NAME

bc - arbitrary-precision decimal arithmetic language and calculator

SYNOPSIS

bc [-ghilPqRsvVw] [--global-stacks] [--help] [--interactive] [--mathlib] [--no-prompt] [--no-read-prompt] [--quiet] [--standard] [--warn] [--version] [-e expr] [--expression=expr...] [-f file...] [--file=file...] [file...]

DESCRIPTION

bc(1) is an interactive processor for a language first standardized in 1991 by POSIX. (The current standard is here (https://pubs.opengroup.org/onlinepubs/9699919799/utilities/bc.html).) 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 stdin.

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

Note: If running this bc(1) on any 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 -r keyword, where keyword is the keyword that is used as a name in the script. For more information, see the OPTIONS section.

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

OPTIONS

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

-g, --global-stacks: Turns the globals ibase, obase, scale, and seed into stacks.

This has the effect that a copy of the current value of all four are pushed onto a stack for every function call, as well as popped when every function returns. This means that functions can assign to any and all of those globals without worrying that the change will affect other functions. Thus, a hypothetical function named output(x,b) that simply printed x in base b could be written like this:


define void output(x, b) {
    obase=b
    x
}

instead of like this:


define void output(x, b) {
    auto c
    c=obase
    obase=b
    x
    obase=c
}

This makes writing functions much easier.

(Note: the function output(x,b) exists in the extended math library. See the LIBRARY section.)

However, since using this flag means that functions cannot set ibase, obase, scale, or seed globally, functions that are made to do so cannot work anymore. There are two possible use cases for that, and each has a solution.

First, if a function is called on startup to turn bc(1) into a number converter, it is possible to replace that capability with various shell aliases. Examples:


alias d2o="bc -e ibase=A -e obase=8"
alias h2b="bc -e ibase=G -e obase=2"

Second, if the purpose of a function is to set ibase, obase, scale, or seed globally for any other purpose, it could be split into one to four functions (based on how many globals it sets) and each of those functions could return the desired value for a global.

For functions that set seed, the value assigned to seed is not propagated to parent functions. This means that the sequence of pseudo-random numbers that they see will not be the same sequence of pseudo-random numbers that any parent sees. This is only the case once seed has been set.

If a function desires to not affect the sequence of pseudo-random numbers of its parents, but wants to use the same seed, it can use the following line:


seed = seed

If the behavior of this option is desired for every run of bc(1), then users could make sure to define BC_ENV_ARGS and include this option (see the ENVIRONMENT VARIABLES section for more details).

If -s, -w, or any equivalents are used, this option is ignored.

This is a non-portable extension.

-h, --help: Prints a usage message and quits.
-i, --interactive: Forces interactive mode. (See the INTERACTIVE MODE section.)

This is a non-portable extension.

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

This is a non-portable extension.

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

To learn what is in the libraries, see the LIBRARY section.

-P, --no-prompt: Disables the prompt in TTY mode. (The prompt is only enabled in TTY mode. See the TTY MODE 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 BC_ENV_ARGS (see the ENVIRONMENT VARIABLES section).

These options override the BC_PROMPT and BC_TTY_MODE environment variables (see the ENVIRONMENT VARIABLES section).

This is a non-portable extension.

-R, --no-read-prompt: Disables the read prompt in TTY mode. (The read prompt is only enabled in TTY mode. See the TTY MODE 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 BC_ENV_ARGS (see the ENVIRONMENT VARIABLES section). This option is also useful in hash bang lines of bc(1) scripts that prompt for user input.

This option does not disable the regular prompt because the read prompt is only used when the read() built-in function is called.

These options do override the BC_PROMPT and BC_TTY_MODE environment variables (see the ENVIRONMENT VARIABLES section), but only for the read prompt.

This is a non-portable extension.

-r keyword, --redefine=keyword: Redefines keyword 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.

