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| .TH "BC" "1" "April 2021" "Gavin D. Howard" "General Commands Manual" |
| .SH NAME |
| .PP |
| bc - arbitrary-precision decimal arithmetic language and calculator |
| .SH SYNOPSIS |
| .PP |
| \f[B]bc\f[R] [\f[B]-ghilPqRsvVw\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]\&...] |
| .SH DESCRIPTION |
| .PP |
| 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. |
| .PP |
| 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]. |
| .PP |
| 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. |
| .SH OPTIONS |
| .PP |
| The following are the options that bc(1) accepts. |
| .TP |
| \f[B]-g\f[R], \f[B]--global-stacks\f[R] |
| Turns the globals \f[B]ibase\f[R], \f[B]obase\f[R], \f[B]scale\f[R], and |
| \f[B]seed\f[R] into stacks. |
| .RS |
| .PP |
| 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 \f[B]output(x,b)\f[R] that simply |
| printed \f[B]x\f[R] in base \f[B]b\f[R] could be written like this: |
| .IP |
| .nf |
| \f[C] |
| define void output(x, b) { |
| obase=b |
| x |
| } |
| \f[R] |
| .fi |
| .PP |
| instead of like this: |
| .IP |
| .nf |
| \f[C] |
| define void output(x, b) { |
| auto c |
| c=obase |
| obase=b |
| x |
| obase=c |
| } |
| \f[R] |
| .fi |
| .PP |
| This makes writing functions much easier. |
| .PP |
| (\f[B]Note\f[R]: the function \f[B]output(x,b)\f[R] exists in the |
| extended math library. |
| See the \f[B]LIBRARY\f[R] section.) |
| .PP |
| However, since using this flag means that functions cannot set |
| \f[B]ibase\f[R], \f[B]obase\f[R], \f[B]scale\f[R], or \f[B]seed\f[R] |
| globally, functions that are made to do so cannot work anymore. |
| There are two possible use cases for that, and each has a solution. |
| .PP |
| 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: |
| .IP |
| .nf |
| \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] |
| .fi |
| .PP |
| Second, if the purpose of a function is to set \f[B]ibase\f[R], |
| \f[B]obase\f[R], \f[B]scale\f[R], or \f[B]seed\f[R] 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. |
| .PP |
| For functions that set \f[B]seed\f[R], the value assigned to |
| \f[B]seed\f[R] 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 \f[B]seed\f[R] has been set. |
| .PP |
| If a function desires to not affect the sequence of pseudo-random |
| numbers of its parents, but wants to use the same \f[B]seed\f[R], it can |
| use the following line: |
| .IP |
| .nf |
| \f[C] |
| seed = seed |
| \f[R] |
| .fi |
| .PP |
| If the behavior of this option is desired for every run of bc(1), then |
| users could make sure to define \f[B]BC_ENV_ARGS\f[R] and include this |
| option (see the \f[B]ENVIRONMENT VARIABLES\f[R] section for more |
| details). |
| .PP |
| If \f[B]-s\f[R], \f[B]-w\f[R], or any equivalents are used, this option |
| is ignored. |
| .PP |
| This is a \f[B]non-portable extension\f[R]. |
| .RE |
| .TP |
| \f[B]-h\f[R], \f[B]--help\f[R] |
| Prints a usage message and quits. |
| .TP |
| \f[B]-i\f[R], \f[B]--interactive\f[R] |
| Forces interactive mode. |
| (See the \f[B]INTERACTIVE MODE\f[R] section.) |
| .RS |
| .PP |
| This is a \f[B]non-portable extension\f[R]. |
| .RE |
| .TP |
| \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 and the extended math library before |
| running any code, including any expressions or files specified on the |
| command line. |
| .RS |
| .PP |
| To learn what is in the libraries, see the \f[B]LIBRARY\f[R] section. |
| .RE |
| .TP |
| \f[B]-P\f[R], \f[B]--no-prompt\f[R] |
| This option is a no-op. |
| .RS |
| .PP |
| This is a \f[B]non-portable extension\f[R]. |
| .RE |
| .TP |
| \f[B]-R\f[R], \f[B]--no-read-prompt\f[R] |
| Because bc(1) was built without support for prompts, this option is a |
| no-op. |
| .RS |
| .PP |
| This is a \f[B]non-portable extension\f[R]. |
| .RE |
| .TP |
| \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. |
| .RS |
| .PP |
| This is a \f[B]non-portable extension\f[R]. |
| .RE |
| .TP |
| \f[B]-s\f[R], \f[B]--standard\f[R] |
| Process exactly the language defined by the |
| standard (https://pubs.opengroup.org/onlinepubs/9699919799/utilities/bc.html) |
| and error if any extensions are used. |
| .RS |
| .PP |
| This is a \f[B]non-portable extension\f[R]. |
| .RE |
| .TP |
| \f[B]-v\f[R], \f[B]-V\f[R], \f[B]--version\f[R] |
| Print the version information (copyright header) and exit. |
| .RS |
| .PP |
| This is a \f[B]non-portable extension\f[R]. |
| .RE |
| .TP |
| \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. |
| .RS |
| .PP |
| This is a \f[B]non-portable extension\f[R]. |
| .RE |
| .TP |
| \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 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. |
| .RS |
| .PP |
| If this option is given on the command-line (i.e., not in |
| \f[B]BC_ENV_ARGS\f[R], see the \f[B]ENVIRONMENT VARIABLES\f[R] section), |
| then after processing all expressions and files, bc(1) will exit, unless |
| \f[B]-\f[R] (\f[B]stdin\f[R]) was given as an argument at least once to |
| \f[B]-f\f[R] or \f[B]--file\f[R], whether on the command-line or in |
| \f[B]BC_ENV_ARGS\f[R]. |
| However, if any other \f[B]-e\f[R], \f[B]--expression\f[R], |
| \f[B]-f\f[R], or \f[B]--file\f[R] arguments are given after |
| \f[B]-f-\f[R] or equivalent is given, bc(1) will give a fatal error and |
| exit. |
| .PP |
| This is a \f[B]non-portable extension\f[R]. |
| .RE |
| .TP |
| \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 above), the expressions are evaluated |
| in the order given. |
| .RS |
| .PP |
| If this option is given on the command-line (i.e., not in |
| \f[B]BC_ENV_ARGS\f[R], see the \f[B]ENVIRONMENT VARIABLES\f[R] section), |
| then after processing all expressions and files, bc(1) will exit, unless |
| \f[B]-\f[R] (\f[B]stdin\f[R]) was given as an argument at least once to |
| \f[B]-f\f[R] or \f[B]--file\f[R]. |
| However, if any other \f[B]-e\f[R], \f[B]--expression\f[R], |
| \f[B]-f\f[R], or \f[B]--file\f[R] arguments are given after |
| \f[B]-f-\f[R] or equivalent is given, bc(1) will give a fatal error and |
| exit. |
| .PP |
| This is a \f[B]non-portable extension\f[R]. |
| .RE |
| .PP |
| All long options are \f[B]non-portable extensions\f[R]. |
| .SH STDOUT |
| .PP |
| 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]. |
| .PP |
| \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. |
| .PP |
| 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]. |
| .SH STDERR |
| .PP |
| Any error output is written to \f[B]stderr\f[R]. |
| .PP |
| \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. |
| .PP |
| 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]. |
| .SH SYNTAX |
| .PP |
| 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. |
| .PP |
| 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. |
| .PP |
| 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]. |
| .PP |
| \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. |
| .PP |
| \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]0\f[R]. |
| If \f[B]obase\f[R] is \f[B]0\f[R], values are output in scientific |
| notation, and if \f[B]obase\f[R] is \f[B]1\f[R], values are output in |
| engineering notation. |
| Otherwise, values are output in the specified base. |
