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op-common.h
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/* Software floating-point emulation. Common operations.
Copyright (C) 1997,1998,1999,2006 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Contributed by Richard Henderson ([email protected]),
Jakub Jelinek ([email protected]),
David S. Miller ([email protected]) and
Peter Maydell ([email protected]).
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, write to the Free
Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
02111-1307 USA. */
#define _FP_DECL(wc, X) \
_FP_I_TYPE X##_c __attribute__((unused)), X##_s, X##_e; \
_FP_FRAC_DECL_##wc(X)
/*
* Finish truely 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_HIGH_RAW_##fs(X) & _FP_QNANBIT_##fs)) \
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_SET_EXCEPTION(FP_EX_OVERFLOW); \
FP_SET_EXCEPTION(FP_EX_INEXACT); \
_FP_FRAC_SET_##wc(X, _FP_MAXFRAC_##wc); \
} \
} 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_HIGH_##fs(X) & _FP_QNANBIT_SH_##fs)) \
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)
/* 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 { \
_FP_ROUND(wc, X); \
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 (!_FP_EXP_NORMAL(fs, wc, X) && !_FP_FRAC_ZEROP_##wc(X)) \
{ \
if (X##_e == 0) \
FP_SET_EXCEPTION(FP_EX_UNDERFLOW); \
else \
{ \
if (!_FP_KEEPNANFRACP) \
{ \
_FP_FRAC_SET_##wc(X, _FP_NANFRAC_##fs); \
X##_s = _FP_NANSIGN_##fs; \
} \
else \
_FP_FRAC_HIGH_RAW_##fs(X) |= _FP_QNANBIT_##fs; \
} \
} \
} 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 */ \
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); \
} \
else \
{ \
X##_e = 0; \
_FP_FRAC_SRL_##wc(X, _FP_WORKBITS); \
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_FRAC_HIGH_RAW_##fs(X) |= _FP_QNANBIT_##fs; \
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_HIGH_RAW_##fs(X) & _FP_QNANBIT_##fs)) \
__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. FIXME -- when we care about setting exception
* bits reliably, this will not do. We should examine all of the fp classes.
*/
#define _FP_NEG(fs, wc, R, X) \
do { \
_FP_FRAC_COPY_##wc(R, X); \
R##_c = X##_c; \
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; \
switch (_FP_CLS_COMBINE(X##_c, Y##_c)) \
{ \
case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_NORMAL): \
R##_c = FP_CLS_NORMAL; \
R##_e = X##_e + Y##_e + 1; \
\
_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)
/*
* Main division routine. The input values should be cooked.
*/
#define _FP_DIV(fs, wc, R, X, Y) \
do { \
R##_s = X##_s ^ Y##_s; \
switch (_FP_CLS_COMBINE(X##_c, Y##_c)) \
{ \
case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_NORMAL): \
R##_c = FP_CLS_NORMAL; \
R##_e = X##_e - Y##_e; \
\
_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; /* sNAN */ \
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) \
{ \