The keywords this bc(1) allows to be redefined are:

•: abs
•: asciify
•: continue
•: divmod
•: else
•: halt
•: irand
•: last
•: limits
•: maxibase
•: maxobase
•: maxrand
•: maxscale
•: modexp
•: print
•: rand
•: read
•: seed
•: stream

If any of those keywords are used as a function, variable, or array name in a script, use this option with the keyword as the argument. If multiple are used, use this option for all of them; it can be used multiple times.

Keywords are not redefined when parsing the builtin math library (see the LIBRARY section).

It is a fatal error to redefine keywords mandated by the POSIX standard. It is a fatal error to attempt to redefine words that this bc(1) does not reserve as keywords.

-q, --quiet: 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 -v, -V, or --version options are given.

This is a non-portable extension.

-s, --standard: Process exactly the language defined by the standard (https://pubs.opengroup.org/onlinepubs/9699919799/utilities/bc.html) and error if any extensions are used.

This is a non-portable extension.

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

This is a non-portable extension.

-w, --warn: Like -s and --standard, except that warnings (and not errors) are printed for non-standard extensions and execution continues normally.

This is a non-portable extension.

-z, --leading-zeroes: Makes bc(1) print all numbers greater than -1 and less than 1, and not equal to 0, with a leading zero.

This can be set for individual numbers with the plz(x), plznl(x)**, pnlz(x), and pnlznl(x) functions in the extended math library (see the LIBRARY section).

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.

If this option is given on the command-line (i.e., not in BC_ENV_ARGS, see the ENVIRONMENT VARIABLES section), then after processing all expressions and files, bc(1) will exit, unless - (stdin) was given as an argument at least once to -f or --file, whether on the command-line or in BC_ENV_ARGS. However, if any other -e, --expression, -f, or --file arguments are given after -f- or equivalent is given, bc(1) will give a fatal error and exit.

This is a non-portable extension.

-f file, --file=file: Reads in file and evaluates it, line by line, as though it were read through stdin. If expressions are also given (see above), the expressions are evaluated in the order given.

If this option is given on the command-line (i.e., not in BC_ENV_ARGS, see the ENVIRONMENT VARIABLES section), then after processing all expressions and files, bc(1) will exit, unless - (stdin) was given as an argument at least once to -f or --file. However, if any other -e, --expression, -f, or --file arguments are given after -f- or equivalent is given, bc(1) will give a fatal error and exit.

This is a non-portable extension.

All long options are non-portable extensions.

STDIN

If no files or expressions are given by the -f, --file, -e, or --expression options, then bc(1) read from stdin.

However, there are a few caveats to this.

First, stdin 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, if statement, or loop without ending it will also cause bc(1) to not execute.

Second, after an if statement, bc(1) doesn’t know if an else statement will follow, so it will not execute until it knows there will not be an else statement.

STDOUT

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

Note: Unlike other bc(1) implementations, this bc(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 >&-, it will quit with an error. This is done so that bc(1) can report problems when stdout 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 stdout to /dev/null.

STDERR

Any error output is written to stderr.

Note: Unlike other bc(1) implementations, this bc(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 2>&-, it will quit with an error. This is done so that bc(1) can exit with an error code when stderr 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 stderr to /dev/null.

SYNTAX

The syntax for bc(1) programs is mostly C-like, with some differences. This bc(1) follows the POSIX standard (https://pubs.opengroup.org/onlinepubs/9699919799/utilities/bc.html), 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, E means expression, S means statement, and I means identifier.

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

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

obase is a global variable 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 and can be queried in bc(1) programs with the maxobase() built-in function. The min allowable value for obase is 0. If obase is 0, values are output in scientific notation, and if obase is 1, values are output in engineering notation. Otherwise, values are output in the specified base.

Outputting in scientific and engineering notations are non-portable extensions.

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 global variable that sets the precision of any operations, with exceptions. scale is initially 0. scale cannot be negative. The max allowable value for scale is BC_SCALE_MAX and can be queried in bc(1) programs with the maxscale() built-in function.

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

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

Either semicolons or newlines may separate statements.

Comments

There are two kinds of comments:

1.: Block comments are enclosed in /* and */.
2.: Line comments go from # until, and not including, the next newline. This is a non-portable extension.

