- fixed atan2_evalf()
authorChristian Bauer <Christian.Bauer@uni-mainz.de>
Mon, 5 Apr 2004 20:30:25 +0000 (20:30 +0000)
committerChristian Bauer <Christian.Bauer@uni-mainz.de>
Mon, 5 Apr 2004 20:30:25 +0000 (20:30 +0000)
- improved eval functions of trigonometric functions (mostly negative
  arguments)
- added #undef log2 in utils.h (may help with cygwin?)

ginac/inifcns_trans.cpp
ginac/utils.cpp
ginac/utils.h

index c12df144c8bcedeb534318f57bba695b2a053520..7df32121680621edec85c584de21c5c1243e7554 100644 (file)
@@ -55,6 +55,7 @@ static ex exp_eval(const ex & x)
        if (x.is_zero()) {
                return _ex1;
        }
+
        // exp(n*Pi*I/2) -> {+1|+I|-1|-I}
        const ex TwoExOverPiI=(_ex2*x)/(Pi*I);
        if (TwoExOverPiI.info(info_flags::integer)) {
@@ -68,11 +69,12 @@ static ex exp_eval(const ex & x)
                if (z.is_equal(_num3))
                        return ex(-I);
        }
+
        // exp(log(x)) -> x
        if (is_ex_the_function(x, log))
                return x.op(0);
        
-       // exp(float)
+       // exp(float) -> float
        if (x.info(info_flags::numeric) && !x.info(info_flags::crational))
                return exp(ex_to<numeric>(x));
        
@@ -117,10 +119,12 @@ static ex log_eval(const ex & x)
                        return (Pi*I*_num1_2);
                if (x.is_equal(-I))      // log(-I) -> -Pi*I/2
                        return (Pi*I*_num_1_2);
-               // log(float)
+
+               // log(float) -> float
                if (!x.info(info_flags::crational))
                        return log(ex_to<numeric>(x));
        }
+
        // log(exp(t)) -> t (if -Pi < t.imag() <= Pi):
        if (is_ex_the_function(x, exp)) {
                const ex &t = x.op(0);
@@ -271,15 +275,18 @@ static ex sin_eval(const ex & x)
                if (z.is_equal(_num30)) // sin(Pi/2)    -> 1
                        return sign;
        }
-       
+
        if (is_exactly_a<function>(x)) {
                const ex &t = x.op(0);
+
                // sin(asin(x)) -> x
                if (is_ex_the_function(x, asin))
                        return t;
+
                // sin(acos(x)) -> sqrt(1-x^2)
                if (is_ex_the_function(x, acos))
                        return sqrt(_ex1-power(t,_ex2));
+
                // sin(atan(x)) -> x/sqrt(1+x^2)
                if (is_ex_the_function(x, atan))
                        return t*power(_ex1+power(t,_ex2),_ex_1_2);
@@ -288,6 +295,10 @@ static ex sin_eval(const ex & x)
        // sin(float) -> float
        if (x.info(info_flags::numeric) && !x.info(info_flags::crational))
                return sin(ex_to<numeric>(x));
+
+       // sin() is odd
+       if (x.info(info_flags::negative))
+               return -sin(-x);
        
        return sin(x).hold();
 }
@@ -352,15 +363,18 @@ static ex cos_eval(const ex & x)
                if (z.is_equal(_num30)) // cos(Pi/2)    -> 0
                        return _ex0;
        }
-       
+
        if (is_exactly_a<function>(x)) {
                const ex &t = x.op(0);
+
                // cos(acos(x)) -> x
                if (is_ex_the_function(x, acos))
                        return t;
+
                // cos(asin(x)) -> sqrt(1-x^2)
                if (is_ex_the_function(x, asin))
                        return sqrt(_ex1-power(t,_ex2));
+
                // cos(atan(x)) -> 1/sqrt(1+x^2)
                if (is_ex_the_function(x, atan))
                        return power(_ex1+power(t,_ex2),_ex_1_2);
@@ -370,6 +384,10 @@ static ex cos_eval(const ex & x)
        if (x.info(info_flags::numeric) && !x.info(info_flags::crational))
                return cos(ex_to<numeric>(x));
        
+       // cos() is even
+       if (x.info(info_flags::negative))
+               return cos(-x);
+       
        return cos(x).hold();
 }
 
@@ -429,15 +447,18 @@ static ex tan_eval(const ex & x)
                if (z.is_equal(_num30)) // tan(Pi/2)    -> infinity
                        throw (pole_error("tan_eval(): simple pole",1));
        }
-       
+
        if (is_exactly_a<function>(x)) {
                const ex &t = x.op(0);
+
                // tan(atan(x)) -> x
                if (is_ex_the_function(x, atan))
                        return t;
+
                // tan(asin(x)) -> x/sqrt(1+x^2)
                if (is_ex_the_function(x, asin))
                        return t*power(_ex1-power(t,_ex2),_ex_1_2);
+
                // tan(acos(x)) -> sqrt(1-x^2)/x
                if (is_ex_the_function(x, acos))
                        return power(t,_ex_1)*sqrt(_ex1-power(t,_ex2));
@@ -448,6 +469,10 @@ static ex tan_eval(const ex & x)
                return tan(ex_to<numeric>(x));
        }
        
