--- /dev/null
+/* mpfr_expm1 -- Compute exp(x)-1
+
+Copyright 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009 Free Software Foundation, Inc.
+Contributed by the Arenaire and Cacao 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 2.1 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.LIB. If not, 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 expm1 is done by
+ expm1(x)=exp(x)-1
+ */
+
+int
+mpfr_expm1 (mpfr_ptr y, mpfr_srcptr x , mp_rnd_t rnd_mode)
+{
+ int inexact;
+ mp_exp_t ex;
+ MPFR_SAVE_EXPO_DECL (expo);
+
+ if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x)))
+ {
+ if (MPFR_IS_NAN (x))
+ {
+ MPFR_SET_NAN (y);
+ MPFR_RET_NAN;
+ }
+ /* check for inf or -inf (expm1(-inf)=-1) */
+ else if (MPFR_IS_INF (x))
+ {
+ if (MPFR_IS_POS (x))
+ {
+ MPFR_SET_INF (y);
+ MPFR_SET_POS (y);
+ MPFR_RET (0);
+ }
+ else
+ return mpfr_set_si (y, -1, rnd_mode);
+ }
+ else
+ {
+ MPFR_ASSERTD (MPFR_IS_ZERO (x));
+ MPFR_SET_ZERO (y); /* expm1(+/- 0) = +/- 0 */
+ MPFR_SET_SAME_SIGN (y, x);
+ MPFR_RET (0);
+ }
+ }
+
+ ex = MPFR_GET_EXP (x);
+ if (ex < 0)
+ {
+ /* For -1 < x < 0, abs(expm1(x)-x) < x^2/2.
+ For 0 < x < 1, abs(expm1(x)-x) < x^2. */
+ if (MPFR_IS_POS (x))
+ MPFR_FAST_COMPUTE_IF_SMALL_INPUT (y, x, - ex, 0, 1, rnd_mode, {});
+ else
+ MPFR_FAST_COMPUTE_IF_SMALL_INPUT (y, x, - ex, 1, 0, rnd_mode, {});
+ }
+
+ MPFR_SAVE_EXPO_MARK (expo);
+
+ if (MPFR_IS_NEG (x) && ex > 5) /* x <= -32 */
+ {
+ mpfr_t minus_one, t;
+ mp_exp_t err;
+
+ mpfr_init2 (minus_one, 2);
+ mpfr_init2 (t, 64);
+ mpfr_set_si (minus_one, -1, GMP_RNDN);
+ mpfr_const_log2 (t, GMP_RNDU); /* round upward since x is negative */
+ mpfr_div (t, x, t, GMP_RNDU); /* > x / ln(2) */
+ err = mpfr_cmp_si (t, MPFR_EMIN_MIN >= -LONG_MAX ?
+ MPFR_EMIN_MIN : -LONG_MAX) <= 0 ?
+ - (MPFR_EMIN_MIN >= -LONG_MAX ? MPFR_EMIN_MIN : -LONG_MAX) :
+ - mpfr_get_si (t, GMP_RNDU);
+ /* exp(x) = 2^(x/ln(2))
+ <= 2^max(MPFR_EMIN_MIN,-LONG_MAX,ceil(x/ln(2)+epsilon))
+ with epsilon > 0 */
+ mpfr_clear (t);
+ MPFR_SMALL_INPUT_AFTER_SAVE_EXPO (y, minus_one, err, 0, 0, rnd_mode,
+ expo, { mpfr_clear (minus_one); });
+ mpfr_clear (minus_one);
+ }
+
+ /* General case */
+ {
+ /* Declaration of the intermediary variable */
+ mpfr_t t;
+ /* Declaration of the size variable */
+ mp_prec_t Ny = MPFR_PREC(y); /* target precision */
+ mp_prec_t Nt; /* working precision */
+ mp_exp_t err, exp_te; /* error */
+ MPFR_ZIV_DECL (loop);
+
+ /* compute the precision of intermediary variable */
+ /* the optimal number of bits : see algorithms.tex */
+ Nt = Ny + MPFR_INT_CEIL_LOG2 (Ny) + 6;
+
+ /* if |x| is smaller than 2^(-e), we will loose about e bits in the
+ subtraction exp(x) - 1 */
+ if (ex < 0)
+ Nt += - ex;
+
+ /* initialize auxiliary variable */
+ mpfr_init2 (t, Nt);
+
+ /* First computation of expm1 */
+ MPFR_ZIV_INIT (loop, Nt);
+ for (;;)
+ {
+ MPFR_BLOCK_DECL (flags);
+
+ /* exp(x) may overflow and underflow */
+ MPFR_BLOCK (flags, mpfr_exp (t, x, GMP_RNDN));
+ if (MPFR_OVERFLOW (flags))
+ {
+ inexact = mpfr_overflow (y, rnd_mode, MPFR_SIGN_POS);
+ MPFR_SAVE_EXPO_UPDATE_FLAGS (expo, MPFR_FLAGS_OVERFLOW);
+ break;
+ }
+ else if (MPFR_UNDERFLOW (flags))
+ {
+ inexact = mpfr_set_si (y, -1, rnd_mode);
+ MPFR_ASSERTD (inexact == 0);
+ inexact = -1;
+ if (MPFR_IS_LIKE_RNDZ (rnd_mode, 1))
+ {
+ inexact = 1;
+ mpfr_nexttozero (y);
+ }
+ break;
+ }
+
+ exp_te = MPFR_GET_EXP (t); /* FIXME: exp(x) may overflow! */
+ mpfr_sub_ui (t, t, 1, GMP_RNDN); /* exp(x)-1 */
+
+ /* error estimate */
+ /*err=Nt-(__gmpfr_ceil_log2(1+pow(2,MPFR_EXP(te)-MPFR_EXP(t))));*/
+ err = Nt - (MAX (exp_te - MPFR_GET_EXP (t), 0) + 1);
+
+ if (MPFR_LIKELY (MPFR_CAN_ROUND (t, err, Ny, rnd_mode)))
+ {
+ inexact = mpfr_set (y, t, rnd_mode);
+ break;
+ }
+
+ /* increase the precision */
+ MPFR_ZIV_NEXT (loop, Nt);
+ mpfr_set_prec (t, Nt);
+ }
+ MPFR_ZIV_FREE (loop);
+
+ mpfr_clear (t);
+ }
+
+ MPFR_SAVE_EXPO_FREE (expo);
+ return mpfr_check_range (y, inexact, rnd_mode);
+}
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