Named Expressions

The following are named expressions in bc(1):

1.: Variables: I
2.: Array Elements: I[E]
3.: ibase
4.: obase
5.: scale
6.: seed
7.: last or a single dot (.)

Numbers 6 and 7 are non-portable extensions.

The meaning of seed is dependent on the current pseudo-random number generator but is guaranteed to not change except for new major versions.

The scale and sign of the value may be significant.

If a previously used seed value is assigned to seed and used again, the pseudo-random number generator is guaranteed to produce the same sequence of pseudo-random numbers as it did when the seed value was previously used.

The exact value assigned to seed is not guaranteed to be returned if seed is queried again immediately. However, if seed does return a different value, both values, when assigned to seed, are guaranteed to produce the same sequence of pseudo-random numbers. This means that certain values assigned to seed will not produce unique sequences of pseudo-random numbers. The value of seed will change after any use of the rand() and irand(E) operands (see the Operands subsection below), except if the parameter passed to irand(E) is 0, 1, or negative.

There is no limit to the length (number of significant decimal digits) or scale of the value that can be assigned to seed.

Variables and arrays do not interfere; users can have arrays named the same as variables. This also applies to functions (see the FUNCTIONS 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 increment/decrement operators and as the left side of assignment operators (see the Operators subsection).

Operands

The following are valid operands in bc(1):

1.: Numbers (see the Numbers subsection below).
2.: Array indices (I[E]).
3.: (E): The value of E (used to change precedence).
4.: sqrt(E): The square root of E. E must be non-negative.
5.: length(E): The number of significant decimal digits in E. Returns 1 for 0 with no decimal places. If given a string, the length of the string is returned. Passing a string to length(E) is a non-portable extension.
6.: length(I[]): The number of elements in the array I. This is a non-portable extension.
7.: scale(E): The scale of E.
8.: abs(E): The absolute value of E. This is a non-portable extension.
9.: modexp(E, E, E): Modular exponentiation, where the first expression is the base, the second is the exponent, and the third is the modulus. All three values must be integers. The second argument must be non-negative. The third argument must be non-zero. This is a non-portable extension.
10.: divmod(E, E, I[]): Division and modulus in one operation. This is for optimization. The first expression is the dividend, and the second is the divisor, which must be non-zero. The return value is the quotient, and the modulus is stored in index 0 of the provided array (the last argument). This is a non-portable extension.
11.: asciify(E): If E is a string, returns a string that is the first letter of its argument. If it is a number, calculates the number mod 256 and returns that number as a one-character string. This is a non-portable extension.
12.: I(), I(E), I(E, E), and so on, where I is an identifier for a non-void function (see the Void Functions subsection of the FUNCTIONS section). The E argument(s) may also be arrays of the form I[], which will automatically be turned into array references (see the Array References subsection of the FUNCTIONS section) if the corresponding parameter in the function definition is an array reference.
13.: read(): Reads a line from stdin and uses that as an expression. The result of that expression is the result of the read() operand. This is a non-portable extension.
14.: maxibase(): The max allowable ibase. This is a non-portable extension.
15.: maxobase(): The max allowable obase. This is a non-portable extension.
16.: maxscale(): The max allowable scale. This is a non-portable extension.
17.: line_length(): The line length set with BC_LINE_LENGTH (see the ENVIRONMENT VARIABLES section). This is a non-portable extension.
18.: global_stacks(): 0 if global stacks are not enabled with the -g or --global-stacks options, non-zero otherwise. See the OPTIONS section. This is a non-portable extension.
19.: leading_zero(): 0 if leading zeroes are not enabled with the -z or –leading-zeroes options, non-zero otherwise. See the OPTIONS section. This is a non-portable extension.
20.: rand(): A pseudo-random integer between 0 (inclusive) and BC_RAND_MAX (inclusive). Using this operand will change the value of seed. This is a non-portable extension.
21.: irand(E): A pseudo-random integer between 0 (inclusive) and the value of E (exclusive). If E is negative or is a non-integer (E’s scale is not 0), an error is raised, and bc(1) resets (see the RESET section) while seed remains unchanged. If E is larger than BC_RAND_MAX, the higher bound is honored by generating several pseudo-random integers, multiplying them by appropriate powers of BC_RAND_MAX+1, and adding them together. Thus, the size of integer that can be generated with this operand is unbounded. Using this operand will change the value of seed, unless the value of E is 0 or 1. In that case, 0 is returned, and seed is not changed. This is a non-portable extension.
22.: maxrand(): The max integer returned by rand(). This is a non-portable extension.

