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.TH "BC" "1" "July 2020" "Gavin D. Howard" "General Commands Manual"




.SH NAME




.PP




bc \ arbitrary\precision arithmetic language and calculator




.SH SYNOPSIS




.PP




\f[B]bc\f[] [\f[B]\ghilPqsvVw\f[]] [\f[B]\\global\stacks\f[]]




[\f[B]\\help\f[]] [\f[B]\\interactive\f[]] [\f[B]\\mathlib\f[]]




[\f[B]\\no\prompt\f[]] [\f[B]\\quiet\f[]] [\f[B]\\standard\f[]]




[\f[B]\\warn\f[]] [\f[B]\\version\f[]] [\f[B]\e\f[] \f[I]expr\f[]]




[\f[B]\\expression\f[]=\f[I]expr\f[]...] [\f[B]\f\f[]




\f[I]file\f[]...] [\f[B]\file\f[]=\f[I]file\f[]...] [\f[I]file\f[]...]




.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[].




.PP




This bc(1) is a drop\in replacement for \f[I]any\f[] bc(1), including




(and especially) the GNU bc(1).




.SH OPTIONS




.PP




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




.IP \[bu] 2




\f[B]\g\f[], \f[B]\\global\stacks\f[]




.RS 2




.PP




Turns the globals \f[B]ibase\f[], \f[B]obase\f[], and \f[B]scale\f[]




into stacks.




.PP




This has the effect that a copy of the current value of all three 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[] that simply




printed \f[B]x\f[] in base \f[B]b\f[] could be written like this:




.IP




.nf




\f[C]




define\ void\ output(x,\ b)\ {




\ \ \ \ obase=b




\ \ \ \ x




}




\f[]




.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[]




.fi




.PP




This makes writing functions much easier.




.PP




However, since using this flag means that functions cannot set




\f[B]ibase\f[], \f[B]obase\f[], or \f[B]scale\f[] 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="bc\ \e\ ibase=A\ \e\ obase=8"




alias\ h2b="bc\ \e\ ibase=G\ \e\ obase=2"




\f[]




.fi




.PP




Second, if the purpose of a function is to set \f[B]ibase\f[],




\f[B]obase\f[], or \f[B]scale\f[] globally for any other purpose, it




could be split into one to three functions (based on how many globals it




sets) and each of those functions could return the desired value for a




global.




.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[] and include this




option (see the \f[B]ENVIRONMENT VARIABLES\f[] section for more




details).




.PP




If \f[B]\s\f[], \f[B]\w\f[], or any equivalents are used, this option




is ignored.




.PP




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




.RE




.IP \[bu] 2




\f[B]\h\f[], \f[B]\\help\f[]




.RS 2




.PP




Prints a usage message and quits.




.RE




.IP \[bu] 2




\f[B]\i\f[], \f[B]\\interactive\f[]




.RS 2




.PP




Forces interactive mode.




(See the \f[B]INTERACTIVE MODE\f[] section.)




.PP




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




.RE




.IP \[bu] 2




\f[B]\l\f[], \f[B]\\mathlib\f[]




.RS 2




.PP




Sets \f[B]scale\f[] (see the \f[B]SYNTAX\f[] section) to \f[B]20\f[] and




loads the included math library before running any code, including any




expressions or files specified on the command line.




.PP




To learn what is in the library, see the \f[B]LIBRARY\f[] section.




.RE




.IP \[bu] 2




\f[B]\P\f[], \f[B]\\no\prompt\f[]




.RS 2




.PP




Disables the prompt in TTY mode.




(The prompt is only enabled in TTY mode.




See the \f[B]TTY MODE\f[] section) This is mostly for those users that




do not want a prompt or are not used to having them in bc(1).




Most of those users would want to put this option in




\f[B]BC_ENV_ARGS\f[] (see the \f[B]ENVIRONMENT VARIABLES\f[] section).




.PP




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




.RE




.IP \[bu] 2




\f[B]\q\f[], \f[B]\\quiet\f[]




.RS 2




.PP




Do not print copyright header.




bc(1) will also suppress the header in non\interactive mode.