+       // tan() is odd
+       if (x.info(info_flags::negative))
+               return -tan(-x);
+       
        return tan(x).hold();
 }
 
@@ -496,24 +521,34 @@ static ex asin_evalf(const ex & x)
 static ex asin_eval(const ex & x)
 {
        if (x.info(info_flags::numeric)) {
+
                // asin(0) -> 0
                if (x.is_zero())
                        return x;
+
                // asin(1/2) -> Pi/6
                if (x.is_equal(_ex1_2))
                        return numeric(1,6)*Pi;
+
                // asin(1) -> Pi/2
                if (x.is_equal(_ex1))
                        return _num1_2*Pi;
+
                // asin(-1/2) -> -Pi/6
                if (x.is_equal(_ex_1_2))
                        return numeric(-1,6)*Pi;
+
                // asin(-1) -> -Pi/2
                if (x.is_equal(_ex_1))
                        return _num_1_2*Pi;
+
                // asin(float) -> float
                if (!x.info(info_flags::crational))
                        return asin(ex_to<numeric>(x));
+
+               // asin() is odd
+               if (x.info(info_flags::negative))
+                       return -asin(-x);
        }
        
        return asin(x).hold();
@@ -547,24 +582,34 @@ static ex acos_evalf(const ex & x)
 static ex acos_eval(const ex & x)
 {
        if (x.info(info_flags::numeric)) {
+
                // acos(1) -> 0
                if (x.is_equal(_ex1))
                        return _ex0;
+
                // acos(1/2) -> Pi/3
                if (x.is_equal(_ex1_2))
                        return _ex1_3*Pi;
+
                // acos(0) -> Pi/2
                if (x.is_zero())
                        return _ex1_2*Pi;
+
                // acos(-1/2) -> 2/3*Pi
                if (x.is_equal(_ex_1_2))
                        return numeric(2,3)*Pi;
+
                // acos(-1) -> Pi
                if (x.is_equal(_ex_1))
                        return Pi;
+
                // acos(float) -> float
                if (!x.info(info_flags::crational))
                        return acos(ex_to<numeric>(x));
+
+               // acos(-x) -> Pi-acos(x)
+               if (x.info(info_flags::negative))
+                       return Pi-acos(-x);
        }
        
        return acos(x).hold();
@@ -598,20 +643,29 @@ static ex atan_evalf(const ex & x)
 static ex atan_eval(const ex & x)
 {
        if (x.info(info_flags::numeric)) {
+
                // atan(0) -> 0
                if (x.is_zero())
                        return _ex0;
+
                // atan(1) -> Pi/4
                if (x.is_equal(_ex1))
                        return _ex1_4*Pi;
+
                // atan(-1) -> -Pi/4
                if (x.is_equal(_ex_1))
                        return _ex_1_4*Pi;
+
                if (x.is_equal(I) || x.is_equal(-I))
                        throw (pole_error("atan_eval(): logarithmic pole",0));
+
                // atan(float) -> float
                if (!x.info(info_flags::crational))
                        return atan(ex_to<numeric>(x));
+
+               // atan() is odd
+               if (x.info(info_flags::negative))
+                       return -atan(-x);
        }
        
        return atan(x).hold();
@@ -681,19 +735,79 @@ REGISTER_FUNCTION(atan, eval_func(atan_eval).
 static ex atan2_evalf(const ex &y, const ex &x)
 {
        if (is_exactly_a<numeric>(y) && is_exactly_a<numeric>(x))
-               return atan2(ex_to<numeric>(y), ex_to<numeric>(x));
+               return atan(ex_to<numeric>(y), ex_to<numeric>(x));
        