| .PP |
| Outputting in scientific and engineering notations are \f[B]non-portable |
| extensions\f[R]. |
| .PP |
| 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. |
| .PP |
| 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. |
| .PP |
| All of the above applies to arrays as well. |
| .PP |
| 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. |
| .PP |
| 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]. |
| .PP |
| Either semicolons or newlines may separate statements. |
| .SS Comments |
| .PP |
| There are two kinds of comments: |
| .IP "1." 3 |
| Block comments are enclosed in \f[B]/*\f[R] and \f[B]*/\f[R]. |
| .IP "2." 3 |
| Line comments go from \f[B]#\f[R] until, and not including, the next |
| newline. |
| This is a \f[B]non-portable extension\f[R]. |
| .SS Named Expressions |
| .PP |
| The following are named expressions in bc(1): |
| .IP "1." 3 |
| Variables: \f[B]I\f[R] |
| .IP "2." 3 |
| Array Elements: \f[B]I[E]\f[R] |
| .IP "3." 3 |
| \f[B]ibase\f[R] |
| .IP "4." 3 |
| \f[B]obase\f[R] |
| .IP "5." 3 |
| \f[B]scale\f[R] |
| .IP "6." 3 |
| \f[B]seed\f[R] |
| .IP "7." 3 |
| \f[B]last\f[R] or a single dot (\f[B].\f[R]) |
| .PP |
| Numbers 6 and 7 are \f[B]non-portable extensions\f[R]. |
| .PP |
| The meaning of \f[B]seed\f[R] is dependent on the current pseudo-random |
| number generator but is guaranteed to not change except for new major |
| versions. |
| .PP |
| The \f[I]scale\f[R] and sign of the value may be significant. |
| .PP |
| If a previously used \f[B]seed\f[R] value is assigned to \f[B]seed\f[R] |
| and used again, the pseudo-random number generator is guaranteed to |
| produce the same sequence of pseudo-random numbers as it did when the |
| \f[B]seed\f[R] value was previously used. |
| .PP |
| The exact value assigned to \f[B]seed\f[R] is not guaranteed to be |
| returned if \f[B]seed\f[R] is queried again immediately. |
| However, if \f[B]seed\f[R] \f[I]does\f[R] return a different value, both |
| values, when assigned to \f[B]seed\f[R], are guaranteed to produce the |
| same sequence of pseudo-random numbers. |
| This means that certain values assigned to \f[B]seed\f[R] will |
| \f[I]not\f[R] produce unique sequences of pseudo-random numbers. |
| The value of \f[B]seed\f[R] will change after any use of the |
| \f[B]rand()\f[R] and \f[B]irand(E)\f[R] operands (see the |
| \f[I]Operands\f[R] subsection below), except if the parameter passed to |
| \f[B]irand(E)\f[R] is \f[B]0\f[R], \f[B]1\f[R], or negative. |
| .PP |
| There is no limit to the length (number of significant decimal digits) |
| or \f[I]scale\f[R] of the value that can be assigned to \f[B]seed\f[R]. |
| .PP |
| 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. |
| .PP |
| 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). |
| .SS Operands |
| .PP |
| The following are valid operands in bc(1): |
| .IP " 1." 4 |
| Numbers (see the \f[I]Numbers\f[R] subsection below). |
| .IP " 2." 4 |
| Array indices (\f[B]I[E]\f[R]). |
| .IP " 3." 4 |
| \f[B](E)\f[R]: The value of \f[B]E\f[R] (used to change precedence). |
| .IP " 4." 4 |
| \f[B]sqrt(E)\f[R]: The square root of \f[B]E\f[R]. |
| \f[B]E\f[R] must be non-negative. |
| .IP " 5." 4 |
| \f[B]length(E)\f[R]: The number of significant decimal digits in |
| \f[B]E\f[R]. |
| .IP " 6." 4 |
| \f[B]length(I[])\f[R]: The number of elements in the array \f[B]I\f[R]. |
| This is a \f[B]non-portable extension\f[R]. |
| .IP " 7." 4 |
| \f[B]scale(E)\f[R]: The \f[I]scale\f[R] of \f[B]E\f[R]. |
| .IP " 8." 4 |
| \f[B]abs(E)\f[R]: The absolute value of \f[B]E\f[R]. |
| This is a \f[B]non-portable extension\f[R]. |
| .IP " 9." 4 |
| \f[B]I()\f[R], \f[B]I(E)\f[R], \f[B]I(E, E)\f[R], and so on, where |
| \f[B]I\f[R] is an identifier for a non-\f[B]void\f[R] function (see the |
| \f[I]Void Functions\f[R] subsection of the \f[B]FUNCTIONS\f[R] section). |
| The \f[B]E\f[R] argument(s) may also be arrays of the form |
| \f[B]I[]\f[R], which will automatically be turned into array references |
| (see the \f[I]Array References\f[R] subsection of the |
| \f[B]FUNCTIONS\f[R] section) if the corresponding parameter in the |
| function definition is an array reference. |
| .IP "10." 4 |
| \f[B]read()\f[R]: Reads a line from \f[B]stdin\f[R] and uses that as an |
| expression. |
| The result of that expression is the result of the \f[B]read()\f[R] |
| operand. |
| This is a \f[B]non-portable extension\f[R]. |
| .IP "11." 4 |
| \f[B]maxibase()\f[R]: The max allowable \f[B]ibase\f[R]. |
| This is a \f[B]non-portable extension\f[R]. |
| .IP "12." 4 |
| \f[B]maxobase()\f[R]: The max allowable \f[B]obase\f[R]. |
| This is a \f[B]non-portable extension\f[R]. |
| .IP "13." 4 |
| \f[B]maxscale()\f[R]: The max allowable \f[B]scale\f[R]. |
| This is a \f[B]non-portable extension\f[R]. |
| .IP "14." 4 |
| \f[B]rand()\f[R]: A pseudo-random integer between \f[B]0\f[R] |
| (inclusive) and \f[B]BC_RAND_MAX\f[R] (inclusive). |
| Using this operand will change the value of \f[B]seed\f[R]. |
| This is a \f[B]non-portable extension\f[R]. |
| .IP "15." 4 |
| \f[B]irand(E)\f[R]: A pseudo-random integer between \f[B]0\f[R] |
| (inclusive) and the value of \f[B]E\f[R] (exclusive). |
| If \f[B]E\f[R] is negative or is a non-integer (\f[B]E\f[R]\[cq]s |
| \f[I]scale\f[R] is not \f[B]0\f[R]), an error is raised, and bc(1) |
| resets (see the \f[B]RESET\f[R] section) while \f[B]seed\f[R] remains |
| unchanged. |
| If \f[B]E\f[R] is larger than \f[B]BC_RAND_MAX\f[R], the higher bound is |
| honored by generating several pseudo-random integers, multiplying them |
| by appropriate powers of \f[B]BC_RAND_MAX+1\f[R], 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 \f[B]seed\f[R], unless the |
| value of \f[B]E\f[R] is \f[B]0\f[R] or \f[B]1\f[R]. |
| In that case, \f[B]0\f[R] is returned, and \f[B]seed\f[R] is |
| \f[I]not\f[R] changed. |
| This is a \f[B]non-portable extension\f[R]. |
| .IP "16." 4 |
| \f[B]maxrand()\f[R]: The max integer returned by \f[B]rand()\f[R]. |
| This is a \f[B]non-portable extension\f[R]. |
| .PP |
| The integers generated by \f[B]rand()\f[R] and \f[B]irand(E)\f[R] are |
| guaranteed to be as unbiased as possible, subject to the limitations of |
| the pseudo-random number generator. |
| .PP |
| \f[B]Note\f[R]: The values returned by the pseudo-random number |
| generator with \f[B]rand()\f[R] and \f[B]irand(E)\f[R] are guaranteed to |
| \f[I]NOT\f[R] be cryptographically secure. |
| This is a consequence of using a seeded pseudo-random number generator. |
| However, they \f[I]are\f[R] guaranteed to be reproducible with identical |
| \f[B]seed\f[R] values. |
| This means that the pseudo-random values from bc(1) should only be used |
| where a reproducible stream of pseudo-random numbers is |
| \f[I]ESSENTIAL\f[R]. |
| In any other case, use a non-seeded pseudo-random number generator. |
| .SS Numbers |
| .PP |
| 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] + their position in the |
| alphabet (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], they are set to the value of the highest valid digit in |
| \f[B]ibase\f[R]. |
| .PP |
| Single-character numbers (i.e., \f[B]A\f[R] alone) take the value that |