.PP




This is mostly for compatibility with the GNU




bc(1) (https://www.gnu.org/software/bc/).




.PP




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




.RE




.IP \[bu] 2




\f[B]\s\f[], \f[B]\\standard\f[]




.RS 2




.PP




Process exactly the language defined by the




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




and error if any extensions are used.




.PP




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




.RE




.IP \[bu] 2




\f[B]\v\f[], \f[B]\V\f[], \f[B]\\version\f[]




.RS 2




.PP




Print the version information (copyright header) and exit.




.PP




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




.RE




.IP \[bu] 2




\f[B]\w\f[], \f[B]\\warn\f[]




.RS 2




.PP




Like \f[B]\s\f[] and \f[B]\\standard\f[], except that warnings (and




not errors) are printed for non\standard extensions and execution




continues normally.




.PP




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




.RE




.IP \[bu] 2




\f[B]\e\f[] \f[I]expr\f[], \f[B]\\expression\f[]=\f[I]expr\f[]




.RS 2




.PP




Evaluates \f[I]expr\f[].




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.




.PP




In other bc(1) implementations, this option causes the program to




execute the expressions and then exit.




This bc(1) does not, unless the \f[B]BC_EXPR_EXIT\f[] is defined (see




the \f[B]ENVIRONMENT VARIABLES\f[] section).




.PP




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




.RE




.IP \[bu] 2




\f[B]\f\f[] \f[I]file\f[], \f[B]\\file\f[]=\f[I]file\f[]




.RS 2




.PP




Reads in \f[I]file\f[] and evaluates it.




If expressions are also given (see above), the expressions are evaluated




in the order given.




.PP




In other bc(1) implementations, this option causes the program to




execute the files and then exit.




This bc(1) does not, unless the \f[B]BC_EXPR_EXIT\f[] is defined (see




the \f[B]ENVIRONMENT VARIABLES\f[] section).




.PP




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




.RE




.PP




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




.SH STDOUT




.PP




Any non\error output is written to \f[B]stdout\f[].




.PP




\f[B]Note\f[]: Unlike other bc(1) implementations, this bc(1) will issue




a fatal error (see the \f[B]EXIT STATUS\f[] section) if it cannot write




to \f[B]stdout\f[], so if \f[B]stdout\f[] is closed, as in \f[B]bc




>&\\f[], it will quit with an error.




This is done so that bc(1) can report problems when \f[B]stdout\f[] 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[] to \f[B]/dev/null\f[].




.SH STDERR




.PP




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




.PP




\f[B]Note\f[]: Unlike other bc(1) implementations, this bc(1) will issue




a fatal error (see the \f[B]EXIT STATUS\f[] section) if it cannot write




to \f[B]stderr\f[], so if \f[B]stderr\f[] is closed, as in \f[B]bc




2>&\\f[], it will quit with an error.




This is done so that bc(1) can exit with an error code when




\f[B]stderr\f[] 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[] to \f[B]/dev/null\f[].




.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[] means expression, \f[B]S\f[] means




statement, and \f[B]I\f[] means identifier.




.PP




Identifiers (\f[B]I\f[]) start with a lowercase letter and can be




followed by any number (up to \f[B]BC_NAME_MAX\1\f[]) of lowercase




letters (\f[B]a\z\f[]), digits (\f[B]0\9\f[]), and underscores




(\f[B]_\f[]).




The regex is \f[B][a\z][a\z0\9_]*\f[].




Identifiers with more than one character (letter) are a




\f[B]non\portable extension\f[].




.PP




\f[B]ibase\f[] is a global variable determining how to interpret




constant numbers.




It is the "input" base, or the number base used for interpreting input




numbers.




\f[B]ibase\f[] is initially \f[B]10\f[].




If the \f[B]\s\f[] (\f[B]\\standard\f[]) and \f[B]\w\f[]




(\f[B]\\warn\f[]) flags were not given on the command line, the max




allowable value for \f[B]ibase\f[] is \f[B]36\f[].




Otherwise, it is \f[B]16\f[].




