142 lines
5.2 KiB
Text
142 lines
5.2 KiB
Text
.bp
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.P1 "TYPE REPRESENTATIONS"
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.PP
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The representations used for typed objects are not precisely
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specified by EM.
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Sometimes we only specify that a typed object occupies a
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certain amount of space and state no further restrictions.
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If one wants to have a different representation of the value of
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an object on the stack one has to use a convert instruction
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in most cases.
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We do specify some relations between the representations of
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types.
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This allows some intermixed use of operators for different types
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on the same object(s).
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For example, the instruction ZER pushes signed and
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unsigned integers with the value zero and empty sets.
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ZER has as only argument the size of the object.
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.QQ
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The representation of floating point numbers is a good example,
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it allows widely varying implementations.
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The only ways to create floating point numbers are via
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initialization and via conversions from integer numbers.
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Only by using conversions to integers and comparing
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two floating point numbers with each other, can these numbers
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be converted to human readable output.
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Implementations may use base 10, base 2 or any other
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base for exponents, and have freedom in choosing the range of
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exponent and mantissa.
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.QQ
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Other types are more precisely described.
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In the following paragraphs a description will be given of the
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restrictions imposed on the representation of the types used.
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A number \fBn\fP used in these paragraphs indicates the size of
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the object in \fIbits\fP.
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.P2 "Unsigned integers"
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.PP
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The range of unsigned integers is 0..
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.Ex 2 "\fBn\fP" -1.
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A binary representation is assumed.
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The order of the bits within an object is knowingly left
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unspecified.
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Discussing bit order within each 8-bit byte is academic,
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so the only real freedom of this specification lies in the byte
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order.
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We really do not care whether an implementation of a 4-byte
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integer has its bytes in a particular order of significance.
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This of course means that some sequences of instructions have
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unpredictable effects.
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For example:
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.DS
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LOC 258 ; STL 0 ; LAL 0 ; LOI 1 ( wordsize >=2 )
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.DE
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The value on the stack after executing this sequence
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can be anything,
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but will most likely be 1 or 2.
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.QQ
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Conversion between unsigned integers of different sizes have to
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be done with explicit convert instructions.
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One cannot simply pad an unsigned integer with zero's at either end
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and expect a correct result.
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.QQ
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We assume existence of at least single word unsigned arithmetic
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in any implementation.
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.P2 "Signed Integers"
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.PP
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The range of signed integers is
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.Ex \-2 "\fBn\fP\-1" ~..
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.Ex 2 "\fBn\fP\-1" \-1,
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in other words the range of signed integers of \fBn\fP bits
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using two's complement arithmetic.
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The representation is the same as for unsigned integers except the range
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.Ex 2 "\fBn\fP\-1" ~..
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.Ex 2 "\fBn\fP" \-1
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is mapped on the
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range
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.Ex \-2 "\fBn\fP\-1" ~..~\-1.
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In other words, the most significant bit is used as sign bit.
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The convert instructions between signed and unsigned integers
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of the same size can be used to catch errors.
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.QQ
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The value
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.Ex \-2 "\fBn\fP\-1"
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is used for undefined
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signed integers.
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EM implementations should trap when this value is used in an
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operation on signed integers.
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The instruction mask, accessed with SIM and LIM \-~see chapter 9~\-,
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can be used to disable such traps.
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.QQ
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We assume existence of at least single word signed arithmetic
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in any implementation.
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.P2 "Floating point values"
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.PP
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Floating point values must have a signed mantissa and a signed
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exponent.
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Although no base is specified, base 2 is the normal choice,
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because the FEF instruction pushes the exponent in base 2.
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.QQ
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The implementation of floating point arithmetic is optional.
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The compilers currently in use have runtime parameters for the
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size of the floating point values they should use.
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Common choices are 4 and/or 8 bytes.
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.P2 Pointers
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.PP
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EM has two kinds of pointers: for instruction and for data
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space.
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Each kind can only be used for its own space, conversion between
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these two subtypes is impossible.
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We assume that pointers have a range from 0 upwards.
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Any implementation may have holes in the pointer range between
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fragments.
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One can of course not expect to be able to address two megabyte
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of memory using a 2-byte pointer.
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Normally, a 2-byte pointer allows up to 65536 bytes of
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addressable memory.
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.QQ
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Pointer representation has one restriction.
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The pointer with the same representation as the integer zero of
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the same size should be invalid.
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Some languages and/or runtime systems represent the nil
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pointer as zero.
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.P2 "Bit sets"
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.PP
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All bit sets of size \fBn\fP are subsets of the set
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{~i~|~i>=0,~i<\fBn\fP~}.
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A bit set contains a bit for each element showing its
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presence or absence.
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Bit sets are subdivided into words.
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The word with the lowest EM address governs the subset
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{~i~|~i>=0,~i<\fBm\fP~}, where \fBm\fP is the number of bits in
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a word.
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The next higher words each govern the next higher \fBm\fP set elements.
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The relation between a set with size of
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a word and an unsigned integer word is that
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the value of the unsigned integer is the summation of the
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2\v'-0.5m'i\v'0.5m' where i is in the set.
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.QQ
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Example: a 2-word bit set (wordsize 2) containing the
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elements 1, 6, 8, 15, 18, 21, 27 and 28 is composed of two
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integers, e.g. at addresses 40 and 42.
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The word at 40 contains the value 33090 (or~\-32446),
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the word at 42 contains the value 6180.
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