| they would have if they were valid digits, regardless of the value of |
| \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]. |
| .PP |
| In addition, bc(1) accepts numbers in scientific notation. |
| These have the form \f[B]<number>e<integer>\f[R]. |
| The exponent (the portion after the \f[B]e\f[R]) must be an integer. |
| An example is \f[B]1.89237e9\f[R], which is equal to |
| \f[B]1892370000\f[R]. |
| Negative exponents are also allowed, so \f[B]4.2890e-3\f[R] is equal to |
| \f[B]0.0042890\f[R]. |
| .PP |
| Using scientific notation is an error or warning if the \f[B]-s\f[R] or |
| \f[B]-w\f[R], respectively, command-line options (or equivalents) are |
| given. |
| .PP |
| \f[B]WARNING\f[R]: Both the number and the exponent in scientific |
| notation are interpreted according to the current \f[B]ibase\f[R], but |
| the number is still multiplied by \f[B]10\[ha]exponent\f[R] regardless |
| of the current \f[B]ibase\f[R]. |
| For example, if \f[B]ibase\f[R] is \f[B]16\f[R] and bc(1) is given the |
| number string \f[B]FFeA\f[R], the resulting decimal number will be |
| \f[B]2550000000000\f[R], and if bc(1) is given the number string |
| \f[B]10e-4\f[R], the resulting decimal number will be \f[B]0.0016\f[R]. |
| .PP |
| Accepting input as scientific notation is a \f[B]non-portable |
| extension\f[R]. |
| .SS Operators |
| .PP |
| 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. |
| .TP |
| \f[B]++\f[R] \f[B]--\f[R] |
| Type: Prefix and Postfix |
| .RS |
| .PP |
| Associativity: None |
| .PP |
| Description: \f[B]increment\f[R], \f[B]decrement\f[R] |
| .RE |
| .TP |
| \f[B]-\f[R] \f[B]!\f[R] |
| Type: Prefix |
| .RS |
| .PP |
| Associativity: None |
| .PP |
| Description: \f[B]negation\f[R], \f[B]boolean not\f[R] |
| .RE |
| .TP |
| \f[B]$\f[R] |
| Type: Postfix |
| .RS |
| .PP |
| Associativity: None |
| .PP |
| Description: \f[B]truncation\f[R] |
| .RE |
| .TP |
| \f[B]\[at]\f[R] |
| Type: Binary |
| .RS |
| .PP |
| Associativity: Right |
| .PP |
| Description: \f[B]set precision\f[R] |
| .RE |
| .TP |
| \f[B]\[ha]\f[R] |
| Type: Binary |
| .RS |
| .PP |
| Associativity: Right |
| .PP |
| Description: \f[B]power\f[R] |
| .RE |
| .TP |
| \f[B]*\f[R] \f[B]/\f[R] \f[B]%\f[R] |
| Type: Binary |
| .RS |
| .PP |
| Associativity: Left |
| .PP |
| Description: \f[B]multiply\f[R], \f[B]divide\f[R], \f[B]modulus\f[R] |
| .RE |
| .TP |
| \f[B]+\f[R] \f[B]-\f[R] |
| Type: Binary |
| .RS |
| .PP |
| Associativity: Left |
| .PP |
| Description: \f[B]add\f[R], \f[B]subtract\f[R] |
| .RE |
| .TP |
| \f[B]<<\f[R] \f[B]>>\f[R] |
| Type: Binary |
| .RS |
| .PP |
| Associativity: Left |
| .PP |
| Description: \f[B]shift left\f[R], \f[B]shift right\f[R] |
| .RE |
| .TP |
| \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]/=\f[R] \f[B]%=\f[R] \f[B]\[ha]=\f[R] \f[B]\[at]=\f[R] |
| Type: Binary |
| .RS |
| .PP |
| Associativity: Right |
| .PP |
| Description: \f[B]assignment\f[R] |
| .RE |
| .TP |
| \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 |
| .RS |
| .PP |
| Associativity: Left |
| .PP |
| Description: \f[B]relational\f[R] |
| .RE |
| .TP |
| \f[B]&&\f[R] |
| Type: Binary |
| .RS |
| .PP |
| Associativity: Left |
| .PP |
| Description: \f[B]boolean and\f[R] |
| .RE |
| .TP |
| \f[B]||\f[R] |
| Type: Binary |
| .RS |
| .PP |
| Associativity: Left |
| .PP |
| Description: \f[B]boolean or\f[R] |
| .RE |
| .PP |
| The operators will be described in more detail below. |
| .TP |
| \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. |
| .RS |
| .PP |
| The prefix versions of these operators are more efficient; use them |
| where possible. |
| .RE |
| .TP |
| \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. |
| .TP |
| \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. |
| .RS |
| .PP |
| This is a \f[B]non-portable extension\f[R]. |
| .RE |
| .TP |
| \f[B]$\f[R] |
| The \f[B]truncation\f[R] operator returns a copy of the given expression |
| with all of its \f[I]scale\f[R] removed. |
| .RS |
| .PP |
| This is a \f[B]non-portable extension\f[R]. |
| .RE |
| .TP |
| \f[B]\[at]\f[R] |
| The \f[B]set precision\f[R] operator takes two expressions and returns a |
| copy of the first with its \f[I]scale\f[R] equal to the value of the |
| second expression. |
| That could either mean that the number is returned without change (if |
| the \f[I]scale\f[R] of the first expression matches the value of the |
| second expression), extended (if it is less), or truncated (if it is |
| more). |
| .RS |
| .PP |
| The second expression must be an integer (no \f[I]scale\f[R]) and |
| non-negative. |
| .PP |
| This is a \f[B]non-portable extension\f[R]. |
| .RE |
| .TP |
| \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]. |
| .RS |
| .PP |
| The second expression must be an integer (no \f[I]scale\f[R]), and if it |
| is negative, the first value must be non-zero. |
| .RE |
| .TP |
| \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. |
| .TP |
| \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]. |
| .RS |
| .PP |
| The second expression must be non-zero. |
| .RE |
| .TP |
| \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]. |
| .RS |
| .PP |
| The second expression must be non-zero. |
| .RE |
| .TP |
| \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]. |
| .TP |
| \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]. |
| .TP |
| \f[B]<<\f[R] |
| The \f[B]left shift\f[R] operator takes two expressions, \f[B]a\f[R] and |
| \f[B]b\f[R], and returns a copy of the value of \f[B]a\f[R] with its |
| decimal point moved \f[B]b\f[R] places to the right. |
| .RS |
| .PP |
| The second expression must be an integer (no \f[I]scale\f[R]) and |
| non-negative. |
| .PP |
| This is a \f[B]non-portable extension\f[R]. |
| .RE |
| .TP |
| \f[B]>>\f[R] |
| The \f[B]right shift\f[R] operator takes two expressions, \f[B]a\f[R] |
| and \f[B]b\f[R], and returns a copy of the value of \f[B]a\f[R] with its |
| decimal point moved \f[B]b\f[R] places to the left. |
| .RS |
| .PP |
| The second expression must be an integer (no \f[I]scale\f[R]) and |
| non-negative. |
| .PP |
| This is a \f[B]non-portable extension\f[R]. |
| .RE |
| .TP |
| \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]/=\f[R] \f[B]%=\f[R] \f[B]\[ha]=\f[R] \f[B]\[at]=\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). |
| .RS |
| .PP |
| For \f[B]=\f[R], \f[B]b\f[R] is copied and the result is assigned to |
| \f[B]a\f[R]. |
| For all others, \f[B]a\f[R] and \f[B]b\f[R] are applied as operands to |
| the corresponding arithmetic operator and the result is assigned to |
| \f[B]a\f[R]. |
| .PP |
| The \f[B]assignment\f[R] operators that correspond to operators that are |
| extensions are themselves \f[B]non-portable extensions\f[R]. |
| .RE |
| .TP |
| \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]. |
| .RS |
| .PP |
| Note that unlike in C, these operators have a lower precedence than the |
| \f[B]assignment\f[R] operators, which means that \f[B]a=b>c\f[R] is |
| interpreted as \f[B](a=b)>c\f[R]. |
| .PP |
| 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 \f[B]non-portable extension\f[R]. |
| .RE |
| .TP |
| \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. |
| .RS |
| .PP |
