merge fmod, remaider and remquo into a single file rem1.c.

merge code into a single internal function mpfr_rem1.
fix false statement in mpfr.texi: rop and op1 have the same sign for mpfr_fmod
but not for mpfr_remainder and mpfr_remquo.


git-svn-id: svn://scm.gforge.inria.fr/svn/mpfr/trunk@4869 280ebfd0-de03-0410-8827-d642c229c3f4

1 files changed, 232 insertions, 0 deletions

diff --git a/rem1.c b/rem1.c
new file mode 100644
index 000000000..c03400b91
--- /dev/null
+++ b/rem1.c
@@ -0,0 +1,232 @@
+/* mpfr_rem1 -- internal function
+   mpfr_fmod -- compute the floating-point remainder of x/y
+   mpfr_remquo and mpfr_remainder -- argument reduction functions
+
+Copyright 2007 Free Software Foundation, Inc.
+Contributed by the Arenaire and Cacao projects, INRIA.
+
+This file is part of the MPFR Library.
+
+The MPFR Library is free software; you can redistribute it and/or modify
+it under the terms of the GNU Lesser General Public License as published by
+the Free Software Foundation; either version 2.1 of the License, or (at your
+option) any later version.
+
+The MPFR Library is distributed in the hope that it will be useful, but
+WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
+License for more details.
+
+You should have received a copy of the GNU Lesser General Public License
+along with the MPFR Library; see the file COPYING.LIB.  If not, write to
+the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston,
+MA 02110-1301, USA. */
+
+# include "mpfr-impl.h"
+
+/* we return as many bits as we can, keeping just one bit for the sign */
+# define WANTED_BITS (sizeof(long) * CHAR_BIT - 1)
+
+/*
+  rem1 works as follows:
+  The first rounding mode rnd_q indicate if we are actually computing 
+  a fmod (GMP_RNDZ) or a remainder/remquo (GMP_RNDN).
+  
+  Let q = x/y rounded to an integer in the direction rnd_q.
+  Put x - q*y in rem, rounded according to rnd.
+  If quo is not null, the value stored in *quo has the sign of q,
+  and agrees with q with the 2^n low order bits. 
+  In other words, *quo = q (mod 2^n) and *quo q >= 0.
+  If rem is zero, then it has the sign of x.
+  The returned 'int' is the inexact flag giving the place of rem wrt x - q*y.
+
+  If x or y is NaN: *quo is undefined, rem is NaN.
+  If x is Inf, whatever y: *quo is undefined, rem is NaN.
+  If y is Inf, x not NaN nor Inf: *quo is 0, rem is x.
+  If y is 0, whatever x: *quo is undefined, rem is NaN.
+  If x is 0, whatever y (not NaN nor 0): *quo is 0, rem is x.
+
+  Otherwise if x and y are neither NaN, Inf nor 0, q is always defined,
+  thus *quo is.
+  Since |x - q*y| <= y/2, no overflow is possible.
+  Only an underflow is possible when y is very small.
+ */
+
+static int
+mpfr_rem1 (mpfr_ptr rem, long *quo, mp_rnd_t rnd_q,
+           mpfr_srcptr x, mpfr_srcptr y, mp_rnd_t rnd)
+{
+  mp_exp_t ex, ey;
+  int compare, inex, q_is_odd, sign, signx = MPFR_SIGN (x);
+  mpz_t mx, my, r;
+
+  MPFR_ASSERTD (rnd_q == GMP_RNDN || rnd_q == GMP_RNDZ);
+
+  if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x) || MPFR_IS_SINGULAR (y)))
+    {
+      if (MPFR_IS_NAN (x) || MPFR_IS_NAN (y) || MPFR_IS_INF (x)
+          || MPFR_IS_ZERO (y))
+        {
+          /* for remquo, quo is undefined */
+          MPFR_SET_NAN (rem);
+          MPFR_RET_NAN;
+        }
+      else                      /* either y is Inf and x is 0 or non-special,
+                                   or x is 0 and y is non-special,
+                                   in both cases the quotient is zero. */
+        {
+          if (quo)
+            *quo = 0;
+          return mpfr_set (rem, x, rnd);
+        }
+    }
+
+  /* now neither x nor y is NaN, Inf or zero */
+
+  mpz_init (mx);
+  mpz_init (my);
+  mpz_init (r);
+
+  ex = mpfr_get_z_exp (mx, x);  /* x = mx*2^ex */
+  ey = mpfr_get_z_exp (my, y);  /* y = my*2^ey */
+
+  /* to get rid of sign problems, we compute it separately:
+     quo(-x,-y) = quo(x,y), rem(-x,-y) = -rem(x,y)
+     quo(-x,y) = -quo(x,y), rem(-x,y)  = -rem(x,y)
+     thus quo = sign(x/y)*quo(|x|,|y|), rem = sign(x)*rem(|x|,|y|) */
