mirror of
https://sourceware.org/git/glibc.git
synced 2024-11-16 10:00:12 +00:00
688903eb3e
* All files with FSF copyright notices: Update copyright dates using scripts/update-copyrights. * locale/programs/charmap-kw.h: Regenerated. * locale/programs/locfile-kw.h: Likewise.
291 lines
7.9 KiB
C
291 lines
7.9 KiB
C
/* Manipulation of the bit representation of 'long double' quantities.
|
|
Copyright (C) 2006-2018 Free Software Foundation, Inc.
|
|
This file is part of the GNU C Library.
|
|
|
|
The GNU C 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 C 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 C Library; if not, see
|
|
<http://www.gnu.org/licenses/>. */
|
|
|
|
#ifndef _MATH_LDBL_H_
|
|
#define _MATH_LDBL_H_ 1
|
|
|
|
#include <ieee754.h>
|
|
#include <stdint.h>
|
|
|
|
/* To suit our callers we return *hi64 and *lo64 as if they came from
|
|
an ieee854 112 bit mantissa, that is, 48 bits in *hi64 (plus one
|
|
implicit bit) and 64 bits in *lo64. */
|
|
|
|
static inline void
|
|
ldbl_extract_mantissa (int64_t *hi64, uint64_t *lo64, int *exp, long double x)
|
|
{
|
|
/* We have 105 bits of mantissa plus one implicit digit. Since
|
|
106 bits are representable we use the first implicit digit for
|
|
the number before the decimal point and the second implicit bit
|
|
as bit 53 of the mantissa. */
|
|
uint64_t hi, lo;
|
|
union ibm_extended_long_double u;
|
|
|
|
u.ld = x;
|
|
*exp = u.d[0].ieee.exponent - IEEE754_DOUBLE_BIAS;
|
|
|
|
lo = ((uint64_t) u.d[1].ieee.mantissa0 << 32) | u.d[1].ieee.mantissa1;
|
|
hi = ((uint64_t) u.d[0].ieee.mantissa0 << 32) | u.d[0].ieee.mantissa1;
|
|
|
|
if (u.d[0].ieee.exponent != 0)
|
|
{
|
|
int ediff;
|
|
|
|
/* If not a denormal or zero then we have an implicit 53rd bit. */
|
|
hi |= (uint64_t) 1 << 52;
|
|
|
|
if (u.d[1].ieee.exponent != 0)
|
|
lo |= (uint64_t) 1 << 52;
|
|
else
|
|
/* A denormal is to be interpreted as having a biased exponent
|
|
of 1. */
|
|
lo = lo << 1;
|
|
|
|
/* We are going to shift 4 bits out of hi later, because we only
|
|
want 48 bits in *hi64. That means we want 60 bits in lo, but
|
|
we currently only have 53. Shift the value up. */
|
|
lo = lo << 7;
|
|
|
|
/* The lower double is normalized separately from the upper.
|
|
We may need to adjust the lower mantissa to reflect this.
