added new function mpfr_exp10m1

git-svn-id: https://scm.gforge.inria.fr/anonscm/svn/mpfr/trunk@14388 280ebfd0-de03-0410-8827-d642c229c3f4

1 files changed, 179 insertions, 0 deletions

diff --git a/src/exp10m1.c b/src/exp10m1.c
new file mode 100644
index 000000000..d5a7663b4
--- /dev/null
+++ b/src/exp10m1.c
@@ -0,0 +1,179 @@
+/* mpfr_exp10m1 -- Compute 10^x-1
+
+Copyright 2001-2021 Free Software Foundation, Inc.
+Contributed by the AriC and Caramba 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
+https://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 exp10m1 is done by expm1(x) = 10^x-1 */
+
+/* In case x is small in absolute value, 10^x - 1 ~ x*log(10).
+   If this is enough to deduce correct rounding, put in the auxiliary variable
+   t the approximation that will be rounded to get y, and return non-zero.
+   If we put 0 in t, it means underflow.
+   Otherwise return 0. */
+static int
+mpfr_exp10m1_small (mpfr_ptr y, mpfr_srcptr x , mpfr_rnd_t rnd_mode,
+                    mpfr_ptr t)
+{
+  mpfr_prec_t prec;
+  mpfr_exp_t e;
+
+  /* for |x| < 0.25, we have |10^x-1-x*log(10)| < 4*x^2 */
+  if (MPFR_EXP(x) > -2)
+    return 0;
+  /* now EXP(x) <= -2, thus x < 0.25 */
+  prec = MPFR_PREC(t);
+  mpfr_log_ui (t, 10, MPFR_RNDN);
+  /* t = log(10)*(1 + theta) with |theta| <= 2^(-prec) */
+  mpfr_mul (t, t, x, MPFR_RNDN);
+  /* no underflow can occur, since log(10) > 1 */
+  /* t = x*log(10)*(1 + theta)^2 with |theta| <= 2^(-prec) */
+  /* |t - x*log(10)| <= ((1 + theta)^2 - 1) * |t| <= 3*2^(-prec)*|t| */
+  /* |t - x*log(10)| < 3*2^(EXP(t)-prec) */
+  e = 2 * MPFR_GET_EXP (x) + 2 + prec - MPFR_GET_EXP(t);
+  /* |4*x^2| < 2^e*2^(EXP(t)-prec) thus
+     |t - exp10m1(x)| < (3+2^e)*2^(EXP(t)-prec) */
+  e = (e <= 1) ? 2 + (e == 1) : e + 1;
+  /* now |t - exp10m1(x)| < 2^e*2^(EXP(t)-prec) */
+  return MPFR_CAN_ROUND (t, prec - e, MPFR_PREC(y), rnd_mode);
+}
+
+int
+mpfr_exp10m1 (mpfr_ptr y, mpfr_srcptr x , mpfr_rnd_t rnd_mode)
+{
+  int inexact, nloop;
+  mpfr_t t;
+  mpfr_prec_t Ny = MPFR_PREC(y);   /* target precision */
+  mpfr_prec_t Nt;                  /* working precision */
+  mpfr_exp_t err, exp_te;          /* error */
+  MPFR_ZIV_DECL (loop);
+  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_IS_SINGULAR (x))
+    return mpfr_expm1 (y, x, rnd_mode); /* singular cases are identical */
+
+  MPFR_ASSERTN(!MPFR_IS_ZERO(x));
+
+  MPFR_SAVE_EXPO_MARK (expo);
+
+  /* Check case where result is -1 or nextabove(-1) because x is a huge
+     negative number. */
+  if (MPFR_IS_NEG(x) && mpfr_cmpabs_ui (x, 2 + (MPFR_PREC(y) - 1) / 3) > 0)
+    {
+      MPFR_SAVE_EXPO_UPDATE_FLAGS (expo, MPFR_FLAGS_INEXACT);
+      /* 1/2*ulp(-1) = 2^(-PREC(y)):
