* functions. */
/*
- * GiNaC Copyright (C) 1999-2004 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2009 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
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
- * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
*/
-#include <vector>
-#include <stdexcept>
-
#include "inifcns.h"
#include "ex.h"
#include "constant.h"
#include "pseries.h"
#include "utils.h"
+#include <stdexcept>
+#include <vector>
+
namespace GiNaC {
//////////
// exp(n*Pi*I/2) -> {+1|+I|-1|-I}
const ex TwoExOverPiI=(_ex2*x)/(Pi*I);
if (TwoExOverPiI.info(info_flags::integer)) {
- const numeric z = mod(ex_to<numeric>(TwoExOverPiI),_num4);
- if (z.is_equal(_num0))
+ const numeric z = mod(ex_to<numeric>(TwoExOverPiI),*_num4_p);
+ if (z.is_equal(*_num0_p))
return _ex1;
- if (z.is_equal(_num1))
+ if (z.is_equal(*_num1_p))
return ex(I);
- if (z.is_equal(_num2))
+ if (z.is_equal(*_num2_p))
return _ex_1;
- if (z.is_equal(_num3))
+ if (z.is_equal(*_num3_p))
return ex(-I);
}
return exp(x);
}
+static ex exp_real_part(const ex & x)
+{
+ return exp(GiNaC::real_part(x))*cos(GiNaC::imag_part(x));
+}
+
+static ex exp_imag_part(const ex & x)
+{
+ return exp(GiNaC::real_part(x))*sin(GiNaC::imag_part(x));
+}
+
REGISTER_FUNCTION(exp, eval_func(exp_eval).
evalf_func(exp_evalf).
derivative_func(exp_deriv).
+ real_part_func(exp_real_part).
+ imag_part_func(exp_imag_part).
latex_name("\\exp"));
//////////
if (x.info(info_flags::numeric)) {
if (x.is_zero()) // log(0) -> infinity
throw(pole_error("log_eval(): log(0)",0));
- if (x.info(info_flags::real) && x.info(info_flags::negative))
- //if (x.info(info_flags::rational) && x.info(info_flags::negative))
+ if (x.info(info_flags::rational) && x.info(info_flags::negative))
return (log(-x)+I*Pi);
if (x.is_equal(_ex1)) // log(1) -> 0
return _ex0;
if (x.is_equal(I)) // log(I) -> Pi*I/2
- return (Pi*I*_num1_2);
+ return (Pi*I*_ex1_2);
if (x.is_equal(-I)) // log(-I) -> -Pi*I/2
- return (Pi*I*_num_1_2);
+ return (Pi*I*_ex_1_2);
// log(float) -> float
if (!x.info(info_flags::crational))
// log(exp(t)) -> t (if -Pi < t.imag() <= Pi):
if (is_ex_the_function(x, exp)) {
const ex &t = x.op(0);
- if (is_a<symbol>(t) && t.info(info_flags::real)) {
+ if (t.info(info_flags::real))
return t;
- }
- if (t.info(info_flags::numeric)) {
- const numeric &nt = ex_to<numeric>(t);
- if (nt.is_real())
- return t;
- }
}
return log(x).hold();
throw do_taylor(); // caught by function::series()
}
+static ex log_real_part(const ex & x)
+{
+ if (x.info(info_flags::nonnegative))
+ return log(x).hold();
+ return log(abs(x));
+}
+
+static ex log_imag_part(const ex & x)
+{
+ if (x.info(info_flags::nonnegative))
+ return 0;
+ return atan2(GiNaC::imag_part(x), GiNaC::real_part(x));
+}
+
REGISTER_FUNCTION(log, eval_func(log_eval).
evalf_func(log_evalf).
derivative_func(log_deriv).
series_func(log_series).
+ real_part_func(log_real_part).
+ imag_part_func(log_imag_part).