The integers generated by rand() and irand(E) are guaranteed to be as unbiased as possible, subject to the limitations of the pseudo-random number generator.

Note: The values returned by the pseudo-random number generator with rand() and irand(E) are guaranteed to NOT be cryptographically secure. This is a consequence of using a seeded pseudo-random number generator. However, they are guaranteed to be reproducible with identical seed values. This means that the pseudo-random values from bc(1) should only be used where a reproducible stream of pseudo-random numbers is ESSENTIAL. In any other case, use a non-seeded pseudo-random number generator.

Numbers

Numbers are strings made up of digits, uppercase letters, and at most 1 period for a radix. Numbers can have up to BC_NUM_MAX digits. Uppercase letters are equal to 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 alone) take the value that they would have if they were valid digits, regardless of the value of ibase. This means that A alone always equals decimal 10 and Z alone always equals decimal 35.

In addition, bc(1) accepts numbers in scientific notation. These have the form <number>e<integer>. The exponent (the portion after the e) must be an integer. An example is 1.89237e9, which is equal to 1892370000. Negative exponents are also allowed, so 4.2890e-3 is equal to 0.0042890.

Using scientific notation is an error or warning if the -s or -w, respectively, command-line options (or equivalents) are given.

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 bc(1) is given the number string FFeA, the resulting decimal number will be 2550000000000, and if bc(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.

Operators

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.

++ --: Type: Prefix and Postfix

Associativity: None

Description: increment, decrement

- !: Type: Prefix

Associativity: None

Description: negation, boolean not

$: Type: Postfix

Associativity: None

Description: truncation

@: Type: Binary

Associativity: Right

Description: set precision

^: Type: Binary

Associativity: Right

Description: power

* / %: Type: Binary

Associativity: Left

Description: multiply, divide, modulus

+ -: Type: Binary

Associativity: Left

Description: add, subtract

<< >>: Type: Binary

Associativity: Left

Description: shift left, shift right

= <<= >>= += -= *= /= %= ^= @=: Type: Binary

Associativity: Right

Description: assignment

== <= >= != < >: Type: Binary

Associativity: Left

Description: relational

&&: Type: Binary

Associativity: Left

Description: boolean and

||: Type: Binary

Associativity: Left

Description: boolean or

The operators will be described in more detail below.

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

The prefix versions of these operators are more efficient; use them where possible.

-: The negation operator returns 0 if a user attempts to negate any expression with the value 0. Otherwise, a copy of the expression with its sign flipped is returned.
!: The boolean not operator returns 1 if the expression is 0, or 0 otherwise.

This is a non-portable extension.

$: The truncation operator returns a copy of the given expression with all of its scale removed.

This is a non-portable extension.

@: The set precision operator takes two expressions and returns a copy of the first with its scale equal to the value of the second expression. That could either mean that the number is returned without change (if the scale of the first expression matches the value of the second expression), extended (if it is less), or truncated (if it is more).

The second expression must be an integer (no scale) and non-negative.

This is a non-portable extension.

^: The power operator (not the exclusive or operator, as it would be in C) takes two expressions and raises the first to the power of the value of the second. The scale of the result is equal to scale.

The second expression must be an integer (no scale), and if it is negative, the first value must be non-zero.

*: The multiply operator takes two expressions, multiplies them, and returns the product. 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 divide operator takes two expressions, divides them, and returns the quotient. The scale of the result shall be the value of scale.

The second expression must be non-zero.

%: The modulus operator takes two expressions, a and b, and evaluates them by 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 second expression must be non-zero.

