private double abs(double real, double imag)
{
double temp;
if (real < 0)
{
real = -real;
}
if (imag < 0)
{
imag = -imag;
}
if (imag > real)
{
temp = real;
real = imag;
imag = temp;
}
if ((real + imag) == real)
{
return(real);
}
temp = imag / real;
temp = real * Math.Sqrt(1.0 + temp * temp);
return(temp);
}
internal virtual int cfs(double x)
{
if (x < 0)
{
return(cfs(-x));
}
int a0 = ( int )Math.floor(x);
if (x == ( double )a0)
{
return(a0);
}
int a1 = ( int )Math.floor(1.0 / (x - a0));
int z = a0 * a1 + 1;
if (Math.abs(( double )z / ( double )a1 - x) < 1.0e-6)
{
return(z);
}
return(0);
}
internal override Symbol PreEval(Symbol x)
{
Complex z = x.ToComplex();
if (z.Im == 0.0)
{
return(new Complex(Math.tan(z.Re)));
}
return(( Symbol )evalx(trigrule, z));
}
internal override Symbol PreEval(Symbol x)
{
var z = x.ToComplex();
if (z.Re < 0 || z.Im != 0.0)
{
return(new Complex(Math.log(z.Re * z.Re + z.Im * z.Im) / 2, Math.atan2(z.Im, z.Re)));
}
return(new Complex(Math.log(z.Re)));
}
internal override Symbol PreEval(Symbol x)
{
var z = x.ToComplex();
var r = Math.exp(z.Re);
if (z.Im != 0.0)
{
return(new Complex(r * Math.cos(z.Im), r * Math.sin(z.Im)));
}
return(new Complex(r));
}
public override int Eval(Stack st)
{
int narg = GetNarg(st);
Algebraic x = GetAlgebraic(st);
if (x.IsScalar() && !x.IsConstant())
{
throw new SymbolicException("Unknown variable dimension: " + x);
}
Matrix m = new Matrix(x);
st.Push(new Complex(( double )Math.max(m.Cols(), m.Rows())));
return(0);
}
internal static long kleinsterTeiler(long X, long start)
{
long stop = ( long )Math.ceil(Math.Sqrt(( double )X));
if (start > stop)
{
return(X);
}
long b = start / 30L;
b *= 30L;
long m = start % 30L;
int i = 0;
while (m > mod[i])
{
i++;
}
while (start <= stop)
{
if (Session.Proc.CheckInterrupt())
{
return(-1L);
}
if (X % start == 0)
{
return(start);
}
i++;
if (i >= mod.Length)
{
i = 0;
b += 30L;
start = b;
}
start += moddif[i];
}
return(X);
}
internal override Algebraic SymEval(Algebraic x, Algebraic y)
{
if (y is Complex && !y.IsComplex() && x is Complex && !x.IsComplex())
{
return(new Complex(Math.atan2((( Complex )y).Re, (( Complex )x).Re)));
}
if (Symbol.ZERO != x)
{
return(FunctionVariable.Create("atan", y / x) + FunctionVariable.Create("sign", y) * (Symbol.ONE - FunctionVariable.Create("sign", x)) * Symbol.PI / Symbol.TWO);
}
else
{
return((FunctionVariable.Create("sign", y) * Symbol.PI) / Symbol.TWO);
}
}
internal static void dft(double[] re, double[] im, double[] outRe, double[] outIm)
{
int N = re.Length;
for (int k = 0; k < N; k++)
{
outRe[k] = outIm[k] = 0.0;
for (int n = 0; n < N; n++)
{
var ang = -2.0 * Math.PI * k * n / N;
var eim = Math.sin(ang);
var ere = Math.cos(ang);
outRe[k] += re[n] * ere - im[n] * eim;
outIm[k] += re[n] * eim + im[n] * ere;
}
}
}
public override double Norm()
{
double r;
if (Math.abs(Re) > Math.abs(Im))
{
r = Im / Re;
r = Math.abs(Re) * Math.Sqrt(1 + r * r);
}
else if (Im != 0)
{
r = Re / Im;
r = Math.abs(Im) * Math.Sqrt(1 + r * r);
}
else
{
r = 0.0;
}
return(r);
}
public override int Eval(Stack st)
{
int narg = GetNarg(st);
var x = GetVector(st);
x = ( Vector )(new ExpandConstants()).SymEval(x);
var re = (( Vector )x.RealPart()).Double;
var im = (( Vector )x.ImagPart()).Double;
int n = re.Length;
var power = Math.log(n) / Math.log(2.0);
if (power != Math.round(power))
{
var outRe = new double[n];
var outIm = new double[n];
dft(re, im, outRe, outIm);
re = outRe;
im = outIm;
}
else
{
ifft_1d(re, im, -1);
}
var a = new Number[n];
for (int i = 0; i < n; i++)
