mirror of https://github.com/CGAL/cgal
added concept RingNumberType
added concept FieldNumberType
This commit is contained in:
Michael Hemmer
parent
1c82d5ebb2
commit
022429aa60
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@ -14,7 +14,7 @@ Moreover, we require $q$ to be minimized with respect to the proper integer norm
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\ccIgnore{
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For types representing \Z, this is round $q$ towards zero.
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For univariat polynomials this has no effect at all.
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For univariate polynomials this has no effect at all.
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MP_Float Z[1/2] is not clear yet.
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}
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@ -1,30 +1,15 @@
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\begin{ccRefConcept}{FieldNumberType}
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The concept \ccRefName\ defines the syntactic requirements of a number type
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to be used as a template parameter for the Cartesian kernels. This number
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type supports the operations $+$, $-$, $*$ and $/$. This implies that
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\ccc{CGAL::Number_type_traits<FieldNumberType>::Has_division} is
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\ccc{CGAL::Tag_true}.
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\ccDefinition
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The concept \ccRefName\ combines the requirements of the concepts
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\ccc{Field} and \ccc{RealEmbeddable}.
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A model of \ccRefName\ can be used as a template parameter
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for Cartesian kernels.
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\ccRefines
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RingNumberType
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\ccCreationVariable{n1}
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\ccOperations
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\ccFunction{FieldNumberType operator/(const FieldNumberType &n1,
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const FieldNumberType &n2);} {}
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\ccGlue
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\ccFunction{FieldNumberType operator/(int n1,
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const FieldNumberType &n2);} {}
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\ccGlue
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\ccFunction{FieldNumberType operator/(const FieldNumberType &n1,
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int n2);} {}
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\ccGlue
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\ccMethod{FieldNumberType operator/=(const FieldNumberType &n2) const;}{}
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\ccGlue
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\ccMethod{FieldNumberType operator/=(int n2) const;}{}
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\ccc{Field}\\
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\ccc{RealEmbeddable}
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\ccHasModels
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\ccc{float} \\
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@ -39,8 +24,7 @@ RingNumberType
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\ccc{leda_real} \\
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\ccSeeAlso
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\ccRefConceptPage{EuclideanRingNumberType} \\
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\ccRefConceptPage{RingNumberType} \\
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\ccRefConceptPage{Kernel} \\
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\ccRefIdfierPage{CGAL::Field_tag} \\
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\end{ccRefConcept}
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@ -2,145 +2,15 @@
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\ccDefinition
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The concept \ccRefName\ defines the syntactic requirements a number type must
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meet in order to be used in \cgal\ as a ring type. This implies that
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\ccc{CGAL::Number_type_traits<RingNumberType>::Has_division} is not required
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to be \ccc{CGAL::Tag_true}. Unsigned numbers are excluded due to
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semantical limitations in the ordering.
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The concept \ccRefName\ combines the requirements of the concepts
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\ccc{IntegralDomainWithoutDivision} and \ccc{RealEmbeddable}.
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A model of \ccRefName\ can be used as a template parameter
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for Homogeneous kernels.
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\ccRefines
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CopyConstructible, Assignable
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\ccSetTwoColumns{}{\hspace*{8.5cm}}
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\ccCreation
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\ccCreationVariable{n1}
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\ccConstructor{RingNumberType();}
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{Declaration of a variable.}
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\ccConstructor{RingNumberType(int i);}
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{Declaration and initialization with a small integer
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constant $i$, $0 \leq i \leq 127$. The neutral elements for addition
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(zero) and multiplication (one) are needed quite often, but sometimes
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other small constants are useful too. The value 127 was chosen such
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that even signed 8 bit number types can fulfill this condition.}
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\ccSetThreeColumns{RingNumberTypeXXX}{}{\hspace*{8.5cm}}
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\ccOperations
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The comparison operators need to be provided.
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\ccFunction{bool operator==(const RingNumberType &n1,
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const RingNumberType &n2);} {}
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\ccGlue
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\ccFunction{bool operator!=(const RingNumberType &n1,
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const RingNumberType &n2);} {}
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\ccGlue
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\ccFunction{bool operator<(const RingNumberType &n1,
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const RingNumberType &n2);} {}
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\ccGlue
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\ccFunction{bool operator>(const RingNumberType &n1,
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const RingNumberType &n2);} {}
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\ccGlue
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\ccFunction{bool operator<=(const RingNumberType &n1,
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const RingNumberType &n2);} {}
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\ccGlue
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\ccFunction{bool operator>=(const RingNumberType &n1,
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const RingNumberType &n2);} {}
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In addition, the comparisons with small values of type \ccc{int} are also
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required.
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\ccFunction{bool operator==(int n1, const RingNumberType &n2);} {}
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\ccGlue
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\ccFunction{bool operator!=(int n1, const RingNumberType &n2);} {}
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\ccGlue
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\ccFunction{bool operator<(int n1, const RingNumberType &n2);} {}
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\ccGlue
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\ccFunction{bool operator>(int n1, const RingNumberType &n2);} {}
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\ccGlue
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\ccFunction{bool operator<=(int n1, const RingNumberType &n2);} {}
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\ccGlue
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\ccFunction{bool operator>=(int n1, const RingNumberType &n2);} {}
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\ccGlue
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\ccFunction{bool operator==(const RingNumberType &n1, int n2);} {}
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\ccGlue
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\ccFunction{bool operator!=(const RingNumberType &n1, int n2);} {}
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\ccGlue
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\ccFunction{bool operator<(const RingNumberType &n1, int n2);} {}
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\ccGlue
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\ccFunction{bool operator>(const RingNumberType &n1, int n2);} {}
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\ccGlue
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\ccFunction{bool operator<=(const RingNumberType &n1, int n2);} {}
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\ccGlue
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\ccFunction{bool operator>=(const RingNumberType &n1, int n2);} {}
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The arithmetic operators for the addition, subtraction and multiplication
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are required as well.