+: The add operator takes two expressions, a and b, and returns the sum, with a scale equal to the max of the scales of a and b.
-: The subtract operator takes two expressions, a and b, and returns the difference, with a scale equal to the max of the scales of a and b.
<<: The left shift operator takes two expressions, a and b, and returns a copy of the value of a with its decimal point moved b places to the right.

The second expression must be an integer (no scale) and non-negative.

This is a non-portable extension.

>>: The right shift operator takes two expressions, a and b, and returns a copy of the value of a with its decimal point moved b places to the left.

The second expression must be an integer (no scale) and non-negative.

This is a non-portable extension.

= <<= >>= += -= *= /= %= ^= @=: The assignment operators take two expressions, a and b where a is a named expression (see the Named Expressions subsection).

For =, b is copied and the result is assigned to a. For all others, a and b are applied as operands to the corresponding arithmetic operator and the result is assigned to a.

The assignment operators that correspond to operators that are extensions are themselves non-portable extensions.

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

Note that unlike in C, these operators have a lower precedence than the assignment operators, which means that a=b>c is interpreted as (a=b)>c.

Also, unlike the standard (https://pubs.opengroup.org/onlinepubs/9699919799/utilities/bc.html) requires, these operators can appear anywhere any other expressions can be used. This allowance is a non-portable extension.

&&: The boolean and operator takes two expressions and returns 1 if both expressions are non-zero, 0 otherwise.

This is not a short-circuit operator.

This is a non-portable extension.

||: The boolean or operator takes two expressions and returns 1 if one of the expressions is non-zero, 0 otherwise.

This is not a short-circuit operator.

This is a non-portable extension.

Statements

The following items are statements:

1.: E
2.: { S ; ... ; S }
3.: if ( E ) S
4.: if ( E ) S else S
5.: while ( E ) S
6.: for ( E ; E ; E ) S
7.: An empty statement
8.: break
9.: continue
10.: quit
11.: halt
12.: limits
13.: A string of characters, enclosed in double quotes
14.: print E , ... , E
15.: stream E , ... , E
16.: I(), I(E), I(E, E), and so on, where I is an identifier for a void function (see the Void Functions subsection of the FUNCTIONS section). The E argument(s) may also be arrays of the form I[], which will automatically be turned into array references (see the Array References subsection of the FUNCTIONS section) if the corresponding parameter in the function definition is an array reference.

Numbers 4, 9, 11, 12, 14, 15, and 16 are non-portable extensions.

Also, as a non-portable extension, 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 1.

The break statement causes a loop to stop iterating and resume execution immediately following a loop. This is only allowed in loops.

The continue 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 if else statement does the same thing as in C.

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

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

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

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

Both scientific notation and engineering notation are available for printing the results of expressions. Scientific notation is activated by assigning 0 to obase, and engineering notation is activated by assigning 1 to obase. To deactivate them, just assign a different value to obase.

Scientific notation and engineering notation are disabled if bc(1) is run with either the -s or -w command-line options (or equivalents).

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

Strings

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 RESET section).

Assigning strings to variables and array elements and passing them to functions are non-portable extensions.

Print Statement

The “expressions” in a print 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:

\a: \a

\b: \b

\\: \

\e: \

\f: \f

\n: \n

\q: “

\r: \r

\t: \t

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 last, like any other expression that is printed.

Stream Statement

The “expressions in a stream statement may also be strings.

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

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

Order of Evaluation

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


a[i++] = i++

the first (or 0th) element of a is set to 1, and i is equal to 2 at the end of the expression.

This includes function arguments. Thus, assuming i is equal to 0, this means that in the expression


x(i++, i++)

the first argument passed to x() is 0, and the second argument is 1, while i is equal to 2 before the function starts executing.

FUNCTIONS

Function definitions are as follows:


define I(I,...,I){
    auto I,...,I
    S;...;S
    return(E)
}

Any I in the parameter list or auto list may be replaced with I[] to make a parameter or auto var an array, and any I in the parameter list may be replaced with *I[] 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 I[] like normal array parameters and will be automatically converted into references.

