crosstool-ng/patches/mpfr/3.1.0/200-gamma-overunderflow.patch

diff -Naurd mpfr-3.1.0-a/PATCHES mpfr-3.1.0-b/PATCHES
--- mpfr-3.1.0-a/PATCHES	2012-05-07 18:52:45.000000000 +0000
+++ mpfr-3.1.0-b/PATCHES	2012-05-07 18:52:45.000000000 +0000
@@ -0,0 +1 @@
+gamma-overunderflow
diff -Naurd mpfr-3.1.0-a/VERSION mpfr-3.1.0-b/VERSION
--- mpfr-3.1.0-a/VERSION	2012-04-27 01:13:15.000000000 +0000
+++ mpfr-3.1.0-b/VERSION	2012-05-07 18:52:45.000000000 +0000
@@ -1 +1 @@
-3.1.0-p9
+3.1.0-p10
diff -Naurd mpfr-3.1.0-a/src/gamma.c mpfr-3.1.0-b/src/gamma.c
--- mpfr-3.1.0-a/src/gamma.c	2012-04-27 01:13:15.000000000 +0000
+++ mpfr-3.1.0-b/src/gamma.c	2012-05-07 18:52:45.000000000 +0000
@@ -100,7 +100,8 @@
   mpfr_t xp, GammaTrial, tmp, tmp2;
   mpz_t fact;
   mpfr_prec_t realprec;
-  int compared, inex, is_integer;
+  int compared, is_integer;
+  int inex = 0;  /* 0 means: result gamma not set yet */
   MPFR_GROUP_DECL (group);
   MPFR_SAVE_EXPO_DECL (expo);
   MPFR_ZIV_DECL (loop);
@@ -377,6 +378,15 @@
       mpfr_mul (GammaTrial, tmp2, xp, MPFR_RNDN); /* Pi*(2-x), error (1+u)^2 */
       err_g = MPFR_GET_EXP(GammaTrial);
       mpfr_sin (GammaTrial, GammaTrial, MPFR_RNDN); /* sin(Pi*(2-x)) */
+      /* If tmp is +Inf, we compute exp(lngamma(x)). */
+      if (mpfr_inf_p (tmp))
+        {
+          inex = mpfr_explgamma (gamma, x, &expo, tmp, tmp2, rnd_mode);
+          if (inex)
+            goto end;
+          else
+            goto ziv_next;
+        }
       err_g = err_g + 1 - MPFR_GET_EXP(GammaTrial);
       /* let g0 the true value of Pi*(2-x), g the computed value.
          We have g = g0 + h with |h| <= |(1+u^2)-1|*g.
@@ -411,11 +421,16 @@
       if (MPFR_LIKELY (MPFR_CAN_ROUND (GammaTrial, realprec - err_g,
                                        MPFR_PREC(gamma), rnd_mode)))
         break;
+
+    ziv_next:
       MPFR_ZIV_NEXT (loop, realprec);
     }
+
+ end:
   MPFR_ZIV_FREE (loop);
 
-  inex = mpfr_set (gamma, GammaTrial, rnd_mode);
+  if (inex == 0)
+    inex = mpfr_set (gamma, GammaTrial, rnd_mode);
   MPFR_GROUP_CLEAR (group);
   mpz_clear (fact);
 
diff -Naurd mpfr-3.1.0-a/src/lngamma.c mpfr-3.1.0-b/src/lngamma.c
--- mpfr-3.1.0-a/src/lngamma.c	2012-03-08 15:17:03.000000000 +0000
+++ mpfr-3.1.0-b/src/lngamma.c	2012-05-07 18:52:45.000000000 +0000
@@ -49,9 +49,72 @@
     mpfr_set_ui_2exp (s, 9, -1, MPFR_RNDN); /* 4.5 */
 }
 