The min allowable value for \f[B]ibase\f[] is \f[B]2\f[].




The max allowable value for \f[B]ibase\f[] can be queried in bc(1)




programs with the \f[B]maxibase()\f[] built\in function.




.PP




\f[B]obase\f[] is a global variable determining how to output results.




It is the "output" base, or the number base used for outputting numbers.




\f[B]obase\f[] is initially \f[B]10\f[].




The max allowable value for \f[B]obase\f[] is \f[B]BC_BASE_MAX\f[] and




can be queried in bc(1) programs with the \f[B]maxobase()\f[] built\in




function.




The min allowable value for \f[B]obase\f[] is \f[B]2\f[].




Values are output in the specified base.




.PP




The \f[I]scale\f[] of an expression is the number of digits in the




result of the expression right of the decimal point, and \f[B]scale\f[]




is a global variable that sets the precision of any operations, with




exceptions.




\f[B]scale\f[] is initially \f[B]0\f[].




\f[B]scale\f[] cannot be negative.




The max allowable value for \f[B]scale\f[] is \f[B]BC_SCALE_MAX\f[] and




can be queried in bc(1) programs with the \f[B]maxscale()\f[] built\in




function.




.PP




bc(1) has both \f[I]global\f[] variables and \f[I]local\f[] variables.




All \f[I]local\f[] variables are local to the function; they are




parameters or are introduced in the \f[B]auto\f[] list of a function




(see the \f[B]FUNCTIONS\f[] section).




If a variable is accessed which is not a parameter or in the




\f[B]auto\f[] list, it is assumed to be \f[I]global\f[].




If a parent function has a \f[I]local\f[] variable version of a variable




that a child function considers \f[I]global\f[], the value of that




\f[I]global\f[] 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[] 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[] the expression is




notsurrounded by parentheses.




.PP




The value that is printed is also assigned to the special variable




\f[B]last\f[].




A single dot (\f[B].\f[]) may also be used as a synonym for




\f[B]last\f[].




These are \f[B]non\portable extensions\f[].




.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[] and \f[B]*/\f[].




.IP "2." 3




Line comments go from \f[B]#\f[] until, and not including, the next




newline.




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




.SS Named Expressions




.PP




The following are named expressions in bc(1):




.IP "1." 3




Variables: \f[B]I\f[]




.IP "2." 3




Array Elements: \f[B]I[E]\f[]




.IP "3." 3




\f[B]ibase\f[]




.IP "4." 3




\f[B]obase\f[]




.IP "5." 3




\f[B]scale\f[]




.IP "6." 3




\f[B]last\f[] or a single dot (\f[B].\f[])




.PP




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




.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[] 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[]/\f[B]decrement\f[] operators and as the left side of




\f[B]assignment\f[] operators (see the \f[I]Operators\f[] subsection).




.SS Operands




.PP




The following are valid operands in bc(1):




.IP " 1." 4




Numbers (see the \f[I]Numbers\f[] subsection below).




.IP " 2." 4




Array indices (\f[B]I[E]\f[]).




.IP " 3." 4




\f[B](E)\f[]: The value of \f[B]E\f[] (used to change precedence).




.IP " 4." 4




\f[B]sqrt(E)\f[]: The square root of \f[B]E\f[].




\f[B]E\f[] must be non\negative.




.IP " 5." 4




\f[B]length(E)\f[]: The number of significant decimal digits in




\f[B]E\f[].




.IP " 6." 4




\f[B]length(I[])\f[]: The number of elements in the array \f[B]I\f[].




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




.IP " 7." 4




\f[B]scale(E)\f[]: The \f[I]scale\f[] of \f[B]E\f[].




.IP " 8." 4




\f[B]abs(E)\f[]: The absolute value of \f[B]E\f[].




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




.IP " 9." 4




\f[B]I()\f[], \f[B]I(E)\f[], \f[B]I(E, E)\f[], and so on, where




\f[B]I\f[] is an identifier for a non\\f[B]void\f[] function (see the




\f[I]Void Functions\f[] subsection of the \f[B]FUNCTIONS\f[] section).




