path: root/src/algebra/data.spad.pamphlet

\documentclass{article}
\usepackage{open-axiom}

\author{Gabriel Dos~Reis}

\begin{document}

\begin{abstract}
\end{abstract}

\tableofcontents
\eject

\section{The Byte domain}

<<domain BYTE Byte>>=
import NonNegativeInteger
import OutputForm
)abbrev domain BYTE Byte
++ Author: Gabriel Dos Reis
++ Date Created: April 19, 2008
++ Date Last Updated: July 18, 2010
++ Basic Operations: byte, bitand, bitor, bitxor
++ Related Constructor: NonNegativeInteger
++ Description:
++   Byte is the datatype of 8-bit sized unsigned integer values.
Byte(): Public == Private where
  Public == Join(OrderedFinite, HomotopicTo Character,Logic) with
    byte: NonNegativeInteger -> %
      ++ byte(x) injects the unsigned integer value `v' into
      ++ the Byte algebra.  `v' must be non-negative and less than 256.
    bitand: (%,%) -> %
      ++ bitand(x,y) returns the bitwise `and' of `x' and `y'.
    bitior: (%,%) -> %
      ++ bitor(x,y) returns the bitwise `inclusive or' of `x' and `y'.
    sample: %
      ++ \spad{sample} gives a sample datum of type Byte.
  Private == SubDomain(NonNegativeInteger, #1 < 256) add
    import %beq: (%,%) -> Boolean from Foreign Builtin
    import %blt: (%,%) -> Boolean from Foreign Builtin
    import %bgt: (%,%) -> Boolean from Foreign Builtin
    import %ble: (%,%) -> Boolean from Foreign Builtin
    import %bge: (%,%) -> Boolean from Foreign Builtin
    import %bitand: (%,%) -> %    from Foreign Builtin
    import %bitior: (%,%) -> %    from Foreign Builtin
    import %bcompl: % -> %        from Foreign Builtin

    byte(x: NonNegativeInteger): % == per x
    sample = 0$Foreign(Builtin)
    coerce(c: Character) == per ord c
    coerce(x: %): Character == char rep x
    x = y == %beq(x,y)
    x < y == %blt(x,y)
    x > y == %bgt(x,y)
    x <= y == %ble(x,y)
    x >= y == %bge(x,y)
    min() == per 0
    max() == per 255
    size() == 256
    index n == byte((n - 1) pretend NonNegativeInteger)
    lookup x == (rep x + 1) pretend PositiveInteger
    random() == byte random(size())$NonNegativeInteger
    bitand(x,y) == %bitand(x,y)
    bitior(x,y) == %bitior(x,y)
    x /\ y == bitand(x,y)
    x \/ y == bitior(x,y)
    ~ x == %bcompl x

@

<<domain BYTEORD ByteOrder>>=
)abbrev domain BYTEORD ByteOrder
++ Author: Gabriel Dos Reis
++ Date Created: February 06, 2009
++ Date Last Modified:
++ Description:
++   This datatype describes byte order of machine values stored memory.
ByteOrder(): Public == Private where
  Public == SetCategory with
    littleEndian: %   ++ \spad{littleEndian} describes little endian host
    bigEndian: %      ++ \spad{bigEndian} describes big endian host
    unknownEndian: %  ++ \spad{unknownEndian} for none of the above.
  Private == add
    unknownEndian == %unknownEndian$Foreign(Builtin)
    littleEndian == %littleEndian$Foreign(Builtin)
    bigEndian == %bigEndian$Foreign(Builtin)
    x = y == %peq(x,y)$Foreign(Builtin)
    coerce(x: %): OutputForm ==
      outputForm
        x = littleEndian => 'litteEndian
        x = bigEndian => 'bigEndian
        'unknownEndian

