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442 lines
16 KiB
442 lines
16 KiB
// Ring operations.
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#ifndef _CL_RING_H
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#define _CL_RING_H
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#include "cln/object.h"
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#include "cln/malloc.h"
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#include "cln/proplist.h"
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#include "cln/number.h"
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#include "cln/io.h"
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namespace cln {
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class cl_I;
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// This file defines the general layout of rings, ring elements, and
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// operations available on ring elements. Any subclass of `cl_ring'
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// must implement these operations, with the same memory layout.
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// (Because generic packages like the polynomial rings access the base
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// ring's operation vectors through inline functions defined in this file.)
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class cl_heap_ring;
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// Rings are reference counted, but not freed immediately when they aren't
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// used any more. Hence they inherit from `cl_rcpointer'.
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// Vectors of function pointers are more efficient than virtual member
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// functions. But it constrains us not to use multiple or virtual inheritance.
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//
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// Note! We are passing raw `cl_heap_ring*' pointers to the operations
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// for efficiency (compared to passing `const cl_ring&', we save a memory
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// access, and it is easier to cast to a `cl_heap_ring_specialized*').
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// These raw pointers are meant to be used downward (in the dynamic extent
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// of the call) only. If you need to save them in a data structure, cast
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// to `cl_ring'; this will correctly increment the reference count.
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// (This technique is safe because the inline wrapper functions make sure
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// that we have a `cl_ring' somewhere containing the pointer, so there
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// is no danger of dangling pointers.)
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//
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// Note! Because the `cl_heap_ring*' -> `cl_ring' conversion increments
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// the reference count, you have to use the `cl_private_thing' -> `cl_ring'
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// conversion if the reference count is already incremented.
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class cl_ring : public cl_rcpointer {
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public:
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// Constructor. Takes a cl_heap_ring*, increments its refcount.
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cl_ring (cl_heap_ring* r);
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// Private constructor. Doesn't increment the refcount.
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cl_ring (cl_private_thing);
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// Copy constructor.
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cl_ring (const cl_ring&);
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// Assignment operator.
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cl_ring& operator= (const cl_ring&);
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// Default constructor.
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cl_ring ();
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// Automatic dereferencing.
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cl_heap_ring* operator-> () const
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{ return (cl_heap_ring*)heappointer; }
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};
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CL_DEFINE_COPY_CONSTRUCTOR2(cl_ring,cl_rcpointer)
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CL_DEFINE_ASSIGNMENT_OPERATOR(cl_ring,cl_ring)
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// Normal constructor for `cl_ring'.
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inline cl_ring::cl_ring (cl_heap_ring* r)
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{ cl_inc_pointer_refcount((cl_heap*)r); pointer = r; }
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// Private constructor for `cl_ring'.
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inline cl_ring::cl_ring (cl_private_thing p)
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{ pointer = p; }
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inline bool operator== (const cl_ring& R1, const cl_ring& R2)
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{ return (R1.pointer == R2.pointer); }
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inline bool operator!= (const cl_ring& R1, const cl_ring& R2)
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{ return (R1.pointer != R2.pointer); }
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inline bool operator== (const cl_ring& R1, cl_heap_ring* R2)
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{ return (R1.pointer == R2); }
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inline bool operator!= (const cl_ring& R1, cl_heap_ring* R2)
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{ return (R1.pointer != R2); }
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// Representation of an element of a ring.
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//
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// In order to support true polymorphism (without C++ templates), all
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// ring elements share the same basic layout:
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// cl_ring ring; // the ring
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// cl_gcobject rep; // representation of the element
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// The representation of the element depends on the ring, of course,
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// but we constrain it to be a single pointer into the heap or an immediate
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// value.
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//
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// Any arithmetic operation on a ring R (like +, -, *) must return a value
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// with ring = R. This is
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// a. necessary if the computation is to proceed correctly (e.g. in cl_RA,
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// ((3/4)*4 mod 3) is 0, simplifying it to ((cl_I)4 mod (cl_I)3) = 1
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// wouldn't be correct),
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// b. possible even if R is an extension ring of some ring R1 (e.g. cl_N
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// being an extension ring of cl_R). Automatic retraction from R to R1
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// can be done through dynamic typing: An element of R which happens
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// to lie in R1 is stored using the internal representation of R1,
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// but with ring = R. Elements of R1 and R\R1 can be distinguished
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// through rep's type.
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// c. an advantage for the implementation of polynomials and other
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// entities which contain many elements of the same ring. They need
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// to store only the elements' representations, and a single pointer
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// to the ring.
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//
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// The ring operations exist in two versions:
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// - Low-level version, which only operates on the representation.
