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328 lines
9.8 KiB
C
328 lines
9.8 KiB
C
/* mpfr_set_d -- convert a machine double precision float to
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a multiple precision floating-point number
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Copyright 1999-2004, 2006-2025 Free Software Foundation, Inc.
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Contributed by the Pascaline and Caramba projects, INRIA.
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This file is part of the GNU MPFR Library.
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The GNU MPFR Library is free software; you can redistribute it and/or modify
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it under the terms of the GNU Lesser General Public License as published by
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the Free Software Foundation; either version 3 of the License, or (at your
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option) any later version.
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The GNU MPFR Library is distributed in the hope that it will be useful, but
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WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
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License for more details.
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You should have received a copy of the GNU Lesser General Public License
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along with the GNU MPFR Library; see the file COPYING.LESSER.
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If not, see <https://www.gnu.org/licenses/>. */
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#include <float.h> /* For DOUBLE_ISINF and DOUBLE_ISNAN */
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#define MPFR_NEED_LONGLONG_H
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#include "mpfr-impl.h"
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/* Extracts the bits of |d| in rp[0..n-1] where n=ceil(53/GMP_NUMB_BITS).
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Assumes d finite and <> 0.
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Returns the corresponding exponent such that |d| = {rp, n} * 2^exp,
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with the value of {rp, n} in [1/2, 1).
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The int type should be sufficient for exp.
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*/
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static int
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extract_double (mpfr_limb_ptr rp, double d)
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{
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int exp;
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mp_limb_t man[MPFR_LIMBS_PER_DOUBLE];
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/* FIXME: Generalize to handle GMP_NUMB_BITS < 16. */
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MPFR_ASSERTD(!DOUBLE_ISNAN(d));
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MPFR_ASSERTD(!DOUBLE_ISINF(d));
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MPFR_ASSERTD(d != 0.0);
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#if _MPFR_IEEE_FLOATS
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{
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union mpfr_ieee_double_extract x;
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x.d = d;
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exp = x.s.exp;
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if (exp)
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{
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/* x.s.manh has 20 bits (in its low bits), x.s.manl has 32 bits */
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#if GMP_NUMB_BITS >= 64
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man[0] = ((MPFR_LIMB_ONE << (GMP_NUMB_BITS - 1)) |
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((mp_limb_t) x.s.manh << (GMP_NUMB_BITS - 21)) |
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((mp_limb_t) x.s.manl << (GMP_NUMB_BITS - 53)));
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#elif GMP_NUMB_BITS == 32
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man[1] = (MPFR_LIMB_ONE << 31) | (x.s.manh << 11) | (x.s.manl >> 21);
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man[0] = x.s.manl << 11;
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#elif GMP_NUMB_BITS == 16
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MPFR_STAT_STATIC_ASSERT (GMP_NUMB_BITS == 16);
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man[3] = (MPFR_LIMB_ONE << 15) | (x.s.manh >> 5);
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man[2] = (x.s.manh << 11) | (x.s.manl >> 21);
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man[1] = x.s.manl >> 5;
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man[0] = MPFR_LIMB_LSHIFT(x.s.manl,11);
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#else
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MPFR_STAT_STATIC_ASSERT (GMP_NUMB_BITS == 8);
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man[6] = (MPFR_LIMB_ONE << 7) | (x.s.manh >> 13);
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man[5] = (mp_limb_t) (x.s.manh >> 5);
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man[4] = MPFR_LIMB_LSHIFT(x.s.manh, 3) | (mp_limb_t) (x.s.manl >> 29);
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man[3] = (mp_limb_t) (x.s.manl >> 21);
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man[2] = (mp_limb_t) (x.s.manl >> 13);
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man[1] = (mp_limb_t) (x.s.manl >> 5);
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man[0] = MPFR_LIMB_LSHIFT(x.s.manl,3);
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#endif
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exp -= 1022;
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}
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else /* subnormal number */
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{
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int cnt;
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exp = -1021;
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#if GMP_NUMB_BITS >= 64
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man[0] = (((mp_limb_t) x.s.manh << (GMP_NUMB_BITS - 21)) |
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((mp_limb_t) x.s.manl << (GMP_NUMB_BITS - 53)));
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count_leading_zeros (cnt, man[0]);
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#elif GMP_NUMB_BITS == 32
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man[1] = (x.s.manh << 11) /* high 21 bits */
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| (x.s.manl >> 21); /* middle 11 bits */
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man[0] = x.s.manl << 11; /* low 21 bits */
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if (man[1] == 0)