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\ccFunction{RingNumberType operator+(const RingNumberType &n1,
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const RingNumberType &n2);} {}
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\ccGlue
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\ccFunction{RingNumberType operator-(const RingNumberType &n1,
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const RingNumberType &n2);} {}
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\ccGlue
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\ccFunction{RingNumberType operator*(const RingNumberType &n1,
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const RingNumberType &n2);} {}
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\ccGlue
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\ccFunction{RingNumberType operator-(const RingNumberType &n);} {}
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\ccGlue
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\ccMethod{RingNumberType operator+=(const RingNumberType &n2) const;} {}
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\ccGlue
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\ccMethod{RingNumberType operator-=(const RingNumberType &n2) const;} {}
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\ccGlue
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\ccMethod{RingNumberType operator*=(const RingNumberType &n2) const;} {}
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And similarly, the mixed operators with small values of type \ccc{int} are also
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required.
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\ccFunction{RingNumberType operator+(int n1, const RingNumberType &n2);} {}
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\ccGlue
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\ccFunction{RingNumberType operator-(int n1, const RingNumberType &n2);} {}
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\ccGlue
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\ccFunction{RingNumberType operator*(int n1, const RingNumberType &n2);} {}
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\ccGlue
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\ccFunction{RingNumberType operator+(const RingNumberType &n1, int n2);} {}
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\ccGlue
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\ccFunction{RingNumberType operator-(const RingNumberType &n1, int n2);} {}
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\ccGlue
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\ccFunction{RingNumberType operator*(const RingNumberType &n1, int n2);} {}
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\ccGlue
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\ccMethod{RingNumberType operator+=(int n2) const;} {}
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\ccGlue
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\ccMethod{RingNumberType operator-=(int n2) const;} {}
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\ccGlue
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\ccMethod{RingNumberType operator*=(int n2) const;} {}
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The following accessory functions are needed for special purposes :
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\ccFunction{bool is_valid(const RingNumberType &n);}
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{Not all values of a number type need be valid. The function
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\ccStyle{is_valid} checks this. For example, an expression like
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\ccStyle{NT(0)/NT(0)} can result in an invalid number. Routines may
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have as a precondition that all numerical values are valid.}
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\ccFunction{bool is_finite(const RingNumberType &n);}
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{ When two large values are multiplied, the result may not fit in a
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\ccStyle{NT}.
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Some number types (e.g. the standard \ccc{float} and \ccc{double} types)
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have a way to represent a too big value as infinity.
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\ccStyle{is_finite} implies \ccStyle{is_valid}.}
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\ccFunction{double to_double(const RingNumberType &n);}
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{gives the double value for a number type.
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This is usually an approximation for the real (stored) value.
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It can be used to send numbers to a renderer or to store them
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in a file.}
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\ccFunction{std::pair<double,double> to_interval(const RingNumberType &n);}
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{gives a double interval that encloses \ccc{n}.}
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\ccc{IntegralDomainWithoutDivision}\\
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\ccc{RealEmbeddable}
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\ccHasModels
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@ -158,8 +28,6 @@ have as a precondition that all numerical values are valid.}
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\ccc{leda_real} \\
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\ccSeeAlso
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\ccRefConceptPage{EuclideanRingNumberType} \\
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\ccRefConceptPage{FieldNumberType} \\
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\ccRefIdfierPage{CGAL::Ring_tag} \\
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\end{ccRefConcept}
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@ -120,7 +120,7 @@
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\subsection*{Miscellaneous}
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\subsubsection*{Concepts}
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%\ccRefConceptPage{RingNumberType}\\
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%\ccRefConceptPage{FieldNumberType}\\
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\ccRefConceptPage{RingNumberType}\\
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\ccRefConceptPage{FieldNumberType}\\
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\ccRefConceptPage{FromIntConstructible}\\
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\ccRefConceptPage{FromDoubleConstructible}\\
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@ -104,7 +104,7 @@
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%Miscellaneous
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%\input{Algebraic_foundations_ref/RingNumberType.tex}
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%\input{Algebraic_foundations_ref/FieldNumberType.tex}
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\input{Algebraic_foundations_ref/RingNumberType.tex}
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\input{Algebraic_foundations_ref/FieldNumberType.tex}
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@ -27,8 +27,6 @@ TODO:
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\item add a new entry in the globally maintained Bib file.
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\item extra review of \ccc{Root_of_2}
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\item add isModel to traits classes and hasModels to concepts
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\item add concept FieldNumberType
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\item add concept RingNumberType
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\item rm inexact version of \ccc{MP_float}.
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\item Functions \ccc{min}, \ccc{max}, \ccc{is_valid} are considered to be more
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basic than this package. We added a file utils.h for this.
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@ -71,7 +69,7 @@ Keep in mind:
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\subsection{Changes}
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\begin{itemize}
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\item rm IsFinite from \ccc{RealEmeddable} concept
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\item rm IsFinite from \ccc{RealEmbeddable} concept
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function \ccc{CGAL::is_finite} for float, double, long double
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\item Moved Max/Min/Is\_valid/Boolean\_tag.. to STL-extension
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\item mv \ccc{AdaptableUnaryFunction} and \ccc{AdaptableBinaryFunction}
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