/* Software floating-point emulation.
Definitions for IEEE Extended Precision.
Copyright (C) 1999-2014 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Contributed by Jakub Jelinek (jj@ultra.linux.cz).
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.
In addition to the permissions in the GNU Lesser General Public
License, the Free Software Foundation gives you unlimited
permission to link the compiled version of this file into
combinations with other programs, and to distribute those
combinations without any restriction coming from the use of this
file. (The Lesser General Public License restrictions do apply in
other respects; for example, they cover modification of the file,
and distribution when not linked into a combine executable.)
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/>. */
#if _FP_W_TYPE_SIZE < 32
# error "Here's a nickel, kid. Go buy yourself a real computer."
#endif
#if _FP_W_TYPE_SIZE < 64
# define _FP_FRACTBITS_E (4*_FP_W_TYPE_SIZE)
# define _FP_FRACTBITS_DW_E (8*_FP_W_TYPE_SIZE)
#else
# define _FP_FRACTBITS_E (2*_FP_W_TYPE_SIZE)
# define _FP_FRACTBITS_DW_E (4*_FP_W_TYPE_SIZE)
#endif
#define _FP_FRACBITS_E 64
#define _FP_FRACXBITS_E (_FP_FRACTBITS_E - _FP_FRACBITS_E)
#define _FP_WFRACBITS_E (_FP_WORKBITS + _FP_FRACBITS_E)
#define _FP_WFRACXBITS_E (_FP_FRACTBITS_E - _FP_WFRACBITS_E)
#define _FP_EXPBITS_E 15
#define _FP_EXPBIAS_E 16383
#define _FP_EXPMAX_E 32767
#define _FP_QNANBIT_E \
((_FP_W_TYPE) 1 << (_FP_FRACBITS_E-2) % _FP_W_TYPE_SIZE)
#define _FP_QNANBIT_SH_E \
((_FP_W_TYPE) 1 << (_FP_FRACBITS_E-2+_FP_WORKBITS) % _FP_W_TYPE_SIZE)
#define _FP_IMPLBIT_E \
((_FP_W_TYPE) 1 << (_FP_FRACBITS_E-1) % _FP_W_TYPE_SIZE)
#define _FP_IMPLBIT_SH_E \
((_FP_W_TYPE) 1 << (_FP_FRACBITS_E-1+_FP_WORKBITS) % _FP_W_TYPE_SIZE)
#define _FP_OVERFLOW_E \
((_FP_W_TYPE) 1 << (_FP_WFRACBITS_E % _FP_W_TYPE_SIZE))
#define _FP_WFRACBITS_DW_E (2 * _FP_WFRACBITS_E)
#define _FP_WFRACXBITS_DW_E (_FP_FRACTBITS_DW_E - _FP_WFRACBITS_DW_E)
#define _FP_HIGHBIT_DW_E \
((_FP_W_TYPE) 1 << (_FP_WFRACBITS_DW_E - 1) % _FP_W_TYPE_SIZE)
typedef float XFtype __attribute__ ((mode (XF)));
#if _FP_W_TYPE_SIZE < 64
union _FP_UNION_E
{
XFtype flt;
struct _FP_STRUCT_LAYOUT
{
# if __BYTE_ORDER == __BIG_ENDIAN
unsigned long pad1 : _FP_W_TYPE_SIZE;
unsigned long pad2 : (_FP_W_TYPE_SIZE - 1 - _FP_EXPBITS_E);
