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z3/test/interval_arithmetic.cpp
Leonardo de Moura 68269c43a6 other components 
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2012-10-02 11:48:48 -07:00

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8.7 KiB
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/*++
Copyright (c) 2006 Microsoft Corporation
Module Name:
interval_arithmetic.cpp
Abstract:
Test interval arithmetic
Author:
Nikolaj Bjorner (nbjorner) 2006-12-05.
Revision History:
--*/
#include<iostream>
#include"interval_arithmetic.h"
#include"trace.h"
template<class number, class epsilon>
void tst_ext_number() {
typedef ext_number<number, epsilon> num;
num zero;
num one(1);
num eps(num::epsilon());
num m_eps(num::epsilon().neg());
num two(number(2));
num half(number(1,2));
num inf = num::infinity();
num eps1 = num::epsilon();
num three(number(3));
num three_e = num::plus(three, num::epsilon());
SASSERT(zero.get_sign() == num::ZERO);
SASSERT(one.get_sign() == num::POSITIVE);
SASSERT(m_eps.get_sign() == num::NEGATIVE);
SASSERT(inf.get_sign() == num::POSITIVE);
SASSERT(zero.is_zero());
SASSERT(!one.is_zero());
SASSERT(!inf.is_zero());
SASSERT(inf.is_infinite());
SASSERT(!one.is_infinite());
SASSERT(one.is_pos());
SASSERT(m_eps.is_neg());
SASSERT(one != zero);
SASSERT(inf != one);
SASSERT(inf != zero);
SASSERT(zero == zero);
SASSERT(zero < one);
SASSERT(eps < two);
SASSERT(zero < eps);
SASSERT(zero < inf);
SASSERT(zero == min(zero, eps));
SASSERT(zero == min(zero, inf));
SASSERT(eps == max(zero, eps));
SASSERT(inf == max(zero, inf));
SASSERT(min(zero,eps) == min(eps,zero));
SASSERT(num::plus(zero, eps) == eps);
SASSERT(num::plus(zero, one) == one);
SASSERT(num::plus(zero, inf) == inf);
SASSERT(num::plus(inf, inf) == inf);
SASSERT(inf.neg() < inf);
SASSERT(inf.neg() < zero);
SASSERT(num::minus(zero, one) == one.neg());
SASSERT(num::minus(zero, eps) == eps.neg());
SASSERT(num::minus(zero, inf) == inf.neg());
SASSERT(num::minus(zero, inf.neg()) == inf);
SASSERT(num::minus(inf, inf.neg()) == inf);
// sup_mult, inf_mult
SASSERT(sup_mult(zero, one) == zero);
SASSERT(sup_mult(one, one) == one);
SASSERT(sup_mult(one, one.neg()) == one.neg());
SASSERT(inf_mult(zero, one) == zero);
SASSERT(inf_mult(one, one) == one);
SASSERT(inf_mult(one, one.neg()) == one.neg());
// sup_div, inf_div
SASSERT(one < sup_div(three_e, three));
SASSERT(inf_div(three, three_e) < one);
SASSERT(inf_div(three_e, three) < two);
SASSERT(inf_div(three.neg(), three_e.neg()) < one);
SASSERT(one < sup_div(three_e.neg(), three.neg()));
SASSERT(inf_div(three_e.neg(), three.neg()) < two);
// sup_power, inf_power
SASSERT(sup_power(one,3) == one);
SASSERT(sup_power(one,3) > zero);
SASSERT(sup_power(num::plus(one, num::epsilon()),3) > one);
SASSERT(sup_power(one,2) == one);
SASSERT(sup_power(one,2) > zero);
SASSERT(sup_power(num::plus(one, num::epsilon()),2) > one);
// sup_root, inf_root
SASSERT(sup_root(one,2) >= zero);
SASSERT(inf_root(one,2) <= one);
SASSERT(sup_root(zero,2) >= zero);
SASSERT(inf_root(zero,2) <= zero);
}
template<class number, class epsilon>
void tst_interval()
{
typedef interval<number, epsilon> interval;
typedef ext_number<number, epsilon> ext_num;
ext_num m_inf(ext_num::infinity().neg());
ext_num m_three(ext_num(3).neg());
ext_num m_three_m_e(ext_num::plus(ext_num(3), ext_num::epsilon()).neg());
ext_num m_three_p_e(ext_num::plus(ext_num(3), ext_num::epsilon().neg()).neg());
ext_num m_eps(ext_num::epsilon().neg());
ext_num zero(0);
ext_num eps(ext_num::epsilon());
ext_num three(ext_num(3));
ext_num three_m_e(ext_num::minus(ext_num(3), ext_num::epsilon()));
