| /* mpfr_sqrt -- square root of a floating-point number |
| |
| Copyright 1999-2017 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 |
| http://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc., |
| 51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA. */ |
| |
| #include "third_party/mpfr/v3_1_6/src/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; |
| } |
| /* now rsize = MPFR_LIMB_SIZE(r) */ |
| if (mpn_add_1 (rp0, rp, rsize, MPFR_LIMB_ONE << sh)) |
| { |
| expr ++; |
| rp0[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); |
| } |
