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@ -4,27 +4,35 @@
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#include "r3.h"
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/* caller must ensure that x-y does not overflow */
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static int smaller_mask(int x,int y)
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static int
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smaller_mask(int x, int y)
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{
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return (x - y) >> 31;
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}
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static void vectormod3_product(small *z,int len,const small *x,const small c)
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static void
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vectormod3_product(small *z, int len, const small *x, const small c)
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{
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int i;
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for (i = 0;i < len;++i) z[i] = mod3_product(x[i],c);
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for(i = 0; i < len; ++i)
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z[i] = mod3_product(x[i], c);
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}
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static void vectormod3_minusproduct(small *z,int len,const small *x,const small *y,const small c)
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static void
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vectormod3_minusproduct(small *z, int len, const small *x, const small *y,
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const small c)
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{
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int i;
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for (i = 0;i < len;++i) z[i] = mod3_minusproduct(x[i],y[i],c);
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for(i = 0; i < len; ++i)
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z[i] = mod3_minusproduct(x[i], y[i], c);
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}
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static void vectormod3_shift(small *z,int len)
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static void
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vectormod3_shift(small *z, int len)
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{
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int i;
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for (i = len - 1;i > 0;--i) z[i] = z[i - 1];
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for(i = len - 1; i > 0; --i)
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z[i] = z[i - 1];
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z[0] = 0;
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}
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@ -34,42 +42,45 @@ or returning -1 if s is not invertible mod m
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r,s are polys of degree <p
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m is x^p-x-1
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*/
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int r3_recip(small *r,const small *s)
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#define LOOPS (2 * p + 1)
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int
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r3_recip(small *r, const small *s)
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{
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const int loops = 2*p + 1;
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int loop;
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small f[p + 1];
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small g[p + 1];
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#ifdef _MSC_VER
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small f[p + 1];
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small g[p + 1];
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small u[LOOPS + 1];
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small v[LOOPS + 1];
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#else
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small u[loops + 1];
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small v[loops + 1];
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#endif
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small c;
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int i;
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int d = p;
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int e = p;
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int swapmask;
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for (i = 2;i < p;++i) f[i] = 0;
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for(i = 2; i < p; ++i)
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f[i] = 0;
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f[0] = -1;
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f[1] = -1;
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f[p] = 1;
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/* generalization: can initialize f to any polynomial m */
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/* requirements: m has degree exactly p, nonzero constant coefficient */
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for (i = 0;i < p;++i) g[i] = s[i];
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for(i = 0; i < p; ++i)
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g[i] = s[i];
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g[p] = 0;
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for (i = 0;i <= loops;++i) u[i] = 0;
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for(i = 0; i <= LOOPS; ++i)
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u[i] = 0;
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v[0] = 1;
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for (i = 1;i <= loops;++i) v[i] = 0;
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for(i = 1; i <= LOOPS; ++i)
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v[i] = 0;
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loop = 0;
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for (;;) {
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for(;;)
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{
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/* e == -1 or d + e + loop <= 2*p */
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/* f has degree p: i.e., f[p]!=0 */
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@ -80,29 +91,35 @@ int r3_recip(small *r,const small *s)
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/* u has degree <=loop (so it fits in loop+1 coefficients) */
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/* u[i]==0 for i < p-d */
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/* if invertible: u[i]==0 for i < loop-p (so can look at just p+1 coefficients) */
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/* if invertible: u[i]==0 for i < loop-p (so can look at just p+1
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* coefficients) */
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/* v has degree <=loop (so it fits in loop+1 coefficients) */
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/* v[i]==0 for i < p-e */
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/* v[i]==0 for i < loop-p (so can look at just p+1 coefficients) */
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if (loop >= loops) break;
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if(loop >= LOOPS)
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break;
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c = mod3_quotient(g[p],f[p]);
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c = mod3_quotient(g[p], f[p]);
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vectormod3_minusproduct(g,p + 1,g,f,c);
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vectormod3_shift(g,p + 1);
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vectormod3_minusproduct(g, p + 1, g, f, c);
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vectormod3_shift(g, p + 1);
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#ifdef SIMPLER
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vectormod3_minusproduct(v,loops + 1,v,u,c);
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vectormod3_shift(v,loops + 1);
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vectormod3_minusproduct(v, loops + 1, v, u, c);
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vectormod3_shift(v, loops + 1);
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#else
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if (loop < p) {
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vectormod3_minusproduct(v,loop + 1,v,u,c);
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vectormod3_shift(v,loop + 2);
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} else {
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vectormod3_minusproduct(v + loop - p,p + 1,v + loop - p,u + loop - p,c);
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vectormod3_shift(v + loop - p,p + 2);
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if(loop < p)
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{
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vectormod3_minusproduct(v, loop + 1, v, u, c);
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vectormod3_shift(v, loop + 2);
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}
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else
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{
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vectormod3_minusproduct(v + loop - p, p + 1, v + loop - p, u + loop - p,
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c);
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vectormod3_shift(v + loop - p, p + 2);
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}
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#endif
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@ -110,22 +127,25 @@ int r3_recip(small *r,const small *s)
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++loop;
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swapmask = smaller_mask(e,d) & mod3_nonzero_mask(g[p]);
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swap(&e,&d,sizeof e,swapmask);
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swap(f,g,(p + 1) * sizeof(small),swapmask);
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swapmask = smaller_mask(e, d) & mod3_nonzero_mask(g[p]);
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swap(&e, &d, sizeof e, swapmask);
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swap(f, g, (p + 1) * sizeof(small), swapmask);
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#ifdef SIMPLER
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swap(u,v,(loops + 1) * sizeof(small),swapmask);
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swap(u, v, (loops + 1) * sizeof(small), swapmask);
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#else
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if (loop < p) {
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swap(u,v,(loop + 1) * sizeof(small),swapmask);
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} else {
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swap(u + loop - p,v + loop - p,(p + 1) * sizeof(small),swapmask);
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if(loop < p)
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{
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swap(u, v, (loop + 1) * sizeof(small), swapmask);
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}
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else
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{
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swap(u + loop - p, v + loop - p, (p + 1) * sizeof(small), swapmask);
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}
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#endif
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}
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c = mod3_reciprocal(f[p]);
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vectormod3_product(r,p,u + p,c);
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return smaller_mask(0,d);
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vectormod3_product(r, p, u + p, c);
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return smaller_mask(0, d);
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}
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Jeff Becker
6 years ago