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Add skeleton for the realclosure package
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
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Leonardo de Moura
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5 changed files with 856 additions and 3 deletions
265
src/math/realclosure/realclosure.h
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265
src/math/realclosure/realclosure.h
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/*++
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Copyright (c) 2013 Microsoft Corporation
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Module Name:
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realclosure.h
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Abstract:
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Package for computing with elements of the realclosure of a field containing
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- all rationals
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- extended with computable transcendental real numbers (e.g., pi and e)
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- infinitesimals
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Author:
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Leonardo (leonardo) 2013-01-02
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Notes:
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--*/
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#ifndef _REALCLOSURE_H_
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#define _REALCLOSURE_H_
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#include"mpq.h"
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#include"params.h"
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#include"scoped_numeral.h"
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#include"scoped_numeral_vector.h"
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#include"interval.h"
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namespace realclosure {
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class num;
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typedef interval_manager<im_default_config> mpqi_manager;
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class mk_interval {
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public:
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virtual void operator()(unsigned k, mpqi_manager & im, mpqi_manager::interval & r) = 0;
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};
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class manager {
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public:
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struct imp;
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private:
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imp * m_imp;
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public:
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manager(unsynch_mpq_manager & m, params_ref const & p = params_ref(), small_object_allocator * a = 0);
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~manager();
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typedef num numeral;
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typedef svector<numeral> numeral_vector;
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typedef _scoped_numeral<manager> scoped_numeral;
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typedef _scoped_numeral_vector<manager> scoped_numeral_vector;
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static void get_param_descrs(param_descrs & r);
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static void collect_param_descrs(param_descrs & r) { get_param_descrs(r); }
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void set_cancel(bool f);
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void cancel() { set_cancel(true); }
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void reset_cancel() { set_cancel(false); }
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void updt_params(params_ref const & p);
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unsynch_mpq_manager & qm() const;
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void del(numeral & a);
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/**
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\brief Add a new infinitesimal to the current field. The new infinitesimal is smaller than any positive element in the field.
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*/
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void mk_infinitesimal(char const * prefix_name, numeral & r);
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void mk_infinitesimal(numeral & r) { mk_infinitesimal("eps", r); }
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/**
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\brief Add a new transcendental real value to the field.
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The functor \c mk_interval is used to compute approximations of the transcendental value.
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This procedure should be used with care, if the value is not really transcendental with respect to the current
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field, computations with the new numeral may not terminate.
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Example: we extended the field with Pi. Pi is transcendental with respect to a field that contains only algebraic real numbers.
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So, this step is fine. Let us call the resultant field F.
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Then, we extend the field F with 1 - Pi. 1 - Pi is transcendental with respect to algebraic real numbers, but it is NOT transcendental
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with respect to F, since F contains Pi.
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*/
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void mk_transcendental(char const * prefix_name, mk_interval & proc, numeral & r);
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void mk_transcendental(mk_interval & proc, numeral & r) { mk_transcendental("k", proc, r); }
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/**
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\brief Isolate the roots of the univariate polynomial as[0] + as[1]*x + ... + as[n-1]*x^{n-1}
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The roots are stored in \c roots.
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*/
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void isolate_roots(char const * prefix_name, unsigned n, numeral const * as, numeral_vector & roots);
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void isolate_roots(unsigned n, numeral const * as, numeral_vector & roots) { isolate_roots("a", n, as, roots); }
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/**
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\brief a <- 0
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*/
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void reset(numeral & a);
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/**
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\brief Return the sign of a.
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*/
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int sign(numeral const & a);
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/**
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\brief Return true if a is zero.
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*/
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bool is_zero(numeral const & a);
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/**
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\brief Return true if a is positive.
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*/
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bool is_pos(numeral const & a);
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/**
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\brief Return true if a is negative.
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*/
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bool is_neg(numeral const & a);
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/**
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\brief Return true if a is an integer.
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*/
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bool is_int(numeral const & a);
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/**
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\brief Return true if a is a real number.
