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466 lines
15 KiB
466 lines
15 KiB
// Modular integer operations.
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#ifndef _CL_MODINTEGER_H
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#define _CL_MODINTEGER_H
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#include "cln/object.h"
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#include "cln/ring.h"
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#include "cln/integer.h"
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#include "cln/random.h"
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#include "cln/malloc.h"
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#include "cln/io.h"
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#include "cln/proplist.h"
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#include "cln/condition.h"
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#include "cln/abort.h"
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#undef random // Linux defines random() as a macro!
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namespace cln {
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// Representation of an element of a ring Z/mZ.
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// To protect against mixing elements of different modular rings, such as
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// (3 mod 4) + (2 mod 5), every modular integer carries its ring in itself.
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// Representation of a ring Z/mZ.
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class cl_heap_modint_ring;
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class cl_modint_ring : public cl_ring {
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public:
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// Default constructor.
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cl_modint_ring ();
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// Constructor. Takes a cl_heap_modint_ring*, increments its refcount.
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cl_modint_ring (cl_heap_modint_ring* r);
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// Copy constructor.
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cl_modint_ring (const cl_modint_ring&);
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// Assignment operator.
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cl_modint_ring& operator= (const cl_modint_ring&);
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// Automatic dereferencing.
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cl_heap_modint_ring* operator-> () const
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{ return (cl_heap_modint_ring*)heappointer; }
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};
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// Z/0Z
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extern const cl_modint_ring cl_modint0_ring;
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// Default constructor. This avoids dealing with NULL pointers.
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inline cl_modint_ring::cl_modint_ring ()
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: cl_ring (as_cl_private_thing(cl_modint0_ring)) {}
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CL_REQUIRE(cl_MI)
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// Copy constructor and assignment operator.
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CL_DEFINE_COPY_CONSTRUCTOR2(cl_modint_ring,cl_ring)
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CL_DEFINE_ASSIGNMENT_OPERATOR(cl_modint_ring,cl_modint_ring)
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// Normal constructor for `cl_modint_ring'.
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inline cl_modint_ring::cl_modint_ring (cl_heap_modint_ring* r)
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: cl_ring ((cl_private_thing) (cl_inc_pointer_refcount((cl_heap*)r), r)) {}
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// Operations on modular integer rings.
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inline bool operator== (const cl_modint_ring& R1, const cl_modint_ring& R2)
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{ return (R1.pointer == R2.pointer); }
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inline bool operator!= (const cl_modint_ring& R1, const cl_modint_ring& R2)
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{ return (R1.pointer != R2.pointer); }
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inline bool operator== (const cl_modint_ring& R1, cl_heap_modint_ring* R2)
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{ return (R1.pointer == R2); }
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inline bool operator!= (const cl_modint_ring& R1, cl_heap_modint_ring* R2)
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{ return (R1.pointer != R2); }
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// Condition raised when a probable prime is discovered to be composite.
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struct cl_composite_condition : public cl_condition {
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SUBCLASS_cl_condition()
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cl_I p; // the non-prime
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cl_I factor; // a nontrivial factor, or 0
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// Constructors.
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cl_composite_condition (const cl_I& _p)
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: p (_p), factor (0)
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{ print(std::cerr); }
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cl_composite_condition (const cl_I& _p, const cl_I& _f)
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: p (_p), factor (_f)
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{ print(std::cerr); }
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// Implement general condition methods.
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const char * name () const;
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void print (cl_ostream) const;
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~cl_composite_condition () {}
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};
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// Representation of an element of a ring Z/mZ.
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class _cl_MI /* cf. _cl_ring_element */ {
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public:
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cl_I rep; // representative, integer >=0, <m
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// (maybe the Montgomery representative!)
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// Default constructor.
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_cl_MI () : rep () {}
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public: /* ugh */
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// Constructor.
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_cl_MI (const cl_heap_modint_ring* R, const cl_I& r) : rep (r) { (void)R; }
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_cl_MI (const cl_modint_ring& R, const cl_I& r) : rep (r) { (void)R; }
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public:
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// Conversion.
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CL_DEFINE_CONVERTER(_cl_ring_element)
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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, _cl_MI* 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_MI /* cf. cl_ring_element */ : public _cl_MI {
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protected:
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cl_modint_ring _ring; // ring Z/mZ
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public:
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const cl_modint_ring& ring () const { return _ring; }
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// Default constructor.
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cl_MI () : _cl_MI (), _ring () {}
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public: /* ugh */
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// Constructor.
