X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Fnumeric.cpp;h=f1be0bcbe960d0df61609a9809e70b931c01efff;hp=b1a4033cd73fe5c57f51dd0cb858bc843b8d2fcc;hb=eb2c8f314d8cd32f8313837101881043594fd949;hpb=27d6204effdef95a00af461fff98024e290dbaa7

diff --git a/ginac/numeric.cpp b/ginac/numeric.cpp
index b1a4033c..f1be0bcb 100644
--- a/ginac/numeric.cpp
+++ b/ginac/numeric.cpp
@@ -29,20 +29,13 @@
 #include <vector>
 #include <stdexcept>
 #include <string>
-
-#if defined(HAVE_SSTREAM)
 #include <sstream>
-#elif defined(HAVE_STRSTREAM)
-#include <strstream>
-#else
-#error Need either sstream or strstream
-#endif
 
 #include "numeric.h"
 #include "ex.h"
 #include "print.h"
 #include "archive.h"
-#include "debugmsg.h"
+#include "tostring.h"
 #include "utils.h"
 
 // CLN should pollute the global namespace as little as possible.  Hence, we
@@ -69,14 +62,12 @@ namespace GiNaC {
 GINAC_IMPLEMENT_REGISTERED_CLASS(numeric, basic)
 
 //////////
-// default ctor, dtor, copy ctor assignment
-// operator and helpers
+// default ctor, dtor, copy ctor, assignment operator and helpers
 //////////
 
 /** default ctor. Numerically it initializes to an integer zero. */
 numeric::numeric() : basic(TINFO_numeric)
 {
-	debugmsg("numeric default ctor", LOGLEVEL_CONSTRUCT);
 	value = cln::cl_I(0);
 	setflag(status_flags::evaluated | status_flags::expanded);
 }
@@ -97,13 +88,12 @@ DEFAULT_DESTROY(numeric)
 
 numeric::numeric(int i) : basic(TINFO_numeric)
 {
-	debugmsg("numeric ctor from int",LOGLEVEL_CONSTRUCT);
 	// Not the whole int-range is available if we don't cast to long
 	// first.  This is due to the behaviour of the cl_I-ctor, which
-	// emphasizes efficiency.  However, if the integer is small enough, 
-	// i.e. satisfies cl_immediate_p(), we save space and dereferences by
-	// using an immediate type:
-	if (cln::cl_immediate_p(i))
+	// emphasizes efficiency.  However, if the integer is small enough
+	// we save space and dereferences by using an immediate type.
+	// (C.f. <cln/object.h>)
+	if (i < (1U<<cl_value_len-1))
 		value = cln::cl_I(i);
 	else
 		value = cln::cl_I((long) i);
@@ -113,13 +103,12 @@ numeric::numeric(int i) : basic(TINFO_numeric)
 
 numeric::numeric(unsigned int i) : basic(TINFO_numeric)
 {
-	debugmsg("numeric ctor from uint",LOGLEVEL_CONSTRUCT);
 	// Not the whole uint-range is available if we don't cast to ulong
 	// first.  This is due to the behaviour of the cl_I-ctor, which
-	// emphasizes efficiency.  However, if the integer is small enough, 
-	// i.e. satisfies cl_immediate_p(), we save space and dereferences by
-	// using an immediate type:
-	if (cln::cl_immediate_p(i))
+	// emphasizes efficiency.  However, if the integer is small enough
+	// we save space and dereferences by using an immediate type.
+	// (C.f. <cln/object.h>)
+	if (i < (1U<<cl_value_len-1))
 		value = cln::cl_I(i);
 	else
 		value = cln::cl_I((unsigned long) i);
@@ -129,7 +118,6 @@ numeric::numeric(unsigned int i) : basic(TINFO_numeric)
 
 numeric::numeric(long i) : basic(TINFO_numeric)
 {
-	debugmsg("numeric ctor from long",LOGLEVEL_CONSTRUCT);
 	value = cln::cl_I(i);
 	setflag(status_flags::evaluated | status_flags::expanded);
 }
@@ -137,7 +125,6 @@ numeric::numeric(long i) : basic(TINFO_numeric)
 
