev: Printing Commands,  Up: Top

4 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 is the largest of the
     precision value, the number of fraction digits in the multiplier,
     or the number of fraction digits in the multiplicand; but in no
     event exceeding the number of digits required for an exact result.

'/'
     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.)  (This command is a GNU extension.)

'^'
     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 the result may not be accurate if the modulus
     is not 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.  (This command
     is a GNU extension.)

'v'
     Pops one value, computes its square root, and pushes that.  The
     maximum of the precision value and the precision of the argument is
     used to determine 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.

File: dc.info,  Node: Stack Control,  Next: Registers,  Prev: Arithmetic,  Up: Top

5 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'.)
     (This command is a GNU extension.)

'R'
     Pops the top-of-stack as an integer N.  Cyclically rotates the top
     N items on the updated stack.  If N is positive, then the rotation
     direction will make the topmost element the second-from top; if N
     is negative, then the rotation will make the topmost element the
     N-th element from the top.  If the stack depth is less than N then
     the entire stack is rotated (in the appropriate direction), without
     any error being reported.  (This command is a GNU extension.)

File: dc.info,  Node: Registers,  Next: Parameters,  Prev: Stack Control,  Up: Top

6 Registers
***********

'dc' provides at least 256 memory registers(1), each named by a single
character.  You can store a number 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.  The
     value '0' is retrieved if the register is uninitialized or its
     stack has become empty.  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.

   ---------- Footnotes ----------

   (1) The exact number of registers provided by 'dc' depends on the
range of an 'unsigned char' in the C compiler used to create the 'dc'
executable.

File: dc.info,  Node: Parameters,  Next: Strings,  Prev: Registers,  Up: Top

7 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.

File: dc.info,  Node: Strings,  Next: Status Inquiry,  Prev: Parameters,  Up: Top

8 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).  Both 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 and pushes it on the stack.
     For example, '[foo]P' prints the characters 'foo' (with no
     newline).  Note that all square brackets ('['s and ']'s) must be
     balanced; there is no mechanism provided for handling unbalanced
     square brackets.

'a'
     The mnemonic for this is somewhat erroneous: asciify.  The
     top-of-stack is popped.  If it was a number, then the low-order
     byte of this number is converted into a 1-character string and
     pushed onto the stack.  Otherwise the top-of-stack was a string,
     and the first character of that string is pushed back.  (This
     command is a GNU extension.)

'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 the 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 (is 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 (is 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'
     During the execution of a macro, this command exits from the 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.

File: dc.info,  Node: Status Inquiry,  Next: Miscellaneous,  Prev: Strings,  Up: Top

9 Status Inquiry
****************

'Z'
     Pops a value off the stack, calculates the number of decimal digits
     it has (or number of characters, if it is a string) and pushes that
     number.

     Note that the digit count for a number does _not_ include any
     leading zeros, even if those appear to the right of the radix
     point.  This may seem a bit strange at first, but it is compatible
     with historical implementations of 'dc', and can be argued to be
     useful for computing the magnitude of a value: 'dSaXLaZ-' will
     compute the power-of-ten multiplier which would be needed to shift
     the decimal point to be immediately before the leftmost non-zero
     digit.

'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.

File: dc.info,  Node: Miscellaneous,  Next: Reporting bugs,  Prev: Status Inquiry,  Up: Top

10 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.  (This command is
     a GNU extension.)

':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.

File: dc.info,  Node: Reporting bugs,  Prev: Miscellaneous,  Up: Top

11 Reporting bugs
*****************

Email bug reports to <bug-dc AT gnu.org>.


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