| This is \f[I]not\f[R] a short-circuit operator. |
| .PP |
| This is a \f[B]non-portable extension\f[R]. |
| .RE |
| .TP |
| \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. |
| .RS |
| .PP |
| This is \f[I]not\f[R] a short-circuit operator. |
| .PP |
| This is a \f[B]non-portable extension\f[R]. |
| .RE |
| .SS Statements |
| .PP |
| The following items are statements: |
| .IP " 1." 4 |
| \f[B]E\f[R] |
| .IP " 2." 4 |
| \f[B]{\f[R] \f[B]S\f[R] \f[B];\f[R] \&... \f[B];\f[R] \f[B]S\f[R] |
| \f[B]}\f[R] |
| .IP " 3." 4 |
| \f[B]if\f[R] \f[B](\f[R] \f[B]E\f[R] \f[B])\f[R] \f[B]S\f[R] |
| .IP " 4." 4 |
| \f[B]if\f[R] \f[B](\f[R] \f[B]E\f[R] \f[B])\f[R] \f[B]S\f[R] |
| \f[B]else\f[R] \f[B]S\f[R] |
| .IP " 5." 4 |
| \f[B]while\f[R] \f[B](\f[R] \f[B]E\f[R] \f[B])\f[R] \f[B]S\f[R] |
| .IP " 6." 4 |
| \f[B]for\f[R] \f[B](\f[R] \f[B]E\f[R] \f[B];\f[R] \f[B]E\f[R] |
| \f[B];\f[R] \f[B]E\f[R] \f[B])\f[R] \f[B]S\f[R] |
| .IP " 7." 4 |
| An empty statement |
| .IP " 8." 4 |
| \f[B]break\f[R] |
| .IP " 9." 4 |
| \f[B]continue\f[R] |
| .IP "10." 4 |
| \f[B]quit\f[R] |
| .IP "11." 4 |
| \f[B]halt\f[R] |
| .IP "12." 4 |
| \f[B]limits\f[R] |
| .IP "13." 4 |
| A string of characters, enclosed in double quotes |
| .IP "14." 4 |
| \f[B]print\f[R] \f[B]E\f[R] \f[B],\f[R] \&... \f[B],\f[R] \f[B]E\f[R] |
| .IP "15." 4 |
| \f[B]I()\f[R], \f[B]I(E)\f[R], \f[B]I(E, E)\f[R], and so on, where |
| \f[B]I\f[R] is an identifier for a \f[B]void\f[R] function (see the |
| \f[I]Void Functions\f[R] subsection of the \f[B]FUNCTIONS\f[R] section). |
| The \f[B]E\f[R] argument(s) may also be arrays of the form |
| \f[B]I[]\f[R], which will automatically be turned into array references |
| (see the \f[I]Array References\f[R] subsection of the |
| \f[B]FUNCTIONS\f[R] section) if the corresponding parameter in the |
| function definition is an array reference. |
| .PP |
| Numbers 4, 9, 11, 12, 14, and 15 are \f[B]non-portable extensions\f[R]. |
| .PP |
| 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]. |
| .PP |
| 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. |
| .PP |
| 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. |
| .PP |
| The \f[B]if\f[R] \f[B]else\f[R] statement does the same thing as in C. |
| .PP |
| 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). |
| .PP |
| 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.) |
| .PP |
| 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. |
| .PP |
| An expression by itself is evaluated and printed, followed by a newline. |
| .PP |
| Both scientific notation and engineering notation are available for |
| printing the results of expressions. |
| Scientific notation is activated by assigning \f[B]0\f[R] to |
| \f[B]obase\f[R], and engineering notation is activated by assigning |
| \f[B]1\f[R] to \f[B]obase\f[R]. |
| To deactivate them, just assign a different value to \f[B]obase\f[R]. |
| .PP |
| Scientific notation and engineering notation are disabled if bc(1) is |
| run with either the \f[B]-s\f[R] or \f[B]-w\f[R] command-line options |
| (or equivalents). |
| .PP |
| Printing numbers in scientific notation and/or engineering notation is a |
| \f[B]non-portable extension\f[R]. |
| .SS Print Statement |
| .PP |
| 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: |
| .PP |
| \f[B]\[rs]a\f[R]: \f[B]\[rs]a\f[R] |
| .PP |
| \f[B]\[rs]b\f[R]: \f[B]\[rs]b\f[R] |
| .PP |
| \f[B]\[rs]\[rs]\f[R]: \f[B]\[rs]\f[R] |
| .PP |
| \f[B]\[rs]e\f[R]: \f[B]\[rs]\f[R] |
| .PP |
| \f[B]\[rs]f\f[R]: \f[B]\[rs]f\f[R] |
| .PP |
| \f[B]\[rs]n\f[R]: \f[B]\[rs]n\f[R] |
| .PP |
| \f[B]\[rs]q\f[R]: \f[B]\[lq]\f[R] |
| .PP |
| \f[B]\[rs]r\f[R]: \f[B]\[rs]r\f[R] |
| .PP |
| \f[B]\[rs]t\f[R]: \f[B]\[rs]t\f[R] |
| .PP |
| Any other character following a backslash causes the backslash and |
| character to be printed as-is. |
| .PP |
| Any non-string expression in a print statement shall be assigned to |
| \f[B]last\f[R], like any other expression that is printed. |
| .SS Order of Evaluation |
| .PP |
| 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 |
| .IP |
| .nf |
| \f[C] |
| a[i++] = i++ |
| \f[R] |
| .fi |
| .PP |
| 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. |
| .PP |
| 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 |
| .IP |
| .nf |
| \f[C] |
| x(i++, i++) |
| \f[R] |
| .fi |
| .PP |
| 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. |
| .SH FUNCTIONS |
| .PP |
| Function definitions are as follows: |
| .IP |
| .nf |
| \f[C] |
| define I(I,...,I){ |
| auto I,...,I |
| S;...;S |
| return(E) |
| } |
| \f[R] |
| .fi |
| .PP |
| 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. |
| .PP |
| 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. |
| .PP |
| As a \f[B]non-portable extension\f[R], the return statement may also be |
| in one of the following forms: |
| .IP "1." 3 |
| \f[B]return\f[R] |
| .IP "2." 3 |
| \f[B]return\f[R] \f[B](\f[R] \f[B])\f[R] |
| .IP "3." 3 |
| \f[B]return\f[R] \f[B]E\f[R] |
| .PP |
| 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). |
| .SS Void Functions |
| .PP |
| Functions can also be \f[B]void\f[R] functions, defined as follows: |
| .IP |
| .nf |
| \f[C] |
| define void I(I,...,I){ |
| auto I,...,I |
| S;...;S |
| return |
| } |
| \f[R] |
| .fi |
| .PP |
| They can only be used as standalone expressions, where such an |
| expression would be printed alone, except in a print statement. |
| .PP |
| Void functions can only use the first two \f[B]return\f[R] statements |
| listed above. |
| They can also omit the return statement entirely. |
| .PP |
| 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. |
| .PP |
| This is a \f[B]non-portable extension\f[R]. |
| .SS Array References |
| .PP |
| For any array in the parameter list, if the array is declared in the |
| form |
| .IP |
| .nf |
| \f[C] |
| *I[] |
| \f[R] |
| .fi |
| .PP |
| 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. |
| .PP |
| Other than this, all function arguments are passed by value. |
| .PP |
| This is a \f[B]non-portable extension\f[R]. |
| .SH LIBRARY |
| .PP |
| All of the functions below, including the functions in the extended math |
| library (see the \f[I]Extended Library\f[R] subsection below), are |
| available when the \f[B]-l\f[R] or \f[B]--mathlib\f[R] command-line |
| flags are given, except that the extended math library is not available |
| when the \f[B]-s\f[R] option, the \f[B]-w\f[R] option, or equivalents |
| are given. |
| .SS Standard Library |
| .PP |
| The |
| standard (https://pubs.opengroup.org/onlinepubs/9699919799/utilities/bc.html) |
| defines the following functions for the math library: |
| .TP |
| \f[B]s(x)\f[R] |
| Returns the sine of \f[B]x\f[R], which is assumed to be in radians. |
| .RS |
| .PP |
| This is a transcendental function (see the \f[I]Transcendental |
| Functions\f[R] subsection below). |
| .RE |
| .TP |
| \f[B]c(x)\f[R] |
| Returns the cosine of \f[B]x\f[R], which is assumed to be in radians. |
| .RS |
| .PP |
| This is a transcendental function (see the \f[I]Transcendental |
| Functions\f[R] subsection below). |
| .RE |
| .TP |
| \f[B]a(x)\f[R] |
| Returns the arctangent of \f[B]x\f[R], in radians. |
| .RS |
| .PP |
| This is a transcendental function (see the \f[I]Transcendental |
