aboutsummaryrefslogtreecommitdiff
path: root/src/algebra/data.spad.pamphlet
blob: f40d8b1a4cb602baaba3eee660cd2ce27b044d27 (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
\documentclass{article}
\usepackage{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: January 6, 2009
++ 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) 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: () -> %
      ++ sample() returns a sample datum of type Byte.
  Private == SubDomain(NonNegativeInteger, #1 < 256) add
    byte(x: NonNegativeInteger): % == per x
    sample() = 0$Lisp
    coerce(c: Character) == per ord c
    coerce(x: %): Character == char rep x
    x = y == byteEqual(x,y)$Lisp
    x < y ==  byteLessThan(x,y)$Lisp
    min() == per 0
    max() == per 255
    bitand(x,y) == bitand(x,y)$Lisp
    bitior(x,y) == bitior(x,y)$Lisp

@

<<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$Lisp
    littleEndian == %littleEndian$Lisp
    bigEndian == %bigEndian$Lisp
    x = y == EQ(x,y)$Lisp
    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
  Private == SubDomain(Integer, length #1 <= N) add
    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()$Integer rem rep max)

@

<<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 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 == OrderedFinite with
    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: () -> %
      ++ sample() returns a sample datum of type Byte.
  Private == SubDomain(NonNegativeInteger, length #1 <= N) add
    min == per 0
    max == per((shift(1,N)-1)::NonNegativeInteger)
    sample() == min
    bitand(x,y) == BOOLE(BOOLE_-AND$Lisp,x,y)$Lisp
    bitior(x,y) == BOOLE(BOOLE_-IOR$Lisp,x,y)$Lisp

@

<<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

@


\section{The ByteBuffer domain}

<<domain BYTEBUF ByteBuffer>>=
import Byte
)abbrev domain BYTEBUF ByteBuffer
++ Author: Gabriel Dos Reis
++ Date Created: April 19, 2008
++ 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 String) with
    byteBuffer: NonNegativeInteger -> %
      ++ byteBuffer(n) creates a buffer of capacity n, and length 0.
    _#: % -> NonNegativeInteger
      ++ #buf returns the number of active elements in the buffer.
    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.
  Private == add
    makeByteBuffer(n: NonNegativeInteger): % ==
      makeByteBuffer(n)$Lisp

    byteBuffer n == 
      buf := makeByteBuffer n
      setLength!(buf,0)
      buf

    empty() == byteBuffer 0

    new(n,b) == makeByteBuffer(n,b)$Lisp

    qelt(buf,i) ==
      AREF(buf,i)$Lisp

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

    qsetelt!(buf,i,b) ==
      SETF(AREF(buf,i)$Lisp,b)$Lisp

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

    capacity buf == ARRAY_-DIMENSION(buf,0)$Lisp

    minIndex buf == 0

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

    # buf == LENGTH(buf)$Lisp

    x = y == 
      EQUAL(x,y)$Lisp

    setLength!(buf,n) == 
      n > capacity buf => 
        error "attempt to set length higher than capacity"
      SETF(FILL_-POINTER(buf)$Lisp,n)$Lisp

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

    qelt(b,i) == 
      getSimpleArrayEntry(b,i)$Lisp

    qsetelt(b,i,x) ==
      setSimpleArrayEntry(b,i,x)$Lisp

    x = y ==
      EQUAL(x,y)$Lisp

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


\section{License}
<<license>>=
--Copyright (C) 2007-2008, 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 SYSNNI SystemNonNegativeInteger>>
<<domain UINT8 UInt8>>
<<domain UINT16 UInt16>>
<<domain UINT32 UInt32>>

@

\end{document}