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/* mpfr_sub1sp -- internal function to perform a "real" subtraction
All the op must have the same precision
Copyright 2003-2019 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"
/* Check if we have to check the result of mpfr_sub1sp with mpfr_sub1 */
#if MPFR_WANT_ASSERT >= 2
int mpfr_sub1sp_ref (mpfr_ptr, mpfr_srcptr, mpfr_srcptr, mpfr_rnd_t);
int mpfr_sub1sp (mpfr_ptr a, mpfr_srcptr b, mpfr_srcptr c, mpfr_rnd_t rnd_mode)
{
mpfr_t tmpa, tmpb, tmpc;
mpfr_flags_t old_flags, flags, flags2;
int inexb, inexc, inexact, inexact2;
if (rnd_mode == MPFR_RNDF)
return mpfr_sub1sp_ref (a, b, c, rnd_mode);
old_flags = __gmpfr_flags;
mpfr_init2 (tmpa, MPFR_PREC (a));
mpfr_init2 (tmpb, MPFR_PREC (b));
mpfr_init2 (tmpc, MPFR_PREC (c));
inexb = mpfr_set (tmpb, b, MPFR_RNDN);
MPFR_ASSERTN (inexb == 0);
inexc = mpfr_set (tmpc, c, MPFR_RNDN);
MPFR_ASSERTN (inexc == 0);
MPFR_ASSERTN (__gmpfr_flags == old_flags);
inexact2 = mpfr_sub1 (tmpa, tmpb, tmpc, rnd_mode);
flags2 = __gmpfr_flags;
__gmpfr_flags = old_flags;
inexact = mpfr_sub1sp_ref (a, b, c, rnd_mode);
flags = __gmpfr_flags;
if (! mpfr_equal_p (tmpa, a) || inexact != inexact2 || flags != flags2)
{
fprintf (stderr, "sub1 & sub1sp return different values for %s\n"
"Prec_a = %lu, Prec_b = %lu, Prec_c = %lu\nB = ",
mpfr_print_rnd_mode (rnd_mode),
(unsigned long) MPFR_PREC (a),
(unsigned long) MPFR_PREC (b),
(unsigned long) MPFR_PREC (c));
mpfr_fdump (stderr, tmpb);
fprintf (stderr, "C = ");
mpfr_fdump (stderr, tmpc);
fprintf (stderr, "sub1 : ");
mpfr_fdump (stderr, tmpa);
fprintf (stderr, "sub1sp: ");
mpfr_fdump (stderr, a);
fprintf (stderr, "Inexact sp = %d | Inexact = %d\n"
"Flags sp = %u | Flags = %u\n",
inexact, inexact2, flags, flags2);
MPFR_ASSERTN (0);
}
mpfr_clears (tmpa, tmpb, tmpc, (mpfr_ptr) 0);
return inexact;
}
# define mpfr_sub1sp mpfr_sub1sp_ref
#endif /* MPFR_WANT_ASSERT >= 2 */
#if !defined(MPFR_GENERIC_ABI)
/* special code for p < GMP_NUMB_BITS */
static int
mpfr_sub1sp1 (mpfr_ptr a, mpfr_srcptr b, mpfr_srcptr c, mpfr_rnd_t rnd_mode,
mpfr_prec_t p)
{
mpfr_exp_t bx = MPFR_GET_EXP (b);
mpfr_exp_t cx = MPFR_GET_EXP (c);
mp_limb_t *ap = MPFR_MANT(a);
mp_limb_t *bp = MPFR_MANT(b);
mp_limb_t *cp = MPFR_MANT(c);
mpfr_prec_t cnt, INITIALIZED(sh);
mp_limb_t rb; /* round bit */
mp_limb_t sb; /* sticky bit */
mp_limb_t a0;
mp_limb_t mask;
mpfr_uexp_t d;
MPFR_ASSERTD(p < GMP_NUMB_BITS);
if (bx == cx)
{
a0 = bp[0] - cp[0];
if (a0 == 0) /* result is zero */
{
if (rnd_mode == MPFR_RNDD)
MPFR_SET_NEG(a);
else
MPFR_SET_POS(a);
MPFR_SET_ZERO(a);
MPFR_RET (0);
}
else if (a0 > bp[0]) /* borrow: |c| > |b| */
{
MPFR_SET_OPPOSITE_SIGN (a, b);
a0 = -a0;
}
else /* bp[0] > cp[0] */
MPFR_SET_SAME_SIGN (a, b);
/* now a0 != 0 */
MPFR_ASSERTD(a0 != 0);
count_leading_zeros (cnt, a0);
ap[0] = a0 << cnt;
bx -= cnt;
rb = sb = 0;
/* Note: sh is not initialized, but will not be used in this case. */
}
else if (bx > cx)
{
MPFR_SET_SAME_SIGN (a, b);
BGreater1:
d = (mpfr_uexp_t) bx - cx;
sh = GMP_NUMB_BITS - p;
mask = MPFR_LIMB_MASK(sh);
if (d < GMP_NUMB_BITS)
{
sb = - (cp[0] << (GMP_NUMB_BITS - d)); /* neglected part of -c */
/* Note that "a0 = bp[0] - (cp[0] >> d) - (sb != 0);" is faster
on some other machines and has no immediate dependencies for
the first subtraction. In the future, make sure that the code
is recognized as a *single* subtraction with borrow and/or use
a builtin when available (currently provided by Clang, but not
by GCC); create a new macro for that. See the TODO later.
Note also that with Clang, the constant 0 for the first
subtraction instead of a variable breaks the optimization:
https://llvm.org/bugs/show_bug.cgi?id=31754 */
a0 = bp[0] - (sb != 0) - (cp[0] >> d);
/* a0 cannot be zero here since:
a) if d >= 2, then a0 >= 2^(w-1) - (2^(w-2)-1) with
w = GMP_NUMB_BITS, thus a0 - 1 >= 2^(w-2),
b) if d = 1, then since p < GMP_NUMB_BITS we have sb=0.
*/
MPFR_ASSERTD(a0 > 0);
count_leading_zeros (cnt, a0);
if (cnt)
a0 = (a0 << cnt) | (sb >> (GMP_NUMB_BITS - cnt));
sb <<= cnt;
bx -= cnt;
/* sh > 0 since p < GMP_NUMB_BITS */
MPFR_ASSERTD(sh > 0);
rb = a0 & (MPFR_LIMB_ONE << (sh - 1));
sb |= (a0 & mask) ^ rb;
ap[0] = a0 & ~mask;
}
else /* d >= GMP_NUMB_BITS */
{
if (bp[0] > MPFR_LIMB_HIGHBIT)
{
/* We compute b - ulp(b), and the remainder ulp(b) - c satisfies:
1/2 ulp(b) < ulp(b) - c < ulp(b), thus rb = sb = 1. */
ap[0] = bp[0] - (MPFR_LIMB_ONE << sh);
rb = 1;
}
else
{
/* Warning: since we have an exponent decrease, when
p = GMP_NUMB_BITS - 1 and d = GMP_NUMB_BITS, the round bit
corresponds to the upper bit of -c. In that case rb = 0 and
sb = 1, except when c0 = MPFR_LIMB_HIGHBIT where rb = 1 and
sb = 0. */
rb = sh > 1 || d > GMP_NUMB_BITS || cp[0] == MPFR_LIMB_HIGHBIT;
/* sb=1 below is incorrect when p = GMP_NUMB_BITS - 1,
d = GMP_NUMB_BITS and c0 = MPFR_LIMB_HIGHBIT, but in
that case the even rule wound round up too. */
ap[0] = ~mask;
bx --;
/* Warning: if d = GMP_NUMB_BITS and c0 = 1000...000, then
b0 - c0 = |0111...111|1000...000|, which after the shift
becomes |111...111|000...000| thus if p = GMP_NUMB_BITS-1
we have rb = 1 but sb = 0. However in this case the round
even rule will round up, which is what we get with sb = 1:
the final result will be correct, while sb is incorrect. */
}
sb = 1;
}
}
else /* cx > bx */
{
mpfr_exp_t tx;
mp_limb_t *tp;
tx = bx; bx = cx; cx = tx;
tp = bp; bp = cp; cp = tp;
MPFR_SET_OPPOSITE_SIGN (a, b);
goto BGreater1;
}
/* now perform rounding */
/* Warning: MPFR considers underflow *after* rounding with an unbounded
exponent range. However since b and c have same precision p, they are
multiples of 2^(emin-p), likewise for b-c. Thus if bx < emin, the
