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Signed primitive integers defined on top of the existing unsigned ones
with two's complement.
The module Sint63 includes the theory of signed primitive integers that
differs from the unsigned case.
Additions to the kernel:
les (signed <=), lts (signed <), compares (signed compare),
divs (signed division), rems (signed remainder),
asr (arithmetic shift right)
(The s suffix is not used when importing the Sint63 module.)
The printing and parsing of primitive ints was updated and the
int63_syntax_plugin was removed (we use Number Notation instead).
A primitive int is parsed / printed as unsigned or signed depending on
the scope. In the default (Set Printing All) case, it is printed in
hexadecimal.
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Add headers to a few files which were missing them.
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* Fix the implementations and add tests
* Change shift from int63 to Z (was always used as a Z)
* Update FloatLemmas.v accordingly
Co-authored-by: Erik Martin-Dorel <erik.martin-dorel@irit.fr>
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Flag -fexcess-precision=standard is not enough on x86_32
where -msse2 -mfpmath=sse is required (-msse is not enough)
to avoid double rounding issues in the VM.
Most floating-point operation are now implemented in C because OCaml
is suffering double rounding issues on x86_32 with 80 bits extended
precision registers used for floating-point values, causing double
rounding making floating-point arithmetic incorrect with respect to
its specification.
Add a runtime test for double roundings.
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Beware of 0. = -0. issue for primitive floats
The IEEE 754 declares that 0. and -0. are treated equal but we cannot
say that this is true with Leibniz equality.
Therefore we must patch the equality and the total comparison inside the
kernel to prevent inconsistency.
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- remove the architecture component (we don't do anything
arch-specific so it was just a rewording of int_size)
- have configure tell the make build system about int_size instead of
reimplementing cp
As a bonus, add the copyright header to uint63.mli.
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Primitive operations addc, addcarryc, subc, subcarryc, and diveucl are
implemented in the kernel so that they can be used by OCaml code (e.g.,
extracted code) as the other primitives.
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There are three implementations of this primitive:
* one in OCaml on 63 bits integer in kernel/uint63_amd64.ml
* one in OCaml on Int64 in kernel/uint63_x86.ml
* one in C on unsigned 64 bit integers in kernel/byterun/coq_uint63_native.h
Its specification is the axiom `diveucl_21_spec` in
theories/Numbers/Cyclic/Int63/Int63.v
* comment the implementations with loop invariants to enable an easy
pen&paper proof of correctness (note to reviewers: the one in
uint63_amd64.ml might be the easiest to read)
* make sure the three implementations are equivalent
* fix the specification in Int63.v
(only the lowest part of the result is actually returned)
* make a little optimisation in div21 enabled by the proof of correctness
(cmp is computed at the end of the first loop rather than at the beginning,
potentially saving one loop iteration while remaining correct)
* update the proofs in Int63.v and Cyclic63.v to take into account the
new specifiation of div21
* add a test
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This work makes it possible to take advantage of a compact
representation for integers in the entire system, as opposed to only
in some reduction machines. It is useful for heavily computational
applications, where even constructing terms is not possible without such
a representation.
Concretely, it replaces part of the retroknowledge machinery with
a primitive construction for integers in terms, and introduces a kind of
FFI which maps constants to operators (on integers). Properties of these
operators are expressed as explicit axioms, whereas they were hidden in
the retroknowledge-based approach.
This has been presented at the Coq workshop and some Coq Working Groups,
and has been used by various groups for STM trace checking,
computational analysis, etc.
Contributions by Guillaume Bertholon and Pierre Roux <Pierre.Roux@onera.fr>
Co-authored-by: Benjamin Grégoire <Benjamin.Gregoire@inria.fr>
Co-authored-by: Vincent Laporte <Vincent.Laporte@fondation-inria.fr>
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