| Functions\f[R] subsection below). |
| .RE |
| .TP |
| \f[B]l(x)\f[R] |
| Returns the natural logarithm of \f[B]x\f[R]. |
| .RS |
| .PP |
| This is a transcendental function (see the \f[I]Transcendental |
| Functions\f[R] subsection below). |
| .RE |
| .TP |
| \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]. |
| .RS |
| .PP |
| This is a transcendental function (see the \f[I]Transcendental |
| Functions\f[R] subsection below). |
| .RE |
| .TP |
| \f[B]j(x, n)\f[R] |
| Returns the bessel integer order \f[B]n\f[R] (truncated) of \f[B]x\f[R]. |
| .RS |
| .PP |
| This is a transcendental function (see the \f[I]Transcendental |
| Functions\f[R] subsection below). |
| .RE |
| .SS Extended Library |
| .PP |
| The extended library is \f[I]not\f[R] loaded when the |
| \f[B]-s\f[R]/\f[B]--standard\f[R] or \f[B]-w\f[R]/\f[B]--warn\f[R] |
| options are given since they are not part of the library defined by the |
| standard (https://pubs.opengroup.org/onlinepubs/9699919799/utilities/bc.html). |
| .PP |
| The extended library is a \f[B]non-portable extension\f[R]. |
| .TP |
| \f[B]p(x, y)\f[R] |
| Calculates \f[B]x\f[R] to the power of \f[B]y\f[R], even if \f[B]y\f[R] |
| is not an integer, and returns the result to the current |
| \f[B]scale\f[R]. |
| .RS |
| .PP |
| It is an error if \f[B]y\f[R] is negative and \f[B]x\f[R] is |
| \f[B]0\f[R]. |
| .PP |
| This is a transcendental function (see the \f[I]Transcendental |
| Functions\f[R] subsection below). |
| .RE |
| .TP |
| \f[B]r(x, p)\f[R] |
| Returns \f[B]x\f[R] rounded to \f[B]p\f[R] decimal places according to |
| the rounding mode round half away from |
| \f[B]0\f[R] (https://en.wikipedia.org/wiki/Rounding#Round_half_away_from_zero). |
| .TP |
| \f[B]ceil(x, p)\f[R] |
| Returns \f[B]x\f[R] rounded to \f[B]p\f[R] decimal places according to |
| the rounding mode round away from |
| \f[B]0\f[R] (https://en.wikipedia.org/wiki/Rounding#Rounding_away_from_zero). |
| .TP |
| \f[B]f(x)\f[R] |
| Returns the factorial of the truncated absolute value of \f[B]x\f[R]. |
| .TP |
| \f[B]perm(n, k)\f[R] |
| Returns the permutation of the truncated absolute value of \f[B]n\f[R] |
| of the truncated absolute value of \f[B]k\f[R], if \f[B]k <= n\f[R]. |
| If not, it returns \f[B]0\f[R]. |
| .TP |
| \f[B]comb(n, k)\f[R] |
| Returns the combination of the truncated absolute value of \f[B]n\f[R] |
| of the truncated absolute value of \f[B]k\f[R], if \f[B]k <= n\f[R]. |
| If not, it returns \f[B]0\f[R]. |
| .TP |
| \f[B]l2(x)\f[R] |
| Returns the logarithm base \f[B]2\f[R] of \f[B]x\f[R]. |
| .RS |
| .PP |
| This is a transcendental function (see the \f[I]Transcendental |
| Functions\f[R] subsection below). |
| .RE |
| .TP |
| \f[B]l10(x)\f[R] |
| Returns the logarithm base \f[B]10\f[R] of \f[B]x\f[R]. |
| .RS |
| .PP |
| This is a transcendental function (see the \f[I]Transcendental |
| Functions\f[R] subsection below). |
| .RE |
| .TP |
| \f[B]log(x, b)\f[R] |
| Returns the logarithm base \f[B]b\f[R] of \f[B]x\f[R]. |
| .RS |
| .PP |
| This is a transcendental function (see the \f[I]Transcendental |
| Functions\f[R] subsection below). |
| .RE |
| .TP |
| \f[B]cbrt(x)\f[R] |
| Returns the cube root of \f[B]x\f[R]. |
| .TP |
| \f[B]root(x, n)\f[R] |
| Calculates the truncated value of \f[B]n\f[R], \f[B]r\f[R], and returns |
| the \f[B]r\f[R]th root of \f[B]x\f[R] to the current \f[B]scale\f[R]. |
| .RS |
| .PP |
| If \f[B]r\f[R] is \f[B]0\f[R] or negative, this raises an error and |
| causes bc(1) to reset (see the \f[B]RESET\f[R] section). |
| It also raises an error and causes bc(1) to reset if \f[B]r\f[R] is even |
| and \f[B]x\f[R] is negative. |
| .RE |
| .TP |
| \f[B]pi(p)\f[R] |
| Returns \f[B]pi\f[R] to \f[B]p\f[R] decimal places. |
| .RS |
| .PP |
| This is a transcendental function (see the \f[I]Transcendental |
| Functions\f[R] subsection below). |
| .RE |
| .TP |
| \f[B]t(x)\f[R] |
| Returns the tangent of \f[B]x\f[R], which is assumed to be in radians. |
| .RS |
| .PP |
| This is a transcendental function (see the \f[I]Transcendental |
| Functions\f[R] subsection below). |
| .RE |
| .TP |
| \f[B]a2(y, x)\f[R] |
| Returns the arctangent of \f[B]y/x\f[R], in radians. |
| If both \f[B]y\f[R] and \f[B]x\f[R] are equal to \f[B]0\f[R], it raises |
| an error and causes bc(1) to reset (see the \f[B]RESET\f[R] section). |
| Otherwise, if \f[B]x\f[R] is greater than \f[B]0\f[R], it returns |
| \f[B]a(y/x)\f[R]. |
| If \f[B]x\f[R] is less than \f[B]0\f[R], and \f[B]y\f[R] is greater than |
| or equal to \f[B]0\f[R], it returns \f[B]a(y/x)+pi\f[R]. |
| If \f[B]x\f[R] is less than \f[B]0\f[R], and \f[B]y\f[R] is less than |
| \f[B]0\f[R], it returns \f[B]a(y/x)-pi\f[R]. |
| If \f[B]x\f[R] is equal to \f[B]0\f[R], and \f[B]y\f[R] is greater than |
| \f[B]0\f[R], it returns \f[B]pi/2\f[R]. |
| If \f[B]x\f[R] is equal to \f[B]0\f[R], and \f[B]y\f[R] is less than |
| \f[B]0\f[R], it returns \f[B]-pi/2\f[R]. |
| .RS |
| .PP |
| This function is the same as the \f[B]atan2()\f[R] function in many |
| programming languages. |
| .PP |
| This is a transcendental function (see the \f[I]Transcendental |
| Functions\f[R] subsection below). |
| .RE |
| .TP |
| \f[B]sin(x)\f[R] |
| Returns the sine of \f[B]x\f[R], which is assumed to be in radians. |
| .RS |
| .PP |
| This is an alias of \f[B]s(x)\f[R]. |
| .PP |
| This is a transcendental function (see the \f[I]Transcendental |
| Functions\f[R] subsection below). |
| .RE |
| .TP |
| \f[B]cos(x)\f[R] |
| Returns the cosine of \f[B]x\f[R], which is assumed to be in radians. |
| .RS |
| .PP |
| This is an alias of \f[B]c(x)\f[R]. |
| .PP |
| This is a transcendental function (see the \f[I]Transcendental |
| Functions\f[R] subsection below). |
| .RE |
| .TP |
| \f[B]tan(x)\f[R] |
| Returns the tangent of \f[B]x\f[R], which is assumed to be in radians. |
| .RS |
| .PP |
| If \f[B]x\f[R] is equal to \f[B]1\f[R] or \f[B]-1\f[R], this raises an |
| error and causes bc(1) to reset (see the \f[B]RESET\f[R] section). |
| .PP |
| This is an alias of \f[B]t(x)\f[R]. |
| .PP |
| This is a transcendental function (see the \f[I]Transcendental |
| Functions\f[R] subsection below). |
| .RE |
| .TP |
| \f[B]atan(x)\f[R] |
| Returns the arctangent of \f[B]x\f[R], in radians. |
| .RS |
| .PP |
| This is an alias of \f[B]a(x)\f[R]. |
| .PP |
| This is a transcendental function (see the \f[I]Transcendental |
| Functions\f[R] subsection below). |
| .RE |
| .TP |
| \f[B]atan2(y, x)\f[R] |
| Returns the arctangent of \f[B]y/x\f[R], in radians. |
| If both \f[B]y\f[R] and \f[B]x\f[R] are equal to \f[B]0\f[R], it raises |
| an error and causes bc(1) to reset (see the \f[B]RESET\f[R] section). |
| Otherwise, if \f[B]x\f[R] is greater than \f[B]0\f[R], it returns |
| \f[B]a(y/x)\f[R]. |
| If \f[B]x\f[R] is less than \f[B]0\f[R], and \f[B]y\f[R] is greater than |
| or equal to \f[B]0\f[R], it returns \f[B]a(y/x)+pi\f[R]. |
| If \f[B]x\f[R] is less than \f[B]0\f[R], and \f[B]y\f[R] is less than |
| \f[B]0\f[R], it returns \f[B]a(y/x)-pi\f[R]. |
| If \f[B]x\f[R] is equal to \f[B]0\f[R], and \f[B]y\f[R] is greater than |
| \f[B]0\f[R], it returns \f[B]pi/2\f[R]. |
| If \f[B]x\f[R] is equal to \f[B]0\f[R], and \f[B]y\f[R] is less than |
