diff options
Diffstat (limited to 'Build/source/libs/mpfr/mpfr-3.1.2/src/sqrt.c')
-rw-r--r-- | Build/source/libs/mpfr/mpfr-3.1.2/src/sqrt.c | 231 |
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); +} |