 numeric::numeric(unsigned long i) : basic(TINFO_numeric)
 {
-	debugmsg("numeric ctor from ulong",LOGLEVEL_CONSTRUCT);
 	value = cln::cl_I(i);
 	setflag(status_flags::evaluated | status_flags::expanded);
 }
@@ -147,7 +134,6 @@ numeric::numeric(unsigned long i) : basic(TINFO_numeric)
  *  @exception overflow_error (division by zero) */
 numeric::numeric(long numer, long denom) : basic(TINFO_numeric)
 {
-	debugmsg("numeric ctor from long/long",LOGLEVEL_CONSTRUCT);
 	if (!denom)
 		throw std::overflow_error("division by zero");
 	value = cln::cl_I(numer) / cln::cl_I(denom);
@@ -157,7 +143,6 @@ numeric::numeric(long numer, long denom) : basic(TINFO_numeric)
 
 numeric::numeric(double d) : basic(TINFO_numeric)
 {
-	debugmsg("numeric ctor from double",LOGLEVEL_CONSTRUCT);
 	// We really want to explicitly use the type cl_LF instead of the
 	// more general cl_F, since that would give us a cl_DF only which
 	// will not be promoted to cl_LF if overflow occurs:
@@ -170,40 +155,47 @@ numeric::numeric(double d) : basic(TINFO_numeric)
  *  notation like "2+5*I". */
 numeric::numeric(const char *s) : basic(TINFO_numeric)
 {
-	debugmsg("numeric ctor from string",LOGLEVEL_CONSTRUCT);
 	cln::cl_N ctorval = 0;
 	// parse complex numbers (functional but not completely safe, unfortunately
 	// std::string does not understand regexpese):
 	// ss should represent a simple sum like 2+5*I
-	std::string ss(s);
-	// make it safe by adding explicit sign
+	std::string ss = s;
+	std::string::size_type delim;
+
+	// make this implementation safe by adding explicit sign
 	if (ss.at(0) != '+' && ss.at(0) != '-' && ss.at(0) != '#')
 		ss = '+' + ss;
-	std::string::size_type delim;
+
+	// We use 'E' as exponent marker in the output, but some people insist on
+	// writing 'e' at input, so let's substitute them right at the beginning:
+	while ((delim = ss.find("e"))!=std::string::npos)
+		ss.replace(delim,1,"E");
+
+	// main parser loop:
 	do {
 		// chop ss into terms from left to right
 		std::string term;
 		bool imaginary = false;
 		delim = ss.find_first_of(std::string("+-"),1);
 		// Do we have an exponent marker like "31.415E-1"?  If so, hop on!
-		if ((delim != std::string::npos) && (ss.at(delim-1) == 'E'))
+		if (delim!=std::string::npos && ss.at(delim-1)=='E')
 			delim = ss.find_first_of(std::string("+-"),delim+1);
 		term = ss.substr(0,delim);
-		if (delim != std::string::npos)
+		if (delim!=std::string::npos)
 			ss = ss.substr(delim);
 		// is the term imaginary?
-		if (term.find("I") != std::string::npos) {
+		if (term.find("I")!=std::string::npos) {
 			// erase 'I':
-			term = term.replace(term.find("I"),1,"");
+			term.erase(term.find("I"),1);
 			// erase '*':
-			if (term.find("*") != std::string::npos)
-				term = term.replace(term.find("*"),1,"");
+			if (term.find("*")!=std::string::npos)
+				term.erase(term.find("*"),1);
 			// correct for trivial +/-I without explicit factor on I:
-			if (term.size() == 1)
-				term += "1";
+			if (term.size()==1)
+				term += '1';
 			imaginary = true;
 		}
-		if (term.find(".") != std::string::npos) {
+		if (term.find('.')!=std::string::npos || term.find('E')!=std::string::npos) {
 			// CLN's short type cl_SF is not very useful within the GiNaC
 			// framework where we are mainly interested in the arbitrary
 			// precision type cl_LF.  Hence we go straight to the construction
@@ -214,33 +206,25 @@ numeric::numeric(const char *s) : basic(TINFO_numeric)
 			// 31.4E-1   -->   31.4e-1_<Digits>
 			// and s on.
 			// No exponent marker?  Let's add a trivial one.
-			if (term.find("E") == std::string::npos)
+			if (term.find("E")==std::string::npos)
 				term += "E0";
 			// E to lower case
 			term = term.replace(term.find("E"),1,"e");
 			// append _<Digits> to term
-#if defined(HAVE_SSTREAM)
-			std::ostringstream buf;
-			buf << unsigned(Digits) << std::ends;
-			term += "_" + buf.str();
-#else
-			char buf[14];
-			std::ostrstream(buf,sizeof(buf)) << unsigned(Digits) << std::ends;
-			term += "_" + std::string(buf);
-#endif
+			term += "_" + ToString((unsigned)Digits);
 			// construct float using cln::cl_F(const char *) ctor.
 			if (imaginary)
 				ctorval = ctorval + cln::complex(cln::cl_I(0),cln::cl_F(term.c_str()));
 			else
 				ctorval = ctorval + cln::cl_F(term.c_str());
 		} else {
-			// not a floating point number...
+			// this is not a floating point number...
 			if (imaginary)
 				ctorval = ctorval + cln::complex(cln::cl_I(0),cln::cl_R(term.c_str()));
 			else
 				ctorval = ctorval + cln::cl_R(term.c_str());
 		}
-	} while(delim != std::string::npos);
+	} while (delim != std::string::npos);
 	value = ctorval;
 	setflag(status_flags::evaluated | status_flags::expanded);
 }
@@ -250,7 +234,6 @@ numeric::numeric(const char *s) : basic(TINFO_numeric)
  *  only. */
 numeric::numeric(const cln::cl_N &z) : basic(TINFO_numeric)
 {
-	debugmsg("numeric ctor from cl_N", LOGLEVEL_CONSTRUCT);
 	value = z;
 	setflag(status_flags::evaluated | status_flags::expanded);
 }
@@ -261,17 +244,12 @@ numeric::numeric(const cln::cl_N &z) : basic(TINFO_numeric)
 
