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<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"><html><head>  <meta content="text/html; charset=ISO-8859-1" http-equiv="content-type">  <title>GNU Make Standard Library</title></head> <body><h1>GNU Make Standard Library</h1>The GNU Make Standard Library (GMSL) is a collection of functionsimplemented using native GNU Make functionality that provide list andstring manipulation, integer arithmetic, associative arrays, stacks,and debugging facilities.&nbsp; The GMSL is released under the BSD License.<br><br><a href="http://sourceforge.net/projects/gmsl/">[Project Page]</a> <a href="http://sourceforge.net/project/showfiles.php?group_id=129887">[Download]</a><a href="http://sourceforge.net/forum/forum.php?forum_id=443916">[DiscussionForum]</a><br><h2>Using GMSL</h2>The two files needed are <span style="font-family: monospace;">gmsl</span>and <span style="font-family: monospace;">__gmsl</span>.&nbsp; Toinclude the GMSL in your Makefile do<br><pre style="margin-left: 40px;">include gmsl</pre><span style="font-family: monospace;">gmsl</span> automatically includes<span style="font-family: monospace;"> __gmsl</span>.&nbsp; To check thatyou have the right version of <span style="font-family: monospace;">gmsl</span>use the <span style="font-family: monospace;">gmsl_compatible</span>function (seebelow). The current version is <span style="font-family: monospace;">1 1 6</span>.<br><br>The GMSL package also includes a test suite for GMSL.&nbsp; Just run <span style="font-family: monospace;">make -f gmsl-tests</span>.<br><h2>Logical Operators</h2>GMSL has boolean $(true) (a non-empty string)and $(false) (an empty string).&nbsp; The following operators can beused with those variables.<br><br><hr style="width: 100%; height: 2px;"><span style="font-weight: bold;">not</span><br> <br> <span style="font-family: monospace;">Arguments: A boolean value</span><br style="font-family: monospace;"> <span style="font-family: monospace;">Returns:&nbsp;&nbsp; Returns $(true) if the boolean is $(false) and vice versa</span><br style="font-family: monospace;"> <hr style="width: 100%; height: 2px; font-family: monospace;"><span style="font-weight: bold;"></span><span style="font-weight: bold;">and</span><br><br><span style="font-family: monospace;">Arguments: Two boolean values</span><br style="font-family: monospace;"><span style="font-family: monospace;">Returns:&nbsp;&nbsp; Returns $(true) if both of the booleans are true</span><br style="font-family: monospace;"><hr style="width: 100%; height: 2px; font-family: monospace;"><span style="font-weight: bold;">or</span><br><br><span style="font-family: monospace;">Arguments: Two boolean values</span><br style="font-family: monospace;"><span style="font-family: monospace;">Returns:&nbsp;&nbsp; Returns $(true) if either of the booleans is true</span><br style="font-family: monospace;"><hr style="width: 100%; height: 2px; font-family: monospace;"><span style="font-weight: bold;">xor</span><br style="font-weight: bold;"><br><span style="font-family: monospace;">Arguments: Two boolean values</span><br style="font-family: monospace;"><span style="font-family: monospace;">Returns:&nbsp;&nbsp; Returns $(true) if exactly one of the booleans is true</span><br style="font-family: monospace;"><hr style="width: 100%; height: 2px; font-family: monospace;"><span style="font-weight: bold;">nand</span><br><br><span style="font-family: monospace;">Arguments: Two boolean values</span><br style="font-family: monospace;"><span style="font-family: monospace;">Returns:&nbsp;&nbsp; Returns value of 'not and'</span><br style="font-family: monospace;"><hr style="width: 100%; height: 2px; font-family: monospace;"><span style="font-weight: bold;">nor</span><br><br><span style="font-family: monospace;">Arguments: Two boolean values</span><br style="font-family: monospace;"><span style="font-family: monospace;">Returns:&nbsp;&nbsp; Returns value of 'not or'</span><br style="font-family: monospace;"><hr style="width: 100%; height: 2px; font-family: monospace;"><span style="font-weight: bold;">xnor</span><br><br><span style="font-family: monospace;">Arguments: Two boolean values</span><br style="font-family: monospace;"><span style="font-family: monospace;">Returns:&nbsp;&nbsp; Returns value of 'not xor'</span><br style="font-family: monospace;"><hr style="width: 100%; height: 2px; font-family: monospace;"><h2>List Manipulation Functions</h2>&nbsp;A list is a string of characters; the list separator is a space.