-#ifndef IS_GAMMA
+#ifdef IS_GAMMA
+
+/* This function is called in case of intermediate overflow/underflow.
+   The s1 and s2 arguments are temporary MPFR numbers, having the
+   working precision. If the result could be determined, then the
+   flags are updated via pexpo, y is set to the result, and the
+   (non-zero) ternary value is returned. Otherwise 0 is returned
+   in order to perform the next Ziv iteration. */
 static int
-unit_bit (mpfr_srcptr (x))
+mpfr_explgamma (mpfr_ptr y, mpfr_srcptr x, mpfr_save_expo_t *pexpo,
+                mpfr_ptr s1, mpfr_ptr s2, mpfr_rnd_t rnd)
+{
+  mpfr_t t1, t2;
+  int inex1, inex2, sign;
+  MPFR_BLOCK_DECL (flags1);
+  MPFR_BLOCK_DECL (flags2);
+  MPFR_GROUP_DECL (group);
+
+  MPFR_BLOCK (flags1, inex1 = mpfr_lgamma (s1, &sign, x, MPFR_RNDD));
+  MPFR_ASSERTN (inex1 != 0);
+  /* s1 = RNDD(lngamma(x)), inexact */
+  if (MPFR_UNLIKELY (MPFR_OVERFLOW (flags1)))
+    {
+      if (MPFR_SIGN (s1) > 0)
+        {
+          MPFR_SAVE_EXPO_UPDATE_FLAGS (*pexpo, MPFR_FLAGS_OVERFLOW);
+          return mpfr_overflow (y, rnd, sign);
+        }
+      else
+        {
+          MPFR_SAVE_EXPO_UPDATE_FLAGS (*pexpo, MPFR_FLAGS_UNDERFLOW);
+          return mpfr_underflow (y, rnd == MPFR_RNDN ? MPFR_RNDZ : rnd, sign);
+        }
+    }
+
+  mpfr_set (s2, s1, MPFR_RNDN);     /* exact */
+  mpfr_nextabove (s2);              /* v = RNDU(lngamma(z0)) */
+
+  if (sign < 0)
+    rnd = MPFR_INVERT_RND (rnd);  /* since the result with be negated */
+  MPFR_GROUP_INIT_2 (group, MPFR_PREC (y), t1, t2);
+  MPFR_BLOCK (flags1, inex1 = mpfr_exp (t1, s1, rnd));
+  MPFR_BLOCK (flags2, inex2 = mpfr_exp (t2, s2, rnd));
+  /* t1 is the rounding with mode 'rnd' of a lower bound on |Gamma(x)|,
+     t2 is the rounding with mode 'rnd' of an upper bound, thus if both
+     are equal, so is the wanted result. If t1 and t2 differ or the flags
+     differ, at some point of Ziv's loop they should agree. */
+  if (mpfr_equal_p (t1, t2) && flags1 == flags2)
+    {
+      MPFR_ASSERTN ((inex1 > 0 && inex2 > 0) || (inex1 < 0 && inex2 < 0));
+      mpfr_set4 (y, t1, MPFR_RNDN, sign);  /* exact */
+      if (sign < 0)
+        inex1 = - inex1;
+      MPFR_SAVE_EXPO_UPDATE_FLAGS (*pexpo, flags1);
+    }
+  else
+    inex1 = 0;  /* couldn't determine the result */
+  MPFR_GROUP_CLEAR (group);
+
+  return inex1;
+}
+
+#else
+
+static int
+unit_bit (mpfr_srcptr x)
 {
   mpfr_exp_t expo;
   mpfr_prec_t prec;
@@ -75,6 +138,7 @@
 
   return (x0 >> (prec % GMP_NUMB_BITS)) & 1;
 }
+
 #endif
 
 /* lngamma(x) = log(gamma(x)).
@@ -99,12 +163,14 @@
   mpfr_t s, t, u, v, z;
   unsigned long m, k, maxm;
   mpz_t *INITIALIZED(B);  /* variable B declared as initialized */
-  int inexact, compared;
+  int compared;
+  int inexact = 0;  /* 0 means: result y not set yet */
   mpfr_exp_t err_s, err_t;
   unsigned long Bm = 0; /* number of allocated B[] */
   unsigned long oldBm;
   double d;
   MPFR_SAVE_EXPO_DECL (expo);
+  MPFR_ZIV_DECL (loop);
 
   compared = mpfr_cmp_ui (z0, 1);
 
