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<!-- bit-vector.mldoc -->
<!-- Entities.sgml entry 
<!ENTITY BitVector SDATA "bit-vector-sig.sml">
 -->

<!DOCTYPE ML-DOC SYSTEM>

<COPYRIGHT OWNER="Bell Labs, Lucent Technologies" YEAR=1998>
<VERSION VERID="1.0" YEAR=1998 MONTH=6 DAY=9>
<TITLE>The BitVector structure</TITLE>

<INTERFACE>
<HEAD>The <CD/BitVector/ structure</HEAD>
<SEEALSO>
    <STRREF/BitArray/
    <SIGREF DOCUMENT=SML-BASIS-DOC/MONO_VECTOR/
</SEEALSO>

<PP>
The <STRREF NOLINK/BitVector/ structure  
provides compacted vectors of booleans,
with one bit for each boolean value. A 0 (1) bit corresponds
to the boolean value <CD/false/ (<CD/true/), respectively. These vectors can be
used to implement sets of integers. Member testing takes constant time.

<STRUCTURE STRID="BitVector">
  <SIGBODY SIGID="BIT_VECTOR" FILE=BIT-VECTOR>
    <SPEC>
      <INCLUDE><SIGREF DOCUMENT=SML-BASIS-DOC>MONO_VECTOR</SIGREF>
        <WHERETYPE><ID>elem<TY>bool</WHERETYPE>
    <SPEC>
      <VAL>fromString<TY>string -> vector
      <RAISES><EXNREF STRID="General" DOCUMENT=SML-BASIS-DOC/Fail/
        <COMMENT>
          <PROTOTY>
          fromString <ARG/s/
          </PROTOTY>
          creates a vector from the string argument <ARG/s/, which should
          contain a hexadecimal representation of the bits set in the vector.
          Characters 0-9, a-f and A-F are allowed. For example, 
          <CD/fromString "1af8" = 0001101011111000/. (By convention, 0 
          corresponds to <CD/false/ and 1 corresponds to <CD/true/, 
          bit 0 appears on the right, and indices increase to the left.) 
          The length of the vector will be <CD/4*(size <ARG/s/)/. 
          Raises <EXNREF STRID="General" DOCUMENT=SML-BASIS-DOC/Fail/ if a non-hexadecimal character 
          appears in the string.
    <SPEC>
      <VAL>bits<TY>(int * int list) -> vector
      <RAISES><EXNREF STRID="General" DOCUMENT=SML-BASIS-DOC/Subscript/
        <COMMENT>
          <PROTOTY>
          bits (<ARG/sz/, <ARG/l/)
          </PROTOTY>
          creates a vector of length <ARG/sz/ with the indices of its set bits  
          given by <ARG/l/.
	  Raises <EXNREF STRID="General" DOCUMENT=SML-BASIS-DOC/Subscript/ 
          if a list item is less than 0, or greater than or equal to <ARG/sz/.
    <SPEC>
      <VAL>getBits<TY>vector -> int list
        <COMMENT>
          <PROTOTY>
          getBits <ARG/vec/
          </PROTOTY>
          returns a list of indices of the bits set in <ARG/vec/, 
          in increasing order.
    <SPEC>
      <VAL>toString<TY>vector -> string
        <COMMENT>
          <PROTOTY>
          toString <ARG/vec/
          </PROTOTY>
          encodes a bit vector as a string. The bit vector is zero-padded to 
          the next length that is a multiple of 4.
    <SPEC>
      <VAL>isZero<TY>vector -> bool
        <COMMENT>
          <PROTOTY>
          isZero <ARG/vec/
          </PROTOTY>
          returns true if and only if no bits are set.
    <SPEC>
      <VAL>extend0<TY>(vector * int) -> vector
      <RAISES><EXNREF STRID="General" DOCUMENT=SML-BASIS-DOC/Size/
      <VAL>extend1<TY>(vector * int) -> vector