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// - High-level version, which operates on full cl_ring_elements.
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// We make this distinction for performance: Multiplication of polynomials
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// over Z/nZ, operating on the high-level operations, spends 40% of its
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// computing time with packing and unpacking of cl_ring_elements.
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// The low-level versions have an underscore prepended and are unsafe.
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class _cl_ring_element {
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public:
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cl_gcobject rep; // representation of the element
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// Default constructor.
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_cl_ring_element ();
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public: /* ugh */
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// Constructor.
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_cl_ring_element (const cl_heap_ring* R, const cl_gcobject& r) : rep (as_cl_private_thing(r)) { (void)R; }
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_cl_ring_element (const cl_ring& R, const cl_gcobject& r) : rep (as_cl_private_thing(r)) { (void)R; }
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public: // Ability to place an object at a given address.
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void* operator new (size_t size) { return malloc_hook(size); }
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void* operator new (size_t size, void* ptr) { (void)size; return ptr; }
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void operator delete (void* ptr) { free_hook(ptr); }
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};
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class cl_ring_element : public _cl_ring_element {
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protected:
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cl_ring _ring; // ring
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public:
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const cl_ring& ring () const { return _ring; }
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// Default constructor.
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cl_ring_element ();
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public: /* ugh */
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// Constructor.
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cl_ring_element (const cl_ring& R, const cl_gcobject& r) : _cl_ring_element (R,r), _ring (R) {}
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cl_ring_element (const cl_ring& R, const _cl_ring_element& r) : _cl_ring_element (r), _ring (R) {}
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public: // Debugging output.
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void debug_print () const;
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// Ability to place an object at a given address.
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void* operator new (size_t size) { return malloc_hook(size); }
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void* operator new (size_t size, void* ptr) { (void)size; return ptr; }
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void operator delete (void* ptr) { free_hook(ptr); }
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};
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// The ring operations are encoded as vectors of function pointers. You
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// can add more operations to the end of each vector or add new vectors,
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// but you must not reorder the operations nor reorder the vectors nor
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// change the functions' signatures incompatibly.
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// There should ideally be a template class for each vector, but unfortunately
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// you lose the ability to initialize the vector using "= { ... }" syntax
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// when you subclass it.
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struct _cl_ring_setops {
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// print
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void (* fprint) (cl_heap_ring* R, std::ostream& stream, const _cl_ring_element& x);
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// equality
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cl_boolean (* equal) (cl_heap_ring* R, const _cl_ring_element& x, const _cl_ring_element& y);
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// ...
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};
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struct _cl_ring_addops {
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// 0
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const _cl_ring_element (* zero) (cl_heap_ring* R);
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cl_boolean (* zerop) (cl_heap_ring* R, const _cl_ring_element& x);
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// x+y
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const _cl_ring_element (* plus) (cl_heap_ring* R, const _cl_ring_element& x, const _cl_ring_element& y);
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// x-y
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const _cl_ring_element (* minus) (cl_heap_ring* R, const _cl_ring_element& x, const _cl_ring_element& y);
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// -x
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const _cl_ring_element (* uminus) (cl_heap_ring* R, const _cl_ring_element& x);
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// ...
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};
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struct _cl_ring_mulops {
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// 1
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const _cl_ring_element (* one) (cl_heap_ring* R);
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// canonical homomorphism
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const _cl_ring_element (* canonhom) (cl_heap_ring* R, const cl_I& x);
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// x*y
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const _cl_ring_element (* mul) (cl_heap_ring* R, const _cl_ring_element& x, const _cl_ring_element& y);
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// x^2
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const _cl_ring_element (* square) (cl_heap_ring* R, const _cl_ring_element& x);
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// x^y, y Integer >0
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const _cl_ring_element (* expt_pos) (cl_heap_ring* R, const _cl_ring_element& x, const cl_I& y);
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// ...
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};
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typedef const _cl_ring_setops cl_ring_setops;
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typedef const _cl_ring_addops cl_ring_addops;
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typedef const _cl_ring_mulops cl_ring_mulops;
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// Representation of a ring in memory.
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class cl_heap_ring : public cl_heap {
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public:
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// Allocation.
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void* operator new (size_t size) { return malloc_hook(size); }
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// Deallocation.
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void operator delete (void* ptr) { free_hook(ptr); }
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private:
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cl_property_list properties;
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protected:
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cl_ring_setops* setops;
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cl_ring_addops* addops;
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cl_ring_mulops* mulops;
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public:
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// More information comes here.
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// ...
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public:
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// Low-level operations.
