crosstool-ng/patches/mpfr/3.1.3/200-can_round.patch

diff -Naurd mpfr-3.1.3-a/PATCHES mpfr-3.1.3-b/PATCHES
--- mpfr-3.1.3-a/PATCHES	2016-02-15 15:19:24.210647274 +0000
+++ mpfr-3.1.3-b/PATCHES	2016-02-15 15:19:24.274647313 +0000
@@ -0,0 +1 @@
+can_round
diff -Naurd mpfr-3.1.3-a/VERSION mpfr-3.1.3-b/VERSION
--- mpfr-3.1.3-a/VERSION	2016-02-15 15:17:39.282577552 +0000
+++ mpfr-3.1.3-b/VERSION	2016-02-15 15:19:24.274647313 +0000
@@ -1 +1 @@
-3.1.3-p9
+3.1.3-p10
diff -Naurd mpfr-3.1.3-a/src/div.c mpfr-3.1.3-b/src/div.c
--- mpfr-3.1.3-a/src/div.c	2015-06-19 19:55:09.000000000 +0000
+++ mpfr-3.1.3-b/src/div.c	2016-02-15 15:19:24.250647299 +0000
@@ -310,24 +310,23 @@
 
       qp = MPFR_TMP_LIMBS_ALLOC (n);
       qh = mpfr_divhigh_n (qp, ap, bp, n);
+      MPFR_ASSERTD (qh == 0 || qh == 1);
       /* in all cases, the error is at most (2n+2) ulps on qh*B^n+{qp,n},
          cf algorithms.tex */
 
       p = n * GMP_NUMB_BITS - MPFR_INT_CEIL_LOG2 (2 * n + 2);
-      /* if qh is 1, then we need only PREC(q)-1 bits of {qp,n},
-         if rnd=RNDN, we need to be able to round with a directed rounding
-            and one more bit */
+      /* If rnd=RNDN, we need to be able to round with a directed rounding
+         and one more bit. */
+      if (qh == 1)
+        {
+          mpn_rshift (qp, qp, n, 1);
+          qp[n - 1] |= MPFR_LIMB_HIGHBIT;
+        }
       if (MPFR_LIKELY (mpfr_round_p (qp, n, p,
-                                 MPFR_PREC(q) + (rnd_mode == MPFR_RNDN) - qh)))
+                                     MPFR_PREC(q) + (rnd_mode == MPFR_RNDN))))
         {
           /* we can round correctly whatever the rounding mode */
-          if (qh == 0)
-            MPN_COPY (q0p, qp + 1, q0size);
-          else
-            {
-              mpn_rshift (q0p, qp + 1, q0size, 1);
-              q0p[q0size - 1] ^= MPFR_LIMB_HIGHBIT;
-            }
+          MPN_COPY (q0p, qp + 1, q0size);
           q0p[0] &= ~MPFR_LIMB_MASK(sh); /* put to zero low sh bits */
 
           if (rnd_mode == MPFR_RNDN) /* round to nearest */
@@ -335,15 +334,10 @@
               /* we know we can round, thus we are never in the even rule case:
                  if the round bit is 0, we truncate
                  if the round bit is 1, we add 1 */
-              if (qh == 0)
-                {
-                  if (sh > 0)
-                    round_bit = (qp[1] >> (sh - 1)) & 1;
-                  else
-                    round_bit = qp[0] >> (GMP_NUMB_BITS - 1);
-                }
-              else /* qh = 1 */
-                round_bit = (qp[1] >> sh) & 1;
+              if (sh > 0)
+                round_bit = (qp[1] >> (sh - 1)) & 1;
+              else
+                round_bit = qp[0] >> (GMP_NUMB_BITS - 1);
               if (round_bit == 0)
                 {
                   inex = -1;
diff -Naurd mpfr-3.1.3-a/src/mpfr.h mpfr-3.1.3-b/src/mpfr.h
--- mpfr-3.1.3-a/src/mpfr.h	2016-02-15 15:17:39.282577552 +0000
+++ mpfr-3.1.3-b/src/mpfr.h	2016-02-15 15:19:24.270647311 +0000
@@ -27,7 +27,7 @@
 #define MPFR_VERSION_MAJOR 3
 #define MPFR_VERSION_MINOR 1
 #define MPFR_VERSION_PATCHLEVEL 3
-#define MPFR_VERSION_STRING "3.1.3-p9"
+#define MPFR_VERSION_STRING "3.1.3-p10"
 