{
a[i] = new Number(re[i], im[i]);
}
st.Push(new Vector(a));
return(0);
}
internal override Algebraic SymEval(Algebraic x)
{
if (x is Rational)
{
var xr = ( Rational )x;
if (xr.den.Var is FunctionVariable &&
(( FunctionVariable )xr.den.Var).Name.Equals("exp") &&
(( FunctionVariable )xr.den.Var).Var.IsComplex())
{
var fv = ( FunctionVariable )xr.den.Var;
int maxdeg = Math.max(Poly.Degree(xr.nom, fv), Poly.Degree(xr.den, fv));
if (maxdeg % 2 == 0)
{
return(divExponential(xr.nom, fv, maxdeg / 2) / divExponential(xr.den, fv, maxdeg / 2));
}
else
{
var fv2 = new FunctionVariable("exp", (( FunctionVariable )xr.den.Var).Var / Symbol.TWO, (( FunctionVariable )xr.den.Var).Body);
Algebraic ex = new Polynomial(fv2, new Algebraic[] { Symbol.ZERO, Symbol.ZERO, Symbol.ONE });
var xr1 = xr.nom.Value(xr.den.Var, ex) / xr.den.Value(xr.den.Var, ex);
return(SymEval(xr1));
}
}
}
if (x is Polynomial && (( Polynomial )x).Var is FunctionVariable)
{
var xp = ( Polynomial )x;
Algebraic xf = null;
var fvar = ( FunctionVariable )xp.Var;
if (fvar.Name.Equals("exp"))
{
var re = fvar.Var.RealPart();
var im = fvar.Var.ImagPart();
if (im != Symbol.ZERO)
{
bool _minus = minus(im);
if (_minus)
{
im = -im;
}
var a = FunctionVariable.Create("exp", re);
var b = FunctionVariable.Create("cos", im);
var c = FunctionVariable.Create("sin", im) * Symbol.IONE;
xf = a * (_minus ? b - c : b + c);
}
}
if (fvar.Name.Equals("log"))
{
var arg = fvar.Var;
Algebraic factor = Symbol.ONE, sum = Symbol.ZERO;
if (arg is Polynomial &&
(( Polynomial )arg).Degree() == 1 &&
(( Polynomial )arg).Var is FunctionVariable &&
(( Polynomial )arg)[0].Equals(Symbol.ZERO) &&
(( FunctionVariable )(( Polynomial )arg).Var).Name.Equals("sqrt"))
{
sum = FunctionVariable.Create("log", (( Polynomial )arg)[1]);
factor = new Complex(0.5);
arg = (( FunctionVariable )(( Polynomial )arg).Var).Var;
xf = FunctionVariable.Create("log", arg);
}
try
{
var re = arg.RealPart();
var im = arg.ImagPart();
if (im != Symbol.ZERO)
{
bool min_im = minus(im);
if (min_im)
{
im = -im;
}
var a1 = new SqrtExpand().SymEval(arg * arg.Conj());
var a = FunctionVariable.Create("log", a1) / Symbol.TWO;
var b1 = SymEval(re / im);
var b = FunctionVariable.Create("atan", b1) * Symbol.IONE;
xf = min_im ? a + b : a - b;
var pi2 = Symbol.PI * Symbol.IONE / Symbol.TWO;
xf = min_im ? xf - pi2 : xf + pi2;
}
}
catch (SymbolicException)
{
}
if (xf != null)
{
xf = xf * factor + sum;
}
}
if (xf == null)
{
return(x.Map(this));
}
Algebraic r = Symbol.ZERO;
for (int i = xp.Coeffs.Length - 1; i > 0; i--)
{
r = (r + SymEval(xp[i])) * xf;
}
if (xp.Coeffs.Length > 0)
{
r = r + SymEval(xp[0]);
}
return(r);
}
return(x.Map(this));
}
public override bool IsInteger()
{
return(Im == 0.0 && Math.round(Re) == Re);
}
internal override Symbol PreEval(Symbol x)
{
return(new Complex(Math.logGamma(x.ToComplex().Re)));
}
public virtual string ToString(double x)
{
if (x < 0.0)
{
return("-" + ToString(-x));
}
if (x == 0.0)
{
return("0");
}
int exp = nsign - 1;
while (x < mantisse_min)
{
exp--;
x *= dbase;
}
while (x >= mantisse_min)
{
exp++;
x /= dbase;
}
long xl = ( long )Math.round(x);
string r = "";
int nc = nsign;
while (xl != 0L)
{
nc--;
int _digit = digit(xl % ibase);
if (!(r.Equals("") && _digit == '0'))
{
r = ( char )_digit + r;
}
xl = xl / ibase;
}
exp -= nc;
if (exp > nsign - 1 || exp < -1)
{
if (r.Length == 1)
{
r = r + "0";
}
return(sub(r, 0, 1) + "." + sub(r, 1, r.Length) + "E" + exp);
}
if (exp == -1)
{
return("0." + r);
}
else
{
return(sub(r, 0, exp + 1) + (r.Length > exp + 1 ? "." + sub(r, exp + 1, r.Length) : ""));
