mirror of
https://github.com/autc04/Retro68.git
synced 2024-09-10 03:54:48 +00:00
1707 lines
51 KiB
C
1707 lines
51 KiB
C
/* Software floating-point emulation. Common operations.
|
|
Copyright (C) 1997-2014 Free Software Foundation, Inc.
|
|
This file is part of the GNU C Library.
|
|
Contributed by Richard Henderson (rth@cygnus.com),
|
|
Jakub Jelinek (jj@ultra.linux.cz),
|
|
David S. Miller (davem@redhat.com) and
|
|
Peter Maydell (pmaydell@chiark.greenend.org.uk).
|
|
|
|
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/>. */
|
|
|
|
#define _FP_DECL(wc, X) \
|
|
_FP_I_TYPE X##_c __attribute__ ((unused)); \
|
|
_FP_I_TYPE X##_s __attribute__ ((unused)); \
|
|
_FP_I_TYPE X##_e __attribute__ ((unused)); \
|
|
_FP_FRAC_DECL_##wc (X)
|
|
|
|
/* Test whether the qNaN bit denotes a signaling NaN. */
|
|
#define _FP_FRAC_SNANP(fs, X) \
|
|
((_FP_QNANNEGATEDP) \
|
|
? (_FP_FRAC_HIGH_RAW_##fs (X) & _FP_QNANBIT_##fs) \
|
|
: !(_FP_FRAC_HIGH_RAW_##fs (X) & _FP_QNANBIT_##fs))
|
|
#define _FP_FRAC_SNANP_SEMIRAW(fs, X) \
|
|
((_FP_QNANNEGATEDP) \
|
|
? (_FP_FRAC_HIGH_##fs (X) & _FP_QNANBIT_SH_##fs) \
|
|
: !(_FP_FRAC_HIGH_##fs (X) & _FP_QNANBIT_SH_##fs))
|
|
|
|
/*
|
|
* Finish truly unpacking a native fp value by classifying the kind
|
|
* of fp value and normalizing both the exponent and the fraction.
|
|
*/
|
|
|
|
#define _FP_UNPACK_CANONICAL(fs, wc, X) \
|
|
do \
|
|
{ \
|
|
switch (X##_e) \
|
|
{ \
|
|
default: \
|
|
_FP_FRAC_HIGH_RAW_##fs (X) |= _FP_IMPLBIT_##fs; \
|
|
_FP_FRAC_SLL_##wc (X, _FP_WORKBITS); \
|
|
X##_e -= _FP_EXPBIAS_##fs; \
|
|
X##_c = FP_CLS_NORMAL; \
|
|
break; \
|
|
\
|
|
case 0: \
|
|
if (_FP_FRAC_ZEROP_##wc (X)) \
|
|
X##_c = FP_CLS_ZERO; \
|
|
else \
|
|
{ \
|
|
/* a denormalized number */ \
|
|
_FP_I_TYPE _shift; \
|
|
_FP_FRAC_CLZ_##wc (_shift, X); \
|
|
_shift -= _FP_FRACXBITS_##fs; \
|
|
_FP_FRAC_SLL_##wc (X, (_shift+_FP_WORKBITS)); \
|
|
X##_e -= _FP_EXPBIAS_##fs - 1 + _shift; \
|
|
X##_c = FP_CLS_NORMAL; \
|
|
FP_SET_EXCEPTION (FP_EX_DENORM); \
|
|
} \
|
|
break; \
|
|
\
|
|
case _FP_EXPMAX_##fs: \
|
|
if (_FP_FRAC_ZEROP_##wc (X)) \
|
|
X##_c = FP_CLS_INF; \
|
|
else \
|
|
{ \
|
|
X##_c = FP_CLS_NAN; \
|
|
/* Check for signaling NaN */ \
|
|
if (_FP_FRAC_SNANP (fs, X)) \
|
|
FP_SET_EXCEPTION (FP_EX_INVALID); \
|
|
} \
|
|
break; \
|
|
} \
|
|
} \
|
|
while (0)
|
|
|
|
/* Finish unpacking an fp value in semi-raw mode: the mantissa is
|
|
shifted by _FP_WORKBITS but the implicit MSB is not inserted and
|
|
other classification is not done. */
|
|
#define _FP_UNPACK_SEMIRAW(fs, wc, X) _FP_FRAC_SLL_##wc (X, _FP_WORKBITS)
|
|
|
|
/* A semi-raw value has overflowed to infinity. Adjust the mantissa
|
|
and exponent appropriately. */
|
|
#define _FP_OVERFLOW_SEMIRAW(fs, wc, X) \
|
|
do \
|
|
{ \
|
|
if (FP_ROUNDMODE == FP_RND_NEAREST \
|
|
|| (FP_ROUNDMODE == FP_RND_PINF && !X##_s) \
|
|
|| (FP_ROUNDMODE == FP_RND_MINF && X##_s)) \
|
|
{ \
|
|
X##_e = _FP_EXPMAX_##fs; \
|
|
_FP_FRAC_SET_##wc (X, _FP_ZEROFRAC_##wc); \
|
|
} \
|
|
else \
|
|
{ \
|
|
X##_e = _FP_EXPMAX_##fs - 1; \
|
|
_FP_FRAC_SET_##wc (X, _FP_MAXFRAC_##wc); \
|
|
} \
|
|
FP_SET_EXCEPTION (FP_EX_INEXACT); \
|
|
FP_SET_EXCEPTION (FP_EX_OVERFLOW); \
|
|
} \
|
|
while (0)
|
|
|
|
/* Check for a semi-raw value being a signaling NaN and raise the
|
|
invalid exception if so. */
|
|
#define _FP_CHECK_SIGNAN_SEMIRAW(fs, wc, X) \
|
|
do \
|
|
{ \
|
|
if (X##_e == _FP_EXPMAX_##fs \
|
|
&& !_FP_FRAC_ZEROP_##wc (X) \
|
|
&& _FP_FRAC_SNANP_SEMIRAW (fs, X)) \
|
|
FP_SET_EXCEPTION (FP_EX_INVALID); \
|
|
} \
|
|
while (0)
|
|
|
|
/* Choose a NaN result from an operation on two semi-raw NaN
|
|
values. */
|
|
#define _FP_CHOOSENAN_SEMIRAW(fs, wc, R, X, Y, OP) \
|
|
do \
|
|
{ \
|
|
/* _FP_CHOOSENAN expects raw values, so shift as required. */ \
|
|
_FP_FRAC_SRL_##wc (X, _FP_WORKBITS); \
|
|
_FP_FRAC_SRL_##wc (Y, _FP_WORKBITS); \
|
|
_FP_CHOOSENAN (fs, wc, R, X, Y, OP); \
|
|
_FP_FRAC_SLL_##wc (R, _FP_WORKBITS); \
|
|
} \
|
|
while (0)
|
|
|
|
/* Make the fractional part a quiet NaN, preserving the payload
|
|
if possible, otherwise make it the canonical quiet NaN and set
|
|
the sign bit accordingly. */
|
|
#define _FP_SETQNAN(fs, wc, X) \
|
|
do \
|
|
{ \
|
|
if (_FP_QNANNEGATEDP) \
|
|
{ \
|
|
_FP_FRAC_HIGH_RAW_##fs (X) &= _FP_QNANBIT_##fs - 1; \
|
|
if (_FP_FRAC_ZEROP_##wc (X)) \
|
|
{ \
|
|
X##_s = _FP_NANSIGN_##fs; \
|
|
_FP_FRAC_SET_##wc (X, _FP_NANFRAC_##fs); \
|
|
} \
|
|
} \
|
|
else \
|
|
_FP_FRAC_HIGH_RAW_##fs (X) |= _FP_QNANBIT_##fs; \
|
|
} \
|
|
while (0)
|
|
#define _FP_SETQNAN_SEMIRAW(fs, wc, X) \
|
|
do \
|
|
{ \
|
|
if (_FP_QNANNEGATEDP) \
|
|
{ \
|
|
_FP_FRAC_HIGH_##fs (X) &= _FP_QNANBIT_SH_##fs - 1; \
|
|
if (_FP_FRAC_ZEROP_##wc (X)) \
|
|
{ \
|
|
X##_s = _FP_NANSIGN_##fs; \
|
|
_FP_FRAC_SET_##wc (X, _FP_NANFRAC_##fs); \
|
|
_FP_FRAC_SLL_##wc (X, _FP_WORKBITS); \
|
|
} \
|
|
} \
|
|
else \
|
|
_FP_FRAC_HIGH_##fs (X) |= _FP_QNANBIT_SH_##fs; \
|
|
} \
|
|
while (0)
|
|
|
|
/* Test whether a biased exponent is normal (not zero or maximum). */
|
|
#define _FP_EXP_NORMAL(fs, wc, X) (((X##_e + 1) & _FP_EXPMAX_##fs) > 1)
|
|
|
|
/* Prepare to pack an fp value in semi-raw mode: the mantissa is
|
|
rounded and shifted right, with the rounding possibly increasing
|
|
the exponent (including changing a finite value to infinity). */
|
|
#define _FP_PACK_SEMIRAW(fs, wc, X) \
|
|
do \
|
|
{ \
|
|
int _FP_PACK_SEMIRAW_is_tiny \
|
|
= X##_e == 0 && !_FP_FRAC_ZEROP_##wc (X); \
|
|
if (_FP_TININESS_AFTER_ROUNDING \
|
|
&& _FP_PACK_SEMIRAW_is_tiny) \
|
|
{ \
|
|
FP_DECL_##fs (_FP_PACK_SEMIRAW_T); \
|
|
_FP_FRAC_COPY_##wc (_FP_PACK_SEMIRAW_T, X); \
|
|
_FP_PACK_SEMIRAW_T##_s = X##_s; \
|
|
_FP_PACK_SEMIRAW_T##_e = X##_e; \
|
|
_FP_FRAC_SLL_##wc (_FP_PACK_SEMIRAW_T, 1); \
|
|
_FP_ROUND (wc, _FP_PACK_SEMIRAW_T); \
|
|
if (_FP_FRAC_OVERP_##wc (fs, _FP_PACK_SEMIRAW_T)) \
|
|
_FP_PACK_SEMIRAW_is_tiny = 0; \
|
|
} \
|
|
_FP_ROUND (wc, X); \
|
|
if (_FP_PACK_SEMIRAW_is_tiny) \
|
|
{ \
|
|
if ((FP_CUR_EXCEPTIONS & FP_EX_INEXACT) \
|
|
|| (FP_TRAPPING_EXCEPTIONS & FP_EX_UNDERFLOW)) \
|
|
FP_SET_EXCEPTION (FP_EX_UNDERFLOW); \
|
|
} \
|
|
if (_FP_FRAC_HIGH_##fs (X) \
|
|
& (_FP_OVERFLOW_##fs >> 1)) \
|
|
{ \
|
|
_FP_FRAC_HIGH_##fs (X) &= ~(_FP_OVERFLOW_##fs >> 1); \
|
|
X##_e++; \
|
|
if (X##_e == _FP_EXPMAX_##fs) \
|
|
_FP_OVERFLOW_SEMIRAW (fs, wc, X); \
|
|
} \
|
|
_FP_FRAC_SRL_##wc (X, _FP_WORKBITS); \
|
|
if (X##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc (X)) \
|
|
{ \
|
|
if (!_FP_KEEPNANFRACP) \
|
|
{ \
|
|
_FP_FRAC_SET_##wc (X, _FP_NANFRAC_##fs); \
|
|
X##_s = _FP_NANSIGN_##fs; \
|
|
} \
|
|
else \
|
|
_FP_SETQNAN (fs, wc, X); \
|
|
} \
|
|
} \
|
|
while (0)
|
|
|
|
/*
|
|
* Before packing the bits back into the native fp result, take care
|
|
* of such mundane things as rounding and overflow. Also, for some
|
|
* kinds of fp values, the original parts may not have been fully
|
|
* extracted -- but that is ok, we can regenerate them now.
