implemented exact rounding (but no ternary flag)

git-svn-id: svn://scm.gforge.inria.fr/svn/mpfr/trunk@1434 280ebfd0-de03-0410-8827-d642c229c3f4

1 files changed, 104 insertions, 48 deletions

diff --git a/pow.c b/pow.c
index 3032c5d72..026137632 100644
--- a/pow.c
+++ b/pow.c
@@ -25,7 +25,7 @@ MA 02111-1307, USA. */
 #include "mpfr.h"
 #include "mpfr-impl.h"
 
-/* sets x to y^n, and returns ceil(log2(max ulp error)) */
+/* sets x to y^n, and return 0 if exact, non-zero otherwise */
 int
 #if __STDC__
 mpfr_pow_ui (mpfr_ptr x, mpfr_srcptr y, unsigned long int n, mp_rnd_t rnd)
@@ -37,56 +37,82 @@ mpfr_pow_ui (x, y, n, rnd)
      mp_rnd_t rnd;
 #endif
 {
-  long int i;
+  long int i, err;
   unsigned long m;
-  double err;
-  mpfr_t ycopy;
+  mpfr_t res;
+  mp_prec_t prec;
+  int inexact;
+  mp_rnd_t rnd1;
 
-  if (MPFR_IS_NAN(y)) { MPFR_SET_NAN(x); return 0; }
+  if (MPFR_IS_NAN(y))
+    {
+      MPFR_SET_NAN(x);
+      MPFR_RET_NAN;
+    }
 
   MPFR_CLEAR_NAN(x);
 
+  if (n == 0) /* x^0 = 1 for any x */
+    {
+      mpfr_set_ui (x, 1, rnd);
+      return 0;
+    }
+
   if (MPFR_IS_INF(y)) 
     {
-      if (n == 0) { MPFR_SET_NAN(x); return 0; }
       /* Inf^n = Inf, (-Inf)^n = Inf for n even, -Inf for n odd */
-      else if ((MPFR_SIGN(y) < 0) && (n % 2 == 1)) {
-	if (MPFR_SIGN(x) > 0) MPFR_CHANGE_SIGN(x);
-      }
+      if ((MPFR_SIGN(y) < 0) && (n % 2 == 1))
+	{
+	  if (MPFR_SIGN(x) > 0)
+	    MPFR_CHANGE_SIGN(x);
+	}
       else if (MPFR_SIGN(x) < 0)
 	MPFR_CHANGE_SIGN(x);
-      MPFR_SET_INF(x); return 0; 
+      MPFR_SET_INF(x);
+      return 0;
     }
   
   MPFR_CLEAR_INF(x);
 
-  if (n==0) { mpfr_set_ui(x, 1, rnd); return 0; }
-
-  if (x == y) {
-    mpfr_init2 (ycopy, MPFR_PREC(y));
-    mpfr_set (ycopy, y, GMP_RNDN); /* exact */
-  }
-
-  mpfr_set(x, y, rnd);
-  err = 1.0;
-  for (m=n, i=0; m; i++, m>>=1);
-  /* now 2^(i-1) <= n < 2^i */
-  for (i-=2; i>=0; i--) {
-    mpfr_mul(x, x, x, rnd); err = 2.0*err+1.0;
-    if (n & (1<<i)) {
-      mpfr_mul(x, x, (x == y) ? ycopy : y, rnd);
-      err += 1.0;
+  mpfr_init (res);
+
+  prec = MPFR_PREC(x);
+
+  rnd1 = (MPFR_SIGN(y) > 0) ? GMP_RNDU : GMP_RNDD; /* away */
+
+  do
+    {
+      prec += 3;
+      for (m=n, i=0; m; i++, m>>=1, prec++);
+      mpfr_set_prec (res, prec);
+      inexact = mpfr_set (res, y, rnd1);
+      err = 1;
+      /* now 2^(i-1) <= n < 2^i */
+      for (i-=2; i>=0; i--)
+	{
+	  if (mpfr_mul (res, res, res, GMP_RNDU))
+	    inexact = 1;
+	  err++;
+	  if (n & (1 << i))
+	    if (mpfr_mul (res, res, y, rnd1))
+	      inexact = 1;
+	}
+      err = prec - err;
+      if (err < 0)
+	err = 0;
     }
-  }
-  
-  if (x == y) mpfr_clear (ycopy);
-  return _mpfr_ceil_log2 (err);
-}
+  while (inexact && (mpfr_can_round (res, err,
+	  (MPFR_SIGN(res) > 0) ? GMP_RNDU : GMP_RNDD, rnd, MPFR_PREC(x)) == 0));
 
-/* sets x to y^n, and returns ceil(log2(max ulp error)) */
+  if (mpfr_set (x, res, rnd))
+    inexact = 1;
 
-/* TODO: gerer l'infini en cas de debordement ? Fait mecaniquement si fait 
-   dans mul ? */
+  mpfr_clear (res);
+
+  return inexact;
+}
+
+/* sets x to y^n, and return 0 if exact, non-zero otherwise */
 
 int
 #if __STDC__
@@ -100,22 +126,52 @@ mpfr_ui_pow_ui (x, y, n, rnd)
      mp_rnd_t rnd;
 #endif
 {
-  long int i; double err;
+  long int i, err;
+  unsigned long m;
+  mpfr_t res;
+  mp_prec_t prec;
+  int inexact;
 
-  MPFR_CLEAR_FLAGS(x); 
-  if (n==0) { mpfr_set_ui(x, 1, rnd); return 0; }
+  MPFR_CLEAR_FLAGS(x);
+
+  if (n == 0) /* x^0 = 1 for any x */
+    {
+      mpfr_set_ui (x, 1, rnd);
+      return 0;
+    }
 
-  mpfr_set_ui(x, y, rnd);
-  err = 1.0;
+  mpfr_init (res);
 
-  for (i=0;(1<<i)<=n;i++);
-  /* now 2^(i-1) <= n < 2^i */
-  for (i-=2; i>=0; i--) {
-    mpfr_mul(x, x, x, rnd); err = 2.0 * err + 1.0;
-    if (n & (1<<i)) {
-      mpfr_mul_ui(x, x, y, rnd);
-      err = err + 1.0;
+  prec = MPFR_PREC(x);
+
+  do
+    {
+      prec += 3;
+      for (m=n, i=0; m; i++, m>>=1, prec++);
+      mpfr_set_prec (res, prec);
+      inexact = mpfr_set_ui (res, y, GMP_RNDU);
+      err = 1;
+      /* now 2^(i-1) <= n < 2^i */
+      for (i-=2; i>=0; i--)
+	{
+	  if (mpfr_mul (res, res, res, GMP_RNDU))
+	    inexact = 1;
+	  err++;
+	  if (n & (1 << i))
+	    if (mpfr_mul_ui (res, res, y, GMP_RNDU))
+	      inexact = 1;
+	}
+      err = prec - err;
+      if (err < 0)
+	err = 0;
     }
-  }
-  return _mpfr_ceil_log2 (err);
+  while (inexact && (mpfr_can_round (res, err,
+	  (MPFR_SIGN(res) > 0) ? GMP_RNDU : GMP_RNDD, rnd, MPFR_PREC(x)) == 0));
+
+  if (mpfr_set (x, res, rnd))
+    inexact = 1;
+
+  mpfr_clear (res);
+
+  return inexact;
 }