X-Git-Url: https://git.distorted.org.uk/~mdw/catacomb/blobdiff_plain/21f82da45054e310c8294c44bb071d7317089e74..HEAD:/math/mpreduce.c

diff --git a/math/mpreduce.c b/math/mpreduce.c
index b4543a66..0fd4b458 100644
--- a/math/mpreduce.c
+++ b/math/mpreduce.c
@@ -47,7 +47,7 @@ DA_DECL(instr_v, mpreduce_instr);
  *
  * Suppose %$x = x' + z 2^k$%, where %$k \ge n$%; then
  * %$x \equiv x' + d z 2^{k-n} \pmod p$%.  We can use this to trim the
- * representation of %$x$%; each time, we reduce %$x$% by a mutliple of
+ * representation of %$x$%; each time, we reduce %$x$% by a multiple of
  * %$2^{k-n} p$%.  We can do this in two passes: firstly by taking whole
  * words off the top, and then (if necessary) by trimming the top word.
  * Finally, if %$p \le x < 2^n$% then %$0 \le x - p < p$% and we're done.
@@ -81,7 +81,10 @@ DA_DECL(instr_v, mpreduce_instr);
  * Arguments:	@gfreduce *r@ = structure to fill in
  *		@mp *x@ = an integer
  *
- * Returns:	Zero if successful; nonzero on failure.
+ * Returns:	Zero if successful; nonzero on failure.  The current
+ *		algorithm always succeeds when given positive @x@.  Earlier
+ *		versions used to fail on particular kinds of integers, but
+ *		this is guaranteed not to happen any more.
  *
  * Use:		Initializes a context structure for reduction.
  */
@@ -180,21 +183,6 @@ int mpreduce_create(mpreduce *r, mp *p)
    * the instruction's immediate operands.
    */
 
-#ifdef DEBUG
-  for (i = 0, mp_scan(&sc, p); mp_step(&sc); i++) {
-    switch (st | mp_bit(&sc)) {
-      case  Z | 1: st = Z1; break;
-      case Z1 | 0: st =	 Z; printf("+ %lu\n", i - 1); break;
-      case Z1 | 1: st =	 X; printf("- %lu\n", i - 1); break;
-      case  X | 0: st = X0; break;
-      case X0 | 1: st =	 X; printf("- %lu\n", i - 1); break;
-      case X0 | 0: st =	 Z; printf("+ %lu\n", i - 1); break;
-    }
-  }
-  if (st >= X) printf("+ %lu\n", i - 1);
-  st = Z;
-#endif
-
   bb = MPW_BITS - (d + 1)%MPW_BITS;
   for (i = 0, mp_scan(&sc, p); i < d && mp_step(&sc); i++) {
     switch (st | mp_bit(&sc)) {
@@ -211,18 +199,27 @@ int mpreduce_create(mpreduce *r, mp *p)
     }
   }
 
-  /* --- This doesn't always work --- *
+  /* --- Fix up wrong-sided decompositions --- *
+   *
+   * At this point, we haven't actually finished up the state machine
+   * properly.  We stopped scanning just after bit %$n - 1$% -- the most
+   * significant one, which we know in advance must be set (since @x@ is
+   * strictly positive).  Therefore we are either in state @X@ or @Z1@.  In
+   * the former case, we have nothing to do.  In the latter, there are two
+   * subcases to deal with.  If there are no other instructions, then @x@ is
+   * a perfect power of two, and %$d = 0$%, so again there is nothing to do.
    *
-   * If %$d \ge 2^{n-1}$% then the above recurrence will output a subtraction
-   * as the final instruction, which may sometimes underflow.  (It interprets
-   * such numbers as being in the form %$2^{n-1} + d$%.)  This is clearly
-   * bad, so detect the situation and fail gracefully.
+   * In the remaining case, we have decomposed @x@ as %$2^{n-1} + d$%, for
+   * some positive %$d%, which is unfortunate: if we're asked to reduce
+   * %$2^n$%, say, we'll end up with %$-d$% (or would do, if we weren't
+   * sticking to unsigned arithmetic for good performance).  So instead, we
+   * rewrite this as %$2^n - 2^{n-1} + d$% and everything will be good.
    */
 
-  if (DA_LEN(&iv) && (DA(&iv)[DA_LEN(&iv) - 1].op & ~1u) == MPRI_SUB) {
-    mp_drop(r->p);
-    DA_DESTROY(&iv);
-    return (-1);
+  if (st == Z1 && DA_LEN(&iv)) {
+    w = 1;
+    b = (bb + d)%MPW_BITS;
+    INSTR(MPRI_ADD | !!b, w, b);
   }
 
 #undef INSTR
@@ -278,9 +275,6 @@ int mpreduce_create(mpreduce *r, mp *p)
   }
   DA_DESTROY(&iv);
 
-#ifdef DEBUG
-  mpreduce_dump(r, stdout);
-#endif
   return (0);
 }
 
@@ -301,7 +295,7 @@ void mpreduce_destroy(mpreduce *r)
 
 /* --- @mpreduce_dump@ --- *
  *
- * Arguments:	@mpreduce *r@ = structure to dump
+ * Arguments:	@const mpreduce *r@ = structure to dump
  *		@FILE *fp@ = file to dump on
  *
  * Returns:	---
@@ -309,7 +303,7 @@ void mpreduce_destroy(mpreduce *r)
  * Use:		Dumps a reduction context.
  */
 
