X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Finifcns_trans.cpp;h=81f92a93aca908aa6f698e79dd1a4380d5998d61;hp=eae92385142ce782c2ffb468d244295931fa5453;hb=af0c47009ca7a15af966430bdf1a72fe05c1c6f9;hpb=a6bb52b00bf185271774e7d56215923700a3ec40

diff --git a/ginac/inifcns_trans.cpp b/ginac/inifcns_trans.cpp
index eae92385..81f92a93 100644
--- a/ginac/inifcns_trans.cpp
+++ b/ginac/inifcns_trans.cpp
@@ -4,7 +4,7 @@
  *  functions. */
 
 /*
- *  GiNaC Copyright (C) 1999 Johannes Gutenberg University Mainz, Germany
+ *  GiNaC Copyright (C) 1999-2000 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
@@ -31,11 +31,12 @@
 #include "power.h"
 #include "relational.h"
 #include "symbol.h"
+#include "pseries.h"
 #include "utils.h"
 
-#ifndef NO_GINAC_NAMESPACE
+#ifndef NO_NAMESPACE_GINAC
 namespace GiNaC {
-#endif // ndef NO_GINAC_NAMESPACE
+#endif // ndef NO_NAMESPACE_GINAC
 
 //////////
 // exponential function
@@ -80,15 +81,17 @@ static ex exp_eval(const ex & x)
     return exp(x).hold();
 }
 
-static ex exp_diff(const ex & x, unsigned diff_param)
+static ex exp_deriv(const ex & x, unsigned deriv_param)
 {
-    GINAC_ASSERT(diff_param==0);
+    GINAC_ASSERT(deriv_param==0);
 
     // d/dx exp(x) -> exp(x)
     return exp(x);
 }
 
-REGISTER_FUNCTION(exp, exp_eval, exp_evalf, exp_diff, NULL);
+REGISTER_FUNCTION(exp, eval_func(exp_eval).
+                       evalf_func(exp_evalf).
+                       derivative_func(exp_deriv));
 
 //////////
 // natural logarithm
@@ -106,16 +109,16 @@ static ex log_evalf(const ex & x)
 static ex log_eval(const ex & x)
 {
     if (x.info(info_flags::numeric)) {
+        if (x.is_equal(_ex0()))  // log(0) -> infinity
+            throw(std::domain_error("log_eval(): log(0)"));
+        if (x.info(info_flags::real) && x.info(info_flags::negative))
+            return (log(-x)+I*Pi);
         if (x.is_equal(_ex1()))  // log(1) -> 0
             return _ex0();
-        if (x.is_equal(_ex_1())) // log(-1) -> I*Pi
-            return (I*Pi);        
         if (x.is_equal(I))       // log(I) -> Pi*I/2
             return (Pi*I*_num1_2());
         if (x.is_equal(-I))      // log(-I) -> -Pi*I/2
             return (Pi*I*_num_1_2());
-        if (x.is_equal(_ex0()))  // log(0) -> infinity
-            throw(std::domain_error("log_eval(): log(0)"));
         // log(float)
         if (!x.info(info_flags::crational))
             return log_evalf(x);
@@ -133,15 +136,40 @@ static ex log_eval(const ex & x)
     return log(x).hold();
 }
 
-static ex log_diff(const ex & x, unsigned diff_param)
+static ex log_deriv(const ex & x, unsigned deriv_param)
 {
-    GINAC_ASSERT(diff_param==0);
-
+    GINAC_ASSERT(deriv_param==0);
+    
     // d/dx log(x) -> 1/x
     return power(x, _ex_1());
 }
 
-REGISTER_FUNCTION(log, log_eval, log_evalf, log_diff, NULL);
+static ex log_series(const ex &x, const relational &rel, int order)
+{
+    const ex x_pt = x.subs(rel);
+    if (!x_pt.info(info_flags::negative) && !x_pt.is_zero())
+        throw do_taylor();  // caught by function::series()
+    // now we either have to care for the branch cut or the branch point:
+    if (x_pt.is_zero()) {  // branch point: return a plain log(x).
+        epvector seq;
+        seq.push_back(expair(log(x), _ex0()));
+        return pseries(rel, seq);
+    } // on the branch cut:
+    const ex point = rel.rhs();
+    const symbol *s = static_cast<symbol *>(rel.lhs().bp);
+    const symbol foo;
+    // compute the formal series:
+    ex replx = series(log(x),*s==foo,order).subs(foo==point);
+    epvector seq;
+    seq.push_back(expair(-I*csgn(x*I)*Pi,_ex0()));
+    seq.push_back(expair(Order(_ex1()),order));
+    return series(replx - I*Pi + pseries(rel, seq),rel,order);
+}
+
+REGISTER_FUNCTION(log, eval_func(log_eval).
+                       evalf_func(log_evalf).
+                       derivative_func(log_deriv).
+                       series_func(log_series));
 
