BC(1)                      POSIX Programmer's Manual                     BC(1)



PPRROOLLOOGG
       This manual page is part of the POSIX Programmer's Manual.  The OS
       implementation of this interface may differ (consult the corresponding
       OS manual page for details of OS behavior), or the interface may not be
       implemented on OS.


NNAAMMEE
       bc -- arbitrary-precision arithmetic language

SSYYNNOOPPSSIISS
       bc [[-l]] [[_f_i_l_e...]]

DDEESSCCRRIIPPTTIIOONN
       The _b_c utility shall implement an arbitrary precision calculator. It
       shall take input from any files given, then read from the standard
       input. If the standard input and standard output to _b_c are attached to
       a terminal, the invocation of _b_c shall be considered to be _i_n_t_e_r_a_c_t_i_v_e,
       causing behavioral constraints described in the following sections.

OOPPTTIIOONNSS
       The _b_c utility shall conform to the Base Definitions volume of
       POSIX.1-2008, _S_e_c_t_i_o_n _1_2_._2, _U_t_i_l_i_t_y _S_y_n_t_a_x _G_u_i_d_e_l_i_n_e_s.

       The following option shall be supported:

       --ll        (The letter ell.) Define the math functions and initialize
                 _s_c_a_l_e to 20, instead of the default zero; see the EXTENDED
                 DESCRIPTION section.

OOPPEERRAANNDDSS
       The following operand shall be supported:

       _f_i_l_e      A pathname of a text file containing _b_c program statements.
                 After all _f_i_l_es have been read, _b_c shall read the standard
                 input.

SSTTDDIINN
       See the INPUT FILES section.

IINNPPUUTT FFIILLEESS
       Input files shall be text files containing a sequence of comments,
       statements, and function definitions that shall be executed as they are
       read.

EENNVVIIRROONNMMEENNTT VVAARRIIAABBLLEESS
       The following environment variables shall affect the execution of _b_c:

       _L_A_N_G      Provide a default value for the internationalization
                 variables that are unset or null. (See the Base Definitions
                 volume of POSIX.1-2008, _S_e_c_t_i_o_n _8_._2, _I_n_t_e_r_n_a_t_i_o_n_a_l_i_z_a_t_i_o_n
                 _V_a_r_i_a_b_l_e_s for the precedence of internationalization
                 variables used to determine the values of locale categories.)

       _L_C___A_L_L    If set to a non-empty string value, override the values of
                 all the other internationalization variables.

       _L_C___C_T_Y_P_E  Determine the locale for the interpretation of sequences of
                 bytes of text data as characters (for example, single-byte as
                 opposed to multi-byte characters in arguments and input
                 files).

       _L_C___M_E_S_S_A_G_E_S
                 Determine the locale that should be used to affect the format
                 and contents of diagnostic messages written to standard
                 error.

       _N_L_S_P_A_T_H   Determine the location of message catalogs for the processing
                 of _L_C___M_E_S_S_A_G_E_S.

AASSYYNNCCHHRROONNOOUUSS EEVVEENNTTSS
       Default.

SSTTDDOOUUTT
       The output of the _b_c utility shall be controlled by the program read,
       and consist of zero or more lines containing the value of all executed
       expressions without assignments. The radix and precision of the output
       shall be controlled by the values of the oobbaassee and ssccaallee variables; see
       the EXTENDED DESCRIPTION section.

SSTTDDEERRRR
       The standard error shall be used only for diagnostic messages.

OOUUTTPPUUTT FFIILLEESS
       None.

EEXXTTEENNDDEEDD DDEESSCCRRIIPPTTIIOONN
   GGrraammmmaarr
       The grammar in this section and the lexical conventions in the
       following section shall together describe the syntax for _b_c programs.
       The general conventions for this style of grammar are described in
       _S_e_c_t_i_o_n _1_._3, _G_r_a_m_m_a_r _C_o_n_v_e_n_t_i_o_n_s.  A valid program can be represented
       as the non-terminal symbol pprrooggrraamm in the grammar. This formal syntax
       shall take precedence over the text syntax description.

           %%ttookkeenn    EEOOFF NNEEWWLLIINNEE SSTTRRIINNGG LLEETTTTEERR NNUUMMBBEERR

           %token    MUL_OP
           /*        '*', '/', '%'                           */

           %token    ASSIGN_OP
           /*        '=', '+=', '-=', '*=', '/=', '%=', '^=' */

           %token    REL_OP
           /*        '==', '<=', '>=', '!=', '<', '>'        */

           %token    INCR_DECR
           /*        '++', '--'                              */

           %token    Define    Break    Quit    Length
           /*        'define', 'break', 'quit', 'length'     */

           %token    Return    For    If    While    Sqrt
           /*        'return', 'for', 'if', 'while', 'sqrt'  */

           %token    Scale    Ibase    Obase    Auto
           /*        'scale', 'ibase', 'obase', 'auto'       */

