bc - arbitrary-precision decimal arithmetic language and calculator

\f[B]bc\f[R] [\f[B]-cCghilPqRsvVw\f[R]] [\f[B]--digit-clamp\f[R]] [\f[B]--no-digit-clamp\f[R]] [\f[B]--global-stacks\f[R]] [\f[B]--help\f[R]] [\f[B]--interactive\f[R]] [\f[B]--mathlib\f[R]] [\f[B]--no-prompt\f[R]] [\f[B]--no-read-prompt\f[R]] [\f[B]--quiet\f[R]] [\f[B]--standard\f[R]] [\f[B]--warn\f[R]] [\f[B]--version\f[R]] [\f[B]-e\f[R] \f[I]expr\f[R]] [\f[B]--expression\f[R]=\f[I]expr\f[R]...] [\f[B]-f\f[R] \f[I]file\f[R]...] [\f[B]--file\f[R]=\f[I]file\f[R]...] [\f[I]file\f[R]...]

bc(1) is an interactive processor for a language first standardized in 1991 by POSIX. (See the \f[B]STANDARDS\f[R] section.) The language provides unlimited precision decimal arithmetic and is somewhat C-like, but there are differences. Such differences will be noted in this document.

After parsing and handling options, this bc(1) reads any files given on the command line and executes them before reading from \f[B]stdin\f[R].

This bc(1) is a drop-in replacement for \f[I]any\f[R] bc(1), including (and especially) the GNU bc(1). It also has many extensions and extra features beyond other implementations.

\f[B]Note\f[R]: If running this bc(1) on \f[I]any\f[R] script meant for another bc(1) gives a parse error, it is probably because a word this bc(1) reserves as a keyword is used as the name of a function, variable, or array. To fix that, use the command-line option \f[B]-r\f[R] \f[I]keyword\f[R], where \f[I]keyword\f[R] is the keyword that is used as a name in the script. For more information, see the \f[B]OPTIONS\f[R] section.

If parsing scripts meant for other bc(1) implementations still does not work, that is a bug and should be reported. See the \f[B]BUGS\f[R] section.

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

\f[B]-C\f[R], \f[B]--no-digit-clamp\f[R] Disables clamping of digits greater than or equal to the current \f[B]ibase\f[R] when parsing numbers.

\f[B]-c\f[R], \f[B]--digit-clamp\f[R] Enables clamping of digits greater than or equal to the current \f[B]ibase\f[R] when parsing numbers.

\f[B]-e\f[R] \f[I]expr\f[R], \f[B]--expression\f[R]=\f[I]expr\f[R] Evaluates \f[I]expr\f[R]. If multiple expressions are given, they are evaluated in order. If files are given as well (see the \f[B]-f\f[R] and \f[B]--file\f[R] options), 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[B]-f\f[R] \f[I]file\f[R], \f[B]--file\f[R]=\f[I]file\f[R] Reads in \f[I]file\f[R] and evaluates it, line by line, as though it were read through \f[B]stdin\f[R]. If expressions are also given (see the \f[B]-e\f[R] and \f[B]--expression\f[R] options), the expressions are evaluated in the order given.

\f[B]-g\f[R], \f[B]--global-stacks\f[R] Turns the globals \f[B]ibase\f[R], \f[B]obase\f[R], and \f[B]scale\f[R] into stacks.

\f[C]
define void output(x, b) {
 obase=b
 x
}
\f[R]

\f[C]
define void output(x, b) {
 auto c
 c=obase
 obase=b
 x
 obase=c
}
\f[R]

\f[C]
alias d2o=\[dq]bc -e ibase=A -e obase=8\[dq]
alias h2b=\[dq]bc -e ibase=G -e obase=2\[dq]
\f[R]

\f[B]-h\f[R], \f[B]--help\f[R] Prints a usage message and exits.

\f[B]-I\f[R] \f[I]ibase\f[R], \f[B]--ibase\f[R]=\f[I]ibase\f[R] Sets the builtin variable \f[B]ibase\f[R] to the value \f[I]ibase\f[R] assuming that \f[I]ibase\f[R] is in base 10. It is a fatal error if \f[I]ibase\f[R] is not a valid number.

\f[B]-i\f[R], \f[B]--interactive\f[R] Forces interactive mode. (See the \f[B]INTERACTIVE MODE\f[R] section.)

\f[B]-L\f[R], \f[B]--no-line-length\f[R] Disables line length checking and prints numbers without backslashes and newlines. In other words, this option sets \f[B]BC_LINE_LENGTH\f[R] to \f[B]0\f[R] (see the \f[B]ENVIRONMENT VARIABLES\f[R] section).

\f[B]-l\f[R], \f[B]--mathlib\f[R] Sets \f[B]scale\f[R] (see the \f[B]SYNTAX\f[R] section) to \f[B]20\f[R] and loads the included math library before running any code, including any expressions or files specified on the command line.

\f[B]-O\f[R] \f[I]obase\f[R], \f[B]--obase\f[R]=\f[I]obase\f[R] Sets the builtin variable \f[B]obase\f[R] to the value \f[I]obase\f[R] assuming that \f[I]obase\f[R] is in base 10. It is a fatal error if \f[I]obase\f[R] is not a valid number.

\f[B]-P\f[R], \f[B]--no-prompt\f[R] Disables the prompt in TTY mode. (The prompt is only enabled in TTY mode. See the \f[B]TTY MODE\f[R] section.) This is mostly for those users that do not want a prompt or are not used to having them in bc(1). Most of those users would want to put this option in \f[B]BC_ENV_ARGS\f[R] (see the \f[B]ENVIRONMENT VARIABLES\f[R] section).

