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-rw-r--r--Build/source/libs/mpfr/mpfr-src/src/sub1.c749
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diff --git a/Build/source/libs/mpfr/mpfr-src/src/sub1.c b/Build/source/libs/mpfr/mpfr-src/src/sub1.c
deleted file mode 100644
index 6ffdcd358a3..00000000000
--- a/Build/source/libs/mpfr/mpfr-src/src/sub1.c
+++ /dev/null
@@ -1,749 +0,0 @@
-/* mpfr_sub1 -- internal function to perform a "real" subtraction
-
-Copyright 2001-2020 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. */
-
-#include "mpfr-impl.h"
-
-/* compute sign(b) * (|b| - |c|), with |b| > |c|, diff_exp = EXP(b) - EXP(c)
- Returns 0 iff result is exact,
- a negative value when the result is less than the exact value,
- a positive value otherwise.
-*/
-
-int
-mpfr_sub1 (mpfr_ptr a, mpfr_srcptr b, mpfr_srcptr c, mpfr_rnd_t rnd_mode)
-{
- int sign;
- mpfr_exp_t diff_exp, exp_a, exp_b;
- mpfr_prec_t cancel, cancel1;
- mp_size_t cancel2, an, bn, cn, cn0;
- mp_limb_t *ap, *bp, *cp;
- mp_limb_t carry, bb, cc;
- mpfr_prec_t aq, bq;
- int inexact, shift_b, shift_c, add_exp = 0;
- int cmp_low = 0; /* used for rounding to nearest: 0 if low(b) = low(c),
- negative if low(b) < low(c), positive if low(b) > low(c) */
- int sh, k;
- MPFR_TMP_DECL(marker);
-
- MPFR_TMP_MARK(marker);
- ap = MPFR_MANT(a);
- an = MPFR_LIMB_SIZE(a);
-
- (void) MPFR_GET_PREC (a);
- (void) MPFR_GET_PREC (b);
- (void) MPFR_GET_PREC (c);
-
- sign = mpfr_cmp2 (b, c, &cancel);
-
- if (MPFR_UNLIKELY(sign == 0))
- {
- MPFR_LOG_MSG (("sign=0\n", 0));
- if (rnd_mode == MPFR_RNDD)
- MPFR_SET_NEG (a);
- else
- MPFR_SET_POS (a);
- MPFR_SET_ZERO (a);
- MPFR_RET (0);
- }
-
- /* sign != 0, so that cancel has a valid value. */
- MPFR_LOG_MSG (("sign=%d cancel=%Pd\n", sign, cancel));
- MPFR_ASSERTD (cancel >= 0 && cancel <= MPFR_PREC_MAX);
-
- /*
- * If subtraction: sign(a) = sign * sign(b)
- * If addition: sign(a) = sign of the larger argument in absolute value.
- *
- * Both cases can be simplified in:
- * if (sign>0)
- * if addition: sign(a) = sign * sign(b) = sign(b)
- * if subtraction, b is greater, so sign(a) = sign(b)
- * else
- * if subtraction, sign(a) = - sign(b)
- * if addition, sign(a) = sign(c) (since c is greater)
- * But if it is an addition, sign(b) and sign(c) are opposed!