           %start    program

           %%

           program              : EOF
                                | input_item program
                                ;

           input_item           : semicolon_list NEWLINE
                                | function
                                ;

           semicolon_list       : /* empty */
                                | statement
                                | semicolon_list ';' statement
                                | semicolon_list ';'
                                ;

           statement_list       : /* empty */
                                | statement
                                | statement_list NEWLINE
                                | statement_list NEWLINE statement
                                | statement_list ';'
                                | statement_list ';' statement
                                ;

           statement            : expression
                                | STRING
                                | Break
                                | Quit
                                | Return
                                | Return '(' return_expression ')'
                                | For '(' expression ';'
                                      relational_expression ';'
                                      expression ')' statement
                                | If '(' relational_expression ')' statement
                                | While '(' relational_expression ')' statement
                                | '{' statement_list '}'
                                ;

           function             : Define LETTER '(' opt_parameter_list ')'
                                      '{' NEWLINE opt_auto_define_list
                                      statement_list '}'
                                ;

           opt_parameter_list   : /* empty */
                                | parameter_list
                                ;

           parameter_list       : LETTER
                                | define_list ',' LETTER
                                ;

           opt_auto_define_list : /* empty */
                                | Auto define_list NEWLINE
                                | Auto define_list ';'
                                ;

           define_list          : LETTER
                                | LETTER '[' ']'
                                | define_list ',' LETTER
                                | define_list ',' LETTER '[' ']'
                                ;

           opt_argument_list    : /* empty */
                                | argument_list
                                ;

           argument_list        : expression
                                | LETTER '[' ']' ',' argument_list
                                ;

           relational_expression : expression
                                | expression REL_OP expression
                                ;

           return_expression    : /* empty */
                                | expression
                                ;

           expression           : named_expression
                                | NUMBER
                                | '(' expression ')'
                                | LETTER '(' opt_argument_list ')'
                                | '-' expression
                                | expression '+' expression
                                | expression '-' expression
                                | expression MUL_OP expression
                                | expression '^' expression
                                | INCR_DECR named_expression
                                | named_expression INCR_DECR
                                | named_expression ASSIGN_OP expression
                                | Length '(' expression ')'
                                | Sqrt '(' expression ')'
                                | Scale '(' expression ')'
                                ;

           named_expression     : LETTER
                                | LETTER '[' expression ']'
                                | Scale
                                | Ibase
                                | Obase
                                ;

   LLeexxiiccaall CCoonnvveennttiioonnss iinn bbcc
       The lexical conventions for _b_c programs, with respect to the preceding
       grammar, shall be as follows:

        1. Except as noted, _b_c shall recognize the longest possible token or
           delimiter beginning at a given point.

        2. A comment shall consist of any characters beginning with the two
           adjacent characters ""//**"" and terminated by the next occurrence of
           the two adjacent characters ""**//"".  Comments shall have no effect
           except to delimit lexical tokens.

        3. The <newline> shall be recognized as the token NNEEWWLLIINNEE.

        4. The token SSTTRRIINNGG shall represent a string constant; it shall
           consist of any characters beginning with the double-quote character
           (''""'') and terminated by another occurrence of the double-quote
           character. The value of the string is the sequence of all
           characters between, but not including, the two double-quote
           characters. All characters shall be taken literally from the input,
           and there is no way to specify a string containing a double-quote
           character. The length of the value of each string shall be limited
           to {BC_STRING_MAX} bytes.

        5. A <blank> shall have no effect except as an ordinary character if
           it appears within a SSTTRRIINNGG token, or to delimit a lexical token
           other than SSTTRRIINNGG.

        6. The combination of a <backslash> character immediately followed by
           a <newline> shall have no effect other than to delimit lexical
           tokens with the following exceptions:

            *  It shall be interpreted as the character sequence ""\\<<nneewwlliinnee>>""
               in SSTTRRIINNGG tokens.

            *  It shall be ignored as part of a multi-line NNUUMMBBEERR token.

        7. The token NNUUMMBBEERR shall represent a numeric constant. It shall be
           recognized by the following grammar:

               NNUUMMBBEERR  :: iinntteeggeerr
                       || ''..'' iinntteeggeerr
                       || iinntteeggeerr ''..''
                       || iinntteeggeerr ''..'' iinntteeggeerr
                       ;;

               integer : digit
                       | integer digit
                       ;

               digit   : 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7
                       | 8 | 9 | A | B | C | D | E | F
                       ;

        8. The value of a NNUUMMBBEERR token shall be interpreted as a numeral in
           the base specified by the value of the internal register iibbaassee
           (described below). Each of the ddiiggiitt characters shall have the
           value from 0 to 15 in the order listed here, and the <period>
           character shall represent the radix point. The behavior is
           undefined if digits greater than or equal to the value of iibbaassee
           appear in the token. However, note the exception for single-digit
           values being assigned to iibbaassee and oobbaassee themselves, in _O_p_e_r_a_t_i_o_n_s
           _i_n _b_c.

        9. The following keywords shall be recognized as tokens:

           aauuttoo     iibbaassee    lleennggtthh   rreettuurrnn   wwhhiillee
           bbrreeaakk    iiff       oobbaassee    ssccaallee
           ddeeffiinnee   ffoorr      qquuiitt     ssqqrrtt

       10. Any of the following characters occurring anywhere except within a
           keyword shall be recognized as the token LLEETTTTEERR:

               aa bb cc dd ee ff gg hh ii jj kk ll mm nn oo pp qq rr ss tt uu vv ww xx yy zz

       11. The following single-character and two-character sequences shall be
           recognized as the token AASSSSIIGGNN__OOPP:

               ==   ++==   --==   **==   //==   %%==   ^^==

       12. If an ''=='' character, as the beginning of a token, is followed by a
           ''--'' character with no intervening delimiter, the behavior is
           undefined.

