--- /dev/null
+/* mpfr_sqrt -- square root of a floating-point number
+
+Copyright 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009 Free Software Foundation, Inc.
+Contributed by the Arenaire and Cacao 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 2.1 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.LIB. If not, write to
+the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston,
+MA 02110-1301, USA. */
+
+#include "mpfr-impl.h"
+
+int
+mpfr_sqrt (mpfr_ptr r, mpfr_srcptr u, mp_rnd_t rnd_mode)
+{
+ mp_size_t rsize; /* number of limbs of r */
+ mp_size_t rrsize;
+ mp_size_t usize; /* number of limbs of u */
+ mp_size_t tsize; /* number of limbs of the sqrtrem remainder */
+ mp_size_t k;
+ mp_size_t l;
+ mp_ptr rp;
+ mp_ptr up;
+ mp_ptr sp;
+ mp_ptr tp;
+ mp_limb_t sticky0; /* truncated part of input */
+ mp_limb_t sticky1; /* truncated part of rp[0] */
+ mp_limb_t sticky;
+ int odd_exp;
+ int sh; /* number of extra bits in rp[0] */
+ int inexact; /* return ternary flag */
+ mp_exp_t expr;
+ MPFR_TMP_DECL(marker);
+
+ MPFR_LOG_FUNC (("x[%#R]=%R rnd=%d", u, u, rnd_mode),
+ ("y[%#R]=%R inexact=%d", r, r, inexact));
+
+ if (MPFR_UNLIKELY(MPFR_IS_SINGULAR(u)))
+ {
+ if (MPFR_IS_NAN(u))
+ {
+ MPFR_SET_NAN(r);
+ MPFR_RET_NAN;
+ }
+ else if (MPFR_IS_ZERO(u))
+ {
+ /* 0+ or 0- */
+ MPFR_SET_SAME_SIGN(r, u);
+ MPFR_SET_ZERO(r);
+ MPFR_RET(0); /* zero is exact */
+ }
+ else
+ {
+ MPFR_ASSERTD(MPFR_IS_INF(u));
+ /* sqrt(-Inf) = NAN */
+ if (MPFR_IS_NEG(u))
+ {
+ MPFR_SET_NAN(r);
+ MPFR_RET_NAN;
+ }
+ MPFR_SET_POS(r);
+ MPFR_SET_INF(r);
+ MPFR_RET(0);
+ }
+ }
+ if (MPFR_UNLIKELY(MPFR_IS_NEG(u)))
+ {
+ MPFR_SET_NAN(r);
+ MPFR_RET_NAN;
+ }
+ MPFR_CLEAR_FLAGS(r);
+ MPFR_SET_POS(r);
+
+ rsize = MPFR_LIMB_SIZE(r); /* number of limbs of r */
+ rrsize = rsize + rsize;
+ usize = MPFR_LIMB_SIZE(u); /* number of limbs of u */
+ rp = MPFR_MANT(r);
+ up = MPFR_MANT(u);
+ sticky0 = MPFR_LIMB_ZERO; /* truncated part of input */
+ sticky1 = MPFR_LIMB_ZERO; /* truncated part of rp[0] */
+ odd_exp = (unsigned int) MPFR_GET_EXP (u) & 1;
+ inexact = -1; /* return ternary flag */
+
+ MPFR_TMP_MARK (marker);
+ sp = (mp_limb_t *) MPFR_TMP_ALLOC (rrsize * sizeof (mp_limb_t));
+
+ /* copy the most significant limbs of u to {sp, rrsize} */
+ if (MPFR_LIKELY(usize <= rrsize)) /* in case r and u have the same precision,
+ we have indeed rrsize = 2 * usize */
+ {
+ k = rrsize - usize;
+ if (MPFR_LIKELY(k))
+ MPN_ZERO (sp, k);
+ if (odd_exp)
+ {
+ if (MPFR_LIKELY(k))
+ sp[k - 1] = mpn_rshift (sp + k, up, usize, 1);
+ else
+ sticky0 = mpn_rshift (sp, up, usize, 1);
+ }
+ else
+ MPN_COPY (sp + rrsize - usize, up, usize);
+ }
+ else /* usize > rrsize: truncate the input */
+ {
+ k = usize - rrsize;
+ if (odd_exp)
+ sticky0 = mpn_rshift (sp, up + k, rrsize, 1);
+ else
+ MPN_COPY (sp, up + k, rrsize);
+ l = k;
+ while (sticky0 == MPFR_LIMB_ZERO && l != 0)
+ sticky0 = up[--l];
+ }
+
+ /* sticky0 is non-zero iff the truncated part of the input is non-zero */
+
+ tsize = mpn_sqrtrem (rp, tp = sp, sp, rrsize);
+
+ l = tsize;
+ sticky = sticky0;
+ while (sticky == MPFR_LIMB_ZERO && l != 0)
+ sticky = tp[--l];
+
+ /* truncated low bits of rp[0] */
+ MPFR_UNSIGNED_MINUS_MODULO(sh,MPFR_PREC(r));
+ sticky1 = rp[0] & MPFR_LIMB_MASK(sh);
+ rp[0] -= sticky1;