\f[B]-q\f[R], \f[B]--quiet\f[R] This option is for compatibility with the GNU bc(1) (https://www.gnu.org/software/bc/); it is a no-op. Without this option, GNU bc(1) prints a copyright header. This bc(1) only prints the copyright header if one or more of the \f[B]-v\f[R], \f[B]-V\f[R], or \f[B]--version\f[R] options are given unless the \f[B]BC_BANNER\f[R] environment variable is set and contains a non-zero integer or if this bc(1) was built with the header displayed by default. If \f[I]any\f[R] of that is the case, then this option \f[I]does\f[R] prevent bc(1) from printing the header.

\f[B]-R\f[R], \f[B]--no-read-prompt\f[R] Disables the read prompt in TTY mode. (The read prompt is only enabled in TTY mode. See the \f[B]TTY MODE\f[R] section.) This is mostly for those users that do not want a read prompt or are not used to having them in bc(1). Most of those users would want to put this option in \f[B]BC_ENV_ARGS\f[R] (see the \f[B]ENVIRONMENT VARIABLES\f[R] section). This option is also useful in hash bang lines of bc(1) scripts that prompt for user input.

\f[B]-r\f[R] \f[I]keyword\f[R], \f[B]--redefine\f[R]=\f[I]keyword\f[R] Redefines \f[I]keyword\f[R] in order to allow it to be used as a function, variable, or array name. This is useful when this bc(1) gives parse errors when parsing scripts meant for other bc(1) implementations.

\f[B]-S\f[R] \f[I]scale\f[R], \f[B]--scale\f[R]=\f[I]scale\f[R] Sets the builtin variable \f[B]scale\f[R] to the value \f[I]scale\f[R] assuming that \f[I]scale\f[R] is in base 10. It is a fatal error if \f[I]scale\f[R] is not a valid number.

\f[B]-s\f[R], \f[B]--standard\f[R] Process exactly the language defined by the standard (see the \f[B]STANDARDS\f[R] section) and error if any extensions are used.

\f[B]-v\f[R], \f[B]-V\f[R], \f[B]--version\f[R] Print the version information (copyright header) and exits.

\f[B]-w\f[R], \f[B]--warn\f[R] Like \f[B]-s\f[R] and \f[B]--standard\f[R], except that warnings (and not errors) are printed for non-standard extensions and execution continues normally.

\f[B]-z\f[R], \f[B]--leading-zeroes\f[R] Makes bc(1) print all numbers greater than \f[B]-1\f[R] and less than \f[B]1\f[R], and not equal to \f[B]0\f[R], with a leading zero.

All long options are \f[B]non-portable extensions\f[R].

If no files or expressions are given by the \f[B]-f\f[R], \f[B]--file\f[R], \f[B]-e\f[R], or \f[B]--expression\f[R] options, then bc(1) reads from \f[B]stdin\f[R].

However, there are a few caveats to this.

First, \f[B]stdin\f[R] is evaluated a line at a time. The only exception to this is if the parse cannot complete. That means that starting a string without ending it or starting a function, \f[B]if\f[R] statement, or loop without ending it will also cause bc(1) to not execute.

Second, after an \f[B]if\f[R] statement, bc(1) doesn\[cq]t know if an \f[B]else\f[R] statement will follow, so it will not execute until it knows there will not be an \f[B]else\f[R] statement.

Any non-error output is written to \f[B]stdout\f[R]. In addition, if history (see the \f[B]HISTORY\f[R] section) and the prompt (see the \f[B]TTY MODE\f[R] section) are enabled, both are output to \f[B]stdout\f[R].

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

If there are scripts that depend on the behavior of other bc(1) implementations, it is recommended that those scripts be changed to redirect \f[B]stdout\f[R] to \f[B]/dev/null\f[R].

Any error output is written to \f[B]stderr\f[R].

\f[B]Note\f[R]: Unlike other bc(1) implementations, this bc(1) will issue a fatal error (see the \f[B]EXIT STATUS\f[R] section) if it cannot write to \f[B]stderr\f[R], so if \f[B]stderr\f[R] is closed, as in \f[B]bc 2>&-\f[R], it will quit with an error. This is done so that bc(1) can exit with an error code when \f[B]stderr\f[R] is redirected to a file.

If there are scripts that depend on the behavior of other bc(1) implementations, it is recommended that those scripts be changed to redirect \f[B]stderr\f[R] to \f[B]/dev/null\f[R].

The syntax for bc(1) programs is mostly C-like, with some differences. This bc(1) follows the POSIX standard (see the \f[B]STANDARDS\f[R] section), which is a much more thorough resource for the language this bc(1) accepts. This section is meant to be a summary and a listing of all the extensions to the standard.

In the sections below, \f[B]E\f[R] means expression, \f[B]S\f[R] means statement, and \f[B]I\f[R] means identifier.

Identifiers (\f[B]I\f[R]) start with a lowercase letter and can be followed by any number (up to \f[B]BC_NAME_MAX-1\f[R]) of lowercase letters (\f[B]a-z\f[R]), digits (\f[B]0-9\f[R]), and underscores (\f[B]_\f[R]). The regex is \f[B][a-z][a-z0-9_]*\f[R]. Identifiers with more than one character (letter) are a \f[B]non-portable extension\f[R].

