195 lines
7.9 KiB
Diff
195 lines
7.9 KiB
Diff
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diff --git a/rp-private.h b/rp-private.h
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index b4c7dad..0c7193e 100644
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--- a/rp-private.h
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+++ b/rp-private.h
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@@ -36,7 +36,7 @@
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#define LONG_SHIFT ((LONG_LENGTH == 16) ? 4 : \
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(LONG_LENGTH == 32) ? 5 : \
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(LONG_LENGTH == 64) ? 6 : 0)
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-#define LONG_MASK (~(-1L<<LONG_SHIFT))
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+#define LONG_MASK (~(-(1L<<LONG_SHIFT)))
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/* Check if SSE instructions can be used.
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We assume that one SSE word of 128 bit is two long's,
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diff --git a/sturm.c b/sturm.c
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index c78d7c6..5fd2cf5 100644
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--- a/sturm.c
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+++ b/sturm.c
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@@ -27,7 +27,6 @@
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***********************************************************************/
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#include "ratpoints.h"
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-
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/**************************************************************************
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* Arguments of _ratpoints_compute_sturm() : (from the args argument) *
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* *
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@@ -53,7 +52,7 @@
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/* A helper function: evaluate the polynomial in cofs[] of given degree
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at num/2^denexp and return the sign. */
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-static long eval_sign(ratpoints_args *args, mpz_t *cofs, long degree,
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+static long eval_sign(const ratpoints_args *args, const mpz_t *cofs, long degree,
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long num, long denexp)
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{
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long n, e, s;
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@@ -70,11 +69,80 @@ static long eval_sign(ratpoints_args *args, mpz_t *cofs, long degree,
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return(s);
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}
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+static const long max = (long)(((unsigned long)(-1))>>1);
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+static const long min = (long)(-(((unsigned long)(-1))>>1));
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+ /* recursive helper function */
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+static void iterate(long nl, long nr, long del, long der, long cleft, long cright,
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+ long sl, long sr, long depth,
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+ ratpoints_interval **iptr, const ratpoints_interval *ivlo,
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+ const ratpoints_args *args, const long k, const long sturm_degs[],
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+ const mpz_t sturm[][args->degree + 1])
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+ { /* nl/2^del, nr/2^der : interval left/right endpoints,
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+ cleft, cright: sign change counts at endpoints,
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+ sl, sr: signs at endpoints,
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+ depth: iteration depth */
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+ long iter = args->sturm;
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+ if(cleft == cright && sl < 0) { return; }
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+ /* here we know the polynomial is negative on the interval */
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+ if((cleft == cright && sl > 0) || depth >= iter)
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+ /* we have to add/extend an interval if we either know that
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+ the polynomial is positive on the interval (first condition)
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+ or the maximal iteration depth has been reached (second condition) */
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+ { double l = ((double)nl)/((double)(1<<del));
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+ double u = ((double)nr)/((double)(1<<der));
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+ if(*iptr == ivlo)
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+ { (*iptr)->low = l; (*iptr)->up = u; (*iptr)++; }
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+ else
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+ { if(((*iptr)-1)->up == l) /* extend interval */
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+ { ((*iptr)-1)->up = u; }
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+ else /* new interval */
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+ { (*iptr)->low = l; (*iptr)->up = u; (*iptr)++; }
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+ }
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+ return;
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+ }
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+ /* now we must split the interval and evaluate the sturm sequence
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+ at the midpoint */
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+ { long nm, dem, s0, s1, s2, s, cmid = 0, n;
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+ if(nl == min)
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+ { if(nr == max) { nm = 0; dem = 0; }
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+ else { nm = (nr == 0) ? -1 : 2*nr; dem = 0; }
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+ }
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+ else
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+ { if(nr == max) { nm = (nl == 0) ? 1 : 2*nl; dem = 0; }
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+ else /* "normal" case */
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+ { if(del == der) /* then both are zero */
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+ { if(((nl+nr) & 1) == 0) { nm = (nl+nr)>>1; dem = 0; }
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+ else { nm = nl+nr; dem = 1; }
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+ }
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+ else /* here one de* is greater */
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+ { if(del > der) { nm = nl + (nr<<(del-der)); dem = del+1; }
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+ else { nm = (nl<<(der-del)) + nr; dem = der+1; }
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+ }
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+ }
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+ }
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+ s0 = eval_sign(args, sturm[0], sturm_degs[0], nm, dem);
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+ s1 = eval_sign(args, sturm[1], sturm_degs[1], nm, dem);
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+ if(s0*s1 == -1) { cmid++; }
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+ s = (s1 == 0) ? s0 : s1;
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+ for(n = 2; n <= k; n++)
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+ { s2 = eval_sign(args, sturm[n], sturm_degs[n], nm, dem);
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+ if(s2 == -s) { cmid++; s = s2; }
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+ else if(s2 != 0) { s = s2; }
