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.\"


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.\" bc.1  the *roff document processor source for the bc manual


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.\"


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.\" This file is part of GNU bc.


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.\" Copyright (C) 19911994, 1997, 2000, 2003, 2006, 2017 Free Software Foundation, Inc.


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.\"


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.\" This program is free software; you can redistribute it and/or modify


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.\" it under the terms of the GNU General Public License as published by


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.\" the Free Software Foundation; either version 2 of the License , or


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.\" (at your option) any later version.


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.\"


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.\" This program is distributed in the hope that it will be useful,


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.\" but WITHOUT ANY WARRANTY; without even the implied warranty of


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.\" MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the


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.\" GNU General Public License for more details.


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.\"


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.\" You should have received a copy of the GNU General Public License


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.\" along with this program; see the file COPYING. If not, write to:


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.\" The Free Software Foundation, Inc.


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.\" 51 Franklin Street, Fifth Floor


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.\" Boston, MA 021101301 USA


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.\"


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.\" You may contact the author by:


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.\" email: philnelson@acm.org


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.\" usmail: Philip A. Nelson


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.\" Computer Science Department, 9062


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.\" Western Washington University


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.\" Bellingham, WA 982269062


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.\"


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.\"


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.TH bc 1 "20060611" "GNU Project"


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.SH NAME


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bc  An arbitrary precision calculator language


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.SH SYNTAX


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\fBbc\fR [ \fBhlwsqv\fR ] [longoptions] [ \fI file ...\fR ]


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.SH DESCRIPTION


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\fBbc\fR is a language that supports arbitrary precision numbers


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with interactive execution of statements. There are some similarities


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in the syntax to the C programming language.


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A standard math library is available by command line option.


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If requested, the math library is defined before processing any files.


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\fBbc\fR starts by processing code from all the files listed


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on the command line in the order listed. After all files have been


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processed, \fBbc\fR reads from the standard input. All code is


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executed as it is read. (If a file contains a command to halt the


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processor, \fBbc\fR will never read from the standard input.)


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.PP


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This version of \fBbc\fR contains several extensions beyond


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traditional \fBbc\fR implementations and the POSIX draft standard.


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Command line options can cause these extensions to print a warning


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or to be rejected. This


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document describes the language accepted by this processor.


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Extensions will be identified as such.


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.SS OPTIONS


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.IP "h, help"


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Print the usage and exit.


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.IP "i, interactive"


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Force interactive mode.


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.IP "l, mathlib"


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Define the standard math library.


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.IP "w, warn"


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Give warnings for extensions to POSIX \fBbc\fR.


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.IP "s, standard"


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Process exactly the POSIX \fBbc\fR language.


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.IP "q, quiet"


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Do not print the normal GNU bc welcome.


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.IP "v, version"


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Print the version number and copyright and quit.


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.SS NUMBERS


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The most basic element in \fBbc\fR is the number. Numbers are


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arbitrary precision numbers. This precision is both in the integer


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part and the fractional part. All numbers are represented internally


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in decimal and all computation is done in decimal. (This version


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truncates results from divide and multiply operations.) There are two


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attributes of numbers, the length and the scale. The length is the


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total number of decimal digits used by \fBbc\fR to represent a number


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and the scale is the total number of decimal digits after the decimal


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point. For example:


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.nf


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.RS


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.000001 has a length of 6 and scale of 6.


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1935.000 has a length of 7 and a scale of 3.


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.RE


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.fi


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.SS VARIABLES


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Numbers are stored in two types of variables, simple variables and


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arrays. Both simple variables and array variables are named. Names


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begin with a letter followed by any number of letters, digits and


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underscores. All letters must be lower case. (Full alphanumeric


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names are an extension. In POSIX \fBbc\fR all names are a single


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lower case letter.) The type of variable is clear by the context


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because all array variable names will be followed by brackets ([]).


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.PP


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There are four special variables, \fBscale, ibase, obase,\fR and


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\fBlast\fR. \fBscale\fR defines how some operations use digits after the


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decimal point. The default value of \fBscale\fR is 0. \fBibase\fR


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and \fBobase\fR define the conversion base for input and output


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numbers. The default for both input and output is base 10.


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\fBlast\fR (an extension) is a variable that has the value of the last


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printed number. These will be discussed in further detail where


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appropriate. All of these variables may have values assigned to them


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as well as used in expressions.


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.SS COMMENTS


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Comments in \fBbc\fR start with the characters \fB/*\fR and end with


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the characters \fB*/\fR. Comments may start anywhere and appear as a


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single space in the input. (This causes comments to delimit other


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input items. For example, a comment can not be found in the middle of


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a variable name.) Comments include any newlines (end of line) between


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the start and the end of the comment.


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.PP


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To support the use of scripts for \fBbc\fR, a single line comment has been


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added as an extension. A single line comment starts at a \fB#\fR


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character and continues to the next end of the line. The end of line


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character is not part of the comment and is processed normally.


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.SS EXPRESSIONS


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The numbers are manipulated by expressions and statements. Since


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the language was designed to be interactive, statements and expressions


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are executed as soon as possible. There is no "main" program. Instead,


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code is executed as it is encountered. (Functions, discussed in


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detail later, are defined when encountered.)


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.PP


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A simple expression is just a constant. \fBbc\fR converts constants


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into internal decimal numbers using the current input base, specified


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by the variable \fBibase\fR. (There is an exception in functions.)