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*/
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bool is_real(numeral const & a);
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/**
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\brief a <- n
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*/
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void set(numeral & a, int n);
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void set(numeral & a, mpz const & n);
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void set(numeral & a, mpq const & n);
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void set(numeral & a, numeral const & n);
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void swap(numeral & a, numeral & b);
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/**
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\brief Return a^{1/k}
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Throws an exception if (a is negative and k is even) or (k is zero).
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*/
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void root(numeral const & a, unsigned k, numeral & b);
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/**
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\brief Return a^k
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Throws an exception if 0^0.
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*/
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void power(numeral const & a, unsigned k, numeral & b);
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/**
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\brief c <- a + b
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*/
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void add(numeral const & a, numeral const & b, numeral & c);
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void add(numeral const & a, mpz const & b, numeral & c);
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/**
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\brief c <- a - b
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*/
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void sub(numeral const & a, numeral const & b, numeral & c);
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/**
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\brief c <- a * b
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*/
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void mul(numeral const & a, numeral const & b, numeral & c);
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/**
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\brief a <- -a
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*/
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void neg(numeral & a);
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/**
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\brief a <- 1/a if a != 0
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*/
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void inv(numeral & a);
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/**
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\brief c <- a/b if b != 0
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*/
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void div(numeral const & a, numeral const & b, numeral & c);
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/**
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Return -1 if a < b
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Return 0 if a == b
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Return 1 if a > b
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*/
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int compare(numeral const & a, numeral const & b);
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/**
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\brief a == b
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*/
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bool eq(numeral const & a, numeral const & b);
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bool eq(numeral const & a, mpq const & b);
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bool eq(numeral const & a, mpz const & b);
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/**
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\brief a != b
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*/
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bool neq(numeral const & a, numeral const & b) { return !eq(a, b); }
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bool neq(numeral const & a, mpq const & b) { return !eq(a, b); }
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bool neq(numeral const & a, mpz const & b) { return !eq(a, b); }
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/**
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\brief a < b
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*/
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bool lt(numeral const & a, numeral const & b);
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bool lt(numeral const & a, mpq const & b);
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bool lt(numeral const & a, mpz const & b);
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/**
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\brief a > b
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*/
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bool gt(numeral const & a, numeral const & b) { return lt(b, a); }
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bool gt(numeral const & a, mpq const & b);
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bool gt(numeral const & a, mpz const & b);
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/**
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\brief a <= b
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*/
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bool le(numeral const & a, numeral const & b) { return !gt(a, b); }
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bool le(numeral const & a, mpq const & b) { return !gt(a, b); }
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bool le(numeral const & a, mpz const & b) { return !gt(a, b); }
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/**
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\brief a >= b
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*/
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bool ge(numeral const & a, numeral const & b) { return !lt(a, b); }
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bool ge(numeral const & a, mpq const & b) { return !lt(a, b); }
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bool ge(numeral const & a, mpz const & b) { return !lt(a, b); }
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/**
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\brief Store in result a value in the interval (prev, next)
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\pre lt(pre, next)
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*/
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void select(numeral const & prev, numeral const & next, numeral & result);
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void display(std::ostream & out, numeral const & a) const;
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/**
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\brief Display a real number in decimal notation.
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A question mark is added based on the precision requested.
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This procedure throws an exception if the \c a is not a real.
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*/
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void display_decimal(std::ostream & out, numeral const & a, unsigned precision = 10) const;
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};
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class value;
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class num {
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friend class manager;
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friend class manager::imp;
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value * m_value;
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public:
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num():m_value(0) {}
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};
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};
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typedef realclosure::manager rcmanager;
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typedef rcmanager::numeral rcnumeral;
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typedef rcmanager::numeral_vector rcnumeral_vector;
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typedef rcmanager::scoped_numeral scoped_rcnumeral;
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typedef rcmanager::scoped_numeral_vector scoped_rcnumeral_vector;
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#endif
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