latex_name("\\ln"));
//////////
const ex SixtyExOverPi = _ex60*x/Pi;
ex sign = _ex1;
if (SixtyExOverPi.info(info_flags::integer)) {
- numeric z = mod(ex_to<numeric>(SixtyExOverPi),_num120);
- if (z>=_num60) {
+ numeric z = mod(ex_to<numeric>(SixtyExOverPi),*_num120_p);
+ if (z>=*_num60_p) {
// wrap to interval [0, Pi)
- z -= _num60;
+ z -= *_num60_p;
sign = _ex_1;
}
- if (z>_num30) {
+ if (z>*_num30_p) {
// wrap to interval [0, Pi/2)
- z = _num60-z;
+ z = *_num60_p-z;
}
- if (z.is_equal(_num0)) // sin(0) -> 0
+ if (z.is_equal(*_num0_p)) // sin(0) -> 0
return _ex0;
- if (z.is_equal(_num5)) // sin(Pi/12) -> sqrt(6)/4*(1-sqrt(3)/3)
+ if (z.is_equal(*_num5_p)) // sin(Pi/12) -> sqrt(6)/4*(1-sqrt(3)/3)
return sign*_ex1_4*sqrt(_ex6)*(_ex1+_ex_1_3*sqrt(_ex3));
- if (z.is_equal(_num6)) // sin(Pi/10) -> sqrt(5)/4-1/4
+ if (z.is_equal(*_num6_p)) // sin(Pi/10) -> sqrt(5)/4-1/4
return sign*(_ex1_4*sqrt(_ex5)+_ex_1_4);
- if (z.is_equal(_num10)) // sin(Pi/6) -> 1/2
+ if (z.is_equal(*_num10_p)) // sin(Pi/6) -> 1/2
return sign*_ex1_2;
- if (z.is_equal(_num15)) // sin(Pi/4) -> sqrt(2)/2
+ if (z.is_equal(*_num15_p)) // sin(Pi/4) -> sqrt(2)/2
return sign*_ex1_2*sqrt(_ex2);
- if (z.is_equal(_num18)) // sin(3/10*Pi) -> sqrt(5)/4+1/4
+ if (z.is_equal(*_num18_p)) // sin(3/10*Pi) -> sqrt(5)/4+1/4
return sign*(_ex1_4*sqrt(_ex5)+_ex1_4);
- if (z.is_equal(_num20)) // sin(Pi/3) -> sqrt(3)/2
+ if (z.is_equal(*_num20_p)) // sin(Pi/3) -> sqrt(3)/2
return sign*_ex1_2*sqrt(_ex3);
- if (z.is_equal(_num25)) // sin(5/12*Pi) -> sqrt(6)/4*(1+sqrt(3)/3)
+ if (z.is_equal(*_num25_p)) // sin(5/12*Pi) -> sqrt(6)/4*(1+sqrt(3)/3)
return sign*_ex1_4*sqrt(_ex6)*(_ex1+_ex1_3*sqrt(_ex3));
- if (z.is_equal(_num30)) // sin(Pi/2) -> 1
+ if (z.is_equal(*_num30_p)) // sin(Pi/2) -> 1
return sign;
}
return cos(x);
}
+static ex sin_real_part(const ex & x)
+{
+ return cosh(GiNaC::imag_part(x))*sin(GiNaC::real_part(x));
+}
+
+static ex sin_imag_part(const ex & x)
+{
+ return sinh(GiNaC::imag_part(x))*cos(GiNaC::real_part(x));
+}
+
REGISTER_FUNCTION(sin, eval_func(sin_eval).
evalf_func(sin_evalf).
derivative_func(sin_deriv).
+ real_part_func(sin_real_part).
+ imag_part_func(sin_imag_part).
latex_name("\\sin"));
//////////
const ex SixtyExOverPi = _ex60*x/Pi;
ex sign = _ex1;
if (SixtyExOverPi.info(info_flags::integer)) {
- numeric z = mod(ex_to<numeric>(SixtyExOverPi),_num120);
- if (z>=_num60) {
+ numeric z = mod(ex_to<numeric>(SixtyExOverPi),*_num120_p);
+ if (z>=*_num60_p) {
// wrap to interval [0, Pi)
- z = _num120-z;
+ z = *_num120_p-z;
}
- if (z>=_num30) {
+ if (z>=*_num30_p) {
// wrap to interval [0, Pi/2)
- z = _num60-z;
+ z = *_num60_p-z;
sign = _ex_1;
}
- if (z.is_equal(_num0)) // cos(0) -> 1
+ if (z.is_equal(*_num0_p)) // cos(0) -> 1
return sign;
- if (z.is_equal(_num5)) // cos(Pi/12) -> sqrt(6)/4*(1+sqrt(3)/3)
+ if (z.is_equal(*_num5_p)) // cos(Pi/12) -> sqrt(6)/4*(1+sqrt(3)/3)
return sign*_ex1_4*sqrt(_ex6)*(_ex1+_ex1_3*sqrt(_ex3));
- if (z.is_equal(_num10)) // cos(Pi/6) -> sqrt(3)/2
+ if (z.is_equal(*_num10_p)) // cos(Pi/6) -> sqrt(3)/2
return sign*_ex1_2*sqrt(_ex3);