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void _fprint (std::ostream& stream, const _cl_ring_element& x)
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{ setops->fprint(this,stream,x); }
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cl_boolean _equal (const _cl_ring_element& x, const _cl_ring_element& y)
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{ return setops->equal(this,x,y); }
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const _cl_ring_element _zero ()
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{ return addops->zero(this); }
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cl_boolean _zerop (const _cl_ring_element& x)
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{ return addops->zerop(this,x); }
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const _cl_ring_element _plus (const _cl_ring_element& x, const _cl_ring_element& y)
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{ return addops->plus(this,x,y); }
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const _cl_ring_element _minus (const _cl_ring_element& x, const _cl_ring_element& y)
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{ return addops->minus(this,x,y); }
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const _cl_ring_element _uminus (const _cl_ring_element& x)
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{ return addops->uminus(this,x); }
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const _cl_ring_element _one ()
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{ return mulops->one(this); }
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const _cl_ring_element _canonhom (const cl_I& x)
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{ return mulops->canonhom(this,x); }
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const _cl_ring_element _mul (const _cl_ring_element& x, const _cl_ring_element& y)
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{ return mulops->mul(this,x,y); }
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const _cl_ring_element _square (const _cl_ring_element& x)
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{ return mulops->square(this,x); }
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const _cl_ring_element _expt_pos (const _cl_ring_element& x, const cl_I& y)
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{ return mulops->expt_pos(this,x,y); }
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// High-level operations.
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void fprint (std::ostream& stream, const cl_ring_element& x)
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{
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if (!(x.ring() == this)) cl_abort();
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_fprint(stream,x);
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}
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cl_boolean equal (const cl_ring_element& x, const cl_ring_element& y)
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{
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if (!(x.ring() == this)) cl_abort();
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if (!(y.ring() == this)) cl_abort();
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return _equal(x,y);
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}
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const cl_ring_element zero ()
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{
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return cl_ring_element(this,_zero());
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}
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cl_boolean zerop (const cl_ring_element& x)
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{
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if (!(x.ring() == this)) cl_abort();
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return _zerop(x);
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}
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const cl_ring_element plus (const cl_ring_element& x, const cl_ring_element& y)
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{
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if (!(x.ring() == this)) cl_abort();
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if (!(y.ring() == this)) cl_abort();
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return cl_ring_element(this,_plus(x,y));
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}
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const cl_ring_element minus (const cl_ring_element& x, const cl_ring_element& y)
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{
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if (!(x.ring() == this)) cl_abort();
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if (!(y.ring() == this)) cl_abort();
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return cl_ring_element(this,_minus(x,y));
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}
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const cl_ring_element uminus (const cl_ring_element& x)
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{
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if (!(x.ring() == this)) cl_abort();
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return cl_ring_element(this,_uminus(x));
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}
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const cl_ring_element one ()
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{
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return cl_ring_element(this,_one());
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}
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const cl_ring_element canonhom (const cl_I& x)
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{
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return cl_ring_element(this,_canonhom(x));
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}
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const cl_ring_element mul (const cl_ring_element& x, const cl_ring_element& y)
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{
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if (!(x.ring() == this)) cl_abort();
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if (!(y.ring() == this)) cl_abort();
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return cl_ring_element(this,_mul(x,y));
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}
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const cl_ring_element square (const cl_ring_element& x)
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{
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if (!(x.ring() == this)) cl_abort();
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return cl_ring_element(this,_square(x));
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}
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const cl_ring_element expt_pos (const cl_ring_element& x, const cl_I& y)
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{
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if (!(x.ring() == this)) cl_abort();
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return cl_ring_element(this,_expt_pos(x,y));
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}
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// Property operations.
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cl_property* get_property (const cl_symbol& key)
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{ return properties.get_property(key); }
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void add_property (cl_property* new_property)
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{ properties.add_property(new_property); }
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// Constructor.
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cl_heap_ring (cl_ring_setops* setopv, cl_ring_addops* addopv, cl_ring_mulops* mulopv)
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: setops (setopv), addops (addopv), mulops (mulopv)
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{ refcount = 0; } // will be incremented by the `cl_ring' constructor
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};
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#define SUBCLASS_cl_heap_ring() \
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public: \
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/* Allocation. */ \
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void* operator new (size_t size) { return malloc_hook(size); } \
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/* Deallocation. */ \
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void operator delete (void* ptr) { free_hook(ptr); }
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// Operations on ring elements.
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// Output.
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inline void fprint (std::ostream& stream, const cl_ring_element& x)
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{ x.ring()->fprint(stream,x); }
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CL_DEFINE_PRINT_OPERATOR(cl_ring_element)
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// Add.
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inline const cl_ring_element operator+ (const cl_ring_element& x, const cl_ring_element& y)
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{ return x.ring()->plus(x,y); }
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// Negate.