}
}
public virtual Complex Arg()
{
return(new Complex(Math.atan2(Im, Re)));
}
internal static void ifft_1d(double[] re, double[] im, int sign)
{
double u_r, u_i, w_r, w_i, t_r, t_i;
int ln, nv2, k, l, le, le1, j, ip, i, n;
n = re.Length;
ln = ( int )(Math.log(( double )n) / Math.log(2) + 0.5);
nv2 = n / 2;
j = 1;
for (i = 1; i < n; i++)
{
if (i < j)
{
t_r = re[i - 1];
t_i = im[i - 1];
re[i - 1] = re[j - 1];
im[i - 1] = im[j - 1];
re[j - 1] = t_r;
im[j - 1] = t_i;
}
k = nv2;
while (k < j)
{
j = j - k;
k = k / 2;
}
j = j + k;
}
for (l = 1; l <= ln; l++)
{
le = ( int )(Math.exp(( double )l * Math.log(2)) + 0.5);
le1 = le / 2;
u_r = 1.0;
u_i = 0.0;
w_r = Math.cos(Math.PI / ( double )le1);
w_i = sign * Math.sin(Math.PI / ( double )le1);
for (j = 1; j <= le1; j++)
{
for (i = j; i <= n; i += le)
{
ip = i + le1;
t_r = re[ip - 1] * u_r - u_i * im[ip - 1];
t_i = im[ip - 1] * u_r + u_i * re[ip - 1];
re[ip - 1] = re[i - 1] - t_r;
im[ip - 1] = im[i - 1] - t_i;
re[i - 1] = re[i - 1] + t_r;
im[i - 1] = im[i - 1] + t_i;
}
t_r = u_r * w_r - w_i * u_i;
u_i = w_r * u_i + w_i * u_r;
u_r = t_r;
}
}
if (sign > 0)
{
for (i = 0; i < n; i++)
{
re[i] /= n;
im[i] /= n;
}
}
}
public override int Eval(Stack st)
{
int narg = GetNarg(st);
if (narg != 4)
{
throw new ParseException("Usage: ROMBERG (exp,var,ll,ul)");
}
var exp = GetAlgebraic(st);
var v = GetVariable(st);
var ll = GetAlgebraic(st);
var ul = GetAlgebraic(st);
LambdaAlgebraic xc = new ExpandConstants();
exp = xc.SymEval(exp);
ll = xc.SymEval(ll);
ul = xc.SymEval(ul);
if (!(ll is Symbol) || !(ul is Symbol))
{
throw new ParseException("Usage: ROMBERG (exp,var,ll,ul)");
}
var rombergtol = 1.0e-4;
int rombergit = 11;
var a1 = Session.Proc.Store.GetNum("rombergit");
if (a1 != null)
{
rombergit = a1.ToInt();
}
a1 = Session.Proc.Store.GetNum("rombergtol");
if (a1 != null)
{
rombergtol = a1.ToComplex().Re;
}
var a = (( Symbol )ll).ToComplex().Re;
var b = (( Symbol )ul).ToComplex().Re;
var I = Matrix.CreateRectangularArray <double>(rombergit, rombergit);
int i = 0, n = 1;
var t = trapez(exp, v, n, a, b);
if (!(t is Symbol))
{
throw new ParseException("Expression must evaluate to number");
}
I[0][0] = (( Symbol )t).ToComplex().Re;
double epsa = 1.1 * rombergtol;
while (epsa > rombergtol && i < rombergit - 1)
{
i++;
n *= 2;
t = trapez(exp, v, n, a, b);
I[0][i] = (( Symbol )t).ToComplex().Re;
double f = 1.0;
for (int k = 1; k <= i; k++)
{
f *= 4;
I[k][i] = I[k - 1][i] + (I[k - 1][i] - I[k - 1][i - 1]) / (f - 1.0);
}
epsa = Math.abs((I[i][i] - I[i - 1][i - 1]) / I[i][i]);
}
st.Push(new Complex(I[i][i]));
return(0);
}
protected internal static Symbol readNumber(StringBuilder s)
{
int kmax = 0;
while (kmax < s.Length && oneof(s[kmax], "0123456789.eE+-"))
{
kmax++;
}
var sub = s.ToString().Substring(0, kmax);
var cultureInfo = new CultureInfo("")
{
NumberFormat = { NumberDecimalSeparator = "." }
};
for (int k = kmax; k > 0; k--)
{
try
{
var ts = sub.Substring(0, k);
var x = double.Parse(ts, cultureInfo);
if (ts.EndsWith(".", StringComparison.Ordinal) && s.Length > k && (s[k] == '^' || s[k] == '/'))
{
continue;
}
bool imag = false;
if (s.Length > k && (s[k] == 'i' || s[k] == 'j'))
{
imag = true;
k++;
}
s.Remove(0, k);
if (Math.abs(x) > 1e15)
{
try
{
var bi = new BigInteger(ts, 10);
return(imag ? ( Symbol )(new Number(bi) * Symbol.IONE) : new Number(bi));
}
catch (Exception)
{
}
}
return(imag ? new Complex(0, x) : new Complex(x));
}
catch (Exception)
{
}
}
throw new ParseException("Internal Error.");
}