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The legal values of \fBibase\fR are 2 through 36. (Bases greater than


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16 are an extension.) Assigning a value outside this range to


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\fBibase\fR will result in a value of 2 or 36. Input numbers may


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contain the characters 09 and AZ. (Note: They must be capitals.


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Lower case letters are variable names.) Single digit numbers always


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have the value of the digit regardless of the value of


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\fBibase\fR. (i.e. A = 10.) For multidigit numbers, \fBbc\fR changes


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all input digits greater or equal to ibase to the value of


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\fBibase\fR1. This makes the number \fBZZZ\fR always be the largest


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3 digit number of the input base.


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.PP


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Full expressions are similar to many other high level languages.


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Since there is only one kind of number, there are no rules for mixing


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types. Instead, there are rules on the scale of expressions. Every


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expression has a scale. This is derived from the scale of original


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numbers, the operation performed and in many cases, the value of the


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variable \fBscale\fR. Legal values of the variable \fBscale\fR are


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0 to the maximum number representable by a C integer.


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.PP


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In the following descriptions of legal expressions, "expr" refers to a


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complete expression and "var" refers to a simple or an array variable.


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A simple variable is just a


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.RS


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\fIname\fR


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.RE


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and an array variable is specified as


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.RS


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\fIname\fR[\fIexpr\fR]


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.RE


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Unless specifically


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mentioned the scale of the result is the maximum scale of the


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expressions involved.


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.IP " expr"


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The result is the negation of the expression.


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.IP "++ var"


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The variable is incremented by one and the new value is the result of


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the expression.


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.IP " var"


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The variable


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is decremented by one and the new value is the result of the


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expression.


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.IP "var ++"


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The result of the expression is the value of


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the variable and then the variable is incremented by one.


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.IP "var "


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The result of the expression is the value of the variable and then


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the variable is decremented by one.


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.IP "expr + expr"


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The result of the expression is the sum of the two expressions.


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.IP "expr  expr"


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The result of the expression is the difference of the two expressions.


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.IP "expr * expr"


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The result of the expression is the product of the two expressions.


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.IP "expr / expr"


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The result of the expression is the quotient of the two expressions.


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The scale of the result is the value of the variable \fBscale\fR.


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.IP "expr % expr"


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The result of the expression is the "remainder" and it is computed in the


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following way. To compute a%b, first a/b is computed to \fBscale\fR


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digits. That result is used to compute a(a/b)*b to the scale of the


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maximum of \fBscale\fR+scale(b) and scale(a). If \fBscale\fR is set


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to zero and both expressions are integers this expression is the


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integer remainder function.


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.IP "expr ^ expr"


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The result of the expression is the value of the first raised to the


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second. The second expression must be an integer. (If the second


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expression is not an integer, a warning is generated and the


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expression is truncated to get an integer value.) The scale of the


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result is \fBscale\fR if the exponent is negative. If the exponent


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is positive the scale of the result is the minimum of the scale of the


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first expression times the value of the exponent and the maximum of


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\fBscale\fR and the scale of the first expression. (e.g. scale(a^b)


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= min(scale(a)*b, max( \fBscale,\fR scale(a))).) It should be noted


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that expr^0 will always return the value of 1.


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.IP "( expr )"


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This alters the standard precedence to force the evaluation of the


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expression.


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.IP "var = expr"


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The variable is assigned the value of the expression.


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.IP "var <op>= expr"


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This is equivalent to "var = var <op> expr" with the exception that


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the "var" part is evaluated only once. This can make a difference if


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"var" is an array.


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.PP


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Relational expressions are a special kind of expression


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that always evaluate to 0 or 1, 0 if the relation is false and 1 if


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the relation is true. These may appear in any legal expression.


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(POSIX bc requires that relational expressions are used only in if,


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while, and for statements and that only one relational test may be


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done in them.) The relational operators are


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.IP "expr1 < expr2"


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The result is 1 if expr1 is strictly less than expr2.


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.IP "expr1 <= expr2"


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The result is 1 if expr1 is less than or equal to expr2.


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.IP "expr1 > expr2"


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The result is 1 if expr1 is strictly greater than expr2.


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.IP "expr1 >= expr2"


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The result is 1 if expr1 is greater than or equal to expr2.


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.IP "expr1 == expr2"


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The result is 1 if expr1 is equal to expr2.


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.IP "expr1 != expr2"


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The result is 1 if expr1 is not equal to expr2.


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.PP


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Boolean operations are also legal. (POSIX \fBbc\fR does NOT have


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boolean operations). The result of all boolean operations are 0 and 1


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(for false and true) as in relational expressions. The boolean


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operators are:


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.IP "!expr"


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The result is 1 if expr is 0.


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.IP "expr && expr"


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The result is 1 if both expressions are nonzero.


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.IP "expr  expr"


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The result is 1 if either expression is nonzero.