ext_num three_p_e(ext_num::plus(ext_num(3), ext_num::epsilon()));
ext_num inf(ext_num::infinity());
ext_num nums[] = { m_inf, m_three_m_e, m_three, m_three_p_e, m_eps, zero, eps, three_m_e, three, three_p_e, inf };
unsigned n_nums = 11;
//
// add_lower
// add_upper
//
for (unsigned i = 0; i < n_nums; ++i) {
for (unsigned j = i+1; j < n_nums; ++j) {
for (unsigned k = 0; k < n_nums; ++k) {
interval i1(nums[i], nums[j]);
bool ok = i1.add_lower(nums[k]);
TRACE("interval_arithmetic", tout << "lower: " << ok << " "
<< nums[k] << " " << i1 << std::endl;);
}
for (unsigned k = 0; k < n_nums; ++k) {
interval i1(nums[i], nums[j]);
bool ok = i1.add_upper(nums[k]);
TRACE("interval_arithmetic", tout << "upper: " << ok << " "
<< nums[k] << " " << i1 << std::endl;);
}
}
}
//
// +
// *
// -
// quotient
//
for (unsigned i = 0; i < n_nums; ++i) {
for (unsigned j = i+1; j < n_nums; ++j) {
interval i1(nums[i],nums[j]);
interval x = i1.power(0);
interval y = i1.power(1);
interval z = i1.power(2);
interval x1 = i1.power(3);
for (unsigned k = 0; k < n_nums; ++k) {
for (unsigned l = k+1; l < n_nums; ++l) {
interval i2(nums[k],nums[l]);
interval i3 = i1 + i2;
interval i4 = i1 - i2;
interval i5 = i1 * i2;
TRACE("interval_arithmetic", tout << i1 << " + " << i2 << " = " << i3 << std::endl;);
TRACE("interval_arithmetic", tout << i1 << " - " << i2 << " = " << i4 << std::endl;);
TRACE("interval_arithmetic", tout << i1 << " * " << i2 << " = " << i5 << std::endl;);
SASSERT(i5 == i2 * i1);
vector<interval, true> intervals;
interval::quotient(i1, i2, intervals);
TRACE("interval_arithmetic",
tout << i1 << " / " << i2 << " = " ;
for (unsigned idx = 0; idx < intervals.size(); ++idx) {
tout << intervals[idx] << " ";
}
tout << std::endl;
);
unsigned changed_bounds;
x = i1;
y = i2;
z = i3;
TRACE("interval_arithmetic", tout << "check: " << i1 << "=" << i2 << "*" << i3 << std::endl;);
if (interval::check_mult(x, y, z, changed_bounds)) {
TRACE("interval_arithmetic", tout << x << "=" << y << "*" << z << std::endl;);
SASSERT (!!(changed_bounds & 0x1) == (x.low() != i1.low()));
SASSERT (!!(changed_bounds & 0x2) == (x.high() != i1.high()));
SASSERT (!!(changed_bounds & 0x4) == (y.low() != i2.low()));
SASSERT (!!(changed_bounds & 0x8) == (y.high() != i2.high()));
SASSERT (!!(changed_bounds & 0x10) == (z.low() != i3.low()));
SASSERT (!!(changed_bounds & 0x20) == (z.high() != i3.high()));
}
else {
TRACE("interval_arithmetic", tout << "unsat" << std::endl;);
}
x = i1;
y = i2;
if (interval::check_power(x, y, 3, changed_bounds)) {
TRACE("interval_arithmetic",
tout << "check: " << i1 << "=" << i2 << "^3" << " -> "
<< x << " = " << y << "^3" << std::endl;);
}
else {
TRACE("interval_arithmetic", tout << "unsat: " << i1 << "=" << i2 << "^4" << std::endl;);
}
x = i1;
y = i2;
if (interval::check_power(x, y, 4, changed_bounds)) {
TRACE("interval_arithmetic",
tout << "check: " << i1 << "=" << i2 << "^4" << " -> "
<< x << " = " << y << "^4" << std::endl;);
}
else {
TRACE("interval_arithmetic", tout << "unsat: " << i1 << "=" << i2 << "^4" << std::endl;);
}
}
}
}
}
// check_mult(i1, i2, i3, change_bounds);
// check_power(i1, i2, power, changed_bounds);
}
struct eps1 { rational operator()() { return rational(1); } };
struct eps0 { inf_rational operator()() { return inf_rational(rational(0),true); } };
void tst_interval_arithmetic() {
TRACE("interval_arithmetic", tout << "starting interval_arithmetic test...\n";);
tst_ext_number<rational, eps1>();
tst_ext_number<inf_rational, eps0>();
tst_interval<rational, eps1>();
tst_interval<inf_rational, eps0>();
}
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