        return atan2(y, x).hold();
 }
 
 static ex atan2_eval(const ex & y, const ex & x)
 {
-       if (y.info(info_flags::numeric) && !y.info(info_flags::crational) &&
-               x.info(info_flags::numeric) && !x.info(info_flags::crational)) {
-               return atan2_evalf(y,x);
+       if (y.info(info_flags::numeric) && x.info(info_flags::numeric)) {
+
+               if (y.is_zero()) {
+
+                       // atan(0, 0) -> 0
+                       if (x.is_zero())
+                               return _ex0;
+
+                       // atan(0, x), x real and positive -> 0
+                       if (x.info(info_flags::positive))
+                               return _ex0;
+
+                       // atan(0, x), x real and negative -> -Pi
+                       if (x.info(info_flags::negative))
+                               return _ex_1*Pi;
+               }
+
+               if (x.is_zero()) {
+
+                       // atan(y, 0), y real and positive -> Pi/2
+                       if (y.info(info_flags::positive))
+                               return _ex1_2*Pi;
+
+                       // atan(y, 0), y real and negative -> -Pi/2
+                       if (y.info(info_flags::negative))
+                               return _ex_1_2*Pi;
+               }
+
+               if (y.is_equal(x)) {
+
+                       // atan(y, y), y real and positive -> Pi/4
+                       if (y.info(info_flags::positive))
+                               return _ex1_4*Pi;
+
+                       // atan(y, y), y real and negative -> -3/4*Pi
+                       if (y.info(info_flags::negative))
+                               return numeric(-3, 4)*Pi;
+               }
+
+               if (y.is_equal(-x)) {
+
+                       // atan(y, -y), y real and positive -> 3*Pi/4
+                       if (y.info(info_flags::positive))
+                               return numeric(3, 4)*Pi;
+
+                       // atan(y, -y), y real and negative -> -Pi/4
+                       if (y.info(info_flags::negative))
+                               return _ex_1_4*Pi;
+               }
+
+               // atan(float, float) -> float
+               if (!y.info(info_flags::crational) && !x.info(info_flags::crational))
+                       return atan(ex_to<numeric>(y), ex_to<numeric>(x));
+
+               // atan(real, real) -> atan(y/x) +/- Pi
+               if (y.info(info_flags::real) && x.info(info_flags::real)) {
+                       if (x.info(info_flags::positive))
+                               return atan(y/x);
+                       else if(y.info(info_flags::positive))
+                               return atan(y/x)+Pi;
+                       else
+                               return atan(y/x)-Pi;
+               }
        }
-       
-       return atan2(y,x).hold();
+
+       return atan2(y, x).hold();
 }    
 
 static ex atan2_deriv(const ex & y, const ex & x, unsigned deriv_param)
@@ -727,10 +841,18 @@ static ex sinh_evalf(const ex & x)
 static ex sinh_eval(const ex & x)
 {
        if (x.info(info_flags::numeric)) {
-               if (x.is_zero())  // sinh(0) -> 0
+
+               // sinh(0) -> 0
+               if (x.is_zero())
                        return _ex0;        
-               if (!x.info(info_flags::crational))  // sinh(float) -> float
+
+               // sinh(float) -> float
+               if (!x.info(info_flags::crational))
                        return sinh(ex_to<numeric>(x));
+
+               // sinh() is odd
+               if (x.info(info_flags::negative))
+                       return -sinh(-x);
        }
        
        if ((x/Pi).info(info_flags::numeric) &&
@@ -739,12 +861,15 @@ static ex sinh_eval(const ex & x)
        
        if (is_exactly_a<function>(x)) {
                const ex &t = x.op(0);
+
                // sinh(asinh(x)) -> x
                if (is_ex_the_function(x, asinh))
                        return t;
+
                // sinh(acosh(x)) -> sqrt(x-1) * sqrt(x+1)
                if (is_ex_the_function(x, acosh))
                        return sqrt(t-_ex1)*sqrt(t+_ex1);
+
                // sinh(atanh(x)) -> x/sqrt(1-x^2)
                if (is_ex_the_function(x, atanh))
                        return t*power(_ex1-power(t,_ex2),_ex_1_2);
@@ -781,10 +906,18 @@ static ex cosh_evalf(const ex & x)
 static ex cosh_eval(const ex & x)
 {
        if (x.info(info_flags::numeric)) {
-               if (x.is_zero())  // cosh(0) -> 1
+
+               // cosh(0) -> 1
+               if (x.is_zero())
                        return _ex1;
-               if (!x.info(info_flags::crational))  // cosh(float) -> float
+
+               // cosh(float) -> float
+               if (!x.info(info_flags::crational))
                        return cosh(ex_to<numeric>(x));
+
+               // cosh() is even
+               if (x.info(info_flags::negative))
+                       return cosh(-x);
        }
        
        if ((x/Pi).info(info_flags::numeric) &&
@@ -793,12 +926,15 @@ static ex cosh_eval(const ex & x)
        