| \f[B]0\f[R], it returns \f[B]-pi/2\f[R]. |
| .RS |
| .PP |
| This function is the same as the \f[B]atan2()\f[R] function in many |
| programming languages. |
| .PP |
| This is an alias of \f[B]a2(y, x)\f[R]. |
| .PP |
| This is a transcendental function (see the \f[I]Transcendental |
| Functions\f[R] subsection below). |
| .RE |
| .TP |
| \f[B]r2d(x)\f[R] |
| Converts \f[B]x\f[R] from radians to degrees and returns the result. |
| .RS |
| .PP |
| This is a transcendental function (see the \f[I]Transcendental |
| Functions\f[R] subsection below). |
| .RE |
| .TP |
| \f[B]d2r(x)\f[R] |
| Converts \f[B]x\f[R] from degrees to radians and returns the result. |
| .RS |
| .PP |
| This is a transcendental function (see the \f[I]Transcendental |
| Functions\f[R] subsection below). |
| .RE |
| .TP |
| \f[B]frand(p)\f[R] |
| Generates a pseudo-random number between \f[B]0\f[R] (inclusive) and |
| \f[B]1\f[R] (exclusive) with the number of decimal digits after the |
| decimal point equal to the truncated absolute value of \f[B]p\f[R]. |
| If \f[B]p\f[R] is not \f[B]0\f[R], then calling this function will |
| change the value of \f[B]seed\f[R]. |
| If \f[B]p\f[R] is \f[B]0\f[R], then \f[B]0\f[R] is returned, and |
| \f[B]seed\f[R] is \f[I]not\f[R] changed. |
| .TP |
| \f[B]ifrand(i, p)\f[R] |
| Generates a pseudo-random number that is between \f[B]0\f[R] (inclusive) |
| and the truncated absolute value of \f[B]i\f[R] (exclusive) with the |
| number of decimal digits after the decimal point equal to the truncated |
| absolute value of \f[B]p\f[R]. |
| If the absolute value of \f[B]i\f[R] is greater than or equal to |
| \f[B]2\f[R], and \f[B]p\f[R] is not \f[B]0\f[R], then calling this |
| function will change the value of \f[B]seed\f[R]; otherwise, \f[B]0\f[R] |
| is returned and \f[B]seed\f[R] is not changed. |
| .TP |
| \f[B]srand(x)\f[R] |
| Returns \f[B]x\f[R] with its sign flipped with probability |
| \f[B]0.5\f[R]. |
| In other words, it randomizes the sign of \f[B]x\f[R]. |
| .TP |
| \f[B]brand()\f[R] |
| Returns a random boolean value (either \f[B]0\f[R] or \f[B]1\f[R]). |
| .TP |
| \f[B]ubytes(x)\f[R] |
| Returns the numbers of unsigned integer bytes required to hold the |
| truncated absolute value of \f[B]x\f[R]. |
| .TP |
| \f[B]sbytes(x)\f[R] |
| Returns the numbers of signed, two\[cq]s-complement integer bytes |
| required to hold the truncated value of \f[B]x\f[R]. |
| .TP |
| \f[B]hex(x)\f[R] |
| Outputs the hexadecimal (base \f[B]16\f[R]) representation of |
| \f[B]x\f[R]. |
| .RS |
| .PP |
| This is a \f[B]void\f[R] function (see the \f[I]Void Functions\f[R] |
| subsection of the \f[B]FUNCTIONS\f[R] section). |
| .RE |
| .TP |
| \f[B]binary(x)\f[R] |
| Outputs the binary (base \f[B]2\f[R]) representation of \f[B]x\f[R]. |
| .RS |
| .PP |
| This is a \f[B]void\f[R] function (see the \f[I]Void Functions\f[R] |
| subsection of the \f[B]FUNCTIONS\f[R] section). |
| .RE |
| .TP |
| \f[B]output(x, b)\f[R] |
| Outputs the base \f[B]b\f[R] representation of \f[B]x\f[R]. |
| .RS |
| .PP |
| This is a \f[B]void\f[R] function (see the \f[I]Void Functions\f[R] |
| subsection of the \f[B]FUNCTIONS\f[R] section). |
| .RE |
| .TP |
| \f[B]uint(x)\f[R] |
| Outputs the representation, in binary and hexadecimal, of \f[B]x\f[R] as |
| an unsigned integer in as few power of two bytes as possible. |
| Both outputs are split into bytes separated by spaces. |
| .RS |
| .PP |
| If \f[B]x\f[R] is not an integer or is negative, an error message is |
| printed instead, but bc(1) is not reset (see the \f[B]RESET\f[R] |
| section). |
| .PP |
| This is a \f[B]void\f[R] function (see the \f[I]Void Functions\f[R] |
| subsection of the \f[B]FUNCTIONS\f[R] section). |
| .RE |
| .TP |
| \f[B]int(x)\f[R] |
| Outputs the representation, in binary and hexadecimal, of \f[B]x\f[R] as |
| a signed, two\[cq]s-complement integer in as few power of two bytes as |
| possible. |
| Both outputs are split into bytes separated by spaces. |
| .RS |
| .PP |
| If \f[B]x\f[R] is not an integer, an error message is printed instead, |
| but bc(1) is not reset (see the \f[B]RESET\f[R] section). |
| .PP |
| This is a \f[B]void\f[R] function (see the \f[I]Void Functions\f[R] |
| subsection of the \f[B]FUNCTIONS\f[R] section). |
| .RE |
| .TP |
| \f[B]uintn(x, n)\f[R] |
| Outputs the representation, in binary and hexadecimal, of \f[B]x\f[R] as |
| an unsigned integer in \f[B]n\f[R] bytes. |
| Both outputs are split into bytes separated by spaces. |
| .RS |
| .PP |
| If \f[B]x\f[R] is not an integer, is negative, or cannot fit into |
| \f[B]n\f[R] bytes, an error message is printed instead, but bc(1) is not |
| reset (see the \f[B]RESET\f[R] section). |
| .PP |
| This is a \f[B]void\f[R] function (see the \f[I]Void Functions\f[R] |
| subsection of the \f[B]FUNCTIONS\f[R] section). |
| .RE |
| .TP |
| \f[B]intn(x, n)\f[R] |
| Outputs the representation, in binary and hexadecimal, of \f[B]x\f[R] as |
| a signed, two\[cq]s-complement integer in \f[B]n\f[R] bytes. |
| Both outputs are split into bytes separated by spaces. |
| .RS |
| .PP |
| If \f[B]x\f[R] is not an integer or cannot fit into \f[B]n\f[R] bytes, |
| an error message is printed instead, but bc(1) is not reset (see the |
| \f[B]RESET\f[R] section). |
| .PP |
| This is a \f[B]void\f[R] function (see the \f[I]Void Functions\f[R] |
| subsection of the \f[B]FUNCTIONS\f[R] section). |
| .RE |
| .TP |
| \f[B]uint8(x)\f[R] |
| Outputs the representation, in binary and hexadecimal, of \f[B]x\f[R] as |
| an unsigned integer in \f[B]1\f[R] byte. |
| Both outputs are split into bytes separated by spaces. |
| .RS |
| .PP |
| If \f[B]x\f[R] is not an integer, is negative, or cannot fit into |
| \f[B]1\f[R] byte, an error message is printed instead, but bc(1) is not |
| reset (see the \f[B]RESET\f[R] section). |
| .PP |
| This is a \f[B]void\f[R] function (see the \f[I]Void Functions\f[R] |
| subsection of the \f[B]FUNCTIONS\f[R] section). |
| .RE |
| .TP |
| \f[B]int8(x)\f[R] |
| Outputs the representation, in binary and hexadecimal, of \f[B]x\f[R] as |
| a signed, two\[cq]s-complement integer in \f[B]1\f[R] byte. |
| Both outputs are split into bytes separated by spaces. |
| .RS |
| .PP |
| If \f[B]x\f[R] is not an integer or cannot fit into \f[B]1\f[R] byte, an |
| error message is printed instead, but bc(1) is not reset (see the |
| \f[B]RESET\f[R] section). |
| .PP |
| This is a \f[B]void\f[R] function (see the \f[I]Void Functions\f[R] |
| subsection of the \f[B]FUNCTIONS\f[R] section). |
| .RE |
| .TP |
| \f[B]uint16(x)\f[R] |
| Outputs the representation, in binary and hexadecimal, of \f[B]x\f[R] as |
| an unsigned integer in \f[B]2\f[R] bytes. |
| Both outputs are split into bytes separated by spaces. |
| .RS |
| .PP |
| If \f[B]x\f[R] is not an integer, is negative, or cannot fit into |
| \f[B]2\f[R] bytes, an error message is printed instead, but bc(1) is not |
| reset (see the \f[B]RESET\f[R] section). |
| .PP |
| This is a \f[B]void\f[R] function (see the \f[I]Void Functions\f[R] |
| subsection of the \f[B]FUNCTIONS\f[R] section). |
| .RE |
| .TP |
| \f[B]int16(x)\f[R] |
| Outputs the representation, in binary and hexadecimal, of \f[B]x\f[R] as |
| a signed, two\[cq]s-complement integer in \f[B]2\f[R] bytes. |