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.PP


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The expression precedence is as follows: (lowest to highest)


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.nf


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.RS


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 operator, left associative


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&& operator, left associative


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! operator, nonassociative


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Relational operators, left associative


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Assignment operator, right associative


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+ and  operators, left associative


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*, / and % operators, left associative


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^ operator, right associative


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unary  operator, nonassociative


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++ and  operators, nonassociative


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.RE


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.fi


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.PP


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This precedence was chosen so that POSIX compliant \fBbc\fR programs


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will run correctly. This will cause the use of the relational and


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logical operators to have some unusual behavior when used with


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assignment expressions. Consider the expression:


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.RS


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a = 3 < 5


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.RE


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.PP


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Most C programmers would assume this would assign the result of "3 <


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5" (the value 1) to the variable "a". What this does in \fBbc\fR is


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assign the value 3 to the variable "a" and then compare 3 to 5. It is


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best to use parenthesis when using relational and logical operators


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with the assignment operators.


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.PP


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There are a few more special expressions that are provided in \fBbc\fR.


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These have to do with user defined functions and standard


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functions. They all appear as "\fIname\fB(\fIparameters\fB)\fR".


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See the section on functions for user defined functions. The standard


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functions are:


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.IP "length ( expression )"


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The value of the length function is the number of significant digits in the


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expression.


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.IP "read ( )"


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The read function (an extension) will read a number from the standard


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input, regardless of where the function occurs. Beware, this can


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cause problems with the mixing of data and program in the standard input.


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The best use for this function is in a previously written program that


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needs input from the user, but never allows program code to be input


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from the user. The value of the read function is the number read from


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the standard input using the current value of the variable


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\fBibase\fR for the conversion base.


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.IP "scale ( expression )"


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The value of the scale function is the number of digits after the decimal


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point in the expression.


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.IP "sqrt ( expression )"


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The value of the sqrt function is the square root of the expression. If


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the expression is negative, a run time error is generated.


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.SS STATEMENTS


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Statements (as in most algebraic languages) provide the sequencing of


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expression evaluation. In \fBbc\fR statements are executed "as soon


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as possible." Execution happens when a newline in encountered and


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there is one or more complete statements. Due to this immediate


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execution, newlines are very important in \fBbc\fR. In fact, both a


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semicolon and a newline are used as statement separators. An


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improperly placed newline will cause a syntax error. Because newlines


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are statement separators, it is possible to hide a newline by using


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the backslash character. The sequence "\e<nl>", where <nl> is the


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newline appears to \fBbc\fR as whitespace instead of a newline. A


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statement list is a series of statements separated by semicolons and


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newlines. The following is a list of \fBbc\fR statements and what


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they do: (Things enclosed in brackets ([]) are optional parts of the


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statement.)


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.IP "expression"


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This statement does one of two things. If the expression starts with


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"<variable> <assignment> ...", it is considered to be an assignment


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statement. If the expression is not an assignment statement, the


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expression is evaluated and printed to the output. After the number


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is printed, a newline is printed. For example, "a=1" is an assignment


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statement and "(a=1)" is an expression that has an embedded


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assignment. All numbers that are printed are printed in the base


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specified by the variable \fBobase\fR. The legal values for \fB


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obase\fR are 2 through BC_BASE_MAX. (See the section LIMITS.) For


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bases 2 through 16, the usual method of writing numbers is used. For


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bases greater than 16, \fBbc\fR uses a multicharacter digit method


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of printing the numbers where each higher base digit is printed as a


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base 10 number. The multicharacter digits are separated by spaces.


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Each digit contains the number of characters required to represent the


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base ten value of "obase1". Since numbers are of arbitrary


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precision, some numbers may not be printable on a single output line.


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These long numbers will be split across lines using the "\e" as the


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last character on a line. The maximum number of characters printed


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per line is 70. Due to the interactive nature of \fBbc\fR, printing


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a number causes the side effect of assigning the printed value to the


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special variable \fBlast\fR. This allows the user to recover the


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last value printed without having to retype the expression that


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printed the number. Assigning to \fBlast\fR is legal and will


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overwrite the last printed value with the assigned value. The newly


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assigned value will remain until the next number is printed or another


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value is assigned to \fBlast\fR. (Some installations may allow the


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use of a single period (.) which is not part of a number as a short


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hand notation for for \fBlast\fR.)


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.IP "string"


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The string is printed to the output. Strings start with a double quote


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character and contain all characters until the next double quote character.


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All characters are take literally, including any newline. No newline


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character is printed after the string.


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.IP "\fBprint\fR list"


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The print statement (an extension) provides another method of output.


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The "list" is a list of strings and expressions separated by commas.


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Each string or expression is printed in the order of the list. No


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terminating newline is printed. Expressions are evaluated and their


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value is printed and assigned to the variable \fBlast\fR. Strings


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in the print statement are printed to the output and may contain


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special characters. Special characters start with the backslash


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character (\e). The special characters recognized by \fBbc\fR are


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"a" (alert or bell), "b" (backspace), "f" (form feed), "n" (newline),


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"r" (carriage return), "q" (double quote), "t" (tab), and "\e" (backslash).


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Any other character following the backslash will be ignored.


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.IP "{ statement_list }"


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This is the compound statement. It allows multiple statements to be


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grouped together for execution.


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.IP "\fBif\fR ( expression ) statement1 [\fBelse\fR statement2]"


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The if statement evaluates the expression and executes statement1 or


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statement2 depending on the value of the expression. If the expression


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is nonzero, statement1 is executed. If statement2 is present and


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the value of the expression is 0, then statement2 is executed. (The


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else clause is an extension.)


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.IP "\fBwhile\fR ( expression ) statement"


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The while statement will execute the statement while the expression


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is nonzero. It evaluates the expression before each execution of


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the statement. Termination of the loop is caused by a zero


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expression value or the execution of a break statement.