@@ -122,7 +188,7 @@
   if (MPFR_EXP(z0) <= - (mpfr_exp_t) MPFR_PREC(y))
     {
       mpfr_t l, h, g;
-      int ok, inex2;
+      int ok, inex1, inex2;
       mpfr_prec_t prec = MPFR_PREC(y) + 14;
       MPFR_ZIV_DECL (loop);
 
@@ -157,14 +223,14 @@
           mpfr_sub (h, h, g, MPFR_RNDD);
           mpfr_mul (g, z0, z0, MPFR_RNDU);
           mpfr_add (h, h, g, MPFR_RNDU);
-          inexact = mpfr_prec_round (l, MPFR_PREC(y), rnd);
+          inex1 = mpfr_prec_round (l, MPFR_PREC(y), rnd);
           inex2 = mpfr_prec_round (h, MPFR_PREC(y), rnd);
           /* Caution: we not only need l = h, but both inexact flags should
              agree. Indeed, one of the inexact flags might be zero. In that
              case if we assume lngamma(z0) cannot be exact, the other flag
              should be correct. We are conservative here and request that both
              inexact flags agree. */
-          ok = SAME_SIGN (inexact, inex2) && mpfr_cmp (l, h) == 0;
+          ok = SAME_SIGN (inex1, inex2) && mpfr_cmp (l, h) == 0;
           if (ok)
             mpfr_set (y, h, rnd); /* exact */
           mpfr_clear (l);
@@ -172,8 +238,9 @@
           mpfr_clear (g);
           if (ok)
             {
+              MPFR_ZIV_FREE (loop);
               MPFR_SAVE_EXPO_FREE (expo);
-              return mpfr_check_range (y, inexact, rnd);
+              return mpfr_check_range (y, inex1, rnd);
             }
           /* since we have log|gamma(x)| = - log|x| - gamma*x + O(x^2),
              if x ~ 2^(-n), then we have a n-bit approximation, thus
@@ -205,9 +272,10 @@
          thus lngamma(x) = log(Pi*(x-1)/sin(Pi*(2-x))) - lngamma(2-x) */
 
       w = precy + MPFR_INT_CEIL_LOG2 (precy);
+      w += MPFR_INT_CEIL_LOG2 (w) + 14;
+      MPFR_ZIV_INIT (loop, w);
       while (1)
         {
-          w += MPFR_INT_CEIL_LOG2 (w) + 14;
           MPFR_ASSERTD(w >= 3);
           mpfr_set_prec (s, w);
           mpfr_set_prec (t, w);
@@ -288,7 +356,9 @@
                                   + (rnd == MPFR_RNDN)))
                 goto end;
             }
+          MPFR_ZIV_NEXT (loop, w);
         }
+      MPFR_ZIV_FREE (loop);
     }
 
   /* now z0 > 1 */
@@ -298,10 +368,10 @@
   /* since k is O(w), the value of log(z0*...*(z0+k-1)) is about w*log(w),
      so there is a cancellation of ~log(w) in the argument reconstruction */
   w = precy + MPFR_INT_CEIL_LOG2 (precy);
-
-  do
+  w += MPFR_INT_CEIL_LOG2 (w) + 13;
+  MPFR_ZIV_INIT (loop, w);
+  while (1)
     {
-      w += MPFR_INT_CEIL_LOG2 (w) + 13;
       MPFR_ASSERTD (w >= 3);
 