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{
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man[1] = man[0];
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man[0] = 0;
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exp -= GMP_NUMB_BITS;
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}
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count_leading_zeros (cnt, man[1]);
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man[1] = (man[1] << cnt) |
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(cnt != 0 ? man[0] >> (GMP_NUMB_BITS - cnt) : 0);
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#elif GMP_NUMB_BITS == 16
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man[3] = x.s.manh >> 5;
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man[2] = (x.s.manh << 11) | (x.s.manl >> 21);
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man[1] = x.s.manl >> 5;
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man[0] = x.s.manl << 11;
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while (man[3] == 0) /* d is assumed <> 0 */
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{
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man[3] = man[2];
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man[2] = man[1];
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man[1] = man[0];
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man[0] = 0;
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exp -= GMP_NUMB_BITS;
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}
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count_leading_zeros (cnt, man[3]);
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if (cnt)
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{
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man[3] = (man[3] << cnt) | (man[2] >> (GMP_NUMB_BITS - cnt));
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man[2] = (man[2] << cnt) | (man[1] >> (GMP_NUMB_BITS - cnt));
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man[1] = (man[1] << cnt) | (man[0] >> (GMP_NUMB_BITS - cnt));
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}
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#else
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MPFR_STAT_STATIC_ASSERT (GMP_NUMB_BITS == 8);
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man[6] = x.s.manh >> 13;
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man[5] = x.s.manh >> 5;
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man[4] = (x.s.manh << 3) | (x.s.manl >> 29);
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man[3] = x.s.manl >> 21;
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man[2] = x.s.manl >> 13;
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man[1] = x.s.manl >> 5;
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man[0] = x.s.manl << 3;
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while (man[6] == 0) /* d is assumed <> 0 */
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{
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man[6] = man[5];
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man[5] = man[4];
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man[4] = man[3];
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man[3] = man[2];
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man[2] = man[1];
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man[1] = man[0];
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man[0] = 0;
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exp -= GMP_NUMB_BITS;
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}
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count_leading_zeros (cnt, man[6]);
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if (cnt)
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{
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int i;
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for (i = 6; i > 0; i--)
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man[i] = (man[i] << cnt) | (man[i-1] >> (GMP_NUMB_BITS - cnt));
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}
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#endif
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man[0] <<= cnt;
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exp -= cnt;
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}
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}
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#else /* _MPFR_IEEE_FLOATS */
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{
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/* Unknown (or known to be non-IEEE) double format. */
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exp = 0;
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d = ABS (d);
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if (d >= 1.0)
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{
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while (d >= 32768.0)
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{
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d *= (1.0 / 65536.0);
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exp += 16;
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}
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while (d >= 1.0)
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{
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d *= 0.5;
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exp += 1;
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}
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}
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else if (d < 0.5)
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{
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while (d < (1.0 / 65536.0))
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{
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d *= 65536.0;
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exp -= 16;
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}
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while (d < 0.5)
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{
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d *= 2.0;
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exp -= 1;
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}
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}
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d *= MP_BASE_AS_DOUBLE;
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#if GMP_NUMB_BITS >= 64
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#ifndef __clang__
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man[0] = d;
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#else
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/* clang up to version 11 produces an invalid exception when d >= 2^63,
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see <https://github.com/llvm/llvm-project/issues/18060>
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(old URL: <https://bugs.llvm.org/show_bug.cgi?id=17686>).
