dc |
[-x] [-e
expression] [file] |
dc is an arbitrary precision arithmetic
package. The overall structure of dc is a stacking
(reverse Polish) calculator i.e. numbers are stored on a stack. Adding a
number pushes it onto the stack. Arithmetic operations pop arguments off the
stack and push the results. See also the
bc(1) utility, which is a preprocessor for
dc providing infix notation and a C-like syntax
which implements functions and reasonable control structures for programs.
The options are as follows:
-e
expression- Evaluate expression. If multiple
-e options are specified, they will be processed
in the order given.
-x- Enable extended register mode. This mode is used by
bc(1) to allow more than 256 registers. See
Registers for a more detailed
description.
If neither expression nor
file are specified on the command line,
dc reads from the standard input. Otherwise
expression and file are
processed and dc exits.
Ordinarily, dc operates on decimal
integers, but one may specify an input base, output base, and a number of
fractional digits (scale) to be maintained. Whitespace is ignored, except
where it signals the end of a number, end of a line or when a register name
is expected. The following constructions are recognized:
- number
- The value of the number is pushed on the stack. A number is an unbroken
string of the digits 0-9 and letters A-F. It may be preceded by an
underscore (‘_’) to input a negative number. A number may
contain a single decimal point. A number may also contain the characters
A-F, with the values 10-15.
+ - / * % ~
^- The top two values on the stack are added (+), subtracted (-), multiplied
(*), divided (/), remaindered (%), divided and remaindered (~), or
exponentiated (^). The two entries are popped off the stack; the result is
pushed on the stack in their place. Any fractional part of an exponent is
ignored.
For addition and subtraction, the scale of the result is the
maximum of scales of the operands. For division the scale of the result
is defined by the scale set by the k operation.
For multiplication, the scale is defined by the expression
min(a+b,max(a,b,scale)),
where a and b are the scales of the
operands, and
scale
is the scale defined by the k operation. For
exponentiation with a non-negative exponent, the scale of the result is
min(a*b,max(scale,a)),
where a is the scale of the base, and
b is the
value
of the exponent. If the exponent is negative, the scale of the result is
the scale defined by the k operation.
In the case of the division and modulus operator (~), the
resultant quotient is pushed first followed by the remainder. This is a
shorthand for the sequence:
The division and modulus operator is a non-portable extension.
a- Pop the top value from the stack. If that value is a number, compute the
integer part of the number modulo 256. If the result is zero, push an
empty string. Otherwise push a one character string by interpreting the
computed value as an ASCII character.
If the top value is a string, push a string containing the
first character of the original string. If the original string is empty,
an empty string is pushed back. The a operator
is a non-portable extension.
c- All values on the stack are popped.
d- The top value on the stack is duplicated.
e- Equivalent to
p, except that the output is written
to the standard error stream. This is a non-portable extension.
f- All values on the stack are printed, separated by newlines.
G- The top two numbers are popped from the stack and compared. A one is
pushed if the top of the stack is equal to the second number on the stack.
A zero is pushed otherwise. This is a non-portable extension.
I- Pushes the input base on the top of the stack.
i- The top value on the stack is popped and used as the base for further
input. The initial input base is 10.
J- Pop the top value from the stack. The recursion level is popped by that
value and, following that, the input is skipped until the first occurrence
of the
M operator. The J
operator is a non-portable extension, used by the
bc(1) command.
K- The current scale factor is pushed onto the stack.
k- The top of the stack is popped, and that value is used as a non-negative
scale factor: the appropriate number of places are printed on output, and
maintained during multiplication, division, and exponentiation. The
interaction of scale factor, input base, and output base will be
reasonable if all are changed together.
Lx- Register x is treated as a stack and its top value
is popped onto the main stack.
lx- The value in register x is pushed on the stack. The
register x is not altered. Initially, all registers
contain the value zero.
M- Mark used by the
J operator. The
M operator is a non-portable extension, used by
the bc(1) command.
N- The top of the stack is replaced by one if the top of the stack is equal
to zero. If the top of the stack is unequal to zero, it is replaced by
zero. This is a non-portable extension.
n- The top value on the stack is popped and printed without a newline. This
is a non-portable extension.
O- Pushes the output base on the top of the stack.
o- The top value on the stack is popped and used as the base for further
output. The initial output base is 10.
P- The top of the stack is popped. If the top of the stack is a string, it is
printed without a trailing newline. If the top of the stack is a number,
it is interpreted as a base 256 number, and each digit of this base 256
number is printed as an ASCII character, without a trailing newline.
p- The top value on the stack is printed with a trailing newline. The top
value remains unchanged.
Q- The top value on the stack is popped and the string execution level is
popped by that value.
q- Exits the program. If executing a string, the recursion level is popped by
two.
R- The top of the stack is removed (popped). This is a non-portable
extension.
r- The top two values on the stack are reversed (swapped). This is a
non-portable extension.