subtraction (with an unbounded exponent range) is exact, so that bx is
also the exponent after rounding with an unbounded exponent range. */
if (MPFR_UNLIKELY(bx < __gmpfr_emin))
{
/* For RNDN, mpfr_underflow always rounds away, thus for |a| <= 2^(emin-2)
we have to change to RNDZ. This corresponds to:
(a) either bx < emin - 1
(b) or bx = emin - 1 and ap[0] = 1000....000 (in this case necessarily
rb = sb = 0 since b-c is multiple of 2^(emin-p) */
if (rnd_mode == MPFR_RNDN &&
(bx < __gmpfr_emin - 1 || ap[0] == MPFR_LIMB_HIGHBIT))
{
MPFR_ASSERTD(rb == 0 && sb == 0);
rnd_mode = MPFR_RNDZ;
}
return mpfr_underflow (a, rnd_mode, MPFR_SIGN(a));
}
MPFR_SET_EXP (a, bx);
if ((rb == 0 && sb == 0) || rnd_mode == MPFR_RNDF)
MPFR_RET (0);
else if (rnd_mode == MPFR_RNDN)
{
if (rb == 0 || (sb == 0 && (ap[0] & (MPFR_LIMB_ONE << sh)) == 0))
goto truncate;
else
goto add_one_ulp;
}
else if (MPFR_IS_LIKE_RNDZ(rnd_mode, MPFR_IS_NEG(a)))
{
truncate:
MPFR_RET(-MPFR_SIGN(a));
}
else /* round away from zero */
{
add_one_ulp:
ap[0] += MPFR_LIMB_ONE << sh;
if (MPFR_UNLIKELY(ap[0] == 0))
{
ap[0] = MPFR_LIMB_HIGHBIT;
/* Note: bx+1 cannot exceed __gmpfr_emax, since |a| <= |b|, thus
bx+1 is at most equal to the original exponent of b. */
MPFR_ASSERTD(bx + 1 <= __gmpfr_emax);
MPFR_SET_EXP (a, bx + 1);
}
MPFR_RET(MPFR_SIGN(a));
}
}
/* special code for p = GMP_NUMB_BITS */
static int
mpfr_sub1sp1n (mpfr_ptr a, mpfr_srcptr b, mpfr_srcptr c, mpfr_rnd_t rnd_mode)
{
mpfr_exp_t bx = MPFR_GET_EXP (b);
mpfr_exp_t cx = MPFR_GET_EXP (c);
mp_limb_t *ap = MPFR_MANT(a);
mp_limb_t *bp = MPFR_MANT(b);
mp_limb_t *cp = MPFR_MANT(c);
mpfr_prec_t cnt;
mp_limb_t rb; /* round bit */
mp_limb_t sb; /* sticky bit */
mp_limb_t a0;
mpfr_uexp_t d;
MPFR_ASSERTD(MPFR_PREC(a) == GMP_NUMB_BITS);
MPFR_ASSERTD(MPFR_PREC(b) == GMP_NUMB_BITS);
MPFR_ASSERTD(MPFR_PREC(c) == GMP_NUMB_BITS);
if (bx == cx)
{
a0 = bp[0] - cp[0];
if (a0 == 0) /* result is zero */
{
if (rnd_mode == MPFR_RNDD)
MPFR_SET_NEG(a);
else
MPFR_SET_POS(a);
MPFR_SET_ZERO(a);
MPFR_RET (0);
}
else if (a0 > bp[0]) /* borrow: |c| > |b| */
{
MPFR_SET_OPPOSITE_SIGN (a, b);
a0 = -a0;
}
else /* bp[0] > cp[0] */
MPFR_SET_SAME_SIGN (a, b);
/* now a0 != 0 */
MPFR_ASSERTD(a0 != 0);
count_leading_zeros (cnt, a0);
ap[0] = a0 << cnt;
bx -= cnt;
rb = sb = 0;
}
else if (bx > cx)
{
MPFR_SET_SAME_SIGN (a, b);
BGreater1:
d = (mpfr_uexp_t) bx - cx;
if (d < GMP_NUMB_BITS)
{
sb = - (cp[0] << (GMP_NUMB_BITS - d)); /* neglected part of -c */
a0 = bp[0] - (sb != 0) - (cp[0] >> d);
/* a0 can only be zero when d=1, b0 = B/2, and c0 = B-1, where
B = 2^GMP_NUMB_BITS, thus b0 - c0/2 = 1/2 */
if (a0 == MPFR_LIMB_ZERO)
{
bx -= GMP_NUMB_BITS;
ap[0] = MPFR_LIMB_HIGHBIT;
rb = sb = 0;
}
else
{
count_leading_zeros (cnt, a0);
if (cnt)
a0 = (a0 << cnt) | (sb >> (GMP_NUMB_BITS - cnt));
sb <<= cnt;
bx -= cnt;
rb = sb & MPFR_LIMB_HIGHBIT;
sb &= ~MPFR_LIMB_HIGHBIT;
ap[0] = a0;
}
}
else /* d >= GMP_NUMB_BITS */
{
/* We compute b - ulp(b) */
if (bp[0] > MPFR_LIMB_HIGHBIT)
{
/* If d = GMP_NUMB_BITS, rb = 0 and sb = 1,
unless c0 = MPFR_LIMB_HIGHBIT in which case rb = 1 and sb = 0.
If d > GMP_NUMB_BITS, rb = sb = 1. */
rb = d > GMP_NUMB_BITS || cp[0] == MPFR_LIMB_HIGHBIT;
sb = d > GMP_NUMB_BITS || cp[0] != MPFR_LIMB_HIGHBIT;
ap[0] = bp[0] - MPFR_LIMB_ONE;
}
else
{
/* Warning: in this case a0 is shifted by one!
If d=GMP_NUMB_BITS:
(a) if c0 = MPFR_LIMB_HIGHBIT, a0 = 111...111, rb = sb = 0
(b) otherwise, a0 = 111...110, rb = -c0 >= 01000...000,
sb = (-c0) << 2
If d=GMP_NUMB_BITS+1: a0 = 111...111
(c) if c0 = MPFR_LIMB_HIGHBIT, rb = 1 and sb = 0
(d) otherwise rb = 0 and sb = 1
If d > GMP_NUMB_BITS+1:
(e) a0 = 111...111, rb = sb = 1
*/
bx --;
if (d == GMP_NUMB_BITS && cp[0] > MPFR_LIMB_HIGHBIT)
{ /* case (b) */
rb = (-cp[0]) >= (MPFR_LIMB_HIGHBIT >> 1);
sb = (-cp[0]) << 2;
ap[0] = -(MPFR_LIMB_ONE << 1);
}
else /* cases (a), (c), (d) and (e) */
{
/* rb=1 in case (e) and case (c) */
rb = d > GMP_NUMB_BITS + 1
|| (d == GMP_NUMB_BITS + 1 && cp[0] == MPFR_LIMB_HIGHBIT);
/* sb = 1 in case (d) and (e) */
sb = d > GMP_NUMB_BITS + 1
|| (d == GMP_NUMB_BITS + 1 && cp[0] > MPFR_LIMB_HIGHBIT);
/* Warning: only set ap[0] last, otherwise in case ap=cp,
the above comparisons involving cp[0] would be wrong */
ap[0] = -MPFR_LIMB_ONE;
}
}
}
}
else /* cx > bx */
{
mpfr_exp_t tx;
mp_limb_t *tp;
tx = bx; bx = cx; cx = tx;
tp = bp; bp = cp; cp = tp;
MPFR_SET_OPPOSITE_SIGN (a, b);
goto BGreater1;
}
/* now perform rounding */
/* Warning: MPFR considers underflow *after* rounding with an unbounded
exponent range. However since b and c have same precision p, they are
multiples of 2^(emin-p), likewise for b-c. Thus if bx < emin, the
subtraction (with an unbounded exponent range) is exact, so that bx is
also the exponent after rounding with an unbounded exponent range. */
if (MPFR_UNLIKELY(bx < __gmpfr_emin))
{
/* For RNDN, mpfr_underflow always rounds away, thus for |a| <= 2^(emin-2)
we have to change to RNDZ. This corresponds to:
(a) either bx < emin - 1
(b) or bx = emin - 1 and ap[0] = 1000....000 (in this case necessarily
rb = sb = 0 since b-c is multiple of 2^(emin-p) */
if (rnd_mode == MPFR_RNDN &&
(bx < __gmpfr_emin - 1 || ap[0] == MPFR_LIMB_HIGHBIT))
{
MPFR_ASSERTD(rb == 0 && sb == 0);
rnd_mode = MPFR_RNDZ;
}
return mpfr_underflow (a, rnd_mode, MPFR_SIGN(a));
}
MPFR_SET_EXP (a, bx);
if ((rb == 0 && sb == 0) || rnd_mode == MPFR_RNDF)
MPFR_RET (0);
else if (rnd_mode == MPFR_RNDN)
{
if (rb == 0 || (sb == 0 && (ap[0] & MPFR_LIMB_ONE) == 0))
goto truncate;
else
goto add_one_ulp;
}
else if (MPFR_IS_LIKE_RNDZ(rnd_mode, MPFR_IS_NEG(a)))
{
truncate:
MPFR_RET(-MPFR_SIGN(a));
}
else /* round away from zero */
{
add_one_ulp:
ap[0] += MPFR_LIMB_ONE;
if (MPFR_UNLIKELY(ap[0] == 0))
{
ap[0] = MPFR_LIMB_HIGHBIT;
/* Note: bx+1 cannot exceed __gmpfr_emax, since |a| <= |b|, thus
bx+1 is at most equal to the original exponent of b. */
MPFR_ASSERTD(bx + 1 <= __gmpfr_emax);
MPFR_SET_EXP (a, bx + 1);
}
MPFR_RET(MPFR_SIGN(a));
}
}
/* special code for GMP_NUMB_BITS < p < 2*GMP_NUMB_BITS */
static int
mpfr_sub1sp2 (mpfr_ptr a, mpfr_srcptr b, mpfr_srcptr c, mpfr_rnd_t rnd_mode,
mpfr_prec_t p)
{
mpfr_exp_t bx = MPFR_GET_EXP (b);
mpfr_exp_t cx = MPFR_GET_EXP (c);
mp_limb_t *ap = MPFR_MANT(a);
mp_limb_t *bp = MPFR_MANT(b);
mp_limb_t *cp = MPFR_MANT(c);
mpfr_prec_t cnt, INITIALIZED(sh);
mp_limb_t rb; /* round bit */
mp_limb_t sb; /* sticky bit */
mp_limb_t mask, a0, a1;
mpfr_uexp_t d;
MPFR_ASSERTD(GMP_NUMB_BITS < p && p < 2 * GMP_NUMB_BITS);
if (bx == cx) /* subtraction is exact in this case */
{
/* first compute a0: if the compiler is smart enough, it will use the generated
borrow to get for free the term (bp[0] < cp[0]) */
a0 = bp[0] - cp[0];
a1 = bp[1] - cp[1] - (bp[0] < cp[0]);
if (a1 == 0 && a0 == 0) /* result is zero */
{
if (rnd_mode == MPFR_RNDD)
MPFR_SET_NEG(a);
else
MPFR_SET_POS(a);
MPFR_SET_ZERO(a);
MPFR_RET (0);
}
else if (a1 >= bp[1]) /* borrow: |c| > |b| */
{
MPFR_SET_OPPOSITE_SIGN (a, b);
/* a = b-c mod 2^(2*GMP_NUMB_BITS) */
a0 = -a0;
a1 = -a1 - (a0 != 0);
}
else /* bp[0] > cp[0] */
MPFR_SET_SAME_SIGN (a, b);
if (a1 == 0)
{
a1 = a0;
a0 = 0;
bx -= GMP_NUMB_BITS;
}
/* now a1 != 0 */
MPFR_ASSERTD(a1 != 0);
count_leading_zeros (cnt, a1);
if (cnt)
{
ap[1] = (a1 << cnt) | (a0 >> (GMP_NUMB_BITS - cnt));
ap[0] = a0 << cnt;
bx -= cnt;
}
else
{
ap[1] = a1;
ap[0] = a0;
}
rb = sb = 0;
/* Note: sh is not initialized, but will not be used in this case. */
}
else if (bx > cx)
{
mp_limb_t t;
MPFR_SET_SAME_SIGN (a, b);
BGreater2:
d = (mpfr_uexp_t) bx - cx;
sh = 2 * GMP_NUMB_BITS - p;
mask = MPFR_LIMB_MASK(sh);
if (d < GMP_NUMB_BITS)
{
t = (cp[1] << (GMP_NUMB_BITS - d)) | (cp[0] >> d);
/* TODO: Change the code to generate a full subtraction with borrow,
avoiding the test on sb and the corresponding correction. Note
that Clang has builtins:
http://clang.llvm.org/docs/LanguageExtensions.html#multiprecision-arithmetic-builtins
but the generated code may not be good:
https://llvm.org/bugs/show_bug.cgi?id=20748
With the current source code, Clang generates on x86_64:
1. sub %rsi,%rbx for the first subtraction in a1;
2. sub %rdi,%rax for the subtraction in a0;
3. sbb $0x0,%rbx for the second subtraction in a1, i.e. just
subtracting the borrow out from (2).
So, Clang recognizes the borrow, but doesn't merge (1) and (3).
Bug: https://llvm.org/bugs/show_bug.cgi?id=25858
For GCC: https://gcc.gnu.org/bugzilla/show_bug.cgi?id=79173
*/
#ifndef MPFR_FULLSUB
a0 = bp[0] - t;
a1 = bp[1] - (cp[1] >> d) - (bp[0] < t);
sb = cp[0] << (GMP_NUMB_BITS - d); /* neglected part of c */
if (sb)
{
a1 -= (a0 == 0);
a0 --;
/* a = a1,a0 cannot become zero here, since:
a) if d >= 2, then a1 >= 2^(w-1) - (2^(w-2)-1) with
w = GMP_NUMB_BITS, thus a1 - 1 >= 2^(w-2),
b) if d = 1, then since p < 2*GMP_NUMB_BITS we have sb=0. */
MPFR_ASSERTD(a1 > 0 || a0 > 0);
sb = -sb; /* 2^GMP_NUMB_BITS - sb */
}
#else
sb = - (cp[0] << (GMP_NUMB_BITS - d));
a0 = bp[0] - t - (sb != 0);
a1 = bp[1] - (cp[1] >> d) - (bp[0] < t || (bp[0] == t && sb != 0));
#endif
if (a1 == 0)
{
/* this implies d=1, which in turn implies sb=0 */
MPFR_ASSERTD(sb == 0);
a1 = a0;
a0 = 0; /* should be a0 = sb */
/* since sb=0 already, no need to set it to 0 */
bx -= GMP_NUMB_BITS;
}
/* now a1 != 0 */
MPFR_ASSERTD(a1 != 0);
count_leading_zeros (cnt, a1);
if (cnt)
{
ap[1] = (a1 << cnt) | (a0 >> (GMP_NUMB_BITS - cnt));
a0 = (a0 << cnt) | (sb >> (GMP_NUMB_BITS - cnt));
sb <<= cnt;
bx -= cnt;
}
else
ap[1] = a1;
/* sh > 0 since p < 2*GMP_NUMB_BITS */
MPFR_ASSERTD(sh > 0);
rb = a0 & (MPFR_LIMB_ONE << (sh - 1));
sb |= (a0 & mask) ^ rb;
ap[0] = a0 & ~mask;
}
else if (d < 2 * GMP_NUMB_BITS)
{ /* GMP_NUMB_BITS <= d < 2*GMP_NUMB_BITS */
/* warning: the most significant bit of sb might become the least
significant bit of a0 below */
sb = (d == GMP_NUMB_BITS) ? cp[0]
: (cp[1] << (2*GMP_NUMB_BITS - d)) | (cp[0] != 0);
t = (cp[1] >> (d - GMP_NUMB_BITS)) + (sb != 0);
/* warning: t might overflow to 0 if d=GMP_NUMB_BITS and sb <> 0 */
a0 = bp[0] - t;
a1 = bp[1] - (bp[0] < t) - (t == 0 && sb != 0);
sb = -sb;
/* since bp[1] has its most significant bit set, we can have an
exponent decrease of at most one */
if (a1 < MPFR_LIMB_HIGHBIT)
{
ap[1] = (a1 << 1) | (a0 >> (GMP_NUMB_BITS - 1));
a0 = (a0 << 1) | (sb >> (GMP_NUMB_BITS - 1));
sb <<= 1;
bx --;
}
else
ap[1] = a1;
rb = a0 & (MPFR_LIMB_ONE << (sh - 1));
sb |= (a0 & mask) ^ rb;
ap[0] = a0 & ~mask;
}
else /* d >= 2*GMP_NUMB_BITS */
{
/* We compute b - ulp(b), and the remainder ulp(b) - c satisfies:
1/2 ulp(b) < ulp(b) - c < ulp(b), thus rb = sb = 1, unless we
had an exponent decrease. */
t = MPFR_LIMB_ONE << sh;
a0 = bp[0] - t;
a1 = bp[1] - (bp[0] < t);
if (a1 < MPFR_LIMB_HIGHBIT)
{
/* necessarily we had b = 1000...000 */
/* Warning: since we have an exponent decrease, when
p = 2*GMP_NUMB_BITS - 1 and d = 2*GMP_NUMB_BITS, the round bit
corresponds to the upper bit of -c. In that case rb = 0 and
sb = 1, except when c = 1000...000 where rb = 1 and sb = 0. */
rb = sh > 1 || d > 2 * GMP_NUMB_BITS
|| (cp[1] == MPFR_LIMB_HIGHBIT && cp[0] == MPFR_LIMB_ZERO);
/* sb=1 below is incorrect when p = 2*GMP_NUMB_BITS - 1,
d = 2*GMP_NUMB_BITS and c = 1000...000, but in
that case the even rule wound round up too. */
ap[0] = ~mask;
ap[1] = MPFR_LIMB_MAX;
bx --;
}
else
{
ap[0] = a0;
ap[1] = a1;
rb = 1;
}
sb = 1;
}
}
else /* cx > bx */
{
mpfr_exp_t tx;
mp_limb_t *tp;