|
|
*/
|
|
|
|
#define _FP_PACK_CANONICAL(fs, wc, X) \
|
|
do \
|
|
{ \
|
|
switch (X##_c) \
|
|
{ \
|
|
case FP_CLS_NORMAL: \
|
|
X##_e += _FP_EXPBIAS_##fs; \
|
|
if (X##_e > 0) \
|
|
{ \
|
|
_FP_ROUND (wc, X); \
|
|
if (_FP_FRAC_OVERP_##wc (fs, X)) \
|
|
{ \
|
|
_FP_FRAC_CLEAR_OVERP_##wc (fs, X); \
|
|
X##_e++; \
|
|
} \
|
|
_FP_FRAC_SRL_##wc (X, _FP_WORKBITS); \
|
|
if (X##_e >= _FP_EXPMAX_##fs) \
|
|
{ \
|
|
/* overflow */ \
|
|
switch (FP_ROUNDMODE) \
|
|
{ \
|
|
case FP_RND_NEAREST: \
|
|
X##_c = FP_CLS_INF; \
|
|
break; \
|
|
case FP_RND_PINF: \
|
|
if (!X##_s) \
|
|
X##_c = FP_CLS_INF; \
|
|
break; \
|
|
case FP_RND_MINF: \
|
|
if (X##_s) \
|
|
X##_c = FP_CLS_INF; \
|
|
break; \
|
|
} \
|
|
if (X##_c == FP_CLS_INF) \
|
|
{ \
|
|
/* Overflow to infinity */ \
|
|
X##_e = _FP_EXPMAX_##fs; \
|
|
_FP_FRAC_SET_##wc (X, _FP_ZEROFRAC_##wc); \
|
|
} \
|
|
else \
|
|
{ \
|
|
/* Overflow to maximum normal */ \
|
|
X##_e = _FP_EXPMAX_##fs - 1; \
|
|
_FP_FRAC_SET_##wc (X, _FP_MAXFRAC_##wc); \
|
|
} \
|
|
FP_SET_EXCEPTION (FP_EX_OVERFLOW); \
|
|
FP_SET_EXCEPTION (FP_EX_INEXACT); \
|
|
} \
|
|
} \
|
|
else \
|
|
{ \
|
|
/* we've got a denormalized number */ \
|
|
int _FP_PACK_CANONICAL_is_tiny = 1; \
|
|
if (_FP_TININESS_AFTER_ROUNDING && X##_e == 0) \
|
|
{ \
|
|
FP_DECL_##fs (_FP_PACK_CANONICAL_T); \
|
|
_FP_FRAC_COPY_##wc (_FP_PACK_CANONICAL_T, X); \
|
|
_FP_PACK_CANONICAL_T##_s = X##_s; \
|
|
_FP_PACK_CANONICAL_T##_e = X##_e; \
|
|
_FP_ROUND (wc, _FP_PACK_CANONICAL_T); \
|
|
if (_FP_FRAC_OVERP_##wc (fs, _FP_PACK_CANONICAL_T)) \
|
|
_FP_PACK_CANONICAL_is_tiny = 0; \
|
|
} \
|
|
X##_e = -X##_e + 1; \
|
|
if (X##_e <= _FP_WFRACBITS_##fs) \
|
|
{ \
|
|
_FP_FRAC_SRS_##wc (X, X##_e, _FP_WFRACBITS_##fs); \
|
|
_FP_ROUND (wc, X); \
|
|
if (_FP_FRAC_HIGH_##fs (X) \
|
|
& (_FP_OVERFLOW_##fs >> 1)) \
|
|
{ \
|
|
X##_e = 1; \
|
|
_FP_FRAC_SET_##wc (X, _FP_ZEROFRAC_##wc); \
|
|
FP_SET_EXCEPTION (FP_EX_INEXACT); \
|
|
} \
|
|
else \
|
|
{ \
|
|
X##_e = 0; \
|
|
_FP_FRAC_SRL_##wc (X, _FP_WORKBITS); \
|
|
} \
|
|
if (_FP_PACK_CANONICAL_is_tiny \
|
|
&& ((FP_CUR_EXCEPTIONS & FP_EX_INEXACT) \
|
|
|| (FP_TRAPPING_EXCEPTIONS \
|
|
& FP_EX_UNDERFLOW))) \
|
|
FP_SET_EXCEPTION (FP_EX_UNDERFLOW); \
|
|
} \
|
|
else \
|
|
{ \
|
|
/* underflow to zero */ \
|
|
X##_e = 0; \
|
|
if (!_FP_FRAC_ZEROP_##wc (X)) \
|
|
{ \
|
|
_FP_FRAC_SET_##wc (X, _FP_MINFRAC_##wc); \
|
|
_FP_ROUND (wc, X); \
|
|
_FP_FRAC_LOW_##wc (X) >>= (_FP_WORKBITS); \
|
|
} \
|
|
FP_SET_EXCEPTION (FP_EX_UNDERFLOW); \
|
|
} \
|
|
} \
|
|
break; \
|
|
\
|
|
case FP_CLS_ZERO: \
|
|
X##_e = 0; \
|
|
_FP_FRAC_SET_##wc (X, _FP_ZEROFRAC_##wc); \
|
|
break; \
|
|
\
|
|
case FP_CLS_INF: \
|
|
X##_e = _FP_EXPMAX_##fs; \
|
|
_FP_FRAC_SET_##wc (X, _FP_ZEROFRAC_##wc); \
|
|
break; \
|
|
\
|
|
case FP_CLS_NAN: \
|
|
X##_e = _FP_EXPMAX_##fs; \
|
|
if (!_FP_KEEPNANFRACP) \
|
|
{ \
|
|
_FP_FRAC_SET_##wc (X, _FP_NANFRAC_##fs); \
|
|
X##_s = _FP_NANSIGN_##fs; \
|
|
} \
|
|
else \
|
|
_FP_SETQNAN (fs, wc, X); \
|
|
break; \
|
|
} \
|
|
} \
|
|
while (0)
|
|
|
|
/* This one accepts raw argument and not cooked, returns
|
|
* 1 if X is a signaling NaN.