 /* Macros dealing with MPFR VERSION */
 #define MPFR_VERSION_NUM(a,b,c) (((a) << 16L) | ((b) << 8) | (c))
diff -Naurd mpfr-3.1.3-a/src/round_p.c mpfr-3.1.3-b/src/round_p.c
--- mpfr-3.1.3-a/src/round_p.c	2015-06-19 19:55:09.000000000 +0000
+++ mpfr-3.1.3-b/src/round_p.c	2016-02-15 15:19:24.250647299 +0000
@@ -31,7 +31,11 @@
 {
   int i1, i2;
 
+  MPFR_ASSERTN(bp[bn - 1] & MPFR_LIMB_HIGHBIT);
+
   i1 = mpfr_round_p_2 (bp, bn, err0, prec);
+
+  /* compare with mpfr_can_round_raw */
   i2 = mpfr_can_round_raw (bp, bn, MPFR_SIGN_POS, err0,
                            MPFR_RNDN, MPFR_RNDZ, prec);
   if (i1 != i2)
@@ -42,6 +46,7 @@
       gmp_fprintf (stderr, "%NX\n", bp, bn);
       MPFR_ASSERTN (0);
     }
+
   return i1;
 }
 # define mpfr_round_p mpfr_round_p_2
@@ -62,6 +67,8 @@
   mp_limb_t tmp, mask;
   int s;
 
+  MPFR_ASSERTD(bp[bn - 1] & MPFR_LIMB_HIGHBIT);
+
   err = (mpfr_prec_t) bn * GMP_NUMB_BITS;
   if (MPFR_UNLIKELY (err0 <= 0 || (mpfr_uexp_t) err0 <= prec || prec >= err))
     return 0;  /* can't round */
diff -Naurd mpfr-3.1.3-a/src/round_prec.c mpfr-3.1.3-b/src/round_prec.c
--- mpfr-3.1.3-a/src/round_prec.c	2015-06-19 19:55:10.000000000 +0000
+++ mpfr-3.1.3-b/src/round_prec.c	2016-02-15 15:19:24.250647299 +0000
@@ -141,24 +141,40 @@
 mpfr_can_round_raw (const mp_limb_t *bp, mp_size_t bn, int neg, mpfr_exp_t err0,
                     mpfr_rnd_t rnd1, mpfr_rnd_t rnd2, mpfr_prec_t prec)
 {
-  mpfr_prec_t err;
+  mpfr_prec_t err, prec0 = prec;
   mp_size_t k, k1, tn;
   int s, s1;
   mp_limb_t cc, cc2;
   mp_limb_t *tmp;
   MPFR_TMP_DECL(marker);
 
+  MPFR_ASSERTD(bp[bn - 1] & MPFR_LIMB_HIGHBIT);
+
   if (MPFR_UNLIKELY(err0 < 0 || (mpfr_uexp_t) err0 <= prec))
     return 0;  /* can't round */
-  else if (MPFR_UNLIKELY (prec > (mpfr_prec_t) bn * GMP_NUMB_BITS))
-    { /* then ulp(b) < precision < error */
-      return rnd2 == MPFR_RNDN && (mpfr_uexp_t) err0 - 2 >= prec;
-      /* can round only in rounding to the nearest and err0 >= prec + 2 */
-    }
 
   MPFR_ASSERT_SIGN(neg);
   neg = MPFR_IS_NEG_SIGN(neg);
 
+  /* Transform RNDD and RNDU to Zero / Away */
+  MPFR_ASSERTD((neg == 0) || (neg == 1));
+  if (rnd1 != MPFR_RNDN)
+    rnd1 = MPFR_IS_LIKE_RNDZ(rnd1, neg) ? MPFR_RNDZ : MPFR_RNDA;
+  if (rnd2 != MPFR_RNDN)
+    rnd2 = MPFR_IS_LIKE_RNDZ(rnd2, neg) ? MPFR_RNDZ : MPFR_RNDA;
+
+  if (MPFR_UNLIKELY (prec > (mpfr_prec_t) bn * GMP_NUMB_BITS))
+    { /* Then prec < PREC(b): we can round:
+         (i) in rounding to the nearest iff err0 >= prec + 2
+         (ii) in directed rounding mode iff rnd1 is compatible with rnd2
+              and err0 >= prec + 1, unless b = 2^k and rnd1=rnd2=RNDA in
+              which case we need err0 >= prec + 2. */
+      if (rnd2 == MPFR_RNDN)
+        return (mpfr_uexp_t) err0 - 2 >= prec;
+      else
+        return (rnd1 == rnd2) && (mpfr_uexp_t) err0 - 2 >= prec;
+    }
+
   /* if the error is smaller than ulp(b), then anyway it will propagate
      up to ulp(b) */
   err = ((mpfr_uexp_t) err0 > (mpfr_prec_t) bn * GMP_NUMB_BITS) ?
@@ -168,19 +184,25 @@
   k = (err - 1) / GMP_NUMB_BITS;
   MPFR_UNSIGNED_MINUS_MODULO(s, err);
   /* the error corresponds to bit s in limb k, the most significant limb
-     being limb 0 */
+     being limb 0; in memory, limb k is bp[bn-1-k]. */
 
