manuals/dc.1.ronn

dc(1) -- arbitrary-precision reverse-Polish notation calculator
===============================================================

SYNOPSIS
--------

`dc` [`-hvVx`] [`--version`] [`--help`] [`--extended-register`] [`-e` *expr*]
[`--expression=`*expr*...] [`-f` *file*...] [`-file=`*file*...] [*file*...]

DESCRIPTION
-----------

dc(1) is an arbitrary-precision calculator. It uses a stack (reverse Polish
notation) to store numbers and results of computations. Arithmetic operations
pop arguments off of the stack and push the results.

If no expressions or files are given on the command line, as in options below,
or for files, as extra command-line arguments, then dc(1) reads from `stdin`.
Otherwise, those expressions and files are processed, and dc(1) will then exit.

OPTIONS
-------

The following are the options that dc(1) accepts.

  * `-h`, `--help`:
    Prints a usage message and quits.

  * `-v`, `-V`, `--version`:
    Print the version information (copyright header) and exit.

  * `-x` `--extended-register`:
    Enables extended register mode. See [REGISTERS](#REGISTERS) for more
    information.

  * `-e` *expr*, `--expression`=*expr*:
    Evaluates `expr`. If multiple expressions are given, they are evaluated in
    order. If files are given as well (see below), the expressions and files are
    evaluated in the order given. This means that if a file is given before an
    expression, the file is read in and evaluated first.

  * `-f` *file*, `--file`=*file*:
    Reads in `file` and evaluates it. If expressions are also given (see above),
    the expressions are evaluated in the order given.

SYNTAX
------

`ibase` is a [register][REGISTERS] determining how to interpret constant
numbers. It is the "input" base, or the number base used for interpreting input
numbers. `ibase` is initially `10`. The max allowable value for `ibase` is `16`.
The min allowable value for `ibase` is `2`.

`obase` is a [register][REGISTERS] determining how to output results. It is the
"output" base, or the number base used for outputting numbers. `obase` is
initially `10`. The max allowable value for `obase` is `BC_BASE_MAX`. The min
allowable value for `obase` is `2`.

The **scale** of an expression is the number of digits in the result of the
expression right of the decimal point, and `scale` is a [register][REGISTERS]
that sets the precision of any operations (with exceptions). `scale` is
initially `0`. `scale` cannot be negative.

Each item ([numbers](#NUMBERS) or [commands](#COMMANDS)) in the input source
code is processed and executed, in order. Input is processed immediately when
entered.

### Comments

Comments go from `#` until, and not including, the next newline. This is a
**non-portable extension**.

NUMBERS
-------

Numbers are strings made up of digits, uppercase letters up to `F`, and at most
`1` period for a radix. Numbers can have up to `BC_NUM_MAX` digits. Uppercase
letters equal `9` + their position in the alphabet (i.e., `A` equals `10`, or
`9 + 1`). If a digit or letter makes no sense with the current value of `ibase`,
they are set to the value of the highest valid digit in `ibase`.

Single-character numbers (i.e., `A`) take the value that they would have if they
were valid digits, regardless of the value of `ibase`. This means that `A`
always equals decimal `10` and `F` always equals decimal `15`.

In addition, if dc(1) was built with the extra math option, it accepts numbers
in scientific notation. For dc(1), an example is `1.89237e9`, which is equal to
`1892370000`. Negative exponents are also allowed, so `4.2890e_3` is equal to
`0.0042890`.

**WARNING**: Both the number and the exponent in scientific notation are
interpreted according to the current `ibase`, but the number is still multiplied
by `10^exponent` regardless of the current `ibase`. For example, if `ibase` is
`16` and dc(1) is given the number string `"FFeA"`, the resulting decimal number
will be `2550000000000`, and if dc(1) is given the number string `"10e_4"`, the
resulting decimal number will be `0.0016`.

Scientific notation is a **non-portable extension**.

COMMANDS
--------

The valid commands are listed below.

### Printing

These commands are used for printing.

Note that if dc(1) has been built with the extra math option enabled, both
scientific notation and engineering notation are available for printing numbers.
Scientific notation is activated by assigning `0` to `obase` (in any other
context, an `obase` of `0` is invalid), and engineering notation is activated by
assigning `1` to `obase` (which is also invalid in any other context). To
deactivate them, just assign a different value to `obase`.