|
|
*/
|
|
#define _FP_ISSIGNAN(fs, wc, X) \
|
|
({ \
|
|
int __ret = 0; \
|
|
if (X##_e == _FP_EXPMAX_##fs) \
|
|
{ \
|
|
if (!_FP_FRAC_ZEROP_##wc (X) \
|
|
&& _FP_FRAC_SNANP (fs, X)) \
|
|
__ret = 1; \
|
|
} \
|
|
__ret; \
|
|
})
|
|
|
|
|
|
|
|
|
|
|
|
/* Addition on semi-raw values. */
|
|
#define _FP_ADD_INTERNAL(fs, wc, R, X, Y, OP) \
|
|
do \
|
|
{ \
|
|
if (X##_s == Y##_s) \
|
|
{ \
|
|
/* Addition. */ \
|
|
R##_s = X##_s; \
|
|
int ediff = X##_e - Y##_e; \
|
|
if (ediff > 0) \
|
|
{ \
|
|
R##_e = X##_e; \
|
|
if (Y##_e == 0) \
|
|
{ \
|
|
/* Y is zero or denormalized. */ \
|
|
if (_FP_FRAC_ZEROP_##wc (Y)) \
|
|
{ \
|
|
_FP_CHECK_SIGNAN_SEMIRAW (fs, wc, X); \
|
|
_FP_FRAC_COPY_##wc (R, X); \
|
|
goto add_done; \
|
|
} \
|
|
else \
|
|
{ \
|
|
FP_SET_EXCEPTION (FP_EX_DENORM); \
|
|
ediff--; \
|
|
if (ediff == 0) \
|
|
{ \
|
|
_FP_FRAC_ADD_##wc (R, X, Y); \
|
|
goto add3; \
|
|
} \
|
|
if (X##_e == _FP_EXPMAX_##fs) \
|
|
{ \
|
|
_FP_CHECK_SIGNAN_SEMIRAW (fs, wc, X); \
|
|
_FP_FRAC_COPY_##wc (R, X); \
|
|
goto add_done; \
|
|
} \
|
|
goto add1; \
|
|
} \
|
|
} \
|
|
else if (X##_e == _FP_EXPMAX_##fs) \
|
|
{ \
|
|
/* X is NaN or Inf, Y is normal. */ \
|
|
_FP_CHECK_SIGNAN_SEMIRAW (fs, wc, X); \
|
|
_FP_FRAC_COPY_##wc (R, X); \
|
|
goto add_done; \
|
|
} \
|
|
\
|
|
/* Insert implicit MSB of Y. */ \
|
|
_FP_FRAC_HIGH_##fs (Y) |= _FP_IMPLBIT_SH_##fs; \
|
|
\
|
|
add1: \
|
|
/* Shift the mantissa of Y to the right EDIFF steps; \
|
|
remember to account later for the implicit MSB of X. */ \
|
|
if (ediff <= _FP_WFRACBITS_##fs) \
|
|
_FP_FRAC_SRS_##wc (Y, ediff, _FP_WFRACBITS_##fs); \
|
|
else if (!_FP_FRAC_ZEROP_##wc (Y)) \
|
|
_FP_FRAC_SET_##wc (Y, _FP_MINFRAC_##wc); \
|
|
_FP_FRAC_ADD_##wc (R, X, Y); \
|
|
} \
|
|
else if (ediff < 0) \
|
|
{ \
|
|
ediff = -ediff; \
|
|
R##_e = Y##_e; \
|
|
if (X##_e == 0) \
|
|
{ \
|
|
/* X is zero or denormalized. */ \
|
|
if (_FP_FRAC_ZEROP_##wc (X)) \
|
|
{ \
|
|
_FP_CHECK_SIGNAN_SEMIRAW (fs, wc, Y); \
|
|
_FP_FRAC_COPY_##wc (R, Y); \
|
|
goto add_done; \
|
|
} \
|
|
else \
|
|
{ \
|
|
FP_SET_EXCEPTION (FP_EX_DENORM); \
|
|
ediff--; \
|
|
if (ediff == 0) \
|
|
{ \
|
|
_FP_FRAC_ADD_##wc (R, Y, X); \
|
|
goto add3; \
|
|
} \
|
|
if (Y##_e == _FP_EXPMAX_##fs) \
|
|
{ \
|
|
_FP_CHECK_SIGNAN_SEMIRAW (fs, wc, Y); \
|
|
_FP_FRAC_COPY_##wc (R, Y); \
|
|
goto add_done; \
|
|
} \
|
|
goto add2; \
|
|
} \
|
|
} \
|
|
else if (Y##_e == _FP_EXPMAX_##fs) \
|
|
{ \
|
|
/* Y is NaN or Inf, X is normal. */ \
|
|
_FP_CHECK_SIGNAN_SEMIRAW (fs, wc, Y); \
|
|
_FP_FRAC_COPY_##wc (R, Y); \
|
|
goto add_done; \
|
|
} \
|
|
\
|
|
/* Insert implicit MSB of X. */ \
|
|
_FP_FRAC_HIGH_##fs (X) |= _FP_IMPLBIT_SH_##fs; \
|
|
\
|
|
add2: \
|
|
/* Shift the mantissa of X to the right EDIFF steps; \
|
|
remember to account later for the implicit MSB of Y. */ \
|
|
if (ediff <= _FP_WFRACBITS_##fs) \
|
|
_FP_FRAC_SRS_##wc (X, ediff, _FP_WFRACBITS_##fs); \
|
|
else if (!_FP_FRAC_ZEROP_##wc (X)) \
|
|
_FP_FRAC_SET_##wc (X, _FP_MINFRAC_##wc); \
|
|
_FP_FRAC_ADD_##wc (R, Y, X); \
|
|
} \
|
|
else \
|
|
{ \
|
|
/* ediff == 0. */ \
|
|
if (!_FP_EXP_NORMAL (fs, wc, X)) \
|
|
{ \
|
|
if (X##_e == 0) \
|
|
{ \
|
|
/* X and Y are zero or denormalized. */ \
|
|
R##_e = 0; \
|
|
if (_FP_FRAC_ZEROP_##wc (X)) \
|
|
{ \
|
|
if (!_FP_FRAC_ZEROP_##wc (Y)) \
|
|
FP_SET_EXCEPTION (FP_EX_DENORM); \
|
|
_FP_FRAC_COPY_##wc (R, Y); \
|
|
goto add_done; \
|
|
} \
|
|
else if (_FP_FRAC_ZEROP_##wc (Y)) \
|
|
{ \
|
|
FP_SET_EXCEPTION (FP_EX_DENORM); \
|
|
_FP_FRAC_COPY_##wc (R, X); \
|
|
goto add_done; \
|
|
} \
|
|
else \
|
|
{ \
|
|
FP_SET_EXCEPTION (FP_EX_DENORM); \
|
|
_FP_FRAC_ADD_##wc (R, X, Y); \
|
|
if (_FP_FRAC_HIGH_##fs (R) & _FP_IMPLBIT_SH_##fs) \
|
|
{ \
|
|
/* Normalized result. */ \
|
|
_FP_FRAC_HIGH_##fs (R) \
|
|
&= ~(_FP_W_TYPE) _FP_IMPLBIT_SH_##fs; \
|
|
R##_e = 1; \
|
|
} \
|
|
goto add_done; \
|
|
} \
|
|
} \
|
|
else \
|
|
{ \
|
|
/* X and Y are NaN or Inf. */ \
|
|
_FP_CHECK_SIGNAN_SEMIRAW (fs, wc, X); \
|
|
_FP_CHECK_SIGNAN_SEMIRAW (fs, wc, Y); \
|
|
R##_e = _FP_EXPMAX_##fs; \
|
|
if (_FP_FRAC_ZEROP_##wc (X)) \
|
|
_FP_FRAC_COPY_##wc (R, Y); \
|
|
else if (_FP_FRAC_ZEROP_##wc (Y)) \
|
|
_FP_FRAC_COPY_##wc (R, X); \
|
|
else \
|
|
_FP_CHOOSENAN_SEMIRAW (fs, wc, R, X, Y, OP); \
|
|
goto add_done; \
|
|
} \
|
|
} \
|
|
/* The exponents of X and Y, both normal, are equal. The \
|
|
implicit MSBs will always add to increase the \
|
|
exponent. */ \
|
|
_FP_FRAC_ADD_##wc (R, X, Y); \
|
|
R##_e = X##_e + 1; \
|
|
_FP_FRAC_SRS_##wc (R, 1, _FP_WFRACBITS_##fs); \
|
|
if (R##_e == _FP_EXPMAX_##fs) \
|
|
/* Overflow to infinity (depending on rounding mode). */ \
|
|
_FP_OVERFLOW_SEMIRAW (fs, wc, R); \
|
|
goto add_done; \
|
|
} \
|
|
add3: \
|
|
if (_FP_FRAC_HIGH_##fs (R) & _FP_IMPLBIT_SH_##fs) \
|
|
{ \
|
|
/* Overflow. */ \
|
|
_FP_FRAC_HIGH_##fs (R) &= ~(_FP_W_TYPE) _FP_IMPLBIT_SH_##fs; \
|
|
R##_e++; \
|
|
_FP_FRAC_SRS_##wc (R, 1, _FP_WFRACBITS_##fs); \
|
|
if (R##_e == _FP_EXPMAX_##fs) \
|
|
/* Overflow to infinity (depending on rounding mode). */ \
|
|
_FP_OVERFLOW_SEMIRAW (fs, wc, R); \
|
|
} \
|
|
add_done: ; \
|
|
} \
|
|
else \
|
|
{ \
|
|
/* Subtraction. */ \
|
|
int ediff = X##_e - Y##_e; \
|
|
if (ediff > 0) \
|
|
{ \
|
|
R##_e = X##_e; \
|
|
R##_s = X##_s; \
|
|
if (Y##_e == 0) \
|
|
{ \
|
|
/* Y is zero or denormalized. */ \
|
|
if (_FP_FRAC_ZEROP_##wc (Y)) \
|
|
{ \
|
|
_FP_CHECK_SIGNAN_SEMIRAW (fs, wc, X); \
|
|
_FP_FRAC_COPY_##wc (R, X); \
|
|
goto sub_done; \
|
|
} \
|
|
else \
|
|
{ \
|
|
FP_SET_EXCEPTION (FP_EX_DENORM); \
|
|
ediff--; \
|
|
if (ediff == 0) \
|
|
{ \
|
|
_FP_FRAC_SUB_##wc (R, X, Y); \
|
|
goto sub3; \
|
|
} \
|
|
if (X##_e == _FP_EXPMAX_##fs) \
|
|
{ \
|
|
_FP_CHECK_SIGNAN_SEMIRAW (fs, wc, X); \
|
|
_FP_FRAC_COPY_##wc (R, X); \
|
|
