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#include "os.h"
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#include <mp.h>
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// extended euclid
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//
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// For a and b it solves, d = gcd(a,b) and finds x and y s.t.
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// ax + by = d
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//
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// Handbook of Applied Cryptography, Menezes et al, 1997, pg 67
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void
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mpeuclid(mpint *a, mpint *b, mpint *d, mpint *x, mpint *y)
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{
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	mpint *tmp, *x0, *x1, *x2, *y0, *y1, *y2, *q, *r;
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	if(mpcmp(a, b) < 0){
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		tmp = a;
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		a = b;
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		b = tmp;
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		tmp = x;
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		x = y;
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		y = tmp;
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	}
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	if(b->top == 0){
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		mpassign(a, d);
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		mpassign(mpone, x);
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		mpassign(mpzero, y);
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		return;
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	}
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	a = mpcopy(a);
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	b = mpcopy(b);
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	x0 = mpnew(0);
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	x1 = mpcopy(mpzero);
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	x2 = mpcopy(mpone);
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	y0 = mpnew(0);
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	y1 = mpcopy(mpone);
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	y2 = mpcopy(mpzero);
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	q = mpnew(0);
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	r = mpnew(0);
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	while(b->top != 0 && b->sign > 0){
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		// q = a/b
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		// r = a mod b
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		mpdiv(a, b, q, r);
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		// x0 = x2 - qx1
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		mpmul(q, x1, x0);
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		mpsub(x2, x0, x0);
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		// y0 = y2 - qy1
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		mpmul(q, y1, y0);
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		mpsub(y2, y0, y0);
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		// rotate values
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		tmp = a;
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		a = b;
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		b = r;
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		r = tmp;
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		tmp = x2;
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		x2 = x1;
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		x1 = x0;
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		x0 = tmp;
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		tmp = y2;
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		y2 = y1;
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		y1 = y0;
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		y0 = tmp;
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	}
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	mpassign(a, d);
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	mpassign(x2, x);
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	mpassign(y2, y);
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	mpfree(x0);
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	mpfree(x1);
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	mpfree(x2);
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	mpfree(y0);
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	mpfree(y1);
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	mpfree(y2);
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	mpfree(q);
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	mpfree(r);
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	mpfree(a);
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	mpfree(b);
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}