new (faster) implementation of mpfr_cos

git-svn-id: svn://scm.gforge.inria.fr/svn/mpfr/trunk@1168 280ebfd0-de03-0410-8827-d642c229c3f4

1 files changed, 150 insertions, 0 deletions

diff --git a/cos.c b/cos.c
new file mode 100644
index 000000000..507dc6fd9
--- /dev/null
+++ b/cos.c
@@ -0,0 +1,150 @@
+/* mpfr_cos -- cosine of a floating-point number
+
+Copyright (C) 2001 Free Software Foundation.
+
+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 Library General Public License as published by
+the Free Software Foundation; either version 2 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 Library General Public
+License for more details.
+
+You should have received a copy of the GNU Library General Public License
+along with the MPFR Library; see the file COPYING.LIB.  If not, write to
+the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
+MA 02111-1307, USA. */
+
+#include <stdio.h>
+#include "gmp.h"
+#include "gmp-impl.h"
+#include "mpfr.h"
+#include "mpfr-impl.h"
+
+int mpfr_cos2_aux       _PROTO ((mpfr_ptr, mpfr_srcptr));
+
+int 
+#if __STDC__
+mpfr_cos (mpfr_ptr y, mpfr_srcptr x, mp_rnd_t rnd_mode) 
+#else
+mpfr_cos (y, x, rnd_mode)
+     mpfr_ptr y;
+     mpfr_srcptr x;
+     mp_rnd_t rnd_mode;
+#endif
+{
+  int K, precy, m, k, l;
+  mpfr_t r, s;
+
+  if (MPFR_IS_NAN(x) || MPFR_IS_INF(x))
+    {
+      MPFR_SET_NAN(y);
+      return 1;
+    }
+
+  if (!MPFR_NOTZERO(x))
+    {
+      mpfr_set_ui(y, 1, GMP_RNDN);
+      return 0;
+    }
+
+  precy = MPFR_PREC(y);
+
+  K = _mpfr_isqrt(precy / 2);
+  if (MPFR_EXP(x) > 0)
+    K += MPFR_EXP(x);
+  /* we need at least K + log2(precy/K) extra bits */
+  m = precy + 3 * K + 3;
+
+  mpfr_init2 (r, m);
+  mpfr_init2 (s, m);
+
+  do
+    {
+      mpfr_mul (r, x, x, GMP_RNDU); /* err <= 1 ulp */
+      mpfr_div_2exp (r, r, 2 * K, GMP_RNDN); /* r = (x/2^K)^2, err <= 1 ulp */
+
+      /* s <- 1 - r/2! + ... + (-1)^l r^l/(2l)! */
+      l = mpfr_cos2_aux (s, r);
+
+      for (k = 0; k < K; k++)
+	{
+	  mpfr_mul (s, s, s, GMP_RNDU); /* err <= 2*olderr */
+	  mpfr_mul_2exp (s, s, 1, GMP_RNDU); /* err <= 4*olderr */
+	  mpfr_sub_ui (s, s, 1, GMP_RNDN);
+	}
+
+      /* absolute error on s is bounded by (2l+1/3)*2^(2K-m) */
+      for (k = 2 * K, l = 2 * l + 1; l > 1; k++, l = (l + 1) >> 1);
+      /* now the error is bounded by 2^(k-m) = 2^(EXP(s)-err) */
+
+      l = mpfr_can_round (s, MPFR_EXP(s) + m - k, GMP_RNDD, rnd_mode, precy);
+
+      if (l == 0)
+	{
+	  m += BITS_PER_MP_LIMB;
+	  mpfr_set_prec (r, m);
+	  mpfr_set_prec (s, m);
+	}
+    }
+  while (l == 0);
+
+  mpfr_set (y, s, rnd_mode);
+
+  mpfr_clear (r);
+  mpfr_clear (s);
+
+  return 1;
+}
+
+/* s <- 1 - r/2! + r^2/4! + ... + (-1)^l r^l/(2l)! + ...
+   Assumes |r| < 1.
+   Returns the index l0 of the last term (-1)^l r^l/(2l)!.
+   The absolute error on s is at most 2 * l0 * 2^(-m).
+*/
+int
+#if __STDC__
+mpfr_cos2_aux (mpfr_ptr s, mpfr_srcptr r)
+#else
+mpfr_cos2_aux (s, r)
+     mpfr_ptr s;
+     mpfr_srcptr r;
+#endif
+{
+  unsigned int l, b = 2;
+  int prec_t, m = MPFR_PREC(s);
+  mpfr_t t;
+
+  assert (MPFR_EXP(r) <= 0);
+  mpfr_init2 (t, m);
+  mpfr_set_ui (t, 1, GMP_RNDN);
+  mpfr_set_ui(s, 1, GMP_RNDN);
+
+  for (l = 1; MPFR_EXP(t) >= -m; l++)
+    {
+      mpfr_mul (t, t, r, GMP_RNDU); /* err <= (3l-1) ulp */
+      mpfr_div_ui (t, t, (2*l-1)*(2*l), GMP_RNDU); /* err <= 3l ulp */
+      if (l % 2 == 0)
+	mpfr_add (s, s, t, GMP_RNDD);
+      else
+	mpfr_sub (s, s, t, GMP_RNDD);
+      assert (MPFR_EXP(s) == 0); /* check 1/2 <= s < 1 */
+      /* err(s) <= l * 2^(-m) */
+      if (3 * l > (1 << b))
+	b++;
+      /* now 3l <= 2^b, we want 3l*ulp(t) <= 2^(-m)
+	 i.e. b+EXP(t)-PREC(t) <= -m */
+      prec_t = m + MPFR_EXP(t) + b;
+      if (prec_t > 0)
+	mpfr_round (t, GMP_RNDN, prec_t);
+    }
+
+  mpfr_clear (t);
+
+  return l;
+}
+