\f[B]ibase\f[R] is a global variable determining how to interpret constant numbers. It is the \[lq]input\[rq] base, or the number base used for interpreting input numbers. \f[B]ibase\f[R] is initially \f[B]10\f[R]. If the \f[B]-s\f[R] (\f[B]--standard\f[R]) and \f[B]-w\f[R] (\f[B]--warn\f[R]) flags were not given on the command line, the max allowable value for \f[B]ibase\f[R] is \f[B]36\f[R]. Otherwise, it is \f[B]16\f[R]. The min allowable value for \f[B]ibase\f[R] is \f[B]2\f[R]. The max allowable value for \f[B]ibase\f[R] can be queried in bc(1) programs with the \f[B]maxibase()\f[R] built-in function.

\f[B]obase\f[R] is a global variable determining how to output results. It is the \[lq]output\[rq] base, or the number base used for outputting numbers. \f[B]obase\f[R] is initially \f[B]10\f[R]. The max allowable value for \f[B]obase\f[R] is \f[B]BC_BASE_MAX\f[R] and can be queried in bc(1) programs with the \f[B]maxobase()\f[R] built-in function. The min allowable value for \f[B]obase\f[R] is \f[B]2\f[R]. Values are output in the specified base.

The \f[I]scale\f[R] of an expression is the number of digits in the result of the expression right of the decimal point, and \f[B]scale\f[R] is a global variable that sets the precision of any operations, with exceptions. \f[B]scale\f[R] is initially \f[B]0\f[R]. \f[B]scale\f[R] cannot be negative. The max allowable value for \f[B]scale\f[R] is \f[B]BC_SCALE_MAX\f[R] and can be queried in bc(1) programs with the \f[B]maxscale()\f[R] built-in function.

bc(1) has both \f[I]global\f[R] variables and \f[I]local\f[R] variables. All \f[I]local\f[R] variables are local to the function; they are parameters or are introduced in the \f[B]auto\f[R] list of a function (see the \f[B]FUNCTIONS\f[R] section). If a variable is accessed which is not a parameter or in the \f[B]auto\f[R] list, it is assumed to be \f[I]global\f[R]. If a parent function has a \f[I]local\f[R] variable version of a variable that a child function considers \f[I]global\f[R], the value of that \f[I]global\f[R] variable in the child function is the value of the variable in the parent function, not the value of the actual \f[I]global\f[R] variable.

All of the above applies to arrays as well.

The value of a statement that is an expression (i.e., any of the named expressions or operands) is printed unless the lowest precedence operator is an assignment operator \f[I]and\f[R] the expression is notsurrounded by parentheses.

The value that is printed is also assigned to the special variable \f[B]last\f[R]. A single dot (\f[B].\f[R]) may also be used as a synonym for \f[B]last\f[R]. These are \f[B]non-portable extensions\f[R].

Either semicolons or newlines may separate statements.

There are two kinds of comments:

The following are named expressions in bc(1):

Number 6 is a \f[B]non-portable extension\f[R].

Variables and arrays do not interfere; users can have arrays named the same as variables. This also applies to functions (see the \f[B]FUNCTIONS\f[R] section), so a user can have a variable, array, and function that all have the same name, and they will not shadow each other, whether inside of functions or not.

Named expressions are required as the operand of \f[B]increment\f[R]/\f[B]decrement\f[R] operators and as the left side of \f[B]assignment\f[R] operators (see the \f[I]Operators\f[R] subsection).

The following are valid operands in bc(1):

Numbers are strings made up of digits, uppercase letters, and at most \f[B]1\f[R] period for a radix. Numbers can have up to \f[B]BC_NUM_MAX\f[R] digits. Uppercase letters are equal to \f[B]9\f[R] plus their position in the alphabet, starting from \f[B]1\f[R] (i.e., \f[B]A\f[R] equals \f[B]10\f[R], or \f[B]9+1\f[R]).

If a digit or letter makes no sense with the current value of \f[B]ibase\f[R] (i.e., they are greater than or equal to the current value of \f[B]ibase\f[R]), then the behavior depends on the existence of the \f[B]-c\f[R]/\f[B]--digit-clamp\f[R] or \f[B]-C\f[R]/\f[B]--no-digit-clamp\f[R] options (see the \f[B]OPTIONS\f[R] section), the existence and setting of the \f[B]BC_DIGIT_CLAMP\f[R] environment variable (see the \f[B]ENVIRONMENT VARIABLES\f[R] section), or the default, which can be queried with the \f[B]-h\f[R]/\f[B]--help\f[R] option.

If clamping is off, then digits or letters that are greater than or equal to the current value of \f[B]ibase\f[R] are not changed. Instead, their given value is multiplied by the appropriate power of \f[B]ibase\f[R] and added into the number. This means that, with an \f[B]ibase\f[R] of \f[B]3\f[R], the number \f[B]AB\f[R] is equal to \f[B]3\[ha]1*A+3\[ha]0*B\f[R], which is \f[B]3\f[R] times \f[B]10\f[R] plus \f[B]11\f[R], or \f[B]41\f[R].

If clamping is on, then digits or letters that are greater than or equal to the current value of \f[B]ibase\f[R] are set to the value of the highest valid digit in \f[B]ibase\f[R] before being multiplied by the appropriate power of \f[B]ibase\f[R] and added into the number. This means that, with an \f[B]ibase\f[R] of \f[B]3\f[R], the number \f[B]AB\f[R] is equal to \f[B]3\[ha]1*2+3\[ha]0*2\f[R], which is \f[B]3\f[R] times \f[B]2\f[R] plus \f[B]2\f[R], or \f[B]8\f[R].

