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<div class="title">rational.cpp</div> </div>
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<a href="rational_8cpp.html">Go to the documentation of this file.</a><div class="fragment"><pre class="fragment"><a name="l00001"></a>00001 <span class="comment">/*****************************************************************************/</span><span class="comment"></span>
<a name="l00002"></a>00002 <span class="comment">/*!</span>
<a name="l00003"></a>00003 <span class="comment"> * \file rational.cpp</span>
<a name="l00004"></a>00004 <span class="comment"> * </span>
<a name="l00005"></a>00005 <span class="comment"> * Author: Sergey Berezin</span>
<a name="l00006"></a>00006 <span class="comment"> * </span>
<a name="l00007"></a>00007 <span class="comment"> * Created: Dec 12 22:00:18 GMT 2002</span>
<a name="l00008"></a>00008 <span class="comment"> *</span>
<a name="l00009"></a>00009 <span class="comment"> * <hr></span>
<a name="l00010"></a>00010 <span class="comment"> *</span>
<a name="l00011"></a>00011 <span class="comment"> * License to use, copy, modify, sell and/or distribute this software</span>
<a name="l00012"></a>00012 <span class="comment"> * and its documentation for any purpose is hereby granted without</span>
<a name="l00013"></a>00013 <span class="comment"> * royalty, subject to the terms and conditions defined in the \ref</span>
<a name="l00014"></a>00014 <span class="comment"> * LICENSE file provided with this distribution.</span>
<a name="l00015"></a>00015 <span class="comment"> * </span>
<a name="l00016"></a>00016 <span class="comment"> * <hr></span>
<a name="l00017"></a>00017 <span class="comment"> * </span>
<a name="l00018"></a>00018 <span class="comment"> */</span>
<a name="l00019"></a>00019 <span class="comment">/*****************************************************************************/</span>
<a name="l00020"></a>00020 <span class="comment">// Class: Rational</span>
<a name="l00021"></a>00021 <span class="comment">// Author: Sergey Berezin, 12/12/2002 (adapted from Bignum)</span>
<a name="l00022"></a>00022 <span class="comment">//</span>
<a name="l00023"></a>00023 <span class="comment">// Description: Implementation of class Rational. See comments in</span>
<a name="l00024"></a>00024 <span class="comment">// rational.h file.</span><span class="comment"></span>
<a name="l00025"></a>00025 <span class="comment">///////////////////////////////////////////////////////////////////////////////</span>
<a name="l00026"></a>00026 <span class="comment"></span>
<a name="l00027"></a>00027 <span class="preprocessor">#ifdef RATIONAL_GMPXX</span>
<a name="l00028"></a>00028 <span class="preprocessor"></span>
<a name="l00029"></a>00029 <span class="preprocessor">#include <gmpxx.h></span>
<a name="l00030"></a>00030 <span class="preprocessor">#include "<a class="code" href="compat__hash__set_8h.html">compat_hash_set.h</a>"</span>
<a name="l00031"></a>00031 <span class="preprocessor">#include "<a class="code" href="rational_8h.html">rational.h</a>"</span>
<a name="l00032"></a>00032
<a name="l00033"></a>00033 <span class="keyword">namespace </span>CVC3 {
<a name="l00034"></a>00034
<a name="l00035"></a>00035 <span class="keyword">using namespace </span>std;
<a name="l00036"></a>00036
<a name="l00037"></a>00037 <span class="comment">// Implementation of the forward-declared internal class</span>
<a name="l00038"></a>00038 <span class="keyword">class </span>Rational::Impl : <span class="keyword">public</span> mpq_class {
<a name="l00039"></a>00039 <span class="keyword">public</span>:
<a name="l00040"></a>00040 <span class="comment">// mpz_class _n;</span>
<a name="l00041"></a>00041 <span class="comment">// Constructors</span>
<a name="l00042"></a>00042 Impl() : mpq_class() { }
<a name="l00043"></a>00043 <span class="comment">// Constructor from integer</span>
<a name="l00044"></a>00044 <span class="comment">// Impl(const mpz_class &x) : mpq_class(x) { }</span>
<a name="l00045"></a>00045 <span class="comment">// Constructor from rational</span>
<a name="l00046"></a>00046 Impl(<span class="keyword">const</span> mpq_class &x) : mpq_class(x) { }
<a name="l00047"></a>00047 <span class="comment">// Copy constructor</span>
<a name="l00048"></a>00048 Impl(<span class="keyword">const</span> Impl &x) : mpq_class(x) { }
<a name="l00049"></a>00049 <span class="comment">// From pair of integers / strings</span>
<a name="l00050"></a>00050 Impl(<span class="keywordtype">int</span> n, <span class="keywordtype">int</span> d) : mpq_class(n,d) { canonicalize(); }
<a name="l00051"></a>00051 Impl(<span class="keyword">const</span> mpz_class& n, <span class="keyword">const</span> mpz_class& d)
<a name="l00052"></a>00052 : mpq_class(n,d) { canonicalize(); }
<a name="l00053"></a>00053 <span class="comment">// From string(s)</span>
<a name="l00054"></a>00054 Impl(<span class="keyword">const</span> <span class="keywordtype">string</span> &n, <span class="keywordtype">int</span> base): mpq_class(n, base) { canonicalize(); }
<a name="l00055"></a>00055 Impl(<span class="keyword">const</span> <span class="keywordtype">string</span> &n, <span class="keyword">const</span> <span class="keywordtype">string</span>& d, <span class="keywordtype">int</span> base)
<a name="l00056"></a>00056 : mpq_class(n + <span class="stringliteral">"/"</span> + d, base) { canonicalize(); }
<a name="l00057"></a>00057 <span class="comment">// Destructor</span>
<a name="l00058"></a>00058 <span class="keyword">virtual</span> ~Impl() { }
<a name="l00059"></a>00059 <span class="comment">// Getting numerator and denominator. DON NOT ASSIGN to the result</span>