      <RAISES><EXNREF STRID="General" DOCUMENT=SML-BASIS-DOC/Size/
        <COMMENT>
          <PROTOTY>
          extend0 (<ARG/vec/, <ARG/len/)
          <PROTO>
          extend1 (<ARG/vec/, <ARG/len/)
          </PROTOTY>
          create a new vectors by extending the argument bit vector 
          by 0's or 1's to given length. If <ARG/vec/ 
          is already as long as <ARG/len/, return a copy of the bit vector. 
          Raises <EXNREF STRID="General" DOCUMENT=SML-BASIS-DOC/Size/
	  if <ARG/len/ is negative.
    <SPEC>
      <VAL>eqBits<TY>(vector * vector) -> bool
        <COMMENT>
          <PROTOTY>
          eqBits (<ARG/vec/, <ARG/vec2/)
          </PROTOTY>
          returns true if the set bits in the two vectors are the same. This
          is equivalent to:
          <CODE>
            getBits <ARG/vec/ = getBits <ARG/vec2/
          </CODE>
    <SPEC>
      <VAL>equal<TY>(vector * vector) -> bool
        <COMMENT>
          <PROTOTY>
          equal (<ARG/vec/, <ARG/vec2/)
          </PROTOTY>
          returns true if the two vectors are equivalent, i.e., have the
          same length and set bits.
    <SPEC>
      <VAL>andb<TY>(vector * vector * int) -> vector
      <VAL>orb<TY>(vector * vector * int) -> vector
      <VAL>xorb<TY>(vector * vector * int) -> vector
        <COMMENT>
          <PROTOTY>
          andb (<ARG/vec/, <ARG/vec2/, <ARG/len/)
          <PROTO>
          orb (<ARG/vec/, <ARG/vec2/, <ARG/len/)
          <PROTO>
          xorb (<ARG/vec/, <ARG/vec2/, <ARG/len/)
          </PROTOTY>
          creates a new vector of length <ARG/len/ by logically combining the 
          bits of <ARG/vec/ and <ARG/vec2/ using and, or and xor, respectively.
          If necessary, the vectors are implicitly extended by 0 to be the 
          same length  as the new array.
    <SPEC>
      <VAL>notb<TY>vector -> vector
        <COMMENT>
          <PROTOTY>
          notb <ARG/vec/
          </PROTOTY>
          creates a new vector with all bits of original vector inverted.
    <SPEC>
      <VAL>lshift<TY>(vector * int) -> vector
      <RAISES><EXNREF STRID="General" DOCUMENT=SML-BASIS-DOC/Fail/
        <COMMENT>
          <PROTOTY>
          lshift (<ARG/vec/, <ARG/i/)
          </PROTOTY>
          creates a new vector by inserting <ARG/n/ 0's on the right 
          of <ARG/vec/. The new vector has 
          length <MATH/<ARG/n/ + <MTEXT><VALREF>length</VALREF></MTEXT> <ARG/vec//.
          Raises <EXNREF STRID="General" DOCUMENT=SML-BASIS-DOC/Fail/ if <ARG/n/ is negative.
    <SPEC>
      <VAL>rshift<TY>(vector * int) -> vector
      <RAISES><EXNREF STRID="General" DOCUMENT=SML-BASIS-DOC/Fail/
        <COMMENT>
          <PROTOTY>
          rshift (<ARG/vec/, <ARG/i/)
          </PROTOTY>
          creates a new vector of 
          length <MATH/max(0,<MTEXT><VALREF>length</VALREF></MTEXT> <ARG/vec/ - <ARG/n/)/ consisting 
          of bits <MATH/n,n+1,...,<MTEXT><VALREF>length</VALREF></MTEXT> <ARG/vec/ - 1/ of <ARG/vec/. 
          If <MATH/<ARG/n/ &GREATEREQ; <MTEXT><VALREF>length</VALREF></MTEXT> <ARG/vec//, the new vector 
          has length 0.
</STRUCTURE>

</INTERFACE>