There is one exception to clamping: single-character numbers (i.e., \f[B]A\f[R] alone). Such numbers are never clamped and always take the value they would have in the highest possible \f[B]ibase\f[R]. This means that \f[B]A\f[R] alone always equals decimal \f[B]10\f[R] and \f[B]Z\f[R] alone always equals decimal \f[B]35\f[R]. This behavior is mandated by the standard (see the STANDARDS section) and is meant to provide an easy way to set the current \f[B]ibase\f[R] (with the \f[B]i\f[R] command) regardless of the current value of \f[B]ibase\f[R].

If clamping is on, and the clamped value of a character is needed, use a leading zero, i.e., for \f[B]A\f[R], use \f[B]0A\f[R].

The following arithmetic and logical operators can be used. They are listed in order of decreasing precedence. Operators in the same group have the same precedence.

\f[B]++\f[R] \f[B]--\f[R] Type: Prefix and Postfix

\f[B]-\f[R] \f[B]!\f[R] Type: Prefix

\f[B]\[ha]\f[R] Type: Binary

\f[B]*\f[R] \f[B]/\f[R] \f[B]%\f[R] Type: Binary

\f[B]+\f[R] \f[B]-\f[R] Type: Binary

\f[B]=\f[R] \f[B]+=\f[R] \f[B]-=\f[R] \f[B]*=\f[R] \f[B]/=\f[R] \f[B]%=\f[R] \f[B]\[ha]=\f[R] Type: Binary

\f[B]==\f[R] \f[B]<=\f[R] \f[B]>=\f[R] \f[B]!=\f[R] \f[B]<\f[R] \f[B]>\f[R] Type: Binary

\f[B]&&\f[R] Type: Binary

\f[B]||\f[R] Type: Binary

The operators will be described in more detail below.

\f[B]++\f[R] \f[B]--\f[R] The prefix and postfix \f[B]increment\f[R] and \f[B]decrement\f[R] operators behave exactly like they would in C. They require a named expression (see the \f[I]Named Expressions\f[R] subsection) as an operand.

\f[B]-\f[R] The \f[B]negation\f[R] operator returns \f[B]0\f[R] if a user attempts to negate any expression with the value \f[B]0\f[R]. Otherwise, a copy of the expression with its sign flipped is returned.

\f[B]!\f[R] The \f[B]boolean not\f[R] operator returns \f[B]1\f[R] if the expression is \f[B]0\f[R], or \f[B]0\f[R] otherwise.

\f[B]\[ha]\f[R] The \f[B]power\f[R] operator (not the \f[B]exclusive or\f[R] operator, as it would be in C) takes two expressions and raises the first to the power of the value of the second. The \f[I]scale\f[R] of the result is equal to \f[B]scale\f[R].

\f[B]*\f[R] The \f[B]multiply\f[R] operator takes two expressions, multiplies them, and returns the product. If \f[B]a\f[R] is the \f[I]scale\f[R] of the first expression and \f[B]b\f[R] is the \f[I]scale\f[R] of the second expression, the \f[I]scale\f[R] of the result is equal to \f[B]min(a+b,max(scale,a,b))\f[R] where \f[B]min()\f[R] and \f[B]max()\f[R] return the obvious values.

\f[B]/\f[R] The \f[B]divide\f[R] operator takes two expressions, divides them, and returns the quotient. The \f[I]scale\f[R] of the result shall be the value of \f[B]scale\f[R].

\f[B]%\f[R] The \f[B]modulus\f[R] operator takes two expressions, \f[B]a\f[R] and \f[B]b\f[R], and evaluates them by 1) Computing \f[B]a/b\f[R] to current \f[B]scale\f[R] and 2) Using the result of step 1 to calculate \f[B]a-(a/b)*b\f[R] to \f[I]scale\f[R] \f[B]max(scale+scale(b),scale(a))\f[R].

\f[B]+\f[R] The \f[B]add\f[R] operator takes two expressions, \f[B]a\f[R] and \f[B]b\f[R], and returns the sum, with a \f[I]scale\f[R] equal to the max of the \f[I]scale\f[R]s of \f[B]a\f[R] and \f[B]b\f[R].

\f[B]-\f[R] The \f[B]subtract\f[R] operator takes two expressions, \f[B]a\f[R] and \f[B]b\f[R], and returns the difference, with a \f[I]scale\f[R] equal to the max of the \f[I]scale\f[R]s of \f[B]a\f[R] and \f[B]b\f[R].

\f[B]=\f[R] \f[B]+=\f[R] \f[B]-=\f[R] \f[B]*=\f[R] \f[B]/=\f[R] \f[B]%=\f[R] \f[B]\[ha]=\f[R] The \f[B]assignment\f[R] operators take two expressions, \f[B]a\f[R] and \f[B]b\f[R] where \f[B]a\f[R] is a named expression (see the \f[I]Named Expressions\f[R] subsection).

\f[B]==\f[R] \f[B]<=\f[R] \f[B]>=\f[R] \f[B]!=\f[R] \f[B]<\f[R] \f[B]>\f[R] The \f[B]relational\f[R] operators compare two expressions, \f[B]a\f[R] and \f[B]b\f[R], and if the relation holds, according to C language semantics, the result is \f[B]1\f[R]. Otherwise, it is \f[B]0\f[R].

\f[B]&&\f[R] The \f[B]boolean and\f[R] operator takes two expressions and returns \f[B]1\f[R] if both expressions are non-zero, \f[B]0\f[R] otherwise.