       13. The following single-characters shall be recognized as the token
           MMUULL__OOPP:

               **   //   %%

       14. The following single-character and two-character sequences shall be
           recognized as the token RREELL__OOPP:

               ====   <<==   >>==   !!==   <<   >>

       15. The following two-character sequences shall be recognized as the
           token IINNCCRR__DDEECCRR:

               ++++   ----

       16. The following single characters shall be recognized as tokens whose
           names are the character:

               <<nneewwlliinnee>>  ((  ))  ,,  ++  --  ;;  [[  ]]  ^^  {{  }}

       17. The token EEOOFF is returned when the end of input is reached.

   OOppeerraattiioonnss iinn bbcc
       There are three kinds of identifiers: ordinary identifiers, array
       identifiers, and function identifiers.  All three types consist of
       single lowercase letters. Array identifiers shall be followed by square
       brackets (""[[]]"").  An array subscript is required except in an argument
       or auto list.  Arrays are singly dimensioned and can contain up to
       {BC_DIM_MAX} elements. Indexing shall begin at zero so an array is
       indexed from 0 to {BC_DIM_MAX}-1.  Subscripts shall be truncated to
       integers. The application shall ensure that function identifiers are
       followed by parentheses, possibly enclosing arguments. The three types
       of identifiers do not conflict.

       The following table summarizes the rules for precedence and
       associativity of all operators. Operators on the same line shall have
       the same precedence; rows are in order of decreasing precedence.

                               TTaabbllee:: OOppeerraattoorrss iinn _b_c

                     +--------------------------+---------------+
                     |        OOppeerraattoorr          | AAssssoocciiaattiivviittyy |
                     +--------------------------+---------------+
                     |++, --                    | N/A           |
                     |unary -                   | N/A           |
                     |^                         | Right to left |
                     |*, /, %                   | Left to right |
                     |+, binary -               | Left to right |
                     |=, +=, -=, *=, /=, %=, ^= | Right to left |
                     |==, <=, >=, !=, <, >      | None          |
                     +--------------------------+---------------+
       Each expression or named expression has a _s_c_a_l_e, which is the number of
       decimal digits that shall be maintained as the fractional portion of
       the expression.

       _N_a_m_e_d _e_x_p_r_e_s_s_i_o_n_s are places where values are stored. Named expressions
       shall be valid on the left side of an assignment. The value of a named
       expression shall be the value stored in the place named. Simple
       identifiers and array elements are named expressions; they have an
       initial value of zero and an initial scale of zero.

       The internal registers ssccaallee, iibbaassee, and oobbaassee are all named
       expressions. The scale of an expression consisting of the name of one
       of these registers shall be zero; values assigned to any of these
       registers are truncated to integers. The ssccaallee register shall contain a
       global value used in computing the scale of expressions (as described
       below). The value of the register ssccaallee is limited to 0 <= ssccaallee <=
       {BC_SCALE_MAX} and shall have a default value of zero. The iibbaassee and
       oobbaassee registers are the input and output number radix, respectively.
       The value of iibbaassee shall be limited to:

           22 <<== iibbaassee <<== 1166

       The value of oobbaassee shall be limited to:

           22 <<== oobbaassee <<== {{BBCC__BBAASSEE__MMAAXX}}

       When either iibbaassee or oobbaassee is assigned a single ddiiggiitt value from the
       list in _L_e_x_i_c_a_l _C_o_n_v_e_n_t_i_o_n_s _i_n _b_c, the value shall be assumed in
       hexadecimal. (For example, iibbaassee=A sets to base ten, regardless of the
       current iibbaassee value.) Otherwise, the behavior is undefined when digits
       greater than or equal to the value of iibbaassee appear in the input. Both
       iibbaassee and oobbaassee shall have initial values of 10.

       Internal computations shall be conducted as if in decimal, regardless
       of the input and output bases, to the specified number of decimal
       digits. When an exact result is not achieved (for example,
       ssccaallee=0; 3.2/1),, the result shall be truncated.

       For all values of oobbaassee specified by this volume of POSIX.1-2008, _b_c
       shall output numeric values by performing each of the following steps
       in order:

        1. If the value is less than zero, a <hyphen> (''--'') character shall be
           output.

        2. One of the following is output, depending on the numerical value:

            *  If the absolute value of the numerical value is greater than or
               equal to one, the integer portion of the value shall be output
               as a series of digits appropriate to oobbaassee (as described
               below), most significant digit first. The most significant non-
               zero digit shall be output next, followed by each successively
               less significant digit.

            *  If the absolute value of the numerical value is less than one
               but greater than zero and the scale of the numerical value is
               greater than zero, it is unspecified whether the character 0 is
               output.

            *  If the numerical value is zero, the character 0 shall be
               output.