- * So sign(a) = - sign(b)
- */
-
- if (sign < 0) /* swap b and c so that |b| > |c| */
- {
- mpfr_srcptr t;
- MPFR_SET_OPPOSITE_SIGN (a,b);
- t = b; b = c; c = t;
- }
- else
- MPFR_SET_SAME_SIGN (a,b);
-
- if (MPFR_UNLIKELY (MPFR_IS_UBF (b) || MPFR_IS_UBF (c)))
- {
- exp_b = MPFR_UBF_GET_EXP (b);
- /* Early underflow detection. Rare, but a test is needed anyway
- since in the "MAX (aq, bq) + 2 <= diff_exp" branch, the exponent
- may decrease and MPFR_EXP_MIN would yield an integer overflow. */
- if (MPFR_UNLIKELY (exp_b < __gmpfr_emin - 1))
- {
- if (rnd_mode == MPFR_RNDN)
- rnd_mode = MPFR_RNDZ;
- return mpfr_underflow (a, rnd_mode, MPFR_SIGN(a));
- }
- diff_exp = mpfr_ubf_diff_exp (b, c);
- MPFR_LOG_MSG (("UBF: exp_b=%" MPFR_EXP_FSPEC "d%s "
- "diff_exp=%" MPFR_EXP_FSPEC "d%s\n",
- (mpfr_eexp_t) exp_b,
- exp_b == MPFR_EXP_MAX ? "=MPFR_EXP_MAX" : "",
- (mpfr_eexp_t) diff_exp,
- diff_exp == MPFR_EXP_MAX ? "=MPFR_EXP_MAX" : ""));
- /* If diff_exp == MPFR_EXP_MAX, the actual value can be larger,
- but anyway, since mpfr_exp_t >= mp_size_t, this will be the
- case c small below, and the exact value does not matter. */
- /* mpfr_set4 below used with MPFR_RNDF does not support UBF. */
- if (rnd_mode == MPFR_RNDF)
- rnd_mode = MPFR_RNDN;
- }
- else
- {
- exp_b = MPFR_GET_EXP (b);
- diff_exp = exp_b - MPFR_GET_EXP (c);
- }
- MPFR_ASSERTD (diff_exp >= 0);
-
- aq = MPFR_GET_PREC (a);
- bq = MPFR_GET_PREC (b);
-
- /* Check if c is too small.
- A more precise test is to replace 2 by
- (rnd == MPFR_RNDN) + mpfr_power2_raw (b)
- but it is more expensive and not very useful */
- if (MPFR_UNLIKELY (MAX (aq, bq) + 2 <= diff_exp))
- {
- MPFR_LOG_MSG (("case c small\n", 0));
-
- /* Remember, we can't have an exact result! */
- /* A.AAAAAAAAAAAAAAAAA
- = B.BBBBBBBBBBBBBBB
- - C.CCCCCCCCCCCCC */
- /* A = S*ABS(B) +/- ulp(a) */
-
- /* since we can't have an exact result, for RNDF we can truncate b */
- if (rnd_mode == MPFR_RNDF)
- return mpfr_set4 (a, b, MPFR_RNDZ, MPFR_SIGN (a));
-
- exp_a = exp_b; /* may be any out-of-range value due to UBF */
- MPFR_RNDRAW_EVEN (inexact, a, MPFR_MANT (b), bq,
- rnd_mode, MPFR_SIGN (a),
- if (exp_a != MPFR_EXP_MAX)
- exp_a ++);
- MPFR_LOG_MSG (("inexact=%d\n", inexact));
- if (inexact == 0 &&
- /* a = b, but the exact value of b - c is a bit below. Then,
- except for directed rounding similar to toward zero and
- before overflow checking: a is the correctly rounded value
- and since |b| - |c| < |a|, the ternary value value is given
- by the sign of a. */
- ! MPFR_IS_LIKE_RNDZ (rnd_mode, MPFR_IS_NEG (a)))
- {
- MPFR_LOG_MSG (("c small, case 1\n", 0));
- inexact = MPFR_INT_SIGN (a);
- }
- else if (inexact != 0 &&
- /* A.AAAAAAAAAAAAAA
- = B.BBBBBBBBBBBBBBB
- - C.CCCCCCCCCCCCC */
- /* It isn't exact, so PREC(b) > PREC(a) and the last
- PREC(b)-PREC(a) bits of b are not all zeros.
- Subtracting c from b will not have an effect on the rounding
- except in case of a midpoint in the round-to-nearest mode,
- when the even rounding was done away from zero instead of
- toward zero.
- In case of even rounding:
- 1.BBBBBBBBBBBBBx10
- - 1.CCCCCCCCCCCC
- = 1.BBBBBBBBBBBBBx01 Rounded to PREC(b)
- = 1.BBBBBBBBBBBBBx Nearest / Rounded to PREC(a)
- Set gives:
- 1.BBBBBBBBBBBBB0 if inexact == EVEN_INEX (x == 0)
- 1.BBBBBBBBBBBBB1+1 if inexact == -EVEN_INEX (x == 1)
- which means we get a wrong rounded result if x == 1,
- i.e. inexact == MPFR_EVEN_INEX (for positive numbers). */
- MPFR_LIKELY (inexact != MPFR_EVEN_INEX * MPFR_INT_SIGN (a)))
- {
- MPFR_LOG_MSG (("c small, case 2\n", 0));
- /* nothing to do */
- }
- else
- {
- /* We need to take the value preceding |a|. We can't use
- mpfr_nexttozero due to a possible out-of-range exponent.