       /* argument reduction: we compute gamma(z0 + k), where the series
@@ -441,6 +511,15 @@
 #ifdef IS_GAMMA
       err_s = MPFR_GET_EXP(s);
       mpfr_exp (s, s, MPFR_RNDN);
+      /* If s is +Inf, we compute exp(lngamma(z0)). */
+      if (mpfr_inf_p (s))
+        {
+          inexact = mpfr_explgamma (y, z0, &expo, s, t, rnd);
+          if (inexact)
+            goto end0;
+          else
+            goto ziv_next;
+        }
       /* before the exponential, we have s = s0 + h where
          |h| <= (2m+48)*ulp(s), thus exp(s0) = exp(s) * exp(-h).
          For |h| <= 1/4, we have |exp(h)-1| <= 1.2*|h| thus
@@ -480,16 +559,26 @@
       err_s = (err_t == err_s) ? 1 + err_s : ((err_t > err_s) ? err_t : err_s);
       err_s += 1 - MPFR_GET_EXP(s);
 #endif
+      if (MPFR_LIKELY (MPFR_CAN_ROUND (s, w - err_s, precy, rnd)))
+        break;
+#ifdef IS_GAMMA
+    ziv_next:
+#endif
+      MPFR_ZIV_NEXT (loop, w);
     }
-  while (MPFR_UNLIKELY (!MPFR_CAN_ROUND (s, w - err_s, precy, rnd)));
 
+#ifdef IS_GAMMA
+ end0:
+#endif
   oldBm = Bm;
   while (Bm--)
     mpz_clear (B[Bm]);
   (*__gmp_free_func) (B, oldBm * sizeof (mpz_t));
 
  end:
-  inexact = mpfr_set (y, s, rnd);
+  if (inexact == 0)
+    inexact = mpfr_set (y, s, rnd);
+  MPFR_ZIV_FREE (loop);
 
   mpfr_clear (s);
   mpfr_clear (t);
diff -Naurd mpfr-3.1.0-a/src/mpfr.h mpfr-3.1.0-b/src/mpfr.h
--- mpfr-3.1.0-a/src/mpfr.h	2012-04-27 01:13:15.000000000 +0000
+++ mpfr-3.1.0-b/src/mpfr.h	2012-05-07 18:52:45.000000000 +0000
@@ -27,7 +27,7 @@
 #define MPFR_VERSION_MAJOR 3
 #define MPFR_VERSION_MINOR 1
 #define MPFR_VERSION_PATCHLEVEL 0
-#define MPFR_VERSION_STRING "3.1.0-p9"
+#define MPFR_VERSION_STRING "3.1.0-p10"
 
 /* Macros dealing with MPFR VERSION */
 #define MPFR_VERSION_NUM(a,b,c) (((a) << 16L) | ((b) << 8) | (c))
diff -Naurd mpfr-3.1.0-a/src/version.c mpfr-3.1.0-b/src/version.c
--- mpfr-3.1.0-a/src/version.c	2012-04-27 01:13:15.000000000 +0000
+++ mpfr-3.1.0-b/src/version.c	2012-05-07 18:52:45.000000000 +0000
@@ -25,5 +25,5 @@
 const char *
 mpfr_get_version (void)
 {
-  return "3.1.0-p9";
+  return "3.1.0-p10";
 }
diff -Naurd mpfr-3.1.0-a/tests/tgamma.c mpfr-3.1.0-b/tests/tgamma.c
--- mpfr-3.1.0-a/tests/tgamma.c	2012-04-27 01:13:15.000000000 +0000
+++ mpfr-3.1.0-b/tests/tgamma.c	2012-05-07 18:52:45.000000000 +0000
@@ -838,6 +838,175 @@
     exit (1);
 }
 