goto sub_done; \
|
|
} \
|
|
goto sub1; \
|
|
} \
|
|
} \
|
|
else if (X##_e == _FP_EXPMAX_##fs) \
|
|
{ \
|
|
/* X is NaN or Inf, Y is normal. */ \
|
|
_FP_CHECK_SIGNAN_SEMIRAW (fs, wc, X); \
|
|
_FP_FRAC_COPY_##wc (R, X); \
|
|
goto sub_done; \
|
|
} \
|
|
\
|
|
/* Insert implicit MSB of Y. */ \
|
|
_FP_FRAC_HIGH_##fs (Y) |= _FP_IMPLBIT_SH_##fs; \
|
|
\
|
|
sub1: \
|
|
/* Shift the mantissa of Y to the right EDIFF steps; \
|
|
remember to account later for the implicit MSB of X. */ \
|
|
if (ediff <= _FP_WFRACBITS_##fs) \
|
|
_FP_FRAC_SRS_##wc (Y, ediff, _FP_WFRACBITS_##fs); \
|
|
else if (!_FP_FRAC_ZEROP_##wc (Y)) \
|
|
_FP_FRAC_SET_##wc (Y, _FP_MINFRAC_##wc); \
|
|
_FP_FRAC_SUB_##wc (R, X, Y); \
|
|
} \
|
|
else if (ediff < 0) \
|
|
{ \
|
|
ediff = -ediff; \
|
|
R##_e = Y##_e; \
|
|
R##_s = Y##_s; \
|
|
if (X##_e == 0) \
|
|
{ \
|
|
/* X is zero or denormalized. */ \
|
|
if (_FP_FRAC_ZEROP_##wc (X)) \
|
|
{ \
|
|
_FP_CHECK_SIGNAN_SEMIRAW (fs, wc, Y); \
|
|
_FP_FRAC_COPY_##wc (R, Y); \
|
|
goto sub_done; \
|
|
} \
|
|
else \
|
|
{ \
|
|
FP_SET_EXCEPTION (FP_EX_DENORM); \
|
|
ediff--; \
|
|
if (ediff == 0) \
|
|
{ \
|
|
_FP_FRAC_SUB_##wc (R, Y, X); \
|
|
goto sub3; \
|
|
} \
|
|
if (Y##_e == _FP_EXPMAX_##fs) \
|
|
{ \
|
|
_FP_CHECK_SIGNAN_SEMIRAW (fs, wc, Y); \
|
|
_FP_FRAC_COPY_##wc (R, Y); \
|
|
goto sub_done; \
|
|
} \
|
|
goto sub2; \
|
|
} \
|
|
} \
|
|
else if (Y##_e == _FP_EXPMAX_##fs) \
|
|
{ \
|
|
/* Y is NaN or Inf, X is normal. */ \
|
|
_FP_CHECK_SIGNAN_SEMIRAW (fs, wc, Y); \
|
|
_FP_FRAC_COPY_##wc (R, Y); \
|
|
goto sub_done; \
|
|
} \
|
|
\
|
|
/* Insert implicit MSB of X. */ \
|
|
_FP_FRAC_HIGH_##fs (X) |= _FP_IMPLBIT_SH_##fs; \
|
|
\
|
|
sub2: \
|
|
/* Shift the mantissa of X to the right EDIFF steps; \
|
|
remember to account later for the implicit MSB of Y. */ \
|
|
if (ediff <= _FP_WFRACBITS_##fs) \
|
|
_FP_FRAC_SRS_##wc (X, ediff, _FP_WFRACBITS_##fs); \
|
|
else if (!_FP_FRAC_ZEROP_##wc (X)) \
|
|
_FP_FRAC_SET_##wc (X, _FP_MINFRAC_##wc); \
|
|
_FP_FRAC_SUB_##wc (R, Y, X); \
|
|
} \
|
|
else \
|
|
{ \
|
|
/* ediff == 0. */ \
|
|
if (!_FP_EXP_NORMAL (fs, wc, X)) \
|
|
{ \
|
|
if (X##_e == 0) \
|
|
{ \
|
|
/* X and Y are zero or denormalized. */ \
|
|
R##_e = 0; \
|
|
if (_FP_FRAC_ZEROP_##wc (X)) \
|
|
{ \
|
|
_FP_FRAC_COPY_##wc (R, Y); \
|
|
if (_FP_FRAC_ZEROP_##wc (Y)) \
|
|
R##_s = (FP_ROUNDMODE == FP_RND_MINF); \
|
|
else \
|
|
{ \
|
|
FP_SET_EXCEPTION (FP_EX_DENORM); \
|
|
R##_s = Y##_s; \
|
|
} \
|
|
goto sub_done; \
|
|
} \
|
|
else if (_FP_FRAC_ZEROP_##wc (Y)) \
|
|
{ \
|
|
FP_SET_EXCEPTION (FP_EX_DENORM); \
|
|
_FP_FRAC_COPY_##wc (R, X); \
|
|
R##_s = X##_s; \
|
|
goto sub_done; \
|
|
} \
|
|
else \
|
|
{ \
|
|
FP_SET_EXCEPTION (FP_EX_DENORM); \
|
|
_FP_FRAC_SUB_##wc (R, X, Y); \
|
|
R##_s = X##_s; \
|
|
if (_FP_FRAC_HIGH_##fs (R) & _FP_IMPLBIT_SH_##fs) \
|
|
{ \
|
|
/* |X| < |Y|, negate result. */ \
|
|
_FP_FRAC_SUB_##wc (R, Y, X); \
|
|
R##_s = Y##_s; \
|
|
} \
|
|
else if (_FP_FRAC_ZEROP_##wc (R)) \
|
|
R##_s = (FP_ROUNDMODE == FP_RND_MINF); \
|
|
goto sub_done; \
|
|
} \
|
|
} \
|
|
else \
|
|
{ \
|
|
/* X and Y are NaN or Inf, of opposite signs. */ \
|
|
_FP_CHECK_SIGNAN_SEMIRAW (fs, wc, X); \
|
|
_FP_CHECK_SIGNAN_SEMIRAW (fs, wc, Y); \
|
|
R##_e = _FP_EXPMAX_##fs; \
|
|
if (_FP_FRAC_ZEROP_##wc (X)) \
|
|
{ \
|
|
if (_FP_FRAC_ZEROP_##wc (Y)) \
|
|
{ \
|
|
/* Inf - Inf. */ \
|
|
R##_s = _FP_NANSIGN_##fs; \
|
|
_FP_FRAC_SET_##wc (R, _FP_NANFRAC_##fs); \
|
|
_FP_FRAC_SLL_##wc (R, _FP_WORKBITS); \
|
|
FP_SET_EXCEPTION (FP_EX_INVALID); \
|
|
} \
|
|
else \
|
|
{ \
|
|
/* Inf - NaN. */ \
|
|
R##_s = Y##_s; \
|
|
_FP_FRAC_COPY_##wc (R, Y); \
|
|
} \
|
|
} \
|
|
else \
|
|
{ \
|
|
if (_FP_FRAC_ZEROP_##wc (Y)) \
|
|
{ \
|
|
/* NaN - Inf. */ \
|
|
R##_s = X##_s; \
|
|
_FP_FRAC_COPY_##wc (R, X); \
|
|
} \
|
|
else \
|
|
{ \
|
|
/* NaN - NaN. */ \
|
|
_FP_CHOOSENAN_SEMIRAW (fs, wc, R, X, Y, OP); \
|
|
} \
|
|
} \
|
|
goto sub_done; \
|
|
} \
|
|
} \
|
|
/* The exponents of X and Y, both normal, are equal. The \
|
|
implicit MSBs cancel. */ \
|
|
R##_e = X##_e; \
|
|
_FP_FRAC_SUB_##wc (R, X, Y); \
|
|
R##_s = X##_s; \
|
|
if (_FP_FRAC_HIGH_##fs (R) & _FP_IMPLBIT_SH_##fs) \
|
|
{ \
|
|
/* |X| < |Y|, negate result. */ \
|
|
_FP_FRAC_SUB_##wc (R, Y, X); \
|
|
R##_s = Y##_s; \
|
|
} \
|
|
else if (_FP_FRAC_ZEROP_##wc (R)) \
|
|
{ \
|
|
R##_e = 0; \
|
|
R##_s = (FP_ROUNDMODE == FP_RND_MINF); \
|
|
goto sub_done; \
|
|
} \
|
|
goto norm; \
|
|
} \
|
|
sub3: \
|
|
if (_FP_FRAC_HIGH_##fs (R) & _FP_IMPLBIT_SH_##fs) \
|
|
{ \
|
|
int diff; \
|
|
/* Carry into most significant bit of larger one of X and Y, \
|
|
canceling it; renormalize. */ \
|
|
_FP_FRAC_HIGH_##fs (R) &= _FP_IMPLBIT_SH_##fs - 1; \
|
|
norm: \
|
|
_FP_FRAC_CLZ_##wc (diff, R); \
|
|
diff -= _FP_WFRACXBITS_##fs; \
|
|
_FP_FRAC_SLL_##wc (R, diff); \
|
|
if (R##_e <= diff) \
|
|
{ \
|
|
/* R is denormalized. */ \
|
|
diff = diff - R##_e + 1; \
|
|
_FP_FRAC_SRS_##wc (R, diff, _FP_WFRACBITS_##fs); \
|
|
R##_e = 0; \
|
|
} \
|
|
else \
|
|
{ \
|
|
R##_e -= diff; \
|
|
_FP_FRAC_HIGH_##fs (R) &= ~(_FP_W_TYPE) _FP_IMPLBIT_SH_##fs; \
|
|
} \
|
|
} \
|
|
sub_done: ; \
|
|
} \
|
|
} \
|
|
while (0)
|
|
|
|
#define _FP_ADD(fs, wc, R, X, Y) _FP_ADD_INTERNAL (fs, wc, R, X, Y, '+')
|
|
#define _FP_SUB(fs, wc, R, X, Y) \
|
|
do \
|
|
{ \
|
|
if (!(Y##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc (Y))) \
|
|
Y##_s ^= 1; \
|
|
_FP_ADD_INTERNAL (fs, wc, R, X, Y, '-'); \
|
|
} \
|
|
while (0)
|
|
|
|
|
|
/*
|
|
* Main negation routine. The input value is raw.
|
|
*/
|
|
|
|
#define _FP_NEG(fs, wc, R, X) \
|
|
do \
|
|
{ \
|
|
_FP_FRAC_COPY_##wc (R, X); \
|
|
R##_e = X##_e; \
|
|
R##_s = 1 ^ X##_s; \
|
|
} \
|
|
while (0)
|
|
|
|
|
|
/*
|
|
* Main multiplication routine. The input values should be cooked.