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Since this is always the case, here, we use the following patch. */
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MPFR_STAT_STATIC_ASSERT (GMP_NUMB_BITS == 64);
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man[0] = 0x8000000000000000 + (mp_limb_t) (d - 0x8000000000000000);
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#endif /* __clang__ */
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#elif GMP_NUMB_BITS == 32
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man[1] = (mp_limb_t) d;
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man[0] = (mp_limb_t) ((d - man[1]) * MP_BASE_AS_DOUBLE);
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#else
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MPFR_STAT_STATIC_ASSERT (GMP_NUMB_BITS == 16);
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{
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double r = d;
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man[3] = (mp_limb_t) r;
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r = (r - man[3]) * MP_BASE_AS_DOUBLE;
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man[2] = (mp_limb_t) r;
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r = (r - man[2]) * MP_BASE_AS_DOUBLE;
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man[1] = (mp_limb_t) r;
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r = (r - man[1]) * MP_BASE_AS_DOUBLE;
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man[0] = (mp_limb_t) r;
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}
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#endif
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}
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#endif /* _MPFR_IEEE_FLOATS */
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rp[0] = man[0];
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#if GMP_NUMB_BITS <= 32
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rp[1] = man[1];
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#endif
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#if GMP_NUMB_BITS <= 16
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rp[2] = man[2];
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rp[3] = man[3];
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#endif
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#if GMP_NUMB_BITS <= 8
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rp[4] = man[4];
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rp[5] = man[5];
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rp[6] = man[6];
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#endif
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MPFR_ASSERTD((rp[MPFR_LIMBS_PER_DOUBLE - 1] & MPFR_LIMB_HIGHBIT) != 0);
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return exp;
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}
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/* End of part included from gmp-2.0.2 */
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int
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mpfr_set_d (mpfr_ptr r, double d, mpfr_rnd_t rnd_mode)
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{
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int inexact;
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mpfr_t tmp;
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mp_limb_t tmpmant[MPFR_LIMBS_PER_DOUBLE];
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MPFR_SAVE_EXPO_DECL (expo);
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if (MPFR_UNLIKELY(DOUBLE_ISNAN(d)))
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{
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/* we don't propagate the sign bit */
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MPFR_SET_NAN(r);
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MPFR_RET_NAN;
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}
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else if (MPFR_UNLIKELY(d == 0))
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{
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#if _MPFR_IEEE_FLOATS
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union mpfr_ieee_double_extract x;
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MPFR_SET_ZERO(r);
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/* set correct sign */
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x.d = d;
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if (x.s.sig == 1)
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MPFR_SET_NEG(r);
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else
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MPFR_SET_POS(r);
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#else /* _MPFR_IEEE_FLOATS */
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MPFR_SET_ZERO(r);
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{
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/* This is to get the sign of zero on non-IEEE hardware
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Some systems support +0.0, -0.0, and unsigned zero.
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Some other systems may just have an unsigned zero.
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We can't use d == +0.0 since it should be always true,
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so we check that the memory representation of d is the
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same as +0.0, etc.
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Note: r is set to -0 only if d is detected as a negative zero
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*and*, for the double type, -0 has a different representation
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from +0. If -0.0 has several representations, the code below
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may not work as expected, but this is hardly fixable in a
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portable way (without depending on a math library) and only
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the sign could be incorrect. Such systems should be taken
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into account on a case-by-case basis. If the code is changed
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here, set_d64.c code should be updated too. */
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double poszero = +0.0, negzero = DBL_NEG_ZERO;
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if (memcmp(&d, &poszero, sizeof(double)) == 0)
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MPFR_SET_POS(r);
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else if (memcmp(&d, &negzero, sizeof(double)) == 0)
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MPFR_SET_NEG(r);
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else
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MPFR_SET_POS(r);
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}
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#endif /* _MPFR_IEEE_FLOATS */
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return 0; /* 0 is exact */
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}
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else if (MPFR_UNLIKELY(DOUBLE_ISINF(d)))
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{
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MPFR_SET_INF(r);
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if (d > 0)
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MPFR_SET_POS(r);
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else
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MPFR_SET_NEG(r);
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return 0; /* infinity is exact */
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}
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/* now d is neither 0, nor NaN nor Inf */
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MPFR_SAVE_EXPO_MARK (expo);
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/* warning: don't use tmp=r here, even if SIZE(r) >= MPFR_LIMBS_PER_DOUBLE,
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since PREC(r) may be different from PREC(tmp), and then both variables
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would have same precision in the mpfr_set4 call below. */
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MPFR_MANT(tmp) = tmpmant;
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MPFR_PREC(tmp) = IEEE_DBL_MANT_DIG;
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/* don't use MPFR_SET_EXP here since the exponent may be out of range */
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MPFR_EXP(tmp) = extract_double (tmpmant, d);
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/* tmp is exact since PREC(tmp)=53 */
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inexact = mpfr_set4 (r, tmp, rnd_mode,
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(d < 0) ? MPFR_SIGN_NEG : MPFR_SIGN_POS);
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MPFR_SAVE_EXPO_FREE (expo);
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return mpfr_check_range (r, inexact, rnd_mode);
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}
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