+/* Test mpfr_gamma in precision p1 by comparing it with exp(lgamma(x))
+   computing with a working precision p2. Assume that x is not an
+   integer <= 2. */
+static void
+exp_lgamma (mpfr_t x, mpfr_prec_t p1, mpfr_prec_t p2)
+{
+  mpfr_t yd, yu, zd, zu;
+  int inexd, inexu, sign;
+  int underflow = -1, overflow = -1;  /* -1: we don't know */
+  int got_underflow, got_overflow;
+
+  if (mpfr_integer_p (x) && mpfr_cmp_si (x, 2) <= 0)
+    {
+      printf ("Warning! x is an integer <= 2 in exp_lgamma: ");
+      mpfr_out_str (stdout, 10, 0, x, MPFR_RNDN); putchar ('\n');
+      return;
+    }
+  mpfr_inits2 (p2, yd, yu, (mpfr_ptr) 0);
+  inexd = mpfr_lgamma (yd, &sign, x, MPFR_RNDD);
+  mpfr_set (yu, yd, MPFR_RNDN);  /* exact */
+  if (inexd)
+    mpfr_nextabove (yu);
+  mpfr_clear_flags ();
+  mpfr_exp (yd, yd, MPFR_RNDD);
+  if (! mpfr_underflow_p ())
+    underflow = 0;
+  if (mpfr_overflow_p ())
+    overflow = 1;
+  mpfr_clear_flags ();
+  mpfr_exp (yu, yu, MPFR_RNDU);
+  if (mpfr_underflow_p ())
+    underflow = 1;
+  if (! mpfr_overflow_p ())
+    overflow = 0;
+  if (sign < 0)
+    {
+      mpfr_neg (yd, yd, MPFR_RNDN);  /* exact */
+      mpfr_neg (yu, yu, MPFR_RNDN);  /* exact */
+      mpfr_swap (yd, yu);
+    }
+  /* yd < Gamma(x) < yu (strict inequalities since x != 1 and x != 2) */
+  mpfr_inits2 (p1, zd, zu, (mpfr_ptr) 0);
+  mpfr_clear_flags ();
+  inexd = mpfr_gamma (zd, x, MPFR_RNDD);  /* zd <= Gamma(x) < yu */
+  got_underflow = underflow == -1 ? -1 : !! mpfr_underflow_p ();
+  got_overflow = overflow == -1 ? -1 : !! mpfr_overflow_p ();
+  if (! mpfr_less_p (zd, yu) || inexd > 0 ||
+      got_underflow != underflow ||
+      got_overflow != overflow)
+    {
+      printf ("Error in exp_lgamma on x = ");
+      mpfr_out_str (stdout, 16, 0, x, MPFR_RNDN); putchar ('\n');
+      printf ("yu = ");
+      mpfr_dump (yu);
+      printf ("zd = ");
+      mpfr_dump (zd);
+      printf ("got inexd = %d, expected <= 0\n", inexd);
+      printf ("got underflow = %d, expected %d\n", got_underflow, underflow);
+      printf ("got overflow = %d, expected %d\n", got_overflow, overflow);
+      exit (1);
+    }
+  mpfr_clear_flags ();
+  inexu = mpfr_gamma (zu, x, MPFR_RNDU);  /* zu >= Gamma(x) > yd */
+  got_underflow = underflow == -1 ? -1 : !! mpfr_underflow_p ();
+  got_overflow = overflow == -1 ? -1 : !! mpfr_overflow_p ();
+  if (! mpfr_greater_p (zu, yd) || inexu < 0 ||
+      got_underflow != underflow ||
+      got_overflow != overflow)
+    {
+      printf ("Error in exp_lgamma on x = ");
+      mpfr_out_str (stdout, 16, 0, x, MPFR_RNDN); putchar ('\n');
+      printf ("yd = ");
+      mpfr_dump (yd);
+      printf ("zu = ");
+      mpfr_dump (zu);
+      printf ("got inexu = %d, expected >= 0\n", inexu);
+      printf ("got underflow = %d, expected %d\n", got_underflow, underflow);
+      printf ("got overflow = %d, expected %d\n", got_overflow, overflow);
+      exit (1);
+    }
+  if (mpfr_equal_p (zd, zu))
+    {
+      if (inexd != 0 || inexu != 0)
+        {
+          printf ("Error in exp_lgamma on x = ");
+          mpfr_out_str (stdout, 16, 0, x, MPFR_RNDN); putchar ('\n');
