/* mpfr_sqrt -- square root of a floating-point number Copyright (C) 1999 PolKA project, Inria Lorraine and Loria This file is part of the MPFR Library. The MPFR Library is free software; you can redistribute it and/or modify it under the terms of the GNU Library General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. The 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 Library General Public License for more details. You should have received a copy of the GNU Library General Public License along with the MPFR Library; see the file COPYING.LIB. If not, write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. */ #include #include #include #include "gmp.h" #include "gmp-impl.h" #include "mpfr.h" #include "longlong.h" /* #define DEBUG */ int mpfr_sqrt (mpfr_ptr r, mpfr_srcptr u, unsigned char rnd_mode) { mp_ptr up, rp, tmp, remp; mp_size_t usize, rrsize; mp_size_t rsize; mp_size_t prec, err; mp_limb_t q_limb; long rw, nw, k; int exact = 0; unsigned long cc = 0; char can_round = 0; TMP_DECL (marker); TMP_DECL(marker0); if (FLAG_NAN(u) || SIGN(u) == -1) { SET_NAN(r); return 0; } prec = PREC(r); if (!NOTZERO(u)) { EXP(r) = 0; MPN_ZERO(MANT(r), ABSSIZE(r)); return 1; } up = MANT(u); #ifdef DEBUG printf("Entering square root : "); for(k = usize - 1; k >= 0; k--) { printf("%lu ", up[k]); } printf(".\n"); #endif /* Compare the mantissas */ usize = (PREC(u) - 1)/BITS_PER_MP_LIMB + 1; rsize = ((PREC(r) + 2 + (EXP(u) & 1))/BITS_PER_MP_LIMB + 1) << 1; rrsize = (PREC(r) + 2 + (EXP(u) & 1))/BITS_PER_MP_LIMB + 1; /* One extra bit is needed in order to get the square root with enough precision ; take one extra bit for rrsize in order to solve more easily the problem of rounding to nearest. Need to have 2*rrsize = rsize... Take one extra bit if the exponent of u is odd since we shall have to shift then. */ TMP_MARK(marker0); if (EXP(u) & 1) /* Shift u one bit to the right */ { if (PREC(u) & (BITS_PER_MP_LIMB - 1)) { up = TMP_ALLOC(usize*BYTES_PER_MP_LIMB); mpn_rshift(up, u->_mp_d, usize, 1); } else { up = TMP_ALLOC((usize + 1)*BYTES_PER_MP_LIMB); if (mpn_rshift(up + 1, u->_mp_d, ABSSIZE(u), 1)) up [0] = ((mp_limb_t) 1) << (BITS_PER_MP_LIMB - 1); else up[0] = 0; usize++; } } EXP(r) = ((EXP(u) + (EXP(u) & 1)) / 2) ; do { TMP_MARK (marker); err = rsize*BITS_PER_MP_LIMB; if (rsize < usize) { err--; } if (err > rrsize * BITS_PER_MP_LIMB) { err = rrsize * BITS_PER_MP_LIMB; } tmp = (mp_ptr) TMP_ALLOC (rsize * BYTES_PER_MP_LIMB); rp = (mp_ptr) TMP_ALLOC (rrsize * BYTES_PER_MP_LIMB); remp = (mp_ptr) TMP_ALLOC (rsize * BYTES_PER_MP_LIMB); if (usize >= rsize) { MPN_COPY (tmp, up + usize - rsize, rsize); } else { MPN_COPY (tmp + rsize - usize, up, usize); MPN_ZERO (tmp, rsize - usize); } /* Do the real job */ #ifdef DEBUG printf("Taking the sqrt of : "); for(k = rsize - 1; k >= 0; k--) { printf("+%lu*2^%lu",tmp[k],k*mp_bits_per_limb); } printf(".\n"); #endif q_limb = kara_sqrtrem (rp, remp, tmp, rsize); #ifdef DEBUG printf("The result is : \n"); printf("sqrt : "); for(k = rrsize - 1; k >= 0; k--) { printf("%lu ", rp[k]); } printf("(q_limb = %lu)\n", q_limb); #endif can_round = (mpfr_can_round_raw(rp, rrsize, 1, err, GMP_RNDZ, rnd_mode, PREC(r))); /* If we used all the limbs of both the dividend and the divisor, then we have the correct RNDZ rounding */ if (!can_round && (rsize < 2*usize)) { #ifdef DEBUG printf("Increasing the precision.\n"); #endif TMP_FREE(marker); } } while (!can_round && (rsize < 2*usize) && (rsize += 2) && (rrsize ++)); /* This part may be deplaced upper to avoid a few mpfr_can_round_raw */ /* when the square root is exact. It is however very unprobable that */ /* it would improve the behaviour of the present code on average. */ if (!q_limb) /* possibly exact */ { /* if we have taken into account the whole of up */ for (k = usize - rsize - 1; k >= 0; k ++) if (up[k]) break; if (k < 0) { exact = 1; goto fin; } } if (can_round) { cc = mpfr_round_raw(rp, rp, err, 0, PREC(r), rnd_mode); rrsize = (PREC(r) - 1)/BITS_PER_MP_LIMB + 1; } else /* Use the return value of sqrtrem to decide of the rounding */ /* Note that at this point the sqrt has been computed */ /* EXACTLY. If rounding = GMP_RNDZ, do nothing [comes from */ /* the fact that the exact square root can end with a bunch of ones, */ /* and in that case we indeed cannot round if we do not know that */ /* the computation was exact. */ switch (rnd_mode) { case GMP_RNDZ : case GMP_RNDD : break; case GMP_RNDN : /* Not in the situation ...0 111111 */ rw = (PREC(r) + 1) & (BITS_PER_MP_LIMB - 1); if (rw) { rw = BITS_PER_MP_LIMB - rw; nw = 0; } else nw = 1; if ((rp[nw] >> rw) & 1 && /* Not 0111111111 */ (q_limb || /* Nonzero remainder */ (rw ? (rp[nw] >> (rw + 1)) & 1 : (rp[nw] >> (BITS_PER_MP_LIMB - 1)) & 1))) /* or even rounding */ cc = mpn_add_1(rp + nw, rp + nw, rrsize, ((mp_limb_t)1) << rw); break; case GMP_RNDU : if (q_limb) cc = mpn_add_1(rp, rp, rrsize, 1 << (BITS_PER_MP_LIMB - (PREC(r) & (BITS_PER_MP_LIMB - 1)))); } if (cc) { mpn_rshift(rp, rp, rrsize, 1); rp[rrsize-1] |= (mp_limb_t) 1 << (BITS_PER_MP_LIMB-1); r->_mp_exp++; } fin: rsize = rrsize; rrsize = (PREC(r) - 1)/BITS_PER_MP_LIMB + 1; MPN_COPY(r->_mp_d, rp + rsize - rrsize, rrsize); if (PREC(r) & (BITS_PER_MP_LIMB - 1)) MANT(r) [0] &= ~(((mp_limb_t)1 << (BITS_PER_MP_LIMB - (PREC(r) & (BITS_PER_MP_LIMB - 1)))) - 1) ; TMP_FREE(marker0); TMP_FREE (marker); return exact; }