tx = bx; bx = cx; cx = tx;
tp = bp; bp = cp; cp = tp;
MPFR_SET_OPPOSITE_SIGN (a, b);
goto BGreater2;
}
/* now perform rounding */
/* Warning: MPFR considers underflow *after* rounding with an unbounded
exponent range. However since b and c have same precision p, they are
multiples of 2^(emin-p), likewise for b-c. Thus if bx < emin, the
subtraction (with an unbounded exponent range) is exact, so that bx is
also the exponent after rounding with an unbounded exponent range. */
if (MPFR_UNLIKELY(bx < __gmpfr_emin))
{
/* for RNDN, mpfr_underflow always rounds away, thus for |a|<=2^(emin-2)
we have to change to RNDZ */
if (rnd_mode == MPFR_RNDN &&
(bx < __gmpfr_emin - 1 ||
(ap[1] == MPFR_LIMB_HIGHBIT && ap[0] == 0)))
rnd_mode = MPFR_RNDZ;
return mpfr_underflow (a, rnd_mode, MPFR_SIGN(a));
}
MPFR_SET_EXP (a, bx);
if ((rb == 0 && sb == 0) || rnd_mode == MPFR_RNDF)
MPFR_RET (0);
else if (rnd_mode == MPFR_RNDN)
{
if (rb == 0 || (sb == 0 && (ap[0] & (MPFR_LIMB_ONE << sh)) == 0))
goto truncate;
else
goto add_one_ulp;
}
else if (MPFR_IS_LIKE_RNDZ(rnd_mode, MPFR_IS_NEG(a)))
{
truncate:
MPFR_RET(-MPFR_SIGN(a));
}
else /* round away from zero */
{
add_one_ulp:
ap[0] += MPFR_LIMB_ONE << sh;
ap[1] += (ap[0] == 0);
if (MPFR_UNLIKELY(ap[1] == 0))
{
ap[1] = MPFR_LIMB_HIGHBIT;
/* Note: bx+1 cannot exceed __gmpfr_emax, since |a| <= |b|, thus
bx+1 is at most equal to the original exponent of b. */
MPFR_ASSERTD(bx + 1 <= __gmpfr_emax);
MPFR_SET_EXP (a, bx + 1);
}
MPFR_RET(MPFR_SIGN(a));
}
}
/* special code for 2*GMP_NUMB_BITS < p < 3*GMP_NUMB_BITS */
static int
mpfr_sub1sp3 (mpfr_ptr a, mpfr_srcptr b, mpfr_srcptr c, mpfr_rnd_t rnd_mode,
mpfr_prec_t p)
{
mpfr_exp_t bx = MPFR_GET_EXP (b);
mpfr_exp_t cx = MPFR_GET_EXP (c);
mp_limb_t *ap = MPFR_MANT(a);
mp_limb_t *bp = MPFR_MANT(b);
mp_limb_t *cp = MPFR_MANT(c);
mpfr_prec_t cnt, INITIALIZED(sh);
mp_limb_t rb; /* round bit */
mp_limb_t sb; /* sticky bit */
mp_limb_t mask, a0, a1, a2;
mpfr_uexp_t d;
MPFR_ASSERTD(2 * GMP_NUMB_BITS < p && p < 3 * GMP_NUMB_BITS);
if (bx == cx) /* subtraction is exact in this case */
{
a0 = bp[0] - cp[0];
a1 = bp[1] - cp[1] - (bp[0] < cp[0]);
/* a borrow is generated for a when either bp[1] < cp[1],
or bp[1] = cp[1] and bp[0] < cp[0] */
a2 = bp[2] - cp[2]
- (bp[1] < cp[1] || (bp[1] == cp[1] && bp[0] < cp[0]));
if (a2 == 0 && a1 == 0 && a0 == 0) /* result is zero */
{
if (rnd_mode == MPFR_RNDD)
MPFR_SET_NEG(a);
else
MPFR_SET_POS(a);
MPFR_SET_ZERO(a);
MPFR_RET (0);
}
else if (a2 >= bp[2]) /* borrow: |c| > |b| */
{
MPFR_SET_OPPOSITE_SIGN (a, b);
/* a = b-c mod 2^(3*GMP_NUMB_BITS) */
a0 = -a0;
a1 = -a1 - (a0 != 0);
a2 = -a2 - (a0 != 0 || a1 != 0);
}
else /* bp[0] > cp[0] */
MPFR_SET_SAME_SIGN (a, b);
if (a2 == 0)
{
a2 = a1;
a1 = a0;
a0 = 0;
bx -= GMP_NUMB_BITS;
if (a2 == 0)
{
a2 = a1;
a1 = 0;
bx -= GMP_NUMB_BITS;
}
}
/* now a2 != 0 */
MPFR_ASSERTD(a2 != 0);
count_leading_zeros (cnt, a2);
if (cnt)
{
ap[2] = (a2 << cnt) | (a1 >> (GMP_NUMB_BITS - cnt));
ap[1] = (a1 << cnt) | (a0 >> (GMP_NUMB_BITS - cnt));
ap[0] = a0 << cnt;
bx -= cnt;
}
else
{
ap[2] = a2;
ap[1] = a1;
ap[0] = a0;
}
rb = sb = 0;
/* Note: sh is not initialized, but will not be used in this case. */
}
else if (bx > cx)
{
MPFR_SET_SAME_SIGN (a, b);
BGreater2:
d = (mpfr_uexp_t) bx - cx;
sh = 3 * GMP_NUMB_BITS - p;
mask = MPFR_LIMB_MASK(sh);
if (d < GMP_NUMB_BITS)
{
mp_limb_t cy;
/* warning: we must have the most significant bit of sb correct
since it might become the round bit below */
sb = cp[0] << (GMP_NUMB_BITS - d); /* neglected part of c */
a0 = bp[0] - ((cp[1] << (GMP_NUMB_BITS - d)) | (cp[0] >> d));
a1 = bp[1] - ((cp[2] << (GMP_NUMB_BITS - d)) | (cp[1] >> d))
- (a0 > bp[0]);
cy = a1 > bp[1] || (a1 == bp[1] && a0 > bp[0]); /* borrow in a1 */
a2 = bp[2] - (cp[2] >> d) - cy;
/* if sb is non-zero, subtract 1 from a2, a1, a0 since we want a
non-negative neglected part */
if (sb)
{
a2 -= (a1 == 0 && a0 == 0);
a1 -= (a0 == 0);
a0 --;
/* a = a2,a1,a0 cannot become zero here, since:
a) if d >= 2, then a2 >= 2^(w-1) - (2^(w-2)-1) with
w = GMP_NUMB_BITS, thus a2 - 1 >= 2^(w-2),
b) if d = 1, then since p < 3*GMP_NUMB_BITS we have sb=0. */
MPFR_ASSERTD(a2 > 0 || a1 > 0 || a0 > 0);
sb = -sb; /* 2^GMP_NUMB_BITS - sb */
}
if (a2 == 0)
{
/* this implies d=1, which in turn implies sb=0 */
MPFR_ASSERTD(sb == 0);
a2 = a1;
a1 = a0;
a0 = 0; /* should be a0 = sb */
/* since sb=0 already, no need to set it to 0 */
bx -= GMP_NUMB_BITS;
if (a2 == 0)
{
a2 = a1;
a1 = 0; /* should be a1 = a0 */
bx -= GMP_NUMB_BITS;
}
}
/* now a1 != 0 */
MPFR_ASSERTD(a2 != 0);
count_leading_zeros (cnt, a2);
if (cnt)
{
ap[2] = (a2 << cnt) | (a1 >> (GMP_NUMB_BITS - cnt));
ap[1] = (a1 << cnt) | (a0 >> (GMP_NUMB_BITS - cnt));
a0 = (a0 << cnt) | (sb >> (GMP_NUMB_BITS - cnt));
sb <<= cnt;
bx -= cnt;
}
else
{
ap[2] = a2;
ap[1] = a1;
}
/* sh > 0 since p < 2*GMP_NUMB_BITS */
MPFR_ASSERTD(sh > 0);
rb = a0 & (MPFR_LIMB_ONE << (sh - 1));
sb |= (a0 & mask) ^ rb;
ap[0] = a0 & ~mask;
}
else if (d < 2 * GMP_NUMB_BITS)
{
mp_limb_t c0shifted;
/* warning: we must have the most significant bit of sb correct
since it might become the round bit below */
sb = (d == GMP_NUMB_BITS) ? cp[0]
: (cp[1] << (2*GMP_NUMB_BITS - d)) | (cp[0] != 0);
c0shifted = (d == GMP_NUMB_BITS) ? cp[1]
: (cp[2] << (2*GMP_NUMB_BITS-d)) | (cp[1] >> (d - GMP_NUMB_BITS));
a0 = bp[0] - c0shifted;
/* TODO: add a non-regression test for cp[2] == MPFR_LIMB_MAX,
d == GMP_NUMB_BITS and a0 > bp[0]. */
a1 = bp[1] - (cp[2] >> (d - GMP_NUMB_BITS)) - (a0 > bp[0]);
a2 = bp[2] - (a1 > bp[1] || (a1 == bp[1] && a0 > bp[0]));
/* if sb is non-zero, subtract 1 from a2, a1, a0 since we want a
non-negative neglected part */
if (sb)
{
a2 -= (a1 == 0 && a0 == 0);