   k1 = (prec - 1) / GMP_NUMB_BITS;
   MPFR_UNSIGNED_MINUS_MODULO(s1, prec);
-  /* the last significant bit is bit s1 in limb k1 */
+  /* the least significant bit is bit s1 in limb k1 */
 
-  /* don't need to consider the k1 most significant limbs */
+  /* We don't need to consider the k1 most significant limbs.
+     They will be considered later only to detect when subtracting
+     the error bound yields a change of binade.
+     Warning! The number with updated bn may no longer be normalized. */
   k -= k1;
   bn -= k1;
   prec -= (mpfr_prec_t) k1 * GMP_NUMB_BITS;
 
-  /* if when adding or subtracting (1 << s) in bp[bn-1-k], it does not
-     change bp[bn-1] >> s1, then we can round */
+  /* We can decide of the correct rounding if rnd2(b-eps) and rnd2(b+eps)
+     give the same result to the target precision 'prec', i.e., if when
+     adding or subtracting (1 << s) in bp[bn-1-k], it does not change the
+     rounding in direction 'rnd2' at ulp-position bp[bn-1] >> s1, taking also
+     into account the possible change of binade. */
   MPFR_TMP_MARK(marker);
   tn = bn;
   k++; /* since we work with k+1 everywhere */
@@ -190,11 +212,6 @@
 
   MPFR_ASSERTD (k > 0);
 
-  /* Transform RNDD and RNDU to Zero / Away */
-  MPFR_ASSERTD((neg == 0) || (neg ==1));
-  if (MPFR_IS_RNDUTEST_OR_RNDDNOTTEST(rnd1, neg))
-    rnd1 = MPFR_RNDZ;
-
   switch (rnd1)
     {
     case MPFR_RNDZ:
@@ -203,33 +220,54 @@
       /* mpfr_round_raw2 returns 1 if one should add 1 at ulp(b,prec),
          and 0 otherwise */
       cc ^= mpfr_round_raw2 (bp, bn, neg, rnd2, prec);
-      /* cc is the new value of bit s1 in bp[bn-1] */
+      /* cc is the new value of bit s1 in bp[bn-1] after rounding 'rnd2' */
+
       /* now round b + 2^(MPFR_EXP(b)-err) */
-      cc2 = mpn_add_1 (tmp + bn - k, bp + bn - k, k, MPFR_LIMB_ONE << s);
+      mpn_add_1 (tmp + bn - k, bp + bn - k, k, MPFR_LIMB_ONE << s);
+      /* if there was a carry here, then necessarily bit s1 of bp[bn-1]
+         changed, thus we surely cannot round for directed rounding, but this
+         will be detected below, with cc2 != cc */
       break;
     case MPFR_RNDN:
       /* Round to nearest */
-       /* first round b+2^(MPFR_EXP(b)-err) */
-      cc = mpn_add_1 (tmp + bn - k, bp + bn - k, k, MPFR_LIMB_ONE << s);
+
+      /* first round b+2^(MPFR_EXP(b)-err) */
+      mpn_add_1 (tmp + bn - k, bp + bn - k, k, MPFR_LIMB_ONE << s);
+      /* same remark as above in case a carry occurs in mpn_add_1() */
       cc = (tmp[bn - 1] >> s1) & 1; /* gives 0 when cc=1 */
       cc ^= mpfr_round_raw2 (tmp, bn, neg, rnd2, prec);
+      /* cc is the new value of bit s1 in bp[bn-1]+eps after rounding 'rnd2' */
+
+    subtract_eps:
       /* now round b-2^(MPFR_EXP(b)-err) */
       cc2 = mpn_sub_1 (tmp + bn - k, bp + bn - k, k, MPFR_LIMB_ONE << s);
+      /* propagate the potential borrow up to the most significant limb
+         (it cannot propagate further since the most significant limb is
+         at least MPFR_LIMB_HIGHBIT) */
+      for (tn = 0; tn + 1 < k1 && (cc2 != 0); tn ++)
+        cc2 = bp[bn + tn] == 0;
+      /* We have an exponent decrease when either:
+           (i) k1 = 0 and tmp[bn-1] < MPFR_LIMB_HIGHBIT
+           (ii) k1 > 0 and cc <> 0 and bp[bn + tn] = MPFR_LIMB_HIGHBIT
+                (then necessarily tn = k1-1).
+         Then for directed rounding we cannot round,
+         and for rounding to nearest we cannot round when err = prec + 1.
+      */
+      if (((k1 == 0 && tmp[bn - 1] < MPFR_LIMB_HIGHBIT) ||
+           (k1 != 0 && cc2 != 0 && bp[bn + tn] == MPFR_LIMB_HIGHBIT)) &&
+          (rnd2 != MPFR_RNDN || err0 == prec0 + 1))
+        {
+          MPFR_TMP_FREE(marker);
+          return 0;
+        }
       break;
     default:
       /* Round away */
       cc = (bp[bn - 1] >> s1) & 1;
       cc ^= mpfr_round_raw2 (bp, bn, neg, rnd2, prec);
-      /* now round b +/- 2^(MPFR_EXP(b)-err) */
-      cc2 = mpn_sub_1 (tmp + bn - k, bp + bn - k, k, MPFR_LIMB_ONE << s);
-      break;
-    }
+      /* cc is the new value of bit s1 in bp[bn-1]+eps after rounding 'rnd2' */
 