 //////////
 // sine (trigonometric function)
@@ -212,15 +240,17 @@ static ex sin_eval(const ex & x)
     return sin(x).hold();
 }
 
-static ex sin_diff(const ex & x, unsigned diff_param)
+static ex sin_deriv(const ex & x, unsigned deriv_param)
 {
-    GINAC_ASSERT(diff_param==0);
+    GINAC_ASSERT(deriv_param==0);
     
     // d/dx sin(x) -> cos(x)
     return cos(x);
 }
 
-REGISTER_FUNCTION(sin, sin_eval, sin_evalf, sin_diff, NULL);
+REGISTER_FUNCTION(sin, eval_func(sin_eval).
+                       evalf_func(sin_evalf).
+                       derivative_func(sin_deriv));
 
 //////////
 // cosine (trigonometric function)
@@ -291,15 +321,17 @@ static ex cos_eval(const ex & x)
     return cos(x).hold();
 }
 
-static ex cos_diff(const ex & x, unsigned diff_param)
+static ex cos_deriv(const ex & x, unsigned deriv_param)
 {
-    GINAC_ASSERT(diff_param==0);
+    GINAC_ASSERT(deriv_param==0);
 
     // d/dx cos(x) -> -sin(x)
     return _ex_1()*sin(x);
 }
 
-REGISTER_FUNCTION(cos, cos_eval, cos_evalf, cos_diff, NULL);
+REGISTER_FUNCTION(cos, eval_func(cos_eval).
+                       evalf_func(cos_evalf).
+                       derivative_func(cos_deriv));
 
 //////////
 // tangent (trigonometric function)
@@ -343,7 +375,7 @@ static ex tan_eval(const ex & x)
         if (z.is_equal(_num25())) // tan(5/12*Pi) -> 2+sqrt(3)
             return sign*(power(_ex3(),_ex1_2())+_ex2());
         if (z.is_equal(_num30())) // tan(Pi/2)    -> infinity
-            throw (std::domain_error("tan_eval(): infinity"));
+            throw (std::domain_error("tan_eval(): simple pole"));
     }
     
     if (is_ex_exactly_of_type(x, function)) {
@@ -367,27 +399,30 @@ static ex tan_eval(const ex & x)
     return tan(x).hold();
 }
 
-static ex tan_diff(const ex & x, unsigned diff_param)
+static ex tan_deriv(const ex & x, unsigned deriv_param)
 {
-    GINAC_ASSERT(diff_param==0);
+    GINAC_ASSERT(deriv_param==0);
     
     // d/dx tan(x) -> 1+tan(x)^2;
     return (_ex1()+power(tan(x),_ex2()));
 }
 
-static ex tan_series(const ex & x, const symbol & s, const ex & pt, int order)
+static ex tan_series(const ex &x, const relational &rel, int order)
 {
     // method:
-    // Taylor series where there is no pole falls back to tan_diff.
+    // Taylor series where there is no pole falls back to tan_deriv.
     // On a pole simply expand sin(x)/cos(x).
-    const ex x_pt = x.subs(s==pt);
+    const ex x_pt = x.subs(rel);
     if (!(2*x_pt/Pi).info(info_flags::odd))
         throw do_taylor();  // caught by function::series()
     // if we got here we have to care for a simple pole
-    return (sin(x)/cos(x)).series(s, pt, order+2);
+    return (sin(x)/cos(x)).series(rel, order+2);
 }
 
-REGISTER_FUNCTION(tan, tan_eval, tan_evalf, tan_diff, tan_series);
+REGISTER_FUNCTION(tan, eval_func(tan_eval).
+                       evalf_func(tan_evalf).
+                       derivative_func(tan_deriv).
+                       series_func(tan_series));
 
 //////////
 // inverse sine (arc sine)
@@ -428,15 +463,17 @@ static ex asin_eval(const ex & x)
     return asin(x).hold();
 }
 
-static ex asin_diff(const ex & x, unsigned diff_param)
+static ex asin_deriv(const ex & x, unsigned deriv_param)
 {
-    GINAC_ASSERT(diff_param==0);
+    GINAC_ASSERT(deriv_param==0);
     
     // d/dx asin(x) -> 1/sqrt(1-x^2)
     return power(1-power(x,_ex2()),_ex_1_2());
 }
 
-REGISTER_FUNCTION(asin, asin_eval, asin_evalf, asin_diff, NULL);
+REGISTER_FUNCTION(asin, eval_func(asin_eval).
+                        evalf_func(asin_evalf).
+                        derivative_func(asin_deriv));
 
 //////////
 // inverse cosine (arc cosine)
@@ -477,15 +514,17 @@ static ex acos_eval(const ex & x)
     return acos(x).hold();
 }
 