|
|
*/
|
|
|
|
#define _FP_MUL(fs, wc, R, X, Y) \
|
|
do \
|
|
{ \
|
|
R##_s = X##_s ^ Y##_s; \
|
|
R##_e = X##_e + Y##_e + 1; \
|
|
switch (_FP_CLS_COMBINE (X##_c, Y##_c)) \
|
|
{ \
|
|
case _FP_CLS_COMBINE (FP_CLS_NORMAL, FP_CLS_NORMAL): \
|
|
R##_c = FP_CLS_NORMAL; \
|
|
\
|
|
_FP_MUL_MEAT_##fs (R, X, Y); \
|
|
\
|
|
if (_FP_FRAC_OVERP_##wc (fs, R)) \
|
|
_FP_FRAC_SRS_##wc (R, 1, _FP_WFRACBITS_##fs); \
|
|
else \
|
|
R##_e--; \
|
|
break; \
|
|
\
|
|
case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_NAN): \
|
|
_FP_CHOOSENAN (fs, wc, R, X, Y, '*'); \
|
|
break; \
|
|
\
|
|
case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_NORMAL): \
|
|
case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_INF): \
|
|
case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_ZERO): \
|
|
R##_s = X##_s; \
|
|
\
|
|
case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_INF): \
|
|
case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_NORMAL): \
|
|
case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_NORMAL): \
|
|
case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_ZERO): \
|
|
_FP_FRAC_COPY_##wc (R, X); \
|
|
R##_c = X##_c; \
|
|
break; \
|
|
\
|
|
case _FP_CLS_COMBINE (FP_CLS_NORMAL, FP_CLS_NAN): \
|
|
case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_NAN): \
|
|
case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_NAN): \
|
|
R##_s = Y##_s; \
|
|
\
|
|
case _FP_CLS_COMBINE (FP_CLS_NORMAL, FP_CLS_INF): \
|
|
case _FP_CLS_COMBINE (FP_CLS_NORMAL, FP_CLS_ZERO): \
|
|
_FP_FRAC_COPY_##wc (R, Y); \
|
|
R##_c = Y##_c; \
|
|
break; \
|
|
\
|
|
case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_ZERO): \
|
|
case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_INF): \
|
|
R##_s = _FP_NANSIGN_##fs; \
|
|
R##_c = FP_CLS_NAN; \
|
|
_FP_FRAC_SET_##wc (R, _FP_NANFRAC_##fs); \
|
|
FP_SET_EXCEPTION (FP_EX_INVALID); \
|
|
break; \
|
|
\
|
|
default: \
|
|
abort (); \
|
|
} \
|
|
} \
|
|
while (0)
|
|
|
|
|
|
/* Fused multiply-add. The input values should be cooked. */
|
|
|
|
#define _FP_FMA(fs, wc, dwc, R, X, Y, Z) \
|
|
do \
|
|
{ \
|
|
FP_DECL_##fs (T); \
|
|
T##_s = X##_s ^ Y##_s; \
|
|
T##_e = X##_e + Y##_e + 1; \
|
|
switch (_FP_CLS_COMBINE (X##_c, Y##_c)) \
|
|
{ \
|
|
case _FP_CLS_COMBINE (FP_CLS_NORMAL, FP_CLS_NORMAL): \
|
|
switch (Z##_c) \
|
|
{ \
|
|
case FP_CLS_INF: \
|
|
case FP_CLS_NAN: \
|
|
R##_s = Z##_s; \
|
|
_FP_FRAC_COPY_##wc (R, Z); \
|
|
R##_c = Z##_c; \
|
|
break; \
|
|
\
|
|
case FP_CLS_ZERO: \
|
|
R##_c = FP_CLS_NORMAL; \
|
|
R##_s = T##_s; \
|
|
R##_e = T##_e; \
|
|
\
|
|
_FP_MUL_MEAT_##fs (R, X, Y); \
|
|
\
|
|
if (_FP_FRAC_OVERP_##wc (fs, R)) \
|
|
_FP_FRAC_SRS_##wc (R, 1, _FP_WFRACBITS_##fs); \
|
|
else \
|
|
R##_e--; \
|
|
break; \
|
|
\
|
|
case FP_CLS_NORMAL:; \
|
|
_FP_FRAC_DECL_##dwc (TD); \
|
|
_FP_FRAC_DECL_##dwc (ZD); \
|
|
_FP_FRAC_DECL_##dwc (RD); \
|
|
_FP_MUL_MEAT_DW_##fs (TD, X, Y); \
|
|
R##_e = T##_e; \
|
|
int tsh = _FP_FRAC_HIGHBIT_DW_##dwc (fs, TD) == 0; \
|
|
T##_e -= tsh; \
|
|
int ediff = T##_e - Z##_e; \
|
|
if (ediff >= 0) \
|
|
{ \
|
|
int shift = _FP_WFRACBITS_##fs - tsh - ediff; \
|
|
if (shift <= -_FP_WFRACBITS_##fs) \
|
|
_FP_FRAC_SET_##dwc (ZD, _FP_MINFRAC_##dwc); \
|
|
else \
|
|
{ \
|
|
_FP_FRAC_COPY_##dwc##_##wc (ZD, Z); \
|
|
if (shift < 0) \
|
|
_FP_FRAC_SRS_##dwc (ZD, -shift, \
|
|
_FP_WFRACBITS_DW_##fs); \
|
|
else if (shift > 0) \
|
|
_FP_FRAC_SLL_##dwc (ZD, shift); \
|
|
} \
|
|
R##_s = T##_s; \
|
|
if (T##_s == Z##_s) \
|
|
_FP_FRAC_ADD_##dwc (RD, TD, ZD); \
|
|
else \
|
|
{ \
|
|
_FP_FRAC_SUB_##dwc (RD, TD, ZD); \
|
|
if (_FP_FRAC_NEGP_##dwc (RD)) \
|
|
{ \
|
|
R##_s = Z##_s; \
|
|
_FP_FRAC_SUB_##dwc (RD, ZD, TD); \
|
|
} \
|
|
} \
|
|
} \
|
|
else \
|
|
{ \
|
|
R##_e = Z##_e; \
|
|
R##_s = Z##_s; \
|
|
_FP_FRAC_COPY_##dwc##_##wc (ZD, Z); \
|
|
_FP_FRAC_SLL_##dwc (ZD, _FP_WFRACBITS_##fs); \
|
|
int shift = -ediff - tsh; \
|
|
if (shift >= _FP_WFRACBITS_DW_##fs) \
|
|
_FP_FRAC_SET_##dwc (TD, _FP_MINFRAC_##dwc); \
|
|
else if (shift > 0) \
|
|
_FP_FRAC_SRS_##dwc (TD, shift, \
|
|
_FP_WFRACBITS_DW_##fs); \
|
|
if (Z##_s == T##_s) \
|
|
_FP_FRAC_ADD_##dwc (RD, ZD, TD); \
|
|
else \
|
|
_FP_FRAC_SUB_##dwc (RD, ZD, TD); \
|
|
} \
|
|
if (_FP_FRAC_ZEROP_##dwc (RD)) \
|
|
{ \
|
|
if (T##_s == Z##_s) \
|
|
R##_s = Z##_s; \
|
|
else \
|
|
R##_s = (FP_ROUNDMODE == FP_RND_MINF); \
|
|
_FP_FRAC_SET_##wc (R, _FP_ZEROFRAC_##wc); \
|
|
R##_c = FP_CLS_ZERO; \
|
|
} \
|
|
else \
|
|
{ \
|
|
int rlz; \
|
|
_FP_FRAC_CLZ_##dwc (rlz, RD); \
|
|
rlz -= _FP_WFRACXBITS_DW_##fs; \
|
|
R##_e -= rlz; \
|
|
int shift = _FP_WFRACBITS_##fs - rlz; \
|
|
if (shift > 0) \
|
|
_FP_FRAC_SRS_##dwc (RD, shift, \
|
|
_FP_WFRACBITS_DW_##fs); \
|
|
else if (shift < 0) \
|
|
_FP_FRAC_SLL_##dwc (RD, -shift); \
|
|
_FP_FRAC_COPY_##wc##_##dwc (R, RD); \
|
|
R##_c = FP_CLS_NORMAL; \
|
|
} \
|
|
break; \
|
|
} \
|
|
goto done_fma; \
|
|
\
|
|
case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_NAN): \
|
|
_FP_CHOOSENAN (fs, wc, T, X, Y, '*'); \
|
|
break; \
|
|
\
|
|
case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_NORMAL): \
|
|
case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_INF): \
|
|
case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_ZERO): \
|
|
T##_s = X##_s; \
|
|
\
|
|
case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_INF): \
|
|
case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_NORMAL): \
|
|
case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_NORMAL): \
|
|
case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_ZERO): \
|
|
_FP_FRAC_COPY_##wc (T, X); \
|
|
T##_c = X##_c; \
|
|
break; \
|
|
\
|
|
case _FP_CLS_COMBINE (FP_CLS_NORMAL, FP_CLS_NAN): \
|
|
case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_NAN): \
|
|
case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_NAN): \
|
|
T##_s = Y##_s; \
|
|
\
|
|
case _FP_CLS_COMBINE (FP_CLS_NORMAL, FP_CLS_INF): \
|
|
case _FP_CLS_COMBINE (FP_CLS_NORMAL, FP_CLS_ZERO): \
|
|
_FP_FRAC_COPY_##wc (T, Y); \
|
|
T##_c = Y##_c; \
|
|
break; \
|
|
\
|
|
case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_ZERO): \
|
|
case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_INF): \
|
|
T##_s = _FP_NANSIGN_##fs; \
|
|
T##_c = FP_CLS_NAN; \
|
|
_FP_FRAC_SET_##wc (T, _FP_NANFRAC_##fs); \
|
|
FP_SET_EXCEPTION (FP_EX_INVALID); \
|
|
break; \
|
|
\
|
|
default: \
|
|
abort (); \
|
|
} \
|
|
\
|
|
/* T = X * Y is zero, infinity or NaN. */ \
|
|
switch (_FP_CLS_COMBINE (T##_c, Z##_c)) \
|
|
{ \
|
|
case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_NAN): \
|
|
_FP_CHOOSENAN (fs, wc, R, T, Z, '+'); \
|
|
break; \
|
|
\
|
|
case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_NORMAL): \
|
|
case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_INF): \
|
|
case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_ZERO): \
|
|
case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_NORMAL): \
|
|
case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_ZERO): \
|
|
R##_s = T##_s; \
|
|
_FP_FRAC_COPY_##wc (R, T); \
|
|
R##_c = T##_c; \
|
|
break; \
|
|
\
|
|
case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_NAN): \
|
|
case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_NAN): \
|
|
case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_NORMAL): \
|
|
case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_INF): \
|
|
R##_s = Z##_s; \
|
|
_FP_FRAC_COPY_##wc (R, Z); \
|
|
R##_c = Z##_c; \
|
|
break; \
|
|
\
|
|
case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_INF): \
|
|
if (T##_s == Z##_s) \
|
|
{ \
|
|
R##_s = Z##_s; \
|
|
_FP_FRAC_COPY_##wc (R, Z); \
|
|
R##_c = Z##_c; \
|
|
} \
|
|
else \
|
|
{ \
|
|
R##_s = _FP_NANSIGN_##fs; \
|
|
R##_c = FP_CLS_NAN; \
|
|
_FP_FRAC_SET_##wc (R, _FP_NANFRAC_##fs); \
|
|
FP_SET_EXCEPTION (FP_EX_INVALID); \
|
|
} \
|
|
break; \
|
|
\
|
|
case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_ZERO): \
|
|
if (T##_s == Z##_s) \
|
|
R##_s = Z##_s; \
|
|
else \
|
|
R##_s = (FP_ROUNDMODE == FP_RND_MINF); \
|
|
_FP_FRAC_COPY_##wc (R, Z); \
|
|
R##_c = Z##_c; \
|
|
break; \
|
|
\
|
|
default: \
|
|
abort (); \
|
|
} \
|
|
done_fma: ; \
|
|
} \
|
|
while (0)
|
|
|
|
|
|
/*
|
|
* Main division routine. The input values should be cooked.