a1 -= (a0 == 0);
a0 --;
/* a = a2,a1,a0 cannot become zero here, since:
a) if d >= 2, then a2 >= 2^(w-1) - (2^(w-2)-1) with
w = GMP_NUMB_BITS, thus a2 - 1 >= 2^(w-2),
b) if d = 1, then since p < 3*GMP_NUMB_BITS we have sb=0. */
MPFR_ASSERTD(a2 > 0 || a1 > 0 || a0 > 0);
sb = -sb; /* 2^GMP_NUMB_BITS - sb */
}
/* since bp[2] has its most significant bit set, we can have an
exponent decrease of at most one */
if (a2 < MPFR_LIMB_HIGHBIT)
{
ap[2] = (a2 << 1) | (a1 >> (GMP_NUMB_BITS - 1));
ap[1] = (a1 << 1) | (a0 >> (GMP_NUMB_BITS - 1));
a0 = (a0 << 1) | (sb >> (GMP_NUMB_BITS - 1));
sb <<= 1;
bx --;
}
else
{
ap[2] = a2;
ap[1] = a1;
}
rb = a0 & (MPFR_LIMB_ONE << (sh - 1));
sb |= (a0 & mask) ^ rb;
ap[0] = a0 & ~mask;
}
else if (d < 3 * GMP_NUMB_BITS) /* 2*GMP_NUMB_BITS<=d<3*GMP_NUMB_BITS */
{
MPFR_ASSERTD (2*GMP_NUMB_BITS <= d && d < 3*GMP_NUMB_BITS);
/* warning: we must have the most significant bit of sb correct
since it might become the round bit below */
if (d == 2 * GMP_NUMB_BITS)
sb = cp[1] | (cp[0] != 0);
else
sb = cp[2] << (3*GMP_NUMB_BITS - d) | (cp[1] != 0) | (cp[0] != 0);
sb = -sb;
/* TODO: add a non-regression test for cp[2] == MPFR_LIMB_MAX,
d == 2*GMP_NUMB_BITS and sb != 0. */
a0 = bp[0] - (cp[2] >> (d - 2*GMP_NUMB_BITS)) - (sb != 0);
a1 = bp[1] - (a0 > bp[0] || (a0 == bp[0] && sb != 0));
a2 = bp[2] - (a1 > bp[1]);
if (a2 < MPFR_LIMB_HIGHBIT)
{
ap[2] = (a2 << 1) | (a1 >> (GMP_NUMB_BITS - 1));
ap[1] = (a1 << 1) | (a0 >> (GMP_NUMB_BITS - 1));
a0 = (a0 << 1) | (sb >> (GMP_NUMB_BITS - 1));
sb <<= 1;
bx --;
}
else
{
ap[2] = a2;
ap[1] = a1;
}
rb = a0 & (MPFR_LIMB_ONE << (sh - 1));
sb |= (a0 & mask) ^ rb;
ap[0] = a0 & ~mask;
}
else /* d >= 3*GMP_NUMB_BITS */
{
/* We compute b - ulp(b), and the remainder ulp(b) - c satisfies:
1/2 ulp(b) < ulp(b) - c < ulp(b), thus rb = sb = 1. */
mp_limb_t t = MPFR_LIMB_ONE << sh;
a0 = bp[0] - t;
a1 = bp[1] - (bp[0] < t);
a2 = bp[2] - (a1 > bp[1]);
if (a2 < MPFR_LIMB_HIGHBIT)
{
/* necessarily we had b = 1000...000 */
/* Warning: since we have an exponent decrease, when
p = 3*GMP_NUMB_BITS - 1 and d = 3*GMP_NUMB_BITS, the round bit
corresponds to the upper bit of -c. In that case rb = 0 and
sb = 1, except when c = 1000...000 where rb = 1 and sb = 0. */
rb = sh > 1 || d > 3 * GMP_NUMB_BITS
|| (cp[2] == MPFR_LIMB_HIGHBIT && cp[1] == MPFR_LIMB_ZERO &&
cp[0] == MPFR_LIMB_ZERO);
/* sb=1 below is incorrect when p = 2*GMP_NUMB_BITS - 1,
d = 2*GMP_NUMB_BITS and c = 1000...000, but in
that case the even rule wound round up too. */
ap[0] = ~mask;
ap[1] = MPFR_LIMB_MAX;
ap[2] = MPFR_LIMB_MAX;
bx --;
}
else
{
ap[0] = a0;
ap[1] = a1;
ap[2] = a2;
rb = 1;
}
sb = 1;
}
}
else /* cx > bx */
{
mpfr_exp_t tx;
mp_limb_t *tp;
tx = bx; bx = cx; cx = tx;
tp = bp; bp = cp; cp = tp;
MPFR_SET_OPPOSITE_SIGN (a, b);
goto BGreater2;
}
/* now perform rounding */
/* Warning: MPFR considers underflow *after* rounding with an unbounded
exponent range. However since b and c have same precision p, they are
multiples of 2^(emin-p), likewise for b-c. Thus if bx < emin, the
subtraction (with an unbounded exponent range) is exact, so that bx is
also the exponent after rounding with an unbounded exponent range. */
if (MPFR_UNLIKELY(bx < __gmpfr_emin))
{
/* for RNDN, mpfr_underflow always rounds away, thus for |a|<=2^(emin-2)
we have to change to RNDZ */
if (rnd_mode == MPFR_RNDN &&
(bx < __gmpfr_emin - 1 ||
(ap[2] == MPFR_LIMB_HIGHBIT && ap[1] == 0 && ap[0] == 0)))
rnd_mode = MPFR_RNDZ;
return mpfr_underflow (a, rnd_mode, MPFR_SIGN(a));
}
MPFR_SET_EXP (a, bx);
if ((rb == 0 && sb == 0) || rnd_mode == MPFR_RNDF)
MPFR_RET (0);
else if (rnd_mode == MPFR_RNDN)
{
if (rb == 0 || (sb == 0 && (ap[0] & (MPFR_LIMB_ONE << sh)) == 0))
goto truncate;
else
goto add_one_ulp;
}
else if (MPFR_IS_LIKE_RNDZ(rnd_mode, MPFR_IS_NEG(a)))
{
truncate:
MPFR_RET(-MPFR_SIGN(a));
}
else /* round away from zero */
{
add_one_ulp:
ap[0] += MPFR_LIMB_ONE << sh;
ap[1] += (ap[0] == 0);
ap[2] += (ap[1] == 0 && ap[0] == 0);
if (MPFR_UNLIKELY(ap[2] == 0))
{
ap[2] = MPFR_LIMB_HIGHBIT;
/* Note: bx+1 cannot exceed __gmpfr_emax, since |a| <= |b|, thus
bx+1 is at most equal to the original exponent of b. */
MPFR_ASSERTD(bx + 1 <= __gmpfr_emax);
MPFR_SET_EXP (a, bx + 1);
}
MPFR_RET(MPFR_SIGN(a));
}
}
#endif /* !defined(MPFR_GENERIC_ABI) */
/* Rounding Sub */
/*
compute sgn(b)*(|b| - |c|) if |b|>|c| else -sgn(b)*(|c| -|b|)
Returns 0 iff result is exact,
a negative value when the result is less than the exact value,
a positive value otherwise.
*/
/* A0...Ap-1
* Cp Cp+1 ....
* <- C'p+1 ->
* Cp = -1 if calculated from c mantissa
* Cp = 0 if 0 from a or c
* Cp = 1 if calculated from a.
* C'p+1 = First bit not null or 0 if there isn't one
*
* Can't have Cp=-1 and C'p+1=1*/
/* RND = MPFR_RNDZ:
* + if Cp=0 and C'p+1=0,1, Truncate.
* + if Cp=0 and C'p+1=-1, SubOneUlp
* + if Cp=-1, SubOneUlp
* + if Cp=1, AddOneUlp
* RND = MPFR_RNDA (Away)
* + if Cp=0 and C'p+1=0,-1, Truncate
* + if Cp=0 and C'p+1=1, AddOneUlp
* + if Cp=1, AddOneUlp
* + if Cp=-1, Truncate
* RND = MPFR_RNDN
* + if Cp=0, Truncate
* + if Cp=1 and C'p+1=1, AddOneUlp
* + if Cp=1 and C'p+1=-1, Truncate
* + if Cp=1 and C'p+1=0, Truncate if Ap-1=0, AddOneUlp else
* + if Cp=-1 and C'p+1=-1, SubOneUlp
* + if Cp=-1 and C'p+1=0, Truncate if Ap-1=0, SubOneUlp else
*
* If AddOneUlp:
* If carry, then it is 11111111111 + 1 = 10000000000000
* ap[n-1]=MPFR_HIGHT_BIT
* If SubOneUlp:
* If we lose one bit, it is 1000000000 - 1 = 0111111111111
* Then shift, and put as last bit x which is calculated
* according Cp, Cp-1 and rnd_mode.
* If Truncate,
* If it is a power of 2,
* we may have to suboneulp in some special cases.
*
* To simplify, we don't use Cp = 1.