-static ex acos_diff(const ex & x, unsigned diff_param)
+static ex acos_deriv(const ex & x, unsigned deriv_param)
 {
-    GINAC_ASSERT(diff_param==0);
+    GINAC_ASSERT(deriv_param==0);
     
     // d/dx acos(x) -> -1/sqrt(1-x^2)
     return _ex_1()*power(1-power(x,_ex2()),_ex_1_2());
 }
 
-REGISTER_FUNCTION(acos, acos_eval, acos_evalf, acos_diff, NULL);
+REGISTER_FUNCTION(acos, eval_func(acos_eval).
+                        evalf_func(acos_evalf).
+                        derivative_func(acos_deriv));
 
 //////////
 // inverse tangent (arc tangent)
@@ -514,15 +553,17 @@ static ex atan_eval(const ex & x)
     return atan(x).hold();
 }    
 
-static ex atan_diff(const ex & x, unsigned diff_param)
+static ex atan_deriv(const ex & x, unsigned deriv_param)
 {
-    GINAC_ASSERT(diff_param==0);
+    GINAC_ASSERT(deriv_param==0);
 
     // d/dx atan(x) -> 1/(1+x^2)
     return power(_ex1()+power(x,_ex2()), _ex_1());
 }
 
-REGISTER_FUNCTION(atan, atan_eval, atan_evalf, atan_diff, NULL);
+REGISTER_FUNCTION(atan, eval_func(atan_eval).
+                        evalf_func(atan_evalf).
+                        derivative_func(atan_deriv));
 
 //////////
 // inverse tangent (atan2(y,x))
@@ -548,11 +589,11 @@ static ex atan2_eval(const ex & y, const ex & x)
     return atan2(y,x).hold();
 }    
 
-static ex atan2_diff(const ex & y, const ex & x, unsigned diff_param)
+static ex atan2_deriv(const ex & y, const ex & x, unsigned deriv_param)
 {
-    GINAC_ASSERT(diff_param<2);
+    GINAC_ASSERT(deriv_param<2);
     
-    if (diff_param==0) {
+    if (deriv_param==0) {
         // d/dy atan(y,x)
         return x*power(power(x,_ex2())+power(y,_ex2()),_ex_1());
     }
@@ -560,7 +601,9 @@ static ex atan2_diff(const ex & y, const ex & x, unsigned diff_param)
     return -y*power(power(x,_ex2())+power(y,_ex2()),_ex_1());
 }
 
-REGISTER_FUNCTION(atan2, atan2_eval, atan2_evalf, atan2_diff, NULL);
+REGISTER_FUNCTION(atan2, eval_func(atan2_eval).
+                         evalf_func(atan2_evalf).
+                         derivative_func(atan2_deriv));
 
 //////////
 // hyperbolic sine (trigonometric function)
@@ -604,15 +647,17 @@ static ex sinh_eval(const ex & x)
     return sinh(x).hold();
 }
 
-static ex sinh_diff(const ex & x, unsigned diff_param)
+static ex sinh_deriv(const ex & x, unsigned deriv_param)
 {
-    GINAC_ASSERT(diff_param==0);
+    GINAC_ASSERT(deriv_param==0);
     
     // d/dx sinh(x) -> cosh(x)
     return cosh(x);
 }
 
-REGISTER_FUNCTION(sinh, sinh_eval, sinh_evalf, sinh_diff, NULL);
+REGISTER_FUNCTION(sinh, eval_func(sinh_eval).
+                        evalf_func(sinh_evalf).
+                        derivative_func(sinh_deriv));
 
 //////////
 // hyperbolic cosine (trigonometric function)
@@ -656,15 +701,18 @@ static ex cosh_eval(const ex & x)
     return cosh(x).hold();
 }
 
-static ex cosh_diff(const ex & x, unsigned diff_param)
+static ex cosh_deriv(const ex & x, unsigned deriv_param)
 {
-    GINAC_ASSERT(diff_param==0);
+    GINAC_ASSERT(deriv_param==0);
     
     // d/dx cosh(x) -> sinh(x)
     return sinh(x);
 }
 
-REGISTER_FUNCTION(cosh, cosh_eval, cosh_evalf, cosh_diff, NULL);
+REGISTER_FUNCTION(cosh, eval_func(cosh_eval).
+                        evalf_func(cosh_evalf).
+                        derivative_func(cosh_deriv));
+
 
 //////////
 // hyperbolic tangent (trigonometric function)
@@ -708,27 +756,30 @@ static ex tanh_eval(const ex & x)
     return tanh(x).hold();
 }
 
-static ex tanh_diff(const ex & x, unsigned diff_param)
+static ex tanh_deriv(const ex & x, unsigned deriv_param)
 {
-    GINAC_ASSERT(diff_param==0);
+    GINAC_ASSERT(deriv_param==0);
     