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inline const cl_ring_element operator- (const cl_ring_element& x)
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{ return x.ring()->uminus(x); }
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// Subtract.
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inline const cl_ring_element operator- (const cl_ring_element& x, const cl_ring_element& y)
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{ return x.ring()->minus(x,y); }
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// Equality.
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inline bool operator== (const cl_ring_element& x, const cl_ring_element& y)
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{ return x.ring()->equal(x,y); }
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inline bool operator!= (const cl_ring_element& x, const cl_ring_element& y)
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{ return !x.ring()->equal(x,y); }
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// Compare against 0.
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inline cl_boolean zerop (const cl_ring_element& x)
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{ return x.ring()->zerop(x); }
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// Multiply.
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inline const cl_ring_element operator* (const cl_ring_element& x, const cl_ring_element& y)
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{ return x.ring()->mul(x,y); }
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// Squaring.
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inline const cl_ring_element square (const cl_ring_element& x)
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{ return x.ring()->square(x); }
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// Exponentiation x^y, where y > 0.
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inline const cl_ring_element expt_pos (const cl_ring_element& x, const cl_I& y)
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{ return x.ring()->expt_pos(x,y); }
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// Scalar multiplication.
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// [Is this operation worth being specially optimized for the case of
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// polynomials?? Polynomials have a faster scalar multiplication.
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// We should use it.??]
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inline const cl_ring_element operator* (const cl_I& x, const cl_ring_element& y)
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{ return y.ring()->mul(y.ring()->canonhom(x),y); }
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inline const cl_ring_element operator* (const cl_ring_element& x, const cl_I& y)
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{ return x.ring()->mul(x.ring()->canonhom(y),x); }
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// Ring of uninitialized elements.
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// Any operation results in a run-time error.
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extern const cl_ring cl_no_ring;
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extern cl_class cl_class_no_ring;
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CL_REQUIRE(cl_no_ring)
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inline cl_ring::cl_ring ()
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: cl_rcpointer (as_cl_private_thing(cl_no_ring)) {}
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inline _cl_ring_element::_cl_ring_element ()
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: rep ((cl_private_thing) cl_combine(cl_FN_tag,0)) {}
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inline cl_ring_element::cl_ring_element ()
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: _cl_ring_element (), _ring () {}
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// Support for built-in number rings.
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// Beware, they are not optimally efficient.
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template <class T>
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struct cl_number_ring_ops {
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cl_boolean (* contains) (const cl_number&);
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cl_boolean (* equal) (const T&, const T&);
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cl_boolean (* zerop) (const T&);
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const T (* plus) (const T&, const T&);
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const T (* minus) (const T&, const T&);
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const T (* uminus) (const T&);
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const T (* mul) (const T&, const T&);
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const T (* square) (const T&);
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const T (* expt_pos) (const T&, const cl_I&);
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};
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class cl_heap_number_ring : public cl_heap_ring {
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public:
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cl_number_ring_ops<cl_number>* ops;
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// Constructor.
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cl_heap_number_ring (cl_ring_setops* setopv, cl_ring_addops* addopv, cl_ring_mulops* mulopv, cl_number_ring_ops<cl_number>* opv)
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: cl_heap_ring (setopv,addopv,mulopv), ops (opv) {}
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};
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class cl_number_ring : public cl_ring {
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public:
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cl_number_ring (cl_heap_number_ring* r)
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: cl_ring (r) {}
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};
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template <class T>
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class cl_specialized_number_ring : public cl_number_ring {
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public:
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cl_specialized_number_ring ();
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};
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// Type test.
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inline cl_boolean instanceof (const cl_number& x, const cl_number_ring& R)
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{
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return ((cl_heap_number_ring*) R.heappointer)->ops->contains(x);
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}
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// Hack section.
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// Conversions to subtypes without checking:
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// The2(cl_MI)(x) converts x to a cl_MI, without change of representation!
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#define The(type) *(const type *) & cl_identity
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#define The2(type) *(const type *) & cl_identity2
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// This inline function is for type checking purposes only.
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inline const cl_ring& cl_identity (const cl_ring& r) { return r; }
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inline const cl_ring_element& cl_identity2 (const cl_ring_element& x) { return x; }
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inline const cl_gcobject& cl_identity (const _cl_ring_element& x) { return x.rep; }
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// Debugging support.
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#ifdef CL_DEBUG
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extern int cl_ring_debug_module;
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CL_FORCE_LINK(cl_ring_debug_dummy, cl_ring_debug_module)
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#endif
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} // namespace cln
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#endif /* _CL_RING_H */
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