<br> <br><hr style="width: 100%; height: 2px;"><b>first</b><br><br><span style="font-family: monospace;">Arguments: 1: A list<br>Returns:&nbsp;&nbsp;&nbsp;Returns the first element of a list<br></span><hr><b>last</b><br><br><span style="font-family: monospace;">Arguments: 1: A list<br>Returns:&nbsp;&nbsp;&nbsp;Returns the last element of a list<br></span><hr><b>rest</b><br><br><span style="font-family: monospace;">Arguments: 1: A list<br>Returns:&nbsp;&nbsp;&nbsp;Returns the list with the first elementremoved<br></span><hr><b>chop</b><br><br><span style="font-family: monospace;">Arguments: 1: A list<br>Returns:&nbsp;&nbsp;&nbsp;Returns the list with the last element removed<br></span><hr><b>map</b><br><br><span style="font-family: monospace;">Arguments: 1: Name of function to$(call) for each element of list<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 2: List toiterate over calling the function in 1<br>Returns:&nbsp;&nbsp;&nbsp;The list after calling the function on eachelement<br></span><hr><b>pairmap</b><br><br><span style="font-family: monospace;">Arguments: 1: Name of function to$(call) for each pair of elements<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 2: List toiterate over calling the function in 1<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 3: Secondlist to iterate over calling the function in 1<br>Returns:&nbsp;&nbsp;&nbsp;The list after calling the function on eachpair of elements<br></span><hr><b>leq</b><br><br><span style="font-family: monospace;">Arguments: 1: A list to compareagainst...<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 2: ...thislist<br>Returns:&nbsp;&nbsp;&nbsp;Returns $(true) if the two lists are identical<br></span><hr><b>lne</b><br><br><span style="font-family: monospace;">Arguments: 1: A list to compareagainst...<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 2: ...thislist<br>Returns:&nbsp;&nbsp;&nbsp;Returns $(true) if the two lists are different<br></span><hr><b>reverse</b><br><br><span style="font-family: monospace;">Arguments: 1: A list to reverse<br>Returns:&nbsp;&nbsp;&nbsp;The list with its elements in reverse order<br></span><hr><b>uniq</b><br><br><span style="font-family: monospace;">Arguments: 1: A list to deduplicate<br>Returns:&nbsp;&nbsp;&nbsp;The list with elements in order without duplicates<br></span><hr><b>length</b><br><br><span style="font-family: monospace;">Arguments: 1: A list<br>Returns:&nbsp;&nbsp;&nbsp;The number of elements in the list<br></span><hr style="width: 100%; height: 2px;"><span style="font-family: monospace;"></span><h2>String Manipulation Functions</h2>A string is any sequence of characters.<br><br><hr style="width: 100%; height: 2px;"><b>seq</b><br><br><span style="font-family: monospace;">Arguments: 1: A string to compareagainst...<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 2: ...thisstring<br>Returns:&nbsp;&nbsp;&nbsp;Returns $(true) if the two strings areidentical<br></span><hr><b>sne</b><br><br><span style="font-family: monospace;">Arguments: 1: A string to compareagainst...<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 2: ...thisstring<br>Returns:&nbsp;&nbsp;&nbsp;Returns $(true) if the two strings are notthe same<br></span><hr><b>strlen</b><br><br><span style="font-family: monospace;">Arguments: 1: A string<br>Returns:&nbsp;&nbsp;&nbsp;Returns the length of the string<br></span><hr><b>substr</b><br><br><span style="font-family: monospace;">Arguments: 1: A string<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 2: Start offset (first character is 1)<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 3: Ending offset (inclusive)<br>Returns:&nbsp;&nbsp;&nbsp;Returns a substring<br></span><hr><b>split</b><br><br><span style="font-family: monospace;">Arguments: 1: The character tosplit on<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 2: Astring to split<br>Returns:&nbsp;&nbsp;&nbsp;Splits a string into a list separated byspaces at the split<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; characterin the first argument<br></span><hr><b>merge</b><br><br><span style="font-family: monospace;">Arguments: 1: The character toput between fields<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 2: A listto merge into a string<br>Returns:&nbsp;&nbsp;&nbsp;Merges a list into a single string, listelements are separated<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; by thecharacter in the first argument<br></span><hr><b>tr</b><br><br><span style="font-family: monospace;">Arguments: 1: The list ofcharacters to translate from <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 2: Thelist of characters to translate to<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 3: Thetext to translate<br>Returns:&nbsp;&nbsp;&nbsp;Returns the text after translating characters<br></span><hr><b>uc</b><br><br><span style="font-family: monospace;">Arguments: 1: Text to upper case<br>Returns:&nbsp;&nbsp;&nbsp;Returns the text in upper case<br></span><hr><b>lc</b><br><br><span style="font-family: monospace;">Arguments: 1: Text to lower case<br>Returns:&nbsp;&nbsp;&nbsp;Returns the text in lower case<br></span><hr style="width: 100%; height: 2px;"><span style="font-family: monospace;"></span><h2>Set Manipulation Functions</h2>Sets are represented by sorted, deduplicated lists.  To create a setfrom a list use <span style="font-family:monospace;">set_create</span>, or start with the <spanstyle="font-family: monospace;">empty_set</span> and <spanstyle="font-family: monospace;">set_insert</span> individual elements.The empty set is defined as <span style="font-family:monospace;">empty_set</span>.<p> <hr><b>set_create</b><br><br><span style="font-family: monospace;">Arguments: 1: A list of set elements<br>Returns:&nbsp;&nbsp;&nbsp;Returns the newly created set<br></span> <hr><b>set_insert</b><br><br><span style="font-family: monospace;">Arguments: 1: A single element to add to a set<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;2: A set<br>Returns:&nbsp;&nbsp;&nbsp;Returns the set with the element added<br></span> <hr><b>set_remove</b><br><br><span style="font-family: monospace;">Arguments: 1: A single element to remove from a set<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;2: A set<br>Returns:&nbsp;&nbsp;&nbsp;Returns the set with the element removed<br></span> <hr><b>set_is_member</b><br><br><span style="font-family: monospace;">Arguments: 1: A single element<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;2: A set<br>Returns:&nbsp;&nbsp;&nbsp;Returns $(true) if the element is in the set<br></span> <hr><b>set_is_not_member</b><br><br><span style="font-family: monospace;">Arguments: 1: A single element<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;2: A set<br>Returns:&nbsp;&nbsp;&nbsp;Returns $(false) if the element is in the set<br></span> <hr><b>set_union</b><br><br><span style="font-family: monospace;">Arguments: 1: A set<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;2: Another set<br>Returns:&nbsp;&nbsp;&nbsp;Returns the union of the two sets<br></span> <hr><b>set_intersection</b><br><br><span style="font-family: monospace;">Arguments: 1: A set<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;2: Another set<br>Returns:&nbsp;&nbsp;&nbsp;Returns the intersection of the two sets<br></span> <hr><b>set_is_subset</b><br><br><span style="font-family: monospace;">Arguments: 1: A set<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;2: Another set<br>Returns:&nbsp;&nbsp;&nbsp;Returns $(true) if the first set is a subset of the second<br></span> <hr><b>set_equal</b><br><br><span style="font-family: monospace;">Arguments: 1: A set<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;2: Another set<br>Returns:&nbsp;&nbsp;&nbsp;Returns $(true) if the two sets are identical<br></span> <hr style="width: 100%; height: 2px;"><span style="font-family: monospace;"></span><h2>Integer Arithmetic Functions</h2>Integers are represented by lists with the equivalent number ofx's.