|
|
The difference between the exponents can be larger than 53
|
|
when the low double is much less than 1ULP of the upper
|
|
(in which case there are significant bits, all 0's or all
|
|
1's, between the two significands). The difference between
|
|
the exponents can be less than 53 when the upper double
|
|
exponent is nearing its minimum value (in which case the low
|
|
double is denormal ie. has an exponent of zero). */
|
|
ediff = u.d[0].ieee.exponent - u.d[1].ieee.exponent - 53;
|
|
if (ediff > 0)
|
|
{
|
|
if (ediff < 64)
|
|
lo = lo >> ediff;
|
|
else
|
|
lo = 0;
|
|
}
|
|
else if (ediff < 0)
|
|
lo = lo << -ediff;
|
|
|
|
if (u.d[0].ieee.negative != u.d[1].ieee.negative
|
|
&& lo != 0)
|
|
{
|
|
hi--;
|
|
lo = ((uint64_t) 1 << 60) - lo;
|
|
if (hi < (uint64_t) 1 << 52)
|
|
{
|
|
/* We have a borrow from the hidden bit, so shift left 1. */
|
|
hi = (hi << 1) | (lo >> 59);
|
|
lo = (((uint64_t) 1 << 60) - 1) & (lo << 1);
|
|
*exp = *exp - 1;
|
|
}
|
|
}
|
|
}
|
|
else
|
|
/* If the larger magnitude double is denormal then the smaller
|
|
one must be zero. */
|
|
hi = hi << 1;
|
|
|
|
*lo64 = (hi << 60) | lo;
|
|
*hi64 = hi >> 4;
|
|
}
|
|
|
|
static inline long double
|
|
ldbl_insert_mantissa (int sign, int exp, int64_t hi64, uint64_t lo64)
|
|
{
|
|
union ibm_extended_long_double u;
|
|
int expnt2;
|
|
uint64_t hi, lo;
|
|
|
|
u.d[0].ieee.negative = sign;
|
|
u.d[1].ieee.negative = sign;
|
|
u.d[0].ieee.exponent = exp + IEEE754_DOUBLE_BIAS;
|
|
u.d[1].ieee.exponent = 0;
|
|
expnt2 = exp - 53 + IEEE754_DOUBLE_BIAS;
|
|
|
|
/* Expect 113 bits (112 bits + hidden) right justified in two longs.
|
|
The low order 53 bits (52 + hidden) go into the lower double */
|
|
lo = (lo64 >> 7) & (((uint64_t) 1 << 53) - 1);
|
|
/* The high order 53 bits (52 + hidden) go into the upper double */
|
|
hi = lo64 >> 60;
|
|
hi |= hi64 << 4;
|
|
|
|
if (lo != 0)
|
|
{
|
|
int lzcount;
|
|
|
|
/* hidden bit of low double controls rounding of the high double.
|
|
If hidden is '1' and either the explicit mantissa is non-zero
|
|
or hi is odd, then round up hi and adjust lo (2nd mantissa)
|
|
plus change the sign of the low double to compensate. */
|
|
if ((lo & ((uint64_t) 1 << 52)) != 0
|
|
&& ((hi & 1) != 0 || (lo & (((uint64_t) 1 << 52) - 1)) != 0))
|
|
{
|
|
hi++;
|
|
if ((hi & ((uint64_t) 1 << 53)) != 0)
|
|
{
|
|
hi = hi >> 1;
|
|
u.d[0].ieee.exponent++;
|
|
}
|
|
u.d[1].ieee.negative = !sign;
|
|
lo = ((uint64_t) 1 << 53) - lo;
|
|
}
|
|
|
|
/* Normalize the low double. Shift the mantissa left until
|
|
the hidden bit is '1' and adjust the exponent accordingly. */
|
|
|
|
if (sizeof (lo) == sizeof (long))
|
|
lzcount = __builtin_clzl (lo);
|
|
else if ((lo >> 32) != 0)
|
|
lzcount = __builtin_clzl ((long) (lo >> 32));
|
|
else
|
|
lzcount = __builtin_clzl ((long) lo) + 32;
|
|
lzcount = lzcount - (64 - 53);
|
|
lo <<= lzcount;
|
|
expnt2 -= lzcount;
|
|
|
|
if (expnt2 >= 1)
|
|
/* Not denormal. */
|
|
u.d[1].ieee.exponent = expnt2;
|
|
else
|
|
{
|
|
/* Is denormal. Note that biased exponent of 0 is treated