Sx- Register x is treated as a stack. The top value of
the main stack is popped and pushed on it.
sx- The top of the stack is popped and stored into a register named
x.
v- Replaces the top element on the stack by its square root. The scale of the
result is the maximum of the scale of the argument and the current value
of scale.
X- Replaces the number on the top of the stack with its scale factor. If the
top of the stack is a string, replace it with the integer 0.
x- Treats the top element of the stack as a character string and executes it
as a string of
dc commands.
Z- Replaces the number on the top of the stack with its length. The length of
a string is its number of characters. The length of a number is its number
of digits, not counting the minus sign and decimal point. The length of a
zero value is its scale.
z- The stack level is pushed onto the stack.
[...]- Puts the bracketed ASCII string onto the top of the stack. If the string
includes brackets, these must be properly balanced. The backslash
character (‘\’) may be used as an escape character, making
it possible to include unbalanced brackets in strings. To include a
backslash in a string, use a double backslash.
<x
>x
=x
!<x
!>x
!=x- The top two elements of the stack are popped and compared. Register
x is executed if they obey the stated relation.
<xey
>xey
=xey
!<xey
!>xey
!=xey- These operations are variants of the comparison operations above. The
first register name is followed by the letter ‘e’ and
another register name. Register x will be executed
if the relation is true, and register y will be
executed if the relation is false. This is a non-portable extension.
(- The top two numbers are popped from the stack and compared. A one is
pushed if the top of the stack is less than the second number on the
stack. A zero is pushed otherwise. This is a non-portable extension.
{- The top two numbers are popped from the stack and compared. A one is
pushed if the top of stack is less than or equal to the second number on
the stack. A zero is pushed otherwise. This is a non-portable
extension.
?- A line of input is taken from the input source (usually the terminal) and
executed.
:r- Pop two values from the stack. The second value on the stack is stored
into the array r indexed by the top of stack.
;r- Pop a value from the stack. The value is used as an index into register
r. The value in this register is pushed onto the
stack.
Array elements initially have the value zero. Each level of a
stacked register has its own array associated with it. The command
sequence
[first] 0:a [dummy] Sa [second] 0:a 0;a p La 0;a p
will print
since the string
‘second’ is written in an array
that is later popped, to reveal the array that stored
‘first’.
#- Skip the rest of the line. This is a non-portable extension.
Registers have a single character name x,
where x may be any character, including space, tab or
any other special character. If extended register mode is enabled using the
-x option and the register identifier
x has the value 255, the next two characters are
interpreted as a two-byte register index. The set of standard single
character registers and the set of extended registers do not overlap.
Extended register mode is a non-portable extension.
An example which prints the first ten values of
n!:
[la1+dsa*pla10>y]sy
0sa1
lyx
Independent of the current input base, the command
will reset the input base to decimal 10.
- %c (0%o) is unimplemented
- an undefined operation was called.
- stack empty
- for not enough elements on the stack to do what was asked.
- stack register '%c' (0%o) is empty
- for an L operation from a stack register that is
empty.
- Runtime warning: non-zero scale in exponent
- for a fractional part of an exponent that is being ignored.
- divide by zero
- for trying to divide by zero.
- remainder by zero
- for trying to take a remainder by zero.
- square root of negative number
- for trying to take the square root of a negative number.
- index too big
- for an array index that is larger than 2048.
- negative index
- for a negative array index.
- input base must be a number between 2 and 16
- for trying to set an illegal input base.
- output base must be a number greater than 1
- for trying to set an illegal output base.
- scale must be a nonnegative number
- for trying to set a negative or zero scale.
- scale too large
- for trying to set a scale that is too large. A scale must be representable
as a 32-bit unsigned number.
- Q command argument exceeded string execution depth
- for trying to pop the recursion level more than the current recursion
level.
- Q command requires a number >= 1
- for trying to pop an illegal number of recursion levels.
- recursion too deep
- for too many levels of nested execution.
The recursion level is increased by one if the
x or ? operation or one of
the compare operations resulting in the execution of register is
executed. As an exception, the recursion level is not increased if the
operation is executed as the last command of a string. For example, the
commands
will execute an endless loop, while the commands
will terminate because of a too deep recursion level.
- J command argument exceeded string execution depth
- for trying to pop the recursion level more than the current recursion
level.
- mark not found
- for a failed scan for an occurrence of the
M
operator.
The arithmetic operations of the dc
utility are expected to conform to the definition listed in the
bc(1) section of the IEEE
Std 1003.2 (“POSIX.2”) specification.
The dc command appeared in
Version 1 AT&T UNIX. A complete rewrite
of the dc command using the
BN_new(3) big number routines first
appeared in OpenBSD 3.5.
The original version of the dc command was
written by Robert Morris and
Lorinda Cherry. The current version of the
dc utility was written by Otto
Moerbeek.
While fractional input in base 10 is always exact, other bases may
suffer from unintuitive rounding. To avoid surprising results, plain integer
division can be used instead of the corresponding floating point
notation.