-void mpreduce_dump(mpreduce *r, FILE *fp)
+void mpreduce_dump(const mpreduce *r, FILE *fp)
 {
   size_t i;
   static const char *opname[] = { "add", "addshift", "sub", "subshift" };
@@ -337,7 +331,7 @@ void mpreduce_dump(mpreduce *r, FILE *fp)
 
 /* --- @mpreduce_do@ --- *
  *
- * Arguments:	@mpreduce *r@ = reduction context
+ * Arguments:	@const mpreduce *r@ = reduction context
  *		@mp *d@ = destination
  *		@mp *x@ = source
  *
@@ -348,15 +342,6 @@ static void run(const mpreduce_instr *i, const mpreduce_instr *il,
 		mpw *v, mpw z)
 {
   for (; i < il; i++) {
-#ifdef DEBUG
-    mp vv;
-    mp_build(&vv, v - i->argx, v + 1);
-    printf("  0x"); mp_writefile(&vv, stdout, 16);
-    printf(" %c (0x%lx << %u) == 0x",
-	   (i->op & ~1u) == MPRI_ADD ? '+' : '-',
-	   (unsigned long)z,
-	   i->argy);
-#endif
     switch (i->op) {
       case MPRI_ADD: MPX_UADDN(v - i->argx, v + 1, z); break;
       case MPRI_ADDLSL: mpx_uaddnlsl(v - i->argx, v + 1, z, i->argy); break;
@@ -365,24 +350,15 @@ static void run(const mpreduce_instr *i, const mpreduce_instr *il,
       default:
 	abort();
     }
-#ifdef DEBUG
-    mp_build(&vv, v - i->argx, v + 1);
-    mp_writefile(&vv, stdout, 16);
-    printf("\n");
-#endif
   }
 }
 
-mp *mpreduce_do(mpreduce *r, mp *d, mp *x)
+mp *mpreduce_do(const mpreduce *r, mp *d, mp *x)
 {
   mpw *v, *vl;
   const mpreduce_instr *il;
   mpw z;
 
-#ifdef DEBUG
-  mp *_r = 0, *_rr = 0;
-#endif
-
   /* --- If source is negative, divide --- */
 
   if (MP_NEGP(x)) {
@@ -398,13 +374,6 @@ mp *mpreduce_do(mpreduce *r, mp *d, mp *x)
 
   /* --- Stage one: trim excess words from the most significant end --- */
 
-#ifdef DEBUG
-  _r = MP_NEW;
-  mp_div(0, &_r, x, r->p);
-  MP_PRINTX("x", x);
-  _rr = 0;
-#endif
-
   il = r->iv + r->in;
   if (MP_LEN(x) >= r->lim) {
     v = x->v + r->lim;
@@ -414,11 +383,6 @@ mp *mpreduce_do(mpreduce *r, mp *d, mp *x)
 	z = *vl;
 	*vl = 0;
 	run(r->iv, il, vl, z);
-#ifdef DEBUG
-	MP_PRINTX("x", x);
-	mp_div(0, &_rr, x, r->p);
-	assert(MP_EQ(_r, _rr));
-#endif
       }
     }
 
@@ -429,11 +393,6 @@ mp *mpreduce_do(mpreduce *r, mp *d, mp *x)
 	z = *vl >> r->s;
 	*vl &= ((1 << r->s) - 1);
 	run(r->iv + r->in, il + r->in, vl, z);
-#ifdef DEBUG
-	MP_PRINTX("x", x);
-	mp_div(0, &_rr, x, r->p);
-	assert(MP_EQ(_r, _rr));
-#endif
       }
     }
   }
@@ -446,17 +405,12 @@ mp *mpreduce_do(mpreduce *r, mp *d, mp *x)
 
   /* --- Done --- */
 
-#ifdef DEBUG
-  assert(MP_EQ(_r, x));
-  mp_drop(_r);
-  mp_drop(_rr);
-#endif
   return (x);
 }
 
 /* --- @mpreduce_exp@ --- *
  *
- * Arguments:	@mpreduce *mr@ = pointer to reduction context
+ * Arguments:	@const mpreduce *mr@ = pointer to reduction context
  *		@mp *d@ = fake destination
  *		@mp *a@ = base
  *		@mp *e@ = exponent
@@ -464,7 +418,7 @@ mp *mpreduce_do(mpreduce *r, mp *d, mp *x)
  * Returns:	Result, %$a^e \bmod m$%.
  */
 
-mp *mpreduce_exp(mpreduce *mr, mp *d, mp *a, mp *e)
+mp *mpreduce_exp(const mpreduce *mr, mp *d, mp *a, mp *e)
 {
   mp *x = MP_ONE;
   mp *spare = (e->f & MP_BURN) ? MP_NEWSEC : MP_NEW;
@@ -489,11 +443,8 @@ mp *mpreduce_exp(mpreduce *mr, mp *d, mp *a, mp *e)
 
 /*----- Test rig ----------------------------------------------------------*/
 
-
 #ifdef TEST_RIG
 
-#define MP(x) mp_readstring(MP_NEW, #x, 0, 0)
-
 static int vreduce(dstr *v)
 {
   mp *d = *(mp **)v[0].buf;