|
|
*/
|
|
|
|
#define _FP_DIV(fs, wc, R, X, Y) \
|
|
do \
|
|
{ \
|
|
R##_s = X##_s ^ Y##_s; \
|
|
R##_e = X##_e - Y##_e; \
|
|
switch (_FP_CLS_COMBINE (X##_c, Y##_c)) \
|
|
{ \
|
|
case _FP_CLS_COMBINE (FP_CLS_NORMAL, FP_CLS_NORMAL): \
|
|
R##_c = FP_CLS_NORMAL; \
|
|
\
|
|
_FP_DIV_MEAT_##fs (R, X, Y); \
|
|
break; \
|
|
\
|
|
case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_NAN): \
|
|
_FP_CHOOSENAN (fs, wc, R, X, Y, '/'); \
|
|
break; \
|
|
\
|
|
case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_NORMAL): \
|
|
case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_INF): \
|
|
case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_ZERO): \
|
|
R##_s = X##_s; \
|
|
_FP_FRAC_COPY_##wc (R, X); \
|
|
R##_c = X##_c; \
|
|
break; \
|
|
\
|
|
case _FP_CLS_COMBINE (FP_CLS_NORMAL, FP_CLS_NAN): \
|
|
case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_NAN): \
|
|
case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_NAN): \
|
|
R##_s = Y##_s; \
|
|
_FP_FRAC_COPY_##wc (R, Y); \
|
|
R##_c = Y##_c; \
|
|
break; \
|
|
\
|
|
case _FP_CLS_COMBINE (FP_CLS_NORMAL, FP_CLS_INF): \
|
|
case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_INF): \
|
|
case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_NORMAL): \
|
|
R##_c = FP_CLS_ZERO; \
|
|
break; \
|
|
\
|
|
case _FP_CLS_COMBINE (FP_CLS_NORMAL, FP_CLS_ZERO): \
|
|
FP_SET_EXCEPTION (FP_EX_DIVZERO); \
|
|
case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_ZERO): \
|
|
case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_NORMAL): \
|
|
R##_c = FP_CLS_INF; \
|
|
break; \
|
|
\
|
|
case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_INF): \
|
|
case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_ZERO): \
|
|
R##_s = _FP_NANSIGN_##fs; \
|
|
R##_c = FP_CLS_NAN; \
|
|
_FP_FRAC_SET_##wc (R, _FP_NANFRAC_##fs); \
|
|
FP_SET_EXCEPTION (FP_EX_INVALID); \
|
|
break; \
|
|
\
|
|
default: \
|
|
abort (); \
|
|
} \
|
|
} \
|
|
while (0)
|
|
|
|
|
|
/*
|
|
* Main differential comparison routine. The inputs should be raw not
|
|
* cooked. The return is -1,0,1 for normal values, 2 otherwise.
|
|
*/
|
|
|
|
#define _FP_CMP(fs, wc, ret, X, Y, un) \
|
|
do \
|
|
{ \
|
|
/* NANs are unordered */ \
|
|
if ((X##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc (X)) \
|
|
|| (Y##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc (Y))) \
|
|
{ \
|
|
ret = un; \
|
|
} \
|
|
else \
|
|
{ \
|
|
int __is_zero_x; \
|
|
int __is_zero_y; \
|
|
\
|
|
__is_zero_x = (!X##_e && _FP_FRAC_ZEROP_##wc (X)) ? 1 : 0; \
|
|
__is_zero_y = (!Y##_e && _FP_FRAC_ZEROP_##wc (Y)) ? 1 : 0; \
|
|
\
|
|
if (__is_zero_x && __is_zero_y) \
|
|
ret = 0; \
|
|
else if (__is_zero_x) \
|
|
ret = Y##_s ? 1 : -1; \
|
|
else if (__is_zero_y) \
|
|
ret = X##_s ? -1 : 1; \
|
|
else if (X##_s != Y##_s) \
|
|
ret = X##_s ? -1 : 1; \
|
|
else if (X##_e > Y##_e) \
|
|
ret = X##_s ? -1 : 1; \
|
|
else if (X##_e < Y##_e) \
|
|
ret = X##_s ? 1 : -1; \
|
|
else if (_FP_FRAC_GT_##wc (X, Y)) \
|
|
ret = X##_s ? -1 : 1; \
|
|
else if (_FP_FRAC_GT_##wc (Y, X)) \
|
|
ret = X##_s ? 1 : -1; \
|
|
else \
|
|
ret = 0; \
|
|
} \
|
|
} \
|
|
while (0)
|
|
|
|
|
|
/* Simplification for strict equality. */
|
|
|
|
#define _FP_CMP_EQ(fs, wc, ret, X, Y) \
|
|
do \
|
|
{ \
|
|
/* NANs are unordered */ \
|
|
if ((X##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc (X)) \
|
|
|| (Y##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc (Y))) \
|
|
{ \
|
|
ret = 1; \
|
|
} \
|
|
else \
|
|
{ \
|
|
ret = !(X##_e == Y##_e \
|
|
&& _FP_FRAC_EQ_##wc (X, Y) \
|
|
&& (X##_s == Y##_s || (!X##_e && _FP_FRAC_ZEROP_##wc (X)))); \
|
|
} \
|
|
} \
|
|
while (0)
|
|
|
|
/* Version to test unordered. */
|
|
|
|
#define _FP_CMP_UNORD(fs, wc, ret, X, Y) \
|
|
do \
|
|
{ \
|
|
ret = ((X##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc (X)) \
|
|
|| (Y##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc (Y))); \
|
|
} \
|
|
while (0)
|
|
|
|
/*
|
|
* Main square root routine. The input value should be cooked.
|
|
*/
|
|
|
|
#define _FP_SQRT(fs, wc, R, X) \
|
|
do \
|
|
{ \
|
|
_FP_FRAC_DECL_##wc (T); \
|
|
_FP_FRAC_DECL_##wc (S); \
|
|
_FP_W_TYPE q; \
|
|
switch (X##_c) \
|
|
{ \
|
|
case FP_CLS_NAN: \
|
|
_FP_FRAC_COPY_##wc (R, X); \
|
|
R##_s = X##_s; \
|
|
R##_c = FP_CLS_NAN; \
|
|
break; \
|
|
case FP_CLS_INF: \
|
|
if (X##_s) \
|
|
{ \
|
|
R##_s = _FP_NANSIGN_##fs; \
|
|
R##_c = FP_CLS_NAN; /* NAN */ \
|
|
_FP_FRAC_SET_##wc (R, _FP_NANFRAC_##fs); \
|
|
FP_SET_EXCEPTION (FP_EX_INVALID); \
|
|
} \
|
|
else \
|
|
{ \
|
|
R##_s = 0; \
|
|
R##_c = FP_CLS_INF; /* sqrt(+inf) = +inf */ \
|
|
} \
|
|
break; \
|
|
case FP_CLS_ZERO: \
|
|
R##_s = X##_s; \
|
|
R##_c = FP_CLS_ZERO; /* sqrt(+-0) = +-0 */ \
|
|
break; \
|
|
case FP_CLS_NORMAL: \
|
|
R##_s = 0; \
|
|
if (X##_s) \
|
|
{ \
|
|
R##_c = FP_CLS_NAN; /* NAN */ \
|
|
R##_s = _FP_NANSIGN_##fs; \
|
|
_FP_FRAC_SET_##wc (R, _FP_NANFRAC_##fs); \
|
|
FP_SET_EXCEPTION (FP_EX_INVALID); \
|
|
break; \
|
|
} \
|
|
R##_c = FP_CLS_NORMAL; \
|
|
if (X##_e & 1) \
|
|
_FP_FRAC_SLL_##wc (X, 1); \
|
|
R##_e = X##_e >> 1; \
|
|
_FP_FRAC_SET_##wc (S, _FP_ZEROFRAC_##wc); \
|
|
_FP_FRAC_SET_##wc (R, _FP_ZEROFRAC_##wc); \
|
|
q = _FP_OVERFLOW_##fs >> 1; \
|
|
_FP_SQRT_MEAT_##wc (R, S, T, X, q); \
|
|
} \
|
|
} \
|
|
while (0)
|
|
|
|
/*
|
|
* Convert from FP to integer. Input is raw.
|
|
*/
|
|
|
|
/* RSIGNED can have following values:
|
|
* 0: the number is required to be 0..(2^rsize)-1, if not, NV is set plus
|
|
* the result is either 0 or (2^rsize)-1 depending on the sign in such
|
|
* case.