\f[B]||\f[R] The \f[B]boolean or\f[R] operator takes two expressions and returns \f[B]1\f[R] if one of the expressions is non-zero, \f[B]0\f[R] otherwise.

The following items are statements:

Numbers 4, 9, 11, 12, 14, 15, and 16 are \f[B]non-portable extensions\f[R].

Also, as a \f[B]non-portable extension\f[R], any or all of the expressions in the header of a for loop may be omitted. If the condition (second expression) is omitted, it is assumed to be a constant \f[B]1\f[R].

The \f[B]break\f[R] statement causes a loop to stop iterating and resume execution immediately following a loop. This is only allowed in loops.

The \f[B]continue\f[R] statement causes a loop iteration to stop early and returns to the start of the loop, including testing the loop condition. This is only allowed in loops.

The \f[B]if\f[R] \f[B]else\f[R] statement does the same thing as in C.

The \f[B]quit\f[R] statement causes bc(1) to quit, even if it is on a branch that will not be executed (it is a compile-time command).

\f[B]Warning\f[R]: The behavior of this bc(1) on \f[B]quit\f[R] is slightly different from other bc(1) implementations. Other bc(1) implementations will exit as soon as they finish parsing the line that a \f[B]quit\f[R] command is on. This bc(1) will execute any completed and executable statements that occur before the \f[B]quit\f[R] statement before exiting.

In other words, for the bc(1) code below:

\f[C]
for (i = 0; i < 3; ++i) i; quit
\f[R]

Other bc(1) implementations will print nothing, and this bc(1) will print \f[B]0\f[R], \f[B]1\f[R], and \f[B]2\f[R] on successive lines before exiting.

The \f[B]halt\f[R] statement causes bc(1) to quit, if it is executed. (Unlike \f[B]quit\f[R] if it is on a branch of an \f[B]if\f[R] statement that is not executed, bc(1) does not quit.)

The \f[B]limits\f[R] statement prints the limits that this bc(1) is subject to. This is like the \f[B]quit\f[R] statement in that it is a compile-time command.

An expression by itself is evaluated and printed, followed by a newline.

If strings appear as a statement by themselves, they are printed without a trailing newline.

In addition to appearing as a lone statement by themselves, strings can be assigned to variables and array elements. They can also be passed to functions in variable parameters.

If any statement that expects a string is given a variable that had a string assigned to it, the statement acts as though it had received a string.

If any math operation is attempted on a string or a variable or array element that has been assigned a string, an error is raised, and bc(1) resets (see the \f[B]RESET\f[R] section).

Assigning strings to variables and array elements and passing them to functions are \f[B]non-portable extensions\f[R].

The \[lq]expressions\[rq] in a \f[B]print\f[R] statement may also be strings. If they are, there are backslash escape sequences that are interpreted specially. What those sequences are, and what they cause to be printed, are shown below:

\f[B]\[rs]a\f[R]: \f[B]\[rs]a\f[R]

\f[B]\[rs]b\f[R]: \f[B]\[rs]b\f[R]

\f[B]\[rs]\[rs]\f[R]: \f[B]\[rs]\f[R]

\f[B]\[rs]e\f[R]: \f[B]\[rs]\f[R]

\f[B]\[rs]f\f[R]: \f[B]\[rs]f\f[R]

\f[B]\[rs]n\f[R]: \f[B]\[rs]n\f[R]

\f[B]\[rs]q\f[R]: \f[B]\[lq]\f[R]

\f[B]\[rs]r\f[R]: \f[B]\[rs]r\f[R]

\f[B]\[rs]t\f[R]: \f[B]\[rs]t\f[R]

Any other character following a backslash causes the backslash and character to be printed as-is.

Any non-string expression in a print statement shall be assigned to \f[B]last\f[R], like any other expression that is printed.

The \[lq]expressions in a \f[B]stream\f[R] statement may also be strings.

If a \f[B]stream\f[R] statement is given a string, it prints the string as though the string had appeared as its own statement. In other words, the \f[B]stream\f[R] statement prints strings normally, without a newline.

If a \f[B]stream\f[R] statement is given a number, a copy of it is truncated and its absolute value is calculated. The result is then printed as though \f[B]obase\f[R] is \f[B]256\f[R] and each digit is interpreted as an 8-bit ASCII character, making it a byte stream.

All expressions in a statment are evaluated left to right, except as necessary to maintain order of operations. This means, for example, assuming that \f[B]i\f[R] is equal to \f[B]0\f[R], in the expression

\f[C]
a[i++] = i++
\f[R]

the first (or 0th) element of \f[B]a\f[R] is set to \f[B]1\f[R], and \f[B]i\f[R] is equal to \f[B]2\f[R] at the end of the expression.

This includes function arguments. Thus, assuming \f[B]i\f[R] is equal to \f[B]0\f[R], this means that in the expression

\f[C]
x(i++, i++)
\f[R]

the first argument passed to \f[B]x()\f[R] is \f[B]0\f[R], and the second argument is \f[B]1\f[R], while \f[B]i\f[R] is equal to \f[B]2\f[R] before the function starts executing.

Function definitions are as follows:

\f[C]
define I(I,...,I){
 auto I,...,I
 S;...;S
 return(E)
}
\f[R]

Any \f[B]I\f[R] in the parameter list or \f[B]auto\f[R] list may be replaced with \f[B]I[]\f[R] to make a parameter or \f[B]auto\f[R] var an array, and any \f[B]I\f[R] in the parameter list may be replaced with \f[B]*I[]\f[R] to make a parameter an array reference. Callers of functions that take array references should not put an asterisk in the call; they must be called with just \f[B]I[]\f[R] like normal array parameters and will be automatically converted into references.