- But this will allow us to have more specific code. */
- MPFR_LOG_MSG (("c small, case 3: correcting the value of a\n", 0));
- sh = (mpfr_prec_t) an * GMP_NUMB_BITS - aq;
- mpn_sub_1 (ap, ap, an, MPFR_LIMB_ONE << sh);
- if (MPFR_UNLIKELY (MPFR_LIMB_MSB (ap[an-1]) == 0))
- {
- exp_a --;
- /* The following is valid whether an = 1 or an > 1. */
- ap[an-1] |= MPFR_LIMB_HIGHBIT;
- }
- inexact = - MPFR_INT_SIGN (a);
- }
- /* The underflow case is possible only with UBF. The overflow case
- is also possible with normal FP due to rounding. */
- if (MPFR_UNLIKELY (exp_a > __gmpfr_emax))
- return mpfr_overflow (a, rnd_mode, MPFR_SIGN (a));
- if (MPFR_UNLIKELY (exp_a < __gmpfr_emin))
- {
- if (rnd_mode == MPFR_RNDN &&
- (exp_a < __gmpfr_emin - 1 ||
- (inexact * MPFR_INT_SIGN (a) >= 0 && mpfr_powerof2_raw (a))))
- rnd_mode = MPFR_RNDZ;
- return mpfr_underflow (a, rnd_mode, MPFR_SIGN(a));
- }
- MPFR_SET_EXP (a, exp_a);
- MPFR_RET (inexact);
- }
-
- /* reserve a space to store b aligned with the result, i.e. shifted by
- (-cancel) % GMP_NUMB_BITS to the right */
- bn = MPFR_LIMB_SIZE (b);
- MPFR_UNSIGNED_MINUS_MODULO (shift_b, cancel);
- cancel1 = (cancel + shift_b) / GMP_NUMB_BITS;
-
- /* the high cancel1 limbs from b should not be taken into account */
- if (MPFR_UNLIKELY (shift_b == 0))
- {
- bp = MPFR_MANT(b); /* no need of an extra space */
- /* Ensure ap != bp */
- if (MPFR_UNLIKELY (ap == bp))
- {
- bp = MPFR_TMP_LIMBS_ALLOC (bn);
- MPN_COPY (bp, ap, bn);
- }
- }
- else
- {
- bp = MPFR_TMP_LIMBS_ALLOC (bn + 1);
- bp[0] = mpn_rshift (bp + 1, MPFR_MANT(b), bn++, shift_b);
- }
-
- /* reserve a space to store c aligned with the result, i.e. shifted by
- (diff_exp-cancel) % GMP_NUMB_BITS to the right */
- cn = MPFR_LIMB_SIZE (c);
- if (IS_POW2 (GMP_NUMB_BITS))
- shift_c = ((mpfr_uexp_t) diff_exp - cancel) % GMP_NUMB_BITS;
- else
- {
- /* The above operation does not work if diff_exp - cancel < 0. */
- shift_c = diff_exp - (cancel % GMP_NUMB_BITS);
- shift_c = (shift_c + GMP_NUMB_BITS) % GMP_NUMB_BITS;
- }
- MPFR_ASSERTD (shift_c >= 0 && shift_c < GMP_NUMB_BITS);
-
- if (MPFR_UNLIKELY(shift_c == 0))
- {
- cp = MPFR_MANT(c);
- /* Ensure ap != cp */
- if (ap == cp)
- {
- cp = MPFR_TMP_LIMBS_ALLOC (cn);
- MPN_COPY(cp, ap, cn);