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.IP "\fBfor\fR ( [expression1] ; [expression2] ; [expression3] ) statement"


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The for statement controls repeated execution of the statement.


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Expression1 is evaluated before the loop. Expression2 is evaluated


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70b277 
before each execution of the statement. If it is nonzero, the statement


Packit 
70b277 
is evaluated. If it is zero, the loop is terminated. After each


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70b277 
execution of the statement, expression3 is evaluated before the reevaluation


Packit 
70b277 
of expression2. If expression1 or expression3 are missing, nothing is


Packit 
70b277 
evaluated at the point they would be evaluated.


Packit 
70b277 
If expression2 is missing, it is the same as substituting


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70b277 
the value 1 for expression2. (The optional expressions are an


Packit 
70b277 
extension. POSIX \fBbc\fR requires all three expressions.)


Packit 
70b277 
The following is equivalent code for the for statement:


Packit 
70b277 
.nf


Packit 
70b277 
.RS


Packit 
70b277 
expression1;


Packit 
70b277 
while (expression2) {


Packit 
70b277 
statement;


Packit 
70b277 
expression3;


Packit 
70b277 
}


Packit 
70b277 
.RE


Packit 
70b277 
.fi


Packit 
70b277 
.IP "\fBbreak\fR"


Packit 
70b277 
This statement causes a forced exit of the most recent enclosing while


Packit 
70b277 
statement or for statement.


Packit 
70b277 
.IP "\fBcontinue\fR"


Packit 
70b277 
The continue statement (an extension) causes the most recent enclosing


Packit 
70b277 
for statement to start the next iteration.


Packit 
70b277 
.IP "\fBhalt\fR"


Packit 
70b277 
The halt statement (an extension) is an executed statement that causes


Packit 
70b277 
the \fBbc\fR processor to quit only when it is executed. For example,


Packit 
70b277 
"if (0 == 1) halt" will not cause \fBbc\fR to terminate because the halt is


Packit 
70b277 
not executed.


Packit 
70b277 
.IP "\fBreturn\fR"


Packit 
70b277 
Return the value 0 from a function. (See the section on functions.)


Packit 
70b277 
.IP "\fBreturn\fR ( expression )"


Packit 
70b277 
Return the value of the expression from a function. (See the section on


Packit 
70b277 
functions.) As an extension, the parenthesis are not required.


Packit 
70b277 
.SS PSEUDO STATEMENTS


Packit 
70b277 
These statements are not statements in the traditional sense. They are


Packit 
70b277 
not executed statements. Their function is performed at "compile" time.


Packit 
70b277 
.IP "\fBlimits\fR"


Packit 
70b277 
Print the local limits enforced by the local version of \fBbc\fR. This


Packit 
70b277 
is an extension.


Packit 
70b277 
.IP "\fBquit\fR"


Packit 
70b277 
When the quit statement is read, the \fBbc\fR processor


Packit 
70b277 
is terminated, regardless of where the quit statement is found. For


Packit 
70b277 
example, "if (0 == 1) quit" will cause \fBbc\fR to terminate.


Packit 
70b277 
.IP "\fBwarranty\fR"


Packit 
70b277 
Print a longer warranty notice. This is an extension.


Packit 
70b277 
.SS FUNCTIONS


Packit 
70b277 
Functions provide a method of defining a computation that can be executed


Packit 
70b277 
later. Functions in


Packit 
70b277 
.B bc


Packit 
70b277 
always compute a value and return it to the caller. Function definitions


Packit 
70b277 
are "dynamic" in the sense that a function is undefined until a definition


Packit 
70b277 
is encountered in the input. That definition is then used until another


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70b277 
definition function for the same name is encountered. The new definition


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70b277 
then replaces the older definition. A function is defined as follows:


Packit 
70b277 
.nf


Packit 
70b277 
.RS


Packit 
70b277 
\fBdefine \fIname \fB( \fIparameters \fB) { \fInewline


Packit 
70b277 
\fI auto_list statement_list \fB}\fR


Packit 
70b277 
.RE


Packit 
70b277 
.fi


Packit 
70b277 
A function call is just an expression of the form


Packit 
70b277 
"\fIname\fB(\fIparameters\fB)\fR".


Packit 
70b277 
.PP


Packit 
70b277 
Parameters are numbers or arrays (an extension). In the function definition,


Packit 
70b277 
zero or more parameters are defined by listing their names separated by


Packit 
70b277 
commas. All parameters are call by value parameters.


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70b277 
Arrays are specified in the parameter definition by


Packit 
70b277 
the notation "\fIname\fB[]\fR". In the function call, actual parameters


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70b277 
are full expressions for number parameters. The same notation is used


Packit 
70b277 
for passing arrays as for defining array parameters. The named array is


Packit 
70b277 
passed by value to the function. Since function definitions are dynamic,


Packit 
70b277 
parameter numbers and types are checked when a function is called. Any


Packit 
70b277 
mismatch in number or types of parameters will cause a runtime error.


Packit 
70b277 
A runtime error will also occur for the call to an undefined function.