unsigned long sign : 1;
unsigned long exp : _FP_EXPBITS_E;
unsigned long frac1 : _FP_W_TYPE_SIZE;
unsigned long frac0 : _FP_W_TYPE_SIZE;
# else
unsigned long frac0 : _FP_W_TYPE_SIZE;
unsigned long frac1 : _FP_W_TYPE_SIZE;
unsigned exp : _FP_EXPBITS_E;
unsigned sign : 1;
# endif /* not bigendian */
} bits __attribute__ ((packed));
};
# define FP_DECL_E(X) _FP_DECL (4, X)
# define FP_UNPACK_RAW_E(X, val) \
do \
{ \
union _FP_UNION_E FP_UNPACK_RAW_E_flo; \
FP_UNPACK_RAW_E_flo.flt = (val); \
\
X##_f[2] = 0; \
X##_f[3] = 0; \
X##_f[0] = FP_UNPACK_RAW_E_flo.bits.frac0; \
X##_f[1] = FP_UNPACK_RAW_E_flo.bits.frac1; \
X##_e = FP_UNPACK_RAW_E_flo.bits.exp; \
X##_s = FP_UNPACK_RAW_E_flo.bits.sign; \
} \
while (0)
# define FP_UNPACK_RAW_EP(X, val) \
do \
{ \
union _FP_UNION_E *FP_UNPACK_RAW_EP_flo \
= (union _FP_UNION_E *) (val); \
\
X##_f[2] = 0; \
X##_f[3] = 0; \
X##_f[0] = FP_UNPACK_RAW_EP_flo->bits.frac0; \
X##_f[1] = FP_UNPACK_RAW_EP_flo->bits.frac1; \
X##_e = FP_UNPACK_RAW_EP_flo->bits.exp; \
X##_s = FP_UNPACK_RAW_EP_flo->bits.sign; \
} \
while (0)
# define FP_PACK_RAW_E(val, X) \
do \
{ \
union _FP_UNION_E FP_PACK_RAW_E_flo; \
\
if (X##_e) \
X##_f[1] |= _FP_IMPLBIT_E; \
else \
X##_f[1] &= ~(_FP_IMPLBIT_E); \
FP_PACK_RAW_E_flo.bits.frac0 = X##_f[0]; \
FP_PACK_RAW_E_flo.bits.frac1 = X##_f[1]; \
FP_PACK_RAW_E_flo.bits.exp = X##_e; \
FP_PACK_RAW_E_flo.bits.sign = X##_s; \
\
(val) = FP_PACK_RAW_E_flo.flt; \
} \
while (0)
# define FP_PACK_RAW_EP(val, X) \
do \
{ \
if (!FP_INHIBIT_RESULTS) \
{ \
union _FP_UNION_E *FP_PACK_RAW_EP_flo \
= (union _FP_UNION_E *) (val); \
\
if (X##_e) \
X##_f[1] |= _FP_IMPLBIT_E; \
else \
X##_f[1] &= ~(_FP_IMPLBIT_E); \
FP_PACK_RAW_EP_flo->bits.frac0 = X##_f[0]; \
FP_PACK_RAW_EP_flo->bits.frac1 = X##_f[1]; \
FP_PACK_RAW_EP_flo->bits.exp = X##_e; \
FP_PACK_RAW_EP_flo->bits.sign = X##_s; \
} \
} \
while (0)
# define FP_UNPACK_E(X, val) \
do \
{ \
FP_UNPACK_RAW_E (X, (val)); \
_FP_UNPACK_CANONICAL (E, 4, X); \
} \
while (0)
# define FP_UNPACK_EP(X, val) \
do \
{ \
FP_UNPACK_RAW_EP (X, (val)); \
_FP_UNPACK_CANONICAL (E, 4, X); \
} \
while (0)
# define FP_UNPACK_SEMIRAW_E(X, val) \
do \
{ \
FP_UNPACK_RAW_E (X, (val)); \
_FP_UNPACK_SEMIRAW (E, 4, X); \
} \
while (0)
# define FP_UNPACK_SEMIRAW_EP(X, val) \
do \
{ \
FP_UNPACK_RAW_EP (X, (val)); \
_FP_UNPACK_SEMIRAW (E, 4, X); \
