diff options
Diffstat (limited to 'Build/source/libs/mpfr/mpfr-src/src/sub1.c')
-rw-r--r-- | Build/source/libs/mpfr/mpfr-src/src/sub1.c | 657 |
1 files changed, 657 insertions, 0 deletions
diff --git a/Build/source/libs/mpfr/mpfr-src/src/sub1.c b/Build/source/libs/mpfr/mpfr-src/src/sub1.c new file mode 100644 index 00000000000..2586fd6ff3c --- /dev/null +++ b/Build/source/libs/mpfr/mpfr-src/src/sub1.c @@ -0,0 +1,657 @@ +/* mpfr_sub1 -- internal function to perform a "real" subtraction + +Copyright 2001-2015 Free Software Foundation, Inc. +Contributed by the AriC and Caramel 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 +http://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_uexp_t diff_exp; + 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; + 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); + + sign = mpfr_cmp2 (b, c, &cancel); + if (MPFR_UNLIKELY(sign == 0)) + { + if (rnd_mode == MPFR_RNDD) + MPFR_SET_NEG (a); + else + MPFR_SET_POS (a); + MPFR_SET_ZERO (a); + MPFR_RET (0); + } + + /* + * If subtraction: sign(a) = sign * sign(b) + * If addition: sign(a) = sign of the larger argument in absolute value. + * + * Both cases can be simplidied 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); + + /* 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 (MPFR_GET_EXP (c) <= MPFR_GET_EXP (b) + - (mpfr_exp_t) MAX (MPFR_PREC (a), MPFR_PREC (b)) - 2)) + { + /* Remember, we can't have an exact result! */ + /* A.AAAAAAAAAAAAAAAAA + = B.BBBBBBBBBBBBBBB + - C.CCCCCCCCCCCCC */ + /* A = S*ABS(B) +/- ulp(a) */ + MPFR_SET_EXP (a, MPFR_GET_EXP (b)); + MPFR_RNDRAW_EVEN (inexact, a, MPFR_MANT (b), MPFR_PREC (b), + rnd_mode, MPFR_SIGN (a), + if (MPFR_UNLIKELY ( ++MPFR_EXP (a) > __gmpfr_emax)) + inexact = mpfr_overflow (a, rnd_mode, MPFR_SIGN (a))); + /* inexact = mpfr_set4 (a, b, rnd_mode, MPFR_SIGN (a)); */ + if (inexact == 0) + { + /* a = b (Exact) + But we know it isn't (Since we have to remove `c') + So if we round to Zero, we have to remove one ulp. + Otherwise the result is correctly rounded. */ + if (MPFR_IS_LIKE_RNDZ (rnd_mode, MPFR_IS_NEG (a))) + { + mpfr_nexttozero (a); + MPFR_RET (- MPFR_INT_SIGN (a)); + } + MPFR_RET (MPFR_INT_SIGN (a)); + } + else + { + /* 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 zeros. + Which means that removing c from b can't generate a carry + execpt in case of even rounding. + In all other case the result and the inexact flag should be + correct (We can't have an exact result). + 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 */ + if (MPFR_UNLIKELY (inexact == MPFR_EVEN_INEX*MPFR_INT_SIGN (a))) + { + mpfr_nexttozero (a); + inexact = -MPFR_INT_SIGN (a); + } + MPFR_RET (inexact); + } + } + + diff_exp = (mpfr_uexp_t) MPFR_GET_EXP (b) - MPFR_GET_EXP (c); + + /* 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 ((UINT_MAX % GMP_NUMB_BITS) == (GMP_NUMB_BITS-1) + && ((-(unsigned) 1)%GMP_NUMB_BITS > 0)) + shift_c = ((mpfr_uexp_t) diff_exp - cancel) % GMP_NUMB_BITS; + else + { + 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); + } + +#ifdef DEBUG + printf ("rnd=%s shift_b=%d shift_c=%d diffexp=%lu\n", + mpfr_print_rnd_mode (rnd_mode), shift_b, shift_c, + (unsigned long) 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 non-negative 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 */ +#ifdef DEBUG + printf ("cancel=%lu cancel1=%lu cancel2=%ld\n", + (unsigned long) cancel, (unsigned long) cancel1, (long) 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); + +#ifdef DEBUG + printf("after copying high(b), a="); mpfr_print_binary(a); putchar('\n'); +#endif + + /* 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); + } + } + +#ifdef DEBUG + printf("after subtracting high(c), a="); + mpfr_print_binary(a); + putchar('\n'); +#endif + + /* now perform rounding */ + sh = (mpfr_prec_t) an * GMP_NUMB_BITS - MPFR_PREC(a); + /* last unused bits from a */ + carry = ap[0] & MPFR_LIMB_MASK (sh); + ap[0] -= carry; + + if (MPFR_LIKELY(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; + +#ifdef DEBUG + printf ("last sh=%d bits from a are %lu, bn=%ld, cn=%ld\n", + sh, (unsigned long) carry, (long) bn, (long) 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; + } + } + +#ifdef DEBUG + printf ("k=%u bb=%lu cc=%lu cmp_low=%d\n", k, + (unsigned long) bb, (unsigned long) 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 */ + if (MPFR_LIKELY(cancel)) + { + mpfr_exp_t exp_a; + + cancel -= add_exp; /* OK: add_exp is an int equal to 0 or 1 */ + exp_a = MPFR_GET_EXP (b) - cancel; + if (MPFR_UNLIKELY(exp_a < __gmpfr_emin)) + { + MPFR_TMP_FREE(marker); + 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)); + } + MPFR_SET_EXP (a, exp_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_exp_t exp_b; + + exp_b = MPFR_GET_EXP (b); + if (MPFR_UNLIKELY(add_exp && exp_b == __gmpfr_emax)) + { + MPFR_TMP_FREE(marker); + return mpfr_overflow (a, rnd_mode, MPFR_SIGN(a)); + } + MPFR_SET_EXP (a, exp_b + add_exp); + } + MPFR_TMP_FREE(marker); +#ifdef DEBUG + printf ("result is a="); mpfr_print_binary(a); putchar('\n'); +#endif + /* check that result is msb-normalized */ + MPFR_ASSERTD(ap[an-1] > ~ap[an-1]); + MPFR_RET (inexact * MPFR_INT_SIGN (a)); +} |