<a name="l00060"></a>00060 mpz_class getNum() { <span class="keywordflow">return</span> get_num(); }
<a name="l00061"></a>00061 mpz_class getDen() { <span class="keywordflow">return</span> get_den(); }
<a name="l00062"></a>00062 };
<a name="l00063"></a>00063
<a name="l00064"></a>00064 <span class="comment">// Constructors</span>
<a name="l00065"></a>00065 <a class="code" href="classCVC3_1_1Rational.html#a8f86f975b54d0a491bc909d677023467">Rational::Rational</a>() : d_n(new Impl) {
<a name="l00066"></a>00066 <span class="preprocessor">#ifdef _DEBUG_RATIONAL_</span>
<a name="l00067"></a>00067 <span class="preprocessor"></span> <span class="keywordtype">int</span> &num_created = getCreated();
<a name="l00068"></a>00068 num_created++;
<a name="l00069"></a>00069 printStats();
<a name="l00070"></a>00070 <span class="preprocessor">#endif</span>
<a name="l00071"></a>00071 <span class="preprocessor"></span> }
<a name="l00072"></a>00072 <span class="comment">// Copy constructor</span>
<a name="l00073"></a>00073 Rational::Rational(<span class="keyword">const</span> Rational &n) : d_n(new Impl(*n.d_n)) {
<a name="l00074"></a>00074 <span class="preprocessor">#ifdef _DEBUG_RATIONAL_</span>
<a name="l00075"></a>00075 <span class="preprocessor"></span> <span class="keywordtype">int</span> &num_created = getCreated();
<a name="l00076"></a>00076 num_created++;
<a name="l00077"></a>00077 printStats();
<a name="l00078"></a>00078 <span class="preprocessor">#endif</span>
<a name="l00079"></a>00079 <span class="preprocessor"></span> }
<a name="l00080"></a>00080
<a name="l00081"></a>00081 <span class="comment">// Private constructor</span>
<a name="l00082"></a>00082 Rational::Rational(<span class="keyword">const</span> Impl& t): d_n(new Impl(t)) {
<a name="l00083"></a>00083 <span class="preprocessor">#ifdef _DEBUG_RATIONAL_</span>
<a name="l00084"></a>00084 <span class="preprocessor"></span> <span class="keywordtype">int</span> &num_created = getCreated();
<a name="l00085"></a>00085 num_created++;
<a name="l00086"></a>00086 printStats();
<a name="l00087"></a>00087 <span class="preprocessor">#endif</span>
<a name="l00088"></a>00088 <span class="preprocessor"></span> }
<a name="l00089"></a>00089 Rational::Rational(<span class="keywordtype">int</span> n, <span class="keywordtype">int</span> d): d_n(new Impl(n, d)) {
<a name="l00090"></a>00090 <span class="preprocessor">#ifdef _DEBUG_RATIONAL_</span>
<a name="l00091"></a>00091 <span class="preprocessor"></span> <span class="keywordtype">int</span> &num_created = getCreated();
<a name="l00092"></a>00092 num_created++;
<a name="l00093"></a>00093 printStats();
<a name="l00094"></a>00094 <span class="preprocessor">#endif</span>
<a name="l00095"></a>00095 <span class="preprocessor"></span> }
<a name="l00096"></a>00096 <span class="comment">// Constructors from strings</span>
<a name="l00097"></a>00097 Rational::Rational(<span class="keyword">const</span> <span class="keywordtype">char</span>* n, <span class="keywordtype">int</span> base)
<a name="l00098"></a>00098 : d_n(new Impl(string(n), base)) {
<a name="l00099"></a>00099 <span class="preprocessor">#ifdef _DEBUG_RATIONAL_</span>
<a name="l00100"></a>00100 <span class="preprocessor"></span> <span class="keywordtype">int</span> &num_created = getCreated();
<a name="l00101"></a>00101 num_created++;
<a name="l00102"></a>00102 printStats();
<a name="l00103"></a>00103 <span class="preprocessor">#endif</span>
<a name="l00104"></a>00104 <span class="preprocessor"></span> }
<a name="l00105"></a>00105 Rational::Rational(<span class="keyword">const</span> <span class="keywordtype">string</span>& n, <span class="keywordtype">int</span> base)
<a name="l00106"></a>00106 : d_n(new Impl(n, base)) {
<a name="l00107"></a>00107 <span class="preprocessor">#ifdef _DEBUG_RATIONAL_</span>
<a name="l00108"></a>00108 <span class="preprocessor"></span> <span class="keywordtype">int</span> &num_created = getCreated();
<a name="l00109"></a>00109 num_created++;
<a name="l00110"></a>00110 printStats();
<a name="l00111"></a>00111 <span class="preprocessor">#endif</span>
<a name="l00112"></a>00112 <span class="preprocessor"></span> }
<a name="l00113"></a>00113 Rational::Rational(<span class="keyword">const</span> <span class="keywordtype">char</span>* n, <span class="keyword">const</span> <span class="keywordtype">char</span>* d, <span class="keywordtype">int</span> base)
<a name="l00114"></a>00114 : d_n(new Impl(string(n), string(d), base)) {
<a name="l00115"></a>00115 <span class="preprocessor">#ifdef _DEBUG_RATIONAL_</span>
<a name="l00116"></a>00116 <span class="preprocessor"></span> <span class="keywordtype">int</span> &num_created = getCreated();
<a name="l00117"></a>00117 num_created++;
<a name="l00118"></a>00118 printStats();
<a name="l00119"></a>00119 <span class="preprocessor">#endif</span>
<a name="l00120"></a>00120 <span class="preprocessor"></span> }
<a name="l00121"></a>00121 Rational::Rational(<span class="keyword">const</span> <span class="keywordtype">string</span>& n, <span class="keyword">const</span> <span class="keywordtype">string</span>& d, <span class="keywordtype">int</span> base)
<a name="l00122"></a>00122 : d_n(new Impl(n, d, base)) {
<a name="l00123"></a>00123 <span class="preprocessor">#ifdef _DEBUG_RATIONAL_</span>
<a name="l00124"></a>00124 <span class="preprocessor"></span> <span class="keywordtype">int</span> &num_created = getCreated();
<a name="l00125"></a>00125 num_created++;
<a name="l00126"></a>00126 printStats();
<a name="l00127"></a>00127 <span class="preprocessor">#endif</span>
<a name="l00128"></a>00128 <span class="preprocessor"></span> }
<a name="l00129"></a>00129 <span class="comment">// Destructor</span>
