The Fortress Language Specification - CiteSeerX

40.5 The Trait Fortress.Core.BinaryWord
A value of type BinaryWordb is a binary word of 2 b bits; b may be any natural number, so BinaryWord0 is a
bit, BinaryWord3 is a byte, BinaryWord6 is a 64-bit word, and BinaryWord10 is a 1024-bit word. In fact,
for convenience, the type abbreviations Bit and Byte are defined:
type Bit = BinaryWord0
type Byte = BinaryWord3
The type BinaryWordb has 2 (2b) distinct values. When the binary word is regarded as an unsigned integer, these
values are identified with the nonnegative integers that are less than 2 (2b) . A binary word may also be regarded as a
signed integer: a value that, when regarded as an unsigned integer, is identified with an integer less than 2 (2b −1) , is
identified with that same integer when regarded as a signed integer; but a value that, when regarded as an unsigned
integer, is identified with an integer not less than 2 (2b −1) , is identified with that same integer less 2 (2b) . (This is the
standard “two’s complement” representation for signed integers.)
A binary word of one bit can have one of two values, 0 or 1. A binary word of more than one bit has two halves, a
high half and a low half, which are binary words of half the size. If v is the unsigned integer value of a binary word
of 2 b bits, b ≥ 1 , h is the unsigned integer value of its high half, and l is the unsigned integer value of its low half,
then v = h · 2 2b−1 + l .
Operations on binary words include bitwise boolean operations, arithmetic operations, shifts and rotates, population
count, and counting of leading and trailing zeros. The type BinaryWordb is not “endian” and has no operations
that depend on endianness. However, if w is binary word, then w.littleEndian is a little-endian version of w and
w.bigEndian is a big-endian version of w ; for example, if w is of type BinaryWord6 , then w.littleEndian 63 is
the most significant bit (the sign bit if the word is regarded as a two’s-complement integer), and w.bigEndian 0 is that
same bit.
trait BinaryWordnat b extends { BasicBinaryWordOperationsBinaryWordb }
comprises {}
where { b ≤ maxBinaryWordBitLog }
coercion int r(x:IntegerStaticr) where { −2 b−1 ≤ r < 2 b }
coercion bool bigEndianBytes,bool bigEndianBits
(x:BinaryEndianWordb,bigEndianBytes,bigEndianBits)
coercion nat b ′ ,nat n,bool bigEndianSequence
(x:BinaryLinearEndianSequenceb ′ , n,bigEndianSequence)
where { 2 b = n · 2 b′ }
coercion nat b ′ ,bool bigEndianBytes,bool bigEndianBits,nat n,bool bigEndianSequence
(x:BinaryEndianLinearEndianSequenceb ′ ,bigEndianBytes,bigEndianBits,
n,bigEndianSequence)
where { 2 b = n · 2 b′ }
bit(m:IndexInt):Bit
getter lowHalf ():BinaryWordb − 1 where { b > 0 }
getter highHalf ():BinaryWordb − 1 where { b > 0 }
opr ‖ nat m(self,other: BinaryWordb): BinaryWordb + 1
where { b < maxBinaryWordBitLog }
bitShuffle(other: BinaryWordb):BinaryWordb + 1
where { b < maxBinaryWordBitLog }
bitUnshuffle():(BinaryWordb − 1, BinaryWordb − 1) where { b > 0 }
end
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