*
*/
MPFR_HOT_FUNCTION_ATTR int
mpfr_sub1sp (mpfr_ptr a, mpfr_srcptr b, mpfr_srcptr c, mpfr_rnd_t rnd_mode)
{
mpfr_exp_t bx, cx;
mpfr_uexp_t d;
mpfr_prec_t p, sh, cnt;
mp_size_t n;
mp_limb_t *ap, *bp, *cp;
mp_limb_t limb;
int inexact;
mp_limb_t bcp,bcp1; /* Cp and C'p+1 */
mp_limb_t bbcp = MPFR_LIMB_MAX, bbcp1 = MPFR_LIMB_MAX; /* Cp+1 and C'p+2,
gcc claims that they might be used uninitialized. We fill them with invalid
values, which should produce a failure if so. See README.dev file. */
MPFR_TMP_DECL(marker);
MPFR_ASSERTD(MPFR_PREC(a) == MPFR_PREC(b) && MPFR_PREC(b) == MPFR_PREC(c));
MPFR_ASSERTD(MPFR_IS_PURE_FP(b));
MPFR_ASSERTD(MPFR_IS_PURE_FP(c));
/* Read prec and num of limbs */
p = MPFR_GET_PREC (b);
#if !defined(MPFR_GENERIC_ABI)
/* special case for p < GMP_NUMB_BITS */
if (p < GMP_NUMB_BITS)
return mpfr_sub1sp1 (a, b, c, rnd_mode, p);
/* special case for GMP_NUMB_BITS < p < 2*GMP_NUMB_BITS */
if (GMP_NUMB_BITS < p && p < 2 * GMP_NUMB_BITS)
return mpfr_sub1sp2 (a, b, c, rnd_mode, p);
/* special case for p = GMP_NUMB_BITS: we put it *after* mpfr_sub1sp2,
in order not to slow down mpfr_sub1sp2, which should be more frequent */
if (p == GMP_NUMB_BITS)
return mpfr_sub1sp1n (a, b, c, rnd_mode);
/* special case for 2*GMP_NUMB_BITS < p < 3*GMP_NUMB_BITS */
if (2 * GMP_NUMB_BITS < p && p < 3 * GMP_NUMB_BITS)
return mpfr_sub1sp3 (a, b, c, rnd_mode, p);
#endif
n = MPFR_PREC2LIMBS (p);
/* Fast cmp of |b| and |c| */
bx = MPFR_GET_EXP (b);
cx = MPFR_GET_EXP (c);
MPFR_TMP_MARK(marker);
if (bx == cx)
{
mp_size_t k = n - 1;
/* Check mantissa since exponents are equal */
bp = MPFR_MANT(b);
cp = MPFR_MANT(c);
while (k >= 0 && MPFR_UNLIKELY(bp[k] == cp[k]))
k--;
if (k < 0)
/* b == c ! */
{
/* Return exact number 0 */
if (rnd_mode == MPFR_RNDD)
MPFR_SET_NEG(a);
else
MPFR_SET_POS(a);
MPFR_SET_ZERO(a);
MPFR_RET(0);
}
else if (bp[k] > cp[k])
goto BGreater;
else
{
MPFR_ASSERTD(bp[k] < cp[k]);
goto CGreater;
}
}
else if (bx < cx)
{
/* Swap b and c and set sign */
mpfr_srcptr t;
mpfr_exp_t tx;
CGreater:
MPFR_SET_OPPOSITE_SIGN(a,b);
t = b; b = c; c = t;
tx = bx; bx = cx; cx = tx;
}
else
{
/* |b| > |c| */
BGreater:
MPFR_SET_SAME_SIGN(a,b);
}
/* Now |b| > |c| */
MPFR_ASSERTD(bx >= cx);
d = (mpfr_uexp_t) bx - cx;
/* printf ("New with diff=%lu\n", (unsigned long) d); */
if (d <= 1)
{
if (d == 0)
{
/* <-- b -->
<-- c --> : exact sub */
ap = MPFR_MANT(a);
mpn_sub_n (ap, MPFR_MANT(b), MPFR_MANT(c), n);
/* Normalize */
ExactNormalize:
limb = ap[n-1];
if (MPFR_LIKELY (limb != 0))
{
/* First limb is not zero. */
count_leading_zeros(cnt, limb);
/* cnt could be == 0 <= SubD1Lose */
if (MPFR_LIKELY(cnt))
{
mpn_lshift(ap, ap, n, cnt); /* Normalize number */
bx -= cnt; /* Update final expo */
}
/* Last limb should be OK */
MPFR_ASSERTD(!(ap[0] & MPFR_LIMB_MASK((unsigned int) (-p)
% GMP_NUMB_BITS)));
}
else
{
/* First limb is zero */
mp_size_t k = n-1, len;
/* Find the first limb not equal to zero. It necessarily exists
since |b| > |c|. */
do
{
MPFR_ASSERTD( k > 0 );
limb = ap[--k];
}
while (limb == 0);
MPFR_ASSERTD(limb != 0);
count_leading_zeros(cnt, limb);
k++;
len = n - k; /* Number of last limb */
MPFR_ASSERTD(k >= 0);
if (cnt)
mpn_lshift (ap + len, ap, k, cnt); /* Normalize the High Limb*/
else
{
/* Must use copyd since src and dst may overlap & dst>=src */
mpn_copyd (ap+len, ap, k);
}
MPN_ZERO(ap, len); /* Zeroing the last limbs */
bx -= cnt + len*GMP_NUMB_BITS; /* Update Expo */
/* Last limb should be OK */
MPFR_ASSERTD(!(ap[len] & MPFR_LIMB_MASK((unsigned int) (-p)
% GMP_NUMB_BITS)));
}
/* Check expo underflow */
if (MPFR_UNLIKELY(bx < __gmpfr_emin))
{
MPFR_TMP_FREE(marker);
/* since b and c have same sign, exponent and precision, the
subtraction is exact */
/* printf("(D==0 Underflow)\n"); */
/* for MPFR_RNDN, mpfr_underflow always rounds away from zero,
thus for |a| <= 2^(emin-2) we change to RNDZ. */
if (rnd_mode == MPFR_RNDN &&
(bx < __gmpfr_emin - 1 || mpfr_powerof2_raw (a)))
rnd_mode = MPFR_RNDZ;
return mpfr_underflow (a, rnd_mode, MPFR_SIGN(a));
}
MPFR_SET_EXP (a, bx);
/* No rounding is necessary since the result is exact */
MPFR_ASSERTD(ap[n-1] > ~ap[n-1]);
MPFR_TMP_FREE(marker);
return 0;
}
else /* if (d == 1) */
{
/* | <-- b -->
| <-- c --> */
mp_limb_t c0, mask;
mp_size_t k;
MPFR_UNSIGNED_MINUS_MODULO(sh, p);
/* If we lose at least one bit, compute 2*b-c (Exact)
* else compute b-c/2 */
bp = MPFR_MANT(b);
cp = MPFR_MANT(c);
k = n-1;
limb = bp[k] - cp[k]/2;
/* we have |b|-|c| >= limb*W^k - (2*W^k-1)/2 >= limb*W^k - W^k + 1/2
thus if limb > W^k/2, |b|-|c| >= 1/2*W^n.
Moreover if trunc(|c|) represents the first p-1 bits of |c|,
minus the last significant bit called c0 below, then we have
|b|-trunc(|c|) >= 1/2*W^n+1, thus the two mpn_sub_n calls
below necessarily yield a > 1/2*W^n. */
if (limb > MPFR_LIMB_HIGHBIT)
{
/* The exponent cannot decrease: compute b-c/2 */
/* Shift c in the allocated temporary block */
SubD1NoLose:
c0 = cp[0] & (MPFR_LIMB_ONE << sh);
mask = ~MPFR_LIMB_MASK(sh);
ap = MPFR_MANT(a);
cp = MPFR_TMP_LIMBS_ALLOC (n);
/* FIXME: it might be faster to have one function shifting c by 1
to the right and adding with b to a, which would read c once
only, and avoid a temporary allocation. */
mpn_rshift (cp, MPFR_MANT(c), n, 1);
cp[0] &= mask; /* Zero last bit of c if set */
mpn_sub_n (ap, bp, cp, n);
MPFR_SET_EXP(a, bx); /* No expo overflow! */
MPFR_ASSERTD(ap[n-1] > ~ap[n-1]);
if (MPFR_LIKELY(c0 == 0))
{
/* Result is exact: no need of rounding! */
MPFR_TMP_FREE(marker);
return 0;
}
MPFR_ASSERTD( !(ap[0] & ~mask) ); /* Check last bits */
/* No normalize is needed */
/* Rounding is necessary since c0 = 1 */
/* Cp =-1 and C'p+1=0 */
bcp = 1; bcp1 = 0;
if (rnd_mode == MPFR_RNDF)
goto truncate; /* low(b) = 0 and low(c) is 0 or 1/2 ulp(b), thus
low(b) - low(c) = 0 or -1/2 ulp(b) */
else if (rnd_mode == MPFR_RNDN)
{
/* Even Rule apply: Check last bit of a. */
if (MPFR_LIKELY( (ap[0] & (MPFR_LIMB_ONE << sh)) == 0) )
goto truncate;
else
goto sub_one_ulp;
}
MPFR_UPDATE_RND_MODE(rnd_mode, MPFR_IS_NEG(a));
if (rnd_mode == MPFR_RNDZ)
goto sub_one_ulp;
else
goto truncate;
}
else if (MPFR_LIKELY(limb < MPFR_LIMB_HIGHBIT))
{
/* |b| - |c| <= (W/2-1)*W^k + W^k-1 = 1/2*W^n - 1 */
/* The exponent decreases by one. */
SubD1Lose:
ap = MPFR_MANT(a);
/* Compute 2*b-c (Exact) */
/* Experiments with __gmpn_rsblsh_n show that it is not always