As a non-portable extension, the opening brace of a define statement may appear on the next line.

As a non-portable extension, the return statement may also be in one of the following forms:

1.: return
2.: return ( )
3.: return E

The first two, or not specifying a return statement, is equivalent to return (0), unless the function is a void function (see the Void Functions subsection below).

Void Functions

Functions can also be void functions, defined as follows:


define void I(I,...,I){
    auto I,...,I
    S;...;S
    return
}

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 return statements listed above. They can also omit the return statement entirely.

The word “void” is not treated as a keyword; it is still possible to have variables, arrays, and functions named void. The word “void” is only treated specially right after the define keyword.

This is a non-portable extension.

Array References

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


*I[]

it is a reference. 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 non-portable extension.

LIBRARY

All of the functions below, including the functions in the extended math library (see the Extended Library subsection below), are available when the -l or --mathlib command-line flags are given, except that the extended math library is not available when the -s option, the -w option, or equivalents are given.

Standard Library

The standard (https://pubs.opengroup.org/onlinepubs/9699919799/utilities/bc.html) defines the following functions for the math library:

s(x): Returns the sine of x, which is assumed to be in radians.

This is a transcendental function (see the Transcendental Functions subsection below).

c(x): Returns the cosine of x, which is assumed to be in radians.

This is a transcendental function (see the Transcendental Functions subsection below).

a(x): Returns the arctangent of x, in radians.

This is a transcendental function (see the Transcendental Functions subsection below).

l(x): Returns the natural logarithm of x.

This is a transcendental function (see the Transcendental Functions subsection below).

e(x): Returns the mathematical constant e raised to the power of x.

This is a transcendental function (see the Transcendental Functions subsection below).

j(x, n): Returns the bessel integer order n (truncated) of x.

This is a transcendental function (see the Transcendental Functions subsection below).

Extended Library

The extended library is not loaded when the -s/--standard or -w/--warn options are given since they are not part of the library defined by the standard (https://pubs.opengroup.org/onlinepubs/9699919799/utilities/bc.html).

The extended library is a non-portable extension.

p(x, y): Calculates x to the power of y, even if y is not an integer, and returns the result to the current scale.

It is an error if y is negative and x is 0.

This is a transcendental function (see the Transcendental Functions subsection below).

r(x, p): Returns x rounded to p decimal places according to the rounding mode round half away from 0 (https://en.wikipedia.org/wiki/Rounding#Round_half_away_from_zero).
ceil(x, p): Returns x rounded to p decimal places according to the rounding mode round away from 0 (https://en.wikipedia.org/wiki/Rounding#Rounding_away_from_zero).
f(x): Returns the factorial of the truncated absolute value of x.
perm(n, k): Returns the permutation of the truncated absolute value of n of the truncated absolute value of k, if k <= n. If not, it returns 0.
comb(n, k): Returns the combination of the truncated absolute value of n of the truncated absolute value of k, if k <= n. If not, it returns 0.
l2(x): Returns the logarithm base 2 of x.

This is a transcendental function (see the Transcendental Functions subsection below).

l10(x): Returns the logarithm base 10 of x.

This is a transcendental function (see the Transcendental Functions subsection below).

log(x, b): Returns the logarithm base b of x.

This is a transcendental function (see the Transcendental Functions subsection below).

cbrt(x): Returns the cube root of x.
root(x, n): Calculates the truncated value of n, r, and returns the rth root of x to the current scale.

If r is 0 or negative, this raises an error and causes bc(1) to reset (see the RESET section). It also raises an error and causes bc(1) to reset if r is even and x is negative.

gcd(a, b): Returns the greatest common divisor (factor) of the truncated absolute value of a and the truncated absolute value of b.
lcm(a, b): Returns the least common multiple of the truncated absolute value of a and the truncated absolute value of b.
pi(p): Returns pi to p decimal places.

This is a transcendental function (see the Transcendental Functions subsection below).

t(x): Returns the tangent of x, which is assumed to be in radians.