} \
while (0)
# define FP_PACK_E(val, X) \
do \
{ \
_FP_PACK_CANONICAL (E, 4, X); \
FP_PACK_RAW_E ((val), X); \
} \
while (0)
# define FP_PACK_EP(val, X) \
do \
{ \
_FP_PACK_CANONICAL (E, 4, X); \
FP_PACK_RAW_EP ((val), X); \
} \
while (0)
# define FP_PACK_SEMIRAW_E(val, X) \
do \
{ \
_FP_PACK_SEMIRAW (E, 4, X); \
FP_PACK_RAW_E ((val), X); \
} \
while (0)
# define FP_PACK_SEMIRAW_EP(val, X) \
do \
{ \
_FP_PACK_SEMIRAW (E, 4, X); \
FP_PACK_RAW_EP ((val), X); \
} \
while (0)
# define FP_ISSIGNAN_E(X) _FP_ISSIGNAN (E, 4, X)
# define FP_NEG_E(R, X) _FP_NEG (E, 4, R, X)
# define FP_ADD_E(R, X, Y) _FP_ADD (E, 4, R, X, Y)
# define FP_SUB_E(R, X, Y) _FP_SUB (E, 4, R, X, Y)
# define FP_MUL_E(R, X, Y) _FP_MUL (E, 4, R, X, Y)
# define FP_DIV_E(R, X, Y) _FP_DIV (E, 4, R, X, Y)
# define FP_SQRT_E(R, X) _FP_SQRT (E, 4, R, X)
# define FP_FMA_E(R, X, Y, Z) _FP_FMA (E, 4, 8, R, X, Y, Z)
/* Square root algorithms:
We have just one right now, maybe Newton approximation
should be added for those machines where division is fast.
This has special _E version because standard _4 square
root would not work (it has to start normally with the
second word and not the first), but as we have to do it
anyway, we optimize it by doing most of the calculations
in two UWtype registers instead of four. */
# define _FP_SQRT_MEAT_E(R, S, T, X, q) \
do \
{ \
(q) = (_FP_W_TYPE) 1 << (_FP_W_TYPE_SIZE - 1); \
_FP_FRAC_SRL_4 (X, (_FP_WORKBITS)); \
while (q) \
{ \
T##_f[1] = S##_f[1] + (q); \
if (T##_f[1] <= X##_f[1]) \
{ \
S##_f[1] = T##_f[1] + (q); \
X##_f[1] -= T##_f[1]; \
R##_f[1] += (q); \
} \
_FP_FRAC_SLL_2 (X, 1); \
(q) >>= 1; \
} \
(q) = (_FP_W_TYPE) 1 << (_FP_W_TYPE_SIZE - 1); \
while (q) \
{ \
T##_f[0] = S##_f[0] + (q); \
T##_f[1] = S##_f[1]; \
if (T##_f[1] < X##_f[1] \
|| (T##_f[1] == X##_f[1] \
&& T##_f[0] <= X##_f[0])) \
{ \
S##_f[0] = T##_f[0] + (q); \
S##_f[1] += (T##_f[0] > S##_f[0]); \
_FP_FRAC_DEC_2 (X, T); \
R##_f[0] += (q); \
} \
_FP_FRAC_SLL_2 (X, 1); \
(q) >>= 1; \
} \
_FP_FRAC_SLL_4 (R, (_FP_WORKBITS)); \
if (X##_f[0] | X##_f[1]) \
{ \
if (S##_f[1] < X##_f[1] \
|| (S##_f[1] == X##_f[1] \
&& S##_f[0] < X##_f[0])) \
R##_f[0] |= _FP_WORK_ROUND; \
R##_f[0] |= _FP_WORK_STICKY; \
} \
} \
while (0)