<a name="l00130"></a>00130 Rational::~Rational() {
<a name="l00131"></a>00131 <span class="keyword">delete</span> d_n;
<a name="l00132"></a>00132 <span class="preprocessor">#ifdef _DEBUG_RATIONAL_</span>
<a name="l00133"></a>00133 <span class="preprocessor"></span> <span class="keywordtype">int</span> &num_deleted = getDeleted();
<a name="l00134"></a>00134 num_deleted++;
<a name="l00135"></a>00135 printStats();
<a name="l00136"></a>00136 <span class="preprocessor">#endif</span>
<a name="l00137"></a>00137 <span class="preprocessor"></span> }
<a name="l00138"></a>00138
<a name="l00139"></a>00139 <span class="comment">// Get components</span>
<a name="l00140"></a>00140 Rational Rational::getNumerator()<span class="keyword"> const</span>
<a name="l00141"></a>00141 <span class="keyword"> </span>{ <span class="keywordflow">return</span> Rational(Impl(d_n->getNum(), 1)); }
<a name="l00142"></a>00142 Rational Rational::getDenominator()<span class="keyword"> const</span>
<a name="l00143"></a>00143 <span class="keyword"> </span>{ <span class="keywordflow">return</span> Rational(Impl(d_n->getDen(), 1)); }
<a name="l00144"></a>00144
<a name="l00145"></a>00145 <span class="keywordtype">bool</span> Rational::isInteger()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> 1 == d_n->getDen(); }
<a name="l00146"></a>00146
<a name="l00147"></a>00147 <span class="comment">// Assignment</span>
<a name="l00148"></a>00148 Rational& Rational::operator=(<span class="keyword">const</span> Rational& n) {
<a name="l00149"></a>00149 <span class="keywordflow">if</span>(<span class="keyword">this</span> == &n) <span class="keywordflow">return</span> *<span class="keyword">this</span>;
<a name="l00150"></a>00150 <span class="keyword">delete</span> d_n;
<a name="l00151"></a>00151 d_n = <span class="keyword">new</span> Impl(*n.d_n);
<a name="l00152"></a>00152 <span class="keywordflow">return</span> *<span class="keyword">this</span>;
<a name="l00153"></a>00153 }
<a name="l00154"></a>00154
<a name="l00155"></a>00155 ostream &<a class="code" href="namespaceCVC3.html#a6b7e38d3c97da1e91e12a6c9555b8163">operator<<</a>(ostream &os, <span class="keyword">const</span> Rational &n) {
<a name="l00156"></a>00156 <span class="keywordflow">return</span>(os << n.toString());
<a name="l00157"></a>00157 }
<a name="l00158"></a>00158
<a name="l00159"></a>00159
<a name="l00160"></a>00160 <span class="comment">// Check that argument is an int and print an error message otherwise</span>
<a name="l00161"></a>00161
<a name="l00162"></a>00162 <span class="keyword">static</span> <span class="keywordtype">void</span> checkInt(<span class="keyword">const</span> Rational& n, <span class="keyword">const</span> <span class="keywordtype">string</span>& funName) {
<a name="l00163"></a>00163 <a class="code" href="debug_8h.html#a40dac3bdb2166ffc852ee8b1489d2b56">DebugAssert</a>(n.isInteger(),
<a name="l00164"></a>00164 (<span class="stringliteral">"CVC3::Rational::"</span> + funName
<a name="l00165"></a>00165 + <span class="stringliteral">": argument is not an integer: "</span> + n.toString()).c_str());
<a name="l00166"></a>00166 }
<a name="l00167"></a>00167
<a name="l00168"></a>00168 <span class="comment">/* Computes gcd and lcm on *integer* values. Result is always a</span>
<a name="l00169"></a>00169 <span class="comment"> positive integer. In this implementation, it is guaranteed by</span>
<a name="l00170"></a>00170 <span class="comment"> GMP. */</span>
<a name="l00171"></a>00171
<a name="l00172"></a>00172 Rational gcd(<span class="keyword">const</span> Rational &x, <span class="keyword">const</span> Rational &y) {
<a name="l00173"></a>00173 mpz_class g;
<a name="l00174"></a>00174 checkInt(x, <span class="stringliteral">"gcd(*x*,y)"</span>);
<a name="l00175"></a>00175 checkInt(y, <span class="stringliteral">"gcd(x,*y*)"</span>);
<a name="l00176"></a>00176 mpz_gcd(g.get_mpz_t(), x.d_n->get_num_mpz_t(), y.d_n->get_num_mpz_t());
<a name="l00177"></a>00177 <span class="keywordflow">return</span> Rational(Rational::Impl(g,1));
<a name="l00178"></a>00178 }
<a name="l00179"></a>00179
<a name="l00180"></a>00180 Rational gcd(<span class="keyword">const</span> vector<Rational> &v) {
<a name="l00181"></a>00181 mpz_class g(1);
<a name="l00182"></a>00182 <span class="keywordflow">if</span>(v.size() > 0) {
<a name="l00183"></a>00183 checkInt(v[0], <span class="stringliteral">"gcd(vector<Rational>[0])"</span>);
<a name="l00184"></a>00184 g = v[0].d_n->getNum();
<a name="l00185"></a>00185 }
<a name="l00186"></a>00186 <span class="keywordflow">for</span>(<span class="keywordtype">unsigned</span> i=1; i<v.size(); i++) {
<a name="l00187"></a>00187 checkInt(v[i], <span class="stringliteral">"gcd(vector<Rational>)"</span>);
<a name="l00188"></a>00188 <span class="keywordflow">if</span>(*v[i].d_n != 0)
<a name="l00189"></a>00189 mpz_gcd(g.get_mpz_t(), g.get_mpz_t(), v[i].d_n->get_num_mpz_t());
<a name="l00190"></a>00190 }
<a name="l00191"></a>00191 <span class="keywordflow">return</span> Rational(Rational::Impl(g,1));
<a name="l00192"></a>00192 }
<a name="l00193"></a>00193
<a name="l00194"></a>00194 Rational lcm(<span class="keyword">const</span> Rational &x, <span class="keyword">const</span> Rational &y) {
<a name="l00195"></a>00195 mpz_class g;
<a name="l00196"></a>00196 checkInt(x, <span class="stringliteral">"lcm(*x*,y)"</span>);
<a name="l00197"></a>00197 checkInt(y, <span class="stringliteral">"lcm(x,*y*)"</span>);
<a name="l00198"></a>00198 mpz_lcm(g.get_mpz_t(), x.d_n->get_num_mpz_t(), y.d_n->get_num_mpz_t());
<a name="l00199"></a>00199 <span class="keywordflow">return</span> Rational(Rational::Impl(g, 1));
<a name="l00200"></a>00200 }
<a name="l00201"></a>00201
