diff options
Diffstat (limited to 'Build/source/libs/mpfr/mpfr-src/src/mul.c')
-rw-r--r-- | Build/source/libs/mpfr/mpfr-src/src/mul.c | 1105 |
1 files changed, 0 insertions, 1105 deletions
diff --git a/Build/source/libs/mpfr/mpfr-src/src/mul.c b/Build/source/libs/mpfr/mpfr-src/src/mul.c deleted file mode 100644 index d13fda1c1d2..00000000000 --- a/Build/source/libs/mpfr/mpfr-src/src/mul.c +++ /dev/null @@ -1,1105 +0,0 @@ -/* mpfr_mul -- multiply two floating-point numbers - -Copyright 1999-2020 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. */ - -#define MPFR_NEED_LONGLONG_H -#include "mpfr-impl.h" - - -/********* BEGINNING CHECK *************/ - -/* Check if we have to check the result of mpfr_mul. - TODO: Find a better (and faster?) check than using old implementation */ -#if MPFR_WANT_ASSERT >= 2 - -int mpfr_mul2 (mpfr_ptr a, mpfr_srcptr b, mpfr_srcptr c, mpfr_rnd_t rnd_mode); -static int -mpfr_mul3 (mpfr_ptr a, mpfr_srcptr b, mpfr_srcptr c, mpfr_rnd_t rnd_mode) -{ - /* Old implementation */ - int sign_product, cc, inexact; - mpfr_exp_t ax; - mp_limb_t *tmp; - mp_limb_t b1; - mpfr_prec_t bq, cq; - mp_size_t bn, cn, tn, k; - MPFR_TMP_DECL(marker); - - /* deal with special cases */ - if (MPFR_ARE_SINGULAR(b,c)) - { - if (MPFR_IS_NAN(b) || MPFR_IS_NAN(c)) - { - MPFR_SET_NAN(a); - MPFR_RET_NAN; - } - sign_product = MPFR_MULT_SIGN( MPFR_SIGN(b) , MPFR_SIGN(c) ); - if (MPFR_IS_INF(b)) - { - if (MPFR_IS_INF(c) || MPFR_NOTZERO(c)) - { - MPFR_SET_SIGN(a, sign_product); - MPFR_SET_INF(a); - MPFR_RET(0); /* exact */ - } - else - { - MPFR_SET_NAN(a); - MPFR_RET_NAN; - } - } - else if (MPFR_IS_INF(c)) - { - if (MPFR_NOTZERO(b)) - { - MPFR_SET_SIGN(a, sign_product); - MPFR_SET_INF(a); - MPFR_RET(0); /* exact */ - } - else - { - MPFR_SET_NAN(a); - MPFR_RET_NAN; - } - } - else - { - MPFR_ASSERTD(MPFR_IS_ZERO(b) || MPFR_IS_ZERO(c)); - MPFR_SET_SIGN(a, sign_product); - MPFR_SET_ZERO(a); - MPFR_RET(0); /* 0 * 0 is exact */ - } - } - sign_product = MPFR_MULT_SIGN( MPFR_SIGN(b) , MPFR_SIGN(c) ); - - ax = MPFR_GET_EXP (b) + MPFR_GET_EXP (c); - - bq = MPFR_PREC (b); - cq = MPFR_PREC (c); - - MPFR_ASSERTN ((mpfr_uprec_t) bq + cq <= MPFR_PREC_MAX); - - bn = MPFR_PREC2LIMBS (bq); /* number of limbs of b */ - cn = MPFR_PREC2LIMBS (cq); /* number of limbs of c */ - k = bn + cn; /* effective nb of limbs used by b*c (= tn or tn+1) below */ - tn = MPFR_PREC2LIMBS (bq + cq); - /* <= k, thus no int overflow */ - MPFR_ASSERTD(tn <= k); - - /* Check for no size_t overflow*/ - MPFR_ASSERTD((size_t) k <= ((size_t) -1) / MPFR_BYTES_PER_MP_LIMB); - MPFR_TMP_MARK(marker); - tmp = MPFR_TMP_LIMBS_ALLOC (k); - - /* multiplies two mantissa in temporary allocated space */ - b1 = (MPFR_LIKELY(bn >= cn)) ? - mpn_mul (tmp, MPFR_MANT(b), bn, MPFR_MANT(c), cn) - : mpn_mul (tmp, MPFR_MANT(c), cn, MPFR_MANT(b), bn); - - /* now tmp[0]..tmp[k-1] contains the product of both mantissa, - with tmp[k-1]>=2^(GMP_NUMB_BITS-2) */ - b1 >>= GMP_NUMB_BITS - 1; /* msb from the product */ - MPFR_ASSERTD (b1 == 0 || b1 == 1); - - /* if the mantissas of b and c are uniformly distributed in ]1/2, 1], - then their product is in ]1/4, 1/2] with probability 2*ln(2)-1 ~ 0.386 - and in [1/2, 1] with probability 2-2*ln(2) ~ 0.614 */ - tmp += k - tn; - if (MPFR_UNLIKELY(b1 == 0)) - mpn_lshift (tmp, tmp, tn, 1); /* tn <= k, so no stack corruption */ - cc = mpfr_round_raw (MPFR_MANT (a), tmp, bq + cq, - MPFR_IS_NEG_SIGN(sign_product), - MPFR_PREC (a), rnd_mode, &inexact); - MPFR_ASSERTD (cc == 0 || cc == 1); - - /* cc = 1 ==> result is a power of two */ - if (MPFR_UNLIKELY(cc)) - MPFR_MANT(a)[MPFR_LIMB_SIZE(a)-1] = MPFR_LIMB_HIGHBIT; - - MPFR_TMP_FREE(marker); - - { - /* We need to cast b1 to a signed integer type in order to use - signed integer arithmetic only, as the expression can involve - negative integers. Let's recall that both b1 and cc are 0 or 1, - and since cc is an int, let's choose int for this part. */ - mpfr_exp_t ax2 = ax + ((int) b1 - 1 + cc); - if (MPFR_UNLIKELY( ax2 > __gmpfr_emax)) - return mpfr_overflow (a, rnd_mode, sign_product); - if (MPFR_UNLIKELY( ax2 < __gmpfr_emin)) - { - /* In the rounding to the nearest mode, if the exponent of the exact - result (i.e. before rounding, i.e. without taking cc into account) - is < __gmpfr_emin - 1 or the exact result is a power of 2 (i.e. if - both arguments are powers of 2) in absolute value, then round to - zero. */ - if (rnd_mode == MPFR_RNDN && - (ax + (mpfr_exp_t) b1 < __gmpfr_emin || - (mpfr_powerof2_raw (b) && mpfr_powerof2_raw (c)))) - rnd_mode = MPFR_RNDZ; - return mpfr_underflow (a, rnd_mode, sign_product); - } - MPFR_SET_EXP (a, ax2); - MPFR_SET_SIGN(a, sign_product); - } - MPFR_RET (inexact); -} - -int -mpfr_mul (mpfr_ptr a, mpfr_srcptr b, mpfr_srcptr c, mpfr_rnd_t rnd_mode) -{ - mpfr_t ta, tb, tc; - mpfr_flags_t old_flags, flags1, flags2; - int inexact1, inexact2; - - if (rnd_mode == MPFR_RNDF) - return mpfr_mul2 (a, b, c, rnd_mode); - - old_flags = __gmpfr_flags; - - mpfr_init2 (ta, MPFR_PREC (a)); - mpfr_init2 (tb, MPFR_PREC (b)); - mpfr_init2 (tc, MPFR_PREC (c)); - MPFR_ASSERTN (mpfr_set (tb, b, MPFR_RNDN) == 0); - MPFR_ASSERTN (mpfr_set (tc, c, MPFR_RNDN) == 0); - - /* Note: If b or c is NaN, then the NaN flag has been set by mpfr_set above. - Thus restore the old flags just below to make sure that mpfr_mul3 is - tested under the real conditions. */ - - __gmpfr_flags = old_flags; - inexact2 = mpfr_mul3 (ta, tb, tc, rnd_mode); - flags2 = __gmpfr_flags; - - __gmpfr_flags = old_flags; - inexact1 = mpfr_mul2 (a, b, c, rnd_mode); - flags1 = __gmpfr_flags; - - /* Convert the ternary values to (-1,0,1). */ - inexact2 = VSIGN (inexact2); - inexact1 = VSIGN (inexact1); - - if (! ((MPFR_IS_NAN (ta) && MPFR_IS_NAN (a)) || mpfr_equal_p (ta, a)) || - inexact1 != inexact2 || flags1 != flags2) - { - /* We do not have MPFR_PREC_FSPEC, so let's use mpfr_eexp_t and - MPFR_EXP_FSPEC since mpfr_prec_t values are guaranteed to be - representable in mpfr_exp_t, thus in mpfr_eexp_t. */ - fprintf (stderr, "mpfr_mul return different values for %s\n" - "Prec_a = %" MPFR_EXP_FSPEC "d, " - "Prec_b = %" MPFR_EXP_FSPEC "d, " - "Prec_c = %" MPFR_EXP_FSPEC "d\n", - mpfr_print_rnd_mode (rnd_mode), - (mpfr_eexp_t) MPFR_PREC (a), - (mpfr_eexp_t) MPFR_PREC (b), - (mpfr_eexp_t) MPFR_PREC (c)); - /* Note: We output tb and tc instead of b and c, in case a = b or c - (this is why tb and tc have been created in the first place). */ - fprintf (stderr, "b = "); - mpfr_fdump (stderr, tb); - fprintf (stderr, "c = "); - mpfr_fdump (stderr, tc); - fprintf (stderr, "OldMul: "); - mpfr_fdump (stderr, ta); - fprintf (stderr, "NewMul: "); - mpfr_fdump (stderr, a); - fprintf (stderr, "OldMul: ternary = %2d, flags =", inexact2); - flags_fout (stderr, flags2); - fprintf (stderr, "NewMul: ternary = %2d, flags =", inexact1); - flags_fout (stderr, flags1); - MPFR_ASSERTN(0); - } - - mpfr_clears (ta, tb, tc, (mpfr_ptr) 0); - return inexact1; -} - -# define mpfr_mul mpfr_mul2 - -#endif /* MPFR_WANT_ASSERT >= 2 */ - -/****** END OF CHECK *******/ - -/* Multiply 2 mpfr_t */ - -#if !defined(MPFR_GENERIC_ABI) - -/* Disabled for now since the mul_1_extracted.c is not formally proven yet. - Once it is proven, replace MPFR_WANT_PROVEN_CODExxx by MPFR_WANT_PROVEN_CODE. */ -#if defined(MPFR_WANT_PROVEN_CODExxx) && GMP_NUMB_BITS == 64 && \ - UINT_MAX == 0xffffffff && MPFR_PREC_BITS == 64 && \ - _MPFR_PREC_FORMAT == 3 && _MPFR_EXP_FORMAT == _MPFR_PREC_FORMAT - -/* The code assumes that mp_limb_t has 64 bits exactly, unsigned int - has 32 bits exactly, mpfr_prec_t and mpfr_exp_t are of type long, - which has 64 bits exactly. */ - -#include "mul_1_extracted.c" - -#else - -/* Special code for prec(a) < GMP_NUMB_BITS and - prec(b), prec(c) <= GMP_NUMB_BITS. - Note: this code was copied in sqr.c, function mpfr_sqr_1 (this saves a few cycles - with respect to have this function exported). As a consequence, any change here - should be reported in mpfr_sqr_1. */ -static int -mpfr_mul_1 (mpfr_ptr a, mpfr_srcptr b, mpfr_srcptr c, mpfr_rnd_t rnd_mode, - mpfr_prec_t p) -{ - mp_limb_t a0; - mpfr_limb_ptr ap = MPFR_MANT(a); - mp_limb_t b0 = MPFR_MANT(b)[0]; - mp_limb_t