@


\section{Sized System Integer datatypes}

<<domain SYSINT SystemInteger>>=
)abbrev domain SYSINT SystemInteger
++ Author: Gabriel Dos Reis
++ Date Created: December 26, 2008
++ Date Last Modified: December 27, 2008
++ Description:
++   This domain implements sized (signed) integer datatypes parameterized
++   by the precision (or width) of the underlying representation.
++   The intent is that they map directly to the hosting hardware
++   natural integer datatypes.  Consequently, natural values for
++   N are: 8, 16, 32, 64, etc.  These datatypes are mostly useful
++   for system programming tasks, i.e. interfacting with the hosting
++   operating system, reading/writing external binary format files.
SystemInteger(N: PositiveInteger): Public == Private where
  Public == OrderedFinite with
    sample: % ++ \spad{sample} gives a sample datum of this type.
  Private == SubDomain(Integer, length #1 <= N) add
    sample == per(0@Integer)
    min == per(-shift(1,N-1))
    max == per(shift(1,N-1)-1)
    size() == (rep max - rep min + 1)::NonNegativeInteger
    index i == per (i + rep min - 1)
    lookup x == (rep x - rep min + 1)::PositiveInteger
    random() == per random(rep max())$Integer

@

<<domain INT8 Int8>>=
)abbrev domain INT8 Int8
++ Author: Gabriel Dos Reis
++ Date Created: January 6, 2009
++ Date Last Modified: January 6, 2009
++ Description:
++   This domain is a datatype for (signed) integer values
++   of precision 8 bits.
Int8() == SystemInteger 8

@

<<domain INT16 Int16>>=
)abbrev domain INT16 Int16
++ Author: Gabriel Dos Reis
++ Date Created: January 6, 2009
++ Date Last Modified: January 6, 2009
++ Description:
++   This domain is a datatype for (signed) integer values
++   of precision 16 bits.
Int16() == SystemInteger 16

@

<<domain INT32 Int32>>=
)abbrev domain INT32 Int32
++ Author: Gabriel Dos Reis
++ Date Created: January 6, 2009
++ Date Last Modified: January 6, 2009
++ Description:
++   This domain is a datatype for (signed) integer values
++   of precision 32 bits.
Int32() == SystemInteger 32

@

<<domain INT64 Int64>>=
)abbrev domain INT64 Int64
++ Author: Gabriel Dos Reis
++ Date Created: March 25, 2009
++ Date Last Modified: March 25, 2009
++ Description:
++   This domain is a datatype for (signed) integer values
++   of precision 64 bits.
Int64() == SystemInteger 64

@


<<domain SYSNNI SystemNonNegativeInteger>>=
)abbrev domain SYSNNI SystemNonNegativeInteger
++ Author: Gabriel Dos Reis
++ Date Created: December 26, 2008
++ Date Last Modified: December 27, 2008
++ Description:
++   This domain implements sized (unsigned) integer datatypes 
++   parameterized by the precision (or width) of the underlying
++   representation. The intent is that they map directly to the
++   hosting hardware natural integer datatypes.  Consequently,
++   natural values for N are: 8, 16, 32, 64, etc.  These datatypes
++   are mostly useful for system programming tasks, i.e. interfacting
++   with the hosting operating system, reading/writing external 
++   binary format files.
SystemNonNegativeInteger(N: PositiveInteger): Public == Private where
  Public == Join(OrderedFinite,Logic) with
    bitand: (%,%) -> %
      ++ bitand(x,y) returns the bitwise `and' of `x' and `y'.
    bitior: (%,%) -> %
      ++ bitior(x,y) returns the bitwise `inclusive or' of `x' and `y'.
    sample: %
      ++ \spad{sample} gives a sample datum of type Byte.
  Private == SubDomain(NonNegativeInteger, length #1 <= N) add
    import %bitand: (%,%) -> % from Foreign Builtin
    import %bitior: (%,%) -> % from Foreign Builtin
    import %bitnot: % -> %     from Foreign Builtin

    min == per 0
    max == per((shift(1,N)-1) : NonNegativeInteger)
    sample == min
    bitand(x,y) == %bitand(x,y)
    bitior(x,y) == %bitior(x,y)
    x /\ y == bitand(x,y)
    x \/ y == bitior(x,y)
    ~ x == per((shift(1,N) + rep %bitnot x) : NonNegativeInteger)

@

<<domain UINT8 UInt8>>=
)abbrev domain UINT8 UInt8
++ Author: Gabriel Dos Reis
++ Date Created: January 6, 2009
++ Date Last Modified: January 6, 2009
++ Description:
++   This domain is a datatype for (unsigned) integer values
++   of precision 8 bits.
UInt8() == SystemNonNegativeInteger 8