- }
- }
- else
- {
- cp = MPFR_TMP_LIMBS_ALLOC (cn + 1);
- cp[0] = mpn_rshift (cp + 1, MPFR_MANT(c), cn++, shift_c);
- }
-
-#if 0
- MPFR_LOG_MSG (("rnd=%s shift_b=%d shift_c=%d diffexp=%" MPFR_EXP_FSPEC
- "d\n", mpfr_print_rnd_mode (rnd_mode), shift_b, shift_c,
- (mpfr_eexp_t) diff_exp));
-#endif
-
- MPFR_ASSERTD (ap != cp);
- MPFR_ASSERTD (bp != cp);
-
- /* here we have shift_c = (diff_exp - cancel) % GMP_NUMB_BITS,
- 0 <= shift_c < GMP_NUMB_BITS
- thus we want cancel2 = ceil((cancel - diff_exp) / GMP_NUMB_BITS) */
-
- /* Possible optimization with a C99 compiler (i.e. well-defined
- integer division): if MPFR_PREC_MAX is reduced to
- ((mpfr_prec_t)((mpfr_uprec_t)(~(mpfr_uprec_t)0)>>1) - GMP_NUMB_BITS + 1)
- and diff_exp is of type mpfr_exp_t (no need for mpfr_uexp_t, since
- the sum or difference of 2 exponents must be representable, as used
- by the multiplication code), then the computation of cancel2 could
- be simplified to
- cancel2 = (cancel - (diff_exp - shift_c)) / GMP_NUMB_BITS;
- because cancel, diff_exp and shift_c are all nonnegative and
- these variables are signed. */
-
- MPFR_ASSERTD (cancel >= 0);
- if (cancel >= diff_exp)
- /* Note that cancel is signed and will be converted to mpfr_uexp_t
- (type of diff_exp) in the expression below, so that this will
- work even if cancel is very large and diff_exp = 0. */
- cancel2 = (cancel - diff_exp + (GMP_NUMB_BITS - 1)) / GMP_NUMB_BITS;
- else
- cancel2 = - (mp_size_t) ((diff_exp - cancel) / GMP_NUMB_BITS);
- /* the high cancel2 limbs from b should not be taken into account */
-#if 0
- MPFR_LOG_MSG (("cancel=%Pd cancel1=%Pd cancel2=%Pd\n",
- cancel, cancel1, cancel2));
-#endif
-
- /* ap[an-1] ap[0]
- <----------------+-----------|---->
- <----------PREC(a)----------><-sh->
- cancel1
- limbs bp[bn-cancel1-1]
- <--...-----><----------------+-----------+----------->
- cancel2
- limbs cp[cn-cancel2-1] cancel2 >= 0
- <--...--><----------------+----------------+---------------->
- (-cancel2) cancel2 < 0
- limbs <----------------+---------------->
- */
-
- /* first part: put in ap[0..an-1] the value of high(b) - high(c),
- where high(b) consists of the high an+cancel1 limbs of b,
- and high(c) consists of the high an+cancel2 limbs of c.