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cl_MI (const cl_modint_ring& R, const cl_I& r) : _cl_MI (R,r), _ring (R) {}
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cl_MI (const cl_modint_ring& R, const _cl_MI& r) : _cl_MI (r), _ring (R) {}
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public:
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// Conversion.
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CL_DEFINE_CONVERTER(cl_ring_element)
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// Debugging output.
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void debug_print () const;
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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, cl_MI* 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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// Representation of an element of a ring Z/mZ or an exception.
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class cl_MI_x {
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private:
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cl_MI value;
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public:
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cl_composite_condition* condition;
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// Constructors.
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cl_MI_x (cl_composite_condition* c) : value (), condition (c) {}
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cl_MI_x (const cl_MI& x) : value (x), condition (NULL) {}
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// Cast operators.
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//operator cl_MI& () { if (condition) cl_abort(); return value; }
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//operator const cl_MI& () const { if (condition) cl_abort(); return value; }
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operator cl_MI () const { if (condition) cl_abort(); return value; }
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};
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// Ring operations.
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struct _cl_modint_setops /* cf. _cl_ring_setops */ {
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// print
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void (* fprint) (cl_heap_modint_ring* R, cl_ostream stream, const _cl_MI& x);
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// equality
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cl_boolean (* equal) (cl_heap_modint_ring* R, const _cl_MI& x, const _cl_MI& y);
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// random number
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const _cl_MI (* random) (cl_heap_modint_ring* R, random_state& randomstate);
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};
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struct _cl_modint_addops /* cf. _cl_ring_addops */ {
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// 0
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const _cl_MI (* zero) (cl_heap_modint_ring* R);
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cl_boolean (* zerop) (cl_heap_modint_ring* R, const _cl_MI& x);
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// x+y
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const _cl_MI (* plus) (cl_heap_modint_ring* R, const _cl_MI& x, const _cl_MI& y);
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// x-y
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const _cl_MI (* minus) (cl_heap_modint_ring* R, const _cl_MI& x, const _cl_MI& y);
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// -x
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const _cl_MI (* uminus) (cl_heap_modint_ring* R, const _cl_MI& x);
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};
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struct _cl_modint_mulops /* cf. _cl_ring_mulops */ {
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// 1
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const _cl_MI (* one) (cl_heap_modint_ring* R);
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// canonical homomorphism
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const _cl_MI (* canonhom) (cl_heap_modint_ring* R, const cl_I& x);
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// x*y
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const _cl_MI (* mul) (cl_heap_modint_ring* R, const _cl_MI& x, const _cl_MI& y);
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// x^2
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const _cl_MI (* square) (cl_heap_modint_ring* R, const _cl_MI& x);
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// x^y, y Integer >0
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const _cl_MI (* expt_pos) (cl_heap_modint_ring* R, const _cl_MI& x, const cl_I& y);
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// x^-1
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const cl_MI_x (* recip) (cl_heap_modint_ring* R, const _cl_MI& x);
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// x*y^-1
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const cl_MI_x (* div) (cl_heap_modint_ring* R, const _cl_MI& x, const _cl_MI& y);
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// x^y, y Integer
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const cl_MI_x (* expt) (cl_heap_modint_ring* R, const _cl_MI& x, const cl_I& y);
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// x -> x mod m for x>=0
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const cl_I (* reduce_modulo) (cl_heap_modint_ring* R, const cl_I& x);
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// some inverse of canonical homomorphism
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const cl_I (* retract) (cl_heap_modint_ring* R, const _cl_MI& x);
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};
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typedef const _cl_modint_setops cl_modint_setops;
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typedef const _cl_modint_addops cl_modint_addops;
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typedef const _cl_modint_mulops cl_modint_mulops;
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// Representation of the ring Z/mZ.
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// Currently rings are garbage collected only when they are not referenced
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// any more and when the ring table gets full.
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// Modular integer rings are kept unique in memory. This way, ring equality
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// can be checked very efficiently by a simple pointer comparison.
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class cl_heap_modint_ring /* cf. cl_heap_ring */ : public cl_heap {
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SUBCLASS_cl_heap_ring()
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private:
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cl_property_list properties;
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protected:
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cl_modint_setops* setops;
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cl_modint_addops* addops;
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cl_modint_mulops* mulops;
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public:
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cl_I modulus; // m, normalized to be >= 0
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public:
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// Low-level operations.
