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+/* mpfr_exp2 -- power of 2 function 2^y
+
+Copyright 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013 Free Software Foundation, Inc.
+Contributed by the AriC and Caramel projects, INRIA.
+
+This file is part of the GNU MPFR Library.
+
+The GNU 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 3 of the License, or (at your
+option) any later version.
+
+The GNU 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 GNU MPFR Library; see the file COPYING.LESSER. If not, see
+http://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc.,
+51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA. */
+
+#define MPFR_NEED_LONGLONG_H
+#include "mpfr-impl.h"
+
+/* The computation of y = 2^z is done by *
+ * y = exp(z*log(2)). The result is exact iff z is an integer. */
+
+int
+mpfr_exp2 (mpfr_ptr y, mpfr_srcptr x, mpfr_rnd_t rnd_mode)
+{
+ int inexact;
+ long xint;
+ mpfr_t xfrac;
+ MPFR_SAVE_EXPO_DECL (expo);
+
+ MPFR_LOG_FUNC
+ (("x[%Pu]=%.*Rg rnd=%d", mpfr_get_prec(x), mpfr_log_prec, x, rnd_mode),
+ ("y[%Pu]=%.*Rg inexact=%d", mpfr_get_prec(y), mpfr_log_prec, y,
+ inexact));
+
+ if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x)))
+ {
+ if (MPFR_IS_NAN (x))
+ {
+ MPFR_SET_NAN (y);
+ MPFR_RET_NAN;
+ }
+ else if (MPFR_IS_INF (x))
+ {
+ if (MPFR_IS_POS (x))
+ MPFR_SET_INF (y);
+ else
+ MPFR_SET_ZERO (y);
+ MPFR_SET_POS (y);
+ MPFR_RET (0);
+ }
+ else /* 2^0 = 1 */
+ {
+ MPFR_ASSERTD (MPFR_IS_ZERO(x));
+ return mpfr_set_ui (y, 1, rnd_mode);
+ }
+ }
+
+ /* since the smallest representable non-zero float is 1/2*2^__gmpfr_emin,
+ if x < __gmpfr_emin - 1, the result is either 1/2*2^__gmpfr_emin or 0 */
+ MPFR_ASSERTN (MPFR_EMIN_MIN >= LONG_MIN + 2);
+ if (MPFR_UNLIKELY (mpfr_cmp_si (x, __gmpfr_emin - 1) < 0))
+ {
+ mpfr_rnd_t rnd2 = rnd_mode;
+ /* in round to nearest mode, round to zero when x <= __gmpfr_emin-2 */
+ if (rnd_mode == MPFR_RNDN &&
+ mpfr_cmp_si_2exp (x, __gmpfr_emin - 2, 0) <= 0)
+ rnd2 = MPFR_RNDZ;
+ return mpfr_underflow (y, rnd2, 1);
+ }
+
+ MPFR_ASSERTN (MPFR_EMAX_MAX <= LONG_MAX);
+ if (MPFR_UNLIKELY (mpfr_cmp_si (x, __gmpfr_emax) >= 0))
+ return mpfr_overflow (y, rnd_mode, 1);
+
+ /* We now know that emin - 1 <= x < emax. */
+
+ MPFR_SAVE_EXPO_MARK (expo);
+
+ /* 2^x = 1 + x*log(2) + O(x^2) for x near zero, and for |x| <= 1 we have
+ |2^x - 1| <= x < 2^EXP(x). If x > 0 we must round away from 0 (dir=1);
+ if x < 0 we must round toward 0 (dir=0). */
+ MPFR_SMALL_INPUT_AFTER_SAVE_EXPO (y, __gmpfr_one, - MPFR_GET_EXP (x), 0,
+ MPFR_SIGN(x) > 0, rnd_mode, expo, {});
+
+ xint = mpfr_get_si (x, MPFR_RNDZ);
+ mpfr_init2 (xfrac, MPFR_PREC (x));
+ mpfr_sub_si (xfrac, x, xint, MPFR_RNDN); /* exact */
+
+ if (MPFR_IS_ZERO (xfrac))
+ {
+ mpfr_set_ui (y, 1, MPFR_RNDN);
+ inexact = 0;
+ }
+ else
+ {
+ /* Declaration of the intermediary variable */
+ mpfr_t t;
+
+ /* Declaration of the size variable */
+ mpfr_prec_t Ny = MPFR_PREC(y); /* target precision */
+ mpfr_prec_t Nt; /* working precision */
+ mpfr_exp_t err; /* error */
+ MPFR_ZIV_DECL (loop);
+
+ /* compute the precision of intermediary variable */
+ /* the optimal number of bits : see algorithms.tex */
+ Nt = Ny + 5 + MPFR_INT_CEIL_LOG2 (Ny);
+
+ /* initialise of intermediary variable */
+ mpfr_init2 (t, Nt);
+
+ /* First computation */
+ MPFR_ZIV_INIT (loop, Nt);
+ for (;;)
+ {
+ /* compute exp(x*ln(2))*/
+ mpfr_const_log2 (t, MPFR_RNDU); /* ln(2) */
+ mpfr_mul (t, xfrac, t, MPFR_RNDU); /* xfrac * ln(2) */
+ err = Nt - (MPFR_GET_EXP (t) + 2); /* Estimate of the error */
+ mpfr_exp (t, t, MPFR_RNDN); /* exp(xfrac * ln(2)) */
+
+ if (MPFR_LIKELY (MPFR_CAN_ROUND (t, err, Ny, rnd_mode)))
+ break;
+
+ /* Actualisation of the precision */
+ MPFR_ZIV_NEXT (loop, Nt);
+ mpfr_set_prec (t, Nt);
+ }
+ MPFR_ZIV_FREE (loop);
+
+ inexact = mpfr_set (y, t, rnd_mode);
+
+ mpfr_clear (t);
+ }
+
+ mpfr_clear (xfrac);
+ mpfr_clear_flags ();
+ mpfr_mul_2si (y, y, xint, MPFR_RNDN); /* exact or overflow */
+ /* Note: We can have an overflow only when t was rounded up to 2. */
+ MPFR_ASSERTD (MPFR_IS_PURE_FP (y) || inexact > 0);
+ MPFR_SAVE_EXPO_UPDATE_FLAGS (expo, __gmpfr_flags);
+ MPFR_SAVE_EXPO_FREE (expo);
+ return mpfr_check_range (y, inexact, rnd_mode);
+}