The \f[B]E\f[] argument(s) may also be arrays of the form \f[B]I[]\f[],




which will automatically be turned into array references (see the




\f[I]Array References\f[] subsection of the \f[B]FUNCTIONS\f[] section)




if the corresponding parameter in the function definition is an array




reference.




.IP "10." 4




\f[B]read()\f[]: Reads a line from \f[B]stdin\f[] and uses that as an




expression.




The result of that expression is the result of the \f[B]read()\f[]




operand.




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




.IP "11." 4




\f[B]maxibase()\f[]: The max allowable \f[B]ibase\f[].




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




.IP "12." 4




\f[B]maxobase()\f[]: The max allowable \f[B]obase\f[].




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




.IP "13." 4




\f[B]maxscale()\f[]: The max allowable \f[B]scale\f[].




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




.SS Numbers




.PP




Numbers are strings made up of digits, uppercase letters, and at most




\f[B]1\f[] period for a radix.




Numbers can have up to \f[B]BC_NUM_MAX\f[] digits.




Uppercase letters are equal to \f[B]9\f[] + their position in the




alphabet (i.e., \f[B]A\f[] equals \f[B]10\f[], or \f[B]9+1\f[]).




If a digit or letter makes no sense with the current value of




\f[B]ibase\f[], they are set to the value of the highest valid digit in




\f[B]ibase\f[].




.PP




Single\character numbers (i.e., \f[B]A\f[] alone) take the value that




they would have if they were valid digits, regardless of the value of




\f[B]ibase\f[].




This means that \f[B]A\f[] alone always equals decimal \f[B]10\f[] and




\f[B]Z\f[] alone always equals decimal \f[B]35\f[].




.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.




.IP \[bu] 2




\f[B]++\f[] \f[B]\\\f[]




.RS 2




.PP




Type: Prefix and Postfix




.PP




Associativity: None




.PP




Description: \f[B]increment\f[], \f[B]decrement\f[]




.RE




.IP \[bu] 2




\f[B]\\f[] \f[B]!\f[]




.RS 2




.PP




Type: Prefix




.PP




Associativity: None




.PP




Description: \f[B]negation\f[], \f[B]boolean not\f[]




.RE




.IP \[bu] 2




\f[B]^\f[]




.RS 2




.PP




Type: Binary




.PP




Associativity: Right




.PP




Description: \f[B]power\f[]




.RE




.IP \[bu] 2




\f[B]*\f[] \f[B]/\f[] \f[B]%\f[]




.RS 2




.PP




Type: Binary




.PP




Associativity: Left




.PP




Description: \f[B]multiply\f[], \f[B]divide\f[], \f[B]modulus\f[]




.RE




.IP \[bu] 2




\f[B]+\f[] \f[B]\\f[]




.RS 2




.PP




Type: Binary




.PP




Associativity: Left




.PP




Description: \f[B]add\f[], \f[B]subtract\f[]




.RE




.IP \[bu] 2




\f[B]=\f[] \f[B]+=\f[] \f[B]\=\f[] \f[B]*=\f[] \f[B]/=\f[] \f[B]%=\f[]




\f[B]^=\f[]




.RS 2




.PP




Type: Binary




.PP




Associativity: Right




.PP




Description: \f[B]assignment\f[]




.RE




.IP \[bu] 2




\f[B]==\f[] \f[B]<=\f[] \f[B]>=\f[] \f[B]!=\f[] \f[B]<\f[] \f[B]>\f[]




.RS 2




.PP




Type: Binary




.PP




Associativity: Left




.PP




Description: \f[B]relational\f[]




.RE




.IP \[bu] 2




\f[B]&&\f[]




.RS 2




.PP




Type: Binary




.PP




Associativity: Left




.PP




Description: \f[B]boolean and\f[]




.RE




.IP \[bu] 2




\f[B]\f[]




.RS 2




.PP




Type: Binary




.PP




Associativity: Left




.PP




Description: \f[B]boolean or\f[]




.RE




.PP




The operators will be described in more detail below.