| Both outputs are split into bytes separated by spaces. |
| .RS |
| .PP |
| If \f[B]x\f[R] is not an integer or cannot fit into \f[B]2\f[R] bytes, |
| an error message is printed instead, but bc(1) is not reset (see the |
| \f[B]RESET\f[R] section). |
| .PP |
| This is a \f[B]void\f[R] function (see the \f[I]Void Functions\f[R] |
| subsection of the \f[B]FUNCTIONS\f[R] section). |
| .RE |
| .TP |
| \f[B]uint32(x)\f[R] |
| Outputs the representation, in binary and hexadecimal, of \f[B]x\f[R] as |
| an unsigned integer in \f[B]4\f[R] bytes. |
| Both outputs are split into bytes separated by spaces. |
| .RS |
| .PP |
| If \f[B]x\f[R] is not an integer, is negative, or cannot fit into |
| \f[B]4\f[R] bytes, an error message is printed instead, but bc(1) is not |
| reset (see the \f[B]RESET\f[R] section). |
| .PP |
| This is a \f[B]void\f[R] function (see the \f[I]Void Functions\f[R] |
| subsection of the \f[B]FUNCTIONS\f[R] section). |
| .RE |
| .TP |
| \f[B]int32(x)\f[R] |
| Outputs the representation, in binary and hexadecimal, of \f[B]x\f[R] as |
| a signed, two\[cq]s-complement integer in \f[B]4\f[R] bytes. |
| Both outputs are split into bytes separated by spaces. |
| .RS |
| .PP |
| If \f[B]x\f[R] is not an integer or cannot fit into \f[B]4\f[R] bytes, |
| an error message is printed instead, but bc(1) is not reset (see the |
| \f[B]RESET\f[R] section). |
| .PP |
| This is a \f[B]void\f[R] function (see the \f[I]Void Functions\f[R] |
| subsection of the \f[B]FUNCTIONS\f[R] section). |
| .RE |
| .TP |
| \f[B]uint64(x)\f[R] |
| Outputs the representation, in binary and hexadecimal, of \f[B]x\f[R] as |
| an unsigned integer in \f[B]8\f[R] bytes. |
| Both outputs are split into bytes separated by spaces. |
| .RS |
| .PP |
| If \f[B]x\f[R] is not an integer, is negative, or cannot fit into |
| \f[B]8\f[R] bytes, an error message is printed instead, but bc(1) is not |
| reset (see the \f[B]RESET\f[R] section). |
| .PP |
| This is a \f[B]void\f[R] function (see the \f[I]Void Functions\f[R] |
| subsection of the \f[B]FUNCTIONS\f[R] section). |
| .RE |
| .TP |
| \f[B]int64(x)\f[R] |
| Outputs the representation, in binary and hexadecimal, of \f[B]x\f[R] as |
| a signed, two\[cq]s-complement integer in \f[B]8\f[R] bytes. |
| Both outputs are split into bytes separated by spaces. |
| .RS |
| .PP |
| If \f[B]x\f[R] is not an integer or cannot fit into \f[B]8\f[R] bytes, |
| an error message is printed instead, but bc(1) is not reset (see the |
| \f[B]RESET\f[R] section). |
| .PP |
| This is a \f[B]void\f[R] function (see the \f[I]Void Functions\f[R] |
| subsection of the \f[B]FUNCTIONS\f[R] section). |
| .RE |
| .TP |
| \f[B]hex_uint(x, n)\f[R] |
| Outputs the representation of the truncated absolute value of |
| \f[B]x\f[R] as an unsigned integer in hexadecimal using \f[B]n\f[R] |
| bytes. |
| Not all of the value will be output if \f[B]n\f[R] is too small. |
| .RS |
| .PP |
| This is a \f[B]void\f[R] function (see the \f[I]Void Functions\f[R] |
| subsection of the \f[B]FUNCTIONS\f[R] section). |
| .RE |
| .TP |
| \f[B]binary_uint(x, n)\f[R] |
| Outputs the representation of the truncated absolute value of |
| \f[B]x\f[R] as an unsigned integer in binary using \f[B]n\f[R] bytes. |
| Not all of the value will be output if \f[B]n\f[R] is too small. |
| .RS |
| .PP |
| This is a \f[B]void\f[R] function (see the \f[I]Void Functions\f[R] |
| subsection of the \f[B]FUNCTIONS\f[R] section). |
| .RE |
| .TP |
| \f[B]output_uint(x, n)\f[R] |
| Outputs the representation of the truncated absolute value of |
| \f[B]x\f[R] as an unsigned integer in the current \f[B]obase\f[R] (see |
| the \f[B]SYNTAX\f[R] section) using \f[B]n\f[R] bytes. |
| Not all of the value will be output if \f[B]n\f[R] is too small. |
| .RS |
| .PP |
| This is a \f[B]void\f[R] function (see the \f[I]Void Functions\f[R] |
| subsection of the \f[B]FUNCTIONS\f[R] section). |
| .RE |
| .TP |
| \f[B]output_byte(x, i)\f[R] |
| Outputs byte \f[B]i\f[R] of the truncated absolute value of \f[B]x\f[R], |
| where \f[B]0\f[R] is the least significant byte and \f[B]number_of_bytes |
| - 1\f[R] is the most significant byte. |
| .RS |
| .PP |
| This is a \f[B]void\f[R] function (see the \f[I]Void Functions\f[R] |
| subsection of the \f[B]FUNCTIONS\f[R] section). |
| .RE |
| .SS Transcendental Functions |
| .PP |
| 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 this |
| article (https://people.eecs.berkeley.edu/~wkahan/LOG10HAF.TXT) explains |
| why it is impossible and unnecessary to calculate exact results for the |
| transcendental functions. |
| .PP |
| 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. |
| .PP |
| The transcendental functions in the standard math library are: |
| .IP \[bu] 2 |
| \f[B]s(x)\f[R] |
| .IP \[bu] 2 |
| \f[B]c(x)\f[R] |
| .IP \[bu] 2 |
| \f[B]a(x)\f[R] |
| .IP \[bu] 2 |
| \f[B]l(x)\f[R] |
| .IP \[bu] 2 |
| \f[B]e(x)\f[R] |
| .IP \[bu] 2 |
| \f[B]j(x, n)\f[R] |
| .PP |
| The transcendental functions in the extended math library are: |
| .IP \[bu] 2 |
| \f[B]l2(x)\f[R] |
| .IP \[bu] 2 |
| \f[B]l10(x)\f[R] |
| .IP \[bu] 2 |
| \f[B]log(x, b)\f[R] |
| .IP \[bu] 2 |
| \f[B]pi(p)\f[R] |
| .IP \[bu] 2 |
| \f[B]t(x)\f[R] |
| .IP \[bu] 2 |
| \f[B]a2(y, x)\f[R] |
| .IP \[bu] 2 |
| \f[B]sin(x)\f[R] |
| .IP \[bu] 2 |
| \f[B]cos(x)\f[R] |
| .IP \[bu] 2 |
| \f[B]tan(x)\f[R] |
| .IP \[bu] 2 |
| \f[B]atan(x)\f[R] |
| .IP \[bu] 2 |
| \f[B]atan2(y, x)\f[R] |
| .IP \[bu] 2 |
| \f[B]r2d(x)\f[R] |
| .IP \[bu] 2 |
| \f[B]d2r(x)\f[R] |
| .SH RESET |
| .PP |
| 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. |
| .PP |
| 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. |
| .PP |
| 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. |
| .PP |
| 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. |
| .SH PERFORMANCE |
| .PP |
| 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. |
| .PP |
| 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]. |
| .PP |
| 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. |
| .PP |
| 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. |
| .SH LIMITS |
| .PP |
| The following are the limits on bc(1): |
| .TP |
| \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). |
| .TP |
| \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]. |
| .TP |
| \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]. |
| .TP |
| \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]. |
| .TP |
| \f[B]BC_BASE_MAX\f[R] |
| The maximum output base. |
| Set at \f[B]BC_BASE_POW\f[R]. |
| .TP |
| \f[B]BC_DIM_MAX\f[R] |
| The maximum size of arrays. |
| Set at \f[B]SIZE_MAX-1\f[R]. |
| .TP |
| \f[B]BC_SCALE_MAX\f[R] |
| The maximum \f[B]scale\f[R]. |
| Set at \f[B]BC_OVERFLOW_MAX-1\f[R]. |
| .TP |
| \f[B]BC_STRING_MAX\f[R] |
| The maximum length of strings. |
| Set at \f[B]BC_OVERFLOW_MAX-1\f[R]. |
| .TP |
| \f[B]BC_NAME_MAX\f[R] |
| The maximum length of identifiers. |
| Set at \f[B]BC_OVERFLOW_MAX-1\f[R]. |
| .TP |
| \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]. |
| .TP |
| \f[B]BC_RAND_MAX\f[R] |
| The maximum integer (inclusive) returned by the \f[B]rand()\f[R] |
| operand. |
| Set at \f[B]2\[ha]BC_LONG_BIT-1\f[R]. |
| .TP |
| Exponent |
