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-rw-r--r--Build/source/libs/mpfr/mpfr-3.1.2/src/sqrt.c231
1 files changed, 231 insertions, 0 deletions
diff --git a/Build/source/libs/mpfr/mpfr-3.1.2/src/sqrt.c b/Build/source/libs/mpfr/mpfr-3.1.2/src/sqrt.c
new file mode 100644
index 00000000000..64a9e025c7a
--- /dev/null
+++ b/Build/source/libs/mpfr/mpfr-3.1.2/src/sqrt.c
@@ -0,0 +1,231 @@
+/* mpfr_sqrt -- square root of a floating-point number
+
+Copyright 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013 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"
+
+int
+mpfr_sqrt (mpfr_ptr r, mpfr_srcptr u, mpfr_rnd_t rnd_mode)
+{
+ mp_size_t rsize; /* number of limbs of r (plus 1 if exact limb multiple) */
+ 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;
+ mpfr_limb_ptr rp, rp0;
+ mpfr_limb_ptr up;
+ mpfr_limb_ptr sp;
+ 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 */
+ mpfr_exp_t expr;
+ MPFR_TMP_DECL(marker);
+
+ MPFR_LOG_FUNC
+ (("x[%Pu]=%.*Rg rnd=%d", mpfr_get_prec (u), mpfr_log_prec, u, rnd_mode),
+ ("y[%Pu]=%.*Rg inexact=%d",
+ mpfr_get_prec (r), mpfr_log_prec, 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_SET_POS(r);
+
+ MPFR_TMP_MARK (marker);
+ MPFR_UNSIGNED_MINUS_MODULO(sh,MPFR_PREC(r));
+ if (sh == 0 && rnd_mode == MPFR_RNDN)
+ sh = GMP_NUMB_BITS; /* ugly case */
+ rsize = MPFR_LIMB_SIZE(r) + (sh == GMP_NUMB_BITS);
+ /* rsize is the number of limbs of r + 1 if exact limb multiple and rounding
+ to nearest, this is the number of wanted limbs for the square root */
+ rrsize = rsize + rsize;
+ usize = MPFR_LIMB_SIZE(u); /* number of limbs of u */
+ rp0 = MPFR_MANT(r);
+ rp = (sh < GMP_NUMB_BITS) ? rp0 : MPFR_TMP_LIMBS_ALLOC (rsize);
+ 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 */
+
+ sp = MPFR_TMP_LIMBS_ALLOC (rrsize);
+
+ /* 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 */
+
+ /* mpn_rootrem with NULL 2nd argument is faster than mpn_sqrtrem, thus use
+ it if available and if the user asked to use GMP internal functions */
+#if defined(WANT_GMP_INTERNALS) && defined(HAVE___GMPN_ROOTREM)
+ tsize = __gmpn_rootrem (rp, NULL, sp, rrsize, 2);
+#else
+ tsize = mpn_sqrtrem (rp, NULL, sp, rrsize);
+#endif
+
+ /* a return value of zero in mpn_sqrtrem indicates a perfect square */
+ sticky = sticky0 || tsize != 0;
+
+ /* truncate low bits of rp[0] */
+ sticky1 = rp[0] & ((sh < GMP_NUMB_BITS) ? MPFR_LIMB_MASK(sh)
+ : ~MPFR_LIMB_ZERO);
+ rp[0] -= sticky1;
+
+ sticky = sticky || sticky1;
+
+ expr = (MPFR_GET_EXP(u) + odd_exp) / 2; /* exact */
+
+ if (rnd_mode == MPFR_RNDZ || rnd_mode == MPFR_RNDD || sticky == MPFR_LIMB_ZERO)
+ {
+ inexact = (sticky == MPFR_LIMB_ZERO) ? 0 : -1;
+ goto truncate;
+ }
+ else if (rnd_mode == MPFR_RNDN)
+ {
+ /* if sh < GMP_NUMB_BITS, 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 the sqrtrem remainder and sticky0. */
+ if (sh < GMP_NUMB_BITS)
+ {
+ 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 /* sh = GMP_NUMB_BITS: the round bit is the most significant bit
+ of rp[0], and the remaining GMP_NUMB_BITS-1 bits contribute to
+ the sticky bit */
+ {
+ if (sticky1 & MPFR_LIMB_HIGHBIT)
+ { /* round bit is set */
+ if (sticky1 == MPFR_LIMB_HIGHBIT && 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 /* rnd_mode=GMP_RDNU, necessarily sticky <> 0, thus add 1 ulp */
+ goto add_one_ulp;
+
+ even_rule: /* has to set inexact */
+ if (sh < GMP_NUMB_BITS)
+ inexact = (rp[0] & (MPFR_LIMB_ONE << sh)) ? 1 : -1;
+ else
+ inexact = (rp[1] & MPFR_LIMB_ONE) ? 1 : -1;
+ if (inexact == -1)
+ goto truncate;
+ /* else go through add_one_ulp */
+
+ add_one_ulp:
+ inexact = 1; /* always here */
+ if (sh == GMP_NUMB_BITS)
+ {
+ rp ++;
+ rsize --;
+ sh = 0;
+ }
+ if (mpn_add_1 (rp0, rp, rsize, MPFR_LIMB_ONE << sh))
+ {
+ expr ++;
+ rp[rsize - 1] = MPFR_LIMB_HIGHBIT;
+ }
+ goto end;
+
+ truncate: /* inexact = 0 or -1 */
+ if (sh == GMP_NUMB_BITS)
+ MPN_COPY (rp0, rp + 1, rsize - 1);
+
+ end:
+ 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);
+}