# define FP_CMP_E(r, X, Y, un, ex) _FP_CMP (E, 4, (r), X, Y, (un), (ex))
# define FP_CMP_EQ_E(r, X, Y, ex) _FP_CMP_EQ (E, 4, (r), X, Y, (ex))
# define FP_CMP_UNORD_E(r, X, Y, ex) _FP_CMP_UNORD (E, 4, (r), X, Y, (ex))
# define FP_TO_INT_E(r, X, rsz, rsg) _FP_TO_INT (E, 4, (r), X, (rsz), (rsg))
# define FP_FROM_INT_E(X, r, rs, rt) _FP_FROM_INT (E, 4, X, (r), (rs), rt)
# define _FP_FRAC_HIGH_E(X) (X##_f[2])
# define _FP_FRAC_HIGH_RAW_E(X) (X##_f[1])
# define _FP_FRAC_HIGH_DW_E(X) (X##_f[4])
#else /* not _FP_W_TYPE_SIZE < 64 */
union _FP_UNION_E
{
XFtype flt;
struct _FP_STRUCT_LAYOUT
{
# if __BYTE_ORDER == __BIG_ENDIAN
_FP_W_TYPE pad : (_FP_W_TYPE_SIZE - 1 - _FP_EXPBITS_E);
unsigned sign : 1;
unsigned exp : _FP_EXPBITS_E;
_FP_W_TYPE frac : _FP_W_TYPE_SIZE;
# else
_FP_W_TYPE frac : _FP_W_TYPE_SIZE;
unsigned exp : _FP_EXPBITS_E;
unsigned sign : 1;
# endif
} bits;
};
# define FP_DECL_E(X) _FP_DECL (2, X)
# define FP_UNPACK_RAW_E(X, val) \
do \
{ \
union _FP_UNION_E FP_UNPACK_RAW_E_flo; \
FP_UNPACK_RAW_E_flo.flt = (val); \
\
X##_f0 = FP_UNPACK_RAW_E_flo.bits.frac; \
X##_f1 = 0; \
X##_e = FP_UNPACK_RAW_E_flo.bits.exp; \
X##_s = FP_UNPACK_RAW_E_flo.bits.sign; \
} \
while (0)
# define FP_UNPACK_RAW_EP(X, val) \
do \
{ \
union _FP_UNION_E *FP_UNPACK_RAW_EP_flo \
= (union _FP_UNION_E *) (val); \
\
X##_f0 = FP_UNPACK_RAW_EP_flo->bits.frac; \
X##_f1 = 0; \
X##_e = FP_UNPACK_RAW_EP_flo->bits.exp; \
X##_s = FP_UNPACK_RAW_EP_flo->bits.sign; \
} \
while (0)
# define FP_PACK_RAW_E(val, X) \
do \
{ \
union _FP_UNION_E FP_PACK_RAW_E_flo; \
\
if (X##_e) \
X##_f0 |= _FP_IMPLBIT_E; \
else \
X##_f0 &= ~(_FP_IMPLBIT_E); \
FP_PACK_RAW_E_flo.bits.frac = X##_f0; \
FP_PACK_RAW_E_flo.bits.exp = X##_e; \
FP_PACK_RAW_E_flo.bits.sign = X##_s; \
\
(val) = FP_PACK_RAW_E_flo.flt; \
} \
while (0)
# define FP_PACK_RAW_EP(fs, val, X) \
do \
{ \
if (!FP_INHIBIT_RESULTS) \
{ \
union _FP_UNION_E *FP_PACK_RAW_EP_flo \
= (union _FP_UNION_E *) (val); \
\
if (X##_e) \
X##_f0 |= _FP_IMPLBIT_E; \
else \
X##_f0 &= ~(_FP_IMPLBIT_E); \
FP_PACK_RAW_EP_flo->bits.frac = X##_f0; \
FP_PACK_RAW_EP_flo->bits.exp = X##_e; \
FP_PACK_RAW_EP_flo->bits.sign = X##_s; \
} \
} \
while (0)
# define FP_UNPACK_E(X, val) \
do \
{ \
FP_UNPACK_RAW_E (X, (val)); \
_FP_UNPACK_CANONICAL (E, 2, X); \
} \
while (0)
# define FP_UNPACK_EP(X, val) \
do \
{ \
FP_UNPACK_RAW_EP (X, (val)); \
_FP_UNPACK_CANONICAL (E, 2, X); \
} \
while (0)
# define FP_UNPACK_SEMIRAW_E(X, val) \
do \