Packit 
70b277 
.PP


Packit 
70b277 
The \fIauto_list\fR is an optional list of variables that are for


Packit 
70b277 
"local" use. The syntax of the auto list (if present) is "\fBauto


Packit 
70b277 
\fIname\fR, ... ;". (The semicolon is optional.) Each \fIname\fR is


Packit 
70b277 
the name of an auto variable. Arrays may be specified by using the


Packit 
70b277 
same notation as used in parameters. These variables have their


Packit 
70b277 
values pushed onto a stack at the start of the function. The


Packit 
70b277 
variables are then initialized to zero and used throughout the


Packit 
70b277 
execution of the function. At function exit, these variables are


Packit 
70b277 
popped so that the original value (at the time of the function call)


Packit 
70b277 
of these variables are restored. The parameters are really auto


Packit 
70b277 
variables that are initialized to a value provided in the function


Packit 
70b277 
call. Auto variables are different than traditional local variables


Packit 
70b277 
because if function A calls function B, B may access function


Packit 
70b277 
A's auto variables by just using the same name, unless function B has


Packit 
70b277 
called them auto variables. Due to the fact that auto variables and


Packit 
70b277 
parameters are pushed onto a stack, \fBbc\fR supports recursive functions.


Packit 
70b277 
.PP


Packit 
70b277 
The function body is a list of \fBbc\fR statements. Again, statements


Packit 
70b277 
are separated by semicolons or newlines. Return statements cause the


Packit 
70b277 
termination of a function and the return of a value. There are two


Packit 
70b277 
versions of the return statement. The first form, "\fBreturn\fR", returns


Packit 
70b277 
the value 0 to the calling expression. The second form,


Packit 
70b277 
"\fBreturn ( \fIexpression \fB)\fR", computes the value of the expression


Packit 
70b277 
and returns that value to the calling expression. There is an implied


Packit 
70b277 
"\fBreturn (0)\fR" at the end of every function. This allows a function


Packit 
70b277 
to terminate and return 0 without an explicit return statement.


Packit 
70b277 
.PP


Packit 
70b277 
Functions also change the usage of the variable \fBibase\fR. All


Packit 
70b277 
constants in the function body will be converted using the value of


Packit 
70b277 
\fBibase\fR at the time of the function call. Changes of \fBibase\fR


Packit 
70b277 
will be ignored during the execution of the function except for the


Packit 
70b277 
standard function \fBread\fR, which will always use the current value


Packit 
70b277 
of \fBibase\fR for conversion of numbers.


Packit 
70b277 
.PP


Packit 
70b277 
Several extensions have been added to functions. First, the format of


Packit 
70b277 
the definition has been slightly relaxed. The standard requires the


Packit 
70b277 
opening brace be on the same line as the \fBdefine\fR keyword and all


Packit 
70b277 
other parts must be on following lines. This version of \fBbc\fR will


Packit 
70b277 
allow any number of newlines before and after the opening brace of the


Packit 
70b277 
function. For example, the following definitions are legal.


Packit 
70b277 
.nf


Packit 
70b277 
.RS


Packit 
70b277 
\f(CW


Packit 
70b277 
define d (n) { return (2*n); }


Packit 
70b277 
define d (n)


Packit 
70b277 
{ return (2*n); }


Packit 
70b277 
\fR


Packit 
70b277 
.RE


Packit 
70b277 
.fi


Packit 
70b277 
.PP


Packit 
70b277 
Functions may be defined as \fBvoid\fR. A void


Packit 
70b277 
funtion returns no value and thus may not be used in any place that needs


Packit 
70b277 
a value. A void function does not produce any output when called by itself


Packit 
70b277 
on an input line. The key word \fBvoid\fR is placed between the key word


Packit 
70b277 
\fBdefine\fR and the function name. For example, consider the following


Packit 
70b277 
session.


Packit 
70b277 
.nf


Packit 
70b277 
.RS


Packit 
70b277 
\f(CW


Packit 
70b277 
define py (y) { print ">", y, "<", "\en"; }


Packit 
70b277 
define void px (x) { print ">", x, "<", "\en"; }


Packit 
70b277 
py(1)


Packit 
70b277 
>1<


Packit 
70b277 
0


Packit 
70b277 
px(1)


Packit 
70b277 
>1<


Packit 
70b277 
\fR


Packit 
70b277 
.RE


Packit 
70b277 
.fi


Packit 
70b277 
Since \fBpy\fR is not a void function, the call of \fBpy(1)\fR prints


Packit 
70b277 
the desired output and then prints a second line that is the value of


Packit 
70b277 
the function. Since the value of a function that is not given an


Packit 
70b277 
explicit return statement is zero, the zero is printed. For \fBpx(1)\fR,


Packit 
70b277 
no zero is printed because the function is a void function.


Packit 
70b277 
.PP


Packit 
70b277 
Also, call by variable for arrays was added. To declare


Packit 
70b277 
a call by variable array, the declaration of the array parameter in the


Packit 
70b277 
function definition looks like "\fI*name\fB[]\fR". The call to the


Packit 
70b277 
function remains the same as call by value arrays.


Packit 
70b277 
.SS MATH LIBRARY


Packit 
70b277 
If \fBbc\fR is invoked with the \fBl\fR option, a math library is preloaded


Packit 
70b277 
and the default scale is set to 20. The math functions will calculate their


Packit 
70b277 
results to the scale set at the time of their call.


Packit 
70b277 
The math library defines the following functions:


Packit 
70b277 
.IP "s (\fIx\fR)"


Packit 
70b277 
The sine of x, x is in radians.