faster than mpn_lshift + mpn_sub_n, thus we don't enable it
for now (HAVE___GMPN_RSBLSH_N -> HAVE___GMPN_RSBLSH_Nxxx). */
#if defined(WANT_GMP_INTERNALS) && defined(HAVE___GMPN_RSBLSH_Nxxx)
/* {ap, n} = 2*{bp, n} - {cp, n} */
__gmpn_rsblsh_n (ap, MPFR_MANT(c), MPFR_MANT(b), n, 1);
#else
bp = MPFR_TMP_LIMBS_ALLOC (n);
/* Shift b in the allocated temporary block */
mpn_lshift (bp, MPFR_MANT(b), n, 1);
mpn_sub_n (ap, bp, cp, n);
#endif
bx--;
goto ExactNormalize;
}
else
{
/* Case: limb = 100000000000 */
/* Check while b[k] == c'[k] (C' is C shifted by 1) */
/* If b[k]<c'[k] => We lose at least one bit*/
/* If b[k]>c'[k] => We don't lose any bit */
/* If k==-1 => We don't lose any bit
AND the result is 100000000000 0000000000 00000000000 */
mp_limb_t carry;
do
{
carry = cp[k] << (GMP_NUMB_BITS - 1);
if (--k < 0)
break;
carry += cp[k] >> 1;
}
while (bp[k] == carry);
if (MPFR_UNLIKELY(k < 0))
{
ap = MPFR_MANT (a);
if (MPFR_UNLIKELY(carry))
{
/* If carry then necessarily the precision is an exact
multiple of GMP_NUMB_BITS, and we lose one bit,
thus the (exact) result is a power of 2 minus 1. */
memset (ap, -1, n * MPFR_BYTES_PER_MP_LIMB);
MPFR_SET_EXP (a, bx - 1);
/* No underflow is possible since cx = bx-1 is a valid
exponent. */
}
else
{
/* No carry: result is a power of 2. */
MPN_ZERO (ap, n - 1);
ap[n-1] = MPFR_LIMB_HIGHBIT;
MPFR_SET_EXP (a, bx); /* No expo overflow! */
}
/* No Normalize is needed */
/* No Rounding is needed */
MPFR_TMP_FREE (marker);
return 0;
}
/* carry = cp[k]/2+(cp[k-1]&1)<<(GMP_NUMB_BITS-1) = c'[k]*/
else if (bp[k] > carry)
goto SubD1NoLose; /* |b|-|c| >= 1/2*W^n */
else
{
MPFR_ASSERTD(bp[k] < carry);
goto SubD1Lose; /* |b|-|c| <= 1/2*W^n-1 and is exact */
}
}
}
}
else if (MPFR_UNLIKELY(d >= p)) /* the difference of exponents is larger
than the precision of all operands, thus
the result is either b or b - 1 ulp,
with a possible exact result when
d = p, b = 2^e and c = 1/2 ulp(b) */
{
ap = MPFR_MANT(a);
MPFR_UNSIGNED_MINUS_MODULO(sh, p);
/* We can't set A before since we use cp for rounding... */
/* Perform rounding: check if a=b or a=b-ulp(b) */
if (MPFR_UNLIKELY(d == p))
{
/* cp == -1 and c'p+1 = ? */
bcp = 1;
/* We need Cp+1 later for a very improbable case. */
bbcp = (MPFR_MANT(c)[n-1] & (MPFR_LIMB_ONE<<(GMP_NUMB_BITS-2)));
/* We need also C'p+1 for an even more unprobable case... */
if (MPFR_LIKELY( bbcp ))
bcp1 = 1;
else
{
cp = MPFR_MANT(c);
if (MPFR_UNLIKELY(cp[n-1] == MPFR_LIMB_HIGHBIT))
{
mp_size_t k = n-1;
do
k--;
while (k >= 0 && cp[k] == 0);
bcp1 = (k >= 0);
}
else
bcp1 = 1;
}
/* printf("(D=P) Cp=-1 Cp+1=%d C'p+1=%d \n", bbcp!=0, bcp1!=0); */
bp = MPFR_MANT (b);
/* Even if src and dest overlap, it is OK using MPN_COPY */
if (MPFR_LIKELY(rnd_mode == MPFR_RNDF))
/* then d = p, and subtracting one ulp of b is ok even in the
exact case b = 2^e and c = 1/2 ulp(b) */
{
MPN_COPY(ap, bp, n);
goto sub_one_ulp;
}
else if (rnd_mode == MPFR_RNDN)
{
if (MPFR_UNLIKELY (bcp != 0 && bcp1 == 0))
/* Cp=-1 and C'p+1=0: Even rule Apply! */
/* Check Ap-1 = Bp-1 */
if ((bp[0] & (MPFR_LIMB_ONE << sh)) == 0)
{
MPN_COPY(ap, bp, n);
goto truncate;
}
MPN_COPY(ap, bp, n);
goto sub_one_ulp;
}
MPFR_UPDATE_RND_MODE(rnd_mode, MPFR_IS_NEG(a));
if (rnd_mode == MPFR_RNDZ)
{
MPN_COPY(ap, bp, n);
goto sub_one_ulp;
}
else
{
MPN_COPY(ap, bp, n);
goto truncate;
}
}
else
{
/* Cp=0, Cp+1=-1 if d==p+1, C'p+1=-1 */
bcp = 0; bbcp = (d==p+1); bcp1 = 1;
/* printf("(D>P) Cp=%d Cp+1=%d C'p+1=%d\n", bcp!=0,bbcp!=0,bcp1!=0); */
/* Need to compute C'p+2 if d==p+1 and if rnd_mode=NEAREST
(Because of a very improbable case) */
if (MPFR_UNLIKELY(d==p+1 && rnd_mode==MPFR_RNDN))
{
cp = MPFR_MANT(c);
if (MPFR_UNLIKELY(cp[n-1] == MPFR_LIMB_HIGHBIT))
{
mp_size_t k = n-1;
do
k--;
while (k >= 0 && cp[k] == 0);
bbcp1 = (k >= 0);
}
else
bbcp1 = 1;
/* printf("(D>P) C'p+2=%d\n", bbcp1!=0); */
}
/* Copy mantissa B in A */
MPN_COPY(ap, MPFR_MANT(b), n);
/* Round */
if (rnd_mode == MPFR_RNDF || rnd_mode == MPFR_RNDN)
goto truncate;
MPFR_UPDATE_RND_MODE(rnd_mode, MPFR_IS_NEG(a));
if (rnd_mode == MPFR_RNDZ)
goto sub_one_ulp;
else /* rnd_mode = AWAY */
goto truncate;
}
}
else /* case 2 <= d < p */
{
mpfr_uexp_t dm;
mp_size_t m;
mp_limb_t mask;
MPFR_UNSIGNED_MINUS_MODULO(sh, p);
cp = MPFR_TMP_LIMBS_ALLOC (n);
/* Shift c in temporary allocated place */
dm = d % GMP_NUMB_BITS;
m = d / GMP_NUMB_BITS;
if (MPFR_UNLIKELY(dm == 0))
{
/* dm = 0 and m > 0: Just copy */
MPFR_ASSERTD(m != 0);
MPN_COPY(cp, MPFR_MANT(c)+m, n-m);
MPN_ZERO(cp+n-m, m);
}
else if (MPFR_LIKELY(m == 0))
{
/* dm >=2 and m == 0: just shift */
MPFR_ASSERTD(dm >= 2);
mpn_rshift(cp, MPFR_MANT(c), n, dm);
}
else
{
/* dm > 0 and m > 0: shift and zero */
mpn_rshift(cp, MPFR_MANT(c)+m, n-m, dm);
MPN_ZERO(cp+n-m, m);
}
/* mpfr_print_mant_binary("Before", MPFR_MANT(c), p); */
/* mpfr_print_mant_binary("B= ", MPFR_MANT(b), p); */
/* mpfr_print_mant_binary("After ", cp, p); */
/* Compute bcp=Cp and bcp1=C'p+1 */
if (MPFR_LIKELY(sh))
{
/* Try to compute them from C' rather than C (FIXME: Faster?) */
bcp = (cp[0] & (MPFR_LIMB_ONE<<(sh-1))) ;
if (cp[0] & MPFR_LIMB_MASK(sh-1))
bcp1 = 1;
else
{
/* We can't compute C'p+1 from C'. Compute it from C */
/* Start from bit x=p-d+sh in mantissa C
(+sh since we have already looked sh bits in C'!) */
mpfr_prec_t x = p-d+sh-1;
if (x > p)
/* We are already looked at all the bits of c, so C'p+1 = 0*/
bcp1 = 0;
else
{
mp_limb_t *tp = MPFR_MANT(c);
mp_size_t kx = n-1 - (x / GMP_NUMB_BITS);
mpfr_prec_t sx = GMP_NUMB_BITS-1-(x%GMP_NUMB_BITS);
/* printf ("(First) x=%lu Kx=%ld Sx=%lu\n",
(unsigned long) x, (long) kx, (unsigned long) sx); */
/* Looks at the last bits of limb kx (if sx=0 does nothing)*/
if (tp[kx] & MPFR_LIMB_MASK(sx))
bcp1 = 1;
else
{
/*kx += (sx==0);*/
/*If sx==0, tp[kx] hasn't been checked*/
do
kx--;
while (kx >= 0 && tp[kx] == 0);
bcp1 = (kx >= 0);
}
}
}
}
else
{
/* Compute Cp and C'p+1 from C with sh=0 */
mp_limb_t *tp = MPFR_MANT(c);
/* Start from bit x=p-d in mantissa C */
mpfr_prec_t x = p-d;
mp_size_t kx = n-1 - (x / GMP_NUMB_BITS);
mpfr_prec_t sx = GMP_NUMB_BITS-1-(x%GMP_NUMB_BITS);
MPFR_ASSERTD(p >= d);
bcp = (tp[kx] & (MPFR_LIMB_ONE<<sx));
/* Looks at the last bits of limb kx (If sx=0, does nothing)*/
if (tp[kx] & MPFR_LIMB_MASK(sx))
bcp1 = 1;
else
{
/*kx += (sx==0);*/ /*If sx==0, tp[kx] hasn't been checked*/
do
kx--;
while (kx >= 0 && tp[kx] == 0);
bcp1 = (kx >= 0);
}
}