.IP \[bu] 2




\f[B]++\f[] \f[B]\\\f[]




.RS 2




.PP




The prefix and postfix \f[B]increment\f[] and \f[B]decrement\f[]




operators behave exactly like they would in C.




They require a named expression (see the \f[I]Named Expressions\f[]




subsection) as an operand.




.PP




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




where possible.




.RE




.IP \[bu] 2




\f[B]\\f[]




.RS 2




.PP




The \f[B]negation\f[] operator returns \f[B]0\f[] if a user attempts to




negate any expression with the value \f[B]0\f[].




Otherwise, a copy of the expression with its sign flipped is returned.




.RE




.IP \[bu] 2




\f[B]!\f[]




.RS 2




.PP




The \f[B]boolean not\f[] operator returns \f[B]1\f[] if the expression




is \f[B]0\f[], or \f[B]0\f[] otherwise.




.PP




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




.RE




.IP \[bu] 2




\f[B]^\f[]




.RS 2




The \f[B]power\f[] operator (not the \f[B]exclusive or\f[] operator, as




it would be in




.IP "C)" 3




takes two expressions and raises the first to the power of the value of




the second.




.PP




The second expression must be an integer (no \f[I]scale\f[]), and if it




is negative, the first value must be non\zero.




.RE




.IP \[bu] 2




\f[B]*\f[]




.RS 2




.PP




The \f[B]multiply\f[] operator takes two expressions, multiplies them,




and returns the product.




If \f[B]a\f[] is the \f[I]scale\f[] of the first expression and




\f[B]b\f[] is the \f[I]scale\f[] of the second expression, the




\f[I]scale\f[] of the result is equal to




\f[B]min(a+b,max(scale,a,b))\f[] where \f[B]min()\f[] and \f[B]max()\f[]




return the obvious values.




.RE




.IP \[bu] 2




\f[B]/\f[]




.RS 2




.PP




The \f[B]divide\f[] operator takes two expressions, divides them, and




returns the quotient.




The \f[I]scale\f[] of the result shall be the value of \f[B]scale\f[].




.PP




The second expression must be non\zero.




.RE




.IP \[bu] 2




\f[B]%\f[]




.RS 2




.PP




The \f[B]modulus\f[] operator takes two expressions, \f[B]a\f[] and




\f[B]b\f[], and evaluates them by 1) Computing \f[B]a/b\f[] to current




\f[B]scale\f[] and 2) Using the result of step 1 to calculate




\f[B]a\(a/b)*b\f[] to \f[I]scale\f[]




\f[B]max(scale+scale(b),scale(a))\f[].




.PP




The second expression must be non\zero.




.RE




.IP \[bu] 2




\f[B]+\f[]




.RS 2




.PP




The \f[B]add\f[] operator takes two expressions, \f[B]a\f[] and




\f[B]b\f[], and returns the sum, with a \f[I]scale\f[] equal to the max




of the \f[I]scale\f[]s of \f[B]a\f[] and \f[B]b\f[].




.RE




.IP \[bu] 2




\f[B]\\f[]




.RS 2




.PP




The \f[B]subtract\f[] operator takes two expressions, \f[B]a\f[] and




\f[B]b\f[], and returns the difference, with a \f[I]scale\f[] equal to




the max of the \f[I]scale\f[]s of \f[B]a\f[] and \f[B]b\f[].




.RE




.IP \[bu] 2




\f[B]=\f[] \f[B]+=\f[] \f[B]\=\f[] \f[B]*=\f[] \f[B]/=\f[] \f[B]%=\f[]




\f[B]^=\f[]




.RS 2




.PP




The \f[B]assignment\f[] operators take two expressions, \f[B]a\f[] and




\f[B]b\f[] where \f[B]a\f[] is a named expression (see the \f[I]Named




Expressions\f[] subsection).




.PP




For \f[B]=\f[], \f[B]b\f[] is copied and the result is assigned to




\f[B]a\f[].




For all others, \f[B]a\f[] and \f[B]b\f[] are applied as operands to the




corresponding arithmetic operator and the result is assigned to




\f[B]a\f[].