Packit 
70b277 
.IP "c (\fIx\fR)"


Packit 
70b277 
The cosine of x, x is in radians.


Packit 
70b277 
.IP "a (\fIx\fR)"


Packit 
70b277 
The arctangent of x, arctangent returns radians.


Packit 
70b277 
.IP "l (\fIx\fR)"


Packit 
70b277 
The natural logarithm of x.


Packit 
70b277 
.IP "e (\fIx\fR)"


Packit 
70b277 
The exponential function of raising e to the value x.


Packit 
70b277 
.IP "j (\fIn,x\fR)"


Packit 
70b277 
The Bessel function of integer order n of x.


Packit 
70b277 
.SS EXAMPLES


Packit 
70b277 
In /bin/sh, the following will assign the value of "pi" to the shell


Packit 
70b277 
variable \fBpi\fR.


Packit 
70b277 
.RS


Packit 
70b277 
\f(CW


Packit 
70b277 
pi=$(echo "scale=10; 4*a(1)"  bc l)


Packit 
70b277 
\fR


Packit 
70b277 
.RE


Packit 
70b277 
.PP


Packit 
70b277 
The following is the definition of the exponential function used in the


Packit 
70b277 
math library. This function is written in POSIX \fBbc\fR.


Packit 
70b277 
.nf


Packit 
70b277 
.RS


Packit 
70b277 
\f(CW


Packit 
70b277 
scale = 20


Packit 
70b277 


Packit 
70b277 
/* Uses the fact that e^x = (e^(x/2))^2


Packit 
70b277 
When x is small enough, we use the series:


Packit 
70b277 
e^x = 1 + x + x^2/2! + x^3/3! + ...


Packit 
70b277 
*/


Packit 
70b277 


Packit 
70b277 
define e(x) {


Packit 
70b277 
auto a, d, e, f, i, m, v, z


Packit 
70b277 


Packit 
70b277 
/* Check the sign of x. */


Packit 
70b277 
if (x<0) {


Packit 
70b277 
m = 1


Packit 
70b277 
x = x


Packit 
70b277 
}


Packit 
70b277 


Packit 
70b277 
/* Precondition x. */


Packit 
70b277 
z = scale;


Packit 
70b277 
scale = 4 + z + .44*x;


Packit 
70b277 
while (x > 1) {


Packit 
70b277 
f += 1;


Packit 
70b277 
x /= 2;


Packit 
70b277 
}


Packit 
70b277 


Packit 
70b277 
/* Initialize the variables. */


Packit 
70b277 
v = 1+x


Packit 
70b277 
a = x


Packit 
70b277 
d = 1


Packit 
70b277 


Packit 
70b277 
for (i=2; 1; i++) {


Packit 
70b277 
e = (a *= x) / (d *= i)


Packit 
70b277 
if (e == 0) {


Packit 
70b277 
if (f>0) while (f) v = v*v;


Packit 
70b277 
scale = z


Packit 
70b277 
if (m) return (1/v);


Packit 
70b277 
return (v/1);


Packit 
70b277 
}


Packit 
70b277 
v += e


Packit 
70b277 
}


Packit 
70b277 
}


Packit 
70b277 
\fR


Packit 
70b277 
.RE


Packit 
70b277 
.fi


Packit 
70b277 
.PP


Packit 
70b277 
The following is code that uses the extended features of \fBbc\fR to


Packit 
70b277 
implement a simple program for calculating checkbook balances. This


Packit 
70b277 
program is best kept in a file so that it can be used many times


Packit 
70b277 
without having to retype it at every use.


Packit 
70b277 
.nf


Packit 
70b277 
.RS


Packit 
70b277 
\f(CW


Packit 
70b277 
scale=2


Packit 
70b277 
print "\enCheck book program!\en"


Packit 
70b277 
print " Remember, deposits are negative transactions.\en"


Packit 
70b277 
print " Exit by a 0 transaction.\en\en"


Packit 
70b277 


Packit 
70b277 
print "Initial balance? "; bal = read()


Packit 
70b277 
bal /= 1


Packit 
70b277 
print "\en"


Packit 
70b277 
while (1) {


Packit 
70b277 
"current balance = "; bal


Packit 
70b277 
"transaction? "; trans = read()


Packit 
70b277 
if (trans == 0) break;


Packit 
70b277 
bal = trans


Packit 
70b277 
bal /= 1


Packit 
70b277 
}


Packit 
70b277 
quit


Packit 
70b277 
\fR


Packit 
70b277 
.RE


Packit 
70b277 
.fi


Packit 
70b277 
.PP


Packit 
70b277 
The following is the definition of the recursive factorial function.


Packit 
70b277 
.nf


Packit 
70b277 
.RS


Packit 
70b277 
\f(CW


Packit 
70b277 
define f (x) {


Packit 
70b277 
if (x <= 1) return (1);


Packit 
70b277 
return (f(x1) * x);


Packit 
70b277 
}


Packit 
70b277 
\fR


Packit 
70b277 
.RE


Packit 
70b277 
.fi


Packit 
70b277 
.SS READLINE AND LIBEDIT OPTIONS


Packit 
70b277 
GNU \fBbc\fR can be compiled (via a configure option) to use the GNU


Packit 
70b277 
\fBreadline\fR input editor library or the BSD \fBlibedit\fR library.