Printing numbers in scientific notation and/or engineering notation is a
**non-portable extension**.

  * `p`:
    Prints the value on top of the stack, whether number or string, and prints a
    newline after.

    This does not alter the stack.

  * `n`:
    Prints the value on top of the tack, whether number or string, and pops it
    off of the stack.

  * `P`:
    Pops a value off the stack.

    If the value is a number, it is truncated and the result's absolute value is
    printed as though `obase` is `UCHAR_MAX + 1` and each digit is interpreted
    as an ASCII character, making it a byte stream.

    If the value is a string, it is printed without a trailing newline.

    This is a **non-portable extension**.

  * `f`:
    Prints the entire contents of the stack, in order from newest to oldest,
    without altering anything.

    Users should use this command when they get lost.

### Arithmetic

These are the commands used for arithmetic.

  * `+`:
    The top two values are popped off the stack, added, and the result is pushed
    onto the stack. The result's **scale** is equal to the max **scale** of both
    operands.

  * `-`:
    The top two values are popped off the stack, subtracted, and the result is
    pushed onto the stack. The result's **scale** is equal to the max **scale**
    of both operands.

  * `*`:
    The top two values are popped off the stack, multiplied, and the result is
    pushed onto the stack. If `a` is the **scale** of the first expression and
    `b` is the **scale** of the second expression, the **scale** of the result
    is equal to `min(a+b,max(scale,a,b))` where `min` and `max` return the
    obvious values.

  * `/`:
    The top two values are popped off the stack, divided, and the result is
    pushed onto the stack. The result's **scale** is equal to `scale`.

  * `%`:
    The top two values are popped off the stack, remaindered, and the result is
    pushed onto the stack.

    Remaindering is equivalent to 1) Computing `a/b` to current `scale`, and 2)
    Using the result of step 1 to calculate `a-(a/b)*b` to **scale**
    `max(scale + scale(b), scale(a))`.

  * `~`:
    The top two values are popped off the stack, divided and remaindered, and
    the results (divided first, remainder second) are pushed onto the stack.
    This is equivalent to `x y / x y %` except that `x` and `y` are only
    evaluated once.

    This is a **non-portable extension**.

  * `^`:
    The top two values are popped off the stack, the second is raised to the
    power of the first, and the result is pushed onto the stack.

    The first value popped off the stack must be an integer.

  * `v`:
    The top value is popped off the stack, its square root is computed, and the
    result is pushed onto the stack. The result's **scale** is equal to `scale`.

  * `_`:
    If this command *immediately* precedes a number (i.e., no spaces or other
    commands), then that number is input as a negative number.

    Otherwise, the top value on the stack is popped and copied, and the copy is
    negated and pushed onto the stack. This behavior without a number is a
    non-portable extension.

  * `b`:
    The top value is popped off the stack and its absolute value is pushed onto
    the stack.

    This is a **non-portable extension**.

  * `|`:
    The top three values are popped off the stack, a modular exponentiation is
    computed, and the result is pushed onto the stack.

    The first value popped is used as the reduction modulus and must be an
    integer and non-zero. The second value popped is used as the exponent and
    must be an integer and non-negative. The third value popped is the base and
    must be an integer.

    This is a **non-portable extension**.

  * `$`:
    The top value is popped off the stack and copied, and the copy is truncated
    and pushed onto the stack.

    This is a **non-portable extension**.

  * `@`:
    The top two values are popped off the stack, and the second's precision is
    set to the value of the first, whether by truncation or extension.

    The first value must be an integer and non-negative.

    This is a **non-portable extension**.

  * `H`:
    The top two values are popped off the stack, and the second is shifted left
    (radix shifted right) to the value of the first.

    The first value must be an integer and non-negative.

    This is a **non-portable extension**.

  * `h`:
    The top two values are popped off the stack, and the second is shifted right
    (radix shifted left) to the value of the first.

    The first value must be an integer and non-negative.

    This is a **non-portable extension**.

  * `G`:
    The top two values are popped off of the stack, they are compared, and a `1`
    is pushed if they are equal, or `0` otherwise.

    This is a **non-portable extension**.

