mirror of
https://github.com/lcn2/calc.git
synced 2025-08-16 01:03:29 +03:00
db77e29a23
Converted all ASCII tabs to ASCII spaces using a 8 character tab stop, for all files, except for all Makefiles (plus rpm.mk). The `git diff -w` reports no changes.
91 lines
2.3 KiB
Plaintext
91 lines
2.3 KiB
Plaintext
/*
|
|
* pell - solve Pell's equation
|
|
*
|
|
* Copyright (C) 1999,2021 David I. Bell
|
|
*
|
|
* Calc is open software; you can redistribute it and/or modify it under
|
|
* the terms of the version 2.1 of the GNU Lesser General Public License
|
|
* as published by the Free Software Foundation.
|
|
*
|
|
* Calc is distributed in the hope that it will be useful, but WITHOUT
|
|
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
|
|
* or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General
|
|
* Public License for more details.
|
|
*
|
|
* A copy of version 2.1 of the GNU Lesser General Public License is
|
|
* distributed with calc under the filename COPYING-LGPL. You should have
|
|
* received a copy with calc; if not, write to Free Software Foundation, Inc.
|
|
* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
|
|
*
|
|
* Under source code control: 1990/02/15 01:50:34
|
|
* File existed as early as: before 1990
|
|
*
|
|
* Share and enjoy! :-) http://www.isthe.com/chongo/tech/comp/calc/
|
|
*/
|
|
|
|
/*
|
|
* Solve Pell's equation; Returns the solution X to: X^2 - D * Y^2 = 1.
|
|
* Type the solution to Pell's equation for a particular D.
|
|
*/
|
|
|
|
|
|
define pell(D)
|
|
{
|
|
local X, Y;
|
|
|
|
X = pellx(D);
|
|
if (isnull(X)) {
|
|
print "D=":D:" is square";
|
|
return;
|
|
}
|
|
Y = isqrt((X^2 - 1) / D);
|
|
print X : "^2 - " : D : "*" : Y : "^2 = " : X^2 - D*Y^2;
|
|
}
|
|
|
|
|
|
/*
|
|
* Function to solve Pell's equation
|
|
* Returns the solution X to:
|
|
* X^2 - D * Y^2 = 1
|
|
*/
|
|
define pellx(D)
|
|
{
|
|
local R, Rp, U, Up, V, Vp, A, T, Q1, Q2, n;
|
|
local mat ans[2,2];
|
|
local mat tmp[2,2];
|
|
|
|
R = isqrt(D);
|
|
Vp = D - R^2;
|
|
if (Vp == 0)
|
|
return;
|
|
Rp = R + R;
|
|
U = Rp;
|
|
Up = U;
|
|
V = 1;
|
|
A = 0;
|
|
n = 0;
|
|
ans[0,0] = 1;
|
|
ans[1,1] = 1;
|
|
tmp[0,1] = 1;
|
|
tmp[1,0] = 1;
|
|
do {
|
|
T = V;
|
|
V = A * (Up - U) + Vp;
|
|
Vp = T;
|
|
A = U // V;
|
|
Up = U;
|
|
U = Rp - U % V;
|
|
tmp[0,0] = A;
|
|
ans *= tmp;
|
|
n++;
|
|
} while (A != Rp);
|
|
Q2 = ans[[1]];
|
|
Q1 = isqrt(Q2^2 * D + 1);
|
|
if (isodd(n)) {
|
|
T = Q1^2 + D * Q2^2;
|
|
Q2 = Q1 * Q2 * 2;
|
|
Q1 = T;
|
|
}
|
|
return Q1;
|
|
}
|