Packit 
70b277 
This allows the user to do editing of lines before sending them


Packit 
70b277 
to \fBbc\fR. It also allows for a history of previous lines typed.


Packit 
70b277 
When this option is selected, \fBbc\fR has one more special variable.


Packit 
70b277 
This special variable, \fBhistory\fR is the number of lines of history


Packit 
70b277 
retained. For \fBreadline\fR, a value of 1 means that an unlimited


Packit 
70b277 
number of history lines are retained. Setting the value of


Packit 
70b277 
\fBhistory\fR to a positive number restricts the number of history


Packit 
70b277 
lines to the number given. The value of 0 disables the history


Packit 
70b277 
feature. The default value is 100. For more information, read the


Packit 
70b277 
user manuals for the GNU \fBreadline\fR, \fBhistory\fR and BSD \fBlibedit\fR


Packit 
70b277 
libraries. One can not enable both \fBreadline\fR and \fBlibedit\fR


Packit 
70b277 
at the same time.


Packit 
70b277 
.SS DIFFERENCES


Packit 
70b277 
This version of


Packit 
70b277 
.B bc


Packit 
70b277 
was implemented from the POSIX P1003.2/D11 draft and contains


Packit 
70b277 
several differences and extensions relative to the draft and


Packit 
70b277 
traditional implementations.


Packit 
70b277 
It is not implemented in the traditional way using


Packit 
70b277 
.I dc(1).


Packit 
70b277 
This version is a single process which parses and runs a byte code


Packit 
70b277 
translation of the program. There is an "undocumented" option (c)


Packit 
70b277 
that causes the program to output the byte code to


Packit 
70b277 
the standard output instead of running it. It was mainly used for


Packit 
70b277 
debugging the parser and preparing the math library.


Packit 
70b277 
.PP


Packit 
70b277 
A major source of differences is


Packit 
70b277 
extensions, where a feature is extended to add more functionality and


Packit 
70b277 
additions, where new features are added.


Packit 
70b277 
The following is the list of differences and extensions.


Packit 
70b277 
.IP "LANG environment"


Packit 
70b277 
This version does not conform to the POSIX standard in the processing


Packit 
70b277 
of the LANG environment variable and all environment variables starting


Packit 
70b277 
with LC_.


Packit 
70b277 
.IP "names"


Packit 
70b277 
Traditional and POSIX


Packit 
70b277 
.B bc


Packit 
70b277 
have single letter names for functions, variables and arrays. They have


Packit 
70b277 
been extended to be multicharacter names that start with a letter and


Packit 
70b277 
may contain letters, numbers and the underscore character.


Packit 
70b277 
.IP "Strings"


Packit 
70b277 
Strings are not allowed to contain NUL characters. POSIX says all characters


Packit 
70b277 
must be included in strings.


Packit 
70b277 
.IP "last"


Packit 
70b277 
POSIX \fBbc\fR does not have a \fBlast\fR variable. Some implementations


Packit 
70b277 
of \fBbc\fR use the period (.) in a similar way.


Packit 
70b277 
.IP "comparisons"


Packit 
70b277 
POSIX \fBbc\fR allows comparisons only in the if statement, the while


Packit 
70b277 
statement, and the second expression of the for statement. Also, only


Packit 
70b277 
one relational operation is allowed in each of those statements.


Packit 
70b277 
.IP "if statement, else clause"


Packit 
70b277 
POSIX \fBbc\fR does not have an else clause.


Packit 
70b277 
.IP "for statement"


Packit 
70b277 
POSIX \fBbc\fR requires all expressions to be present in the for statement.


Packit 
70b277 
.IP "&&, , !"


Packit 
70b277 
POSIX \fBbc\fR does not have the logical operators.


Packit 
70b277 
.IP "read function"


Packit 
70b277 
POSIX \fBbc\fR does not have a read function.


Packit 
70b277 
.IP "print statement"


Packit 
70b277 
POSIX \fBbc\fR does not have a print statement .


Packit 
70b277 
.IP "continue statement"


Packit 
70b277 
POSIX \fBbc\fR does not have a continue statement.


Packit 
70b277 
.IP "return statement"


Packit 
70b277 
POSIX \fBbc\fR requires parentheses around the return expression.


Packit 
70b277 
.IP "array parameters"


Packit 
70b277 
POSIX \fBbc\fR does not (currently) support array parameters in full.


Packit 
70b277 
The POSIX grammar allows for arrays in function definitions, but does


Packit 
70b277 
not provide a method to specify an array as an actual parameter. (This


Packit 
70b277 
is most likely an oversight in the grammar.) Traditional implementations


Packit 
70b277 
of \fBbc\fR have only call by value array parameters.


Packit 
70b277 
.IP "function format"


Packit 
70b277 
POSIX \fBbc\fR requires the opening brace on the same line as the


Packit 
70b277 
\fBdefine\fR key word and the \fBauto\fR statement on the next line.


Packit 
70b277 
.IP "=+, =, =*, =/, =%, =^"


Packit 
70b277 
POSIX \fBbc\fR does not require these "old style" assignment operators to


Packit 
70b277 
be defined. This version may allow these "old style" assignments. Use


Packit 
70b277 
the limits statement to see if the installed version supports them. If


Packit 
70b277 
it does support the "old style" assignment operators, the statement


Packit 
70b277 
"a = 1" will decrement \fBa\fR by 1 instead of setting \fBa\fR to the


Packit 
70b277 
value 1.