.RE




.IP \[bu] 2




\f[B]==\f[] \f[B]<=\f[] \f[B]>=\f[] \f[B]!=\f[] \f[B]<\f[] \f[B]>\f[]




.RS 2




.PP




The \f[B]relational\f[] operators compare two expressions, \f[B]a\f[]




and \f[B]b\f[], and if the relation holds, according to C language




semantics, the result is \f[B]1\f[].




Otherwise, it is \f[B]0\f[].




.PP




Note that unlike in C, these operators have a lower precedence than the




\f[B]assignment\f[] operators, which means that \f[B]a=b>c\f[] is




interpreted as \f[B](a=b)>c\f[].




.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[].




.RE




.IP \[bu] 2




\f[B]&&\f[]




.RS 2




.PP




The \f[B]boolean and\f[] operator takes two expressions and returns




\f[B]1\f[] if both expressions are non\zero, \f[B]0\f[] otherwise.




.PP




This is \f[I]not\f[] a short\circuit operator.




.PP




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




.RE




.IP \[bu] 2




\f[B]\f[]




.RS 2




.PP




The \f[B]boolean or\f[] operator takes two expressions and returns




\f[B]1\f[] if one of the expressions is non\zero, \f[B]0\f[] otherwise.




.PP




This is \f[I]not\f[] a short\circuit operator.




.PP




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




.RE




.SS Statements




.PP




The following items are statements:




.IP " 1." 4




\f[B]E\f[]




.IP " 2." 4




\f[B]{\f[] \f[B]S\f[] \f[B];\f[] ...




\f[B];\f[] \f[B]S\f[] \f[B]}\f[]




.IP " 3." 4




\f[B]if\f[] \f[B](\f[] \f[B]E\f[] \f[B])\f[] \f[B]S\f[]




.IP " 4." 4




\f[B]if\f[] \f[B](\f[] \f[B]E\f[] \f[B])\f[] \f[B]S\f[] \f[B]else\f[]




\f[B]S\f[]




.IP " 5." 4




\f[B]while\f[] \f[B](\f[] \f[B]E\f[] \f[B])\f[] \f[B]S\f[]




.IP " 6." 4




\f[B]for\f[] \f[B](\f[] \f[B]E\f[] \f[B];\f[] \f[B]E\f[] \f[B];\f[]




\f[B]E\f[] \f[B])\f[] \f[B]S\f[]




.IP " 7." 4




An empty statement




.IP " 8." 4




\f[B]break\f[]




.IP " 9." 4




\f[B]continue\f[]




.IP "10." 4




\f[B]quit\f[]




.IP "11." 4




\f[B]halt\f[]




.IP "12." 4




\f[B]limits\f[]




.IP "13." 4




A string of characters, enclosed in double quotes




.IP "14." 4




\f[B]print\f[] \f[B]E\f[] \f[B],\f[] ...




\f[B],\f[] \f[B]E\f[]




.IP "15." 4




\f[B]I()\f[], \f[B]I(E)\f[], \f[B]I(E, E)\f[], and so on, where




\f[B]I\f[] is an identifier for a \f[B]void\f[] function (see the




\f[I]Void Functions\f[] subsection of the \f[B]FUNCTIONS\f[] section).




The \f[B]E\f[] argument(s) may also be arrays of the form \f[B]I[]\f[],




which will automatically be turned into array references (see the




\f[I]Array References\f[] subsection of the \f[B]FUNCTIONS\f[] 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[].




.PP




Also, as a \f[B]non\portable extension\f[], 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[].




.PP




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




.PP




The \f[B]quit\f[] 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[] statement causes bc(1) to quit, if it is executed.




(Unlike \f[B]quit\f[] if it is on a branch of an \f[B]if\f[] statement




that is not executed, bc(1) does not quit.)




.PP




The \f[B]limits\f[] statement prints the limits that this bc(1) is




subject to.




This is like the \f[B]quit\f[] statement in that it is a compile\time




command.