<a name="l00202"></a>00202 Rational lcm(<span class="keyword">const</span> vector<Rational> &v) {
<a name="l00203"></a>00203 mpz_class g(1);
<a name="l00204"></a>00204 <span class="keywordflow">for</span>(<span class="keywordtype">unsigned</span> i=0; i<v.size(); i++) {
<a name="l00205"></a>00205 checkInt(v[i], <span class="stringliteral">"lcm(vector<Rational>)"</span>);
<a name="l00206"></a>00206 <span class="keywordflow">if</span>(*v[i].d_n != 0)
<a name="l00207"></a>00207 mpz_lcm(g.get_mpz_t(), g.get_mpz_t(), v[i].d_n->get_num_mpz_t());
<a name="l00208"></a>00208 }
<a name="l00209"></a>00209 <span class="keywordflow">return</span> Rational(Rational::Impl(g,1));
<a name="l00210"></a>00210 }
<a name="l00211"></a>00211
<a name="l00212"></a>00212 Rational <a class="code" href="namespaceCVC3.html#a39fc111339d6dffdc98d6a25b68dff0e">abs</a>(<span class="keyword">const</span> Rational &x) {
<a name="l00213"></a>00213 <span class="keywordflow">return</span> Rational(Rational::Impl(<a class="code" href="namespaceCVC3.html#a39fc111339d6dffdc98d6a25b68dff0e">abs</a>(*x.d_n)));
<a name="l00214"></a>00214 }
<a name="l00215"></a>00215
<a name="l00216"></a>00216 Rational floor(<span class="keyword">const</span> Rational &x) {
<a name="l00217"></a>00217 mpz_class q;
<a name="l00218"></a>00218 mpz_fdiv_q(q.get_mpz_t(), x.d_n->get_num_mpz_t(), x.d_n->get_den_mpz_t());
<a name="l00219"></a>00219 <span class="keywordflow">return</span> Rational(Rational::Impl(q,1));
<a name="l00220"></a>00220 }
<a name="l00221"></a>00221
<a name="l00222"></a>00222 Rational ceil(<span class="keyword">const</span> Rational &x) {
<a name="l00223"></a>00223 mpz_class q;
<a name="l00224"></a>00224 mpz_cdiv_q(q.get_mpz_t(), x.d_n->get_num_mpz_t(), x.d_n->get_den_mpz_t());
<a name="l00225"></a>00225 <span class="keywordflow">return</span> Rational(Rational::Impl(q,1));
<a name="l00226"></a>00226 }
<a name="l00227"></a>00227
<a name="l00228"></a>00228 Rational mod(<span class="keyword">const</span> Rational &x, <span class="keyword">const</span> Rational &y) {
<a name="l00229"></a>00229 checkInt(x, <span class="stringliteral">"mod(*x*,y)"</span>);
<a name="l00230"></a>00230 checkInt(y, <span class="stringliteral">"mod(x,*y*)"</span>);
<a name="l00231"></a>00231 mpz_class r;
<a name="l00232"></a>00232 mpz_mod(r.get_mpz_t(), x.d_n->get_num_mpz_t(), y.d_n->get_num_mpz_t());
<a name="l00233"></a>00233 <span class="keywordflow">return</span>(Rational(Rational::Impl(r,1)));
<a name="l00234"></a>00234 }
<a name="l00235"></a>00235
<a name="l00236"></a>00236 Rational intRoot(<span class="keyword">const</span> Rational& base, <span class="keywordtype">unsigned</span> <span class="keywordtype">long</span> <span class="keywordtype">int</span> n)
<a name="l00237"></a>00237 {
<a name="l00238"></a>00238 <span class="keywordflow">return</span> Rational(Rational::Impl(0,1));
<a name="l00239"></a>00239 }
<a name="l00240"></a>00240
<a name="l00241"></a>00241 <span class="keywordtype">string</span> Rational::toString(<span class="keywordtype">int</span> base)<span class="keyword"> const </span>{
<a name="l00242"></a>00242 <span class="keywordtype">char</span> *tmp = mpq_get_str(NULL, base, d_n->get_mpq_t());
<a name="l00243"></a>00243 <span class="keywordtype">string</span> res(tmp);
<a name="l00244"></a>00244 <span class="comment">// delete tmp;</span>
<a name="l00245"></a>00245 free(tmp);
<a name="l00246"></a>00246 <span class="keywordflow">return</span>(res);
<a name="l00247"></a>00247 }
<a name="l00248"></a>00248
<a name="l00249"></a>00249 <span class="keywordtype">size_t</span> Rational::hash()<span class="keyword"> const </span>{
<a name="l00250"></a>00250 <a class="code" href="structHash_1_1hash_3_01const_01char_01_5_01_4.html">std::hash<const char *></a> h;
<a name="l00251"></a>00251 <span class="keywordflow">return</span> h(toString().c_str());
<a name="l00252"></a>00252 }
<a name="l00253"></a>00253
<a name="l00254"></a>00254 <span class="keywordtype">void</span> Rational::print()<span class="keyword"> const </span>{
<a name="l00255"></a>00255 cout << (*d_n) << <a class="code" href="group__ExprStream__Manip.html#ga05b0ea7353ec24fa8e7e272d7a7875d8" title="Print the end-of-line.">endl</a>;
<a name="l00256"></a>00256 }
<a name="l00257"></a>00257
<a name="l00258"></a>00258
<a name="l00259"></a>00259
<a name="l00260"></a>00260 <span class="comment">// Unary minus</span>
<a name="l00261"></a>00261 Rational <a class="code" href="namespaceCVC3.html#aacf567dce1c762f957267427472bd959">Rational::operator-</a>()<span class="keyword"> const </span>{
<a name="l00262"></a>00262 <span class="keywordflow">return</span> Rational(Rational::Impl(- (*d_n)));
<a name="l00263"></a>00263 }
<a name="l00264"></a>00264
<a name="l00265"></a>00265 Rational &Rational::operator+=(<span class="keyword">const</span> Rational &n2) {
<a name="l00266"></a>00266 *d_n += (*n2.d_n);
<a name="l00267"></a>00267 <span class="keywordflow">return</span> *<span class="keyword">this</span>;
<a name="l00268"></a>00268 }
<a name="l00269"></a>00269
<a name="l00270"></a>00270 Rational &Rational::operator-=(<span class="keyword">const</span> Rational &n2) {
<a name="l00271"></a>00271 *d_n -= (*n2.d_n);
<a name="l00272"></a>00272 <span class="keywordflow">return</span> *<span class="keyword">this</span>;
<a name="l00273"></a>00273 }
<a name="l00274"></a>00274
<a name="l00275"></a>00275 Rational &Rational::operator*=(<span class="keyword">const</span> Rational &n2) {
<a name="l00276"></a>00276 *d_n *= (*n2.d_n);
<a name="l00277"></a>00277 <span class="keywordflow">return</span> *<span class="keyword">this</span>;
<a name="l00278"></a>00278 }
<a name="l00279"></a>00279