|
|
as if it was 1, hence the extra shift. */
|
|
if (expnt2 > -53)
|
|
lo >>= 1 - expnt2;
|
|
else
|
|
lo = 0;
|
|
}
|
|
}
|
|
else
|
|
u.d[1].ieee.negative = 0;
|
|
|
|
u.d[1].ieee.mantissa1 = lo;
|
|
u.d[1].ieee.mantissa0 = lo >> 32;
|
|
u.d[0].ieee.mantissa1 = hi;
|
|
u.d[0].ieee.mantissa0 = hi >> 32;
|
|
return u.ld;
|
|
}
|
|
|
|
/* Handy utility functions to pack/unpack/cononicalize and find the nearbyint
|
|
of long double implemented as double double. */
|
|
static inline long double
|
|
default_ldbl_pack (double a, double aa)
|
|
{
|
|
union ibm_extended_long_double u;
|
|
u.d[0].d = a;
|
|
u.d[1].d = aa;
|
|
return u.ld;
|
|
}
|
|
|
|
static inline void
|
|
default_ldbl_unpack (long double l, double *a, double *aa)
|
|
{
|
|
union ibm_extended_long_double u;
|
|
u.ld = l;
|
|
*a = u.d[0].d;
|
|
*aa = u.d[1].d;
|
|
}
|
|
|
|
#ifndef ldbl_pack
|
|
# define ldbl_pack default_ldbl_pack
|
|
#endif
|
|
#ifndef ldbl_unpack
|
|
# define ldbl_unpack default_ldbl_unpack
|
|
#endif
|
|
|
|
/* Extract high double. */
|
|
#define ldbl_high(x) ((double) x)
|
|
|
|
/* Convert a finite long double to canonical form.
|
|
Does not handle +/-Inf properly. */
|
|
static inline void
|
|
ldbl_canonicalize (double *a, double *aa)
|
|
{
|
|
double xh, xl;
|
|
|
|
xh = *a + *aa;
|
|
xl = (*a - xh) + *aa;
|
|
*a = xh;
|
|
*aa = xl;
|
|
}
|
|
|
|
/* Simple inline nearbyint (double) function.
|
|
Only works in the default rounding mode
|
|
but is useful in long double rounding functions. */
|
|
static inline double
|
|
ldbl_nearbyint (double a)
|
|
{
|
|
double two52 = 0x1p52;
|
|
|
|
if (__glibc_likely ((__builtin_fabs (a) < two52)))
|
|
{
|
|
if (__glibc_likely ((a > 0.0)))
|
|
{
|
|
a += two52;
|
|
a -= two52;
|
|
}
|
|
else if (__glibc_likely ((a < 0.0)))
|
|
{
|
|
a = two52 - a;
|
|
a = -(a - two52);
|
|
}
|
|
}
|
|
return a;
|
|
}
|
|
|
|
/* Canonicalize a result from an integer rounding function, in any
|
|
rounding mode. *A and *AA are finite and integers, with *A being
|
|
nonzero; if the result is not already canonical, *AA is plus or
|
|
minus a power of 2 that does not exceed the least set bit in
|
|
*A. */
|
|
static inline void
|
|
ldbl_canonicalize_int (double *a, double *aa)
|
|
{
|
|
/* Previously we used EXTRACT_WORDS64 from math_private.h, but in order
|
|
to avoid including internal headers we duplicate that code here. */
|
|
uint64_t ax, aax;
|
|
union { double value; uint64_t word; } extractor;
|
|
extractor.value = *a;
|
|
ax = extractor.word;
|
|
extractor.value = *aa;
|
|
aax = extractor.word;
|
|
|
|
int expdiff = ((ax >> 52) & 0x7ff) - ((aax >> 52) & 0x7ff);
|
|
if (expdiff <= 53)
|
|
{
|
|
if (expdiff == 53)
|
|
{
|
|
/* Half way between two double values; noncanonical iff the
|
|
low bit of A's mantissa is 1. */
|
|
if ((ax & 1) != 0)
|
|
{
|
|
*a += 2 * *aa;
|
|
*aa = -*aa;
|
|
}
|
|
}
|
|
else
|
|
{
|
|
/* The sum can be represented in a single double. */
|
|
*a += *aa;
|
|
*aa = 0;
|
|
}
|
|
}
|
|
}
|
|
|
|
#endif /* math_ldbl.h */
|