  * `N`:
    The top value is popped off of the stack, and if it a `0`, a `1` is pushed;
    otherwise, a `0` is pushed.

    This is a **non-portable extension**.

  * `(`:
    The top two values are popped off of the stack, they are compared, and a `1`
    is pushed if the first is less than the second, or `0` otherwise.

    This is a **non-portable extension**.

  * `{`:
    The top two values are popped off of the stack, they are compared, and a `1`
    is pushed if the first is less than or equal to the second, or `0`
    otherwise.

    This is a **non-portable extension**.

  * `)`:
    The top two values are popped off of the stack, they are compared, and a `1`
    is pushed if the first is greater than the second, or `0` otherwise.

    This is a **non-portable extension**.

  * `}`:
    The top two values are popped off of the stack, they are compared, and a `1`
    is pushed if the first is greater than or equal to the second, or `0`
    otherwise.

    This is a **non-portable extension**.

### Stack Control

These commands control the stack.

  * `c`:
    Removes all items from ("clears") the stack.

  * `d`:
    Copies the item on top of the stack ("duplicates") and pushes the copy onto
    the stack.

  * `r`:
    Swaps ("reverses") the two top items on the stack.

  * `R`:
    Pops ("removes") the top value from the stack.

### Register Control

These commands control [registers](#REGISTERS).

  * `s`*r*:
    Pops the value off the top of the stack and stores it into register `r`.

  * `l`*r*:
    Copies the value in register `r` and pushes it onto the stack. This does not
    alter the contents of `r`.

  * `S`*r*:
    Pops the value off the top of the (main) stack and pushes it onto the stack
    of register `r`. The previous value of the register becomes inaccessible.

  * `L`*r*:
    Pops 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

These commands control the values of `ibase`, `obase`, and `scale` (see
[SYNTAX](#SYNTAX)).

  * `i`:
    Pops the value off of the top of the stack and uses it to set `ibase`, which
    must be between `2` and `16`, inclusive.

    If the value on top of the stack has any **scale**, the **scale** is
    ignored.

  * `o`:
    Pops the value off of the top of the stack and uses it to set `obase`, which
    must be between `2` and `BC_BASE_MAX`, inclusive (see bc(1)).

    If the value on top of the stack has any **scale**, the **scale** is
    ignored.

  * `k`:
    Pops the value off of the top of the stack and uses it to set `scale`, which
    must be non-negative.

    If the value on top of the stack has any **scale**, the **scale** is
    ignored.

  * `I`:
    Pushes the current value of `ibase` onto the main stack.

  * `O`:
    Pushes the current value of `obase` onto the main stack.

  * `K`:
    Pushes the current value of `scale` onto the main stack.

### Strings

The following commands control strings.

dc(1) can work with both numbers and strings, and [registers](#REGISTERS) can
hold both strings and numbers. dc(1) always knows whether a register's contents
are a string or a number.

While arithmetic operations have to have numbers, and will print an error if
given a string, other commands accept strings.

Strings can also be executed as macros. For example, if the string `[1pR]` is
executed as a macro, then the code `1pR` is executed, meaning that the `1` will
be printed with a newline after and then popped from the stack.

  * `[`*characters*`]`:
    Makes a string containing `characters` and pushes it onto the stack.

    If there are brackets (`[` and `]`) in the string, then they must be
    balanced. Unbalanced brackets can be escaped using a backslash (`\`)
    character.

    If there is a backslash character in the string, the character after it
    (even another backslash) is put into the string verbatim, but the (first)
    backslash is not.

  * `a`:
    The value on top of the stack is popped.

    If it is a number, it is truncated and its absolute value is taken. The
    result mod `UCHAR_MAX + 1` is calculated. If that result is `0`, push an
    empty string; otherwise, push a one-character string where the character is
    the result of the mod interpreted as an ASCII character.

    If it is a string, then a new string is made. If the original string is
    empty, the new string is empty. If it is not, then the first character of
    the original string is used to create the new string as a one-character
    string. The new string is then pushed onto the stack.

    This is a **non-portable extension**.

  * `x`:
    Pops a value off of the top of the stack.

    If it is a number, it is pushed onto the stack.

    If it is a string, it is executed as a macro.

    This behavior is the norm whenever a macro is executed, whether by this
    command or by the conditional execution commands below.