-  /* if cc2 is 1, then a carry or borrow propagates to the next limb */
-  if (cc2 && cc)
-    {
-      MPFR_TMP_FREE(marker);
-      return 0;
+      goto subtract_eps;
     }
 
   cc2 = (tmp[bn - 1] >> s1) & 1;
diff -Naurd mpfr-3.1.3-a/src/version.c mpfr-3.1.3-b/src/version.c
--- mpfr-3.1.3-a/src/version.c	2016-02-15 15:17:39.282577552 +0000
+++ mpfr-3.1.3-b/src/version.c	2016-02-15 15:19:24.274647313 +0000
@@ -25,5 +25,5 @@
 const char *
 mpfr_get_version (void)
 {
-  return "3.1.3-p9";
+  return "3.1.3-p10";
 }
diff -Naurd mpfr-3.1.3-a/tests/tcan_round.c mpfr-3.1.3-b/tests/tcan_round.c
--- mpfr-3.1.3-a/tests/tcan_round.c	2015-06-19 19:55:10.000000000 +0000
+++ mpfr-3.1.3-b/tests/tcan_round.c	2016-02-15 15:19:24.250647299 +0000
@@ -1,4 +1,4 @@
-/* Test file for mpfr_can_round.
+/* Test file for mpfr_can_round and mpfr_round_p.
 
 Copyright 1999, 2001-2015 Free Software Foundation, Inc.
 Contributed by the AriC and Caramel projects, INRIA.
@@ -41,6 +41,8 @@
       /* avoid mpn_random which leaks memory */
       for (i = 0; i < n; i++)
         buf[i] = randlimb ();
+      /* force the number to be normalized */
+      buf[n - 1] |= MPFR_LIMB_HIGHBIT;
       p = randlimb() % ((n-1) * GMP_NUMB_BITS) + MPFR_PREC_MIN;
       err = p + randlimb () % GMP_NUMB_BITS;
       r1 = mpfr_round_p (buf, n, err, p);
@@ -57,11 +59,72 @@
     }
 }
 