@

<<domain UINT16 UInt16>>=
)abbrev domain UINT16 UInt16
++ Author: Gabriel Dos Reis
++ Date Created: January 6, 2009
++ Date Last Modified: January 6, 2009
++ Description:
++   This domain is a datatype for (unsigned) integer values
++   of precision 16 bits.
UInt16() == SystemNonNegativeInteger 16

@

<<domain UINT32 UInt32>>=
)abbrev domain UINT32 UInt32
++ Author: Gabriel Dos Reis
++ Date Created: January 6, 2009
++ Date Last Modified: January 6, 2009
++ Description:
++   This domain is a datatype for (unsigned) integer values
++   of precision 32 bits.
UInt32() == SystemNonNegativeInteger 32

@

<<domain UINT64 UInt64>>=
)abbrev domain UINT64 UInt64
++ Author: Gabriel Dos Reis
++ Date Created: March 25, 2009
++ Date Last Modified: March 25, 2009
++ Description:
++   This domain is a datatype for (unsigned) integer values
++   of precision 64 bits.
UInt64() == SystemNonNegativeInteger 64

@

\section{System-level Pointer Datatype.}

<<domain SYSPTR SystemPointer>>=
)abbrev domain SYSPTR SystemPointer
++ Author: Gabriel Dos Reis
++ Date Created: September 8, 2009
++ Date Last Modified: September 8, 2009
++ Description:
++   This domain is a datatype system-level pointer values.
SystemPointer(): SetCategory
  == add
    x = y == EQL(x,y)$Foreign(Builtin)
    coerce(x:%): OutputForm ==
      FORMAT(NIL$Foreign(Builtin),"~A",x)$Foreign(Builtin)
@


\section{The ByteBuffer domain}

<<domain BYTEBUF ByteBuffer>>=
import Byte
)abbrev domain BYTEBUF ByteBuffer
++ Author: Gabriel Dos Reis
++ Date Created: April 19, 2008
++ Date Last Modified: February 15, 2009
++ Related Constructor:
++ Description:
++   ByteBuffer provides datatype for buffers of bytes.  This domain
++   differs from PrimitiveArray Byte in that it is not as rigid
++   as  PrimitiveArray Byte.  That is, the typical use of
++   ByteBuffer is to pre-allocate a vector of Byte of some capacity
++   `n'.  The array can then store up to `n' bytes.   The actual
++   interesting bytes count (the length of the buffer) is therefore 
++   different from the capacity.  The length is no more than the 
++   capacity, but it can be set dynamically as needed.  This 
++   functionality is used for example when reading bytes from
++   input/output devices where we use buffers to transfer data in and 
++   out of the system.
++   Note: a value of type ByteBuffer is 0-based indexed, as opposed
++         Vector, but not unlike PrimitiveArray Byte.
ByteBuffer(): Public == Private where
  Public == Join(OneDimensionalArrayAggregate Byte,_
              CoercibleTo PrimitiveArray Byte,CoercibleTo String) with
    byteBuffer: NonNegativeInteger -> %
      ++ byteBuffer(n) creates a buffer of capacity n, and length 0.
    capacity: % -> NonNegativeInteger
      ++ capacity(buf) returns the pre-allocated maximum size of `buf'.
    setLength!: (%,NonNegativeInteger) -> NonNegativeInteger
      ++ setLength!(buf,n) sets the number of active bytes in the
      ++ `buf'.  Error if `n' is more than the capacity.
    finiteAggregate  ++ A ByteBuffer object is a finite aggregate
  Private == add
    -- A buffer object is a pair of a simple array, and the count
    -- of active number in the array.  Note that we cannot use
    -- Lisp-level fill pointers because that would not guarantee that
    -- the implementation uses a simple representation, therefore
    -- complicating FFI interface.
    Rep == Record(ary: PrimitiveArray Byte, sz: NonNegativeInteger)

    makeByteBuffer(n: NonNegativeInteger): % ==
      per [makeByteBuffer(n)$Foreign(Builtin),n]$Rep

    byteBuffer n == makeByteBuffer n

    empty() == byteBuffer 0

    new(n,b) == per [makeByteBuffer(n,b)$Foreign(Builtin),n]$Rep

    # buf == rep(buf).sz

    capacity buf == # rep(buf).ary

    qelt(buf,i) == qelt(rep(buf).ary,i)$PrimitiveArray(Byte)