This is a transcendental function (see the Transcendental Functions subsection below).

a2(y, x): Returns the arctangent of y/x, in radians. If both y and x are equal to 0, it raises an error and causes bc(1) to reset (see the RESET section). Otherwise, if x is greater than 0, it returns a(y/x). If x is less than 0, and y is greater than or equal to 0, it returns a(y/x)+pi. If x is less than 0, and y is less than 0, it returns a(y/x)-pi. If x is equal to 0, and y is greater than 0, it returns pi/2. If x is equal to 0, and y is less than 0, it returns -pi/2.

This function is the same as the atan2() function in many programming languages.

This is a transcendental function (see the Transcendental Functions subsection below).

sin(x): Returns the sine of x, which is assumed to be in radians.

This is an alias of s(x).

This is a transcendental function (see the Transcendental Functions subsection below).

cos(x): Returns the cosine of x, which is assumed to be in radians.

This is an alias of c(x).

This is a transcendental function (see the Transcendental Functions subsection below).

tan(x): Returns the tangent of x, which is assumed to be in radians.

If x is equal to 1 or -1, this raises an error and causes bc(1) to reset (see the RESET section).

This is an alias of t(x).

This is a transcendental function (see the Transcendental Functions subsection below).

atan(x): Returns the arctangent of x, in radians.

This is an alias of a(x).

This is a transcendental function (see the Transcendental Functions subsection below).

atan2(y, x): Returns the arctangent of y/x, in radians. If both y and x are equal to 0, it raises an error and causes bc(1) to reset (see the RESET section). Otherwise, if x is greater than 0, it returns a(y/x). If x is less than 0, and y is greater than or equal to 0, it returns a(y/x)+pi. If x is less than 0, and y is less than 0, it returns a(y/x)-pi. If x is equal to 0, and y is greater than 0, it returns pi/2. If x is equal to 0, and y is less than 0, it returns -pi/2.

This function is the same as the atan2() function in many programming languages.

This is an alias of a2(y, x).

This is a transcendental function (see the Transcendental Functions subsection below).

r2d(x): Converts x from radians to degrees and returns the result.

This is a transcendental function (see the Transcendental Functions subsection below).

d2r(x): Converts x from degrees to radians and returns the result.

This is a transcendental function (see the Transcendental Functions subsection below).

frand(p): Generates a pseudo-random number between 0 (inclusive) and 1 (exclusive) with the number of decimal digits after the decimal point equal to the truncated absolute value of p. If p is not 0, then calling this function will change the value of seed. If p is 0, then 0 is returned, and seed is not changed.
ifrand(i, p): Generates a pseudo-random number that is between 0 (inclusive) and the truncated absolute value of i (exclusive) with the number of decimal digits after the decimal point equal to the truncated absolute value of p. If the absolute value of i is greater than or equal to 2, and p is not 0, then calling this function will change the value of seed; otherwise, 0 is returned and seed is not changed.
srand(x): Returns x with its sign flipped with probability 0.5. In other words, it randomizes the sign of x.
brand(): Returns a random boolean value (either 0 or 1).
band(a, b): Takes the truncated absolute value of both a and b and calculates and returns the result of the bitwise and operation between them.

If you want to use signed two’s complement arguments, use s2u(x) to convert.

bor(a, b): Takes the truncated absolute value of both a and b and calculates and returns the result of the bitwise or operation between them.

If you want to use signed two’s complement arguments, use s2u(x) to convert.

bxor(a, b): Takes the truncated absolute value of both a and b and calculates and returns the result of the bitwise xor operation between them.

If you want to use signed two’s complement arguments, use s2u(x) to convert.

bshl(a, b): Takes the truncated absolute value of both a and b and calculates and returns the result of a bit-shifted left by b places.

If you want to use signed two’s complement arguments, use s2u(x) to convert.

bshr(a, b): Takes the truncated absolute value of both a and b and calculates and returns the truncated result of a bit-shifted right by b places.

If you want to use signed two’s complement arguments, use s2u(x) to convert.

bnotn(x, n): Takes the truncated absolute value of x and does a bitwise not as though it has the same number of bytes as the truncated absolute value of n.