c0 = MPFR_MANT(c)[0]; - mpfr_exp_t ax; - mpfr_prec_t sh = GMP_NUMB_BITS - p; - mp_limb_t rb, sb, mask = MPFR_LIMB_MASK(sh); - - /* When prec(b), prec(c) <= GMP_NUMB_BITS / 2, we could replace umul_ppmm - by a limb multiplication as follows, but we assume umul_ppmm is as fast - as a limb multiplication on modern processors: - a0 = (b0 >> (GMP_NUMB_BITS / 2)) * (c0 >> (GMP_NUMB_BITS / 2)); - sb = 0; - */ - ax = MPFR_GET_EXP(b) + MPFR_GET_EXP(c); - umul_ppmm (a0, sb, b0, c0); - if (a0 < MPFR_LIMB_HIGHBIT) - { - ax --; - /* TODO: This is actually an addition with carry (no shifts and no OR - needed in asm). Make sure that GCC generates optimized code once - it supports carry-in. */ - a0 = (a0 << 1) | (sb >> (GMP_NUMB_BITS - 1)); - sb <<= 1; - } - rb = a0 & (MPFR_LIMB_ONE << (sh - 1)); - sb |= (a0 & mask) ^ rb; - ap[0] = a0 & ~mask; - - MPFR_SIGN(a) = MPFR_MULT_SIGN (MPFR_SIGN (b), MPFR_SIGN (c)); - - /* rounding */ - if (MPFR_UNLIKELY(ax > __gmpfr_emax)) - return mpfr_overflow (a, rnd_mode, MPFR_SIGN(a)); - - /* Warning: underflow should be checked *after* rounding, thus when rounding - away and when a > 0.111...111*2^(emin-1), or when rounding to nearest and - a >= 0.111...111[1]*2^(emin-1), there is no underflow. */ - if (MPFR_UNLIKELY(ax < __gmpfr_emin)) - { - if (ax == __gmpfr_emin - 1 && ap[0] == MPFR_LIMB(~mask) && - ((rnd_mode == MPFR_RNDN && rb) || - (MPFR_IS_LIKE_RNDA(rnd_mode, MPFR_IS_NEG (a)) && (rb | sb)))) - goto rounding; /* no underflow */ - /* For RNDN, mpfr_underflow always rounds away, thus for |a| <= 2^(emin-2) - we have to change to RNDZ. This corresponds to: - (a) either ax < emin - 1 - (b) or ax = emin - 1 and ap[0] = 1000....000 and rb = sb = 0 */ - if (rnd_mode == MPFR_RNDN && - (ax < __gmpfr_emin - 1 || - (ap[0] == MPFR_LIMB_HIGHBIT && (rb | sb) == 0))) - rnd_mode = MPFR_RNDZ; - return mpfr_underflow (a, rnd_mode, MPFR_SIGN(a)); - } - - rounding: - MPFR_EXP (a) = ax; /* Don't use MPFR_SET_EXP since ax might be < __gmpfr_emin - in the cases "goto rounding" above. */ - if ((rb == 0 && sb == 0) || rnd_mode == MPFR_RNDF) - { - MPFR_ASSERTD(ax >= __gmpfr_emin); - 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_ASSERTD(ax >= __gmpfr_emin); - MPFR_RET(-MPFR_SIGN(a)); - } - else /* round away from zero */ - { - add_one_ulp: - ap[0] += MPFR_LIMB_ONE << sh; - if (ap[0] == 0) - { - ap[0] = MPFR_LIMB_HIGHBIT; - if (MPFR_UNLIKELY(ax + 1 > __gmpfr_emax)) - return mpfr_overflow (a, rnd_mode, MPFR_SIGN(a)); - MPFR_ASSERTD(ax + 1 <= __gmpfr_emax); - MPFR_ASSERTD(ax + 1 >= __gmpfr_emin); - MPFR_SET_EXP (a, ax + 1); - } - MPFR_RET(MPFR_SIGN(a)); - } -} - -#endif /* MPFR_WANT_PROVEN_CODE */ - -/* Special code for prec(a) = GMP_NUMB_BITS and - prec(b), prec(c) <= GMP_NUMB_BITS. */ -static int -mpfr_mul_1n (mpfr_ptr a, mpfr_srcptr b, mpfr_srcptr c, mpfr_rnd_t rnd_mode) -{ - mp_limb_t a0; - mpfr_limb_ptr ap = MPFR_MANT(a); - mp_limb_t b0 = MPFR_MANT(b)[0]; - mp_limb_t c0 = MPFR_MANT(c)[0]; - mpfr_exp_t ax; - mp_limb_t rb, sb; - - ax = MPFR_GET_EXP(b) + MPFR_GET_EXP(c); - umul_ppmm (a0, sb, b0, c0); - if (a0 < MPFR_LIMB_HIGHBIT) - { - ax --; - /* TODO: This is actually an addition with carry (no shifts and no OR - needed in asm). Make sure that GCC generates optimized code once - it supports carry-in. */ - a0 = (a0 << 1) | (sb >> (GMP_NUMB_BITS - 1)); - sb <<= 1; - } - rb = sb & MPFR_LIMB_HIGHBIT; - sb = sb & ~MPFR_LIMB_HIGHBIT; - ap[0] = a0; - - MPFR_SIGN(a) = MPFR_MULT_SIGN (MPFR_SIGN (b), MPFR_SIGN (c)); - - /* rounding */ - if (MPFR_UNLIKELY(ax > __gmpfr_emax)) - return mpfr_overflow (a, rnd_mode, MPFR_SIGN(a)); - - /* Warning: underflow should be checked *after* rounding, thus when rounding - away and when a > 0.111...111*2^(emin-1), or when rounding to nearest and - a >= 0.111...111[1]*2^(emin-1), there is no underflow. - Note: this case can only occur when the initial a0 (after the umul_ppmm - call above) had its most significant bit 0, since the largest a0 is - obtained for b0 = c0 = B-1 where B=2^GMP_NUMB_BITS, thus b0*c0 <= (B-1)^2 - thus a0 <= B-2. */ - if (MPFR_UNLIKELY(ax < __gmpfr_emin)) - { - if (ax == __gmpfr_emin - 1 && ap[0] == ~MPFR_LIMB_ZERO && - ((rnd_mode == MPFR_RNDN && rb) || - (MPFR_IS_LIKE_RNDA(rnd_mode, MPFR_IS_NEG (a)) && (rb | sb)))) - goto rounding; /* no underflow */ - /* For RNDN, mpfr_underflow always rounds away, thus for |a| <= 2^(emin-2) - we have to change to RNDZ. This corresponds to: - (a) either ax < emin - 1 - (b) or ax = emin - 1 and ap[0] = 1000....000 and rb = sb = 0 */ - if (rnd_mode == MPFR_RNDN && - (ax < __gmpfr_emin - 1 || - (ap[0] == MPFR_LIMB_HIGHBIT && (rb | sb) == 0))) - rnd_mode = MPFR_RNDZ; - return mpfr_underflow (a, rnd_mode, MPFR_SIGN(a)); - } - - rounding: - MPFR_EXP (a) = ax; /* Don't use MPFR_SET_EXP since ax might be < __gmpfr_emin - in the cases "goto rounding" above. */ - if ((rb == 0 && sb == 0) || rnd_mode == MPFR_RNDF) - { - MPFR_ASSERTD(ax >= __gmpfr_emin); - 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_ASSERTD(ax >= __gmpfr_emin); - MPFR_RET(-MPFR_SIGN(a)); - } - else /* round away from zero */ - { - add_one_ulp: - ap[0] += MPFR_LIMB_ONE; - if (ap[0] == 0) - { - ap[0] = MPFR_LIMB_HIGHBIT; - if (MPFR_UNLIKELY(ax + 1 > __gmpfr_emax)) - return mpfr_overflow (a, rnd_mode, MPFR_SIGN(a)); - MPFR_ASSERTD(ax + 1 <= __gmpfr_emax); - MPFR_ASSERTD(ax + 1 >= __gmpfr_emin); - MPFR_SET_EXP (a, ax + 1); - } - MPFR_RET(MPFR_SIGN(a)); - } -} - -/* Special code for GMP_NUMB_BITS < prec(a) < 2*GMP_NUMB_BITS and - GMP_NUMB_BITS < prec(b), prec(c) <= 2*GMP_NUMB_BITS. - Note: this code was copied in sqr.c, function mpfr_sqr_2 (this saves a few cycles - with respect to have this function exported). As a consequence, any change here - should be reported in mpfr_sqr_2. */ -static int -mpfr_mul_2 (mpfr_ptr a, mpfr_srcptr b, mpfr_srcptr c, mpfr_rnd_t rnd_mode, - mpfr_prec_t p) -{ - mp_limb_t h, l, u, v, w; - mpfr_limb_ptr ap = MPFR_MANT(a); - mpfr_exp_t ax = MPFR_GET_EXP(b) + MPFR_GET_EXP(c); - mpfr_prec_t sh = 2 * GMP_NUMB_BITS - p; - mp_limb_t rb, sb, sb2, mask = MPFR_LIMB_MASK(sh); - mp_limb_t *bp = MPFR_MANT(b), *cp = MPFR_MANT(c); - - /* we store the 4-limb product in h=ap[1], l=ap[0], sb=ap[-1], sb2=ap[-2] */ - umul_ppmm (h, l, bp[1], cp[1]); - umul_ppmm (u, v, bp[1], cp[0]); - l += u; - h += (l < u); - umul_ppmm (u, w, bp[0], cp[1]); - l += u; - h += (l < u); - - /* now the full product is {h, l, v + w + high(b0*c0), low(b0*c0)}, - where the lower part contributes to less than 3 ulps to {h, l} */ - - /* If h has its most significant bit set and the low sh-1 bits of l are not - 000...000 nor 111...111 nor 111...110, then we can round correctly; - if h has zero as most significant bit, we have to shift left h and l, - thus if the low sh-2 bits are not 000...000 nor 111...111 nor 111...110, - then we can round correctly. To avoid an extra test we consider the latter - case (if we can round, we can also round in the former case). - For sh <= 3, we have mask <= 7, thus (mask>>2) <= 1, and the approximation - cannot be enough. */ - if (MPFR_LIKELY(((l + 2) & (mask >> 2)) > 2)) - sb = sb2 = 1; /* result cannot be exact in that case */ - else - { - umul_ppmm (sb, sb2, bp[0], cp[0]); - /* the full product is {h, l, sb + v + w, sb2} */ - sb += v; - l += (sb < v); - h += (l == 0) && (sb < v); - sb += w; - l += (sb < w); - h += (l == 0) && (sb < w); - } - if (h < MPFR_LIMB_HIGHBIT) - { - ax --; - h = (h << 1) | (l >> (GMP_NUMB_BITS - 1)); - l = (l << 1) | (sb >> (GMP_NUMB_BITS - 1)); - sb <<= 1; - /* no need to shift sb2 since we only want to know if it is zero or not */ - } - ap[1] = h; - rb = l & (MPFR_LIMB_ONE << (sh - 1)); - sb |= ((l & mask) ^ rb) | sb2; - ap[0] = l & ~mask; - - MPFR_SIGN(a) = MPFR_MULT_SIGN (MPFR_SIGN (b), MPFR_SIGN (c)); - - /* rounding */ - if (MPFR_UNLIKELY(ax > __gmpfr_emax)) - return mpfr_overflow (a, rnd_mode, MPFR_SIGN(a)); - - /* Warning: underflow should be checked *after* rounding, thus when rounding - away and when a > 0.111...111*2^(emin-1), or when rounding to nearest and - a >= 0.111...111[1]*2^(emin-1), there is no underflow. */ - if (MPFR_UNLIKELY(ax < __gmpfr_emin)) - { - if (ax == __gmpfr_emin - 1 && - ap[1] == MPFR_LIMB_MAX && - ap[0] == MPFR_LIMB(~mask) && - ((rnd_mode == MPFR_RNDN && rb) || - (MPFR_IS_LIKE_RNDA(rnd_mode, MPFR_IS_NEG (a)) && (rb | sb)))) - goto rounding; /* no underflow */ - /* for RNDN, mpfr_underflow always rounds away, thus for |a| <= 2^(emin-2) - we have to change to RNDZ */ - if (rnd_mode == MPFR_RNDN && - (ax < __gmpfr_emin - 1 || - (ap[1] == MPFR_LIMB_HIGHBIT && ap[0] == 0 && (rb | sb) == 0))) - rnd_mode = MPFR_RNDZ; - return mpfr_underflow (a, rnd_mode, MPFR_SIGN(a)); - } - - rounding: - MPFR_EXP (a) = ax; /* Don't use MPFR_SET_EXP since ax might be < __gmpfr_emin - in the cases "goto rounding" above. */ - if ((rb == 0 && sb == 0) || rnd_mode == MPFR_RNDF) - { - MPFR_ASSERTD(ax >= __gmpfr_emin); - 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_ASSERTD(ax >= __gmpfr_emin); - 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 (ap[1] == 0) - { - ap[1] = MPFR_LIMB_HIGHBIT; - if (MPFR_UNLIKELY(ax + 1 > __gmpfr_emax)) - return mpfr_overflow (a, rnd_mode, MPFR_SIGN(a)); - MPFR_ASSERTD(ax + 1 <= __gmpfr_emax); - MPFR_ASSERTD(ax + 1 >= __gmpfr_emin); - MPFR_SET_EXP (a, ax + 1); - } - MPFR_RET(MPFR_SIGN(a)); - } -} - -/* Special code for 2*GMP_NUMB_BITS < prec(a) < 3*GMP_NUMB_BITS and - 2*GMP_NUMB_BITS < prec(b), prec(c) <= 3*GMP_NUMB_BITS. */ -static int -mpfr_mul_3 (mpfr_ptr a, mpfr_srcptr b, mpfr_srcptr c, mpfr_rnd_t rnd_mode, - mpfr_prec_t p) -{ - mp_limb_t a0, a1, a2, h, l, cy; - mpfr_limb_ptr ap = MPFR_MANT(a); - mpfr_exp_t ax = MPFR_GET_EXP(b) + MPFR_GET_EXP(c); - mpfr_prec_t sh = 3 * GMP_NUMB_BITS - p; - mp_limb_t rb, sb, sb2, mask = MPFR_LIMB_MASK(sh); - mp_limb_t *bp = MPFR_MANT(b), *cp = MPFR_MANT(c); - - /* we store the upper 3-limb product in a2, a1, a0: - b2*c2, b2*c1+b1*c2, b2*c0+b1*c1+b0*c2 */ - umul_ppmm (a2, a1, bp[2], cp[2]); - umul_ppmm (h, a0, bp[2], cp[1]); - a1 += h; - a2 += (a1 < h); - umul_ppmm (h, l, bp[1], cp[2]); - a1 += h; - a2 += (a1 < h); - a0 += l; - cy = a0 < l; /* carry in a1 */ - umul_ppmm (h, l, bp[2], cp[0]); - a0 += h; - cy += (a0 < h); - umul_ppmm (h, l, bp[1], cp[1]); - a0 += h; - cy += (a0 < h); - umul_ppmm (h, l, bp[0], cp[2]); - a0 += h; - cy += (a0 < h); - /* now propagate cy */ - a1 += cy; - a2 += (a1 < cy); - - /* Now the approximate product {a2, a1, a0} has an error of less than - 5 ulps (3 ulps for the ignored low limbs of b2*c0+b1*c1+b0*c2, - plus 2 ulps for the ignored b1*c0+b0*c1 (plus b0*c0)). - Since we might shift by 1 bit, we make sure the low sh-2 bits of a0 - are not 0, -1, -2, -3 or -4. */ - - if (MPFR_LIKELY(((a0 + 4) & (mask >> 2)) > 4)) - sb = sb2 = 1; /* result cannot be exact in that case */ - else - { - mp_limb_t p[6]; - mpn_mul_n (p, bp, cp, 3); - a2 = p[5]; - a1 = p[4]; - a0 = p[3]; - sb = p[2]; - sb2 = p[1] | p[0]; - } - if (a2 < MPFR_LIMB_HIGHBIT) - { - ax --; - a2 = (a2 << 1) | (a1 >> (GMP_NUMB_BITS - 1)); - a1 = (a1 << 1) | (a0 >> (GMP_NUMB_BITS - 1)); - a0 = (a0 << 1) | (sb >> (GMP_NUMB_BITS - 1)); - sb <<= 1; - /* no need to shift sb2: we only need to know if it is zero or not */ - } - ap[2] = a2; - ap[1] = a1; - rb = a0 & (MPFR_LIMB_ONE << (sh - 1)); - sb |= ((a0 & mask) ^ rb) | sb2; - ap[0] = a0 & ~mask; - - MPFR_SIGN(a) = MPFR_MULT_SIGN (MPFR_SIGN (b), MPFR_SIGN (c)); - - /* rounding */ - if (MPFR_UNLIKELY(ax > __gmpfr_emax)) - return mpfr_overflow (a, rnd_mode, MPFR_SIGN(a)); - - /* Warning: underflow should be checked *after* rounding, thus when rounding - away and when a > 0.111...111*2^(emin-1), or when rounding to nearest and - a >= 0.111...111[1]*2^(emin-1), there is no underflow. */ - if (MPFR_UNLIKELY(ax < __gmpfr_emin)) - { - if (ax == __gmpfr_emin - 1 && - ap[2] == MPFR_LIMB_MAX && - ap[1] == MPFR_LIMB_MAX && - ap[0] == MPFR_LIMB(~mask) && - ((rnd_mode == MPFR_RNDN && rb) || - (MPFR_IS_LIKE_RNDA(rnd_mode, MPFR_IS_NEG (a)) && (rb | sb)))) - goto rounding; /* no underflow */ - /* for RNDN, mpfr_underflow always rounds away, thus for |a| <= 2^(emin-2) - we have to change to RNDZ */ - if (rnd_mode == MPFR_RNDN && - (ax < __gmpfr_emin - 1 || - (ap[2] == MPFR_LIMB_HIGHBIT && ap[1] == 0 && ap[0] == 0 - && (rb | sb) == 0))) - rnd_mode = MPFR_RNDZ; - return mpfr_underflow (a, rnd_mode, MPFR_SIGN(a)); - } - - rounding: - MPFR_EXP (a) = ax; /* Don't use MPFR_SET_EXP since ax might be < __gmpfr_emin - in the cases "goto rounding" above. */ - if ((rb == 0 && sb == 0) || rnd_mode == MPFR_RNDF) - { - MPFR_ASSERTD(ax >= __gmpfr_emin); - 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_ASSERTD(ax >= __gmpfr_emin); - 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 (ap[2] == 0) - { - ap[2] = MPFR_LIMB_HIGHBIT; - if (MPFR_UNLIKELY(ax + 1 > __gmpfr_emax)) - return mpfr_overflow (a, rnd_mode, MPFR_SIGN(a)); - MPFR_ASSERTD(ax + 1 <= __gmpfr_emax); - MPFR_ASSERTD(ax + 1 >= __gmpfr_emin); - MPFR_SET_EXP (a, ax + 1); - } - MPFR_RET(MPFR_SIGN(a)); - } -} - -#endif /* !defined(MPFR_GENERIC_ABI) */ - -/* Note: mpfr_sqr will call mpfr_mul if bn > MPFR_SQR_THRESHOLD, - in order to use Mulders' mulhigh, which is handled only here - to avoid partial code duplication. There is some overhead due - to the additional tests, but slowdown should not be noticeable - as this code is not executed in very small precisions. */ - -MPFR_HOT_FUNCTION_ATTR int -mpfr_mul (mpfr_ptr a, mpfr_srcptr b, mpfr_srcptr c, mpfr_rnd_t rnd_mode) -{ - int sign, inexact; - mpfr_exp_t ax, ax2; - mp_limb_t *tmp; - mp_limb_t b1; - mpfr_prec_t aq, bq, cq; - mp_size_t bn, cn, tn, k, threshold; - MPFR_TMP_DECL (marker); - - MPFR_LOG_FUNC - (("b[%Pu]=%.*Rg c[%Pu]=%.*Rg rnd=%d", - mpfr_get_prec (b), mpfr_log_prec, b, - mpfr_get_prec (c), mpfr_log_prec, c, rnd_mode), - ("a[%Pu]=%.*Rg inexact=%d", - mpfr_get_prec (a), mpfr_log_prec, a, inexact)); - - /* deal with special cases */ - if (MPFR_ARE_SINGULAR (b, c)) - { - if (MPFR_IS_NAN (b) || MPFR_IS_NAN (c)) - { - MPFR_SET_NAN (a); - MPFR_RET_NAN; - } - sign = MPFR_MULT_SIGN (MPFR_SIGN (b), MPFR_SIGN (c)); - if (MPFR_IS_INF (b)) - { - if (!MPFR_IS_ZERO (c)) - { - MPFR_SET_SIGN (a, sign); - MPFR_SET_INF (a); - MPFR_RET (0); - } - else - { - MPFR_SET_NAN (a); - MPFR_RET_NAN; - } - } - else if (MPFR_IS_INF (c)) - { - if (!MPFR_IS_ZERO (b)) - { - MPFR_SET_SIGN (a, sign); - MPFR_SET_INF (a); - MPFR_RET(0); - } - else - { - MPFR_SET_NAN (a); - MPFR_RET_NAN; - } - } - else - { - MPFR_ASSERTD (MPFR_IS_ZERO(b) || MPFR_IS_ZERO(c)); - MPFR_SET_SIGN (a, sign); - MPFR_SET_ZERO (a); - MPFR_RET (0); - } - } - - aq = MPFR_GET_PREC (a); - bq = MPFR_GET_PREC (b); - cq = MPFR_GET_PREC (c); - -#if !defined(MPFR_GENERIC_ABI) - if (aq == bq && aq == cq) - { - if (aq < GMP_NUMB_BITS) - return mpfr_mul_1 (a, b, c, rnd_mode, aq); - - if (GMP_NUMB_BITS < aq && aq < 2 * GMP_NUMB_BITS) - return mpfr_mul_2 (a, b, c, rnd_mode, aq); - - if (aq == GMP_NUMB_BITS) - return mpfr_mul_1n (a, b, c, rnd_mode); - - if (2 * GMP_NUMB_BITS < aq && aq < 3 * GMP_NUMB_BITS) - return mpfr_mul_3 (a, b, c, rnd_mode, aq); - } -#endif - - sign = MPFR_MULT_SIGN (MPFR_SIGN (b), MPFR_SIGN (c)); - - ax = MPFR_GET_EXP (b) + MPFR_GET_EXP (c); - /* Note: the exponent of the exact result will be e = bx + cx + ec with - ec in {-1,0,1} and the following assumes that e is representable. */ - - /* FIXME: Useful since we do an exponent check after? - * It is useful iff the precision is big, there is an overflow - * and we are doing further mults...*/ -#ifdef HUGE - if (MPFR_UNLIKELY (ax > __gmpfr_emax + 1)) - return mpfr_overflow (a, rnd_mode, sign); - if (MPFR_UNLIKELY (ax < __gmpfr_emin - 2)) - return mpfr_underflow (a, rnd_mode == MPFR_RNDN ? MPFR_RNDZ : rnd_mode, - sign); -#endif - - MPFR_ASSERTN ((mpfr_uprec_t) bq + cq <= MPFR_PREC_MAX); - - bn = MPFR_PREC2LIMBS (bq); /* number of limbs of b */ - cn = MPFR_PREC2LIMBS (cq); /* number of limbs of c */ - k = bn + cn; /* effective nb of limbs used by b*c (= tn or tn+1) below */ - tn = MPFR_PREC2LIMBS (bq + cq); - MPFR_ASSERTD (tn <= k); /* tn <= k, thus no int overflow */ - - /* Check for no size_t overflow. */ - MPFR_ASSERTD ((size_t) k <= ((size_t) -1) / MPFR_BYTES_PER_MP_LIMB); - MPFR_TMP_MARK (marker); - tmp = MPFR_TMP_LIMBS_ALLOC (k); - - /* multiplies two mantissa in temporary allocated space */ - if (MPFR_UNLIKELY (bn < cn)) - { - mpfr_srcptr z = b; - mp_size_t zn = bn; - b = c; - bn = cn; - c = z; - cn = zn; - } - MPFR_ASSERTD (bn >= cn); - if (bn <= 2) - { - /* The 3 cases perform the same first operation. */ - umul_ppmm (tmp[1], tmp[0], MPFR_MANT (b)[0], MPFR_MANT (c)[0]); - if (bn == 1) - { - /* 1 limb * 1 limb */ - b1 = tmp[1]; - } - else if (MPFR_UNLIKELY (cn == 1)) - { - /* 2 limbs * 1 limb */ - mp_limb_t t; - umul_ppmm (tmp[2], t, MPFR_MANT (b)[1], MPFR_MANT (c)[0]); - add_ssaaaa (tmp[2], tmp[1], tmp[2], tmp[1], 0, t); - b1 = tmp[2]; - } - else - { - /* 2 limbs * 2 limbs */ - mp_limb_t t1, t2, t3; - /* First 2 limbs * 1 limb */ - umul_ppmm (tmp[2], t1, MPFR_MANT (b)[1], MPFR_MANT (c)[0]); - add_ssaaaa (tmp[2], tmp[1], tmp[2], tmp[1], 0, t1); - /* Second, the other 2 limbs * 1 limb product */ - umul_ppmm (t1, t2, MPFR_MANT (b)[0], MPFR_MANT (c)[1]); - umul_ppmm (tmp[3], t3, MPFR_MANT (b)[1], MPFR_MANT (c)[1]); - add_ssaaaa (tmp[3], t1, tmp[3], t1, 0, t3); - /* Sum those two partial products */ - add_ssaaaa (tmp[2], tmp[1], tmp[2], tmp[1], t1, t2); - tmp[3] += (tmp[2] < t1); - b1 = tmp[3]; - } - b1 >>= (GMP_NUMB_BITS - 1); - tmp += k - tn; - if (MPFR_UNLIKELY (b1 == 0)) - mpn_lshift (tmp, tmp, tn, 1); /* tn <= k, so no stack corruption */ - } - else /* bn >= cn and bn >= 3 */ - /* Mulders' mulhigh. This code can also be used via mpfr_sqr, - hence the tests b != c. */ - if (MPFR_UNLIKELY (cn > (threshold = b != c ? - MPFR_MUL_THRESHOLD : MPFR_SQR_THRESHOLD))) - { - mp_limb_t *bp, *cp; - mp_size_t n; - mpfr_prec_t p; - - /* First check if we can reduce the precision of b or c: - exact values are a nightmare for the short product trick */ - bp = MPFR_MANT (b); - cp = MPFR_MANT (c); - MPFR_STAT_STATIC_ASSERT (MPFR_MUL_THRESHOLD >= 1 && - MPFR_SQR_THRESHOLD >= 1); - if (MPFR_UNLIKELY ((bp[0] == 0 && bp[1] == 0) || - (cp[0] == 0 && cp[1] == 0))) - { - mpfr_t b_tmp, c_tmp; - - MPFR_TMP_FREE (marker); - /* Check for b */ - while (*bp == 0) - { - bp++; - bn--; - MPFR_ASSERTD (bn > 0); - } /* This must end since the most significant limb is != 0 */ - - /* Check for c too: if b == c, this will do nothing */ - while (*cp == 0) - { - cp++; - cn--; - MPFR_ASSERTD (cn > 0); - } /* This must end since the most significant limb is != 0 */ - - /* It is not the fastest way, but it is safer. */ - MPFR_SET_SAME_SIGN (b_tmp, b); - MPFR_SET_EXP (b_tmp, MPFR_GET_EXP (b)); - MPFR_PREC (b_tmp) = bn * GMP_NUMB_BITS; - MPFR_MANT (b_tmp) = bp; - - if (b != c) - { - MPFR_SET_SAME_SIGN (c_tmp, c); - MPFR_SET_EXP (c_tmp, MPFR_GET_EXP (c)); - MPFR_PREC (c_tmp) = cn * GMP_NUMB_BITS; - MPFR_MANT (c_tmp) = cp; - - /* Call again mpfr_mul with the fixed arguments */ - return mpfr_mul (a, b_tmp, c_tmp, rnd_mode); - } - else - /* Call mpfr_mul instead of mpfr_sqr as the precision - is probably still high enough. It is thus better to call - mpfr_mul again, but it should not give an infinite loop - if we call mpfr_sqr. */ - return mpfr_mul (a, b_tmp, b_tmp, rnd_mode); - } - - /* Compute estimated precision of mulhigh. - We could use `+ (n < cn) + (n < bn)' instead of `+ 2', - but does it worth it? */ - n = MPFR_LIMB_SIZE (a) + 1; - n = MIN (n, cn); - MPFR_ASSERTD (n >= 1 && 2*n <= k && n <= cn && n <= bn); - p = n * GMP_NUMB_BITS - MPFR_INT_CEIL_LOG2 (n + 2); - bp += bn - n; - cp += cn - n; - - /* Check if MulHigh can produce a roundable result. - We may lose 1 bit due to RNDN, 1 due to final shift. */ - if (MPFR_UNLIKELY (aq > p - 5)) - { - if (MPFR_UNLIKELY (aq > p - 5 + GMP_NUMB_BITS - || bn <= threshold + 1)) - { - /* MulHigh can't produce a roundable result. */ - MPFR_LOG_MSG (("mpfr_mulhigh can't be used (%lu VS %lu)\n", - aq, p)); - goto full_multiply; - } - /* Add one extra limb to mantissa of b and c. */ - if (bn > n) - bp --; - else - { - bp = MPFR_TMP_LIMBS_ALLOC (n + 1); - bp[0] = 0; - MPN_COPY (bp + 1, MPFR_MANT (b) + bn - n, n); - } - if (b != c) - { -#if GMP_NUMB_BITS <= 32 - if (cn > n) - cp --; /* This can only happen on a 32-bit computer, - and is very unlikely to happen. - Indeed, since n = MIN (an + 1, cn), with - an = MPFR_LIMB_SIZE(a), we can have cn > n - only when n = an + 1 < cn. - We are in the case aq > p - 5, with - aq = PREC(a) = an*W - sh, with W = GMP_NUMB_BITS - and 0 <= sh < W, and p = n*W - ceil(log2(n+2)), - thus an*W - sh > n*W - ceil(log2(n+2)) - 5. - Thus n < an + (ceil(log2(n+2)) + 5 - sh)/W. - To get n = an + 1, we need - ceil(log2(n+2)) + 5 - sh > W, thus since sh>=0 - we need ceil(log2(n+2)) + 5 > W. - With W=32 this can only happen for n>=2^27-1, - thus for a precision of 2^32-64 for a, - and with W=64 for n>=2^59-1, which would give - a precision >= 2^64. */ - else -#endif - { - cp = MPFR_TMP_LIMBS_ALLOC (n + 1); - cp[0] = 0; - MPN_COPY (cp + 1, MPFR_MANT (c) + cn - n, n); - } - } - /* We will compute with one extra limb */ - n++; - /* ceil(log2(n+2)) takes into account the lost bits due to - Mulders' short product */ - p = n * GMP_NUMB_BITS - MPFR_INT_CEIL_LOG2 (n + 2); - /* Due to some nasty reasons we can have only 4 bits */ - MPFR_ASSERTD (aq <= p - 4); - - if (MPFR_LIKELY (k < 2*n)) - { - tmp = MPFR_TMP_LIMBS_ALLOC (2 * n); - tmp += 2*n-k; /* `tmp' still points to an area of `k' limbs */ - } - } - MPFR_LOG_MSG (("Use mpfr_mulhigh (%lu VS %lu)\n", aq, p)); - /* Compute an approximation of the product of b and c */ - if (b != c) - mpfr_mulhigh_n (tmp + k - 2 * n, bp, cp, n); - else - mpfr_sqrhigh_n (tmp + k - 2 * n, bp, n); - /* now tmp[k-n]..tmp[k-1] contains an approximation of the n upper - limbs of the product, with tmp[k-1] >= 2^(GMP_NUMB_BITS-2) */ - b1 = tmp[k-1] >> (GMP_NUMB_BITS - 1); /* msb from the product */ - - /* If the mantissas of b and c are uniformly distributed in (1/2, 1], - then their product is in (1/4, 1/2] with probability 2*ln(2)-1 - ~ 0.386 and in [1/2, 1] with probability 2-2*ln(2) ~ 0.614 */ - if (MPFR_UNLIKELY (b1 == 0)) - /* Warning: the mpfr_mulhigh_n call above only surely affects - tmp[k-n-1..k-1], thus we shift only those limbs */ - mpn_lshift (tmp + k - n - 1, tmp + k - n - 1, n + 1, 1); - tmp += k - tn; - /* now the approximation is in tmp[tn-n]...tmp[tn-1] */ - MPFR_ASSERTD (MPFR_LIMB_MSB (tmp[tn-1]) != 0); - - /* for RNDF, we simply use RNDZ, since anyway here we multiply numbers - with large precisions, thus the overhead of RNDZ is small */ - if (rnd_mode == MPFR_RNDF) - rnd_mode = MPFR_RNDZ; - - /* if the most significant bit b1 is zero, we have only p-1 correct - bits */ - if (MPFR_UNLIKELY (!mpfr_round_p (tmp, tn, p + b1 - 1, - aq + (rnd_mode == MPFR_RNDN)))) - { - tmp -= k - tn; /* tmp may have changed, FIX IT!!!!! */ - goto full_multiply; - } - } - else - { - full_multiply: - MPFR_LOG_MSG (("Use mpn_mul\n", 0)); - b1 = mpn_mul (tmp, MPFR_MANT (b), bn, MPFR_MANT (c), cn); - - /* now tmp[0]..tmp[k-1] contains the product of both mantissa, - with tmp[k-1]>=2^(GMP_NUMB_BITS-2) */ - b1 >>= GMP_NUMB_BITS - 1; /* msb from the product */ - - /* if the mantissas of b and c are uniformly distributed in (1/2, 1], - then their product is in (1/4, 1/2] with probability 2*ln(2)-1 - ~ 0.386 and in [1/2, 1] with probability 2-2*ln(2) ~ 0.614 */ - tmp += k - tn; - if (MPFR_UNLIKELY (b1 == 0)) - mpn_lshift (tmp, tmp, tn, 1); /* tn <= k, so no stack corruption */ - } - - /* b1 is 0 or 1 (most significant bit from the raw product) */ - ax2 = ax + ((int) b1 - 1); - MPFR_RNDRAW (inexact, a, tmp, bq + cq, rnd_mode, sign, ax2++); - MPFR_TMP_FREE (marker); - MPFR_EXP (a) = ax2; /* Can't use MPFR_SET_EXP: Expo may be out of range */ - MPFR_SET_SIGN (a, sign); - if (MPFR_UNLIKELY (ax2 > __gmpfr_emax)) - return mpfr_overflow (a, rnd_mode, sign); - if (MPFR_UNLIKELY (ax2 < __gmpfr_emin)) - { - /* In the rounding to the nearest mode, if the exponent of the exact - result (i.e. before rounding, i.e. without taking cc into account) - is < __gmpfr_emin - 1 or the exact result is a power of 2 (i.e. if - both arguments are powers of 2), then round to zero. */ - if (rnd_mode == MPFR_RNDN - && (ax + (mpfr_exp_t) b1 < __gmpfr_emin - || (mpfr_powerof2_raw (b) && mpfr_powerof2_raw (c)))) - rnd_mode = MPFR_RNDZ; - return mpfr_underflow (a, rnd_mode, sign); - } - MPFR_RET (inexact); -} |