&nbsp; For example the number 4 is x x x x.&nbsp; The maximuminteger that the library can handle as <span style="font-style: italic;">input</span> (i.e. as the argument to acall to <span style="font-family: monospace;">int_encode</span>) is65536. There is no limit on integer size for internal computations oroutput.<br><br>The arithmetic library functions come in two forms: one form of eachfunction takes integers as arguments and the other form takes theencoded form (x's created by a call to <span style="font-family: monospace;">int_encode</span>).&nbsp; For example,there are two plus functions: <span style="font-family: monospace;">plus</span>(called with integer arguments and returns an integer) and <span style="font-family: monospace;">int_plus</span> (called with encodedarguments and returns an encoded result).<br><br><span style="font-family: monospace;">plus</span> will be slower than <span style="font-family: monospace;">int_plus</span> because its argumentsand result have to be translated between the x's format andintegers.&nbsp; If doing a complex calculation use the <span style="font-family: monospace;">int_*</span> forms with a singleencoding of inputs and single decoding of the output.&nbsp; For simplecalculations the direct forms can be used.<br><br><hr style="width: 100%; height: 2px;"><b>int_decode</b><br><br><span style="font-family: monospace;">Arguments: 1: A number of x'srepresentation<br>Returns:&nbsp;&nbsp;&nbsp;Returns the integer for human consumptionthat is represented<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; by thestring of x's<br></span><hr><b>int_encode</b><br><br><span style="font-family: monospace;">Arguments: 1: A number inhuman-readable integer form<br>Returns:&nbsp;&nbsp;&nbsp;Returns the integer encoded as a string of x's<br></span><hr><b>int_plus</b><br><br><span style="font-family: monospace;">Arguments: 1: A number in x'srepresentation<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 2: Anothernumber in x's represntation<br>Returns:&nbsp;&nbsp;&nbsp;Returns the sum of the two numbers in x'srepresentation<br></span><hr><b>plus (wrapped version of int_plus)</b><br><br><span style="font-family: monospace;">Arguments: 1: An integer<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 2: Anotherinteger<br>Returns:&nbsp;&nbsp;&nbsp;Returns the sum of the two integers<br></span><hr><b>int_subtract</b><br><br><span style="font-family: monospace;">Arguments: 1: A number in x'srepresentation<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 2: Anothernumber in x's represntation<br>Returns:&nbsp;&nbsp;&nbsp;Returns the difference of the two numbers inx's representation,<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; or outputsan error on a numeric underflow<br></span><hr><b>subtract (wrapped version of int_subtract)</b><br><br><span style="font-family: monospace;">Arguments: 1: An integer<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 2: Anotherinteger<br>Returns:&nbsp;&nbsp;&nbsp;Returns the difference of the two integers,<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; or outputsan error on a numeric underflow<br></span><hr><b>int_multiply</b><br><br><span style="font-family: monospace;">Arguments: 1: A number in x'srepresentation<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 2: Anothernumber in x's represntation<br>Returns:&nbsp;&nbsp;&nbsp;Returns the product of the two numbers in x'srepresentation<br></span><hr><b>multiply (wrapped version of int_multiply)</b><br><br><span style="font-family: monospace;">Arguments: 1: An integer<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 2: Anotherinteger<br>Returns:&nbsp;&nbsp;&nbsp;Returns the product of the two integers<br></span><hr><b>int_divide</b><br><br><span style="font-family: monospace;">Arguments: 1: A number in x'srepresentation<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 2: Anothernumber in x's represntation<br>Returns:&nbsp;&nbsp;&nbsp;Returns the result of integer division ofargument 1 divided<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; byargument 