        3. If the scale of the value is greater than zero and the numeric
           value is not zero, a <period> character shall be output, followed
           by a series of digits appropriate to oobbaassee (as described below)
           representing the most significant portion of the fractional part of
           the value. If _s represents the scale of the value being output, the
           number of digits output shall be _s if oobbaassee is 10, less than or
           equal to _s if oobbaassee is greater than 10, or greater than or equal to
           _s if oobbaassee is less than 10. For oobbaassee values other than 10, this
           should be the number of digits needed to represent a precision of
           10_s.

       For oobbaassee values from 2 to 16, valid digits are the first oobbaassee of the
       single characters:

           00  11  22  33  44  55  66  77  88  99  AA  BB  CC  DD  EE  FF

       which represent the values zero to 15, inclusive, respectively.

       For bases greater than 16, each digit shall be written as a separate
       multi-digit decimal number. Each digit except the most significant
       fractional digit shall be preceded by a single <space>.  For bases from
       17 to 100, _b_c shall write two-digit decimal numbers; for bases from 101
       to 1000, three-digit decimal strings, and so on. For example, the
       decimal number 1024 in base 25 would be written as:

            0011 1155 2244

       and in base 125, as:

            000088 002244

       Very large numbers shall be split across lines with 70 characters per
       line in the POSIX locale; other locales may split at different
       character boundaries. Lines that are continued shall end with a
       <backslash>.

       A function call shall consist of a function name followed by
       parentheses containing a <comma>-separated list of expressions, which
       are the function arguments. A whole array passed as an argument shall
       be specified by the array name followed by empty square brackets. All
       function arguments shall be passed by value. As a result, changes made
       to the formal parameters shall have no effect on the actual arguments.
       If the function terminates by executing a rreettuurrnn statement, the value
       of the function shall be the value of the expression in the parentheses
       of the rreettuurrnn statement or shall be zero if no expression is provided
       or if there is no rreettuurrnn statement.

       The result of ssqqrrtt(_e_x_p_r_e_s_s_i_o_n) shall be the square root of the
       expression. The result shall be truncated in the least significant
       decimal place. The scale of the result shall be the scale of the
       expression or the value of ssccaallee, whichever is larger.

       The result of lleennggtthh(_e_x_p_r_e_s_s_i_o_n) shall be the total number of
       significant decimal digits in the expression. The scale of the result
       shall be zero.

       The result of ssccaallee(_e_x_p_r_e_s_s_i_o_n) shall be the scale of the expression.
       The scale of the result shall be zero.

       A numeric constant shall be an expression. The scale shall be the
       number of digits that follow the radix point in the input representing
       the constant, or zero if no radix point appears.

       The sequence ( _e_x_p_r_e_s_s_i_o_n ) shall be an expression with the same value
       and scale as _e_x_p_r_e_s_s_i_o_n.  The parentheses can be used to alter the
       normal precedence.

       The semantics of the unary and binary operators are as follows:

       -_e_x_p_r_e_s_s_i_o_n
             The result shall be the negative of the _e_x_p_r_e_s_s_i_o_n.  The scale of
             the result shall be the scale of _e_x_p_r_e_s_s_i_o_n.

       The unary increment and decrement operators shall not modify the scale
       of the named expression upon which they operate. The scale of the
       result shall be the scale of that named expression.

       ++_n_a_m_e_d_-_e_x_p_r_e_s_s_i_o_n
             The named expression shall be incremented by one. The result
             shall be the value of the named expression after incrementing.

       --_n_a_m_e_d_-_e_x_p_r_e_s_s_i_o_n
             The named expression shall be decremented by one. The result
             shall be the value of the named expression after decrementing.

       _n_a_m_e_d_-_e_x_p_r_e_s_s_i_o_n++
             The named expression shall be incremented by one. The result
             shall be the value of the named expression before incrementing.

       _n_a_m_e_d_-_e_x_p_r_e_s_s_i_o_n--
             The named expression shall be decremented by one. The result
             shall be the value of the named expression before decrementing.

       The exponentiation operator, <circumflex> (''^^''), shall bind right to
       left.

       _e_x_p_r_e_s_s_i_o_n^_e_x_p_r_e_s_s_i_o_n
             The result shall be the first _e_x_p_r_e_s_s_i_o_n raised to the power of
             the second _e_x_p_r_e_s_s_i_o_n.  If the second expression is not an
             integer, the behavior is undefined.  If _a is the scale of the
             left expression and _b is the absolute value of the right
             expression, the scale of the result shall be:

                 iiff bb >>== 00 mmiinn((aa ** bb,, mmaaxx((ssccaallee,, aa)))) iiff bb << 00 ssccaallee

       The multiplicative operators (''**'', ''//'', ''%%'') shall bind left to right.

       _e_x_p_r_e_s_s_i_o_n*_e_x_p_r_e_s_s_i_o_n
             The result shall be the product of the two expressions. If _a and
             _b are the scales of the two expressions, then the scale of the
             result shall be:

                 mmiinn((aa++bb,,mmaaxx((ssccaallee,,aa,,bb))))

       _e_x_p_r_e_s_s_i_o_n/_e_x_p_r_e_s_s_i_o_n
             The result shall be the quotient of the two expressions. The
             scale of the result shall be the value of ssccaallee.

