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author | letouzey <letouzey@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2010-12-06 15:47:32 +0000 |
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committer | letouzey <letouzey@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2010-12-06 15:47:32 +0000 |
commit | 9764ebbb67edf73a147c536a3c4f4ed0f1a7ce9e (patch) | |
tree | 881218364deec8873c06ca90c00134ae4cac724c /theories/Numbers/Integer/Abstract/ZProperties.v | |
parent | cb74dea69e7de85f427719019bc23ed3c974c8f3 (diff) |
Numbers and bitwise functions.
See NatInt/NZBits.v for the common axiomatization of bitwise functions
over naturals / integers. Some specs aren't pretty, but easier to
prove, see alternate statements in property functors {N,Z}Bits.
Negative numbers are considered via the two's complement convention.
We provide implementations for N (in Ndigits.v), for nat (quite dummy,
just for completeness), for Z (new file Zdigits_def), for BigN
(for the moment partly by converting to N, to be improved soon)
and for BigZ.
NOTA: For BigN.shiftl and BigN.shiftr, the two arguments are now in
the reversed order (for consistency with the rest of the world):
for instance BigN.shiftl 1 10 is 2^10.
NOTA2: Zeven.Zdiv2 is _not_ doing (Zdiv _ 2), but rather (Zquot _ 2)
on negative numbers. For the moment I've kept it intact, and have
just added a Zdiv2' which is truly equivalent to (Zdiv _ 2).
To reorganize someday ?
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13689 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories/Numbers/Integer/Abstract/ZProperties.v')
-rw-r--r-- | theories/Numbers/Integer/Abstract/ZProperties.v | 5 |
1 files changed, 3 insertions, 2 deletions
diff --git a/theories/Numbers/Integer/Abstract/ZProperties.v b/theories/Numbers/Integer/Abstract/ZProperties.v index d04443d9c..c04551960 100644 --- a/theories/Numbers/Integer/Abstract/ZProperties.v +++ b/theories/Numbers/Integer/Abstract/ZProperties.v @@ -7,7 +7,7 @@ (************************************************************************) Require Export ZAxioms ZMaxMin ZSgnAbs ZParity ZPow ZDivTrunc ZDivFloor - ZGcd ZLcm NZLog NZSqrt. + ZGcd ZLcm NZLog NZSqrt ZBits. (** This functor summarizes all known facts about Z. *) @@ -15,4 +15,5 @@ Module Type ZProp (Z:ZAxiomsSig) := ZMaxMinProp Z <+ ZSgnAbsProp Z <+ ZParityProp Z <+ ZPowProp Z <+ NZSqrtProp Z Z <+ NZSqrtUpProp Z Z <+ NZLog2Prop Z Z Z <+ NZLog2UpProp Z Z Z - <+ ZDivProp Z <+ ZQuotProp Z <+ ZGcdProp Z <+ ZLcmProp Z. + <+ ZDivProp Z <+ ZQuotProp Z <+ ZGcdProp Z <+ ZLcmProp Z + <+ ZBitsProp Z. |