|
|
* 1: the number is required to be -(2^(rsize-1))..(2^(rsize-1))-1, if not,
|
|
* NV is set plus the result is either -(2^(rsize-1)) or (2^(rsize-1))-1
|
|
* depending on the sign in such case.
|
|
* -1: the number is required to be -(2^(rsize-1))..(2^rsize)-1, if not, NV is
|
|
* set plus the result is either -(2^(rsize-1)) or (2^(rsize-1))-1
|
|
* depending on the sign in such case.
|
|
*/
|
|
#define _FP_TO_INT(fs, wc, r, X, rsize, rsigned) \
|
|
do \
|
|
{ \
|
|
if (X##_e < _FP_EXPBIAS_##fs) \
|
|
{ \
|
|
r = 0; \
|
|
if (X##_e == 0) \
|
|
{ \
|
|
if (!_FP_FRAC_ZEROP_##wc (X)) \
|
|
{ \
|
|
FP_SET_EXCEPTION (FP_EX_INEXACT); \
|
|
FP_SET_EXCEPTION (FP_EX_DENORM); \
|
|
} \
|
|
} \
|
|
else \
|
|
FP_SET_EXCEPTION (FP_EX_INEXACT); \
|
|
} \
|
|
else if (X##_e >= _FP_EXPBIAS_##fs + rsize - (rsigned > 0 || X##_s) \
|
|
|| (!rsigned && X##_s)) \
|
|
{ \
|
|
/* Overflow or converting to the most negative integer. */ \
|
|
if (rsigned) \
|
|
{ \
|
|
r = 1; \
|
|
r <<= rsize - 1; \
|
|
r -= 1 - X##_s; \
|
|
} else { \
|
|
r = 0; \
|
|
if (!X##_s) \
|
|
r = ~r; \
|
|
} \
|
|
\
|
|
if (rsigned && X##_s && X##_e == _FP_EXPBIAS_##fs + rsize - 1) \
|
|
{ \
|
|
/* Possibly converting to most negative integer; check the \
|
|
mantissa. */ \
|
|
int inexact = 0; \
|
|
(void) ((_FP_FRACBITS_##fs > rsize) \
|
|
? ({ \
|
|
_FP_FRAC_SRST_##wc (X, inexact, \
|
|
_FP_FRACBITS_##fs - rsize, \
|
|
_FP_FRACBITS_##fs); \
|
|
0; \
|
|
}) \
|
|
: 0); \
|
|
if (!_FP_FRAC_ZEROP_##wc (X)) \
|
|
FP_SET_EXCEPTION (FP_EX_INVALID); \
|
|
else if (inexact) \
|
|
FP_SET_EXCEPTION (FP_EX_INEXACT); \
|
|
} \
|
|
else \
|
|
FP_SET_EXCEPTION (FP_EX_INVALID); \
|
|
} \
|
|
else \
|
|
{ \
|
|
_FP_FRAC_HIGH_RAW_##fs (X) |= _FP_IMPLBIT_##fs; \
|
|
if (X##_e >= _FP_EXPBIAS_##fs + _FP_FRACBITS_##fs - 1) \
|
|
{ \
|
|
_FP_FRAC_ASSEMBLE_##wc (r, X, rsize); \
|
|
r <<= X##_e - _FP_EXPBIAS_##fs - _FP_FRACBITS_##fs + 1; \
|
|
} \
|
|
else \
|
|
{ \
|
|
int inexact; \
|
|
_FP_FRAC_SRST_##wc (X, inexact, \
|
|
(_FP_FRACBITS_##fs + _FP_EXPBIAS_##fs - 1 \
|
|
- X##_e), \
|
|
_FP_FRACBITS_##fs); \
|
|
if (inexact) \
|
|
FP_SET_EXCEPTION (FP_EX_INEXACT); \
|
|
_FP_FRAC_ASSEMBLE_##wc (r, X, rsize); \
|
|
} \
|
|
if (rsigned && X##_s) \
|
|
r = -r; \
|
|
} \
|
|
} \
|
|
while (0)
|
|
|
|
/* Convert integer to fp. Output is raw. RTYPE is unsigned even if
|
|
input is signed. */
|
|
#define _FP_FROM_INT(fs, wc, X, r, rsize, rtype) \
|
|
do \
|
|
{ \
|
|
if (r) \
|
|
{ \
|
|
rtype ur_; \
|
|
\
|
|
if ((X##_s = (r < 0))) \
|
|
r = -(rtype) r; \
|
|
\
|
|
ur_ = (rtype) r; \
|
|
(void) ((rsize <= _FP_W_TYPE_SIZE) \
|
|
? ({ \
|
|
int lz_; \
|
|
__FP_CLZ (lz_, (_FP_W_TYPE) ur_); \
|
|
X##_e = _FP_EXPBIAS_##fs + _FP_W_TYPE_SIZE - 1 - lz_; \
|
|
}) \
|
|
: ((rsize <= 2 * _FP_W_TYPE_SIZE) \
|
|
? ({ \
|
|
int lz_; \
|
|
__FP_CLZ_2 (lz_, \
|
|
(_FP_W_TYPE) (ur_ >> _FP_W_TYPE_SIZE), \
|
|
(_FP_W_TYPE) ur_); \
|
|
X##_e = (_FP_EXPBIAS_##fs + 2 * _FP_W_TYPE_SIZE - 1 \
|
|
- lz_); \
|
|
}) \
|
|
: (abort (), 0))); \
|
|
\
|
|
if (rsize - 1 + _FP_EXPBIAS_##fs >= _FP_EXPMAX_##fs \
|
|
&& X##_e >= _FP_EXPMAX_##fs) \
|
|
{ \
|
|
/* Exponent too big; overflow to infinity. (May also \
|
|
happen after rounding below.) */ \
|
|
_FP_OVERFLOW_SEMIRAW (fs, wc, X); \
|
|
goto pack_semiraw; \
|
|
} \
|
|
\
|
|
if (rsize <= _FP_FRACBITS_##fs \
|
|
|| X##_e < _FP_EXPBIAS_##fs + _FP_FRACBITS_##fs) \
|
|
{ \
|
|
/* Exactly representable; shift left. */ \
|
|
_FP_FRAC_DISASSEMBLE_##wc (X, ur_, rsize); \
|
|
if (_FP_EXPBIAS_##fs + _FP_FRACBITS_##fs - 1 - X##_e > 0) \
|
|
_FP_FRAC_SLL_##wc (X, (_FP_EXPBIAS_##fs \
|
|
+ _FP_FRACBITS_##fs - 1 - X##_e)); \
|
|
} \
|
|
else \
|
|
{ \
|
|
/* More bits in integer than in floating type; need to \
|
|
round. */ \
|
|
if (_FP_EXPBIAS_##fs + _FP_WFRACBITS_##fs - 1 < X##_e) \
|
|
ur_ = ((ur_ >> (X##_e - _FP_EXPBIAS_##fs \
|
|
- _FP_WFRACBITS_##fs + 1)) \
|
|
| ((ur_ << (rsize - (X##_e - _FP_EXPBIAS_##fs \
|
|
- _FP_WFRACBITS_##fs + 1))) \
|
|
!= 0)); \
|
|
_FP_FRAC_DISASSEMBLE_##wc (X, ur_, rsize); \
|
|
if ((_FP_EXPBIAS_##fs + _FP_WFRACBITS_##fs - 1 - X##_e) > 0) \
|
|
_FP_FRAC_SLL_##wc (X, (_FP_EXPBIAS_##fs \
|
|
+ _FP_WFRACBITS_##fs - 1 - X##_e)); \
|
|
_FP_FRAC_HIGH_##fs (X) &= ~(_FP_W_TYPE) _FP_IMPLBIT_SH_##fs; \
|
|
pack_semiraw: \
|
|
_FP_PACK_SEMIRAW (fs, wc, X); \
|
|
} \
|
|
} \
|
|
else \
|
|
{ \
|
|
X##_s = 0; \
|
|
X##_e = 0; \
|
|
_FP_FRAC_SET_##wc (X, _FP_ZEROFRAC_##wc); \
|
|
} \
|
|
} \
|
|
while (0)
|
|
|
|
|
|
/* Extend from a narrower floating-point format to a wider one. Input
|
|
and output are raw. */
|
|
#define FP_EXTEND(dfs, sfs, dwc, swc, D, S) \
|
|
do \
|
|
{ \
|
|
if (_FP_FRACBITS_##dfs < _FP_FRACBITS_##sfs \
|
|
|| (_FP_EXPMAX_##dfs - _FP_EXPBIAS_##dfs \
|
|
< _FP_EXPMAX_##sfs - _FP_EXPBIAS_##sfs) \
|
|
|| (_FP_EXPBIAS_##dfs < _FP_EXPBIAS_##sfs + _FP_FRACBITS_##sfs - 1 \
|
|
&& _FP_EXPBIAS_##dfs != _FP_EXPBIAS_##sfs)) \
|
|
abort (); \
|
|
D##_s = S##_s; \
|
|
_FP_FRAC_COPY_##dwc##_##swc (D, S); \
|
|
if (_FP_EXP_NORMAL (sfs, swc, S)) \
|
|
{ \
|
|
D##_e = S##_e + _FP_EXPBIAS_##dfs - _FP_EXPBIAS_##sfs; \
|
|
_FP_FRAC_SLL_##dwc (D, (_FP_FRACBITS_##dfs - _FP_FRACBITS_##sfs)); \
|
|
} \
|
|
else \
|
|
{ \
|
|
if (S##_e == 0) \
|
|
{ \
|
|
if (_FP_FRAC_ZEROP_##swc (S)) \
|
|
D##_e = 0; \
|
|
else if (_FP_EXPBIAS_##dfs \
|
|
< _FP_EXPBIAS_##sfs + _FP_FRACBITS_##sfs - 1) \
|
|
{ \
|
|
FP_SET_EXCEPTION (FP_EX_DENORM); \
|
|
_FP_FRAC_SLL_##dwc (D, (_FP_FRACBITS_##dfs \
|
|
- _FP_FRACBITS_##sfs)); \
|
|
D##_e = 0; \
|
|
} \
|
|
else \
|
|
{ \
|
|
int _lz; \
|
|
FP_SET_EXCEPTION (FP_EX_DENORM); \
|
|
_FP_FRAC_CLZ_##swc (_lz, S); \
|
|
_FP_FRAC_SLL_##dwc (D, \
|
|
_lz + _FP_FRACBITS_##dfs \
|
|
- _FP_FRACTBITS_##sfs); \
|
|
D##_e = (_FP_EXPBIAS_##dfs - _FP_EXPBIAS_##sfs + 1 \
|
|
+ _FP_FRACXBITS_##sfs - _lz); \
|
|
} \
|
|
} \
|
|
else \
|
|
{ \
|
|
D##_e = _FP_EXPMAX_##dfs; \
|
|
if (!_FP_FRAC_ZEROP_##swc (S)) \
|
|
{ \
|
|
if (_FP_FRAC_SNANP (sfs, S)) \
|
|
FP_SET_EXCEPTION (FP_EX_INVALID); \
|
|
_FP_FRAC_SLL_##dwc (D, (_FP_FRACBITS_##dfs \
|
|
- _FP_FRACBITS_##sfs)); \
|
|
_FP_SETQNAN (dfs, dwc, D); \
|
|
} \
|
|
} \
|
|
} \
|
|
} \
|
|
while (0)
|
|
|
|
/* Truncate from a wider floating-point format to a narrower one.
