X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Finifcns.cpp;h=9219039a5581df93d58d0c744507ddc4d911a893;hp=63c2d74f556d74c2c9cce124729107695a3bdf43;hb=0289100f425e420da988a709cd52616b6d69d348;hpb=c28e61da33905ddc69abf893aaffec98aa30d053

diff --git a/ginac/inifcns.cpp b/ginac/inifcns.cpp
index 63c2d74f..9219039a 100644
--- a/ginac/inifcns.cpp
+++ b/ginac/inifcns.cpp
@@ -3,7 +3,7 @@
  *  Implementation of GiNaC's initially known functions. */
 
 /*
- *  GiNaC Copyright (C) 1999-2010 Johannes Gutenberg University Mainz, Germany
+ *  GiNaC Copyright (C) 1999-2011 Johannes Gutenberg University Mainz, Germany
  *
  *  This program is free software; you can redistribute it and/or modify
  *  it under the terms of the GNU General Public License as published by
@@ -319,8 +319,8 @@ REGISTER_FUNCTION(step, eval_func(step_eval).
                         evalf_func(step_evalf).
                         series_func(step_series).
                         conjugate_func(step_conjugate).
-								real_part_func(step_real_part).
-								imag_part_func(step_imag_part));
+                        real_part_func(step_real_part).
+                        imag_part_func(step_imag_part));
 
 //////////
 // Complex sign
@@ -643,10 +643,25 @@ static ex Li2_series(const ex &x, const relational &rel, int order, unsigned opt
 	throw do_taylor();  // caught by function::series()
 }
 
+static ex Li2_conjugate(const ex & x)
+{
+	// conjugate(Li2(x))==Li2(conjugate(x)) unless on the branch cuts which
+	// run along the positive real axis beginning at 1.
+	if (x.info(info_flags::negative)) {
+		return Li2(x);
+	}
+	if (is_exactly_a<numeric>(x) &&
+	    (!x.imag_part().is_zero() || x < *_num1_p)) {
+		return Li2(x.conjugate());
+	}
+	return conjugate_function(Li2(x)).hold();
+}
+
 REGISTER_FUNCTION(Li2, eval_func(Li2_eval).
                        evalf_func(Li2_evalf).
                        derivative_func(Li2_deriv).
                        series_func(Li2_series).
+                       conjugate_func(Li2_conjugate).
                        latex_name("\\mathrm{Li}_2"));
 
 //////////
@@ -992,9 +1007,24 @@ fsolve(const ex& f_in, const symbol& x, const numeric& x1, const numeric& x2)
 	do {
 		xxprev = xx[side];
 		fxprev = fx[side];
-		xx[side] += ex_to<numeric>(ff.subs(x==xx[side]).evalf());
-		fx[side] = ex_to<numeric>(f.subs(x==xx[side]).evalf());
-		if ((side==0 && xx[0]<xxprev) || (side==1 && xx[1]>xxprev) || xx[0]>xx[1]) {
+		ex dx_ = ff.subs(x == xx[side]).evalf();
+		if (!is_a<numeric>(dx_))
+			throw std::runtime_error("fsolve(): function derivative does not evaluate numerically");
+		xx[side] += ex_to<numeric>(dx_);
+		// Now check if Newton-Raphson method shot out of the interval 
+		bool bad_shot = (side == 0 && xx[0] < xxprev) || 
+				(side == 1 && xx[1] > xxprev) || xx[0] > xx[1];
+		if (!bad_shot) {
+			// Compute f(x) only if new x is inside the interval.
+			// The function might be difficult to compute numerically
+			// or even ill defined outside the interval. Also it's
+			// a small optimization. 
+			ex f_x = f.subs(x == xx[side]).evalf();
+			if (!is_a<numeric>(f_x))
+				throw std::runtime_error("fsolve(): function does not evaluate numerically");
+			fx[side] = ex_to<numeric>(f_x);
+		}
+		if (bad_shot) {
 			// Oops, Newton-Raphson method shot out of the interval.
 			// Restore, and try again with the other side instead!
 			xx[side] = xxprev;
@@ -1002,8 +1032,16 @@ fsolve(const ex& f_in, const symbol& x, const numeric& x1, const numeric& x2)
 			side = !side;
 			xxprev = xx[side];
 			fxprev = fx[side];
-			xx[side] += ex_to<numeric>(ff.subs(x==xx[side]).evalf());
-			fx[side] = ex_to<numeric>(f.subs(x==xx[side]).evalf());
+
+			ex dx_ = ff.subs(x == xx[side]).evalf();
+			if (!is_a<numeric>(dx_))
+				throw std::runtime_error("fsolve(): function derivative does not evaluate numerically [2]");
+			xx[side] += ex_to<numeric>(dx_);
+
+			ex f_x = f.subs(x==xx[side]).evalf();
+			if (!is_a<numeric>(f_x))
+				throw std::runtime_error("fsolve(): function does not evaluate numerically [2]");
+			fx[side] = ex_to<numeric>(f_x);
 		}
 		if ((fx[side]<0 && fx[!side]<0) || (fx[side]>0 && fx[!side]>0)) {
 			// Oops, the root isn't bracketed any more.
@@ -1027,7 +1065,10 @@ fsolve(const ex& f_in, const symbol& x, const numeric& x1, const numeric& x2)
 			static const double secant_weight = 0.984375;  // == 63/64 < 1
 			numeric xxmid = (1-secant_weight)*0.5*(xx[0]+xx[1])
 			    + secant_weight*(xx[0]+fx[0]*(xx[0]-xx[1])/(fx[1]-fx[0]));
-			numeric fxmid = ex_to<numeric>(f.subs(x==xxmid).evalf());
+			ex fxmid_ = f.subs(x == xxmid).evalf();
+			if (!is_a<numeric>(fxmid_))
+				throw std::runtime_error("fsolve(): function does not evaluate numerically [3]");
+			numeric fxmid = ex_to<numeric>(fxmid_);
 			if (fxmid.is_zero()) {
 				// Luck strikes...
 				return xxmid;