- if (z.is_equal(_num12)) // cos(Pi/5) -> sqrt(5)/4+1/4
+ if (z.is_equal(*_num12_p)) // cos(Pi/5) -> sqrt(5)/4+1/4
return sign*(_ex1_4*sqrt(_ex5)+_ex1_4);
- if (z.is_equal(_num15)) // cos(Pi/4) -> sqrt(2)/2
+ if (z.is_equal(*_num15_p)) // cos(Pi/4) -> sqrt(2)/2
return sign*_ex1_2*sqrt(_ex2);
- if (z.is_equal(_num20)) // cos(Pi/3) -> 1/2
+ if (z.is_equal(*_num20_p)) // cos(Pi/3) -> 1/2
return sign*_ex1_2;
- if (z.is_equal(_num24)) // cos(2/5*Pi) -> sqrt(5)/4-1/4x
+ if (z.is_equal(*_num24_p)) // cos(2/5*Pi) -> sqrt(5)/4-1/4x
return sign*(_ex1_4*sqrt(_ex5)+_ex_1_4);
- if (z.is_equal(_num25)) // cos(5/12*Pi) -> sqrt(6)/4*(1-sqrt(3)/3)
+ if (z.is_equal(*_num25_p)) // cos(5/12*Pi) -> sqrt(6)/4*(1-sqrt(3)/3)
return sign*_ex1_4*sqrt(_ex6)*(_ex1+_ex_1_3*sqrt(_ex3));
- if (z.is_equal(_num30)) // cos(Pi/2) -> 0
+ if (z.is_equal(*_num30_p)) // cos(Pi/2) -> 0
return _ex0;
}
return -sin(x);
}
+static ex cos_real_part(const ex & x)
+{
+ return cosh(GiNaC::imag_part(x))*cos(GiNaC::real_part(x));
+}
+
+static ex cos_imag_part(const ex & x)
+{
+ return -sinh(GiNaC::imag_part(x))*sin(GiNaC::real_part(x));
+}
+
REGISTER_FUNCTION(cos, eval_func(cos_eval).
evalf_func(cos_evalf).
derivative_func(cos_deriv).
+ real_part_func(cos_real_part).
+ imag_part_func(cos_imag_part).
latex_name("\\cos"));
//////////
const ex SixtyExOverPi = _ex60*x/Pi;
ex sign = _ex1;
if (SixtyExOverPi.info(info_flags::integer)) {
- numeric z = mod(ex_to<numeric>(SixtyExOverPi),_num60);
- if (z>=_num60) {
+ numeric z = mod(ex_to<numeric>(SixtyExOverPi),*_num60_p);
+ if (z>=*_num60_p) {
// wrap to interval [0, Pi)
- z -= _num60;
+ z -= *_num60_p;
}
- if (z>=_num30) {
+ if (z>=*_num30_p) {
// wrap to interval [0, Pi/2)
- z = _num60-z;
+ z = *_num60_p-z;
sign = _ex_1;
}
- if (z.is_equal(_num0)) // tan(0) -> 0
+ if (z.is_equal(*_num0_p)) // tan(0) -> 0
return _ex0;
- if (z.is_equal(_num5)) // tan(Pi/12) -> 2-sqrt(3)
+ if (z.is_equal(*_num5_p)) // tan(Pi/12) -> 2-sqrt(3)
return sign*(_ex2-sqrt(_ex3));
- if (z.is_equal(_num10)) // tan(Pi/6) -> sqrt(3)/3
+ if (z.is_equal(*_num10_p)) // tan(Pi/6) -> sqrt(3)/3
return sign*_ex1_3*sqrt(_ex3);
- if (z.is_equal(_num15)) // tan(Pi/4) -> 1
+ if (z.is_equal(*_num15_p)) // tan(Pi/4) -> 1
return sign;
- if (z.is_equal(_num20)) // tan(Pi/3) -> sqrt(3)
+ if (z.is_equal(*_num20_p)) // tan(Pi/3) -> sqrt(3)
return sign*sqrt(_ex3);
- if (z.is_equal(_num25)) // tan(5/12*Pi) -> 2+sqrt(3)
+ if (z.is_equal(*_num25_p)) // tan(5/12*Pi) -> 2+sqrt(3)
return sign*(sqrt(_ex3)+_ex2);
- if (z.is_equal(_num30)) // tan(Pi/2) -> infinity
+ if (z.is_equal(*_num30_p)) // tan(Pi/2) -> infinity
throw (pole_error("tan_eval(): simple pole",1));
}
return (_ex1+power(tan(x),_ex2));
}
+static ex tan_real_part(const ex & x)
+{
+ ex a = GiNaC::real_part(x);
+ ex b = GiNaC::imag_part(x);
+ return tan(a)/(1+power(tan(a),2)*power(tan(b),2));
+}
+
+static ex tan_imag_part(const ex & x)
+{
+ ex a = GiNaC::real_part(x);
+ ex b = GiNaC::imag_part(x);
+ return tanh(b)/(1+power(tan(a),2)*power(tan(b),2));
+}
+
static ex tan_series(const ex &x,
const relational &rel,
int order,
evalf_func(tan_evalf).