- */
-
- /* copy high(b) into a */
- if (MPFR_LIKELY(an + (mp_size_t) cancel1 <= bn))
- /* a: <----------------+-----------|---->
- b: <-----------------------------------------> */
- MPN_COPY (ap, bp + bn - (an + cancel1), an);
- else
- /* a: <----------------+-----------|---->
- b: <-------------------------> */
- if ((mp_size_t) cancel1 < bn) /* otherwise b does not overlap with a */
- {
- MPN_ZERO (ap, an + cancel1 - bn);
- MPN_COPY (ap + (an + cancel1 - bn), bp, bn - cancel1);
- }
- else
- MPN_ZERO (ap, an);
-
- /* subtract high(c) */
- if (MPFR_LIKELY(an + cancel2 > 0)) /* otherwise c does not overlap with a */
- {
- mp_limb_t *ap2;
-
- if (cancel2 >= 0)
- {
- if (an + cancel2 <= cn)
- /* a: <----------------------------->
- c: <-----------------------------------------> */
- mpn_sub_n (ap, ap, cp + cn - (an + cancel2), an);
- else
- /* a: <---------------------------->
- c: <-------------------------> */
- {
- ap2 = ap + an + (cancel2 - cn);
- if (cn > cancel2)
- mpn_sub_n (ap2, ap2, cp, cn - cancel2);
- }
- }
- else /* cancel2 < 0 */
- {
- mp_limb_t borrow;
-
- if (an + cancel2 <= cn)
- /* a: <----------------------------->
- c: <-----------------------------> */
- borrow = mpn_sub_n (ap, ap, cp + cn - (an + cancel2),
- an + cancel2);
- else
- /* a: <---------------------------->
- c: <----------------> */
- {
- ap2 = ap + an + cancel2 - cn;
- borrow = mpn_sub_n (ap2, ap2, cp, cn);
- }
- ap2 = ap + an + cancel2;
- mpn_sub_1 (ap2, ap2, -cancel2, borrow);
- }
- }
-
- /* now perform rounding */
- sh = (mpfr_prec_t) an * GMP_NUMB_BITS - aq;
- /* last unused bits from a */
- carry = ap[0] & MPFR_LIMB_MASK (sh);
- ap[0] -= carry;
-
- if (rnd_mode == MPFR_RNDF)
- {
- inexact = 0;
- /* truncating is always correct since -1 ulp < low(b) - low(c) < 1 ulp */
- goto truncate;
- }
- else if (rnd_mode == MPFR_RNDN)
- {
- if (MPFR_LIKELY(sh))
- {
- /* can decide except when carry = 2^(sh-1) [middle]
- or carry = 0 [truncate, but cannot decide inexact flag] */
- if (carry > (MPFR_LIMB_ONE << (sh - 1)))
- goto add_one_ulp;
- else if ((0 < carry) && (carry < (MPFR_LIMB_ONE << (sh - 1))))
- {
- inexact = -1; /* result if smaller than exact value */
- goto truncate;
- }
- /* now carry = 2^(sh-1), in which case cmp_low=2,
- or carry = 0, in which case cmp_low=0 */
- cmp_low = (carry == 0) ? 0 : 2;
- }
- }
- else /* directed rounding: set rnd_mode to RNDZ iff toward zero */
- {
- if (MPFR_IS_RNDUTEST_OR_RNDDNOTTEST(rnd_mode, MPFR_IS_NEG(a)))
- rnd_mode = MPFR_RNDZ;
-
- if (carry)
- {
- if (rnd_mode == MPFR_RNDZ)
- {
- inexact = -1;
- goto truncate;
- }
- else /* round away */
- goto add_one_ulp;
- }
- }
-
- /* we have to consider the low (bn - (an+cancel1)) limbs from b,
- and the (cn - (an+cancel2)) limbs from c. */
- bn -= an + cancel1;
- cn0 = cn;
- cn -= an + cancel2;
-
-#if 0
- MPFR_LOG_MSG (("last sh=%d bits from a are %Mu, bn=%Pd, cn=%Pd\n",
- sh, carry, (mpfr_prec_t) bn, (mpfr_prec_t) cn));
-#endif
-
- /* for rounding to nearest, we couldn't conclude up to here in the following
- cases:
- 1. sh = 0, then cmp_low=0: we can either truncate, subtract one ulp
- or add one ulp: -1 ulp < low(b)-low(c) < 1 ulp
- 2. sh > 0 but the low sh bits from high(b)-high(c) equal 2^(sh-1):
- -0.5 ulp <= -1/2^sh < low(b)-low(c)-0.5 < 1/2^sh <= 0.5 ulp