  * `>`*r*:
    Pops two values off of the stack that must be numbers and compares them. If
    the first value is greater than the second, then the contents of register
    `r` are executed.

    For example, `0 1>a` will execute the contents of register `a`, and `1 0>a`
    will not.

  * `>`*r*`e`*s*:
    Like the above, but will execute register `s` if the comparison fails.

    This is a **non-portable extension**.

  * `!>`*r*:
    Pops two values off of the stack that must be numbers and compares them. If
    the first value is not greater than the second (less than or equal to), then
    the contents of register `r` are executed.

  * `!>`*r*`e`*s*:
    Like the above, but will execute register `s` if the comparison fails.

    This is a **non-portable extension**.

  * `<`*r*:
    Pops two values off of the stack that must be numbers and compares them. If
    the first value is less than the second, then the contents of register `r`
    are executed.

  * `<`*r*`e`*s*:
    Like the above, but will execute register `s` if the comparison fails.

    This is a **non-portable extension**.

  * `!<`*r*:
    Pops two values off of the stack that must be numbers and compares them. If
    the first value is not less than the second (greater than or equal to), then
    the contents of register `r` are executed.

  * `!<`*r*`e`*s*:
    Like the above, but will execute register `s` if the comparison fails.

    This is a **non-portable extension**.

  * `=`*r*:
    Pops two values off of the stack that must be numbers and compares them. If
    the first value is equal to the second (greater than or equal to), then the
    contents of register `r` are executed.

  * `=`*r*`e`*s*:
    Like the above, but will execute register `s` if the comparison fails.

    This is a **non-portable extension**.

  * `!=`*r*:
    Pops two values off of the stack that must be numbers and compares them. If
    the first value is not equal to the second (greater than or equal to), then
    the contents of register `r` are executed.

  * `!=`*r*`e`*s*:
    Like the above, but will execute register `s` if the comparison fails.

    This is a **non-portable extension**.

  * `?`:
    Reads a line from the `stdin` and executes it. This is to allow macros to
    request input from users.

  * `q`:
    During execution of a macro, this exits that macro's execution and the
    execution of the macro that executed it. If there are no macros, or only one
    macro executing, dc(1) exits.

  * `Q`:
    Pops a value from the stack which must be non-negative and is used the
    number of macro executions to pop off of the execution stack. If the number
    of levels to pop is greater than the number of executing macros, dc(1)
    exits.

### Status

These commands query status of the stack or its top value.

  * `Z`:
    Pops a value off of the stack.

    If it is a number, calculates the number of significant decimal digits it
    has and pushes the result.

    If it is a string, pushes the number of characters the string has.

  * `X`:
    Pops a value off of the stack.

    If it is a number, pushes the **scale** of the value onto the stack.

    If it is a string, pushes `0`.

  * `z`:
    Pushes the current stack depth (before execution of this command).

### Arrays

These commands manipulate arrays.

  * `:`*r*:
    Pops the top two values off of the stack. The second value will be stored in
    the array `r` (see [Registers](#REGISTERS)), indexed by the first value.

  * `;`*r*:
    Pops the value on top of the stack and uses it as an index into the array
    `r`. The selected value is then pushed onto the stack.

REGISTERS
---------

Registers are names that can store strings, numbers, and arrays. (Number/string
registers do not interfere with array registers.)

Each register is also its own stack, so the current register value is the top of
the register's stack. All registers, when first referenced, have one value (`0`)
in their stack.

In non-extended register mode, a register name is just the single character that
follows any command that needs a register name. The only exception is a newline
(`'\n'`); it is a parse error for a newline to be used as a register name.

### Extended Register Mode

Unlike most other dc(1) implentations, this dc(1) provides nearly unlimited
amounts of registers, if extended register mode is enabled.

If extended register mode is enabled (`-x` or `--extended-register` command-line
arguments are given), then normal single character registers are used
***unless*** the character immediately following a command that needs a register
name is a space (according to `isspace()`) and not a newline (`'\n'`).

In that case, the register name is found according to the regex
`[a-z][a-z0-9_]*` (like bc(1)), and it is a parse error if the next
non-space characters do not match that regex.

LIMITS
------

The following are the limits on dc(1):

  * `DC_BASE_MAX`:
    The maximum output base. Set at `ULONG_MAX`.