+
+ sticky = sticky || sticky1;
+
+ expr = (MPFR_GET_EXP(u) + odd_exp) / 2; /* exact */
+
+ if (rnd_mode == GMP_RNDZ || rnd_mode == GMP_RNDD || sticky == MPFR_LIMB_ZERO)
+ {
+ inexact = (sticky == MPFR_LIMB_ZERO) ? 0 : -1;
+ goto truncate;
+ }
+ else if (rnd_mode == GMP_RNDN)
+ {
+ /* if sh>0, the round bit is bit (sh-1) of sticky1
+ and the sticky bit is formed by the low sh-1 bits from
+ sticky1, together with {tp, tsize} and sticky0. */
+ if (sh)
+ {
+ if (sticky1 & (MPFR_LIMB_ONE << (sh - 1)))
+ { /* round bit is set */
+ if (sticky1 == (MPFR_LIMB_ONE << (sh - 1)) && tsize == 0
+ && sticky0 == 0)
+ goto even_rule;
+ else
+ goto add_one_ulp;
+ }
+ else /* round bit is zero */
+ goto truncate; /* with the default inexact=-1 */
+ }
+ else
+ {
+ /* if sh=0, we have to compare {tp, tsize} with {rp, rsize}:
+ if {tp, tsize} < {rp, rsize}: truncate
+ if {tp, tsize} > {rp, rsize}: round up
+ if {tp, tsize} = {rp, rsize}: compare the truncated part of the
+ input to 1/4
+ if < 1/4: truncate
+ if > 1/4: round up
+ if = 1/4: even rounding rule
+ Set inexact = -1 if truncate
+ inexact = 1 if add one ulp
+ inexact = 0 if even rounding rule
+ */
+ if (tsize < rsize)
+ inexact = -1;
+ else if (tsize > rsize) /* FIXME: may happen? */
+ inexact = 1;
+ else /* tsize = rsize */
+ {
+ int cmp;
+
+ cmp = mpn_cmp (tp, rp, rsize);
+ if (cmp > 0)
+ inexact = 1;
+ else if (cmp < 0 || sticky0 == MPFR_LIMB_ZERO)
+ inexact = -1;
+ /* now tricky case {tp, tsize} = {rp, rsize} */
+ /* in case usize <= rrsize, the only case where sticky0 <> 0
+ is when the exponent of u is odd and usize = rrsize (k=0),
+ but in that case the truncated part is exactly 1/2, thus
+ we have to round up.
+ If the exponent of u is odd, and up[k] is odd, the truncated
+ part is >= 1/2, so we round up too. */
+ else if (usize <= rrsize || (odd_exp && (up[k] & MPFR_LIMB_ONE)))
+ inexact = 1;
+ else
+ {
+ /* now usize > rrsize:
+ (a) if the exponent of u is even, the 1/4 bit is the
+ 2nd most significant bit of up[k-1];
+ (b) if the exponent of u is odd, the 1/4 bit is the
+ 1st most significant bit of up[k-1]; */
+ sticky1 = MPFR_LIMB_ONE << (BITS_PER_MP_LIMB - 2 + odd_exp);
+ if (up[k - 1] < sticky1)
+ inexact = -1;
+ else if (up[k - 1] > sticky1)
+ inexact = 1;
+ else
+ {
+ /* up[k - 1] == sticky1: consider low k-1 limbs */
+ while (--k > 0 && up[k - 1] == MPFR_LIMB_ZERO)
+ ;
+ inexact = (k != 0);
+ }
+ } /* end of case {tp, tsize} = {rp, rsize} */
+ } /* end of case tsize = rsize */
+ if (inexact == -1)
+ goto truncate;
+ else if (inexact == 1)
+ goto add_one_ulp;
+ /* else go through even_rule */
+ }
+ }
+ else /* rnd_mode=GMP_RDNU, necessarily sticky <> 0, thus add 1 ulp */
+ goto add_one_ulp;
+
+ even_rule: /* has to set inexact */
+ inexact = (rp[0] & (MPFR_LIMB_ONE << sh)) ? 1 : -1;
+ if (inexact == -1)
+ goto truncate;
+ /* else go through add_one_ulp */
+
+ add_one_ulp:
+ inexact = 1; /* always here */
+ if (mpn_add_1 (rp, rp, rsize, MPFR_LIMB_ONE << sh))
+ {
+ expr ++;
+ rp[rsize - 1] = MPFR_LIMB_HIGHBIT;
+ }
+
+ truncate: /* inexact = 0 or -1 */
+
+ MPFR_ASSERTN (expr >= MPFR_EMIN_MIN && expr <= MPFR_EMAX_MAX);
+ MPFR_EXP (r) = expr;
+
+ MPFR_TMP_FREE(marker);
+ return mpfr_check_range (r, inexact, rnd_mode);
+}
projects / msp430-gcc.git / blobdiff