    elt(buf: %,i: Integer) == 
      i >= # buf => error "index out of range"
      qelt(buf,i)

    qsetelt!(buf,i,b) ==
      qsetelt!(rep(buf).ary,i,b)$PrimitiveArray(Byte)

    setelt(buf: %,i: Integer, b: Byte) == 
      i >= # buf => error "index out of range"
      qsetelt!(rep(buf).ary,i,b)

    minIndex buf == 0

    maxIndex buf == (# buf)::Integer - 1

    x = y == rep x = rep y

    setLength!(buf,n) == 
      n > capacity buf => 
        error "attempt to set length higher than capacity"
      rep(buf).sz := n

    coerce(buf: %): PrimitiveArray Byte ==
      rep(buf).ary

    coerce(buf: %): String == 
      s: String := MAKE_-STRING(#buf)$Foreign(Builtin)
      for i in 0..maxIndex buf repeat
        qsetelt!(s,i + 1,qelt(buf,i)::Character)$String
      s

    construct l ==
      buf := makeByteBuffer(#l)
      for b in l for i in 0.. repeat
        buf.i := b
      buf

    concat(x: %, y:%) ==
      nx := #x
      ny := #y
      buf := makeByteBuffer(nx + ny)
      for i in 0..(nx - 1) repeat
        buf.i := x.i
      for i in 0..(ny - 1) repeat
        buf.(nx + i) := y.i
      buf

@


\section{The DataArray domain}

<<domain DATAARY DataArray>>=
)abbrev domain DATAARY DataArray
++ Author: Gabriel Dos Reis
++ Date Created: August 23, 2008
++ Description:
++   This domain provides for a fixed-sized homogeneous data buffer.
DataArray(N: PositiveInteger, T: SetCategory): Public == Private where
  Public == SetCategory with
    new: () -> %
      ++ new() returns a fresly allocated data buffer or length N.
    qelt: (%,NonNegativeInteger) -> T
      ++ elt(b,i) returns the ith element in buffer `b'.  Indexing
      ++ is 0-based.
    qsetelt: (%,NonNegativeInteger,T) -> T
      ++ setelt(b,i,x) sets the ith entry of data buffer `b' to `x'.
      ++ Indexing is 0-based.
  Private == add
    new() == 
      makeSimpleArray(getVMType(T)$Foreign(Builtin),N)$Foreign(Builtin)

    qelt(b,i) == 
      getSimpleArrayEntry(b,i)$Foreign(Builtin)

    qsetelt(b,i,x) ==
      setSimpleArrayEntry(b,i,x)$Foreign(Builtin)

    x = y ==
      EQUAL(x,y)$Foreign(Builtin)

    coerce(b: %): OutputForm ==
      bracket([qelt(b,i)::OutputForm for i in 0..(N-1)])
@


\section{License}
<<license>>=
--Copyright (C) 2007-2009, Gabriel Dos Reis.
--All rights reserved.
--
--Redistribution and use in source and binary forms, with or without
--modification, are permitted provided that the following conditions are
--met:
--
--    - Redistributions of source code must retain the above copyright
--      notice, this list of conditions and the following disclaimer.
--
--    - Redistributions in binary form must reproduce the above copyright
--      notice, this list of conditions and the following disclaimer in
--      the documentation and/or other materials provided with the
--      distribution.
--
--    - Neither the name of The Numerical Algorithms Group Ltd. nor the
--      names of its contributors may be used to endorse or promote products
--      derived from this software without specific prior written permission.
--
--THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS
--IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
--TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
--PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER
--OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
--EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
--PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
--PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
--LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
--NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
--SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
@


<<*>>=
<<license>>
<<domain BYTE Byte>>
<<domain BYTEBUF ByteBuffer>>
<<domain DATAARY DataArray>>

<<domain SYSINT SystemInteger>>
<<domain INT8 Int8>>
<<domain INT16 Int16>>
<<domain INT32 Int32>>
<<domain INT64 Int64>>

<<domain SYSNNI SystemNonNegativeInteger>>
<<domain UINT8 UInt8>>
<<domain UINT16 UInt16>>
<<domain UINT32 UInt32>>
<<domain UINT64 UInt64>>

<<domain SYSPTR SystemPointer>>

@

\end{document}