- we can't decide the rounding, in that case cmp_low=2:
- either we truncate and flag=-1, or we add one ulp and flag=1
- 3. the low sh>0 bits from high(b)-high(c) equal 0: we know we have to
- truncate but we can't decide the ternary value, here cmp_low=0:
- -0.5 ulp <= -1/2^sh < low(b)-low(c) < 1/2^sh <= 0.5 ulp
- we always truncate and inexact can be any of -1,0,1
- */
-
- /* note: here cn might exceed cn0, in which case we consider a zero limb */
- for (k = 0; (bn > 0) || (cn > 0); k = 1)
- {
- /* if cmp_low < 0, we know low(b) - low(c) < 0
- if cmp_low > 0, we know low(b) - low(c) > 0
- (more precisely if cmp_low = 2, low(b) - low(c) = 0.5 ulp so far)
- if cmp_low = 0, so far low(b) - low(c) = 0 */
-
- /* get next limbs */
- bb = (bn > 0) ? bp[--bn] : 0;
- if ((cn > 0) && (cn-- <= cn0))
- cc = cp[cn];
- else
- cc = 0;
-
- /* cmp_low compares low(b) and low(c) */
- if (cmp_low == 0) /* case 1 or 3 */
- cmp_low = (bb < cc) ? -2+k : (bb > cc) ? 1 : 0;
-
- /* Case 1 for k=0 splits into 7 subcases:
- 1a: bb > cc + half
- 1b: bb = cc + half
- 1c: 0 < bb - cc < half
- 1d: bb = cc
- 1e: -half < bb - cc < 0
- 1f: bb - cc = -half
- 1g: bb - cc < -half
-
- Case 2 splits into 3 subcases:
- 2a: bb > cc
- 2b: bb = cc
- 2c: bb < cc
-
- Case 3 splits into 3 subcases:
- 3a: bb > cc
- 3b: bb = cc
- 3c: bb < cc
- */
-
- /* the case rounding to nearest with sh=0 is special since one couldn't
- subtract above 1/2 ulp in the trailing limb of the result */
- if (rnd_mode == MPFR_RNDN && sh == 0 && k == 0) /* case 1 for k=0 */
- {
- mp_limb_t half = MPFR_LIMB_HIGHBIT;
-
- /* add one ulp if bb > cc + half
- truncate if cc - half < bb < cc + half
- sub one ulp if bb < cc - half
- */
-
- if (cmp_low < 0) /* bb < cc: -1 ulp < low(b) - low(c) < 0,
- cases 1e, 1f and 1g */
- {
- if (cc >= half)
- cc -= half;
- else /* since bb < cc < half, bb+half < 2*half */
- bb += half;
- /* now we have bb < cc + half:
- we have to subtract one ulp if bb < cc,
- and truncate if bb > cc */
- }
- else if (cmp_low >= 0) /* bb >= cc, cases 1a to 1d */
- {
- if (cc < half)
- cc += half;
- else /* since bb >= cc >= half, bb - half >= 0 */
- bb -= half;
- /* now we have bb > cc - half: we have to add one ulp if bb > cc,
- and truncate if bb < cc */
- if (cmp_low > 0)
- cmp_low = 2;
- }
- }
-
-#if 0
- MPFR_LOG_MSG (("k=%d bb=%Mu cc=%Mu cmp_low=%d\n", k, bb, cc, cmp_low));
-#endif
-
- if (cmp_low < 0) /* low(b) - low(c) < 0: either truncate or subtract
- one ulp */
- {
- if (rnd_mode == MPFR_RNDZ)
- goto sub_one_ulp; /* set inexact=-1 */
- else if (rnd_mode != MPFR_RNDN) /* round away */
- {
- inexact = 1;
- goto truncate;
- }
- else /* round to nearest */
- {
- /* If cmp_low < 0 and bb > cc, then -0.5 ulp < low(b)-low(c) < 0,
- whatever the value of sh.
- If sh>0, then cmp_low < 0 implies that the initial neglected
- sh bits were 0 (otherwise cmp_low=2 initially), thus the
- weight of the new bits is less than 0.5 ulp too.
- If k > 0 (and sh=0) this means that either the first neglected
- limbs bb and cc were equal (thus cmp_low was 0 for k=0),
- or we had bb - cc = -0.5 ulp or 0.5 ulp.
- The last case is not possible here since we would have
- cmp_low > 0 which is sticky.
- In the first case (where we have cmp_low = -1), we truncate,
- whereas in the 2nd case we have cmp_low = -2 and we subtract
- one ulp.
