/* mpfr_set -- copy of a floating-point number Copyright 1999, 2001-2021 Free Software Foundation, Inc. Contributed by the AriC and Caramba projects, INRIA. This file is part of the GNU MPFR Library. The GNU MPFR Library is free software; you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation; either version 3 of the License, or (at your option) any later version. The GNU MPFR Library is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details. You should have received a copy of the GNU Lesser General Public License along with the GNU MPFR Library; see the file COPYING.LESSER. If not, see https://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA. */ #include "mpfr-impl.h" /* set a to abs(b) * signb: a=b when signb = SIGN(b), a=abs(b) when signb=1 */ MPFR_HOT_FUNCTION_ATTR int mpfr_set4 (mpfr_ptr a, mpfr_srcptr b, mpfr_rnd_t rnd_mode, int signb) { /* Sign is ALWAYS copied */ MPFR_SET_SIGN (a, signb); /* Exponent is also always copied since if the number is singular, the exponent field determined the number. Can't use MPFR_SET_EXP since the exponent may be singular */ MPFR_EXP (a) = MPFR_EXP (b); if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (b))) { /* MPFR_SET_NAN, MPFR_SET_ZERO and MPFR_SET_INF are useless since MPFR_EXP (a) = MPFR_EXP (b) does the job */ if (MPFR_IS_NAN (b)) MPFR_RET_NAN; else MPFR_RET (0); } else if (MPFR_PREC (b) == MPFR_PREC (a)) { /* Same precision and b is not singular: * just copy the mantissa, and set the exponent and the sign * The result is exact. */ MPN_COPY (MPFR_MANT (a), MPFR_MANT (b), MPFR_LIMB_SIZE (b)); MPFR_RET (0); } else { int inex; /* Else Round B inside a */ MPFR_RNDRAW (inex, a, MPFR_MANT (b), MPFR_PREC (b), rnd_mode, signb, if (MPFR_UNLIKELY (++ MPFR_EXP (a) > __gmpfr_emax)) return mpfr_overflow (a, rnd_mode, signb) ); MPFR_RET (inex); } } /* Set a to b */ #undef mpfr_set int mpfr_set (mpfr_ptr a, mpfr_srcptr b, mpfr_rnd_t rnd_mode) { return mpfr_set4 (a, b, rnd_mode, MPFR_SIGN (b)); } /* Set a to |b| */ #undef mpfr_abs int mpfr_abs (mpfr_ptr a, mpfr_srcptr b, mpfr_rnd_t rnd_mode) { return mpfr_set4 (a, b, rnd_mode, MPFR_SIGN_POS); } /* Round (u, inex) into s with rounding mode rnd_mode, where inex is the ternary value associated with u, which has been obtained using the *same* rounding mode rnd_mode. Assumes PREC(u) = 2*PREC(s). The generic algorithm is the following: 1. inex2 = mpfr_set (s, u, rnd_mode); 2. if (inex2 != 0) return inex2; else return inex; except in the double-rounding case: in MPFR_RNDN, when u is in the middle of two consecutive PREC(s)-bit numbers, if inex and inex2 are both > 0 (resp. both < 0), we correct s to nextbelow(s) (resp. nextabove(s)), and return the opposite of inex. Note: this function can be called with rnd_mode == MPFR_RNDF, in which case, the rounding direction and the returned ternary value are unspecified. */ int mpfr_set_1_2 (mpfr_ptr s, mpfr_srcptr u, mpfr_rnd_t rnd_mode, int inex) { mpfr_prec_t p = MPFR_PREC(s); mpfr_prec_t sh = GMP_NUMB_BITS - p; mp_limb_t rb, sb; mp_limb_t *sp = MPFR_MANT(s); mp_limb_t *up = MPFR_MANT(u); mp_limb_t mask; int inex2; if (MPFR_UNLIKELY(MPFR_IS_SINGULAR(u))) { mpfr_set (s, u, rnd_mode); return inex; } MPFR_ASSERTD(MPFR_PREC(u) == 2 * p); if (p < GMP_NUMB_BITS) { mask = MPFR_LIMB_MASK(sh); if (MPFR_PREC(u) <= GMP_NUMB_BITS) { mp_limb_t u0 = up[0]; /* it suffices to round (u0, inex) */ rb = u0 & (MPFR_LIMB_ONE << (sh - 1)); sb = (u0 & mask) ^ rb; sp[0] = u0 & ~mask; } else { mp_limb_t u1 = up[1]; /* we need to round (u1, u0, inex) */ mask = MPFR_LIMB_MASK(sh); rb = u1 & (MPFR_LIMB_ONE << (sh - 1)); sb = ((u1 & mask) ^ rb) | up[0]; sp[0] = u1 & ~mask; } inex2 = inex * MPFR_SIGN(u); MPFR_SIGN(s) = MPFR_SIGN(u); MPFR_EXP(s) = MPFR_EXP(u); /* in case inex2 > 0, the value of u is rounded away, thus we need to subtract something from (u0, rb, sb): (a) if sb is not zero, since the subtracted value is < 1, we can leave sb as it is; (b) if rb <> 0 and sb = 0: change to rb = 0 and sb = 1 (c) if rb = sb = 0: change to rb = 1 and sb = 1, and subtract 1 */ if (inex2 > 0) { if (rb && sb == 0) { rb = 0; sb = 1; } } else /* inex2 <= 0 */ sb |= inex; /* now rb, sb are the round and sticky bits, together with the value of sp[0], except possibly in the case rb = sb = 0 and inex2 > 0 */ if (rb == 0 && sb == 0) { if (inex2 <= 0) MPFR_RET(0); else /* inex2 > 0 can only occur for RNDN and RNDA: RNDN: return sp[0] and inex RNDA: return sp[0] and inex */ MPFR_RET(inex); } else if (rnd_mode == MPFR_RNDN) { if (rb == 0 || (sb == 0 && (sp[0] & (MPFR_LIMB_ONE << sh)) == 0)) goto truncate; else goto add_one_ulp; } else if (MPFR_IS_LIKE_RNDZ(rnd_mode, MPFR_IS_NEG(s))) { truncate: MPFR_RET(-MPFR_SIGN(s)); } else /* round away from zero */ { add_one_ulp: sp[0] += MPFR_LIMB_ONE << sh; if (MPFR_UNLIKELY(sp[0] == 0)) { sp[0] = MPFR_LIMB_HIGHBIT; if (MPFR_EXP(s) + 1 <= __gmpfr_emax) MPFR_SET_EXP (s, MPFR_EXP(s) + 1); else /* overflow */ return mpfr_overflow (s, rnd_mode, MPFR_SIGN(s)); } MPFR_RET(MPFR_SIGN(s)); } } /* general case PREC(s) >= GMP_NUMB_BITS */ inex2 = mpfr_set (s, u, rnd_mode); /* Check the double-rounding case, i.e. with u = middle of two consecutive PREC(s)-bit numbers, which is equivalent to u being exactly representable on PREC(s) + 1 bits but not on PREC(s) bits. Moreover, since PREC(u) = 2*PREC(s), u and s cannot be identical (as pointers), thus u was not changed. */ if (rnd_mode == MPFR_RNDN && inex * inex2 > 0 && mpfr_min_prec (u) == p + 1) { if (inex > 0) mpfr_nextbelow (s); else mpfr_nextabove (s); return -inex; } return inex2 != 0 ? inex2 : inex; }