<a name="l00280"></a>00280 Rational &Rational::operator/=(<span class="keyword">const</span> Rational &n2) {
<a name="l00281"></a>00281 *d_n /= (*n2.d_n);
<a name="l00282"></a>00282 <span class="keywordflow">return</span> *<span class="keyword">this</span>;
<a name="l00283"></a>00283 }
<a name="l00284"></a>00284
<a name="l00285"></a>00285 <span class="keywordtype">int</span> Rational::getInt()<span class="keyword"> const </span>{
<a name="l00286"></a>00286 checkInt(*<span class="keyword">this</span>, <span class="stringliteral">"getInt()"</span>);
<a name="l00287"></a>00287 <span class="keywordflow">return</span> mpz_get_si(d_n->get_num_mpz_t());
<a name="l00288"></a>00288 }
<a name="l00289"></a>00289
<a name="l00290"></a>00290 <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> Rational::getUnsigned()<span class="keyword"> const </span>{
<a name="l00291"></a>00291 checkInt(*<span class="keyword">this</span>, <span class="stringliteral">"getUnsigned()"</span>);
<a name="l00292"></a>00292 <span class="keywordflow">return</span> mpz_get_ui(d_n->get_num_mpz_t());
<a name="l00293"></a>00293 }
<a name="l00294"></a>00294
<a name="l00295"></a>00295 <span class="preprocessor">#ifdef _DEBUG_RATIONAL_</span>
<a name="l00296"></a>00296 <span class="preprocessor"></span> <span class="keywordtype">void</span> Rational::printStats() {
<a name="l00297"></a>00297 <span class="keywordtype">int</span> &num_created = getCreated();
<a name="l00298"></a>00298 <span class="keywordtype">int</span> &num_deleted = getDeleted();
<a name="l00299"></a>00299 <span class="keywordflow">if</span>(num_created % 1000 == 0 || num_deleted % 1000 == 0) {
<a name="l00300"></a>00300 std::cerr << <span class="stringliteral">"Rational("</span> << *d_n << <span class="stringliteral">"): created "</span> << num_created
<a name="l00301"></a>00301 << <span class="stringliteral">", deleted "</span> << num_deleted
<a name="l00302"></a>00302 << <span class="stringliteral">", currently alive "</span> << num_created-num_deleted
<a name="l00303"></a>00303 << <a class="code" href="group__ExprStream__Manip.html#ga05b0ea7353ec24fa8e7e272d7a7875d8" title="Print the end-of-line.">std::endl</a>;
<a name="l00304"></a>00304 }
<a name="l00305"></a>00305 }
<a name="l00306"></a>00306 <span class="preprocessor">#endif</span>
<a name="l00307"></a>00307 <span class="preprocessor"></span>
<a name="l00308"></a>00308 <span class="keywordtype">bool</span> <a class="code" href="namespaceCVC3.html#a8e164436388f2d87c971d9bbde973c58">operator==</a>(<span class="keyword">const</span> Rational &n1, <span class="keyword">const</span> Rational &n2) {
<a name="l00309"></a>00309 <span class="keywordflow">return</span>(*n1.d_n == *n2.d_n);
<a name="l00310"></a>00310 }
<a name="l00311"></a>00311
<a name="l00312"></a>00312 <span class="keywordtype">bool</span> <a class="code" href="namespaceCVC3.html#ad3e3964a0b8cd9e2749de47b053b9d97">operator<</a>(<span class="keyword">const</span> Rational &n1, <span class="keyword">const</span> Rational &n2) {
<a name="l00313"></a>00313 <span class="keywordflow">return</span>(*n1.d_n < *n2.d_n);
<a name="l00314"></a>00314 }
<a name="l00315"></a>00315
<a name="l00316"></a>00316 <span class="keywordtype">bool</span> <a class="code" href="namespaceCVC3.html#abccc88aac4f7652def737f1081dc7a89">operator<=</a>(<span class="keyword">const</span> Rational &n1, <span class="keyword">const</span> Rational &n2) {
<a name="l00317"></a>00317 <span class="keywordflow">return</span>(*n1.d_n <= *n2.d_n);
<a name="l00318"></a>00318 }
<a name="l00319"></a>00319
<a name="l00320"></a>00320 <span class="keywordtype">bool</span> <a class="code" href="namespaceCVC3.html#a0d82fd3eb68860cbd01ae86b2b9e3c66">operator></a>(<span class="keyword">const</span> Rational &n1, <span class="keyword">const</span> Rational &n2) {
<a name="l00321"></a>00321 <span class="keywordflow">return</span>(*n1.d_n > *n2.d_n);
<a name="l00322"></a>00322 }
<a name="l00323"></a>00323
<a name="l00324"></a>00324 <span class="keywordtype">bool</span> <a class="code" href="namespaceCVC3.html#af997ba8407b661bf2ffe2cb6f52c3e3b">operator>=</a>(<span class="keyword">const</span> Rational &n1, <span class="keyword">const</span> Rational &n2) {
<a name="l00325"></a>00325 <span class="keywordflow">return</span>(*n1.d_n >= *n2.d_n);
<a name="l00326"></a>00326 }
<a name="l00327"></a>00327
<a name="l00328"></a>00328 <span class="keywordtype">bool</span> <a class="code" href="namespaceCVC3.html#a5aa953c549c2e103f3834c48bf6cb9a1">operator!=</a>(<span class="keyword">const</span> Rational &n1, <span class="keyword">const</span> Rational &n2) {
<a name="l00329"></a>00329 <span class="keywordflow">return</span>(*n1.d_n != *n2.d_n);
<a name="l00330"></a>00330 }
<a name="l00331"></a>00331
<a name="l00332"></a>00332 Rational <a class="code" href="namespaceCVC3.html#a286cf8699acada708816e72c6b436b90">operator+</a>(<span class="keyword">const</span> Rational &n1, <span class="keyword">const</span> Rational &n2) {
<a name="l00333"></a>00333 <span class="keywordflow">return</span> Rational(Rational::Impl(*n1.d_n + *n2.d_n));
<a name="l00334"></a>00334 }
<a name="l00335"></a>00335
<a name="l00336"></a>00336 Rational <a class="code" href="namespaceCVC3.html#aacf567dce1c762f957267427472bd959">operator-</a>(<span class="keyword">const</span> Rational &n1, <span class="keyword">const</span> Rational &n2) {
<a name="l00337"></a>00337 <span class="keywordflow">return</span> Rational(Rational::Impl((*n1.d_n) - (*n2.d_n)));
<a name="l00338"></a>00338 }
<a name="l00339"></a>00339
<a name="l00340"></a>00340 Rational <a class="code" href="namespaceCVC3.html#a300bc9244236ebdb1bff90b0b453034c">operator*</a>(<span class="keyword">const</span> Rational &n1, <span class="keyword">const</span> Rational &n2) {