|
|
Input and output are semi-raw. */
|
|
#define FP_TRUNC(dfs, sfs, dwc, swc, D, S) \
|
|
do \
|
|
{ \
|
|
if (_FP_FRACBITS_##sfs < _FP_FRACBITS_##dfs \
|
|
|| (_FP_EXPBIAS_##sfs < _FP_EXPBIAS_##dfs + _FP_FRACBITS_##dfs - 1 \
|
|
&& _FP_EXPBIAS_##sfs != _FP_EXPBIAS_##dfs)) \
|
|
abort (); \
|
|
D##_s = S##_s; \
|
|
if (_FP_EXP_NORMAL (sfs, swc, S)) \
|
|
{ \
|
|
D##_e = S##_e + _FP_EXPBIAS_##dfs - _FP_EXPBIAS_##sfs; \
|
|
if (D##_e >= _FP_EXPMAX_##dfs) \
|
|
_FP_OVERFLOW_SEMIRAW (dfs, dwc, D); \
|
|
else \
|
|
{ \
|
|
if (D##_e <= 0) \
|
|
{ \
|
|
if (D##_e < 1 - _FP_FRACBITS_##dfs) \
|
|
{ \
|
|
_FP_FRAC_SET_##swc (S, _FP_ZEROFRAC_##swc); \
|
|
_FP_FRAC_LOW_##swc (S) |= 1; \
|
|
} \
|
|
else \
|
|
{ \
|
|
_FP_FRAC_HIGH_##sfs (S) |= _FP_IMPLBIT_SH_##sfs; \
|
|
_FP_FRAC_SRS_##swc (S, (_FP_WFRACBITS_##sfs \
|
|
- _FP_WFRACBITS_##dfs \
|
|
+ 1 - D##_e), \
|
|
_FP_WFRACBITS_##sfs); \
|
|
} \
|
|
D##_e = 0; \
|
|
} \
|
|
else \
|
|
_FP_FRAC_SRS_##swc (S, (_FP_WFRACBITS_##sfs \
|
|
- _FP_WFRACBITS_##dfs), \
|
|
_FP_WFRACBITS_##sfs); \
|
|
_FP_FRAC_COPY_##dwc##_##swc (D, S); \
|
|
} \
|
|
} \
|
|
else \
|
|
{ \
|
|
if (S##_e == 0) \
|
|
{ \
|
|
D##_e = 0; \
|
|
if (_FP_FRAC_ZEROP_##swc (S)) \
|
|
_FP_FRAC_SET_##dwc (D, _FP_ZEROFRAC_##dwc); \
|
|
else \
|
|
{ \
|
|
FP_SET_EXCEPTION (FP_EX_DENORM); \
|
|
if (_FP_EXPBIAS_##sfs \
|
|
< _FP_EXPBIAS_##dfs + _FP_FRACBITS_##dfs - 1) \
|
|
{ \
|
|
_FP_FRAC_SRS_##swc (S, (_FP_WFRACBITS_##sfs \
|
|
- _FP_WFRACBITS_##dfs), \
|
|
_FP_WFRACBITS_##sfs); \
|
|
_FP_FRAC_COPY_##dwc##_##swc (D, S); \
|
|
} \
|
|
else \
|
|
{ \
|
|
_FP_FRAC_SET_##dwc (D, _FP_ZEROFRAC_##dwc); \
|
|
_FP_FRAC_LOW_##dwc (D) |= 1; \
|
|
} \
|
|
} \
|
|
} \
|
|
else \
|
|
{ \
|
|
D##_e = _FP_EXPMAX_##dfs; \
|
|
if (_FP_FRAC_ZEROP_##swc (S)) \
|
|
_FP_FRAC_SET_##dwc (D, _FP_ZEROFRAC_##dwc); \
|
|
else \
|
|
{ \
|
|
_FP_CHECK_SIGNAN_SEMIRAW (sfs, swc, S); \
|
|
_FP_FRAC_SRL_##swc (S, (_FP_WFRACBITS_##sfs \
|
|
- _FP_WFRACBITS_##dfs)); \
|
|
_FP_FRAC_COPY_##dwc##_##swc (D, S); \
|
|
/* Semi-raw NaN must have all workbits cleared. */ \
|
|
_FP_FRAC_LOW_##dwc (D) \
|
|
&= ~(_FP_W_TYPE) ((1 << _FP_WORKBITS) - 1); \
|
|
_FP_SETQNAN_SEMIRAW (dfs, dwc, D); \
|
|
} \
|
|
} \
|
|
} \
|
|
} \
|
|
while (0)
|
|
|
|
/*
|
|
* Helper primitives.
|
|
*/
|
|
|
|
/* Count leading zeros in a word. */
|
|
|
|
#ifndef __FP_CLZ
|
|
/* GCC 3.4 and later provide the builtins for us. */
|
|
# define __FP_CLZ(r, x) \
|
|
do \
|
|
{ \
|
|
if (sizeof (_FP_W_TYPE) == sizeof (unsigned int)) \
|
|
r = __builtin_clz (x); \
|
|
else if (sizeof (_FP_W_TYPE) == sizeof (unsigned long)) \
|
|
r = __builtin_clzl (x); \
|
|
else if (sizeof (_FP_W_TYPE) == sizeof (unsigned long long)) \
|
|
r = __builtin_clzll (x); \
|
|
else \
|
|
abort (); \
|
|
} \
|
|
while (0)
|
|
#endif /* ndef __FP_CLZ */
|
|
|
|
#define _FP_DIV_HELP_imm(q, r, n, d) \
|
|
do \
|
|
{ \
|
|
q = n / d, r = n % d; \
|
|
} \
|
|
while (0)
|
|
|
|
|
|
/* A restoring bit-by-bit division primitive. */
|
|
|
|
#define _FP_DIV_MEAT_N_loop(fs, wc, R, X, Y) \
|
|
do \
|
|
{ \
|
|
int count = _FP_WFRACBITS_##fs; \
|
|
_FP_FRAC_DECL_##wc (u); \
|
|
_FP_FRAC_DECL_##wc (v); \
|
|
_FP_FRAC_COPY_##wc (u, X); \
|
|
_FP_FRAC_COPY_##wc (v, Y); \
|
|
_FP_FRAC_SET_##wc (R, _FP_ZEROFRAC_##wc); \
|
|
/* Normalize U and V. */ \
|
|
_FP_FRAC_SLL_##wc (u, _FP_WFRACXBITS_##fs); \
|
|
_FP_FRAC_SLL_##wc (v, _FP_WFRACXBITS_##fs); \
|
|
/* First round. Since the operands are normalized, either the \
|
|
first or second bit will be set in the fraction. Produce a \
|
|
normalized result by checking which and adjusting the loop \
|
|
count and exponent accordingly. */ \
|
|
if (_FP_FRAC_GE_1 (u, v)) \
|
|
{ \
|
|
_FP_FRAC_SUB_##wc (u, u, v); \
|
|
_FP_FRAC_LOW_##wc (R) |= 1; \
|
|
count--; \
|
|
} \
|
|
else \
|
|
R##_e--; \
|
|
/* Subsequent rounds. */ \
|
|
do \
|
|
{ \
|
|
int msb = (_FP_WS_TYPE) _FP_FRAC_HIGH_##wc (u) < 0; \
|
|
_FP_FRAC_SLL_##wc (u, 1); \
|
|
_FP_FRAC_SLL_##wc (R, 1); \
|
|
if (msb || _FP_FRAC_GE_1 (u, v)) \
|
|
{ \
|
|
_FP_FRAC_SUB_##wc (u, u, v); \
|
|
_FP_FRAC_LOW_##wc (R) |= 1; \
|
|
} \
|
|
} \
|
|
while (--count > 0); \
|
|
/* If there's anything left in U, the result is inexact. */ \
|
|
_FP_FRAC_LOW_##wc (R) |= !_FP_FRAC_ZEROP_##wc (u); \
|
|
} \
|
|
while (0)
|
|
|
|
#define _FP_DIV_MEAT_1_loop(fs, R, X, Y) _FP_DIV_MEAT_N_loop (fs, 1, R, X, Y)
|
|
#define _FP_DIV_MEAT_2_loop(fs, R, X, Y) _FP_DIV_MEAT_N_loop (fs, 2, R, X, Y)
|
|
#define _FP_DIV_MEAT_4_loop(fs, R, X, Y) _FP_DIV_MEAT_N_loop (fs, 4, R, X, Y)
|