+/* check x=2^i with precision px, error at most 1, and target precision prec */
+static void
+test_pow2 (mpfr_exp_t i, mpfr_prec_t px, mpfr_rnd_t r1, mpfr_rnd_t r2,
+           mpfr_prec_t prec)
+{
+  mpfr_t x;
+  int b, expected_b, b2;
+
+  mpfr_init2 (x, px);
+  mpfr_set_ui_2exp (x, 1, i, MPFR_RNDN);
+  b = !!mpfr_can_round (x, i+1, r1, r2, prec);
+  /* Note: If mpfr_can_round succeeds for both
+     (r1,r2) = (MPFR_RNDD,MPFR_RNDN) and
+     (r1,r2) = (MPFR_RNDU,MPFR_RNDN), then it should succeed for
+     (r1,r2) = (MPFR_RNDN,MPFR_RNDN). So, the condition on prec below
+     for r1 = MPFR_RNDN should be the most restrictive between those
+     for r1 = any directed rounding mode.
+     For r1 like MPFR_RNDA, the unrounded, unknown number may be anyone
+     in [2^i-1,i]. As both 2^i-1 and 2^i fit on i bits, one cannot round
+     in any precision >= i bits, hence the condition prec < i; prec = i-1
+     will work here for r2 = MPFR_RNDN thanks to the even-rounding rule
+     (and also with rounding ties away from zero). */
+  expected_b =
+    MPFR_IS_LIKE_RNDD (r1, MPFR_SIGN_POS) ?
+    (MPFR_IS_LIKE_RNDU (r2, MPFR_SIGN_POS) ? 0 : prec <= i) :
+    MPFR_IS_LIKE_RNDU (r1, MPFR_SIGN_POS) ?
+    (MPFR_IS_LIKE_RNDD (r2, MPFR_SIGN_POS) ? 0 : prec < i) :
+    (r2 != MPFR_RNDN ? 0 : prec < i);
+  /* We only require mpfr_can_round to return 1 when we can really
+     round, it is allowed to return 0 in some rare boundary cases,
+     for example when x = 2^k and the error is 0.25 ulp.
+     Note: if this changes in the future, the test could be improved by
+     removing the "&& expected_b == 0" below. */
+  if (b != expected_b && expected_b == 0)
+    {
+      printf ("Error for x=2^%d, px=%lu, err=%d, r1=%s, r2=%s, prec=%d\n",
+              (int) i, (unsigned long) px, (int) i + 1,
+              mpfr_print_rnd_mode (r1), mpfr_print_rnd_mode (r2), (int) prec);
+      printf ("Expected %d, got %d\n", expected_b, b);
+      exit (1);
+    }
+
+  if (r1 == MPFR_RNDN && r2 == MPFR_RNDZ)
+    {
+      /* Similar test to the one done in src/round_p.c
+         for MPFR_WANT_ASSERT >= 2. */
+      b2 = !!mpfr_round_p (MPFR_MANT(x), MPFR_LIMB_SIZE(x), i+1, prec);
+      if (b2 != b)
+        {
+          printf ("Error for x=2^%d, px=%lu, err=%d, prec=%d\n",
+                  (int) i, (unsigned long) px, (int) i + 1, (int) prec);
+          printf ("mpfr_can_round gave %d, mpfr_round_p gave %d\n", b, b2);
+          exit (1);
+        }
+    }
+
+  mpfr_clear (x);
+}
+
 int
 main (void)
 {
   mpfr_t x;
-  mpfr_prec_t i, j;
+  mpfr_prec_t i, j, k;
+  int r1, r2;
+  int n;
 
   tests_start_mpfr ();
 
@@ -111,12 +174,30 @@
   mpfr_set_str (x, "0.ff4ca619c76ba69", 16, MPFR_RNDZ);
   for (i = 30; i < 99; i++)
     for (j = 30; j < 99; j++)
-      {
-        int r1, r2;
-        for (r1 = 0; r1 < MPFR_RND_MAX ; r1++)
-          for (r2 = 0; r2 < MPFR_RND_MAX ; r2++)
-            mpfr_can_round (x, i, (mpfr_rnd_t) r1, (mpfr_rnd_t) r2, j); /* test for assertions */
-      }
+      for (r1 = 0; r1 < MPFR_RND_MAX; r1++)
+        for (r2 = 0; r2 < MPFR_RND_MAX; r2++)
+          {
+            /* test for assertions */
+            mpfr_can_round (x, i, (mpfr_rnd_t) r1, (mpfr_rnd_t) r2, j);
+          }
+
+  test_pow2 (32, 32, MPFR_RNDN, MPFR_RNDN, 32);
+  test_pow2 (174, 174, MPFR_RNDN, MPFR_RNDN, 174);
+  test_pow2 (174, 174, MPFR_RNDU, MPFR_RNDN, 174);
+  test_pow2 (176, 129, MPFR_RNDU, MPFR_RNDU, 174);
+  test_pow2 (176, 2, MPFR_RNDZ, MPFR_RNDZ, 174);
+  test_pow2 (176, 2, MPFR_RNDU, MPFR_RNDU, 176);
+
+  /* Tests for x = 2^i (E(x) = i+1) with error at most 1 = 2^0. */
+  for (n = 0; n < 100; n++)
+    {
+      i = (randlimb() % 200) + 4;
+      for (j = i - 2; j < i + 2; j++)
+        for (r1 = 0; r1 < MPFR_RND_MAX; r1++)
+          for (r2 = 0; r2 < MPFR_RND_MAX; r2++)
+            for (k = MPFR_PREC_MIN; k <= i + 2; k++)
+              test_pow2 (i, k, (mpfr_rnd_t) r1, (mpfr_rnd_t) r2, j);
+    }
 
   mpfr_clear (x);