<a name="l00341"></a>00341 <span class="keywordflow">return</span> Rational(Rational::Impl((*n1.d_n) * (*n2.d_n)));
<a name="l00342"></a>00342 }
<a name="l00343"></a>00343
<a name="l00344"></a>00344 Rational <a class="code" href="namespaceCVC3.html#a069aa16342bb9958a3d576a18a390248">operator/</a>(<span class="keyword">const</span> Rational &n1, <span class="keyword">const</span> Rational &n2) {
<a name="l00345"></a>00345 <span class="keywordflow">return</span> Rational(Rational::Impl(*n1.d_n / *n2.d_n));
<a name="l00346"></a>00346 }
<a name="l00347"></a>00347
<a name="l00348"></a>00348 Rational operator%(<span class="keyword">const</span> Rational &n1, <span class="keyword">const</span> Rational &n2) {
<a name="l00349"></a>00349 <span class="keywordflow">return</span> Rational(Rational::Impl(*n1.d_n + *n2.d_n));
<a name="l00350"></a>00350 }
<a name="l00351"></a>00351
<a name="l00352"></a>00352
<a name="l00353"></a>00353 <span class="comment">// Implementation of the forward-declared internal class</span>
<a name="l00354"></a>00354 <span class="keyword">class </span>Unsigned::Impl : <span class="keyword">public</span> mpz_class {
<a name="l00355"></a>00355 <span class="keyword">public</span>:
<a name="l00356"></a>00356 <span class="comment">// mpz_class _n;</span>
<a name="l00357"></a>00357 <span class="comment">// Constructors</span>
<a name="l00358"></a>00358 Impl() : mpz_class() { }
<a name="l00359"></a>00359 <span class="comment">// Constructor from integer</span>
<a name="l00360"></a>00360 <span class="comment">// Impl(const mpz_class &x) : mpq_class(x) { }</span>
<a name="l00361"></a>00361 <span class="comment">// Constructor from rational</span>
<a name="l00362"></a>00362 Impl(<span class="keyword">const</span> mpz_class &x) : mpz_class(x) { }
<a name="l00363"></a>00363 <span class="comment">// Copy constructor</span>
<a name="l00364"></a>00364 Impl(<span class="keyword">const</span> Impl &x) : mpz_class(x) { }
<a name="l00365"></a>00365 <span class="comment">// From pair of integers / strings</span>
<a name="l00366"></a>00366 Impl(<span class="keywordtype">int</span> n) : mpz_class(n) { }
<a name="l00367"></a>00367 Impl(<span class="keyword">const</span> mpz_class& n, <span class="keyword">const</span> mpz_class& d)
<a name="l00368"></a>00368 : mpq_class(n,d) { canonicalize(); }
<a name="l00369"></a>00369 <span class="comment">// From string(s)</span>
<a name="l00370"></a>00370 Impl(<span class="keyword">const</span> <span class="keywordtype">string</span> &n, <span class="keywordtype">int</span> base): mpz_class(n, base) { }
<a name="l00371"></a>00371 <span class="comment">// Destructor</span>
<a name="l00372"></a>00372 <span class="keyword">virtual</span> ~Impl() { }
<a name="l00373"></a>00373 };
<a name="l00374"></a>00374
<a name="l00375"></a>00375 <span class="comment">// Constructors</span>
<a name="l00376"></a>00376 Unsigned::Unsigned() : d_n(new Impl) { }
<a name="l00377"></a>00377 <span class="comment">// Copy constructor</span>
<a name="l00378"></a>00378 Unsigned::Unsigned(<span class="keyword">const</span> Unsigned &n) : d_n(new Impl(*n.d_n)) { }
<a name="l00379"></a>00379
<a name="l00380"></a>00380 <span class="comment">// Private constructor</span>
<a name="l00381"></a>00381 Unsigned::Unsigned(<span class="keyword">const</span> Impl& t): d_n(new Impl(t)) { }
<a name="l00382"></a>00382 <span class="comment">// Constructors from strings</span>
<a name="l00383"></a>00383 Unsigned::Unsigned(<span class="keyword">const</span> <span class="keywordtype">char</span>* n, <span class="keywordtype">int</span> base)
<a name="l00384"></a>00384 : d_n(new Impl(string(n), base)) { }
<a name="l00385"></a>00385 Unsigned::Unsigned(<span class="keyword">const</span> <span class="keywordtype">string</span>& n, <span class="keywordtype">int</span> base)
<a name="l00386"></a>00386 : d_n(new Impl(n, base)) { }
<a name="l00387"></a>00387 <span class="comment">// Destructor</span>
<a name="l00388"></a>00388 Unsigned::~Unsigned() {
<a name="l00389"></a>00389 <span class="keyword">delete</span> d_n;
<a name="l00390"></a>00390 }
<a name="l00391"></a>00391
<a name="l00392"></a>00392 <span class="comment">// Assignment</span>
<a name="l00393"></a>00393 Unsigned& Unsigned::operator=(<span class="keyword">const</span> Unsigned& n) {
<a name="l00394"></a>00394 <span class="keywordflow">if</span>(<span class="keyword">this</span> == &n) <span class="keywordflow">return</span> *<span class="keyword">this</span>;
<a name="l00395"></a>00395 <span class="keyword">delete</span> d_n;
<a name="l00396"></a>00396 d_n = <span class="keyword">new</span> Impl(*n.d_n);
<a name="l00397"></a>00397 <span class="keywordflow">return</span> *<span class="keyword">this</span>;
<a name="l00398"></a>00398 }
<a name="l00399"></a>00399
<a name="l00400"></a>00400 ostream &<a class="code" href="namespaceCVC3.html#a6b7e38d3c97da1e91e12a6c9555b8163">operator<<</a>(ostream &os, <span class="keyword">const</span> Unsigned &n) {
<a name="l00401"></a>00401 <span class="keywordflow">return</span>(os << n.toString());
<a name="l00402"></a>00402 }
<a name="l00403"></a>00403
<a name="l00404"></a>00404
<a name="l00405"></a>00405 <span class="comment">/* Computes gcd and lcm on *integer* values. Result is always a</span>
<a name="l00406"></a>00406 <span class="comment"> positive integer. In this implementation, it is guaranteed by</span>
<a name="l00407"></a>00407 <span class="comment"> GMP. */</span>
<a name="l00408"></a>00408
<a name="l00409"></a>00409 Unsigned gcd(<span class="keyword">const</span> Unsigned &x, <span class="keyword">const</span> Unsigned &y) {