.PP




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




.SS Print Statement




.PP




The "expressions" in a \f[B]print\f[] 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:




.IP \[bu] 2




\f[B]\\a\f[]: \f[B]\\a\f[]




.IP \[bu] 2




\f[B]\\b\f[]: \f[B]\\b\f[]




.IP \[bu] 2




\f[B]\\\\\f[]: \f[B]\\\f[]




.IP \[bu] 2




\f[B]\\e\f[]: \f[B]\\\f[]




.IP \[bu] 2




\f[B]\\f\f[]: \f[B]\\f\f[]




.IP \[bu] 2




\f[B]\\n\f[]: \f[B]\\n\f[]




.IP \[bu] 2




\f[B]\\q\f[]: \f[B]"\f[]




.IP \[bu] 2




\f[B]\\r\f[]: \f[B]\\r\f[]




.IP \[bu] 2




\f[B]\\t\f[]: \f[B]\\t\f[]




.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[], 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[] is equal to




\f[B]0\f[], in the expression




.IP




.nf




\f[C]




a[i++]\ =\ i++




\f[]




.fi




.PP




the first (or 0th) element of \f[B]a\f[] is set to \f[B]1\f[], and




\f[B]i\f[] is equal to \f[B]2\f[] at the end of the expression.




.PP




This includes function arguments.




Thus, assuming \f[B]i\f[] is equal to \f[B]0\f[], this means that in the




expression




.IP




.nf




\f[C]




x(i++,\ i++)




\f[]




.fi




.PP




the first argument passed to \f[B]x()\f[] is \f[B]0\f[], and the second




argument is \f[B]1\f[], while \f[B]i\f[] is equal to \f[B]2\f[] 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[]




.fi




.PP




Any \f[B]I\f[] in the parameter list or \f[B]auto\f[] list may be




replaced with \f[B]I[]\f[] to make a parameter or \f[B]auto\f[] var an




array, and any \f[B]I\f[] in the parameter list may be replaced with




\f[B]*I[]\f[] 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[] like




normal array parameters and will be automatically converted into




references.




.PP




As a \f[B]non\portable extension\f[], the opening brace of a




\f[B]define\f[] statement may appear on the next line.




.PP




As a \f[B]non\portable extension\f[], the return statement may also be




in one of the following forms:




.IP "1." 3




\f[B]return\f[]




.IP "2." 3




\f[B]return\f[] \f[B](\f[] \f[B])\f[]




.IP "3." 3




\f[B]return\f[] \f[B]E\f[]




.PP




The first two, or not specifying a \f[B]return\f[] statement, is




equivalent to \f[B]return (0)\f[], unless the function is a




\f[B]void\f[] function (see the \f[I]Void Functions\f[] subsection




below).




.SS Void Functions




.PP




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




.IP




.nf




\f[C]




define\ void\ I(I,...,I){




\ \ \ \ auto\ I,...,I




\ \ \ \ S;...;S




\ \ \ \ return




}




\f[]




.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[] statements




listed above.




They can also omit the return statement entirely.




.PP




The word "void" is not treated as a keyword; it is still possible to




have variables, arrays, and functions named \f[B]void\f[].




The word "void" is only treated specially right after the




\f[B]define\f[] keyword.




.PP




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




.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[]




.fi




.PP




it is a \f[B]reference\f[].




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[].




.SH LIBRARY




.PP




All of the functions below are available when the \f[B]\l\f[] or




\f[B]\\mathlib\f[] command\line flags 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:




.IP \[bu] 2




\f[B]s(x)\f[]




.RS 2




.PP




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




.PP




This is a transcendental function (see the \f[I]Transcendental




Functions\f[] subsection below).




.RE




.IP \[bu] 2




\f[B]c(x)\f[]




.RS 2




.PP




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




.PP




This is a transcendental function (see the \f[I]Transcendental




Functions\f[] subsection below).




.RE




.IP \[bu] 2




\f[B]a(x)\f[]




.RS 2




.PP




Returns the arctangent of \f[B]x\f[], in radians.




.PP




This is a transcendental function (see the \f[I]Transcendental




Functions\f[] subsection below).