| The maximum allowable exponent (positive or negative). |
| Set at \f[B]BC_OVERFLOW_MAX\f[R]. |
| .TP |
| Number of vars |
| The maximum number of vars/arrays. |
| Set at \f[B]SIZE_MAX-1\f[R]. |
| .PP |
| The actual values can be queried with the \f[B]limits\f[R] statement. |
| .PP |
| 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. |
| .SH ENVIRONMENT VARIABLES |
| .PP |
| bc(1) recognizes the following environment variables: |
| .TP |
| \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. |
| .TP |
| \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. |
| .RS |
| .PP |
| The code that parses \f[B]BC_ENV_ARGS\f[R] will correctly handle quoted |
| arguments, but it does not understand escape sequences. |
| For example, the string \f[B]\[lq]/home/gavin/some bc file.bc\[rq]\f[R] |
| will be correctly parsed, but the string \f[B]\[lq]/home/gavin/some |
| \[dq]bc\[dq] file.bc\[rq]\f[R] will include the backslashes. |
| .PP |
| The quote parsing will handle either kind of quotes, \f[B]\[cq]\f[R] or |
| \f[B]\[lq]\f[R]. |
| Thus, if you have a file with any number of single quotes in the name, |
| you can use double quotes as the outside quotes, as in \f[B]\[lq]some |
| `bc' file.bc\[rq]\f[R], and vice versa if you have a file with double |
| quotes. |
| However, handling a file with both kinds of quotes in |
| \f[B]BC_ENV_ARGS\f[R] is not supported due to the complexity of the |
| parsing, though such files are still supported on the command-line where |
| the parsing is done by the shell. |
| .RE |
| .TP |
| \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]. |
| .SH EXIT STATUS |
| .PP |
| bc(1) returns the following exit statuses: |
| .TP |
| \f[B]0\f[R] |
| No error. |
| .TP |
| \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. |
| .RS |
| .PP |
| Math errors include divide by \f[B]0\f[R], taking the square root of a |
| negative number, using a negative number as a bound for the |
| pseudo-random number generator, attempting to convert a negative number |
| to a hardware integer, overflow when converting a number to a hardware |
| integer, overflow when calculating the size of a number, and attempting |
| to use a non-integer where an integer is required. |
| .PP |
| Converting to a hardware integer happens for the second operand of the |
| power (\f[B]\[ha]\f[R]), places (\f[B]\[at]\f[R]), left shift |
| (\f[B]<<\f[R]), and right shift (\f[B]>>\f[R]) operators and their |
| corresponding assignment operators. |
| .RE |
| .TP |
| \f[B]2\f[R] |
| A parse error occurred. |
| .RS |
| .PP |
| Parse errors include unexpected \f[B]EOF\f[R], using an invalid |
| character, failing to find the end of a string or comment, using a token |
| where it is invalid, giving an invalid expression, giving an invalid |
| print statement, giving an invalid function definition, attempting to |
| assign to an expression that is not a named expression (see the |
| \f[I]Named Expressions\f[R] subsection of the \f[B]SYNTAX\f[R] section), |
| giving an invalid \f[B]auto\f[R] list, having a duplicate |
| \f[B]auto\f[R]/function parameter, failing to find the end of a code |
| block, attempting to return a value from a \f[B]void\f[R] function, |
| attempting to use a variable as a reference, and using any extensions |
| when the option \f[B]-s\f[R] or any equivalents were given. |
| .RE |
| .TP |
| \f[B]3\f[R] |
| A runtime error occurred. |
| .RS |
| .PP |
| Runtime errors include assigning an invalid number to \f[B]ibase\f[R], |
| \f[B]obase\f[R], or \f[B]scale\f[R]; give a bad expression to a |
| \f[B]read()\f[R] call, calling \f[B]read()\f[R] inside of a |
| \f[B]read()\f[R] call, type errors, passing the wrong number of |
| arguments to functions, attempting to call an undefined function, and |
| attempting to use a \f[B]void\f[R] function call as a value in an |
| expression. |
| .RE |
| .TP |
| \f[B]4\f[R] |
| A fatal error occurred. |
| .RS |
| .PP |
| Fatal errors include memory allocation errors, I/O errors, failing to |
| open files, attempting to use files that do not have only ASCII |
| characters (bc(1) only accepts ASCII characters), attempting to open a |
| directory as a file, and giving invalid command-line options. |
| .RE |
| .PP |
| 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. |
| .PP |
| 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. |
| .PP |
| 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. |
| .SH INTERACTIVE MODE |
| .PP |
| Per the |
| standard (https://pubs.opengroup.org/onlinepubs/9699919799/utilities/bc.html), |
| 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 cases. |
| .PP |
| 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. |
| .SH TTY MODE |
| .PP |
| If \f[B]stdin\f[R], \f[B]stdout\f[R], and \f[B]stderr\f[R] are all |
| connected to a TTY, bc(1) turns on \[lq]TTY mode.\[rq] |
| .PP |
| TTY mode is required for history to be enabled (see the \f[B]COMMAND |
| LINE HISTORY\f[R] section). |
| It is also required to enable special handling for \f[B]SIGINT\f[R] |
| signals. |
| .PP |
| TTY mode is different from interactive mode because interactive mode is |
| required in the bc(1) |
| specification (https://pubs.opengroup.org/onlinepubs/9699919799/utilities/bc.html), |
| and interactive mode requires only \f[B]stdin\f[R] and \f[B]stdout\f[R] |
| to be connected to a terminal. |
| .SH SIGNAL HANDLING |
| .PP |
| Sending a \f[B]SIGINT\f[R] will cause bc(1) to stop execution of the |
| current input. |
| If bc(1) is in TTY mode (see the \f[B]TTY MODE\f[R] section), it will |
| reset (see the \f[B]RESET\f[R] section). |
| Otherwise, it will clean up and exit. |
| .PP |
| 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 TTY mode, it will |
| ask for more input. |
| If bc(1) is processing input from a file in TTY 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. |
| .PP |
| 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. |
| .PP |
| \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, when bc(1) is in |
| TTY mode, a \f[B]SIGHUP\f[R] will cause bc(1) to clean up and exit. |
| .SH COMMAND LINE HISTORY |
| .PP |
| bc(1) supports interactive command-line editing. |
| If bc(1) is in TTY mode (see the \f[B]TTY MODE\f[R] section), history is |
| enabled. |
| Previous lines can be recalled and edited with the arrow keys. |
| .PP |
| \f[B]Note\f[R]: tabs are converted to 8 spaces. |
| .SH LOCALES |
| .PP |
| This bc(1) ships with support for adding error messages for different |
| locales and thus, supports \f[B]LC_MESSAGES\f[R]. |
| .SH SEE ALSO |
| .PP |
| dc(1) |
| .SH STANDARDS |
| .PP |
| bc(1) is compliant with the IEEE Std 1003.1-2017 |
| (\[lq]POSIX.1-2017\[rq]) (https://pubs.opengroup.org/onlinepubs/9699919799/utilities/bc.html) |
| specification. |
| The flags \f[B]-efghiqsvVw\f[R], all long options, and the extensions |
| noted above are extensions to that specification. |
| .PP |
| 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]. |
| .PP |
| This bc(1) supports error messages for different locales, and thus, it |
| supports \f[B]LC_MESSAGES\f[R]. |
| .SH BUGS |
| .PP |
| None are known. |
| Report bugs at https://git.yzena.com/gavin/bc. |
| .SH AUTHORS |
| .PP |
| Gavin D. |
| Howard <gavin@yzena.com> and contributors. |