{ \
FP_UNPACK_RAW_E (X, (val)); \
_FP_UNPACK_SEMIRAW (E, 2, X); \
} \
while (0)
# define FP_UNPACK_SEMIRAW_EP(X, val) \
do \
{ \
FP_UNPACK_RAW_EP (X, (val)); \
_FP_UNPACK_SEMIRAW (E, 2, X); \
} \
while (0)
# define FP_PACK_E(val, X) \
do \
{ \
_FP_PACK_CANONICAL (E, 2, X); \
FP_PACK_RAW_E ((val), X); \
} \
while (0)
# define FP_PACK_EP(val, X) \
do \
{ \
_FP_PACK_CANONICAL (E, 2, X); \
FP_PACK_RAW_EP ((val), X); \
} \
while (0)
# define FP_PACK_SEMIRAW_E(val, X) \
do \
{ \
_FP_PACK_SEMIRAW (E, 2, X); \
FP_PACK_RAW_E ((val), X); \
} \
while (0)
# define FP_PACK_SEMIRAW_EP(val, X) \
do \
{ \
_FP_PACK_SEMIRAW (E, 2, X); \
FP_PACK_RAW_EP ((val), X); \
} \
while (0)
# define FP_ISSIGNAN_E(X) _FP_ISSIGNAN (E, 2, X)
# define FP_NEG_E(R, X) _FP_NEG (E, 2, R, X)
# define FP_ADD_E(R, X, Y) _FP_ADD (E, 2, R, X, Y)
# define FP_SUB_E(R, X, Y) _FP_SUB (E, 2, R, X, Y)
# define FP_MUL_E(R, X, Y) _FP_MUL (E, 2, R, X, Y)
# define FP_DIV_E(R, X, Y) _FP_DIV (E, 2, R, X, Y)
# define FP_SQRT_E(R, X) _FP_SQRT (E, 2, R, X)
# define FP_FMA_E(R, X, Y, Z) _FP_FMA (E, 2, 4, R, X, Y, Z)
/* Square root algorithms:
We have just one right now, maybe Newton approximation
should be added for those machines where division is fast.
We optimize it by doing most of the calculations
in one UWtype registers instead of two, although we don't
have to. */
# define _FP_SQRT_MEAT_E(R, S, T, X, q) \
do \
{ \
(q) = (_FP_W_TYPE) 1 << (_FP_W_TYPE_SIZE - 1); \
_FP_FRAC_SRL_2 (X, (_FP_WORKBITS)); \
while (q) \
{ \
T##_f0 = S##_f0 + (q); \
if (T##_f0 <= X##_f0) \
{ \
S##_f0 = T##_f0 + (q); \
X##_f0 -= T##_f0; \
R##_f0 += (q); \
} \
_FP_FRAC_SLL_1 (X, 1); \
(q) >>= 1; \
} \
_FP_FRAC_SLL_2 (R, (_FP_WORKBITS)); \
if (X##_f0) \
{ \
if (S##_f0 < X##_f0) \
R##_f0 |= _FP_WORK_ROUND; \
R##_f0 |= _FP_WORK_STICKY; \
} \
} \
while (0)
# define FP_CMP_E(r, X, Y, un, ex) _FP_CMP (E, 2, (r), X, Y, (un), (ex))
# define FP_CMP_EQ_E(r, X, Y, ex) _FP_CMP_EQ (E, 2, (r), X, Y, (ex))
# define FP_CMP_UNORD_E(r, X, Y, ex) _FP_CMP_UNORD (E, 2, (r), X, Y, (ex))
# define FP_TO_INT_E(r, X, rsz, rsg) _FP_TO_INT (E, 2, (r), X, (rsz), (rsg))
# define FP_FROM_INT_E(X, r, rs, rt) _FP_FROM_INT (E, 2, X, (r), (rs), rt)
# define _FP_FRAC_HIGH_E(X) (X##_f1)
# define _FP_FRAC_HIGH_RAW_E(X) (X##_f0)
# define _FP_FRAC_HIGH_DW_E(X) (X##_f[2])
#endif /* not _FP_W_TYPE_SIZE < 64 */