       _e_x_p_r_e_s_s_i_o_n%_e_x_p_r_e_s_s_i_o_n
             For expressions _a and _b, _a%_b shall be evaluated equivalent to the
             steps:

              1. Compute _a/_b to current scale.

              2. Use the result to compute:

                     aa -- ((aa // bb)) ** bb

                 to scale:

                     mmaaxx((ssccaallee ++ ssccaallee((bb)),, ssccaallee((aa))))

             The scale of the result shall be:

                 mmaaxx((ssccaallee ++ ssccaallee((bb)),, ssccaallee((aa))))

             When ssccaallee is zero, the ''%%'' operator is the mathematical
             remainder operator.

       The additive operators (''++'', ''--'') shall bind left to right.

       _e_x_p_r_e_s_s_i_o_n+_e_x_p_r_e_s_s_i_o_n
             The result shall be the sum of the two expressions. The scale of
             the result shall be the maximum of the scales of the expressions.

       _e_x_p_r_e_s_s_i_o_n-_e_x_p_r_e_s_s_i_o_n
             The result shall be the difference of the two expressions. The
             scale of the result shall be the maximum of the scales of the
             expressions.

       The assignment operators (''=='', ""++=="", ""--=="", ""**=="", ""//=="", ""%%=="", ""^^=="")
       shall bind right to left.

       _n_a_m_e_d_-_e_x_p_r_e_s_s_i_o_n=_e_x_p_r_e_s_s_i_o_n
             This expression shall result in assigning the value of the
             expression on the right to the named expression on the left. The
             scale of both the named expression and the result shall be the
             scale of _e_x_p_r_e_s_s_i_o_n.

       The compound assignment forms:

           _n_a_m_e_d_-_e_x_p_r_e_s_s_i_o_n <_o_p_e_r_a_t_o_r>= _e_x_p_r_e_s_s_i_o_n

       shall be equivalent to:

           _n_a_m_e_d_-_e_x_p_r_e_s_s_i_o_n=_n_a_m_e_d_-_e_x_p_r_e_s_s_i_o_n <_o_p_e_r_a_t_o_r> _e_x_p_r_e_s_s_i_o_n

       except that the _n_a_m_e_d_-_e_x_p_r_e_s_s_i_o_n shall be evaluated only once.

       Unlike all other operators, the relational operators (''<<'', ''>>'', ""<<=="",
       "">>=="", ""===="", ""!!=="") shall be only valid as the object of an iiff, wwhhiillee, or
       inside a ffoorr statement.

       _e_x_p_r_e_s_s_i_o_n_1<_e_x_p_r_e_s_s_i_o_n_2
             The relation shall be true if the value of _e_x_p_r_e_s_s_i_o_n_1 is
             strictly less than the value of _e_x_p_r_e_s_s_i_o_n_2.

       _e_x_p_r_e_s_s_i_o_n_1>_e_x_p_r_e_s_s_i_o_n_2
             The relation shall be true if the value of _e_x_p_r_e_s_s_i_o_n_1 is
             strictly greater than the value of _e_x_p_r_e_s_s_i_o_n_2.

       _e_x_p_r_e_s_s_i_o_n_1<=_e_x_p_r_e_s_s_i_o_n_2
             The relation shall be true if the value of _e_x_p_r_e_s_s_i_o_n_1 is less
             than or equal to the value of _e_x_p_r_e_s_s_i_o_n_2.

       _e_x_p_r_e_s_s_i_o_n_1>=_e_x_p_r_e_s_s_i_o_n_2
             The relation shall be true if the value of _e_x_p_r_e_s_s_i_o_n_1 is greater
             than or equal to the value of _e_x_p_r_e_s_s_i_o_n_2.

       _e_x_p_r_e_s_s_i_o_n_1==_e_x_p_r_e_s_s_i_o_n_2
             The relation shall be true if the values of _e_x_p_r_e_s_s_i_o_n_1 and
             _e_x_p_r_e_s_s_i_o_n_2 are equal.

       _e_x_p_r_e_s_s_i_o_n_1!=_e_x_p_r_e_s_s_i_o_n_2
             The relation shall be true if the values of _e_x_p_r_e_s_s_i_o_n_1 and
             _e_x_p_r_e_s_s_i_o_n_2 are unequal.

       There are only two storage classes in _b_c: global and automatic (local).
       Only identifiers that are local to a function need be declared with the
       aauuttoo command. The arguments to a function shall be local to the
       function.  All other identifiers are assumed to be global and available
       to all functions. All identifiers, global and local, have initial
       values of zero. Identifiers declared as auto shall be allocated on
       entry to the function and released on returning from the function. They
       therefore do not retain values between function calls. Auto arrays
       shall be specified by the array name followed by empty square brackets.
       On entry to a function, the old values of the names that appear as
       parameters and as automatic variables shall be pushed onto a stack.
       Until the function returns, reference to these names shall refer only
       to the new values.

       References to any of these names from other functions that are called
       from this function also refer to the new value until one of those
       functions uses the same name for a local variable.

       When a statement is an expression, unless the main operator is an
       assignment, execution of the statement shall write the value of the
       expression followed by a <newline>.

       When a statement is a string, execution of the statement shall write
       the value of the string.