/* printf("sh=%lu Cp=%d C'p+1=%d\n", sh, bcp!=0, bcp1!=0); */
/* Check if we can lose a bit, and if so compute Cp+1 and C'p+2 */
bp = MPFR_MANT(b);
if (MPFR_UNLIKELY (bp[n-1] - cp[n-1] <= MPFR_LIMB_HIGHBIT))
{
/* We can lose a bit so we precompute Cp+1 and C'p+2 */
/* Test for trivial case: since C'p+1=0, Cp+1=0 and C'p+2 =0 */
if (MPFR_LIKELY(bcp1 == 0))
{
bbcp = 0;
bbcp1 = 0;
}
else /* bcp1 != 0 */
{
/* We can lose a bit:
compute Cp+1 and C'p+2 from mantissa C */
mp_limb_t *tp = MPFR_MANT(c);
/* Start from bit x=(p+1)-d in mantissa C */
mpfr_prec_t x = p+1-d;
mp_size_t kx = n-1 - (x / GMP_NUMB_BITS);
mpfr_prec_t sx = GMP_NUMB_BITS-1 - (x % GMP_NUMB_BITS);
MPFR_ASSERTD(p > d);
/* printf ("(pre) x=%lu Kx=%ld Sx=%lu\n",
(unsigned long) x, (long) kx, (unsigned long) sx); */
bbcp = (tp[kx] & (MPFR_LIMB_ONE<<sx)) ;
/* Looks at the last bits of limb kx (If sx=0, does nothing)*/
/* If Cp+1=0, since C'p+1!=0, C'p+2=1 ! */
if (MPFR_LIKELY (bbcp == 0 || (tp[kx] & MPFR_LIMB_MASK(sx))))
bbcp1 = 1;
else
{
/*kx += (sx==0);*/ /*If sx==0, tp[kx] hasn't been checked*/
do
kx--;
while (kx >= 0 && tp[kx] == 0);
bbcp1 = (kx >= 0);
/* printf ("(Pre) Scan done for %ld\n", (long) kx); */
}
} /*End of Bcp1 != 0*/
/* printf("(Pre) Cp+1=%d C'p+2=%d\n", bbcp!=0, bbcp1!=0); */
} /* End of "can lose a bit" */
/* Clean shifted C' */
mask = ~MPFR_LIMB_MASK (sh);
cp[0] &= mask;
/* Subtract the mantissa c from b in a */
ap = MPFR_MANT(a);
mpn_sub_n (ap, bp, cp, n);
/* mpfr_print_mant_binary("Sub= ", ap, p); */
/* Normalize: we lose at max one bit*/
if (MPFR_UNLIKELY(MPFR_LIMB_MSB(ap[n-1]) == 0))
{
/* High bit is not set and we have to fix it! */
/* Ap >= 010000xxx001 */
mpn_lshift(ap, ap, n, 1);
/* Ap >= 100000xxx010 */
if (MPFR_UNLIKELY(bcp != 0)) /* Check if Cp = -1 */
/* Since Cp == -1, we have to subtract one more */
{
mpn_sub_1(ap, ap, n, MPFR_LIMB_ONE<<sh);
MPFR_ASSERTD(MPFR_LIMB_MSB(ap[n-1]) != 0);
}
/* Ap >= 10000xxx001 */
/* Final exponent -1 since we have shifted the mantissa */
bx--;
/* Update bcp and bcp1 */
MPFR_ASSERTD(bbcp != MPFR_LIMB_MAX);
MPFR_ASSERTD(bbcp1 != MPFR_LIMB_MAX);
bcp = bbcp;
bcp1 = bbcp1;
/* We don't have anymore a valid Cp+1!
But since Ap >= 100000xxx001, the final sub can't unnormalize!*/
}
MPFR_ASSERTD( !(ap[0] & ~mask) );
/* Rounding */
if (MPFR_LIKELY(rnd_mode == MPFR_RNDF))
goto truncate;
else if (MPFR_LIKELY(rnd_mode == MPFR_RNDN))
{
if (MPFR_LIKELY(bcp == 0))
goto truncate;
else if (bcp1 != 0 || (ap[0] & (MPFR_LIMB_ONE << sh)) != 0)
goto sub_one_ulp;
else
goto truncate;
}
/* Update rounding mode */
MPFR_UPDATE_RND_MODE(rnd_mode, MPFR_IS_NEG(a));
if (rnd_mode == MPFR_RNDZ && MPFR_LIKELY (bcp != 0 || bcp1 != 0))
goto sub_one_ulp;
goto truncate;
}
MPFR_RET_NEVER_GO_HERE ();
/* Sub one ulp to the result */
sub_one_ulp:
mpn_sub_1 (ap, ap, n, MPFR_LIMB_ONE << sh);
/* Result should be smaller than exact value: inexact=-1 */
inexact = -1;
/* Check normalization */
if (MPFR_UNLIKELY(ap[n-1] < MPFR_LIMB_HIGHBIT))
{
/* ap was a power of 2, and we lose a bit */
/* Now it is 0111111111111111111[00000 */
/* The following 2 lines are equivalent to: mpn_lshift(ap, ap, n, 1); */
ap[0] <<= 1;
ap[n-1] |= MPFR_LIMB_HIGHBIT;
bx--;
/* And the lost bit x depends on Cp+1, and Cp */
/* Compute Cp+1 if it isn't already computed (ie d==1) */
/* Note: we can't have d = 1 here, since the only "goto sub_one_ulp"
for d = 1 are in the "SubD1NoLose" case, and in that case
|b|-|c| >= 1/2*W^n, thus round(|b|-|c|) >= 1/2*W^n, and ap[n-1]
cannot go below MPFR_LIMB_HIGHBIT. */
/* printf("(SubOneUlp)Cp=%d, Cp+1=%d C'p+1=%d\n", bcp!=0,bbcp!=0,bcp1!=0); */
/* Compute the last bit (Since we have shifted the mantissa)
we need one more bit! */
MPFR_ASSERTD(bbcp != MPFR_LIMB_MAX);
if ((rnd_mode == MPFR_RNDZ && bcp == 0) ||
(rnd_mode == MPFR_RNDN && bbcp == 0) ||
(bcp != 0 && bcp1 == 0)) /* Exact result */
{
ap[0] |= MPFR_LIMB_ONE << sh;
if (rnd_mode == MPFR_RNDN)
inexact = 1;
/* printf("(SubOneUlp) Last bit set\n"); */
}
/* Result could be exact if C'p+1 = 0 and rnd == Zero
since we have had one more bit to the result */
/* Fixme: rnd_mode == MPFR_RNDZ needed ? */
if (rnd_mode == MPFR_RNDZ && bcp1 == 0)
{
/* printf("(SubOneUlp) Exact result\n"); */
inexact = 0;
}
}
goto end_of_sub;
truncate:
/* Check if the result is an exact power of 2: 100000000000
in which cases, we could have to do sub_one_ulp due to some nasty reasons:
If Result is a Power of 2:
+ If rnd = AWAY,
| If Cp=-1 and C'p+1 = 0, SubOneUlp and the result is EXACT.
If Cp=-1 and C'p+1 =-1, SubOneUlp and the result is above.
Otherwise truncate
+ If rnd = NEAREST,
If Cp= 0 and Cp+1 =-1 and C'p+2=-1, SubOneUlp and the result is above
If cp=-1 and C'p+1 = 0, SubOneUlp and the result is exact.
Otherwise truncate.
X bit should always be set if SubOneUlp*/
if (MPFR_UNLIKELY(ap[n-1] == MPFR_LIMB_HIGHBIT))
{
mp_size_t k = n-1;
do
k--;
while (k >= 0 && ap[k] == 0);
if (MPFR_UNLIKELY (k < 0))
{
/* It is a power of 2! */
/* Compute Cp+1 if it isn't already compute (ie d==1) */
/* Note: if d=1, we have {a, n} > 1/2*W^n, thus we cannot have k < 0. */
/* printf("(Truncate) Cp=%d, Cp+1=%d C'p+1=%d C'p+2=%d\n",
bcp!=0, bbcp!=0, bcp1!=0, bbcp1!=0); */
MPFR_ASSERTD(bbcp != MPFR_LIMB_MAX);
MPFR_ASSERTD(rnd_mode != MPFR_RNDN || bcp != 0 ||
bbcp == 0 || bbcp1 != MPFR_LIMB_MAX);
if ((rnd_mode != MPFR_RNDZ && bcp != 0) ||
(rnd_mode == MPFR_RNDN && bcp == 0 && bbcp != 0 && bbcp1 != 0))
{
/* printf("(Truncate) Do sub\n"); */
mpn_sub_1 (ap, ap, n, MPFR_LIMB_ONE << sh);
ap[n-1] |= MPFR_LIMB_HIGHBIT;
bx--;
/* FIXME: Explain why it works (or why not)... */
inexact = (bcp1 == 0) ? 0 : (rnd_mode == MPFR_RNDN) ? -1 : 1;
goto end_of_sub;
}
}
}
/* Calcul of Inexact flag.*/
inexact = (bcp != 0 || bcp1 != 0);
end_of_sub:
/* Update Exponent */
/* bx >= emin. Proof:
If d==0 : Exact case. This is never called.
if 1 < d < p : bx=MPFR_EXP(b) or MPFR_EXP(b)-1 > MPFR_EXP(c) > emin
if d == 1 : bx=MPFR_EXP(b). If we could lose any bits, the exact
normalization is called.
if d >= p : bx=MPFR_EXP(b) >= MPFR_EXP(c) + p > emin
After SubOneUlp, we could have one bit less.
if 1 < d < p : bx >= MPFR_EXP(b)-2 >= MPFR_EXP(c) > emin
if d == 1 : bx >= MPFR_EXP(b)-1 = MPFR_EXP(c) > emin.
if d >= p : bx >= MPFR_EXP(b)-1 > emin since p>=2.
*/
MPFR_ASSERTD( bx >= __gmpfr_emin);
MPFR_SET_EXP (a, bx);
MPFR_TMP_FREE(marker);
MPFR_RET (inexact * MPFR_INT_SIGN (a));
}
|