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void _fprint (cl_ostream stream, const _cl_MI& x)
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{ setops->fprint(this,stream,x); }
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cl_boolean _equal (const _cl_MI& x, const _cl_MI& y)
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{ return setops->equal(this,x,y); }
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const _cl_MI _random (random_state& randomstate)
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{ return setops->random(this,randomstate); }
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const _cl_MI _zero ()
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{ return addops->zero(this); }
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cl_boolean _zerop (const _cl_MI& x)
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{ return addops->zerop(this,x); }
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const _cl_MI _plus (const _cl_MI& x, const _cl_MI& y)
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{ return addops->plus(this,x,y); }
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const _cl_MI _minus (const _cl_MI& x, const _cl_MI& y)
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{ return addops->minus(this,x,y); }
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const _cl_MI _uminus (const _cl_MI& x)
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{ return addops->uminus(this,x); }
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const _cl_MI _one ()
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{ return mulops->one(this); }
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const _cl_MI _canonhom (const cl_I& x)
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{ return mulops->canonhom(this,x); }
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const _cl_MI _mul (const _cl_MI& x, const _cl_MI& y)
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{ return mulops->mul(this,x,y); }
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const _cl_MI _square (const _cl_MI& x)
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{ return mulops->square(this,x); }
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const _cl_MI _expt_pos (const _cl_MI& x, const cl_I& y)
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{ return mulops->expt_pos(this,x,y); }
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const cl_MI_x _recip (const _cl_MI& x)
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{ return mulops->recip(this,x); }
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const cl_MI_x _div (const _cl_MI& x, const _cl_MI& y)
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{ return mulops->div(this,x,y); }
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const cl_MI_x _expt (const _cl_MI& x, const cl_I& y)
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{ return mulops->expt(this,x,y); }
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const cl_I _reduce_modulo (const cl_I& x)
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{ return mulops->reduce_modulo(this,x); }
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const cl_I _retract (const _cl_MI& x)
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{ return mulops->retract(this,x); }
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// High-level operations.
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void fprint (cl_ostream stream, const cl_MI& 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_MI& x, const cl_MI& 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_MI random (random_state& randomstate = default_random_state)
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{
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return cl_MI(this,_random(randomstate));
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}
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const cl_MI zero ()
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{
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return cl_MI(this,_zero());
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}
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cl_boolean zerop (const cl_MI& 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_MI plus (const cl_MI& x, const cl_MI& 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_MI(this,_plus(x,y));
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}
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const cl_MI minus (const cl_MI& x, const cl_MI& 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_MI(this,_minus(x,y));
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}
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const cl_MI uminus (const cl_MI& x)
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{
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if (!(x.ring() == this)) cl_abort();
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return cl_MI(this,_uminus(x));
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}
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const cl_MI one ()
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{
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return cl_MI(this,_one());
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}
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const cl_MI canonhom (const cl_I& x)
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{
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return cl_MI(this,_canonhom(x));
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}
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const cl_MI mul (const cl_MI& x, const cl_MI& 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_MI(this,_mul(x,y));
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}
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const cl_MI square (const cl_MI& x)
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{
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if (!(x.ring() == this)) cl_abort();
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return cl_MI(this,_square(x));
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}
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const cl_MI expt_pos (const cl_MI& 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_MI(this,_expt_pos(x,y));
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}
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const cl_MI_x recip (const cl_MI& x)
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{
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if (!(x.ring() == this)) cl_abort();
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return _recip(x);
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}
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const cl_MI_x div (const cl_MI& x, const cl_MI& 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 _div(x,y);
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}
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const cl_MI_x expt (const cl_MI& x, const cl_I& y)
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{
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if (!(x.ring() == this)) cl_abort();
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return _expt(x,y);
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}
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const cl_I reduce_modulo (const cl_I& x)
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{
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return _reduce_modulo(x);
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}
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const cl_I retract (const cl_MI& x)
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{
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if (!(x.ring() == this)) cl_abort();
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return _retract(x);
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}
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// Miscellaneous.
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sintL bits; // number of bits needed to represent a representative, or -1
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int log2_bits; // log_2(bits), or -1
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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_modint_ring (cl_I m, cl_modint_setops*, cl_modint_addops*, cl_modint_mulops*);
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// This class is intented to be subclassable, hence needs a virtual destructor.
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virtual ~cl_heap_modint_ring () {}
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private:
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virtual void dummy ();
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};
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#define SUBCLASS_cl_heap_modint_ring() \
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SUBCLASS_cl_heap_ring()
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// Lookup or create a modular integer ring Z/mZ
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extern const cl_modint_ring find_modint_ring (const cl_I& m);
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CL_REQUIRE(cl_MI)
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// Runtime typing support.