As a \f[B]non-portable extension\f[R], the opening brace of a \f[B]define\f[R] statement may appear on the next line.

As a \f[B]non-portable extension\f[R], the return statement may also be in one of the following forms:

The first two, or not specifying a \f[B]return\f[R] statement, is equivalent to \f[B]return (0)\f[R], unless the function is a \f[B]void\f[R] function (see the \f[I]Void Functions\f[R] subsection below).

Functions can also be \f[B]void\f[R] functions, defined as follows:

\f[C]
define void I(I,...,I){
 auto I,...,I
 S;...;S
 return
}
\f[R]

They can only be used as standalone expressions, where such an expression would be printed alone, except in a print statement.

Void functions can only use the first two \f[B]return\f[R] statements listed above. They can also omit the return statement entirely.

The word \[lq]void\[rq] is not treated as a keyword; it is still possible to have variables, arrays, and functions named \f[B]void\f[R]. The word \[lq]void\[rq] is only treated specially right after the \f[B]define\f[R] keyword.

This is a \f[B]non-portable extension\f[R].

For any array in the parameter list, if the array is declared in the form

\f[C]
*I[]
\f[R]

it is a \f[B]reference\f[R]. Any changes to the array in the function are reflected, when the function returns, to the array that was passed in.

Other than this, all function arguments are passed by value.

This is a \f[B]non-portable extension\f[R].

All of the functions below are available when the \f[B]-l\f[R] or \f[B]--mathlib\f[R] command-line flags are given.

The standard (see the \f[B]STANDARDS\f[R] section) defines the following functions for the math library:

\f[B]s(x)\f[R] Returns the sine of \f[B]x\f[R], which is assumed to be in radians.

\f[B]c(x)\f[R] Returns the cosine of \f[B]x\f[R], which is assumed to be in radians.

\f[B]a(x)\f[R] Returns the arctangent of \f[B]x\f[R], in radians.

\f[B]l(x)\f[R] Returns the natural logarithm of \f[B]x\f[R].

\f[B]e(x)\f[R] Returns the mathematical constant \f[B]e\f[R] raised to the power of \f[B]x\f[R].

\f[B]j(x, n)\f[R] Returns the bessel integer order \f[B]n\f[R] (truncated) of \f[B]x\f[R].

All transcendental functions can return slightly inaccurate results, up to 1 ULP (https://en.wikipedia.org/wiki/Unit_in_the_last_place). This is unavoidable, and the article at https://people.eecs.berkeley.edu/\[ti]wkahan/LOG10HAF.TXT explains why it is impossible and unnecessary to calculate exact results for the transcendental functions.

Because of the possible inaccuracy, I recommend that users call those functions with the precision (\f[B]scale\f[R]) set to at least 1 higher than is necessary. If exact results are \f[I]absolutely\f[R] required, users can double the precision (\f[B]scale\f[R]) and then truncate.

The transcendental functions in the standard math library are:

When bc(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 functions 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 bc(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 \f[B]EXIT STATUS\f[R] section), it asks for more input; otherwise, it exits with the appropriate return code.

Note that this reset behavior is different from the GNU bc(1), which attempts to start executing the statement right after the one that caused an error.

Most bc(1) implementations use \f[B]char\f[R] types to calculate the value of \f[B]1\f[R] decimal digit at a time, but that can be slow. This bc(1) does something different.

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

The actual values of \f[B]BC_LONG_BIT\f[R] and \f[B]BC_BASE_DIGS\f[R] can be queried with the \f[B]limits\f[R] statement.

In addition, this bc(1) uses an even larger integer for overflow checking. This integer type depends on the value of \f[B]BC_LONG_BIT\f[R], but is always at least twice as large as the integer type used to store digits.

The following are the limits on bc(1):

\f[B]BC_LONG_BIT\f[R] The number of bits in the \f[B]long\f[R] type in the environment where bc(1) was built. This determines how many decimal digits can be stored in a single large integer (see the \f[B]PERFORMANCE\f[R] section).

\f[B]BC_BASE_DIGS\f[R] The number of decimal digits per large integer (see the \f[B]PERFORMANCE\f[R] section). Depends on \f[B]BC_LONG_BIT\f[R].

\f[B]BC_BASE_POW\f[R] The max decimal number that each large integer can store (see \f[B]BC_BASE_DIGS\f[R]) plus \f[B]1\f[R]. Depends on \f[B]BC_BASE_DIGS\f[R].

\f[B]BC_OVERFLOW_MAX\f[R] The max number that the overflow type (see the \f[B]PERFORMANCE\f[R] section) can hold. Depends on \f[B]BC_LONG_BIT\f[R].

\f[B]BC_BASE_MAX\f[R] The maximum output base. Set at \f[B]BC_BASE_POW\f[R].

\f[B]BC_DIM_MAX\f[R] The maximum size of arrays. Set at \f[B]SIZE_MAX-1\f[R].

\f[B]BC_SCALE_MAX\f[R] The maximum \f[B]scale\f[R]. Set at \f[B]BC_OVERFLOW_MAX-1\f[R].

\f[B]BC_STRING_MAX\f[R] The maximum length of strings. Set at \f[B]BC_OVERFLOW_MAX-1\f[R].

\f[B]BC_NAME_MAX\f[R] The maximum length of identifiers. Set at \f[B]BC_OVERFLOW_MAX-1\f[R].