Packit 
70b277 
.IP "spaces in numbers"


Packit 
70b277 
Other implementations of \fBbc\fR allow spaces in numbers. For example,


Packit 
70b277 
"x=1 3" would assign the value 13 to the variable x. The same statement


Packit 
70b277 
would cause a syntax error in this version of \fBbc\fR.


Packit 
70b277 
.IP "errors and execution"


Packit 
70b277 
This implementation varies from other implementations in terms of what


Packit 
70b277 
code will be executed when syntax and other errors are found in the


Packit 
70b277 
program. If a syntax error is found in a function definition, error


Packit 
70b277 
recovery tries to find the beginning of a statement and continue to


Packit 
70b277 
parse the function. Once a syntax error is found in the function, the


Packit 
70b277 
function will not be callable and becomes undefined.


Packit 
70b277 
Syntax errors in the interactive execution code will invalidate the


Packit 
70b277 
current execution block. The execution block is terminated by an


Packit 
70b277 
end of line that appears after a complete sequence of statements.


Packit 
70b277 
For example,


Packit 
70b277 
.nf


Packit 
70b277 
.RS


Packit 
70b277 
a = 1


Packit 
70b277 
b = 2


Packit 
70b277 
.RE


Packit 
70b277 
.fi


Packit 
70b277 
has two execution blocks and


Packit 
70b277 
.nf


Packit 
70b277 
.RS


Packit 
70b277 
{ a = 1


Packit 
70b277 
b = 2 }


Packit 
70b277 
.RE


Packit 
70b277 
.fi


Packit 
70b277 
has one execution block. Any runtime error will terminate the execution


Packit 
70b277 
of the current execution block. A runtime warning will not terminate the


Packit 
70b277 
current execution block.


Packit 
70b277 
.IP "Interrupts"


Packit 
70b277 
During an interactive session, the SIGINT signal (usually generated by


Packit 
70b277 
the controlC character from the terminal) will cause execution of the


Packit 
70b277 
current execution block to be interrupted. It will display a "runtime"


Packit 
70b277 
error indicating which function was interrupted. After all runtime


Packit 
70b277 
structures have been cleaned up, a message will be printed to notify the


Packit 
70b277 
user that \fBbc\fR is ready for more input. All previously defined functions


Packit 
70b277 
remain defined and the value of all nonauto variables are the value at


Packit 
70b277 
the point of interruption. All auto variables and function parameters


Packit 
70b277 
are removed during the


Packit 
70b277 
clean up process. During a noninteractive


Packit 
70b277 
session, the SIGINT signal will terminate the entire run of \fBbc\fR.


Packit 
70b277 
.SS LIMITS


Packit 
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The following are the limits currently in place for this


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.B bc


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processor. Some of them may have been changed by an installation.


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Use the limits statement to see the actual values.


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.IP "BC_BASE_MAX"


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The maximum output base is currently set at 999. The maximum input base


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is 16.


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.IP "BC_DIM_MAX"


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This is currently an arbitrary limit of 65535 as distributed. Your


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installation may be different.


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.IP "BC_SCALE_MAX"


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The number of digits after the decimal point is limited to INT_MAX digits.


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Also, the number of digits before the decimal point is limited to INT_MAX


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digits.


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.IP "BC_STRING_MAX"


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The limit on the number of characters in a string is INT_MAX characters.


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.IP "exponent"


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The value of the exponent in the raise operation (^) is limited to LONG_MAX.


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.IP "variable names"


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The current limit on the number of unique names is 32767 for each of


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simple variables, arrays and functions.


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.SH ENVIRONMENT VARIABLES


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The following environment variables are processed by \fBbc\fR:


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.IP "POSIXLY_CORRECT"


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This is the same as the \fBs\fR option.


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.IP "BC_ENV_ARGS"


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This is another mechanism to get arguments to \fBbc\fR. The


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format is the same as the command line arguments. These arguments


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are processed first, so any files listed in the environment arguments


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are processed before any command line argument files. This allows


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the user to set up "standard" options and files to be processed


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at every invocation of \fBbc\fR. The files in the environment


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variables would typically contain function definitions for functions


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the user wants defined every time \fBbc\fR is run.


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.IP "BC_LINE_LENGTH"


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This should be an integer specifying the number of characters in an


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output line for numbers. This includes the backslash and newline characters


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for long numbers. As an extension, the value of zero disables the


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multiline feature. Any other value of this variable that is less than


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3 sets the line length to 70.


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.SH DIAGNOSTICS


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If any file on the command line can not be opened, \fBbc\fR will report


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that the file is unavailable and terminate. Also, there are compile


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and run time diagnostics that should be selfexplanatory.


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.SH BUGS


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Error recovery is not very good yet.


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.PP


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Email bug reports to


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.BR bugbc@gnu.org .


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Be sure to include the word ``bc'' somewhere in the ``Subject:'' field.


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.SH AUTHOR


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.nf


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Philip A. Nelson


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philnelson@acm.org


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.fi


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.SH ACKNOWLEDGEMENTS


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The author would like to thank Steve Sommars (Steve.Sommars@att.com) for


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his extensive help in testing the implementation. Many great suggestions


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were given. This is a much better product due to his involvement.