- */
- if (bb > cc || sh > 0 || cmp_low == -1)
- { /* -0.5 ulp < low(b)-low(c) < 0,
- bb > cc corresponds to cases 1e and 1f1
- sh > 0 corresponds to cases 3c and 3b3
- cmp_low = -1 corresponds to case 1d3 (also 3b3) */
- inexact = 1;
- goto truncate;
- }
- else if (bb < cc) /* here sh = 0 and low(b)-low(c) < -0.5 ulp,
- this corresponds to cases 1g and 1f3 */
- goto sub_one_ulp;
- /* the only case where we can't conclude is sh=0 and bb=cc,
- i.e., we have low(b) - low(c) = -0.5 ulp (up to now), thus
- we don't know if we must truncate or subtract one ulp.
- Note: for sh=0 we can't have low(b) - low(c) = -0.5 ulp up to
- now, since low(b) - low(c) > 1/2^sh */
- }
- }
- else if (cmp_low > 0) /* 0 < low(b) - low(c): either truncate or
- add one ulp */
- {
- if (rnd_mode == MPFR_RNDZ)
- {
- inexact = -1;
- goto truncate;
- }
- else if (rnd_mode != MPFR_RNDN) /* round away */
- goto add_one_ulp;
- else /* round to nearest */
- {
- if (bb > cc)
- {
- /* if sh=0, then bb>cc means that low(b)-low(c) > 0.5 ulp,
- and similarly when cmp_low=2 */
- if (cmp_low == 2) /* cases 1a, 1b1, 2a and 2b1 */
- goto add_one_ulp;
- /* sh > 0 and cmp_low > 0: this implies that the sh initial
- neglected bits were 0, and the remaining low(b)-low(c)>0,
- but its weight is less than 0.5 ulp */
- else /* 0 < low(b) - low(c) < 0.5 ulp, this corresponds to
- cases 3a, 1d1 and 3b1 */
- {
- inexact = -1;
- goto truncate;
- }
- }
- else if (bb < cc) /* 0 < low(b) - low(c) < 0.5 ulp, cases 1c,
- 1b3, 2b3 and 2c */
- {
- inexact = -1;
- goto truncate;
- }
- /* the only case where we can't conclude is bb=cc, i.e.,
- low(b) - low(c) = 0.5 ulp (up to now), thus we don't know
- if we must truncate or add one ulp. */
- }
- }
- /* after k=0, we cannot conclude in the following cases, we split them
- according to the values of bb and cc for k=1:
- 1b. sh=0 and cmp_low = 1 and bb-cc = half [around 0.5 ulp]
- 1b1. bb > cc: add one ulp, inex = 1
- 1b2: bb = cc: cannot conclude
- 1b3: bb < cc: truncate, inex = -1
- 1d. sh=0 and cmp_low = 0 and bb-cc = 0 [around 0]
- 1d1: bb > cc: truncate, inex = -1
- 1d2: bb = cc: cannot conclude
- 1d3: bb < cc: truncate, inex = +1
- 1f. sh=0 and cmp_low = -1 and bb-cc = -half [around -0.5 ulp]
- 1f1: bb > cc: truncate, inex = +1
- 1f2: bb = cc: cannot conclude
- 1f3: bb < cc: sub one ulp, inex = -1
- 2b. sh > 0 and cmp_low = 2 and bb=cc [around 0.5 ulp]
- 2b1. bb > cc: add one ulp, inex = 1
- 2b2: bb = cc: cannot conclude
- 2b3: bb < cc: truncate, inex = -1
- 3b. sh > 0 and cmp_low = 0 [around 0]
- 3b1. bb > cc: truncate, inex = -1
- 3b2: bb = cc: cannot conclude
- 3b3: bb < cc: truncate, inex = +1
- */
- }
-
- if ((rnd_mode == MPFR_RNDN) && cmp_low != 0)
- {
- /* even rounding rule */
- if ((ap[0] >> sh) & 1)
- {
- if (cmp_low < 0)
- goto sub_one_ulp;
- else
- goto add_one_ulp;
- }
- else
- inexact = (cmp_low > 0) ? -1 : 1;
- }
- else
- inexact = 0;
- goto truncate;
-
- sub_one_ulp: /* sub one unit in last place to a */