     // d/dx tanh(x) -> 1-tanh(x)^2
     return _ex1()-power(tanh(x),_ex2());
 }
 
-static ex tanh_series(const ex & x, const symbol & s, const ex & pt, int order)
+static ex tanh_series(const ex &x, const relational &rel, int order)
 {
     // method:
-    // Taylor series where there is no pole falls back to tanh_diff.
+    // Taylor series where there is no pole falls back to tanh_deriv.
     // On a pole simply expand sinh(x)/cosh(x).
-    const ex x_pt = x.subs(s==pt);
+    const ex x_pt = x.subs(rel);
     if (!(2*I*x_pt/Pi).info(info_flags::odd))
         throw do_taylor();  // caught by function::series()
     // if we got here we have to care for a simple pole
-    return (sinh(x)/cosh(x)).series(s, pt, order+2);
+    return (sinh(x)/cosh(x)).series(rel, order+2);
 }
 
-REGISTER_FUNCTION(tanh, tanh_eval, tanh_evalf, tanh_diff, tanh_series);
+REGISTER_FUNCTION(tanh, eval_func(tanh_eval).
+                        evalf_func(tanh_evalf).
+                        derivative_func(tanh_deriv).
+                        series_func(tanh_series));
 
 //////////
 // inverse hyperbolic sine (trigonometric function)
@@ -757,15 +808,17 @@ static ex asinh_eval(const ex & x)
     return asinh(x).hold();
 }
 
-static ex asinh_diff(const ex & x, unsigned diff_param)
+static ex asinh_deriv(const ex & x, unsigned deriv_param)
 {
-    GINAC_ASSERT(diff_param==0);
+    GINAC_ASSERT(deriv_param==0);
     
     // d/dx asinh(x) -> 1/sqrt(1+x^2)
     return power(_ex1()+power(x,_ex2()),_ex_1_2());
 }
 
-REGISTER_FUNCTION(asinh, asinh_eval, asinh_evalf, asinh_diff, NULL);
+REGISTER_FUNCTION(asinh, eval_func(asinh_eval).
+                         evalf_func(asinh_evalf).
+                         derivative_func(asinh_deriv));
 
 //////////
 // inverse hyperbolic cosine (trigonometric function)
@@ -800,15 +853,17 @@ static ex acosh_eval(const ex & x)
     return acosh(x).hold();
 }
 
-static ex acosh_diff(const ex & x, unsigned diff_param)
+static ex acosh_deriv(const ex & x, unsigned deriv_param)
 {
-    GINAC_ASSERT(diff_param==0);
+    GINAC_ASSERT(deriv_param==0);
     
     // d/dx acosh(x) -> 1/(sqrt(x-1)*sqrt(x+1))
     return power(x+_ex_1(),_ex_1_2())*power(x+_ex1(),_ex_1_2());
 }
 
-REGISTER_FUNCTION(acosh, acosh_eval, acosh_evalf, acosh_diff, NULL);
+REGISTER_FUNCTION(acosh, eval_func(acosh_eval).
+                         evalf_func(acosh_evalf).
+                         derivative_func(acosh_deriv));
 
 //////////
 // inverse hyperbolic tangent (trigonometric function)
@@ -830,8 +885,8 @@ static ex atanh_eval(const ex & x)
         if (x.is_zero())
             return _ex0();
         // atanh({+|-}1) -> throw
-        if (x.is_equal(_ex1()) || x.is_equal(_ex1()))
-            throw (std::domain_error("atanh_eval(): infinity"));
+        if (x.is_equal(_ex1()) || x.is_equal(_ex_1()))
+            throw (std::domain_error("atanh_eval(): logarithmic pole"));
         // atanh(float) -> float
         if (!x.info(info_flags::crational))
             return atanh_evalf(x);
@@ -840,16 +895,18 @@ static ex atanh_eval(const ex & x)
     return atanh(x).hold();
 }
 
-static ex atanh_diff(const ex & x, unsigned diff_param)
+static ex atanh_deriv(const ex & x, unsigned deriv_param)
 {
-    GINAC_ASSERT(diff_param==0);
+    GINAC_ASSERT(deriv_param==0);
     
     // d/dx atanh(x) -> 1/(1-x^2)
     return power(_ex1()-power(x,_ex2()),_ex_1());
 }
 
-REGISTER_FUNCTION(atanh, atanh_eval, atanh_evalf, atanh_diff, NULL);
+REGISTER_FUNCTION(atanh, eval_func(atanh_eval).
+                         evalf_func(atanh_evalf).
+                         derivative_func(atanh_deriv));
 
-#ifndef NO_GINAC_NAMESPACE
+#ifndef NO_NAMESPACE_GINAC
 } // namespace GiNaC
-#endif // ndef NO_GINAC_NAMESPACE
+#endif // ndef NO_NAMESPACE_GINAC