+  sign = (signx == MPFR_SIGN (y)) ? 1 : -1;
+  mpz_abs (mx, mx);
+  mpz_abs (my, my);
+  q_is_odd = 0;
+
+  /* divide my by 2^k if possible to make operations mod my easier */
+  {
+    unsigned long k = mpz_scan1 (my, 0);
+    ey += k;
+    mpz_div_2exp (my, my, k);
+  }
+
+  if (ex <= ey)
+    {
+      /* q = x/y = mx/(my*2^(ey-ex)) */
+      mpz_mul_2exp (my, my, ey - ex);   /* divide mx by my*2^(ey-ex) */
+      if (rnd_q == GMP_RNDZ)
+	/* 0 <= |r| <= |my|, r has the same sign as mx */
+	mpz_tdiv_qr (mx, r, mx, my);
+      else
+	/* 0 <= |r| <= |my|, r has the same sign as my */
+	mpz_fdiv_qr (mx, r, mx, my);
+					 
+      if (rnd_q == GMP_RNDN)
+        q_is_odd = mpz_tstbit (mx, 0);
+      if (quo)                  /* mx is the quotient */
+        {
+          mpz_tdiv_r_2exp (mx, mx, WANTED_BITS);
+          *quo = mpz_get_si (mx);
+        }
+    }
+  else                          /* ex > ey */
+    {
+      if (quo)
+        /* for remquo, to get the low WANTED_BITS more bits of the quotient,
+           we first compute R =  X mod Y*2^WANTED_BITS, where X and Y are
+           defined below. Then the low WANTED_BITS of the quotient are
+           floor(R/Y). */
+        mpz_mul_2exp (my, my, WANTED_BITS);     /* 2^WANTED_BITS*Y */
+      else
+        /* Let X = mx*2^(ex-ey) and Y = my. Then both X and Y are integers.
+           Assume X = R mod Y, then x = X*2^ey = R*2^ey mod (Y*2^ey=y).
+           To be able to perform the rounding, we need the least significant
+           bit of the quotient, i.e., one more bit in the remainder, 
+           which is obtained by dividing by 2Y. */
+        mpz_mul_2exp (my, my, 1);       /* 2Y */
+
+      mpz_set_ui (r, 2);
+      mpz_powm_ui (r, r, ex - ey, my);  /* 2^(ex-ey) mod my */
+      mpz_mul (r, r, mx);
+      mpz_mod (r, r, my);
+
+      if (quo)                  /* now 0 <= r < 2^WANTED_BITS*Y */
+        {
+          mpz_div_2exp (my, my, WANTED_BITS);   /* back to Y */
+          mpz_tdiv_qr (mx, r, r, my);
+          /* oldr = mx*my + newr */
+          *quo = mpz_get_si (mx);
+          q_is_odd = *quo & 1;
+        }
+      else                      /* now 0 <= r < 2Y */
+        {
+          mpz_div_2exp (my, my, 1);     /* back to Y */
+          if (rnd_q == GMP_RNDN)
+            {
+              /* least significant bit of q */
+              q_is_odd = mpz_cmpabs (r, my) >= 0;
+              if (q_is_odd)
+                mpz_sub (r, r, my);
+            }
+        }
+      /* now 0 <= |r| < |my|, and if needed, 
+         q_is_odd is the least significant bit of q */
+    }
+
+  if (mpz_cmp_ui (r, 0) == 0)
+    inex = mpfr_set_ui (rem, 0, GMP_RNDN);
+  else 
+    {
+      if (rnd_q == GMP_RNDN)
+	{
+	  /* FIXME: the comparison 2*r < my could be done more efficiently
+	     at the mpn level */
+	  mpz_mul_2exp (r, r, 1);
+	  compare = mpz_cmpabs (r, my);
+	  mpz_div_2exp (r, r, 1);
+	  compare = ((compare > 0) ||
+		     ((rnd_q == GMP_RNDN) && (compare == 0) && q_is_odd));
+	  /* if compare != 0, we need to subtract my to r, and add 1 to quo */
+	  if (compare)
+	    {
+	      mpz_sub (r, r, my);
+	      if (quo && (rnd_q == GMP_RNDN))
+		*quo += 1;
+	    }
+	}   
+      inex = mpfr_set_z (rem, r, rnd);
+      /* if ex > ey, rem should be multiplied by 2^ey, else by 2^ex */
+      MPFR_EXP (rem) += (ex > ey) ? ey : ex;
+    }
+
+  if (quo)
+    *quo *= sign;
+
+  /* take into account sign of x */
+  if (signx < 0)
+    {
+      mpfr_neg (rem, rem, GMP_RNDN);
+      inex = -inex;
+    }
+
+  mpz_clear (mx);
+  mpz_clear (my);
+  mpz_clear (r);
+
+  return inex;
+}
+
+int
+mpfr_remainder (mpfr_ptr rem, mpfr_srcptr x, mpfr_srcptr y, mp_rnd_t rnd)
+{
+  return mpfr_rem1 (rem, (long *) 0, GMP_RNDN, x, y, rnd);
+}
+
+int
+mpfr_remquo (mpfr_ptr rem, long *quo,
+             mpfr_srcptr x, mpfr_srcptr y, mp_rnd_t rnd)
+{
+  return mpfr_rem1 (rem, quo, GMP_RNDN, x, y, rnd);
+}
+
+int
+mpfr_fmod (mpfr_ptr rem, mpfr_srcptr x, mpfr_srcptr y, mp_rnd_t rnd)
+{
+  return mpfr_rem1 (rem, (long *) 0, GMP_RNDZ, x, y, rnd);
+}