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/* mpfr_log2p1 -- Compute log2(1+x)
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 /* needed for MPFR_INT_CEIL_LOG2 */
#include "mpfr-impl.h"
#define ULSIZE (sizeof (unsigned long) * CHAR_BIT)
/* return non-zero if log2(1+x) is exactly representable in infinite precision,
and in such case the returned value is k such that 1+x = 2^k (the case k=0
cannot happen since we assume x<>0) */
static mpfr_exp_t
mpfr_log2p1_isexact (mpfr_srcptr x)
{
/* log2(1+x) is exactly representable when 1+x is a power of two,
we thus simply compute 1+x with 1-bit precision and check whether
the addition is exact. This routine is called with extended exponent
range, thus no need to extend it. */
mpfr_t t;
int inex;
mpfr_exp_t e;
mpfr_init2 (t, 1);
inex = mpfr_add_ui (t, x, 1, MPFR_RNDZ);
e = MPFR_GET_EXP (t);
mpfr_clear (t);
return inex == 0 ? e - 1 : 0;
}
/* in case x=2^k and we can decide of the correct rounding,
put the correctly-rounded value in y and return the corresponding
ternary value (which is necessarily non-zero),
otherwise return 0 */
static int
mpfr_log2p1_special (mpfr_ptr y, mpfr_srcptr x, mpfr_rnd_t rnd_mode)
{
mpfr_exp_t expx = MPFR_GET_EXP(x);
mpfr_exp_t k = expx - 1, expk;
mpfr_prec_t prec;
mpfr_t t;
int inex;
if (k <= 0 || mpfr_cmp_si_2exp (x, 1, k) != 0)
return 0;
/* k < log2(1+x) < k + 1/x/log(2) < k + 2/x */
expk = MPFR_INT_CEIL_LOG2(k); /* exponent of k */
/* 2/x < 2^(2-EXP(x)) thus if 2-EXP(x) < expk - PREC(y) - 1,
we have 2/x < 1/4*ulp(k) and we can decide the correct rounding */
if (2 - expx >= expk - MPFR_PREC(y) - 1)
return 0;
prec = (MPFR_PREC(y) + 2 <= ULSIZE) ? ULSIZE : MPFR_PREC(y) + 2;
mpfr_init2 (t, prec);
mpfr_set_ui (t, k, MPFR_RNDZ); /* exact since prec >= ULSIZE */
mpfr_nextabove (t);
/* now k < t < k + 2/x and round(t) = round(log2(1+x)) */
inex = mpfr_set (y, t, rnd_mode);
mpfr_clear (t);
/* Warning: for RNDF, the mpfr_set calls above might return 0 */
return (rnd_mode == MPFR_RNDF) ? 1 : inex;
}
/* The computation of log2p1 is done by log2p1(x) = log1p(x)/log(2) */
int
mpfr_log2p1 (mpfr_ptr y, mpfr_srcptr x, mpfr_rnd_t rnd_mode)
{
int comp, inexact, nloop;
mpfr_t t, lg2;
mpfr_prec_t Ny = MPFR_PREC(y), prec;
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_UNLIKELY (MPFR_IS_SINGULAR (x)))
return mpfr_log1p (y, x, rnd_mode); /* same result for singular cases */
comp = mpfr_cmp_si (x, -1);
/* log2p1(x) is undefined for x < -1 */
if (MPFR_UNLIKELY(comp <= 0))
{
if (comp == 0)
/* x=0: log2p1(-1)=-inf (divide-by-zero exception) */
{
MPFR_SET_INF (y);
MPFR_SET_NEG (y);
MPFR_SET_DIVBY0 ();
MPFR_RET (0);
}
MPFR_SET_NAN (y);
MPFR_RET_NAN;
}
MPFR_SAVE_EXPO_MARK (expo);
prec = Ny + MPFR_INT_CEIL_LOG2 (Ny) + 6;
mpfr_init2 (t, prec);
mpfr_init2 (lg2, prec);
MPFR_ZIV_INIT (loop, prec);
for (nloop = 0; ; nloop++)
{
mpfr_log1p (t, x, MPFR_RNDN);
mpfr_const_log2 (lg2, MPFR_RNDN);
mpfr_div (t, t, lg2, MPFR_RNDN);
/* t = log2(1+x) * (1 + theta)^3 where |theta| < 2^-prec,
for prec >= 2 we have |(1 + theta)^3 - 1| < 4*theta.
Note: contrary to log10p1, no underflow is possible in extended
exponent range, since for tiny x, |log2(1+x)| ~ |x|/log(2) >= |x|,
and x is representable, thus x/log(2) too. */
if (MPFR_LIKELY (MPFR_CAN_ROUND (t, prec - 2, Ny, rnd_mode)))
break;
if (nloop == 0)
{
/* check for exact cases */
mpfr_exp_t k;
MPFR_LOG_MSG (("check for exact cases\n", 0));
k = mpfr_log2p1_isexact (x);
if (k != 0) /* 1+x = 2^k */
{
inexact = mpfr_set_si (y, k, rnd_mode);
goto end;
}
/* if x = 2^k with huge k, Ziv's loop will fail */
inexact = mpfr_log2p1_special (y, x, rnd_mode);
if (inexact != 0)
goto end;
}
MPFR_ZIV_NEXT (loop, prec);
mpfr_set_prec (t, prec);
mpfr_set_prec (lg2, prec);
}
inexact = mpfr_set (y, t, rnd_mode);
end:
MPFR_ZIV_FREE (loop);
mpfr_clear (t);
mpfr_clear (lg2);
MPFR_SAVE_EXPO_FREE (expo);
return mpfr_check_range (y, inexact, rnd_mode);
}
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