<a name="l00410"></a>00410 mpz_class g;
<a name="l00411"></a>00411 mpz_gcd(g, *(x.d_n), *(y.d_n));
<a name="l00412"></a>00412 <span class="keywordflow">return</span> Unsigned(Unsigned::Impl(g));
<a name="l00413"></a>00413 }
<a name="l00414"></a>00414
<a name="l00415"></a>00415 Unsigned gcd(<span class="keyword">const</span> vector<Unsigned> &v) {
<a name="l00416"></a>00416 mpz_class g(1);
<a name="l00417"></a>00417 <span class="keywordflow">if</span>(v.size() > 0) {
<a name="l00418"></a>00418 g = *(v[0].d_n);
<a name="l00419"></a>00419 }
<a name="l00420"></a>00420 <span class="keywordflow">for</span>(<span class="keywordtype">unsigned</span> i=1; i<v.size(); i++) {
<a name="l00421"></a>00421 <span class="keywordflow">if</span>(*v[i].d_n != 0)
<a name="l00422"></a>00422 mpz_gcd(g, g, *(v[i].d_n));
<a name="l00423"></a>00423 }
<a name="l00424"></a>00424 <span class="keywordflow">return</span> Unsigned(Unsigned::Impl(g));
<a name="l00425"></a>00425 }
<a name="l00426"></a>00426
<a name="l00427"></a>00427 Unsigned lcm(<span class="keyword">const</span> Unsigned &x, <span class="keyword">const</span> Unsigned &y) {
<a name="l00428"></a>00428 mpz_class g;
<a name="l00429"></a>00429 mpz_lcm(g, *x.d_n, *y.d_n);
<a name="l00430"></a>00430 <span class="keywordflow">return</span> Unsigned(Unsigned::Impl(g));
<a name="l00431"></a>00431 }
<a name="l00432"></a>00432
<a name="l00433"></a>00433 Unsigned lcm(<span class="keyword">const</span> vector<Unsigned> &v) {
<a name="l00434"></a>00434 mpz_class g(1);
<a name="l00435"></a>00435 <span class="keywordflow">for</span>(<span class="keywordtype">unsigned</span> i=0; i<v.size(); i++) {
<a name="l00436"></a>00436 <span class="keywordflow">if</span>(*v[i].d_n != 0)
<a name="l00437"></a>00437 mpz_lcm(g, g, *v[i].d_n);
<a name="l00438"></a>00438 }
<a name="l00439"></a>00439 <span class="keywordflow">return</span> Unsigned(Unsigned::Impl(g));
<a name="l00440"></a>00440 }
<a name="l00441"></a>00441
<a name="l00442"></a>00442 Unsigned <a class="code" href="namespaceCVC3.html#a39fc111339d6dffdc98d6a25b68dff0e">abs</a>(<span class="keyword">const</span> Unsigned &x) {
<a name="l00443"></a>00443 <span class="keywordflow">return</span> Unsigned(Unsigned::Impl(<a class="code" href="namespaceCVC3.html#a39fc111339d6dffdc98d6a25b68dff0e">abs</a>(*x.d_n)));
<a name="l00444"></a>00444 }
<a name="l00445"></a>00445
<a name="l00446"></a>00446 Unsigned mod(<span class="keyword">const</span> Unsigned &x, <span class="keyword">const</span> Unsigned &y) {
<a name="l00447"></a>00447 mpz_class r;
<a name="l00448"></a>00448 mpz_mod(r, *x.d_n, *y.d_n);
<a name="l00449"></a>00449 <span class="keywordflow">return</span>(Unsigned(Unsigned::Impl(r)));
<a name="l00450"></a>00450 }
<a name="l00451"></a>00451
<a name="l00452"></a>00452 Unsigned intRoot(<span class="keyword">const</span> Unsigned& base, <span class="keywordtype">unsigned</span> <span class="keywordtype">long</span> <span class="keywordtype">int</span> n)
<a name="l00453"></a>00453 {
<a name="l00454"></a>00454 <span class="keywordflow">return</span> Unsigned(Unsigned::Impl(0,1));
<a name="l00455"></a>00455 }
<a name="l00456"></a>00456
<a name="l00457"></a>00457 <span class="keywordtype">string</span> Unsigned::toString(<span class="keywordtype">int</span> base)<span class="keyword"> const </span>{
<a name="l00458"></a>00458 <span class="keywordtype">char</span> *tmp = mpz_get_str(NULL, base, *d_n);
<a name="l00459"></a>00459 <span class="keywordtype">string</span> res(tmp);
<a name="l00460"></a>00460 <span class="comment">// delete tmp;</span>
<a name="l00461"></a>00461 free(tmp);
<a name="l00462"></a>00462 <span class="keywordflow">return</span>(res);
<a name="l00463"></a>00463 }
<a name="l00464"></a>00464
<a name="l00465"></a>00465 <span class="keywordtype">size_t</span> Unsigned::hash()<span class="keyword"> const </span>{
<a name="l00466"></a>00466 <a class="code" href="structHash_1_1hash_3_01const_01char_01_5_01_4.html">std::hash<const char *></a> h;
<a name="l00467"></a>00467 <span class="keywordflow">return</span> h(toString().c_str());
<a name="l00468"></a>00468 }
<a name="l00469"></a>00469
<a name="l00470"></a>00470 <span class="keywordtype">void</span> Unsigned::print()<span class="keyword"> const </span>{
<a name="l00471"></a>00471 cout << (*d_n) << <a class="code" href="group__ExprStream__Manip.html#ga05b0ea7353ec24fa8e7e272d7a7875d8" title="Print the end-of-line.">endl</a>;
<a name="l00472"></a>00472 }
<a name="l00473"></a>00473
<a name="l00474"></a>00474
<a name="l00475"></a>00475
<a name="l00476"></a>00476 <span class="comment">// Unary minus</span>
<a name="l00477"></a>00477 Unsigned <a class="code" href="namespaceCVC3.html#aacf567dce1c762f957267427472bd959">Unsigned::operator-</a>()<span class="keyword"> const </span>{
<a name="l00478"></a>00478 <span class="keywordflow">return</span> Unsigned(Unsigned::Impl(- (*d_n)));
<a name="l00479"></a>00479 }
<a name="l00480"></a>00480
<a name="l00481"></a>00481 Unsigned &Unsigned::operator+=(<span class="keyword">const</span> Unsigned &n2) {
<a name="l00482"></a>00482 *d_n += (*n2.d_n);
<a name="l00483"></a>00483 <span class="keywordflow">return</span> *<span class="keyword">this</span>;
<a name="l00484"></a>00484 }
<a name="l00485"></a>00485
<a name="l00486"></a>00486 Unsigned &Unsigned::operator-=(<span class="keyword">const</span> Unsigned &n2) {
<a name="l00487"></a>00487 *d_n -= (*n2.d_n);
<a name="l00488"></a>00488 <span class="keywordflow">return</span> *<span class="keyword">this</span>;
<a name="l00489"></a>00489 }
<a name="l00490"></a>00490
<a name="l00491"></a>00491 Unsigned &Unsigned::operator*=(<span class="keyword">const</span> Unsigned &n2) {