\f[B]BC_NUM_MAX\f[R] The maximum length of a number (in decimal digits), which includes digits after the decimal point. Set at \f[B]BC_OVERFLOW_MAX-1\f[R].

Exponent The maximum allowable exponent (positive or negative). Set at \f[B]BC_OVERFLOW_MAX\f[R].

Number of vars The maximum number of vars/arrays. Set at \f[B]SIZE_MAX-1\f[R].

The actual values can be queried with the \f[B]limits\f[R] 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.

As \f[B]non-portable extensions\f[R], bc(1) recognizes the following environment variables:

\f[B]POSIXLY_CORRECT\f[R] If this variable exists (no matter the contents), bc(1) behaves as if the \f[B]-s\f[R] option was given.

\f[B]BC_ENV_ARGS\f[R] This is another way to give command-line arguments to bc(1). They should be in the same format as all other command-line arguments. These are always processed first, so any files given in \f[B]BC_ENV_ARGS\f[R] will be processed before arguments and files given on the command-line. This gives the user the ability to set up \[lq]standard\[rq] 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 bc(1) runs.

\f[B]BC_LINE_LENGTH\f[R] If this environment variable exists and contains an integer that is greater than \f[B]1\f[R] and is less than \f[B]UINT16_MAX\f[R] (\f[B]2\[ha]16-1\f[R]), bc(1) will output lines to that length, including the backslash (\f[B]\[rs]\f[R]). The default line length is \f[B]70\f[R].

\f[B]BC_BANNER\f[R] If this environment variable exists and contains an integer, then a non-zero value activates the copyright banner when bc(1) is in interactive mode, while zero deactivates it.

\f[B]BC_SIGINT_RESET\f[R] If bc(1) is not in interactive mode (see the \f[B]INTERACTIVE MODE\f[R] section), then this environment variable has no effect because bc(1) exits on \f[B]SIGINT\f[R] when not in interactive mode.

\f[B]BC_TTY_MODE\f[R] If TTY mode is \f[I]not\f[R] available (see the \f[B]TTY MODE\f[R] section), then this environment variable has no effect.

\f[B]BC_PROMPT\f[R] If TTY mode is \f[I]not\f[R] available (see the \f[B]TTY MODE\f[R] section), then this environment variable has no effect.

\f[B]BC_EXPR_EXIT\f[R] If any expressions or expression files are given on the command-line with \f[B]-e\f[R], \f[B]--expression\f[R], \f[B]-f\f[R], or \f[B]--file\f[R], then if this environment variable exists and contains an integer, a non-zero value makes bc(1) exit after executing the expressions and expression files, and a zero value makes bc(1) not exit.

\f[B]BC_DIGIT_CLAMP\f[R] When parsing numbers and if this environment variable exists and contains an integer, a non-zero value makes bc(1) clamp digits that are greater than or equal to the current \f[B]ibase\f[R] so that all such digits are considered equal to the \f[B]ibase\f[R] minus 1, and a zero value disables such clamping so that those digits are always equal to their value, which is multiplied by the power of the \f[B]ibase\f[R].

bc(1) returns the following exit statuses:

\f[B]0\f[R] No error.

\f[B]1\f[R] A math error occurred. This follows standard practice of using \f[B]1\f[R] for expected errors, since math errors will happen in the process of normal execution.

\f[B]2\f[R] A parse error occurred.

\f[B]3\f[R] A runtime error occurred.

\f[B]4\f[R] A fatal error occurred.

The exit status \f[B]4\f[R] is special; when a fatal error occurs, bc(1) always exits and returns \f[B]4\f[R], no matter what mode bc(1) is in.

The other statuses will only be returned when bc(1) is not in interactive mode (see the \f[B]INTERACTIVE MODE\f[R] section), since bc(1) resets its state (see the \f[B]RESET\f[R] 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 \f[B]-i\f[R] flag or \f[B]--interactive\f[R] option.

These exit statuses allow bc(1) to be used in shell scripting with error checking, and its normal behavior can be forced by using the \f[B]-i\f[R] flag or \f[B]--interactive\f[R] option.

Per the standard (see the \f[B]STANDARDS\f[R] section), bc(1) has an interactive mode and a non-interactive mode. Interactive mode is turned on automatically when both \f[B]stdin\f[R] and \f[B]stdout\f[R] are hooked to a terminal, but the \f[B]-i\f[R] flag and \f[B]--interactive\f[R] option can turn it on in other situations.

In interactive mode, bc(1) attempts to recover from errors (see the \f[B]RESET\f[R] section), and in normal execution, flushes \f[B]stdout\f[R] as soon as execution is done for the current input. bc(1) may also reset on \f[B]SIGINT\f[R] instead of exit, depending on the contents of, or default for, the \f[B]BC_SIGINT_RESET\f[R] environment variable (see the \f[B]ENVIRONMENT VARIABLES\f[R] section).

If \f[B]stdin\f[R], \f[B]stdout\f[R], and \f[B]stderr\f[R] are all connected to a TTY, then \[lq]TTY mode\[rq] is considered to be available, and thus, bc(1) can turn on TTY mode, subject to some settings.

If there is the environment variable \f[B]BC_TTY_MODE\f[R] in the environment (see the \f[B]ENVIRONMENT VARIABLES\f[R] section), then if that environment variable contains a non-zero integer, bc(1) will turn on TTY mode when \f[B]stdin\f[R], \f[B]stdout\f[R], and \f[B]stderr\f[R] are all connected to a TTY. If the \f[B]BC_TTY_MODE\f[R] environment variable exists but is \f[I]not\f[R] a non-zero integer, then bc(1) will not turn TTY mode on.