       Statements separated by <semicolon> or <newline> characters shall be
       executed sequentially. In an interactive invocation of _b_c, each time a
       <newline> is read that satisfies the grammatical production:

           iinnppuutt__iitteemm :: sseemmiiccoolloonn__lliisstt NNEEWWLLIINNEE

       the sequential list of statements making up the sseemmiiccoolloonn__lliisstt shall be
       executed immediately and any output produced by that execution shall be
       written without any delay due to buffering.

       In an iiff statement (iiff(_r_e_l_a_t_i_o_n) _s_t_a_t_e_m_e_n_t), the _s_t_a_t_e_m_e_n_t shall be
       executed if the relation is true.

       The wwhhiillee statement (wwhhiillee(_r_e_l_a_t_i_o_n) _s_t_a_t_e_m_e_n_t) implements a loop in
       which the _r_e_l_a_t_i_o_n is tested; each time the _r_e_l_a_t_i_o_n is true, the
       _s_t_a_t_e_m_e_n_t shall be executed and the _r_e_l_a_t_i_o_n retested. When the
       _r_e_l_a_t_i_o_n is false, execution shall resume after _s_t_a_t_e_m_e_n_t.

       A ffoorr statement(ffoorr(_e_x_p_r_e_s_s_i_o_n; _r_e_l_a_t_i_o_n; _e_x_p_r_e_s_s_i_o_n) _s_t_a_t_e_m_e_n_t) shall
       be the same as:

           _f_i_r_s_t_-_e_x_p_r_e_s_s_i_o_n
           wwhhiillee ((_r_e_l_a_t_i_o_n)) {{
               _s_t_a_t_e_m_e_n_t
               _l_a_s_t_-_e_x_p_r_e_s_s_i_o_n
           }

       The application shall ensure that all three expressions are present.

       The bbrreeaakk statement shall cause termination of a ffoorr or wwhhiillee
       statement.

       The aauuttoo statement (aauuttoo _i_d_e_n_t_i_f_i_e_r [[,_i_d_e_n_t_i_f_i_e_r]] ...) shall cause the
       values of the identifiers to be pushed down.  The identifiers can be
       ordinary identifiers or array identifiers. Array identifiers shall be
       specified by following the array name by empty square brackets. The
       application shall ensure that the aauuttoo statement is the first statement
       in a function definition.

       A ddeeffiinnee statement:

           ddeeffiinnee _L_E_T_T_E_R (( _o_p_t___p_a_r_a_m_e_t_e_r___l_i_s_t )) {{
               _o_p_t___a_u_t_o___d_e_f_i_n_e___l_i_s_t
               _s_t_a_t_e_m_e_n_t___l_i_s_t
           }

       defines a function named LLEETTTTEERR.  If a function named LLEETTTTEERR was
       previously defined, the ddeeffiinnee statement shall replace the previous
       definition. The expression:

           LLEETTTTEERR (( _o_p_t___a_r_g_u_m_e_n_t___l_i_s_t )

       shall invoke the function named LLEETTTTEERR.  The behavior is undefined if
       the number of arguments in the invocation does not match the number of
       parameters in the definition. Functions shall be defined before they
       are invoked. A function shall be considered to be defined within its
       own body, so recursive calls are valid. The values of numeric constants
       within a function shall be interpreted in the base specified by the
       value of the iibbaassee register when the function is invoked.

       The rreettuurrnn statements (rreettuurrnn and rreettuurrnn(_e_x_p_r_e_s_s_i_o_n)) shall cause
       termination of a function, popping of its auto variables, and
       specification of the result of the function. The first form shall be
       equivalent to rreettuurrnn(0).  The value and scale of the result returned by
       the function shall be the value and scale of the expression returned.

       The qquuiitt statement (qquuiitt) shall stop execution of a _b_c program at the
       point where the statement occurs in the input, even if it occurs in a
       function definition, or in an iiff, ffoorr, or wwhhiillee statement.

       The following functions shall be defined when the --ll option is
       specified:

       ss( _e_x_p_r_e_s_s_i_o_n )
             Sine of argument in radians.

       cc( _e_x_p_r_e_s_s_i_o_n )
             Cosine of argument in radians.

       aa( _e_x_p_r_e_s_s_i_o_n )
             Arctangent of argument.

       ll( _e_x_p_r_e_s_s_i_o_n )
             Natural logarithm of argument.

       ee( _e_x_p_r_e_s_s_i_o_n )
             Exponential function of argument.

       jj( _e_x_p_r_e_s_s_i_o_n, _e_x_p_r_e_s_s_i_o_n )
             Bessel function of integer order.

       The scale of the result returned by these functions shall be the value
       of the ssccaallee register at the time the function is invoked. The value of
       the ssccaallee register after these functions have completed their execution
       shall be the same value it had upon invocation. The behavior is
       undefined if any of these functions is invoked with an argument outside
       the domain of the mathematical function.

EEXXIITT SSTTAATTUUSS
       The following exit values shall be returned:

       0         All input files were processed successfully.

       _u_n_s_p_e_c_i_f_i_e_d
                 An error occurred.

CCOONNSSEEQQUUEENNCCEESS OOFF EERRRROORRSS
       If any _f_i_l_e operand is specified and the named file cannot be accessed,
       _b_c shall write a diagnostic message to standard error and terminate
       without any further action.