- mpn_sub_1 (ap, ap, an, MPFR_LIMB_ONE << sh);
- inexact = -1;
- goto end_of_sub;
-
- add_one_ulp: /* add one unit in last place to a */
- if (MPFR_UNLIKELY(mpn_add_1 (ap, ap, an, MPFR_LIMB_ONE << sh)))
- /* result is a power of 2: 11111111111111 + 1 = 1000000000000000 */
- {
- ap[an-1] = MPFR_LIMB_HIGHBIT;
- add_exp = 1;
- }
- inexact = 1; /* result larger than exact value */
-
- truncate:
- if (MPFR_UNLIKELY((ap[an-1] >> (GMP_NUMB_BITS - 1)) == 0))
- /* case 1 - epsilon */
- {
- ap[an-1] = MPFR_LIMB_HIGHBIT;
- add_exp = 1;
- }
-
- end_of_sub:
- /* we have to set MPFR_EXP(a) to MPFR_EXP(b) - cancel + add_exp, taking
- care of underflows/overflows in that computation, and of the allowed
- exponent range */
- MPFR_TMP_FREE (marker);
- if (MPFR_LIKELY(cancel))
- {
- cancel -= add_exp; /* OK: add_exp is an int equal to 0 or 1 */
- MPFR_ASSERTD (cancel >= 0);
- /* Detect an underflow case to avoid a possible integer overflow
- with UBF in the computation of exp_a. */
- if (MPFR_UNLIKELY (exp_b < __gmpfr_emin - 1))
- {
- if (rnd_mode == MPFR_RNDN)
- rnd_mode = MPFR_RNDZ;
- return mpfr_underflow (a, rnd_mode, MPFR_SIGN(a));
- }
- exp_a = exp_b - cancel;
- /* The following assertion corresponds to a limitation of the MPFR
- implementation. It may fail with a 32-bit ABI and huge precisions,
- but this is practically impossible with a 64-bit ABI. This kind
- of issue is not specific to this function. */
- MPFR_ASSERTN (exp_b != MPFR_EXP_MAX || exp_a > __gmpfr_emax);
- if (MPFR_UNLIKELY (exp_a < __gmpfr_emin))
- {
- underflow:
- if (rnd_mode == MPFR_RNDN &&
- (exp_a < __gmpfr_emin - 1 ||
- (inexact >= 0 && mpfr_powerof2_raw (a))))
- rnd_mode = MPFR_RNDZ;
- return mpfr_underflow (a, rnd_mode, MPFR_SIGN(a));
- }
- /* We cannot have an overflow here, except for UBFs. Indeed:
- exp_a = exp_b - cancel + add_exp <= emax - 1 + 1 <= emax.
- For UBFs, we can have exp_b > emax. */
- if (exp_a > __gmpfr_emax)
- {
- MPFR_ASSERTD (exp_b > __gmpfr_emax); /* since exp_b >= exp_a */
- return mpfr_overflow (a, rnd_mode, MPFR_SIGN (a));
- }
- }
- else /* cancel = 0: MPFR_EXP(a) <- MPFR_EXP(b) + add_exp */
- {
- /* in case cancel = 0, add_exp can still be 1, in case b is just
- below a power of two, c is very small, prec(a) < prec(b),
- and rnd=away or nearest */
- MPFR_ASSERTD (add_exp == 0 || add_exp == 1);
- /* Overflow iff exp_b + add_exp > __gmpfr_emax in Z, but we do
- a subtraction below to avoid a potential integer overflow in
- the case exp_b == MPFR_EXP_MAX. */
- if (MPFR_UNLIKELY (exp_b > __gmpfr_emax - add_exp))
- return mpfr_overflow (a, rnd_mode, MPFR_SIGN (a));
- exp_a = exp_b + add_exp;
- /* Warning: an underflow can happen for UBFs, for example when
- mpfr_add is called from mpfr_fmma or mpfr_fmms. */
- if (MPFR_UNLIKELY (exp_a < __gmpfr_emin))
- goto underflow;
- MPFR_ASSERTD (exp_a >= __gmpfr_emin);
- }
- MPFR_SET_EXP (a, exp_a);
- /* check that result is msb-normalized */
- MPFR_ASSERTD(ap[an-1] > ~ap[an-1]);
- MPFR_RET (inexact * MPFR_INT_SIGN (a));
-}