If the environment variable \f[B]BC_TTY_MODE\f[R] does \f[I]not\f[R] exist, the default setting is used. The default setting can be queried with the \f[B]-h\f[R] or \f[B]--help\f[R] options.

TTY mode is different from interactive mode because interactive mode is required in the bc(1) standard (see the \f[B]STANDARDS\f[R] section), and interactive mode requires only \f[B]stdin\f[R] and \f[B]stdout\f[R] to be connected to a terminal.

Command-line history is only enabled if TTY mode is, i.e., that \f[B]stdin\f[R], \f[B]stdout\f[R], and \f[B]stderr\f[R] are connected to a TTY and the \f[B]BC_TTY_MODE\f[R] environment variable (see the \f[B]ENVIRONMENT VARIABLES\f[R] section) and its default do not disable TTY mode. See the \f[B]COMMAND LINE HISTORY\f[R] section for more information.

If TTY mode is available, then a prompt can be enabled. Like TTY mode itself, it can be turned on or off with an environment variable: \f[B]BC_PROMPT\f[R] (see the \f[B]ENVIRONMENT VARIABLES\f[R] section).

If the environment variable \f[B]BC_PROMPT\f[R] exists and is a non-zero integer, then the prompt is turned on when \f[B]stdin\f[R], \f[B]stdout\f[R], and \f[B]stderr\f[R] are connected to a TTY and the \f[B]-P\f[R] and \f[B]--no-prompt\f[R] options were not used. The read prompt will be turned on under the same conditions, except that the \f[B]-R\f[R] and \f[B]--no-read-prompt\f[R] options must also not be used.

However, if \f[B]BC_PROMPT\f[R] does not exist, the prompt can be enabled or disabled with the \f[B]BC_TTY_MODE\f[R] environment variable, the \f[B]-P\f[R] and \f[B]--no-prompt\f[R] options, and the \f[B]-R\f[R] and \f[B]--no-read-prompt\f[R] options. See the \f[B]ENVIRONMENT VARIABLES\f[R] and \f[B]OPTIONS\f[R] sections for more details.

Sending a \f[B]SIGINT\f[R] will cause bc(1) to do one of two things.

If bc(1) is not in interactive mode (see the \f[B]INTERACTIVE MODE\f[R] section), or the \f[B]BC_SIGINT_RESET\f[R] environment variable (see the \f[B]ENVIRONMENT VARIABLES\f[R] section), or its default, is either not an integer or it is zero, bc(1) will exit.

However, if bc(1) is in interactive mode, and the \f[B]BC_SIGINT_RESET\f[R] or its default is an integer and non-zero, then bc(1) will stop executing the current input and reset (see the \f[B]RESET\f[R] section) upon receiving a \f[B]SIGINT\f[R].

Note that \[lq]current input\[rq] can mean one of two things. If bc(1) is processing input from \f[B]stdin\f[R] in interactive mode, it will ask for more input. If bc(1) is processing input from a file in interactive mode, it will stop processing the file and start processing the next file, if one exists, or ask for input from \f[B]stdin\f[R] if no other file exists.

This means that if a \f[B]SIGINT\f[R] is sent to bc(1) as it is executing a file, it can seem as though bc(1) did not respond to the signal since it will immediately start executing the next file. This is by design; most files that users execute when interacting with bc(1) have function definitions, which are quick to parse. If a file takes a long time to execute, there may be a bug in that file. The rest of the files could still be executed without problem, allowing the user to continue.

\f[B]SIGTERM\f[R] and \f[B]SIGQUIT\f[R] cause bc(1) to clean up and exit, and it uses the default handler for all other signals. The one exception is \f[B]SIGHUP\f[R]; in that case, and only when bc(1) is in TTY mode (see the \f[B]TTY MODE\f[R] section), a \f[B]SIGHUP\f[R] will cause bc(1) to clean up and exit.

bc(1) supports interactive command-line editing.

If bc(1) can be in TTY mode (see the \f[B]TTY MODE\f[R] section), history can be enabled. This means that command-line history can only be enabled when \f[B]stdin\f[R], \f[B]stdout\f[R], and \f[B]stderr\f[R] are all connected to a TTY.

Like TTY mode itself, it can be turned on or off with the environment variable \f[B]BC_TTY_MODE\f[R] (see the \f[B]ENVIRONMENT VARIABLES\f[R] section).

If history is enabled, previous lines can be recalled and edited with the arrow keys.

\f[B]Note\f[R]: tabs are converted to 8 spaces.

dc(1)

bc(1) is compliant with the IEEE Std 1003.1-2017 (\[lq]POSIX.1-2017\[rq]) specification at https://pubs.opengroup.org/onlinepubs/9699919799/utilities/bc.html . The flags \f[B]-efghiqsvVw\f[R], all long options, and the extensions noted above are extensions to that specification.

In addition, the behavior of the \f[B]quit\f[R] implements an interpretation of that specification that is different from all known implementations. For more information see the \f[B]Statements\f[R] subsection of the \f[B]SYNTAX\f[R] section.

Note that the specification explicitly says that bc(1) only accepts numbers that use a period (\f[B].\f[R]) as a radix point, regardless of the value of \f[B]LC_NUMERIC\f[R].

Before version \f[B]6.1.0\f[R], this bc(1) had incorrect behavior for the \f[B]quit\f[R] statement.

No other bugs are known. Report bugs at https://git.gavinhoward.com/gavin/bc .

Gavin D. Howard <gavin@gavinhoward.com> and contributors.