       In an interactive invocation of _b_c, the utility should print an error
       message and recover following any error in the input. In a non-
       interactive invocation of _b_c, invalid input causes undefined behavior.

       _T_h_e _f_o_l_l_o_w_i_n_g _s_e_c_t_i_o_n_s _a_r_e _i_n_f_o_r_m_a_t_i_v_e_.

AAPPPPLLIICCAATTIIOONN UUSSAAGGEE
       Automatic variables in _b_c do not work in exactly the same way as in
       either C or PL/1.

       For historical reasons, the exit status from _b_c cannot be relied upon
       to indicate that an error has occurred.  Returning zero after an error
       is possible. Therefore, _b_c should be used primarily by interactive
       users (who can react to error messages) or by application programs that
       can somehow validate the answers returned as not including error
       messages.

       The _b_c utility always uses the <period> (''..'')  character to represent a
       radix point, regardless of any decimal-point character specified as
       part of the current locale. In languages like C or _a_w_k, the <period>
       character is used in program source, so it can be portable and
       unambiguous, while the locale-specific character is used in input and
       output. Because there is no distinction between source and input in _b_c,
       this arrangement would not be possible. Using the locale-specific
       character in _b_c's input would introduce ambiguities into the language;
       consider the following example in a locale with a <comma> as the
       decimal-point character:

           ddeeffiinnee ff((aa,,bb)) {{
               ......
           }}
           ......

           f(1,2,3)

       Because of such ambiguities, the <period> character is used in input.
       Having input follow different conventions from output would be
       confusing in either pipeline usage or interactive usage, so the
       <period> is also used in output.

EEXXAAMMPPLLEESS
       In the shell, the following assigns an approximation of the first ten
       digits of ''--nn'' to the variable _x:

           xx==$$((pprriinnttff ""%%ss\\nn"" ''ssccaallee == 1100;; 110044334488//3333221155'' || bbcc))

       The following _b_c program prints the same approximation of ''--nn'', with a
       label, to standard output:

           ssccaallee == 1100
           ""ppii eeqquuaallss ""
           110044334488 // 3333221155

       The following defines a function to compute an approximate value of the
       exponential function (note that such a function is predefined if the --ll
       option is specified):

           ssccaallee == 2200
           ddeeffiinnee ee((xx)){{
               aauuttoo aa,, bb,, cc,, ii,, ss
               aa == 11
               bb == 11
               ss == 11
               ffoorr ((ii == 11;; 11 ==== 11;; ii++++)){{
                   aa == aa**xx
                   bb == bb**ii
                   cc == aa//bb
                   iiff ((cc ==== 00)) {{
                        rreettuurrnn((ss))
                   }}
                   ss == ss++cc
               }}
           }}

       The following prints approximate values of the exponential function of
       the first ten integers:

           ffoorr ((ii == 11;; ii <<== 1100;; ++++ii)) {{
               ee((ii))
           }}

RRAATTIIOONNAALLEE
       The _b_c utility is implemented historically as a front-end processor for
       _d_c; _d_c was not selected to be part of this volume of POSIX.1-2008
       because _b_c was thought to have a more intuitive programmatic interface.
       Current implementations that implement _b_c using _d_c are expected to be
       compliant.

       The exit status for error conditions has been left unspecified for
       several reasons:

        *  The _b_c utility is used in both interactive and non-interactive
           situations.  Different exit codes may be appropriate for the two
           uses.

        *  It is unclear when a non-zero exit should be given; divide-by-zero,
           undefined functions, and syntax errors are all possibilities.

        *  It is not clear what utility the exit status has.

        *  In the 4.3 BSD, System V, and Ninth Edition implementations, _b_c
           works in conjunction with _d_c.  The _d_c utility is the parent, _b_c is
           the child. This was done to cleanly terminate _b_c if _d_c aborted.

       The decision to have _b_c exit upon encountering an inaccessible input
       file is based on the belief that _b_c _f_i_l_e_1 _f_i_l_e_2 is used most often when
       at least _f_i_l_e_1 contains data/function declarations/initializations.
       Having _b_c continue with prerequisite files missing is probably not
       useful. There is no implication in the CONSEQUENCES OF ERRORS section
       that _b_c must check all its files for accessibility before opening any
       of them.

       There was considerable debate on the appropriateness of the language
       accepted by _b_c.  Several reviewers preferred to see either a pure
       subset of the C language or some changes to make the language more
       compatible with C.  While the _b_c language has some obvious similarities
       to C, it has never claimed to be compatible with any version of C. An
       interpreter for a subset of C might be a very worthwhile utility, and
       it could potentially make _b_c obsolete. However, no such utility is
       known in historical practice, and it was not within the scope of this
       volume of POSIX.1-2008 to define such a language and utility. If and
       when they are defined, it may be appropriate to include them in a
       future version of this standard. This left the following alternatives:

        1. Exclude any calculator language from this volume of POSIX.1-2008.

           The consensus of the standard developers was that a simple
           programmatic calculator language is very useful for both
           applications and interactive users. The only arguments for
           excluding any calculator were that it would become obsolete if and
           when a C-compatible one emerged, or that the absence would
           encourage the development of such a C-compatible one. These
           arguments did not sufficiently address the needs of current
           application developers.