2 in x's representation<br></span><hr><b>divide (wrapped version of int_divide)</b><br><br><span style="font-family: monospace;">Arguments: 1: An integer<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 2: Anotherinteger<br>Returns:&nbsp;&nbsp;&nbsp;Returns the integer division of the firstargument by the second<br></span><hr><b>int_modulo</b><br><br><span style="font-family: monospace;">Arguments: 1: A number in x'srepresentation<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 2: Anothernumber in x's represntation<br>Returns:&nbsp;&nbsp;&nbsp;Returns the remainder of integer division ofargument 1 divided<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; byargument 2 in x's representation<br></span><hr><b>modulo (wrapped version of int_modulo)</b><br><br><span style="font-family: monospace;">Arguments: 1: An integer<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 2: Anotherinteger<br>Returns:&nbsp;&nbsp;&nbsp;Returns the remainder of integer division of the firstargument by the second<br></span><hr><b>int_max, int_min</b><br><br><span style="font-family: monospace;">Arguments: 1: A number in x'srepresentation<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 2: Anothernumber in x's represntation<br>Returns:&nbsp;&nbsp;&nbsp;Returns the maximum or minimum of itsarguments in x's<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;representation<br></span><hr><b>max, min</b><br><br><span style="font-family: monospace;">Arguments: 1: An integer<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 2: Anotherinteger<br>Returns:&nbsp;&nbsp;&nbsp;Returns the maximum or minimum of its integerarguments<br></span><hr><b>int_gt, int_gte, int_lt, int_lte, int_eq, int_ne</b><br><br><span style="font-family: monospace;">Arguments: Two x's representationnumbers to be compared<br>Returns:&nbsp;&nbsp;&nbsp;$(true) or $(false)<br><br>int_gt First argument greater than second argument<br>int_gte First argument greater than or equal to second argument<br>int_lt First argument less than second argument <br>int_lte First argument less than or equal to second argument<br>int_eq First argument is numerically equal to the second argument<br>int_ne First argument is not numerically equal to the second argument<br></span><hr><b>gt, gte, lt, lte, eq, ne</b><br><br><span style="font-family: monospace;">Arguments: Two integers to becompared<br>Returns:&nbsp;&nbsp;&nbsp;$(true) or $(false)<br><br>gt First argument greater than second argument<br>gte First argument greater than or equal to second argument<br>lt First argument less than second argument <br>lte First argument less than or equal to second argument<br>eq First argument is numerically equal to the second argument<br>ne First argument is not numerically equal to the second argument<br></span>increment adds 1 to its argument, decrement subtracts 1. Note that<br>decrement does not range check and hence will not underflow, but<br>will incorrectly say that 0 - 1 = 0<br><hr><b>int_inc</b><br><br><span style="font-family: monospace;">Arguments: 1: A number in x'srepresentation<br>Returns:&nbsp;&nbsp;&nbsp;The number incremented by 1 in x'srepresentation<br></span><hr><b>inc</b><br><br><span style="font-family: monospace;">Arguments: 1: An integer<br>Returns:&nbsp;&nbsp;&nbsp;The argument incremented by 1<br></span><hr><b>int_dec</b><br><br><span style="font-family: monospace;">Arguments: 1: A number in x'srepresentation<br>Returns:&nbsp;&nbsp;&nbsp;The number decremented by 1 in x'srepresentation<br></span><hr><b>dec</b><br><br><span style="font-family: monospace;">Arguments: 1: An integer<br>Returns:&nbsp;&nbsp;&nbsp;The argument decremented by 1<br></span><hr><b>int_double</b><br><br><span style="font-family: monospace;">Arguments: 1: A number in x'srepresentation<br>Returns:&nbsp;&nbsp;&nbsp;The number doubled (i.e. * 2) and returned inx's representation<br></span><hr><b>double</b><br><br><span style="font-family: monospace;">Arguments: 1: An integer<br>Returns:&nbsp;&nbsp;&nbsp;The integer times 2<br></span><hr><b>int_halve</b><br><br>

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