<a name="l00492"></a>00492 *d_n *= (*n2.d_n);
<a name="l00493"></a>00493 <span class="keywordflow">return</span> *<span class="keyword">this</span>;
<a name="l00494"></a>00494 }
<a name="l00495"></a>00495
<a name="l00496"></a>00496 Unsigned &Unsigned::operator/=(<span class="keyword">const</span> Unsigned &n2) {
<a name="l00497"></a>00497 *d_n /= (*n2.d_n);
<a name="l00498"></a>00498 <span class="keywordflow">return</span> *<span class="keyword">this</span>;
<a name="l00499"></a>00499 }
<a name="l00500"></a>00500
<a name="l00501"></a>00501 <span class="keywordtype">int</span> Unsigned::getInt()<span class="keyword"> const </span>{
<a name="l00502"></a>00502 <span class="keywordflow">return</span> mpz_get_si(*d_n);
<a name="l00503"></a>00503 }
<a name="l00504"></a>00504
<a name="l00505"></a>00505 <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> Unsigned::getUnsigned()<span class="keyword"> const </span>{
<a name="l00506"></a>00506 <span class="keywordflow">return</span> mpz_get_ui(*d_n);
<a name="l00507"></a>00507 }
<a name="l00508"></a>00508
<a name="l00509"></a>00509 <span class="keywordtype">bool</span> <a class="code" href="namespaceCVC3.html#a8e164436388f2d87c971d9bbde973c58">operator==</a>(<span class="keyword">const</span> Unsigned &n1, <span class="keyword">const</span> Unsigned &n2) {
<a name="l00510"></a>00510 <span class="keywordflow">return</span>(*n1.d_n == *n2.d_n);
<a name="l00511"></a>00511 }
<a name="l00512"></a>00512
<a name="l00513"></a>00513 <span class="keywordtype">bool</span> <a class="code" href="namespaceCVC3.html#ad3e3964a0b8cd9e2749de47b053b9d97">operator<</a>(<span class="keyword">const</span> Unsigned &n1, <span class="keyword">const</span> Unsigned &n2) {
<a name="l00514"></a>00514 <span class="keywordflow">return</span>(*n1.d_n < *n2.d_n);
<a name="l00515"></a>00515 }
<a name="l00516"></a>00516
<a name="l00517"></a>00517 <span class="keywordtype">bool</span> <a class="code" href="namespaceCVC3.html#abccc88aac4f7652def737f1081dc7a89">operator<=</a>(<span class="keyword">const</span> Unsigned &n1, <span class="keyword">const</span> Unsigned &n2) {
<a name="l00518"></a>00518 <span class="keywordflow">return</span>(*n1.d_n <= *n2.d_n);
<a name="l00519"></a>00519 }
<a name="l00520"></a>00520
<a name="l00521"></a>00521 <span class="keywordtype">bool</span> <a class="code" href="namespaceCVC3.html#a0d82fd3eb68860cbd01ae86b2b9e3c66">operator></a>(<span class="keyword">const</span> Unsigned &n1, <span class="keyword">const</span> Unsigned &n2) {
<a name="l00522"></a>00522 <span class="keywordflow">return</span>(*n1.d_n > *n2.d_n);
<a name="l00523"></a>00523 }
<a name="l00524"></a>00524
<a name="l00525"></a>00525 <span class="keywordtype">bool</span> <a class="code" href="namespaceCVC3.html#af997ba8407b661bf2ffe2cb6f52c3e3b">operator>=</a>(<span class="keyword">const</span> Unsigned &n1, <span class="keyword">const</span> Unsigned &n2) {
<a name="l00526"></a>00526 <span class="keywordflow">return</span>(*n1.d_n >= *n2.d_n);
<a name="l00527"></a>00527 }
<a name="l00528"></a>00528
<a name="l00529"></a>00529 <span class="keywordtype">bool</span> <a class="code" href="namespaceCVC3.html#a5aa953c549c2e103f3834c48bf6cb9a1">operator!=</a>(<span class="keyword">const</span> Unsigned &n1, <span class="keyword">const</span> Unsigned &n2) {
<a name="l00530"></a>00530 <span class="keywordflow">return</span>(*n1.d_n != *n2.d_n);
<a name="l00531"></a>00531 }
<a name="l00532"></a>00532
<a name="l00533"></a>00533 Unsigned <a class="code" href="namespaceCVC3.html#a286cf8699acada708816e72c6b436b90">operator+</a>(<span class="keyword">const</span> Unsigned &n1, <span class="keyword">const</span> Unsigned &n2) {
<a name="l00534"></a>00534 <span class="keywordflow">return</span> Unsigned(Unsigned::Impl(*n1.d_n + *n2.d_n));
<a name="l00535"></a>00535 }
<a name="l00536"></a>00536
<a name="l00537"></a>00537 Unsigned <a class="code" href="namespaceCVC3.html#aacf567dce1c762f957267427472bd959">operator-</a>(<span class="keyword">const</span> Unsigned &n1, <span class="keyword">const</span> Unsigned &n2) {
<a name="l00538"></a>00538 <span class="keywordflow">return</span> Unsigned(Unsigned::Impl((*n1.d_n) - (*n2.d_n)));
<a name="l00539"></a>00539 }
<a name="l00540"></a>00540
<a name="l00541"></a>00541 Unsigned <a class="code" href="namespaceCVC3.html#a300bc9244236ebdb1bff90b0b453034c">operator*</a>(<span class="keyword">const</span> Unsigned &n1, <span class="keyword">const</span> Unsigned &n2) {
<a name="l00542"></a>00542 <span class="keywordflow">return</span> Unsigned(Unsigned::Impl((*n1.d_n) * (*n2.d_n)));
<a name="l00543"></a>00543 }
<a name="l00544"></a>00544
<a name="l00545"></a>00545 Unsigned <a class="code" href="namespaceCVC3.html#a069aa16342bb9958a3d576a18a390248">operator/</a>(<span class="keyword">const</span> Unsigned &n1, <span class="keyword">const</span> Unsigned &n2) {
<a name="l00546"></a>00546 <span class="keywordflow">return</span> Unsigned(Unsigned::Impl(*n1.d_n / *n2.d_n));
<a name="l00547"></a>00547 }
<a name="l00548"></a>00548
<a name="l00549"></a>00549 Unsigned operator%(<span class="keyword">const</span> Unsigned &n1, <span class="keyword">const</span> Unsigned &n2) {
<a name="l00550"></a>00550 <span class="keywordflow">return</span> Unsigned(Unsigned::Impl(*n1.d_n + *n2.d_n));
<a name="l00551"></a>00551 }
<a name="l00552"></a>00552
<a name="l00553"></a>00553 }; <span class="comment">/* close namespace */</span>
<a name="l00554"></a>00554
<a name="l00555"></a>00555
<a name="l00556"></a>00556 <span class="preprocessor">#endif</span>
</pre></div></div>
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