        if (is_exactly_a<function>(x)) {
                const ex &t = x.op(0);
+
                // cosh(acosh(x)) -> x
                if (is_ex_the_function(x, acosh))
                        return t;
+
                // cosh(asinh(x)) -> sqrt(1+x^2)
                if (is_ex_the_function(x, asinh))
                        return sqrt(_ex1+power(t,_ex2));
+
                // cosh(atanh(x)) -> 1/sqrt(1-x^2)
                if (is_ex_the_function(x, atanh))
                        return power(_ex1-power(t,_ex2),_ex_1_2);
@@ -835,10 +971,18 @@ static ex tanh_evalf(const ex & x)
 static ex tanh_eval(const ex & x)
 {
        if (x.info(info_flags::numeric)) {
-               if (x.is_zero())  // tanh(0) -> 0
+
+               // tanh(0) -> 0
+               if (x.is_zero())
                        return _ex0;
-               if (!x.info(info_flags::crational))  // tanh(float) -> float
+
+               // tanh(float) -> float
+               if (!x.info(info_flags::crational))
                        return tanh(ex_to<numeric>(x));
+
+               // tanh() is odd
+               if (x.info(info_flags::negative))
+                       return -tanh(-x);
        }
        
        if ((x/Pi).info(info_flags::numeric) &&
@@ -847,12 +991,15 @@ static ex tanh_eval(const ex & x)
        
        if (is_exactly_a<function>(x)) {
                const ex &t = x.op(0);
+
                // tanh(atanh(x)) -> x
                if (is_ex_the_function(x, atanh))
                        return t;
+
                // tanh(asinh(x)) -> x/sqrt(1+x^2)
                if (is_ex_the_function(x, asinh))
                        return t*power(_ex1+power(t,_ex2),_ex_1_2);
+
                // tanh(acosh(x)) -> sqrt(x-1)*sqrt(x+1)/x
                if (is_ex_the_function(x, acosh))
                        return sqrt(t-_ex1)*sqrt(t+_ex1)*power(t,_ex_1);
@@ -906,12 +1053,18 @@ static ex asinh_evalf(const ex & x)
 static ex asinh_eval(const ex & x)
 {
        if (x.info(info_flags::numeric)) {
+
                // asinh(0) -> 0
                if (x.is_zero())
                        return _ex0;
+
                // asinh(float) -> float
                if (!x.info(info_flags::crational))
                        return asinh(ex_to<numeric>(x));
+
+               // asinh() is odd
+               if (x.info(info_flags::negative))
+                       return -asinh(-x);
        }
        
        return asinh(x).hold();
@@ -944,18 +1097,26 @@ static ex acosh_evalf(const ex & x)
 static ex acosh_eval(const ex & x)
 {
        if (x.info(info_flags::numeric)) {
+
                // acosh(0) -> Pi*I/2
                if (x.is_zero())
                        return Pi*I*numeric(1,2);
+
                // acosh(1) -> 0
                if (x.is_equal(_ex1))
                        return _ex0;
+
                // acosh(-1) -> Pi*I
                if (x.is_equal(_ex_1))
                        return Pi*I;
+
                // acosh(float) -> float
                if (!x.info(info_flags::crational))
                        return acosh(ex_to<numeric>(x));
+
+               // acosh(-x) -> Pi*I-acosh(x)
+               if (x.info(info_flags::negative))
+                       return Pi*I-acosh(-x);
        }
        
        return acosh(x).hold();
@@ -988,15 +1149,22 @@ static ex atanh_evalf(const ex & x)
 static ex atanh_eval(const ex & x)
 {
        if (x.info(info_flags::numeric)) {
+
                // atanh(0) -> 0
                if (x.is_zero())
                        return _ex0;
+
                // atanh({+|-}1) -> throw
                if (x.is_equal(_ex1) || x.is_equal(_ex_1))
                        throw (pole_error("atanh_eval(): logarithmic pole",0));
+
                // atanh(float) -> float
                if (!x.info(info_flags::crational))
                        return atanh(ex_to<numeric>(x));
+
+               // atanh() is odd
+               if (x.info(info_flags::negative))
+                       return -atanh(-x);
        }
        
        return atanh(x).hold();
index 6e34832d0c7a39bf2ebd6e81ce8e944d7dec2957..7964825858b64b98f4a760f471fb9188aed4c9a3 100644 (file)
@@ -44,8 +44,6 @@ int pole_error::degree() const
        return deg;
 }
 
-// some compilers (e.g. cygwin) define a macro log2, causing confusion
-#ifndef log2
 /** Integer binary logarithm */
 unsigned log2(unsigned n)
 {
@@ -54,7 +52,6 @@ unsigned log2(unsigned n)
                ++k;
        return k;
 }
-#endif
 
 
 //////////
index 651ac342e1fdc7a68c3187d8861b60b7e3a8e2b7..9b8a7c94ec32cf54331d668b01ce36042efc28c5 100644 (file)
@@ -38,10 +38,12 @@ namespace GiNaC {
 class dunno {};
 
 // some compilers (e.g. cygwin) define a macro log2, causing confusion
-#ifndef log2
-unsigned log2(unsigned n);
+#ifdef log2
+#undef log2
 #endif
 
+unsigned log2(unsigned n);
+
 /** Compare two pointers (just to establish some sort of canonical order).
  *  @return -1, 0, or 1 */
 template <class T>