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+ }
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+ /* now recurse */
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+ iterate(nl, nm, del, dem, cleft, (s0==0) ? (cmid+1) : cmid,
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+ sl, (s0==0) ? -s1 : s0, depth+1,
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+ iptr, ivlo, args, k, sturm_degs, sturm);
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+ iterate(nm, nr, dem, der, cmid, cright,
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+ (s0==0) ? s1 : s0, sr, depth+1,
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+ iptr, ivlo, args, k, sturm_degs, sturm);
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+ }
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+ } /* end iterate() */
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+
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long _ratpoints_compute_sturm(ratpoints_args *args)
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{
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mpz_t *cofs = args->cof;
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long degree = args->degree;
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- long iter = args->sturm;
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ratpoints_interval *ivlist = args->domain;
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long num_iv = args->num_inter;
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long n, m, k, new_num;
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@@ -165,75 +233,12 @@ long _ratpoints_compute_sturm(ratpoints_args *args)
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/* recall: typedef struct {double low; double up;} ratpoints_interval; */
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{ ratpoints_interval ivlocal[1 + (degree>>1)];
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ratpoints_interval *iptr = &ivlocal[0];
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- long max = (long)(((unsigned long)(-1))>>1);
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- long min = -max;
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long num_intervals;
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long slcf = mpz_cmp_si(cofs[degree], 0);
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- /* recursive helper function */
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- void iterate(long nl, long nr, long del, long der, long cleft, long cright,
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- long sl, long sr, long depth)
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- { /* nl/2^del, nr/2^der : interval left/right endpoints,
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- cleft, cright: sign change counts at endpoints,
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- sl, sr: signs at endpoints,
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- depth: iteration depth */
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- if(cleft == cright && sl < 0) { return; }
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- /* here we know the polynomial is negative on the interval */
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- if((cleft == cright && sl > 0) || depth >= iter)
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- /* we have to add/extend an interval if we either know that
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- the polynomial is positive on the interval (first condition)
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- or the maximal iteration depth has been reached (second condition) */
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- { double l = ((double)nl)/((double)(1<<del));
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- double u = ((double)nr)/((double)(1<<der));
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- if(iptr == &ivlocal[0])
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- { iptr->low = l; iptr->up = u; iptr++; }
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- else
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- { if((iptr-1)->up == l) /* extend interval */
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- { (iptr-1)->up = u; }
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- else /* new interval */
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- { iptr->low = l; iptr->up = u; iptr++; }
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- }
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- return;
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- }
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- /* now we must split the interval and evaluate the sturm sequence
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- at the midpoint */
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- { long nm, dem, s0, s1, s2, s, cmid = 0, n;
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- if(nl == min)
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- { if(nr == max) { nm = 0; dem = 0; }
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- else { nm = (nr == 0) ? -1 : 2*nr; dem = 0; }
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- }
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- else
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- { if(nr == max) { nm = (nl == 0) ? 1 : 2*nl; dem = 0; }
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- else /* "normal" case */
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- { if(del == der) /* then both are zero */
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- { if(((nl+nr) & 1) == 0) { nm = (nl+nr)>>1; dem = 0; }
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- else { nm = nl+nr; dem = 1; }
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- }
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- else /* here one de* is greater */
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- { if(del > der) { nm = nl + (nr<<(del-der)); dem = del+1; }
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- else { nm = (nl<<(der-del)) + nr; dem = der+1; }
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- }
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- }
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- }
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- s0 = eval_sign(args, sturm[0], sturm_degs[0], nm, dem);
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- s1 = eval_sign(args, sturm[1], sturm_degs[1], nm, dem);
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- if(s0*s1 == -1) { cmid++; }
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- s = (s1 == 0) ? s0 : s1;
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- for(n = 2; n <= k; n++)
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- { s2 = eval_sign(args, sturm[n], sturm_degs[n], nm, dem);
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- if(s2 == -s) { cmid++; s = s2; }
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- else if(s2 != 0) { s = s2; }
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- }
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- /* now recurse */
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- iterate(nl, nm, del, dem, cleft, (s0==0) ? (cmid+1) : cmid,
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- sl, (s0==0) ? -s1 : s0, depth+1);
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- iterate(nm, nr, dem, der, cmid, cright,
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- (s0==0) ? s1 : s0, sr, depth+1);
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- }
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- } /* end iterate() */
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-
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iterate(min, max, 0, 0, count2, count1,
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- (degree & 1) ? -slcf : slcf, slcf, 0);
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+ (degree & 1) ? -slcf : slcf, slcf, 0,
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+ &iptr, &ivlocal[0], args, k, sturm_degs, sturm);
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num_intervals = iptr - &ivlocal[0];
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/* intersect with given intervals */
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{ ratpoints_interval local_copy[num_iv];
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