+         since |x| >= PREC(y)/3 + 1, then 3*|x| >= PREC(y) + 3,
+         thus 10^x < 8^x <= 2^(-PREC(y)-3) <= 1/2*ulp(-1), thus the
+         result is -1 for RNDA,RNDD,RNDN, and nextabove(-1) for RNDZ,RNDU */
+      mpfr_set_si (y, -1, MPFR_RNDZ);
+      if (!MPFR_IS_LIKE_RNDZ(rnd_mode,1))
+        inexact = -1;
+      else
+        {
+          mpfr_nextabove (y);
+          inexact = 1;
+        }
+      goto end;
+    }
+
+  Nt = Ny + MPFR_INT_CEIL_LOG2 (Ny) + 6;
+
+  mpfr_init2 (t, Nt);
+
+  MPFR_ZIV_INIT (loop, Nt);
+  for (nloop = 0;; nloop++)
+    {
+      int inex1;
+
+      MPFR_BLOCK_DECL (flags);
+
+      /* 10^x may overflow and underflow */
+      MPFR_BLOCK (flags, inex1 = mpfr_exp10 (t, x, MPFR_RNDN));
+
+      if (MPFR_OVERFLOW (flags)) /* overflow case */
+        {
+          inexact = mpfr_overflow (y, rnd_mode, MPFR_SIGN_POS);
+          MPFR_SAVE_EXPO_UPDATE_FLAGS (expo, MPFR_FLAGS_OVERFLOW);
+          goto clear;
+        }
+
+      /* integer case */
+      if (inex1 == 0)
+        {
+          inexact = mpfr_sub_ui (y, t, 1, rnd_mode);
+          goto clear;
+        }
+
+      /* The case of underflow in 10^x (huge negative x)
+         was already detected before Ziv's loop. */
+      MPFR_ASSERTD(!MPFR_UNDERFLOW (flags));
+
+      MPFR_ASSERTN(!MPFR_IS_ZERO(t));
+      exp_te = MPFR_GET_EXP (t);
+      mpfr_sub_ui (t, t, 1, MPFR_RNDN);   /* 10^x-1 */
+
+      /* error estimate */
+      /* err = __gmpfr_ceil_log2(1+pow(2,MPFR_EXP(te)-MPFR_EXP(t))) */
+      if (!MPFR_IS_ZERO(t))
+        {
+          err = MAX (exp_te - MPFR_GET_EXP (t), 0) + 1;
+          /* if inex1=0, this means that t=o(10^x) is exact, thus the correct
+             rounding is simply o(t-1) */
+          if (inex1 == 0 ||
+              MPFR_LIKELY (MPFR_CAN_ROUND (t, Nt - err, Ny, rnd_mode)))
+            break;
+        }
+
+      /* check small case: we need to do it at each step of Ziv's loop,
+         since the multiplication x*log(10) might not enable correct
+         rounding at the first loop */
+      if (mpfr_exp10m1_small (y, x, rnd_mode, t))
+        {
+          if (MPFR_IS_ZERO(t)) /* underflow */
+            {
+              mpfr_clear (t);
+              MPFR_SAVE_EXPO_FREE (expo);
+              return mpfr_underflow (y, (rnd_mode == MPFR_RNDN) ? MPFR_RNDZ
+                                     : rnd_mode, 1);
+            }
+          break;
+        }
+
+      /* increase the precision */
+      MPFR_ZIV_NEXT (loop, Nt);
+      mpfr_set_prec (t, Nt);
+    }
+
+  inexact = mpfr_set (y, t, rnd_mode);
+ clear:
+  MPFR_ZIV_FREE (loop);
+  mpfr_clear (t);
+
+ end:
+  MPFR_SAVE_EXPO_FREE (expo);
+  return mpfr_check_range (y, inexact, rnd_mode);
+}