 numeric::numeric(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
 {
-	debugmsg("numeric ctor from archive_node", LOGLEVEL_CONSTRUCT);
 	cln::cl_N ctorval = 0;
 
 	// Read number as string
 	std::string str;
 	if (n.find_string("number", str)) {
-#ifdef HAVE_SSTREAM
 		std::istringstream s(str);
-#else
-		std::istrstream s(str.c_str(), str.size() + 1);
-#endif
 		cln::cl_idecoded_float re, im;
 		char c;
 		s.get(c);
@@ -301,12 +279,7 @@ void numeric::archive(archive_node &n) const
 	inherited::archive(n);
 
 	// Write number as string
-#ifdef HAVE_SSTREAM
 	std::ostringstream s;
-#else
-	char buf[1024];
-	std::ostrstream s(buf, 1024);
-#endif
 	if (this->is_crational())
 		s << cln::the<cln::cl_N>(value);
 	else {
@@ -324,13 +297,7 @@ void numeric::archive(archive_node &n) const
 			s << im.sign << " " << im.mantissa << " " << im.exponent;
 		}
 	}
-#ifdef HAVE_SSTREAM
 	n.add_string("number", s.str());
-#else
-	s << ends;
-	std::string str(buf);
-	n.add_string("number", str);
-#endif
 }
 
 DEFAULT_UNARCHIVE(numeric)
@@ -376,8 +343,6 @@ static void print_real_number(const print_context & c, const cln::cl_R &x)
  *  @see print_real_number() */
 void numeric::print(const print_context & c, unsigned level) const
 {
-	debugmsg("numeric print", LOGLEVEL_PRINT);
-
 	if (is_a<print_tree>(c)) {
 
 		c.s << std::string(level, ' ') << cln::the<cln::cl_N>(value)
@@ -424,6 +389,8 @@ void numeric::print(const print_context & c, unsigned level) const
 		const std::string mul_sym   = is_a<print_latex>(c) ? " " : "*";
 		const cln::cl_R r = cln::realpart(cln::the<cln::cl_N>(value));
 		const cln::cl_R i = cln::imagpart(cln::the<cln::cl_N>(value));
+		if (is_a<print_python_repr>(c))
+			c.s << class_name() << "('";
 		if (cln::zerop(i)) {
 			// case 1, real:  x  or  -x
 			if ((precedence() <= level) && (!this->is_nonneg_integer())) {
@@ -481,6 +448,8 @@ void numeric::print(const print_context & c, unsigned level) const
 					c.s << par_close;
 			}
 		}
+		if (is_a<print_python_repr>(c))
+			c.s << "')";
 	}
 }
 
