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152 lines
3.0 KiB
C
152 lines
3.0 KiB
C
#include "params.h"
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#include "swap.h"
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#include "rq.h"
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/* caller must ensure that x-y does not overflow */
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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
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vectormodq_product(modq *z, int len, const modq *x, const modq c)
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{
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int i;
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for(i = 0; i < len; ++i)
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z[i] = modq_product(x[i], c);
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}
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static void
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vectormodq_minusproduct(modq *z, int len, const modq *x, const modq *y,
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const modq c)
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{
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int i;
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for(i = 0; i < len; ++i)
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z[i] = modq_minusproduct(x[i], y[i], c);
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}
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static void
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vectormodq_shift(modq *z, int len)
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{
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int i;
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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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/*
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r = (3s)^(-1) mod m, returning 0, if s is invertible mod m
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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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#define LOOPS (2 * p + 1)
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int
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rq_recip3(modq *r, const small *s)
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{
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int loop;
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modq f[p + 1];
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modq g[p + 1];
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modq u[LOOPS + 1];
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modq v[LOOPS + 1];
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modq 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)
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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)
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g[i] = 3 * s[i];
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g[p] = 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)
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v[i] = 0;
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loop = 0;
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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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/* f[i]==0 for i < p-d */
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/* g has degree <=p (so it fits in p+1 coefficients) */
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/* g[i]==0 for i < p-e */
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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
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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)
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break;
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c = modq_quotient(g[p], f[p]);
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vectormodq_minusproduct(g, p + 1, g, f, c);
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vectormodq_shift(g, p + 1);
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#ifdef SIMPLER
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vectormodq_minusproduct(v, loops + 1, v, u, c);
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vectormodq_shift(v, loops + 1);
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#else
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if(loop < p)
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{
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vectormodq_minusproduct(v, loop + 1, v, u, c);
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vectormodq_shift(v, loop + 2);
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}
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else
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{
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vectormodq_minusproduct(v + loop - p, p + 1, v + loop - p, u + loop - p,
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c);
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vectormodq_shift(v + loop - p, p + 2);
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}
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#endif
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e -= 1;
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++loop;
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swapmask = smaller_mask(e, d) & modq_nonzero_mask(g[p]);
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swap(&e, &d, sizeof e, swapmask);
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swap(f, g, (p + 1) * sizeof(modq), swapmask);
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#ifdef SIMPLER
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swap(u, v, (loops + 1) * sizeof(modq), swapmask);
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#else
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if(loop < p)
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{
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swap(u, v, (loop + 1) * sizeof(modq), 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(modq), swapmask);
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}
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#endif
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}
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c = modq_reciprocal(f[p]);
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vectormodq_product(r, p, u + p, c);
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return smaller_mask(0, d);
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}
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