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extern cl_class cl_class_modint_ring;
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// Operations on modular integers.
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// Output.
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inline void fprint (cl_ostream stream, const cl_MI& x)
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{ x.ring()->fprint(stream,x); }
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CL_DEFINE_PRINT_OPERATOR(cl_MI)
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// Add.
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inline const cl_MI operator+ (const cl_MI& x, const cl_MI& y)
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{ return x.ring()->plus(x,y); }
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inline const cl_MI operator+ (const cl_MI& x, const cl_I& y)
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{ return x.ring()->plus(x,x.ring()->canonhom(y)); }
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inline const cl_MI operator+ (const cl_I& x, const cl_MI& y)
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{ return y.ring()->plus(y.ring()->canonhom(x),y); }
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// Negate.
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inline const cl_MI operator- (const cl_MI& x)
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{ return x.ring()->uminus(x); }
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// Subtract.
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inline const cl_MI operator- (const cl_MI& x, const cl_MI& y)
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{ return x.ring()->minus(x,y); }
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inline const cl_MI operator- (const cl_MI& x, const cl_I& y)
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{ return x.ring()->minus(x,x.ring()->canonhom(y)); }
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inline const cl_MI operator- (const cl_I& x, const cl_MI& y)
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{ return y.ring()->minus(y.ring()->canonhom(x),y); }
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// Shifts.
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extern const cl_MI operator<< (const cl_MI& x, sintL y); // assume 0 <= y < 2^31
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extern const cl_MI operator>> (const cl_MI& x, sintL y); // assume m odd, 0 <= y < 2^31
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// Equality.
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inline bool operator== (const cl_MI& x, const cl_MI& y)
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{ return x.ring()->equal(x,y); }
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inline bool operator!= (const cl_MI& x, const cl_MI& y)
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{ return !x.ring()->equal(x,y); }
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inline bool operator== (const cl_MI& x, const cl_I& y)
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{ return x.ring()->equal(x,x.ring()->canonhom(y)); }
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inline bool operator!= (const cl_MI& x, const cl_I& y)
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{ return !x.ring()->equal(x,x.ring()->canonhom(y)); }
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inline bool operator== (const cl_I& x, const cl_MI& y)
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{ return y.ring()->equal(y.ring()->canonhom(x),y); }
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inline bool operator!= (const cl_I& x, const cl_MI& y)
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{ return !y.ring()->equal(y.ring()->canonhom(x),y); }
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// Compare against 0.
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inline cl_boolean zerop (const cl_MI& x)
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{ return x.ring()->zerop(x); }
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// Multiply.
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inline const cl_MI operator* (const cl_MI& x, const cl_MI& y)
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{ return x.ring()->mul(x,y); }
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// Squaring.
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inline const cl_MI square (const cl_MI& 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_MI expt_pos (const cl_MI& x, const cl_I& y)
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{ return x.ring()->expt_pos(x,y); }
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// Reciprocal.
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inline const cl_MI recip (const cl_MI& x)
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{ return x.ring()->recip(x); }
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// Division.
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inline const cl_MI div (const cl_MI& x, const cl_MI& y)
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{ return x.ring()->div(x,y); }
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inline const cl_MI div (const cl_MI& x, const cl_I& y)
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{ return x.ring()->div(x,x.ring()->canonhom(y)); }
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inline const cl_MI div (const cl_I& x, const cl_MI& y)
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{ return y.ring()->div(y.ring()->canonhom(x),y); }
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// Exponentiation x^y.
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inline const cl_MI expt (const cl_MI& x, const cl_I& y)
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{ return x.ring()->expt(x,y); }
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// Scalar multiplication.
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inline const cl_MI operator* (const cl_I& x, const cl_MI& y)
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{ return y.ring()->mul(y.ring()->canonhom(x),y); }
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inline const cl_MI operator* (const cl_MI& x, const cl_I& y)
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{ return x.ring()->mul(x.ring()->canonhom(y),x); }
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// TODO: implement gcd, index (= gcd), unitp, sqrtp
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// Debugging support.
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#ifdef CL_DEBUG
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extern int cl_MI_debug_module;
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static void* const cl_MI_debug_dummy[] = { &cl_MI_debug_dummy,
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&cl_MI_debug_module
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};
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#endif
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} // namespace cln
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#endif /* _CL_MODINTEGER_H */
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