@@ -1519,7 +1488,7 @@ const numeric bernoulli(const numeric &nn)
 {
 	if (!nn.is_integer() || nn.is_negative())
 		throw std::range_error("numeric::bernoulli(): argument must be integer >= 0");
-	
+
 	// Method:
 	//
 	// The Bernoulli numbers are rational numbers that may be computed using
@@ -1543,45 +1512,61 @@ const numeric bernoulli(const numeric &nn)
 	// But if somebody works with the n'th Bernoulli number she is likely to
 	// also need all previous Bernoulli numbers. So we need a complete remember
 	// table and above divide and conquer algorithm is not suited to build one
-	// up.  The code below is adapted from Pari's function bernvec().
+	// up.  The formula below accomplishes this.  It is a modification of the
+	// defining formula above but the computation of the binomial coefficients
+	// is carried along in an inline fashion.  It also honors the fact that
+	// B_n is zero when n is odd and greater than 1.
 	// 
 	// (There is an interesting relation with the tangent polynomials described
-	// in `Concrete Mathematics', which leads to a program twice as fast as our
-	// implementation below, but it requires storing one such polynomial in
+	// in `Concrete Mathematics', which leads to a program a little faster as
+	// our implementation below, but it requires storing one such polynomial in
 	// addition to the remember table.  This doubles the memory footprint so
 	// we don't use it.)
-	
+
+	const unsigned n = nn.to_int();
+
 	// the special cases not covered by the algorithm below
-	if (nn.is_equal(_num1))
-		return _num_1_2;
-	if (nn.is_odd())
-		return _num0;
-	
+	if (n & 1)
+		return (n==1) ? _num_1_2 : _num0;
+	if (!n)
+		 return _num1;
+
 	// store nonvanishing Bernoulli numbers here
 	static std::vector< cln::cl_RA > results;
-	static int highest_result = 0;
-	// algorithm not applicable to B(0), so just store it
-	if (results.empty())
-		results.push_back(cln::cl_RA(1));
-	
-	int n = nn.to_long();
-	for (int i=highest_result; i<n/2; ++i) {
-		cln::cl_RA B = 0;
-		long n = 8;
-		long m = 5;
-		long d1 = i;
-		long d2 = 2*i-1;
-		for (int j=i; j>0; --j) {
-			B = cln::cl_I(n*m) * (B+results[j]) / (d1*d2);
-			n += 4;
-			m += 2;
-			d1 -= 1;
-			d2 -= 2;
-		}
-		B = (1 - ((B+1)/(2*i+3))) / (cln::cl_I(1)<<(2*i+2));
-		results.push_back(B);
-		++highest_result;
+	static unsigned next_r = 0;
+
+	// algorithm not applicable to B(2), so just store it
+	if (!next_r) {
+		results.push_back(); // results[0] is not used
+		results.push_back(cln::recip(cln::cl_RA(6)));
+		next_r = 4;
+	}
+	if (n<next_r)
+		return results[n/2];
+
+	results.reserve(n/2 + 1);
+	for (unsigned p=next_r; p<=n;  p+=2) {
+		cln::cl_I  c = 1;  // seed for binonmial coefficients
+		cln::cl_RA b = cln::cl_RA(1-p)/2;
+		const unsigned p3 = p+3;
+		const unsigned pm = p-2;
+		unsigned i, k, p_2;
+		// test if intermediate unsigned int can be represented by immediate
+		// objects by CLN (i.e. < 2^29 for 32 Bit machines, see <cln/object.h>)
+		if (p < (1UL<<cl_value_len/2)) {
+			for (i=2, k=1, p_2=p/2; i<=pm; i+=2, ++k, --p_2) {
+				c = cln::exquo(c * ((p3-i) * p_2), (i-1)*k);
+				b = b + c*results[k];
+			}
+		} else {
+			for (i=2, k=1, p_2=p/2; i<=pm; i+=2, ++k, --p_2) {
+				c = cln::exquo((c * (p3-i)) * p_2, cln::cl_I(i-1)*k);
+				b = b + c*results[k];
+			}
+ 		}
+		results.push_back(-b/(p+1));
 	}
+	next_r = n+2;
 	return results[n/2];
 }
 
@@ -1864,7 +1849,6 @@ _numeric_digits::operator long()
 /** Append global Digits object to ostream. */
 void _numeric_digits::print(std::ostream &os) const
 {
-	debugmsg("_numeric_digits print", LOGLEVEL_PRINT);
 	os << digits;
 }