DC(1)

NAME
dc - arbitrary-precision reverse-Polish notation calculator

SYNOPSIS
dc [-hiPvVx] [--version] [--help] [--interactive] [--no-prompt] [--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 files are given on the command-line as extra arguments (i.e., not as -f or --file arguments), then dc(1) reads from stdin. Otherwise, those files are processed, and dc(1) will then exit.

This is different from the dc(1) on OpenBSD and possibly other dc(1) implementations, where -e (--expression) and -f (--file) arguments cause dc(1) to execute them and exit. The reason for this is that this dc(1) allows users to set arguments in the environment variable DC_ENV_ARGS (see the ENVIRONMENT VARIABLES section). Any expressions given on the command-line should be used to set up a standard environment. For example, if a user wants the scale always set to 10, they can set DC_ENV_ARGS to "-e 10k", and this dc(1) will always start with a scale of 10.

If users want to have dc(1) exit after processing all input from -e and -f arguments (and their equivalents), then they can just simply add "-e q" as the last command-line argument.

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.

-i, --interactive
    Forces interactive mode.

    dc(1) has an interactive mode and a non-interactive mode. The interactive mode is turned on automatically when both stdin and stdout are hooked to a terminal, but this flag can turn it on in other cases. In interactive mode, dc(1) attempts to recover from errors (see the RESET section), and in normal execution, flushes stdout as soon as execution is done for the current input.

    This is a non-portable extension.

-P, --no-prompt
    Disables the prompt in interactive mode. This is mostly for those users that do not want a prompt or are not used to having them in dc. Most of those users would want to put this option in DC_ENV_ARGS.

    If the prompt has been disabled while building bc(1), this option is a no-op.

    This is a non-portable extension.

-x --extended-register
    Enables extended register mode. See the REGISTERS section for more information.

    This is a non-portable extension.

-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.

    In other dc(1) implementations, this option causes the program to execute the expressions and then exit. This dc(1) does not, unless the DC_EXPR_EXIT is defined (see the ENVIRONMENT VARIABLES section).

    This is a non-portable extension.

-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.

    In other dc(1) implementations, this option causes the program to execute the files and then exit. This dc(1) does not, unless the DC_EXPR_EXIT is defined (see the ENVIRONMENT VARIABLES section).

    This is a non-portable extension.

STDOUT
Any non-error output is written to stdout.

Note: Unlike other dc(1) implementations, this dc(1) will issue a fatal error (see the EXIT STATUS section) if it cannot write to stdout, so if stdout is closed, as in bc <file> >&-, it will quit with an error. This is done so that dc(1) can report problems when stdout is redirected to a file.

If there are scripts that depend on the behavior of other dc(1) implementations, it is recommended that those scripts be changed to redirect stdout to /dev/null.

STDERR
Any error output is written to stderr.

Note: Unlike other dc(1) implementations, this dc(1) will issue a fatal error (see the EXIT STATUS section) if it cannot write to stderr, so if stderr is closed, as in bc <file> 2>&-, it will quit with an error. This is done so that dc(1) can report problems when stderr is redirected to a file.

If there are scripts that depend on the behavior of other dc(1) implementations, it is recommended that those scripts be changed to redirect stderr to /dev/null.

SYNTAX
ibase is a register (see the REGISTERS section) 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. The max allowable value for ibase can be queried in dc(1) programs with the T command.

obase is a register (see the REGISTERS section) 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 DC_BASE_MAX. The min allowable value for obase is 2 unless dc(1) was built with the extra math option. If it was, then the min allowable value is 0. In this case, if obase is 0, values are output in scientific notation, and if obase is 1, values are output in engineering notation. (Outputting in scientific or engineering notation are non-portable extensions.) The max allowable value for obase can be queried in dc(1) programs with the U command.

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 (see the REGISTERS section) that sets the precision of any operations (with exceptions). scale is initially 0. scale cannot be negative. The max allowable value for scale can be queried in dc(1) programs with the V command.

Each item in the input source code, either a number (see the NUMBERS section) or a command (see the COMMANDS section), 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 DC_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.

Accepting input as 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 using 0o (in any other context, an obase of 0 is invalid), and engineering notation is activated by assigning 1 to obase using 1o (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 stack, 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 (see the REGISTERS section).

sr  Pops the value off the top of the stack and stores it into register r.

lr  Copies the value in register r and pushes it onto the stack. This does not alter the contents of r.