        2. Standardize the historical _d_c, possibly with minor modifications.

           The consensus of the standard developers was that _d_c is a
           fundamentally less usable language and that that would be far too
           severe a penalty for avoiding the issue of being similar to but
           incompatible with C.

        3. Standardize the historical _b_c, possibly with minor modifications.

           This was the approach taken. Most of the proponents of changing the
           language would not have been satisfied until most or all of the
           incompatibilities with C were resolved. Since most of the changes
           considered most desirable would break historical applications and
           require significant modification to historical implementations,
           almost no modifications were made. The one significant modification
           that was made was the replacement of the historical _b_c assignment
           operators ""==++"", and so on, with the more modern ""++=="", and so on.
           The older versions are considered to be fundamentally flawed
           because of the lexical ambiguity in uses like _a=-1.

           In order to permit implementations to deal with backwards-
           compatibility as they see fit, the behavior of this one ambiguous
           construct was made undefined. (At least three implementations have
           been known to support this change already, so the degree of change
           involved should not be great.)

       The ''%%'' operator is the mathematical remainder operator when ssccaallee is
       zero. The behavior of this operator for other values of ssccaallee is from
       historical implementations of _b_c, and has been maintained for the sake
       of historical applications despite its non-intuitive nature.

       Historical implementations permit setting iibbaassee and oobbaassee to a broader
       range of values. This includes values less than 2, which were not seen
       as sufficiently useful to standardize. These implementations do not
       interpret input properly for values of iibbaassee that are greater than 16.
       This is because numeric constants are recognized syntactically, rather
       than lexically, as described in this volume of POSIX.1-2008. They are
       built from lexical tokens of single hexadecimal digits and <period>
       characters. Since <blank> characters between tokens are not visible at
       the syntactic level, it is not possible to recognize the multi-digit
       ``digits'' used in the higher bases properly. The ability to recognize
       input in these bases was not considered useful enough to require
       modifying these implementations.  Note that the recognition of numeric
       constants at the syntactic level is not a problem with conformance to
       this volume of POSIX.1-2008, as it does not impact the behavior of
       conforming applications (and correct _b_c programs). Historical
       implementations also accept input with all of the digits ''00''-''99'' and
       ''AA''-''FF'' regardless of the value of iibbaassee; since digits with value
       greater than or equal to iibbaassee are not really appropriate, the behavior
       when they appear is undefined, except for the common case of:

           iibbaassee==88;;
               //** PPrroocceessss iinn ooccttaall bbaassee.. **//
           ......
           iibbaassee==AA
               //** RReessttoorree ddeecciimmaall bbaassee.. **//

       In some historical implementations, if the expression to be written is
       an uninitialized array element, a leading <space> and/or up to four
       leading 0 characters may be output before the character zero. This
       behavior is considered a bug; it is unlikely that any currently
       conforming application relies on:

           eecchhoo ''bb[[33]]'' || bbcc

       returning 00000 rather than 0.

       Exact calculation of the number of fractional digits to output for a
       given value in a base other than 10 can be computationally expensive.
       Historical implementations use a faster approximation, and this is
       permitted. Note that the requirements apply only to values of oobbaassee
       that this volume of POSIX.1-2008 requires implementations to support
       (in particular, not to 1, 0, or negative bases, if an implementation
       supports them as an extension).

       Historical implementations of _b_c did not allow array parameters to be
       passed as the last parameter to a function. New implementations are
       encouraged to remove this restriction even though it is not required by
       the grammar.

FFUUTTUURREE DDIIRREECCTTIIOONNSS
       None.

SSEEEE AALLSSOO
       _S_e_c_t_i_o_n _1_._3, _G_r_a_m_m_a_r _C_o_n_v_e_n_t_i_o_n_s, _a_w_k

       The Base Definitions volume of POSIX.1-2008, _C_h_a_p_t_e_r _8, _E_n_v_i_r_o_n_m_e_n_t
       _V_a_r_i_a_b_l_e_s, _S_e_c_t_i_o_n _1_2_._2, _U_t_i_l_i_t_y _S_y_n_t_a_x _G_u_i_d_e_l_i_n_e_s

CCOOPPYYRRIIGGHHTT
       Portions of this text are reprinted and reproduced in electronic form
       from IEEE Std 1003.1, 2013 Edition, Standard for Information Technology
       -- Portable Operating System Interface (POSIX), The Open Group Base
       Specifications Issue 7, Copyright (C) 2013 by the Institute of
       Electrical and Electronics Engineers, Inc and The Open Group.  (This is
       POSIX.1-2008 with the 2013 Technical Corrigendum 1 applied.) In the
       event of any discrepancy between this version and the original IEEE and
       The Open Group Standard, the original IEEE and The Open Group Standard
       is the referee document. The original Standard can be obtained online
       at http://www.unix.org/online.html .

       Any typographical or formatting errors that appear in this page are
       most likely to have been introduced during the conversion of the source
       files to man page format. To report such errors, see
       https://www.kernel.org/doc/man-pages/reporting_bugs.html .



IEEE/The Open Group                  2013                                BC(1)