  * `DC_DIM_MAX`:
    The maximum size of arrays. Set at `SIZE_MAX-1`.

  * `DC_SCALE_MAX`:
    The maximum `scale`. Set at `SIZE_MAX-1`.

  * `DC_STRING_MAX`:
    The maximum length of strings. Set at `SIZE_MAX-1`.

  * `DC_NAME_MAX`:
    The maximum length of identifiers. Set at `SIZE_MAX-1`.

  * `DC_NUM_MAX`:
    The maximum length of a number (in decimal digits), which includes digits
    after the decimal point. Set at `SIZE_MAX-1`.

  * Exponent:
    The maximum allowable exponent (positive or negative). Set at `ULONG_MAX`.

  * Number of vars:
    The maximum number of vars/arrays. Set at `SIZE_MAX-1`.

Actual values can be queried with the `limits` statement.

These limits are meant to be effectively non-existent; the limits are so large
(at least on 64-bit machines) that there should not be any point at which they
become a problem. In fact, memory should be exhausted before these limits should
be hit.

ENVIRONMENT VARIABLES
---------------------

dc(1) recognizes the following environment variables:

  * `DC_LINE_LENGTH`:
    If this environment variable exists and contains an integer that is greater
    than `1` and is less than `UINT16_MAX` (`2^16-1`), dc(1) will output lines
    to that length, including the backslash newline combo. The default line
    length is `70`.

EXIT STATUS
-----------

dc(1) returns the following exit statuses:

  * `0`:
    No error.

  * `1`:
    A math error occurred. This follows standard practice of using `1` for
    expected errors, since math errors will happen in the process of normal
    execution.

    Math errors include divide by `0`, taking the square root of a negative
    number, attempting to convert a negative number to a hardware integer,
    overflow when converting a number to a hardware integer, and attempting to
    use a non-integer where an integer is required.

    Converting to a hardware integer happens for the second operand of the power
    (`^`), places (`@`), left shift (`H`), and right shift (`h`) operators.

  * `2`:
    A parse error occurred.

    Parse errors include unexpected `EOF`, using an invalid character, failing
    to find the end of a string or comment, and using a token where it's
    invalid.

  * `3`:
    A runtime error occurred.

    Runtime errors include assigning an invalid number to `ibase`, `obase`, or
    `scale`; give a bad expression to a `read()` call, calling `read()` inside
    of a `read()` call, type errors, and attempting an operation when the stack
    has too few elements.

  * `4`:
    A fatal error occurred.

    Fatal errors include memory allocation errors, I/O errors, failing to open
    files, attempting to use files that do not have only ASCII characters (dc(1)
    only accepts ASCII characters), attempting to open a directory as a file,
    and giving invalid command-line options.

The exit status `4` is special; when a fatal error occurs, dc(1) always exits
and returns `4`, no matter what mode dc(1) is in.

The other statuses will only be returned when dc(1) is not in interactive mode,
since dc(1) resets its state and accepts more input when one of those errors
occurs in interactive mode. This is also the case when interactive mode is
forced by the `-i` option.

These exit statuses allow dc(1) to be used in shell scripting with error
checking, and its normal behavior can be forced by using `-i`.

SIGNAL HANDLING
---------------

If dc(1) has been compiled with the signal handling, sending a `SIGINT` will
cause dc(1) to stop  execution of the current input and reset, asking for more
input.

Otherwise, any signals cause dc(1) to exit.

COMMAND LINE HISTORY
--------------------

dc(1) supports interactive command-line editing, if compiled with the history
option enabled. If `stdin` is hooked to a terminal, it is enabled. Previous
lines can be recalled and edited with the arrow keys.

LOCALES
-------

This dc(1) ships with support for adding error messages for different locales.

SEE ALSO
--------

bc(1)

STANDARDS
---------

The dc(1) utility operators are compliant with the operators in the bc(1)
[IEEE Std 1003.1-2017 (“POSIX.1-2017”)][1] specification.

AUTHOR
------

This dc(1) was made from scratch by Gavin D. Howard.

BUGS
----

None are known. Report bugs at https://github.com/gavinhoward/bc.

[1]: https://pubs.opengroup.org/onlinepubs/9699919799/utilities/bc.html