.RE




.IP \[bu] 2




\f[B]l(x)\f[]




.RS 2




.PP




Returns the natural logarithm of \f[B]x\f[].




.PP




This is a transcendental function (see the \f[I]Transcendental




Functions\f[] subsection below).




.RE




.IP \[bu] 2




\f[B]e(x)\f[]




.RS 2




.PP




Returns the mathematical constant \f[B]e\f[] raised to the power of




\f[B]x\f[].




.PP




This is a transcendental function (see the \f[I]Transcendental




Functions\f[] subsection below).




.RE




.IP \[bu] 2




\f[B]j(x, n)\f[]




.RS 2




.PP




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




.PP




This is a transcendental function (see the \f[I]Transcendental




Functions\f[] subsection below).




.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[]) set to at least 1 higher




than is necessary.




If exact results are \f[I]absolutely\f[] required, users can double the




precision (\f[B]scale\f[]) and then truncate.




.PP




The transcendental functions in the standard math library are:




.IP \[bu] 2




\f[B]s(x)\f[]




.IP \[bu] 2




\f[B]c(x)\f[]




.IP \[bu] 2




\f[B]a(x)\f[]




.IP \[bu] 2




\f[B]l(x)\f[]




.IP \[bu] 2




\f[B]e(x)\f[]




.IP \[bu] 2




\f[B]j(x, n)\f[]




.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[] 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[] types to calculate the




value of \f[B]1\f[] 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[] decimal digit




at a time.




If built in a environment where \f[B]BC_LONG_BIT\f[] (see the




\f[B]LIMITS\f[] section) is \f[B]64\f[], then each integer has




\f[B]9\f[] decimal digits.




If built in an environment where \f[B]BC_LONG_BIT\f[] is \f[B]32\f[]




then each integer has \f[B]4\f[] decimal digits.




This value (the number of decimal digits per large integer) is called




\f[B]BC_BASE_DIGS\f[].




.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[], 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):




.IP \[bu] 2




\f[B]BC_LONG_BIT\f[]




.RS 2




.PP




The number of bits in the \f[B]long\f[] 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[] section).




.RE




.IP \[bu] 2




\f[B]BC_BASE_DIGS\f[]




.RS 2




.PP




The number of decimal digits per large integer (see the




\f[B]PERFORMANCE\f[] section).




Depends on \f[B]BC_LONG_BIT\f[].




.RE




.IP \[bu] 2




\f[B]BC_BASE_POW\f[]




.RS 2




.PP




The max decimal number that each large integer can store (see




\f[B]BC_BASE_DIGS\f[]) plus \f[B]1\f[].




Depends on \f[B]BC_BASE_DIGS\f[].




.RE




.IP \[bu] 2




\f[B]BC_OVERFLOW_MAX\f[]




.RS 2




.PP




The max number that the overflow type (see the \f[B]PERFORMANCE\f[]




section) can hold.




Depends on \f[B]BC_LONG_BIT\f[].




.RE




.IP \[bu] 2




\f[B]BC_BASE_MAX\f[]




.RS 2




.PP




The maximum output base.




Set at \f[B]BC_BASE_POW\f[].




.RE




.IP \[bu] 2




\f[B]BC_DIM_MAX\f[]




.RS 2




.PP




The maximum size of arrays.




Set at \f[B]SIZE_MAX\1\f[].




.RE




.IP \[bu] 2




\f[B]BC_SCALE_MAX\f[]




.RS 2




.PP




The maximum \f[B]scale\f[].




Set at \f[B]BC_OVERFLOW_MAX\1\f[].




.RE




.IP \[bu] 2




\f[B]BC_STRING_MAX\f[]




.RS 2




.PP




The maximum length of strings.




Set at \f[B]BC_OVERFLOW_MAX\1\f[].




.RE




.IP \[bu] 2




\f[B]BC_NAME_MAX\f[]




.RS 2




.PP




The maximum length of identifiers.




Set at \f[B]BC_OVERFLOW_MAX\1\f[].




.RE




.IP \[bu] 2