+          printf ("zd = zu, thus exact, but inexd = %d and inexu = %d\n",
+                  inexd, inexu);
+          exit (1);
+        }
+      MPFR_ASSERTN (got_underflow == 0);
+      MPFR_ASSERTN (got_overflow == 0);
+    }
+  else if (inexd == 0 || inexu == 0)
+    {
+      printf ("Error in exp_lgamma on x = ");
+          mpfr_out_str (stdout, 16, 0, x, MPFR_RNDN); putchar ('\n');
+          printf ("zd != zu, thus inexact, but inexd = %d and inexu = %d\n",
+                  inexd, inexu);
+          exit (1);
+    }
+  mpfr_clears (yd, yu, zd, zu, (mpfr_ptr) 0);
+}
+
+static void
+exp_lgamma_tests (void)
+{
+  mpfr_t x;
+  mpfr_exp_t emin, emax;
+  int i;
+
+  emin = mpfr_get_emin ();
+  emax = mpfr_get_emax ();
+  set_emin (MPFR_EMIN_MIN);
+  set_emax (MPFR_EMAX_MAX);
+
+  mpfr_init2 (x, 96);
+  for (i = 3; i <= 8; i++)
+    {
+      mpfr_set_ui (x, i, MPFR_RNDN);
+      exp_lgamma (x, 53, 64);
+      mpfr_nextbelow (x);
+      exp_lgamma (x, 53, 64);
+      mpfr_nextabove (x);
+      mpfr_nextabove (x);
+      exp_lgamma (x, 53, 64);
+    }
+  mpfr_set_str (x, "1.7", 10, MPFR_RNDN);
+  exp_lgamma (x, 53, 64);
+  mpfr_set_str (x, "-4.6308260837372266e+07", 10, MPFR_RNDN);
+  exp_lgamma (x, 53, 64);
+  mpfr_set_str (x, "-90.6308260837372266e+15", 10, MPFR_RNDN);
+  exp_lgamma (x, 53, 64);
+  /* The following test gives a large positive result < +Inf */
+  mpfr_set_str (x, "1.2b13fc45a92dea1@14", 16, MPFR_RNDN);
+  exp_lgamma (x, 53, 64);
+  /* Idem for a large negative result > -Inf */
+  mpfr_set_str (x, "-1.2b13fc45a92de81@14", 16, MPFR_RNDN);
+  exp_lgamma (x, 53, 64);
+  /* The following two tests trigger an endless loop in r8186
+     on 64-bit machines (64-bit exponent). The second one (due
+     to undetected overflow) is a direct consequence of the
+     first one, due to the call of Gamma(2-x) if x < 1. */
+  mpfr_set_str (x, "1.2b13fc45a92dec8@14", 16, MPFR_RNDN);
+  exp_lgamma (x, 53, 64);
+  mpfr_set_str (x, "-1.2b13fc45a92dea8@14", 16, MPFR_RNDN);
+  exp_lgamma (x, 53, 64);
+  /* Similar tests (overflow threshold) for 32-bit machines. */
+  mpfr_set_str (x, "2ab68d8.657542f855111c61", 16, MPFR_RNDN);
+  exp_lgamma (x, 12, 64);
+  mpfr_set_str (x, "-2ab68d6.657542f855111c61", 16, MPFR_RNDN);
+  exp_lgamma (x, 12, 64);
+  /* The following test is an overflow on 32-bit and 64-bit machines.
+     Revision r8189 fails on 64-bit machines as the flag is unset. */
+  mpfr_set_str (x, "1.2b13fc45a92ded8@14", 16, MPFR_RNDN);
+  exp_lgamma (x, 53, 64);
+  /* On the following tests, with r8196, one gets an underflow on
+     32-bit machines, while a normal result is expected (see FIXME
+     in gamma.c:382). */
+  mpfr_set_str (x, "-2ab68d6.657542f855111c6104", 16, MPFR_RNDN);
+  exp_lgamma (x, 12, 64);  /* failure on 32-bit machines */
+  mpfr_set_str (x, "-12b13fc45a92deb.1c6c5bc964", 16, MPFR_RNDN);
+  exp_lgamma (x, 12, 64);  /* failure on 64-bit machines */
+  mpfr_clear (x);
+
+  set_emin (emin);
+  set_emax (emax);
+}
+
 int
 main (int argc, char *argv[])
 {
@@ -852,6 +1021,7 @@
   test20071231 ();
   test20100709 ();
   test20120426 ();
+  exp_lgamma_tests ();
 
   data_check ("data/gamma", mpfr_gamma, "mpfr_gamma");