Sr  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.

Lr  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 lr command.

  Parameters
These commands control the values of ibase, obase, and scale (see the SYNTAX section).

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 DC_BASE_MAX, inclusive (see bc(1)). The value can be either 0 or 1 if dc(1) was built with the extra math option.

    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.

T   Pushes the maximum allowable value of ibase onto the main stack.

    This is a non-portable extension.

U   Pushes the maximum allowable value of obase onto the main stack.

    This is a non-portable extension.

V   Pushes the maximum allowable value of scale onto the main stack.

    This is a non-portable extension.

  Strings
The following commands control strings.

dc(1) can work with both numbers and strings, and registers (see the REGISTERS section) 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.

>res
    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.

!>res
    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.

<res
    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.

!<res
    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.

=res
    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.

!=res
    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 the REGISTERS section), 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.

RESET
When dc(1) encounters an error or a signal that it has a non-default handler for, it resets. This means that several things happen.

First, any macros that are executing are stopped and popped off the stack. The behavior is not unlike that of exceptions in programming languages. Then the execution point is set so that any code waiting to execute (after all functions returned) is skipped.

Thus, when dc(1) resets, it skips any remaining code waiting to be executed. Then, if it is interactive mode, and the error was not a fatal error (see the EXIT STATUS section), it asks for more input; otherwise, it exits with the appropriate return code.

PERFORMANCE
Most dc(1) implementations use char types to calculate the value of 1 decimal digit at a time, but that can be slow. This dc(1) does something different.

It uses large integers to calculate more than 1 decimal digit at a time. If built in a environment where DC_LONG_BIT (see the LIMITS section) is 64, then each integer has 9 decimal digits. If built in an environment where DC_LONG_BIT is 32 then each integer has 4 decimal digits. This value (the number of decimal digits per large integer) is called DC_BASE_DIGS.

In addition, this dc(1) uses an even larger integer for overflow checking. This integer type depends on the value of DC_LONG_BIT, but is always at least twice as large as the integer type used to store digits.

LIMITS
The following are the limits on dc(1):

DC_LONG_BIT
    The number of bits in the long type in the environment where dc(1) was built. This determines how many decimal digits can be stored in a single large integer (see the PERFORMANCE section).

DC_BASE_DIGS
    The number of decimal digits per large integer (see the PERFORMANCE section). Depends on DC_LONG_BIT.

DC_BASE_POW
    The max decimal number that each large integer can store (see DC_BASE_DIGS) plus 1. Depends on DC_BASE_DIGS.

DC_OVERFLOW_MAX
    The max number that the overflow type (see the PERFORMANCE section) can hold. Depends on DC_LONG_BIT.

DC_BASE_DIGS
    The number of decimal digits per large integer (see the PERFORMANCE section).

DC_BASE_MAX
    The maximum output base. Set at DC_BASE_POW.

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

DC_SCALE_MAX
    The maximum scale. Set at DC_OVERFLOW_MAX-1.

DC_STRING_MAX
    The maximum length of strings. Set at DC_OVERFLOW_MAX-1.

DC_NAME_MAX
    The maximum length of identifiers. Set at DC_OVERFLOW_MAX-1.

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

Exponent
    The maximum allowable exponent (positive or negative). Set at DC_OVERFLOW_MAX.

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

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_ENV_ARGS
    This is another way to give command-line arguments to dc(1). They should be in the same format as all other command-line arguments. These are always processed first, so any files given in DC_ENV_ARGS will be processed before files given on the command-line. This gives the user the ability to set up "standard" options and files to be used at every invocation. The most useful thing for such files to contain would be useful functions that the user might want every time dc(1) runs. Another use would be to use the -e option to set scale to a value other than 0.

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.

DC_EXPR_EXIT
    If this variable exists (no matter the contents), dc(1) will exit immediately after executing expressions and files given by the -e and/or -f command-line options (and any equivalents).

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 (see the RESET section) 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 (see the RESET section), asking for more input.

Otherwise, SIGTERM and SIGQUIT cause dc(1) to clean up and exit, and it uses the default handler for all other signals.

If dc(1) has not been compiled with signal handling, it uses the default signal handlers for all signals.

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.

Note: when dc(1) is built with history support, tabs are converted to 8 spaces.

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”) https://pubs.opengroup.org/onlinepubs/9699919799/utilities/bc.html 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.