1/* File: canny/bits.pl 2 Author: Roy Ratcliffe 3 Created: Aug 15 2022 4 Purpose: Canny Bits 5 6Copyright (c) 2022, Roy Ratcliffe, Northumberland, United Kingdom 7 8Permission is hereby granted, free of charge, to any person obtaining a 9copy of this software and associated documentation files (the 10"Software"), to deal in the Software without restriction, including 11without limitation the rights to use, copy, modify, merge, publish, 12distribute, sublicense, and/or sell copies of the Software, and to 13permit persons to whom the Software is furnished to do so, subject to 14the following conditions: 15 16 The above copyright notice and this permission notice shall be 17 included in all copies or substantial portions of the Software. 18 19THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS 20OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF 21MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. 22IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY 23CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, 24TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE 25SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. 26 27*/ 28 29:- module(canny_bits, 30 [ bits/5, 31 bits/4, 32 bits/3, 33 bit_fields/3, % +Fields,+Shift,+Int 34 bit_fields/4 % +Fields,+Shift,+Int0,-Int 35 ]). 36 37:- use_module(library(clpfd)). 38 39%! bits(+Shift, +Width, ?Word, ?Bits, ?Rest) is semidet. 40%! bits(+ShiftWidthPair, ?Word, ?Bits, ?Rest) is semidet. 41%! bits(+ShiftWidthPair, ?Word, ?Bits) is semidet. 42% 43% Unifies Bits within a Word using Shift and Width. All arguments are 44% integers treated as words of arbitrary bit-width. 45% 46% The implementation uses relational integer arithmetic, i.e. CLP(FD). 47% Hence allows for forward and backward transformations from Word to 48% Bits and vice versa. Integer Word applies a Shift and bit Width mask 49% to integer Bits. Bits is always a smaller integer. Decomposes the 50% problem into shifting and masking. Treats these operations 51% separately. 52% 53% @arg Width of Bits from Word after Shift. Width of zero always 54% fails. 55 56bits(Shift, Width, Word, Bits, Rest) :- 57 Mask #= (1 << Width - 1) << Shift, 58 Bits0 #= Word /\ Mask, 59 Rest #= Word xor Bits0, 60 Word #= Bits0 /\ Mask \/ Rest, 61 Bits #= Bits0 // (1 << Shift), 62 Bits0 #= Bits << Shift. 63 64bits(Shift-Width, Word, Bits, Rest) :- bits(Shift, Width, Word, Bits, Rest). 65 66bits(Shift-Width, Word, Bits) :- bits(Shift, Width, Word, Bits, _Rest).
The predicates are semi-deterministic. They can fail. Failure occurs when the bit-field Width integers do not sum to Shift.
89bit_fields([], 0, _Int). 90bit_fields([Value:Width|Rest], Shift, Int) :- 91 Shift_ is Shift - Width, 92 Value is (Int >> Shift_) /\ ((1 << Width) - 1), 93 bit_fields(Rest, Shift_, Int). 94 95bit_fields([], 0, Int, Int). 96bit_fields([Value:Width|Rest], Shift, Int0, Int) :- 97 Shift_ is Shift - Width, 98 Int_ is Int0 \/ ((Value /\ ((1 << Width) - 1)) << Shift_), 99 bit_fields(Rest, Shift_, Int_, Int)