derivative_func(tan_deriv).
series_func(tan_series).
+ real_part_func(tan_real_part).
+ imag_part_func(tan_imag_part).
latex_name("\\tan"));
//////////
// asin(1) -> Pi/2
if (x.is_equal(_ex1))
- return _num1_2*Pi;
+ return _ex1_2*Pi;
// asin(-1/2) -> -Pi/6
if (x.is_equal(_ex_1_2))
// asin(-1) -> -Pi/2
if (x.is_equal(_ex_1))
- return _num_1_2*Pi;
+ return _ex_1_2*Pi;
// asin(float) -> float
if (!x.info(info_flags::crational))
static ex atan2_eval(const ex & y, const ex & x)
{
- if (y.info(info_flags::numeric) && x.info(info_flags::numeric)) {
+ if (y.is_zero()) {
- if (y.is_zero()) {
+ // atan(0, 0) -> 0
+ if (x.is_zero())
+ return _ex0;
- // 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 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 Pi;
+ }
- // atan(0, x), x real and negative -> -Pi
- if (x.info(info_flags::negative))
- return _ex_1*Pi;
- }
+ if (x.is_zero()) {
- 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 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;
+ }
- // 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)) {
- 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 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;
+ }
- // 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)) {
- 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 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(y, -y), y real and negative -> -Pi/4
- if (y.info(info_flags::negative))
- return _ex_1_4*Pi;
- }
+ // atan(float, float) -> float
+ if (is_a<numeric>(y) && !y.info(info_flags::crational) &&
+ is_a<numeric>(x) && !x.info(info_flags::crational))
+ return atan(ex_to<numeric>(y), ex_to<numeric>(x));
- // 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;
- }
+ // 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 cosh(x);
}
+static ex sinh_real_part(const ex & x)
+{
+ return sinh(GiNaC::real_part(x))*cos(GiNaC::imag_part(x));
+}
+
+static ex sinh_imag_part(const ex & x)
+{
+ return cosh(GiNaC::real_part(x))*sin(GiNaC::imag_part(x));
+}
+
REGISTER_FUNCTION(sinh, eval_func(sinh_eval).
evalf_func(sinh_evalf).
derivative_func(sinh_deriv).
+ real_part_func(sinh_real_part).
+ imag_part_func(sinh_imag_part).
latex_name("\\sinh"));
//////////
return sinh(x);
}
+static ex cosh_real_part(const ex & x)
+{
+ return cosh(GiNaC::real_part(x))*cos(GiNaC::imag_part(x));
+}
+
+static ex cosh_imag_part(const ex & x)
+{
+ return sinh(GiNaC::real_part(x))*sin(GiNaC::imag_part(x));
+}
+
REGISTER_FUNCTION(cosh, eval_func(cosh_eval).
evalf_func(cosh_evalf).
derivative_func(cosh_deriv).
+ real_part_func(cosh_real_part).
+ imag_part_func(cosh_imag_part).
latex_name("\\cosh"));
//////////
return (sinh(x)/cosh(x)).series(rel, order, options);
}
+static ex tanh_real_part(const ex & x)
+{
+ ex a = GiNaC::real_part(x);
+ ex b = GiNaC::imag_part(x);
+ return tanh(a)/(1+power(tanh(a),2)*power(tan(b),2));
+}
+
+static ex tanh_imag_part(const ex & x)
+{
+ ex a = GiNaC::real_part(x);
+ ex b = GiNaC::imag_part(x);
+ return tan(b)/(1+power(tanh(a),2)*power(tan(b),2));
+}
+
REGISTER_FUNCTION(tanh, eval_func(tanh_eval).
evalf_func(tanh_evalf).
derivative_func(tanh_deriv).
series_func(tanh_series).
+ real_part_func(tanh_real_part).
+ imag_part_func(tanh_imag_part).
latex_name("\\tanh"));
//////////
git://www.ginac.de / ginac.git / blobdiff